U.S. patent application number 16/152743 was filed with the patent office on 2022-01-27 for system and method for estimating tissue heating of a target ablation zone for electrical-energy based therapies.
The applicant listed for this patent is Virginia Tech Intellectual Properties Inc.. Invention is credited to Christopher B. Arena, Rafael V. Davalos, Paulo A. Garcia, Michael B. Sano.
Application Number | 20220022945 16/152743 |
Document ID | / |
Family ID | 1000006075702 |
Filed Date | 2022-01-27 |
United States Patent
Application |
20220022945 |
Kind Code |
A9 |
Garcia; Paulo A. ; et
al. |
January 27, 2022 |
SYSTEM AND METHOD FOR ESTIMATING TISSUE HEATING OF A TARGET
ABLATION ZONE FOR ELECTRICAL-ENERGY BASED THERAPIES
Abstract
Systems and methods are provided for modeling and for providing
a graphical representation of tissue heating and electric field
distributions for medical treatment devices that apply electrical
treatment energy through one or a plurality of electrodes. In
embodiments, methods comprise: providing one or more parameters of
a treatment protocol for delivering one or more electrical pulses
to tissue through a plurality of electrodes; modeling electric and
heat distribution in the tissue based on the parameters; and
displaying a graphical representation of the modeled electric and
heat distribution. In another embodiment, a treatment planning
module is adapted to generate an estimated target ablation zone
based on a combination of one or more parameters for an
irreversible electroporation protocol and one or more
tissue-specific conductivity parameters.
Inventors: |
Garcia; Paulo A.;
(Blacksburg, VA) ; Arena; Christopher B.;
(Burlington, NC) ; Sano; Michael B.; (Durham,
NC) ; Davalos; Rafael V.; (Blacksburg, VA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Virginia Tech Intellectual Properties Inc. |
Blacksburg |
VA |
US |
|
|
Prior
Publication: |
|
Document Identifier |
Publication Date |
|
US 20190029749 A1 |
January 31, 2019 |
|
|
Family ID: |
1000006075702 |
Appl. No.: |
16/152743 |
Filed: |
October 5, 2018 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
14558631 |
Dec 2, 2014 |
10117707 |
|
|
16152743 |
|
|
|
|
14012832 |
Aug 28, 2013 |
9283051 |
|
|
14558631 |
|
|
|
|
12491151 |
Jun 24, 2009 |
8992517 |
|
|
14012832 |
|
|
|
|
12432295 |
Apr 29, 2009 |
9598691 |
|
|
12491151 |
|
|
|
|
14808679 |
Jul 24, 2015 |
|
|
|
12432295 |
|
|
|
|
13332133 |
Dec 20, 2011 |
10448989 |
|
|
14808679 |
|
|
|
|
12757901 |
Apr 9, 2010 |
8926606 |
|
|
13332133 |
|
|
|
|
12491151 |
Jun 24, 2009 |
8992517 |
|
|
12906923 |
Oct 18, 2010 |
|
|
|
12609779 |
Oct 30, 2009 |
8465484 |
|
|
12491151 |
|
|
|
|
12757901 |
Apr 9, 2010 |
8926606 |
|
|
12609779 |
|
|
|
|
12432295 |
Apr 29, 2009 |
9598691 |
|
|
12757901 |
|
|
|
|
61694144 |
Aug 28, 2012 |
|
|
|
61171564 |
Apr 22, 2009 |
|
|
|
61167997 |
Apr 9, 2009 |
|
|
|
61075216 |
Jun 24, 2008 |
|
|
|
61125840 |
Apr 29, 2008 |
|
|
|
61910655 |
Dec 2, 2013 |
|
|
|
61167997 |
Apr 9, 2009 |
|
|
|
61285618 |
Dec 11, 2009 |
|
|
|
61424872 |
Dec 20, 2010 |
|
|
|
61252445 |
Oct 16, 2009 |
|
|
|
61167997 |
Apr 9, 2009 |
|
|
|
61285618 |
Dec 11, 2009 |
|
|
|
61075216 |
Jun 24, 2008 |
|
|
|
61125840 |
Apr 29, 2008 |
|
|
|
61171564 |
Apr 22, 2009 |
|
|
|
61167997 |
Apr 9, 2009 |
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
A61B 18/1477 20130101;
A61B 2018/00892 20130101 |
International
Class: |
A61B 18/14 20060101
A61B018/14 |
Claims
1. A method of treating a tissue with a medical treatment device
that applies electrical treatment energy through one or more
electrodes defining a target treatment area of the tissue and
comprises a display device, the method comprising: providing one or
more parameters of a treatment protocol for delivering one or more
electrical pulses to a tissue through one or more electrodes;
modeling heat distribution and/or electric field distribution in a
tissue surrounding the electrodes based on the one or more
parameters; displaying a graphical representation of the heat
and/or electric field distribution based on the modeled heat
distribution in the display device; modifying one or more of the
parameters of the treatment protocol based on the graphical
representation of the heat distribution; and implanting the
electrodes in the tissue and delivering one or more electrical
pulses to the tissue through the electrodes by way of a voltage
pulse generator based on the one or more modified parameters.
2. The method of claim 1, wherein the one or more parameters are
chosen from one or more of voltage, electrode spacing, electrode
length, treatment duration, number of pulses, pulse width, electric
field intensity, electrode diameter, a baseline conductivity for
the target treatment area, a change in conductivity for the target
treatment area, or a conductivity for a specific tissue type.
3. A method of treatment planning for medical therapies involving
administering electrical treatment energy, the method comprising:
providing one or more parameters of a treatment protocol for
delivering one or more electrical pulses to tissue through one or
more electrodes; modeling heat and/or electric field distribution
in the tissue based on the parameters; and displaying a graphical
representation of the modeled heat and/or electric field
distribution.
4. The method of claim 3, wherein the heat distribution is modeled
to estimate the Joule heating in the tissue and is calculated as:
.rho. .times. .times. C p .times. .differential. T .differential. t
= .gradient. ( k .times. .gradient. T ) + Q jh .function. [ W m 3 ]
##EQU00018## where .rho. is the density, C.sub.p is the heat
capacity, k is the thermal conductivity, and Q.sub.jh are the
resistive losses Q jh = J E .function. [ W m 3 ] ##EQU00019## where
J is the induced current density J = .sigma. .times. .times. E
.function. [ A m 2 ] ##EQU00020## and .sigma. is the tissue
conductivity and E is the electric field E = - .gradient. .PHI.
.function. [ V m ] ##EQU00021##
5. The method of claim 3, further comprising specifying a cutoff
heat distribution value and providing a graphical representation of
the heat and/or electric field distribution curve as an isocontour
line.
6. The method of claim 3, further comprising: modeling an
electrical damage and/or a thermal damage in the tissue based on
the parameters; displaying a graphical representation of the
modeled electrical damage and/or thermal damage.
7. The method of claim 6, wherein the electric field distribution
is calculated as: .gradient..sup.2.PHI.=0 where .PHI. is the
electric potential, this equation is solved with boundary
conditions: {right arrow over (n)}{right arrow over (J)}=0 at the
boundaries .PHI.=V.sub.in at the boundary of the first electrode
.PHI.=0 at the boundary of the second electrode wherein {right
arrow over (n)} is the normal vector to the surface, {right arrow
over (J)} is the electrical current and V.sub.in is the electrical
potential applied.
8. The method of claim 6, further comprising specifying a cutoff
electrical field distribution value and providing a graphical
representation of the electrical field distribution value as an
isocontour line.
9. The method of claim 3, wherein the parameters are chosen from
one or more of voltage, electrode spacing, electrode diameter,
electrode length, number of pulses, treatment duration, pulse
width, electric field intensity, a baseline conductivity for the
target treatment area, a change in conductivity for the target
treatment area, or a conductivity for a specific tissue type.
10. The method of claim 8, further comprising one or more databases
comprising a plurality of sets of parameters for treatment
protocols stored in the database.
11. The method of claim 10, wherein the graphical representations
of the modeled heat and electrical field distributions are derived
from Cassini oval calculations.
12. A system for treatment planning for medical therapies involving
administering electrical treatment energy, the system comprising: a
computer comprising: a memory; a display device; a processor
coupled to the memory and the display device; and a treatment
planning module stored in the memory and executable by the
processor, the treatment planning module adapted to: receive as
input one or more parameters of a treatment protocol for delivering
electrical pulses to tissue through one or more electrodes; model
heat and/or electric field distribution in the tissue based on the
parameters; display a graphical representation of the modeled heat
and/or electric field distribution on the display device.
13. The system of claim 12, further comprising one or more
databases comprising a plurality of sets of parameters for
treatment protocols stored in the databases.
14. The system of claim 12, wherein the inputs are chosen from one
or more of voltage, electrode spacing, treatment duration, pulse
width, electric field intensity, a baseline conductivity for the
target treatment area, a change in conductivity for the target
treatment area, or a conductivity for a specific tissue type.
15. The system of claim 14, wherein the change in conductivity is
expressed as a ratio of the baseline conductivity to the maximum
conductivity of the tissue that is reached during treatment.
16. The system of claim 14, wherein the conductivity for a specific
tissue type is provided in a database for a plurality of
tissues.
17. The system of claim 12, wherein the one or more electrodes is
provided by one or more bipolar probes.
18. The system of claim 12, wherein the one or more electrodes are
provided by one or more single needle electrodes.
19. The system of claim 15, wherein the change in conductivity is
calculated in real-time based on measured voltages and currents
before, during, and/or after pulse delivery.
20. The method of claim 6, wherein the graphical representation of
the modeled thermal damage and/or electrical damage is derived from
Cassini oval calculations.
21-22. (canceled)
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] The present application is a Continuation of U.S. patent
application Ser. No. 14/558,631 filed Dec. 2, 2014, which published
as U.S. Patent Application Publication No. US 2015/0088120 on Mar.
26, 2015. The '631 application is a Continuation-in-Part (CIP) of
U.S. patent application Ser. No. 14/012,832, filed on Aug. 28,
2013, which published as U.S. Patent Application Publication No.
2013/0345697 on Dec. 26, 2013 and issued as U.S. Pat. No. 9,283,051
on Mar. 15, 2016. The '832 application relies on and claims the
benefit of the filing date of U.S. Provisional Application No.
61/694,144, filed on Aug. 28, 2012. The '832 application is also a
CIP of U.S. application Ser. No. 12/491,151, filed on Jun. 24,
2009, which '151 application published as U.S. Patent Application
Publication No. 2010/0030211 on Feb. 4, 2010 and issued as U.S.
Pat. No. 8,992,517 on Mar. 31, 2015. The '151 application relies on
and claims the benefit of the filing dates of U.S. Provisional
Patent Application Nos. 61/171,564, filed on Apr. 22, 2009,
61/167,997, filed on Apr. 9, 2009, and 61/075,216, filed on Jun.
24, 2008. The '151 application is also a CIP of U.S. patent
application Ser. No. 12/432,295, filed on Apr. 29, 2009, which '295
application published as U.S. Patent Application Publication No.
2009/0269317 and issued as U.S. Pat. No. 9,598,691 on Mar. 21,
2017. The '295 application relies on and claims the benefit of the
filing date of U.S. Provisional Patent Application No. 61/125,840,
filed on Apr. 29, 2008. The '631 application also relies on and
claims priority to and the benefit of the filing date of U.S.
Provisional Application No. 61/910,655, filed Dec. 2, 2013. The
disclosures of these patent applications are hereby incorporated by
reference herein in their entireties.
FIELD OF THE INVENTION
[0002] The present invention is related to medical therapies
involving the administering of electrical treatment energy. More
particularly, embodiments of the present invention provide systems
and methods for modeling and providing a graphical representation
of tissue heating and electric field for a medical treatment device
that applies electrical treatment energy through a plurality of
electrodes defining a target treatment area. Embodiments of the
present invention also provide systems and methods providing a
graphical representation of a target ablation zone based on one or
more electrical conductivity parameters that are specific for the
tissue to be treated.
DESCRIPTION OF RELATED ART
[0003] Electroporation-based therapies (EBTs) are clinical
procedures that utilize pulsed electric fields to induce nanoscale
defects in cell membranes. Typically, pulses are applied through
minimally invasive needle electrodes inserted directly into the
target tissue, and the pulse parameters are tuned to create either
reversible or irreversible defects. Reversible electroporation
facilitates the transport of molecules into cells without directly
compromising cell viability. This has shown great promise for
treating cancer when used in combination with chemotherapeutic
agents or plasmid DNA (M. Marty et al., "Electrochemotherapy--An
easy, highly effective and safe treatment of cutaneous and
subcutaneous metastases: Results of ESOPE (European Standard
Operating Procedures of Electrochemotherapy) study," European
Journal of Cancer Supplements, 4, 3-13, 2006; A. I. Daud et al.,
"Phase I Trial of Interleukin-12 Plasmid Electroporation in
Patients With Metastatic Melanoma," Journal of Clinical Oncology,
26, 5896-5903, Dec. 20 2008). Alternatively, irreversible
electroporation (IRE) has been recognized as a non-thermal tissue
ablation modality that produces a tissue lesion, which is visible
in real-time on multiple imaging platforms (R. V. Davalos, L. M.
Mir, and B. Rubinsky, "Tissue ablation with irreversible
electroporation," Ann Biomed Eng, 33, 223-31, February 2005; R. V.
Davalos, D. M. Otten, L. M. Mir, and B. Rubinsky, "Electrical
impedance tomography for imaging tissue electroporation," IEEE
Transactions on Biomedical Engineering, 51, 761-767, 2004; L.
Appelbaum, E. Ben-David, J. Sosna, Y. Nissenbaum, and S. N.
Goldberg, "US Findings after Irreversible Electroporation Ablation:
Radiologic-Pathologic Correlation," Radiology, 262, 117-125, Jan.
1, 2012). Because the mechanism of cell death does not rely on
thermal processes, IRE spares major nerve and blood vessel
architecture and is not subject to local heat sink effects when
using a specific protocol that does not exceed the thermal damage
threshold. (B. Al-Sakere, F. Andre, C. Bernat, E. Connault, P.
Opolon, R. V. Davalos, B. Rubinsky, and L. M. Mir, "Tumor ablation
with irreversible electroporation," PLoS ONE, 2, e1135, 2007).
These unique benefits have translated to the successful treatment
of several surgically "inoperable" tumors (K. R. Thomson et al.,
"Investigation of the safety of irreversible electroporation in
humans," J Vasc Intery Radiol, 22, 611-21, May 2011; R. E. Neal II
et al., "A Case Report on the Successful Treatment of a Large
Soft-Tissue Sarcoma with Irreversible Electroporation," Journal of
Clinical Oncology, 29, 1-6, 2011; P. A. Garcia et al., "Non-thermal
irreversible electroporation (N-TIRE) and adjuvant fractionated
radiotherapeutic multimodal therapy for intracranial malignant
glioma in a canine patient," Technol Cancer Res Treat, 10, 73-83,
2011).
[0004] In EBTs, the electric field distribution is the primary
factor for dictating defect formation and the resulting volume of
treated tissue (J. F. Edd and R. V. Davalos, "Mathematical modeling
of irreversible electroporation for treatment planning," Technology
in Cancer Research and Treatment, 6, 275-286, 2007 ("Edd and
Davalos, 2007"); D. Miklavcic, D. Semrov, H. Mekid, and L. M. Mir,
"A validated model of in vivo electric field distribution in
tissues for electrochemotherapy and for DNA electrotransfer for
gene therapy," Biochimica et Biophysica Acta, 1523, 73-83, 2000).
The electric field is influenced by both the geometry and
positioning of the electrodes as well as the dielectric tissue
properties. Because the pulse duration is typically much longer
than the pulse rise/fall time, static solutions of the Laplace's
equation incorporating only electric conductivity are sufficient
for predicting the electric field distribution. In tissues with
uniform conductivity, solutions can be obtained analytically for
various needle electrode configurations if the exposure length is
much larger than the separation distance (S. Corovic, M. Pavlin,
and D. Miklavcic, "Analytical and numerical quantification and
comparison of the local electric field in the tissue for different
electrode configurations," Biomed Eng Online, 6, 2007; R. Neal II
et al., "Experimental Characterization and Numerical Modeling of
Tissue Electrical Conductivity during Pulsed Electric Fields for
Irreversible Electroporation Treatment Planning," Biomedical
Engineering, IEEE Transactions on, PP, 1-1, 2012 ("Neal et al.,
2012")). This is not often the case in clinical applications where
aberrant masses with a diameter on the order of 1 cm are treated
with an electrode exposure length of similar dimensions.
Additionally, altered membrane permeability due to electroporation
influences the tissue conductivity in a non-linear manner.
Therefore numerical techniques may be used to account for any
electrode configuration and incorporate a tissue-specific function
relating the electrical conductivity to the electric field
distribution (i.e. extent of electroporation).
[0005] Conventional devices for delivering therapeutic energy such
as electrical pulses to tissue include a handle and one or more
electrodes coupled to the handle. Each electrode is connected to an
electrical power source. The power source allows the electrodes to
deliver the therapeutic energy to a targeted tissue, thereby
causing ablation of the tissue.
[0006] Once a target treatment area is located within a patient,
the electrodes of the device are placed in such a way as to create
a treatment zone that surrounds the treatment target area. In some
cases, each electrode is placed by hand into a patient to create a
treatment zone that surrounds a lesion. The medical professional
who is placing the electrodes typically watches an imaging monitor
while placing the electrodes to approximate the most efficient and
accurate placement.
[0007] However, if the electrodes are placed by hand in this
fashion, it is very difficult to predict whether the locations
selected will ablate the entire treatment target area because the
treatment region defined by the electrodes vary greatly depending
on such parameters as the electric field density, the voltage level
of the pulses being applied, size of the electrode and the type of
tissue being treated. Further, it is often difficult or sometimes
not possible to place the electrodes in the correct location of the
tissue to be ablated because the placement involves human error and
avoidance of obstructions such as nerves, blood vessels and the
like.
[0008] Conventionally, to assist the medical professional in
visualizing a treatment region defined by the electrodes, an
estimated treatment region is generated using a numerical model
analysis such as complex finite element analysis. One problem with
such a method is that even a modest two dimensional treatment
region may take at least 30 minutes to several hours to complete
even in a relatively fast personal computer. This means that it
would be virtually impossible to try to obtain on a real time basis
different treatment regions based on different electrode
positions.
[0009] In IRE treatments, the electric field distribution is the
primary factor for dictating defect formation and the resulting
volume of treated tissue (See J. F. Edd and R. V. Davalos,
"Mathematical modeling of irreversible electroporation for
treatment planning," Technol Cancer Res Treat, vol. 6, pp. 275-286,
2007; D. Sel, et al., "Sequential finite element model of tissue
electropermeabilization," IEEE Trans Biomed Eng, vol. 52, pp.
816-27, May 2005). The electric field is influenced by both the
geometry and positioning of the electrodes as well as the
dielectric tissue properties. The application of an electric field
across any conductive media will result in some degree of resistive
losses in which energy is dissipated as heat. Though cell death in
IRE is attributed to non-thermal mechanisms, it is possible to
inadvertently elevate tissue temperatures above thermal damage
thresholds if parameters are not chosen carefully. Since a major
advantage of IRE is the ablation of tissue without deleterious
thermal effects and the therapy is often applied in regions which
cannot clinically sustain thermal injury, it is important to
identify safe operating parameters. Transient heating of tissue in
proximity to the electrode can result in the denaturing of the
extracellular matrix, scar formation, or damage to local blood
vessels and nerves. To avoid these effects, it is important to
understand the extent and geometry of tissue heating.
[0010] Therefore, it would be desirable to provide an improved
system and method to predict a treatment region that avoids
electrical and thermal overexposure and damage in order to
determine safe and effective pulse protocols for administering
electrical energy based therapies, such IRE.
SUMMARY OF THE INVENTION
[0011] In one embodiment, the invention provides a system for
treating a tissue, which system applies electrical treatment energy
through one or more electrodes, such as a plurality of electrodes,
defining a target treatment area of the tissue. The system
comprises a memory, a display device, a processor coupled to the
memory and the display device, and a treatment planning module
stored in the memory and executable by the processor. In one
embodiment, the treatment planning module is adapted to generate an
estimated heat distribution and/or electrical field distribution in
the display device based on one or more parameters for an
electrical energy based protocol, such as an irreversible
electroporation (IRE) protocol. In another embodiment, the
treatment planning module is adapted to generate an estimated
target ablation zone based on a combination of one or more
parameters for an electrical energy based protocol, such as an
IRE-based protocol, and one or more tissue-specific conductivity
parameters.
[0012] In another embodiment, the invention provides a method of
treating a tissue with a medical treatment device that applies
electrical treatment energy through a one or more or a plurality of
electrodes defining a target treatment area of the tissue and
comprises a display device. The method may be executed partially or
completely using the system of the invention. In a specific
embodiment, one or more steps are executed through the treatment
planning module.
[0013] In embodiments, the treatment planning module can be used to
determine a temperature distribution to determine tissue heating at
or around a target ablation zone prior to or during treatment. The
treatment planning module can be used to graphically display
contour lines which represent a specific temperature of tissue
heating. In one embodiment, the treatment planning module estimates
the temperature rise within tissue due to Joule heating effects,
and plots a contour line according to a temperature specified by a
user. Further, the treatment planning module may further plot a
contour line representing an electric field intensity such that
temperature and electric field intensity can be correlated. The
treatment planning module may plot the temperature distribution and
electric field distribution for a bipolar and single needle
electrodes. This capability may allow a user (e.g. treating
physician) to determine heating to surrounding tissues during
treatment planning and adjust parameters to prevent thermal damage
to critical surrounding structures such as nerves and blood
vessels. In one embodiment, the contour lines are Cassini oval
approximations performed according to the equations and procedure
in Example 7.
[0014] In embodiments, the treatment planning module can be used to
provide the electric field distributions using different
configurations of bipolar probes and include the dynamic change in
electrical conductivity from the non-electroporated baseline tissue
electrical conductivity. The treatment planning module may plot
contour lines representing electric field distributions based on a
specific combination of electrode length, separation distance, and
applied voltage. The treatment planning module may incorporate the
dynamic change in electrical conductivity from the baseline during
treatment to account for treatment-related changes in conductivity
for particular tissues such as liver, kidney, brain, etc. This
capability may allow the treating physician to determine electric
field distributions and zones of ablation based on the capacity for
a specific target tissue to change in conductivity during
treatment. In one embodiment, the contour lines are Cassini oval
approximations performed according to the equations and procedure
in Example 7.
[0015] In embodiments, the treatment planning module can be based
on a parametric study of the dynamic conductivity curve so that
variables related to the dynamic conductivity could be used to fit
tissue specific behavior. In embodiments, the treatment planning
module may provide input for one or more electrical conductivity
parameters such as the baseline (e.g., non-electroporated)
conductivity, change in conductivity, the transition zone (how
rapidly the conductivity increases), the electric field at which
the change in conductivity occurs, and the electric field at which
irreversible electroporation occurs. These parameters may be
experimentally derived for different tissues and stored in a
database. This capability may allow the treating physician to
account for different conductivity parameters as they apply to
different target tissues when designing a treatment protocol. Thus,
when considering a specific tissue, the treating physician may
optimize the calculation of an ablation zone for that tissue by
inputting one or more of the tissue-specific conductivity
parameters for the tissue of interest.
BRIEF DESCRIPTION OF THE DRAWINGS
[0016] The accompanying drawings illustrate certain aspects of
embodiments of the present invention, and should not be used to
limit or define the invention. Together with the written
description the drawings serve to explain certain principles of the
invention.
[0017] Further, the application file contains at least one drawing
executed in color. Copies of the patent application publication
with color drawing(s) will be provided by the Office upon request
and payment of the necessary fee.
[0018] FIG. 1 is a schematic diagram of a representative system of
the invention.
[0019] FIG. 2 is a schematic diagram of a representative treatment
control computer of the invention.
[0020] FIG. 3 is schematic diagram illustrating details of the
generator shown in the system of FIG. 1, including elements for
detecting an over-current condition.
[0021] FIG. 4 is a schematic diagram showing IRE zones of ablation
nomenclature (see E. Ben-David, et al., "Characterization of
Irreversible Electroporation Ablation in In Vivo Porcine Liver," Am
J Roentgenol, vol. 198, pp. W62-W68, Jan. 2012).
[0022] FIG. 5 is a graph of the asymmetrical Gompertz function
showing tissue electric conductivity as a function of electric
field.
[0023] FIG. 6 is a graph showing a representative 3D plot of
current [A] as a function of Z (.sigma..sub.max/.sigma..sub.0) and
voltage-to-distance ratio (W) for a separation distance of 1.5 cm
and an electrode exposure length of 2.0 cm as used by Ben-David et
al.
[0024] FIGS. 7A and 7B are graphs showing representative contour
plots of current [A] as a function of electrode exposure and
separation distance using 1500 V/cm for Z=1 (FIG. 7A) and Z=4 (FIG.
7B).
[0025] FIGS. 8A and 8B are tables showing Whole Model Parameter
Estimates and Effect Tests, respectively.
[0026] FIG. 8C is a graph showing a plot of Actual Current vs.
Predicted Current.
[0027] FIGS. 9A-9E are graphs showing the representative (15 mm
gap) correlation between current vs. exposure length and electrode
radius for maximum electrical conductivities (1.times.-6.times.,
respectively).
[0028] FIG. 10A is a table showing experimental validation of the
code for determining the tissue/potato dynamic from in vitro
measurements, referred to as potato experiment #1.
[0029] FIG. 10B is a table showing experimental validation of the
code for determining the tissue/potato dynamic from in vitro
measurements, referred to as potato experiment #2.
[0030] FIGS. 11A and 11B are graphs plotting residual current
versus data point for analytical shape factor (FIG. 11A) and
statistical (numerical) non-linear conductivity (FIG. 11B).
[0031] FIGS. 12A-12C are graphs showing representative contour
plots of the electric field strength at 1.0 cm from the origin
using an edge-to-edge voltage-to-distance ratio of 1500 V/cm
assuming z=1, wherein FIG. 12A is a plot of the x-direction, FIG.
12B is a plot of the y-direction, and FIG. 12C is a plot of the
z-direction.
[0032] FIGS. 13A-13C are 3D plots representing zones of ablation
for a 1500 V/cm ratio, electrode exposure of 2 cm, and electrode
separation of 1.5 cm, at respectively a 1000 V/cm IRE threshold
(FIG. 13A), 750 V/cm IRE threshold (FIG. 13B), and 500 V/cm IRE
threshold (FIG. 13C) using the equation for an ellipsoid.
[0033] FIG. 14A is a schematic diagram showing an experimental
setup of an embodiment of the invention.
[0034] FIG. 14B is a schematic diagram showing dimension labeling
conventions.
[0035] FIG. 14C is a waveform showing 50 V pre-pulse electrical
current at 1 cm separation, grid=0.25 A, where the lack of rise in
intrapulse conductivity suggests no significant membrane
electroporation during pre-pulse delivery.
[0036] FIG. 14D is a waveform showing electrical current for pulses
40-50 of 1750 V at 1 cm separation, grid=5 A, where progressive
intrapulse current rise suggests continued conductivity increase
and electroporation.
[0037] FIGS. 15A and 15B are electric field [V/cm] isocontours for
non-electroporated tissue (FIG. 15A) and electroporated tissue
(FIG. 15B) maps assuming a maximum conductivity to baseline
conductivity ratio of 7.0.times..
[0038] FIGS. 16A and 16B are representative Cassini Oval shapes
when varying the `a=0.5 (red), 0.6 (orange), 0.7 (green), 0.8
(blue), 0.9 (purple), 1.0 (black)` or `b=1.0 (red), 1.05 (orange),
1.1 (green), 1.15 (blue), 1.2 (purple), 1.25 (black)` parameters
individually. Note: If a>1.0 or b<1.0 the lemniscate of
Bernoulli (the point where the two ellipses first connect (a=b=1)
forming ".infin.") disconnects forming non-contiguous shapes.
[0039] FIG. 17 is a graph showing NonlinearModelFit results for the
`a` and `b` parameters used to generate the Cassini curves that
represent the experimental IRE zones of ablation in porcine
liver.
[0040] FIG. 18 shows Cassini curves from a ninety 100-.mu.s pulse
IRE treatment that represent the average zone of ablation (blue
dashed), +SD (red solid), and -SD (black solid) according to
a=0.821.+-.0.062 and b=1.256.+-.0.079 using two single needle
electrodes.
[0041] FIG. 19 is a representation of the Finite Element Analysis
(FEA) model for a 3D Electric Field [V/cm] Distribution in
Non-Electroporated (Baseline) Tissue with 1.5-cm Single Needle
Electrodes at a Separation of 2.0 cm and with 3000 V applied.
[0042] FIGS. 20A-D are representations of the Electric Field [V/cm]
Distributions from the 3D Non-Electroporated (Baseline) Models of
FIG. 19, wherein FIG. 20A represents the x-y plane mid-electrode
length, FIG. 20B represents the x-z plane mid-electrode diameter,
FIG. 20C represents the y-z plane mid-electrode diameter, and FIG.
20D represents the y-z plane between electrodes.
[0043] FIG. 21 is a representation of the Finite Element Analysis
(FEA) model for a 3D Electric Field [V/cm] Distribution in
Electroporated Tissue with 1.5-cm Single Needle Electrodes at a
Separation of 2.0 cm and 3000 V applied assuming
.sigma..sub.max/.sigma..sub.0=3.6.
[0044] FIGS. 22A-22D are representations of the Electric Field
[V/cm] Distributions from the 3D Electroporated Models with 1.5-cm
Electrodes at a Separation of 2.0 cm and 3000 V (cross-sections)
assuming .sigma..sub.max/.sigma..sub.0=3.6, wherein FIG. 22A
represents the x-y plane mid-electrode length, FIG. 22B represents
the x-z plane mid-electrode diameter, FIG. 22C represents the y-z
plane mid-electrode diameter, and FIG. 22D represents the y-z plane
between electrodes.
[0045] FIG. 23 is a representative Cassini curve showing zones of
ablation derived using two single needle electrodes and the
pre-pulse procedure to determine the ratio of maximum conductivity
to baseline conductivity. For comparison purposes the baseline
electric field isocontour is also presented in which no
electroporation is taken into account.
[0046] FIGS. 24A-24D are representative surface plots showing
finite element temperature calculations at different electrode
spacings. The surface plots show temperature distributions at t=90
seconds (Ninety pulses of 100 .mu.s each) for 3000 V treatments
with (A) 1.0 cm, (B) 1.5 cm, (C) 2.0 cm, and (D) 2.5 cm electrode
spacing. Contour lines show approximate electric field correlating
to T=45.degree. C. (A) 900 V/cm, (B) 1075 V/cm, (C) 1100 V/cm, and
(D) 1080 V/cm.
[0047] FIGS. 25A-25D are representative surface plots showing
Cassini Oval Approximations at different electrode spacings. The
surface plots show the temperature distribution at t=90 seconds
(Ninety pulses of 100 .mu.s each) for 3000 V treatments with (A)
1.0 cm, (B) 1.5 cm, (C) 2.0 cm, and (D) 2.5 cm electrode spacing.
Red dashed lines show the Cassini oval correlating to T=45.degree.
C. and the black dotted lines show the Cassini oval correlating to
500 V/cm.
[0048] FIGS. 26A-26D are representative surface plots showing
Cassini Oval Approximations at different times. The surface plots
show the temperature distribution at (A) t=10 seconds, (B) t=40
seconds, (C) t=90 seconds, and (D) t=200 seconds. Treatment
parameters were held constant at 3000 V, 1.5 cm exposure, and 2.5
cm electrode spacing. Red dashed lines show the Cassini oval
correlating to T=45.degree. C. and the black dotted lines show the
Cassini oval correlating to 500 V/cm. The pulses were programmed
with 100 .mu.s duration.
[0049] FIGS. 27A-27D are representative surface plots showing
Cassini Oval Approximations at different temperatures. The surface
plots show the temperature distribution at A) T=37.2.degree. C., B)
T=40.degree. C., C) T=45.degree. C., and D) T=50.degree. C.
Treatment parameters were held constant at 3000V, 1.5 cm exposure,
and 2.5 cm electrode spacing at a time=90 seconds (Ninety pulses of
100 .mu.s each). Red dashed lines show the Cassini oval correlating
to the specified temperatures and the black dotted lines show the
Cassini oval correlating to 500 V/cm.
[0050] FIG. 28 is a screenshot of the Cassini Oval Approximation
Tool using the following parameters: Voltage=3000 V, Gap=10 mm,
Time=90 seconds (Ninety pulses of 100 .mu.s each),
Temperature=50.degree. C., and Electric Field=500 V/cm. The red
dashed line shows the Cassini oval correlating to 50.degree. C. and
the black dotted lines show the Cassini oval correlating to 500
V/cm.
[0051] FIG. 29 is a screenshot of the Cassini Oval Approximation
Tool using the following parameters: Voltage=3000 V, Gap=10 mm,
Time=90 seconds (Ninety pulses of 100 .mu.s each),
Temperature=40.degree. C., and Electric Field=500 V/cm. The red
dashed lines show the Cassini oval correlating to 40.degree. C. and
the black dotted line show the Cassini oval correlating to 500
V/cm.
[0052] FIGS. 30A-30D are representative surface plots showing
Cassini Oval Approximations at different temperature thresholds.
The surface plots show the temperature and electric field
distribution at A) T=40.degree. C., B) T=45.degree. C., C)
T=50.degree. C., and D) T=55.degree. C. The other parameters are
the same as those for FIGS. 28 and 29. The red dashed lines show
the Cassini oval correlating to the specified temperatures and the
black dotted lines show the Cassini oval correlating to 500
V/cm.
[0053] FIGS. 31A-31D are representative surface plots showing
Cassini Oval Approximations at different voltages. The surface
plots show the temperature and electric field distribution at A)
3000 V, B) 2000 V C) 1500 V and D) 1000 V. Other parameters were
Gap=10 mm, Time=90 seconds (Ninety pulses of 100 .mu.s each),
Temperature=40.degree. C., and Electric Field=500 V/cm. The red
dashed lines show the Cassini oval correlating to 40.degree. C. and
the black dotted lines show the Cassini oval correlating to 500
V/cm.
[0054] FIGS. 32A-32D are representative surface plots showing
Cassini Oval Approximations at different electric field thresholds.
The surface plots show the temperature and electric field
distribution at A) 500 V/cm, B) 1000 V/cm, C) 1500 V/cm, and D)
2000 V/cm. Other parameters were Voltage=3000 V, Gap=10 mm, Time=90
seconds (Ninety pulses of 100 .mu.s each), Temperature=40.degree.
C. The red dashed lines show the Cassini oval correlating to
40.degree. C. and the black dotted lines show the Cassini oval
correlating to the specified electric field thresholds.
[0055] FIGS. 33A-33D are representative surface plots showing
Cassini Oval Approximations at different electrode spacings. The
surface plots show the temperature and electric field distribution
at an electrode spacing of 5 mm, 10 mm, 15 mm, and 20 mm. Other
parameters were Voltage=3000 V, Time=90 seconds (Ninety pulses of
100 .mu.s each), Temperature=40.degree. C., and Electric Field=500
V/cm. The red dashed lines show the Cassini oval correlating to
40.degree. C. and the black dotted lines show the Cassini oval
correlating to 500 V/cm.
[0056] FIGS. 34A-34D are representative surface plots showing
Cassini Oval Approximations at different times. The surface plots
show the temperature and electric field distribution at A) 90
seconds (Ninety pulses of 100 .mu.s each), B) 60 seconds (Sixty
pulses of 100 .mu.s each), C) 30 seconds (Thirty pulses of 100
.mu.s each), and D) 10 seconds (Ten pulses of 100 .mu.s each).
Other parameters were Voltage=3000 V, Gap=10 mm,
Temperature=40.degree. C., and Electric Field=500 V/cm. The red
dashed lines show the Cassini oval correlating to 40.degree. C. and
the black dotted lines show the Cassini oval correlating to 500
V/cm.
[0057] FIG. 35 is a representation of the COMSOL three-dimensional
finite element domain and mesh used to calculate Cassini Oval
values for the electric and thermal curves.
[0058] FIGS. 36A-36C show a representation of a visualization tool
providing the 650 V/cm electric field distributions using different
configurations of bipolar probes and includes dynamic change
(3.6.times.) in electrical conductivity from the non-electroporated
baseline for runs 7, 8, and 9 of the visualization.
[0059] FIG. 36D is a table showing parameters of runs 7, 8, and 9
including electrode length, separation distance (insulation), and
applied voltage.
[0060] FIG. 36E is a table showing lesion dimensions for runs 7, 8,
and 9. The results show that as the length of the bipolar electrode
increases the size of the zone of ablation increases.
[0061] FIG. 37 is a graph showing electrical conductivity (S/m,
y-axis) plotted against electric field strength (V/cm, x-axis).
FIG. 37 shows the conductivity changes from 0.1 to 0.35 at an
electric field centered at 500 V/cm.
[0062] FIG. 38A is a representative contour plot showing the
"Goldberg" data (red dashed line) vs a calculated threshold (solid
black line) based on the parameters shown in FIG. 38C. The x and y
axes represent distance [cm].
[0063] FIG. 38B is a representative contour plot showing the
conductivity (blue dotted line) vs. a calculated threshold (solid
black line) based on the parameters shown in FIG. 38C. The x and y
axes represent distance [cm].
[0064] FIG. 38C is a table showing the parameters used to generate
the contour plots of FIGS. 38A and 38B.
[0065] FIGS. 39A-39C are representative contour plots showing the
"Goldberg" data (red dashed line) and calculated threshold (solid
black line) and FIGS. 39D-39F are contour plots showing the
conductivity (blue dotted line) and calculated threshold (solid
black line) for conductivities of 2, 3, and 4, respectively. The
other parameters are the same as those in the table of FIG. 38C.
The x and y axes represent distance [cm].
[0066] FIGS. 40A-40C are representative contour plots showing the
"Goldberg" data (red dashed line) and calculated threshold (solid
black line) and FIGS. 40D-40F are contour plots showing the
conductivity (blue dotted line) and calculated threshold (solid
black line) for conductivity multipliers of 2, 3, and 4,
respectively. Other parameters used to generate the plots of FIGS.
40A-40F include an IRE Threshold of 600 V/cm, a transition zone of
0.4, a Voltage of 700 V, an E-Field of 700 V/cm, and a Sigma
(baseline electrical conductivity) of 0.20 S/m. The x and y axes
represent distance [cm].
[0067] FIGS. 41A-41C are representative contour plots showing the
"Goldberg" data (red dashed line) and calculated threshold (solid
black line) and FIGS. 41D-41F are contour plots showing the
conductivity (blue dotted line) and calculated threshold (solid
black line) for conductivity multipliers of 2, 3, and 4,
respectively. Other parameters used to generate the plots of FIGS.
41A-41F include an IRE Threshold of 1000 V/cm, transition zone of
0.2, Voltage of 2700 V, E-Field of 700 V/cm, and Sigma (baseline
electrical conductivity) of 0.20 S/m. The x and y axes represent
distance [cm].
[0068] FIG. 42 is a representative contour plot of the electric
field distribution assuming a static electrical conductivity using
a bipolar probe. The model assumes an applied voltage of 2700 V
with 7 mm long electrodes separated by an 8 mm insulation
shaft.
[0069] FIGS. 43A-43D are representative contour plots of post-IRE
cell viability predictions with the colored curves illustrating
different cell viability levels. The model assumes using ninety
100-.mu.s pulses at a rate of one pulse per second with 2700 V, and
a viability value of 0.1% (S=0.001) as the complete cell death due
to IRE exposure.
[0070] FIG. 44 is a graph showing the dynamic electric conductivity
function of liver tissue undergoing electroporation. The sigmoid
function includes a baseline of 0.067 S/m and maximum conductivity
of 0.241 S/m.
[0071] FIG. 45 is a representative contour plot showing the
electric field distribution assuming a dynamic electrical
conductivity using the bipolar probe with 3000 V with 7 mm long
electrodes separated by an 8 mm insulation shaft.
[0072] FIGS. 46A-D are representative contour plots showing
post-IRE cell viability, wherein A) corresponds to 20 pulses at
2000 volts, B) corresponds to 20 pulses at 3000 volts, C)
corresponds to 100 pulses at 2000 volts, and D) corresponds to 100
pulses at 3000 volts.
[0073] FIGS. 47A and 47B are representative contour plots showing
post-IRE cell viability after three hundred (FIG. 47A) and three
hundred and sixty (FIG. 47B) 100-.mu.s pulses at a rate of one
pulse per second with an applied voltage of 3000 V.
[0074] FIGS. 48A and 48B are a table showing the results of a
parametric study on bipolar electrode configuration as a function
of electrode length, separation distance, and diameter in the
resulting IRE area and volume.
[0075] FIG. 49 is a table showing the results of a parametric study
on bipolar electrode configuration as a function of applied voltage
and pulse number in the resulting IRE area and volume with 7 mm
long electrodes separated by an 8 mm insulation shaft.
[0076] FIG. 50 is a table showing the results of a parametric study
on bipolar electrode configuration as a function of pulse number in
the resulting IRE area and volume with an applied voltage of 3000 V
with 7 mm long electrodes separated by an 8 mm insulation
shaft.
[0077] FIGS. 51A-C are schematics of representative electrode
geometries.
[0078] FIGS. 51D-F are representative contour plots showing the
resulting electric field distribution corresponding to the
electrode geometries of FIGS. 51A-C.
DETAILED DESCRIPTION OF VARIOUS EMBODIMENTS OF THE INVENTION
[0079] Reference will now be made in detail to various exemplary
embodiments of the invention. Embodiments described in the
description and shown in the figures are illustrative only and are
not intended to limit the scope of the invention. Changes may be
made in the specific embodiments described in this specification
and accompanying drawings that a person of ordinary skill in the
art will recognize are within the scope and spirit of the
invention.
[0080] Throughout the present teachings, any and all of the
features and/or components disclosed or suggested herein,
explicitly or implicitly, may be practiced and/or implemented in
any combination, whenever and wherever appropriate as understood by
one of ordinary skill in the art. The various features and/or
components disclosed herein are all illustrative for the underlying
concepts, and thus are non-limiting to their actual descriptions.
Any means for achieving substantially the same functions are
considered as foreseeable alternatives and equivalents, and are
thus fully described in writing and fully enabled. The various
examples, illustrations, and embodiments described herein are by no
means, in any degree or extent, limiting the broadest scopes of the
claimed inventions presented herein or in any future applications
claiming priority to the instant application.
[0081] Embodiments of the invention include a method for
visualization of heat and electric field distribution within a
target treatment area, the method comprising: selecting as inputs
an applied voltage, electrode spacing, and treatment duration
corresponding to a desired treatment protocol for a target
treatment area; using the inputs in a Cassini approximation of
data, wherein the data comprises measured voltage, electrode
spacing, and time of actual treatment protocols, and determining an
expected temperature distribution and expected electric field
distribution of the target treatment area; and displaying a
graphical representation of a selected temperature and a selected
electric field of the expected temperature and electric field
distributions. Such methods can further comprise as inputs one or
more of a baseline conductivity for the target treatment area, a
change in conductivity for the target treatment area, or a
conductivity for a specific tissue type.
[0082] Such methods can include a method of treatment planning for
medical therapies involving administering electrical treatment
energy, the method comprising: providing one or more parameters of
a treatment protocol for delivering one or more electrical pulses
to tissue through one or more or a plurality of electrodes;
modeling heat distribution in the tissue based on the parameters;
and displaying a graphical representation of the modeled heat
distribution.
[0083] One embodiment of the present invention is illustrated in
FIGS. 1 and 2. Representative components that can be used with the
present invention can include one or more of those that are
illustrated in FIG. 1. For example, in embodiments, one or more
probes 22 can be used to deliver therapeutic energy and are powered
by a voltage pulse generator 10 that generates high voltage pulses
as therapeutic energy such as pulses capable of irreversibly
electroporating the tissue cells. In the embodiment shown, the
voltage pulse generator 10 includes six separate receptacles for
receiving up to six individual probes 22 which are adapted to be
plugged into the respective receptacle. The receptacles are each
labeled with a number in consecutive order. In other embodiments,
the voltage pulse generator can have any number of receptacles for
receiving more or less than six probes.
[0084] For example, a treatment protocol according to the invention
could include a one or more or a plurality of electrodes. According
to the desired treatment pattern, the plurality of electrodes can
be disposed in various positions relative to one another. In a
particular example, a plurality of electrodes can be disposed in a
relatively circular pattern with a single electrode disposed in the
interior of the circle, such as at approximately the center. Any
configuration of electrodes is possible and the arrangement need
not be circular but any shape periphery can be used depending on
the area to be treated, including any regular or irregular polygon
shape, including convex or concave polygon shapes. The single
centrally located electrode can be a ground electrode while the
other electrodes in the plurality can be energized. Any number of
electrodes can be in the plurality such as from about 1 to 20.
Indeed, even 3 electrodes can form a plurality of electrodes where
one ground electrode is disposed between two electrodes capable of
being energized, or 4 electrodes can be disposed in a manner to
provide two electrode pairs (each pair comprising one ground and
one electrode capable of being energized). During treatment,
methods of treating can involve energizing the electrodes in any
sequence, such as energizing one or more electrode simultaneously,
and/or energizing one or more electrode in a particular sequence,
such as sequentially, in an alternating pattern, in a skipping
pattern, and/or energizing multiple electrodes but less than all
electrodes simultaneously, for example.
[0085] In the embodiment shown, each probe 22 includes either a
monopolar electrode or bipolar electrodes having two electrodes
separated by an insulating sleeve. In one embodiment, if the probe
includes a monopolar electrode, the amount of exposure of the
active portion of the electrode can be adjusted by retracting or
advancing an insulating sleeve relative to the electrode. See, for
example, U.S. Pat. No. 7,344,533, which is incorporated by
reference herein in its entirety. The pulse generator 10 is
connected to a treatment control computer 40 having input devices
such as keyboard 12 and a pointing device 14, and an output device
such as a display device 11 for viewing an image of a target
treatment area such as a lesion 300 surrounded by a safety margin
301. The therapeutic energy delivery device 22 is used to treat a
lesion 300 inside a patient 15. An imaging device 30 includes a
monitor 31 for viewing the lesion 300 inside the patient 15 in real
time. Examples of imaging devices 30 include ultrasonic, CT, MRI
and fluoroscopic devices as are known in the art.
[0086] The present invention includes computer software (treatment
planning module 54) which assists a user to plan for, execute, and
review the results of a medical treatment procedure, as will be
discussed in more detail below. For example, the treatment planning
module 54 assists a user to plan for a medical treatment procedure
by enabling a user to more accurately position each of the probes
22 of the therapeutic energy delivery device 20 in relation to the
lesion 300 in a way that will generate the most effective treatment
zone. The treatment planning module 54 can display the anticipated
treatment zone based on the position of the probes and the
treatment parameters. The treatment planning module 54 may also
display a zone of temperature heating according to cutoff values
inputted by the treating physician and correlate this with a value
for the electric field distribution. The treatment planning module
may also allow the treating physician to display the anticipated
treatment zone, or target ablation zone, according to one or more
tissue-specific conductivity parameters inputted by the treating
physician. The conductivity parameters may include the baseline
conductivity of the tissue to be treated, the ratio of the baseline
conductivity to the maximum conductivity of the tissue that is
reached during treatment, the rate at which the conductivity
increases from the baseline to the maximum conductivity, and/or the
electric field at which the conductivity changes during
treatment.
[0087] The treatment planning module 54 can display the progress of
the treatment in real time and can display the results of the
treatment procedure after it is completed. This information can be
displayed in a manner such that it can be used for example by a
treating physician to determine whether the treatment was
successful and/or whether it is necessary or desirable to re-treat
the patient.
[0088] For purposes of this application, the terms "code",
"software", "program", "application", "software code", "computer
readable code", "software module", "module" and "software program"
are used interchangeably to mean software instructions that are
executable by a processor. The "user" can be a physician or other
medical professional. The treatment planning module 54 executed by
a processor outputs various data including text and graphical data
to the monitor 11 associated with the generator 10.
[0089] Referring now to FIG. 2, the treatment control computer 40
of the present invention manages planning of treatment for a
patient. The computer 40 is connected to the communication link 52
through an I/O interface 42 such as a USB (universal serial bus)
interface, which receives information from and sends information
over the communication link 52 to the voltage generator 10. The
computer 40 includes memory storage 44 such as RAM, processor (CPU)
46, program storage 48 such as ROM or EEPROM, and data storage 50
such as a hard disk, all commonly connected to each other through a
bus 53. The program storage 48 stores, among others, a treatment
planning module 54 which includes a user interface module that
interacts with the user in planning for, executing and reviewing
the result of a treatment. Any of the software program modules in
the program storage 48 and data from the data storage 50 can be
transferred to the memory 44 as needed and is executed by the CPU
46.
[0090] In one embodiment, the computer 40 is built into the voltage
generator 10. In another embodiment, the computer 40 is a separate
unit which is connected to the voltage generator through the
communications link 52. In a preferred embodiment, the
communication link 52 is a USB link. In one embodiment, the imaging
device 30 is a standalone device which is not connected to the
computer 40. In the embodiment as shown in FIG. 1, the computer 40
is connected to the imaging device 30 through a communications link
53. As shown, the communication link 53 is a USB link. In this
embodiment, the computer can determine the size and orientation of
the lesion 300 by analyzing the data such as the image data
received from the imaging device 30, and the computer 40 can
display this information on the monitor 11. In this embodiment, the
lesion image generated by the imaging device 30 can be directly
displayed on the grid (not shown) of the display device (monitor)
11 of the computer running the treatment planning module 54. This
embodiment would provide an accurate representation of the lesion
image on the grid, and may eliminate the step of manually inputting
the dimensions of the lesion in order to create the lesion image on
the grid. This embodiment would also be useful to provide an
accurate representation of the lesion image if the lesion has an
irregular shape.
[0091] It should be noted that the software can be used
independently of the pulse generator 10. For example, the user can
plan the treatment in a different computer as will be explained
below and then save the treatment parameters to an external memory
device, such as a USB flash drive (not shown). The data from the
memory device relating to the treatment parameters can then be
downloaded into the computer 40 to be used with the generator 10
for treatment. Additionally, the software can be used for
hypothetical illustration of zones of ablation, temperature
thresholds or cutoffs, and electrical field thresholds or cutoffs
for training purposes to the user on therapies that deliver
electrical energy. For example, the data can be evaluated by a
human to determine or estimate favorable treatment protocols for a
particular patient rather than programmed into a device for
implementing the particular protocol.
[0092] FIG. 3 illustrates one embodiment of a circuitry to detect
an abnormality in the applied pulses such as a high current, low
current, high voltage or low voltage condition. This circuitry is
located within the generator 10 (see FIG. 1). A USB connection 52
carries instructions from the user computer 40 to a controller 71.
The controller can be a computer similar to the computer 40 as
shown in FIG. 2. The controller 71 can include a processor, ASIC
(application-specific integrated circuit), microcontroller or wired
logic. The controller 71 then sends the instructions to a pulse
generation circuit 72. The pulse generation circuit 72 generates
the pulses and sends electrical energy to the probes. For clarity,
only one pair of probes/electrodes are shown. However, the
generator 10 can accommodate any number of probes/electrodes (e.g.,
from 1-10, such as 6 probes) and energizing multiple electrodes
simultaneously for customizing the shape of the ablation zone. In
the embodiment shown, the pulses are applied one pair of electrodes
at a time, and then switched to another pair. The pulse generation
circuit 72 includes a switch, preferably an electronic switch, that
switches the probe pairs based on the instructions received from
the computer 40. A sensor 73 such as a sensor can sense the current
or voltage between each pair of the probes in real time and
communicate such information to the controller 71, which in turn,
communicates the information to the computer 40. If the sensor 73
detects an abnormal condition during treatment such as a high
current or low current condition, then it will communicate with the
controller 71 and the computer 40 which may cause the controller to
send a signal to the pulse generation circuit 72 to discontinue the
pulses for that particular pair of probes. The treatment planning
module 54 can further include a feature that tracks the treatment
progress and provides the user with an option to automatically
retreat for low or missing pulses, or over-current pulses (see
discussion below). Also, if the generator stops prematurely for any
reason, the treatment planning module 54 can restart at the same
point where it terminated, and administer the missing treatment
pulses as part of the same treatment. In other embodiments, the
treatment planning module 54 is able to detect certain errors
during treatment, which include, but are not limited to, "charge
failure", "hardware failure", "high current failure", and "low
current failure".
[0093] General treatment protocols for the destruction (ablation)
of undesirable tissue through electroporation are known. They
involve the insertion (bringing) electroporation electrodes to the
vicinity of the undesirable tissue and in good electrical contact
with the tissue and the application of electrical pulses that cause
irreversible electroporation of the cells throughout the entire
area of the undesirable tissue. The cells whose membrane was
irreversible permeabilized may be removed or left in situ (not
removed) and as such may be gradually removed by the body's immune
system. Cell death is produced by inducing the electrical
parameters of irreversible electroporation in the undesirable
area.
[0094] Electroporation protocols involve the generation of
electrical fields in tissue and are affected by the Joule heating
of the electrical pulses. When designing tissue electroporation
protocols it is important to determine the appropriate electrical
parameters that will maximize tissue permeabilization without
inducing deleterious thermal effects. It has been shown that
substantial volumes of tissue can be electroporated with reversible
electroporation without inducing damaging thermal effects to cells
and has quantified these volumes (Davalos, R. V., B. Rubinsky, and
L. M. Mir, Theoretical analysis of the thermal effects during in
vivo tissue electroporation. Bioelectrochemistry, 2003. Vol.
61(1-2): p. 99-107).
[0095] The electrical pulses used to induce irreversible
electroporation in tissue are typically larger in magnitude and
duration from the electrical pulses required for reversible
electroporation. Further, the duration and strength of the pulses
for irreversible electroporation are different from other
methodologies using electrical pulses such as for intracellular
electro-manipulation or thermal ablation. The methods are very
different even when the intracellular (nano-seconds)
electro-manipulation is used to cause cell death, e.g. ablate the
tissue of a tumor or when the thermal effects produce damage to
cells causing cell death.
[0096] Typical values for pulse length for irreversible
electroporation are in a range of from about 5 microseconds to
about 62,000 milliseconds or about 75 microseconds to about 20,000
milliseconds or about 100 microseconds.+-.10 microseconds. This is
significantly longer than the pulse length generally used in
intracellular (nano-seconds) electro-manipulation which is 1
microsecond or less--see published U.S. application 2002/0010491
published Jan. 24, 2002.
[0097] The pulse is typically administered at voltage of about 100
V/cm to 7,000 V/cm or 200 V/cm to 2000 V/cm or 300V/cm to 1000 V/cm
about 600 V/cm for irreversible electroporation. This is
substantially lower than that used for intracellular
electro-manipulation which is about 10,000 V/cm, see U.S.
application 2002/0010491 published Jan. 24, 2002.
[0098] The voltage expressed above is the voltage gradient (voltage
per centimeter). The electrodes may be different shapes and sizes
and be positioned at different distances from each other. The shape
may be circular, oval, square, rectangular or irregular etc. The
distance of one electrode to another may be 0.5 to 10 cm, 1 to 5
cm, or 2-3 cm. The electrode may have a surface area of 0.1-5 sq.
cm or 1-2 sq. cm.
[0099] The size, shape and distances of the electrodes can vary and
such can change the voltage and pulse duration used. Those skilled
in the art will adjust the parameters in accordance with this
disclosure to obtain the desired degree of electroporation and
avoid thermal damage to surrounding cells.
[0100] Additional features of protocols for electroporation therapy
are provided in U.S. Patent Application Publication No. US
2007/0043345 A1, the disclosure of which is hereby incorporated by
reference in its entirety.
[0101] In one aspect, the systems and methods may have the
capability for estimating a volume of tissue that will be heated at
or above a cutoff value and a volume of tissue that will receive an
electric field at or above a cutoff value for the above medical
treatment device. The cut-off values may be user-specified values
determined by a treating physician or technician. The systems and
methods are provided so that the treating physician may recognize
treatments that produce overheating in the vicinity of the
electrodes of the treatment device. This additional capability of
the treatment device may be based on the Joule heating equations of
Example 8. The values may be plotted as contour lines which may be
displayed with a graphical representation of the estimated
treatment volume above. In one embodiment, the contour lines are
Cassini oval approximations performed according to the equations
and procedure in Example 7.
[0102] In another aspect, the systems and methods may have the
additional capability for providing the electric field
distributions using different configurations of bipolar probes and
include the dynamic change in electrical conductivity from the
baseline non-electroporated tissue. The systems and methods may
allow a user to incorporate tissue-specific values for the dynamic
change in conductivity in estimating a treatment volume. This
additional capability is further described in Example 9. In one
embodiment, the contour lines are Cassini oval approximations
performed according to the equations and procedure in Example
7.
[0103] In another aspect, the systems and methods may have the
additional capability for inputting or adjusting one or more
variables related to the dynamic conductivity so that
tissue-specific behavior can be accounted for when estimating a
treatment volume. In embodiments, the treatment planning module may
provide input for parameters such as the baseline conductivity,
change in conductivity, the transition zone (how rapidly the
conductivity increases), the electric field at which the change in
conductivity occurs, and the electric field at which irreversible
electroporation occurs. These parameters may allow the treating
physician to fine-tune the ablation zone based on the conductivity
characteristics of the target tissue. The present inventors have
recognized that the conductivity characteristics of the tissue,
such as baseline and maximum conductivities, should be determined
before the therapy in order to determine safe and effective pulse
protocols. This additional capability is further described in
Example 10.
[0104] The numerical models and algorithms of the invention, as
provided in the Examples, such as Cassini Oval equations of Example
7 and the Joule Heating Model equations of Example 8, can be
implemented in a system for estimating a 3-dimensional treatment
volume for a medical treatment device that applies treatment energy
through one or more or a plurality of electrodes defining a
treatment area. In one embodiment, the numerical models and
algorithms are implemented in an appropriate computer readable code
as part of the treatment planning module 54 of the system of the
invention. Computing languages available to the skilled artisan for
programming the treatment planning module 54 include general
purpose computing languages such as the C and related languages,
and statistical programming languages such as the "S" family of
languages, including R and S-Plus. The computer readable code may
be stored in a memory 44 of the system of the invention. A
processor 46 is coupled to the memory 44 and a display device 11
and the treatment planning module 54 stored in the memory 44 is
executable by the processor 46. Treatment planning module 54,
through the implemented numerical models, is adapted to generate a
graphical display of an estimated temperature or electric field or
target ablation zone in the display device 11.
[0105] In one embodiment, the invention provides for a system for
estimating and graphically displaying a thermal and/or electric
field value for a medical treatment device that applies treatment
energy through one or more or a plurality of electrodes 22 defining
a treatment area, the system comprising a memory 44, a display
device 11, a processor 46 coupled to the memory 44 and the display
device 11, and a treatment planning module 54 stored in the memory
44 and executable by the processor 46, the treatment planning
module 54 adapted to generate one or more isocontours representing
a value of a temperature and/or electric field for display in the
display device 11 based on modeling of the temperature
distributions or electrical field distributions according to one or
more parameters defining an electrical energy based protocol (e.g.,
irreversible electroporation). The results of modeling the
temperature distributions and electrical field distributions may be
stored in a database or calculated in real-time. The treatment
planning module may generate the isocontours based on the modeling
results.
[0106] In another embodiment, the invention provides for a system
for estimating a target ablation zone for a medical treatment
device that applies treatment energy through one or more or a
plurality of electrodes 22 defining a treatment area, the system
comprising a memory 44, a display device 11, a processor 46 coupled
to the memory 44 and the display device 11, and a treatment
planning module 54 stored in the memory 44 and executable by the
processor 46, the treatment planning module 54 adapted to generate
a target ablation zone in the display device 11 based on a
combination of one or more parameters for a treatment protocol for
irreversible electroporation and one or more tissue-specific
conductivity parameters.
[0107] The foregoing description provides additional instructions
and algorithms for a computer programmer to implement in computer
readable code a treatment planning module 54 that may be executable
through a processor 46 to generate an estimated temperature or
electrical field for display in the display device 11 based on
modeling of a tissue according to one or more parameters for
electroporation, such as IRE. The computer readable code may also
estimate a temperature value and an electric field value according
to equations described in Example 8 and graphically display these
value as contour lines in the display device. In one embodiment,
the contour lines are Cassini oval approximations performed
according to the equations and procedure in Example 7. The computer
readable code may also provide for input on one or more
conductivity parameters for estimating the target ablation zone as
described in Examples 9 and 10.
[0108] FIG. 4 is a schematic diagram showing a three-dimensional
zone of ablation occurring during irreversible electroporation. The
width and depth of this zone of ablation may be modeled
two-dimensionally using the Cassini oval equation. Further, the
mathematical fit of the zone of ablation has similar shape
characteristics as the actual and simulated electric field and
temperature values. For example, a typical single bi-polar probe
will be configured to have a first and second electrode spaced
apart from each other at the distal end of the single probe. Since
the lesion formed by this bi-polar arrangement closely resembles
the 8-like shape of the electric field, the method of the invention
can be used to accurately predict the electric field and
temperature contours. FIGS. 16A and 16B show variations of `a` and
`b` parameters that will closely resemble the 8-like shape of the
electric field according to the Cassini Equation.
[0109] The method of the invention fits data extracted from
numerical simulations to both the `a` and `b` parameters from the
Cassini Equation, providing the flexibility to match potentially
any shape of electric field created by the specific pulse
parameters employed. Also, as illustrated in FIGS. 16A and 16B
since the `a` or `b` parameters are not related to the separation
distance or geometry of the electrodes, the electric field and
temperature contours of the bi-polar probe can be captured
according to the techniques described above.
[0110] Additionally, by adding the cumulative effects of electrode
pairs, the electric field and thermal contours of alternative
multi-electrode arrangements of three or more probes can be
determined. For example, a four single probe electrode box can be
captured by calculating treatment regions based on each combination
of electrode pairs for the fit according to the techniques
described above. Thus, for example, if the four probe electrode box
is configured for treatment using pulses that cycle through probe
combinations 1-2, 3-4, 1-3, 2-4, 2-3 and 1-4 the approximation tool
can find electric field and temperature contours for each probe
combination, then superimpose the results to display the cumulative
effect of that particular pulse protocol in the treatment
region.
[0111] In one embodiment, the treatment planning module 54 provides
for a method for modeling and graphical display of tissue heating
according to a set of parameters defining a treatment protocol. In
a specific embodiment, the set of parameters correspond to a
treatment protocol for inducing irreversible electroporation in a
tissue.
[0112] The treatment planning module 54 may provide one or more
parameters of a treatment protocol for delivering one or more
electrical pulses to a tissue through one or more or a plurality of
electrodes.
[0113] The treatment planning module 54 may model a heat
distribution in a tissue surrounding the one or more or the
plurality of electrodes based on the one or more parameters.
[0114] The treatment planning module 54 may provide a graphical
representation of the heat distribution based on the modeled heat
distribution.
[0115] The treatment planning module 54 may allow a user to
optionally modify one or more of the parameters of the treatment
protocol through input devices 12, 14 based on the graphical
representation of the heat distribution.
[0116] The treatment planning module 54 may be in operable
connection with a controller 71 capable of delivering one or more
electrical pulses to the tissue based on the one or more parameters
stored in the treatment planning module 54.
[0117] The treatment planning module 54 may model the heat
distribution in the tissue based on the Joule heating in the
tissue.
[0118] The treatment planning module 54 may calculate the heat
distribution as:
.rho. .times. .times. C p .times. .differential. T .differential. t
= .gradient. ( k .times. .times. .gradient. T ) + Q jh .function. [
W m 3 ] ##EQU00001##
[0119] where .rho. is the density, C.sub.p is the heat capacity, k
is the thermal conductivity, and Q.sub.jh are the resistive
losses
Q jh = J E .function. [ W m 3 ] ##EQU00002##
[0120] where J is the induced current density
J = .sigma. .times. .times. E .function. [ A m 2 ] ##EQU00003##
[0121] and .sigma. is the tissue conductivity and E is the electric
field
E = - .gradient. .PHI. .function. [ V m ] ##EQU00004##
[0122] The treatment planning module may further calculate the
resistive losses as
jh.Qrh=((jh.Jix+jh.Jex)*duty_cycle*jh.Ex+(jh.Jiy+jh.Jey)*duty_cycle*jh.E-
y+(jh.Jiz+jh.Jez)*duty_cycle*jh.Ez)*)t<=90)+0*(t>90)
according to the Joule Heating Model described in Example 8.
[0123] The treatment planning module 54 may allow a user to specify
a heat distribution value (i.e. temperature) and may provide a
graphical representation of the temperature as an isocontour
line.
[0124] The treatment planning module 54 may model an electric field
distribution in a tissue surrounding the one or more or a plurality
of electrodes based on the one or more parameters of the treatment
protocol.
[0125] The treatment planning module 54 may provide a graphical
representation of the electric field distribution based on the
modeled electrical field distribution.
[0126] The treatment planning module may calculate the electric
field distribution as:
.gradient..sup.2.PHI.=0
[0127] where .PHI. is the electric potential, this equation is
solved with boundary conditions:
[0128] {right arrow over (n)}{right arrow over (J)}=0 at the
boundaries
[0129] .PHI.=V.sub.in at the boundary of the first electrode
[0130] .PHI.=0 at the boundary of the second electrode
[0131] wherein {right arrow over (n)} is the normal vector to the
surface, {right arrow over (J)} is the electrical current and
V.sub.in is the electrical potential applied.
[0132] The treatment planning module 54 may allow a user to specify
a value for an electrical field distribution and provide a
graphical representation of the electrical field distribution value
as an isocontour line.
[0133] The treatment planning module 54 may display isocontour
lines representing the heat and electrical field distributions by
calculating a Cassini oval according to Example 7. The Cassini oval
may be calculated by first modeling the temperature and electrical
field distributions, storing the values in a database, and then
calculating the specific Cassini oval based on parameters chosen by
the user.
[0134] The treatment planning module 54 may allow a user to specify
the one or more parameters of a treatment protocol including
voltage, gap between electrodes, duration, pulse width, and
electric field intensity.
[0135] Alternatively, or in addition, the treatment planning module
54 may allow a user to input one or more of the tissue-specific
conductivity parameters described herein and model the electric
field distribution and tissue heating. The treatment planning
module 54 may then provide graphical representations of one or more
values of the electrical field intensity and tissue
temperature.
[0136] The treatment planning module 54 may provide a graphical
representation of an electrical field distribution and a heat
distribution through a variety of modes of operation. First, the
treatment planning module 54 may model the electrical field
distribution and heat distribution for each set of parameters that
are entered through input devices 12, 14. Thus, every time the
treating physician altered one or more parameters of the treatment
protocol, the treatment planning module 54 software would model the
electrical field and heat distributions according to those
parameters and then graphically display them on the display device
11. In a second approach, the software would first run the modeling
of the heat and electrical field distributions for a wide range of
parameter combinations and store the resulting distributions in the
database stored in memory 44. In this approach, when the treating
physician enters a particular combination of parameters, the
treatment planning module 54 retrieves the heat distribution and
electrical field distribution from values stored in the database.
These values are then used as a basis for Cassini oval calculations
to determine specific contours for the particular combination of
parameters. The Cassini oval calculations are performed according
to the equations and procedure described in Example 7. The Cassini
ovals are then graphically displayed on the display device 11 in
real time. In embodiments, specific contours are provided according
to values for temperature or electrical field intensity set by the
user.
[0137] The treatment planning module 54 may model the heat and
electric field distributions according to mathematical formulas. In
a specific embodiment, the treatment planning module 54 may model
the heat distribution and the electrical field distribution
according to the formulas in Example 8.
[0138] In another embodiment, the invention provides a system for
treating a tissue, which system applies electrical treatment energy
through one or more or a plurality of electrodes defining a target
treatment area of the tissue. The system comprises a computer 40
comprising: a memory 44, a display device 11, a processor 46
coupled to the memory 44 and the display device 11; and a treatment
planning module 54 stored in the memory 44 and executable by the
processor 46. In this embodiment, the treatment planning module 54
is adapted to: provide one or more parameters of a treatment
protocol for delivering one or more electrical pulses to a tissue
through one or more or a plurality of electrodes; model a heat
distribution in a tissue surrounding the at least electrode based
on the one or more parameters; provide a graphical representation
of the heat distribution on the display device 11 based on the
modeled heat distribution. The system further comprises input
devices 12, 14 in operable connection with computer 40, which input
devices are capable of modifying the one or more parameters of the
treatment protocol in the treatment planning module 54. The system
further comprises a generator 10 in operable connection with the
computer through a controller 71, which controller 71 is capable of
instructing the generator 10 to deliver the one or more electrical
pulses to the target tissue through the one or more or the
plurality of electrodes 22 based on the one or more parameters of
the treatment protocol stored in the treatment planning module 54.
The system may further comprise one or more databases stored in the
memory 44 for storing the modeled heat distributions or modeled
electric field distributions for a plurality of sets of parameters
for a treatment protocol.
[0139] In another embodiment, the treatment planning module 54, in
addition to providing one or more parameters of a treatment
protocol for delivering one or more electrical pulses to a tissue
through one or more or a plurality of electrodes, may also provide
one or more conductivity parameters specific for the tissue to be
treated.
[0140] The treatment planning module 54 may estimate the target
ablation zone based on the one or more parameters of the treatment
protocol and the one or more electrical flow characteristics. The
treatment planning module may also display a graphical
representation of the estimation in the display device 11.
[0141] The treatment planning module 54 may optionally allow for
modification of one or more of the parameters of the treatment
protocol through input devices 12, 14 based on the graphical
representation of the target ablation zone.
[0142] Additionally, the treatment planning module 54 may be in
operable communication with a controller 77 and provide one or more
parameters to the controller for delivering one or more electrical
pulses to the tissue.
[0143] The treatment planning module 54 may provide one or more
parameters of a treatment protocol comprise voltage, gap between
electrodes, duration, pulse width, and electric field
intensity.
[0144] Additionally, the one or more conductivity parameters
provided by the treatment planning module 54 may comprise the
baseline conductivity of the tissue to be treated, the ratio of the
baseline conductivity to the maximum conductivity of the tissue
that is reached during treatment, the rate at which the
conductivity increases from the baseline to the maximum
conductivity, or the electric field at which the conductivity
changes during treatment.
[0145] Additionally, one or more conductivity parameters for a
plurality of tissues may be provided in a database stored in memory
44.
[0146] In another embodiment, the invention provides a system for
treating a tissue, which system applies electrical treatment energy
through one or more or a plurality of electrodes 22 defining a
target treatment area of the tissue. The system may comprise a
computer 40 comprising a memory 44, a display device 11, a
processor 46 coupled to memory 44 and the display device 11, and a
treatment planning module 54 stored in the memory 44 and executable
by the processor 46. The treatment planning module 54 may be
adapted to provide one or more parameters of a treatment protocol
for delivering one or more electrical pulses to a tissue through
one or more or a plurality of electrodes, provide one or more
conductivity parameters specific for the tissue to be treated,
estimate the target ablation zone and display a graphical
representation of the estimation in the display device based on the
one or more parameters of the treatment protocol and the one or
more conductivity parameters. The system may further comprise input
devices 12, 14 in operable connection with the computer 40, which
input devices 12, 14 are capable of allowing a user to modify the
one or more parameters of the treatment protocol in the treatment
planning module 54. The system may further comprise a generator 10
in operable connection with the computer 40 through a controller
71, which controller 71 is capable of instructing the generator 10
to deliver the one or more electrical pulses to a tissue through
the one or more or the plurality of electrodes 22 based on the one
or more parameters of the treatment protocol stored in the
treatment planning module 54. Additionally, the system may comprise
a database of conductivity parameters for a plurality of tissues
stored in the memory 44.
[0147] The systems of the invention may be further configured to
include software for displaying a Graphical User Interface in the
display device with various screens for input and display of
information, including those for inputting various parameters or
display of graphical representations of zones of temperature,
electrical field, and ablation. Additionally, the Graphical User
Interface (GUI) may allow a user to input one or more values
related to an irreversible electroporation protocol and
tissue-specific conductivity measurements through the use of text
fields, check boxes, pull-downs, sliders, command buttons, tabs,
and the like.
[0148] In one embodiment, the invention provides a method of
treating a tissue with a medical treatment device that applies
electrical treatment energy through one or more or a plurality of
electrodes defining a target treatment area of the tissue and that
comprises a display device. The method may comprise providing one
or more parameters of a treatment protocol for delivering one or
more electrical pulses to a tissue through one or more or a
plurality of electrodes, modeling a heat distribution in a tissue
surrounding the at least electrode based on the one or more
parameters, displaying a graphical representation of the heat
distribution based on the modeled heat distribution in the display
device, modifying one or more of the parameters of the treatment
protocol based on the graphical representation of the heat
distribution, and implanting one or a plurality of electrodes in
the tissue and delivering one or more electrical pulses to the
tissue through the electrodes based on the one or more modified
parameters.
[0149] In an exemplary implementation of the method, a treating
physician identifies a target treatment area in a tissue of a
patient. For example, the target treatment area may be a tumor that
is unresectable by conventional surgical methods. The treating
physician then uses input devices 12, 14 such as a keyboard or
mouse to interact with the treatment planning module 54 to select
and input one or more parameters for designing an irreversible
electroporation treatment protocol for ablating the tumor. The
treating physician then selects a temperature value to graphically
display a temperature contour profile in the target treatment area
on the display device 11. For example, the treating physician may
select a value of 50.degree. C. The treating physician then may
correlate this temperature contour with imaging from the treatment
area, by overlaying the temperature contour with the imaging on the
display device 11. By visualizing the temperature contour relative
to the imaging, the treating physician then may identify structures
surrounding the treatment area such as nerves and blood vessels
that may be subject to thermal damage. The treating physician then
may modify the irreversible electroporation parameters so that the
temperature contour no longer indicates that critical structures
may be subject to overheating. Irreversible electroporation
parameters that may be modified include the voltage, distance
between electrodes, electrode diameter, period of treatment, pulse
width, number of pulses, and electric field. Similarly, the
treatment planning module 54 may allow the treating physician to
visualize a temperature contour relative to an electric field
contour. Through one or more iterations of adjustment of the
irreversible electroporation parameters and visualization of the
temperature contour and electric field contour on the display
device, the treating physician may ultimately select a final set of
irreversible electroporation parameters to be used for treatment.
The treating physician may then implant a pair of electrodes at the
target treatment area in the tissue and deliver a plurality of
electrical pulses to the treatment area based on the final set of
irreversible electroporation parameters.
[0150] Thus, one embodiment of the method may comprise one or more
of: 1. identifying a target treatment area in a tissue of a
patient; 2. selecting and inputting one or more parameters for
designing an irreversible electroporation treatment protocol for
the target treatment area; 3. selecting a temperature value to
graphically display a temperature contour in a simulation of the
target treatment area; 4. correlating the temperature contour with
imaging from the treatment area; 5. Identifying structures within
or surrounding the target treatment area such as nerves and blood
vessels that may be subject to thermal damage based on the
temperature contour; 6. modifying the irreversible electroporation
parameters through one or more iterations so that the temperature
contour no longer indicates that critical structures may be subject
to overheating; 7. selecting a final set of irreversible
electroporation parameters to be used for treatment; and 8.
implanting a pair of electrodes at the target treatment area in the
tissue and delivering a plurality of electrical pulses to the
treatment area based on the final set of irreversible
electroporation parameters.
[0151] The target treatment area may be imaged through a variety of
imaging modalities including Computed Tomography (CT), Magnetic
Resonance Imaging (MRI), Ultrasound, Positron Emission Tomography
(PET), and the like. The imaging devices may be operably connected
with the display device 11 so that results of the imaging may
overlap or otherwise be available for comparison with the graphical
display of the temperature and electric field contours.
[0152] In another embodiment, the invention provides a method of
treating a tissue with a medical treatment device that applies
electrical treatment energy through one or more or a plurality of
electrodes defining a target treatment area of the tissue, which
medical treatment device comprises a display device. The method may
comprise providing one or more parameters of a treatment protocol
for delivering one or more electrical pulses to a tissue through
one or a plurality of electrodes, and one or more conductivity
parameters specific for the tissue to be treated, estimating the
target ablation zone and displaying a graphical representation of
the estimation in the display device based on the one or more
parameters of the treatment protocol and the one or more
conductivity parameters, modifying one or more of the parameters of
the treatment protocol based on the graphical representation of the
target ablation zone, and implanting one or a plurality of
electrodes in the tissue and delivering one or more electrical
pulses to the tissue through the electrodes based on the one or
more modified parameters. In the context of this specification,
when referring to implanting an electrode, one or more of the
electrode(s) can alternatively or in addition be placed near, or
contact, or otherwise be operably disposed in a manner to
administer electrical energy to the tissue.
[0153] In an exemplary implementation of the method, a treating
physician identifies a target treatment area in a tissue of a
patient. For example, the target treatment area may be a tumor that
is unresectable by conventional surgical methods. The treating
physician then uses input devices 12, 14 such as a keyboard or
mouse to interact with the treatment planning module 54 to select
and input one or more parameters for designing an irreversible
electroporation treatment protocol for ablating the tumor. The
treatment planning module 54 then graphically displays an ablation
zone on the display device 11 based on the one or more parameters
of the irreversible electroporation treatment protocol. The
treating physician then selects one or more conductivity parameters
based on the type of tissue to be treated. The one or more
conductivity parameters may be tissue-specific values based on
experimental data that is stored in a database in memory 44 or may
be obtained by the physician and entered into the treatment
planning module 54 using the keyboard or other input, such as a
hands-free input. In embodiments, tissue-specific conductivity
values may be provided for heart, kidney, liver, lung, spleen,
pancreas, brain, prostrate, breast, small intestine, large
intestine, and stomach.
[0154] The one or more conductivity parameters may include the
baseline conductivity, change in conductivity, the transition zone
(how rapidly the conductivity increases), the electric field at
which the change in conductivity occurs, and the electric field at
which irreversible electroporation occurs. After selecting the one
or more conductivity parameters, the treatment planning module 54
may display a modified ablation zone on the display device 11 based
on the tissue-specific conductivity characteristics inputted by the
physician. The treating physician then may alter the one or more
parameters of the irreversible electroporation protocol to modify
the target ablation zone on the display device 11 to fit a desired
area of treatment. The treating physician may then strategically
place (e.g., implant) a pair of electrodes at the target treatment
area in the tissue and deliver a plurality of electrical pulses to
the treatment area based on the final set of irreversible
electroporation parameters.
[0155] Thus, one embodiment of the method may comprise one or more
of: 1. identifying a target treatment area in a tissue of a
patient; 2. selecting and inputting one or more parameters for
designing an irreversible electroporation treatment protocol for
the target treatment area; 3. displaying a graphical representation
of a target ablation zone on a display device; 4. selecting and
inputting one or more conductivity characteristics based on the
specific tissue to be treated; 5. displaying a modified graphical
representation of the target ablation zone based on the
tissue-specific conductivity characteristics; 6. modifying the one
or more parameters of the irreversible electroporation protocol to
fit a desired area of treatment; and 7. disposing/implanting a pair
of electrodes at the target treatment area in the tissue and
delivering a plurality of electrical pulses to the treatment area
based on the modified IRE parameters.
[0156] As will be apparent to a skilled artisan, the systems and
methods described above may be compatible with a variety of
bi-polar and mono-polar probe combinations and configurations.
Additionally, the calculations may be extended to not only display
an electric field and temperature but also using that information
to calculate an electrical damage and thermal damage component
which take into account the time of exposure to the electric field
and temperatures and can be tissue-specific such as for liver,
kidney, etc. The systems and methods may be capable of displaying
information such as "electric damage" or "thermal damage" once the
electric field and temperature contours are determined, based on
predetermined values for electric damage and thermal damage in the
given tissue type. "Electric damage" and "thermal damage" regions
can be visualized in place of or in combination with electric field
and temperature as isocontour lines, shaded or highlighted areas,
or other forms of graphical representation. In addition, the
inclusion of tissue-specific in-vivo derived data including blood
flow, metabolic heat generation, and one or more conductivity
parameters such as tissue conductivity and ratios of changing
conductivity can be included to reflect dynamic changes within a
specific tissue type.
[0157] Additional details of the algorithms and numerical models
disclosed herein will be provided in the following Examples, which
are intended to further illustrate rather than limit the
invention.
[0158] In Example 1, the present inventors provide a numerical
model that uses an asymmetrical Gompertz function to describe the
response of porcine renal tissue to electroporation pulses.
However, other functions could be used to represent the electrical
response of tissue under exposure to pulsed electric fields such as
a sigmoid function, ramp, and/or interpolation table. This model
can be used to determine baseline conductivity of tissue based on
any combination of electrode exposure length, separation distance,
and non-electroporating electric pulses. In addition, the model can
be scaled to the baseline conductivity and used to determine the
maximum electric conductivity after the electroporation-based
treatment. By determining the ratio of conductivities pre- and
post-treatment, it is possible to predict the shape of the electric
field distribution and thus the treatment volume based on
electrical measurements. An advantage of this numerical model is
that it is easy to implement in computer software code in the
system of the invention and no additional electronics or numerical
simulations are needed to determine the electric conductivities.
The system and method of the invention can also be adapted for
other electrode geometries (sharp electrodes, bipolar probes),
electrode diameter, and other tissues/tumors once their response to
different electric fields has been fully characterized.
[0159] The present inventors provide further details of this
numerical modeling as well as experiments that confirm this
numerical modeling in Example 2. In developing this work, the
present inventors were motivated to develop an IRE treatment
planning method and system that accounts for real-time
voltage/current measurements. As a result of this work, the system
and method of the invention requires no electronics or electrodes
in addition to the NANOKNIFE.RTM. System, a commercial embodiment
of a system for electroporation-based therapies. The work shown in
Example 2 is based on parametric study using blunt tip electrodes,
but can be customized to any other geometry (sharp, plate,
bipolar). The numerical modeling in Example 2 provides the ability
to determine a baseline tissue conductivity based on a low voltage
pre-IRE pulse (non-electroporating .about.50 V/cm), as well as the
maximum tissue conductivity based on high voltage IRE pulses
(during electroporation) and low voltage post-IRE pulse
(non-electroporating .about.50 V/cm). Two numerical models were
developed that examined 720 or 1440 parameter combinations. Results
on IRE lesion were based on in vitro measurements. A major finding
of the modeling in Example 2 is that the electric field
distribution depends on conductivity ratio pre- and post-IRE.
Experimental and clinical IRE studies may be used to determine this
ratio. As a result, one can determine e-field thresholds for tissue
and tumor based on measurements. The 3-D model of Example 2
captures depth, width, and height e-field distributions.
[0160] In Example 3, as a further extension of the inventors work,
the inventors show prediction of IRE treatment volume based on 1000
V/cm, 750 v/cm, and 500 V/cm IRE thresholds as well as other
factors as a representative case of the numerical modeling of the
invention.
[0161] In Example 4, the inventors describe features of the
Specific Conductivity and procedures for implementing it in the
invention.
[0162] In Example 5, the inventors describe in vivo experiments as
a reduction to practice of the invention.
[0163] In Example 6, the inventors describe how to use the ratio of
maximum conductivity to baseline conductivity in modifying the
electric field distribution and thus the Cassini oval equation.
[0164] In Example 7, the inventors describe the Cassini oval
equation and its implementation in the invention.
[0165] In Example 8, the inventors describe mapping of electric
field and thermal contours using a simplified data
cross-referencing approach.
[0166] In Example 9, the inventors describe visualization of
electric field distributions using different configurations of
bipolar probes.
[0167] In Example 10, the inventors describe a method for
determining the IRE threshold for different tissues according to
one or more conductivity parameters.
[0168] In Example 11, the inventors describe correlating
experimental and numerical IRE lesions using the bipolar probe.
EXAMPLES
Example 1
[0169] Materials And Methods
[0170] The tissue was modeled as a 10-cm diameter spherical domain
using a finite element package (Comsol 4.2a, Stockholm, Sweden).
Electrodes were modeled as two 1.0-mm diameter blunt tip needles
with exposure lengths (Y) and edge-to-edge separation distances (X)
given in Table 1. The electrode domains were subtracted from the
tissue domain, effectively modeling the electrodes as boundary
conditions.
TABLE-US-00001 TABLE 1 Electrode configuration and relevant
electroporation-based treatment values used in study. PARAMETER
VALUES MEAN W [V/cm] 500, 1000, 1500, 2000, 1750 2500, 3000 X [cm]
0.5, 1.0, 1.5, 2.0, 2.5 1.5 Y [cm] 0.5, 1.0, 1.5, 2.0, 2.5, 3.0
1.75 Z [cm] 1.0, 1.25, 1.5, 2.0, 3.0, 4.0, 2.96875 5.0, 6.0
[0171] The electric field distribution associated with the applied
pulse is given by solving the Laplace equation:
.gradient.(.sigma.(|E|).gradient..phi.)=0 (1)
[0172] where .sigma. is the electrical conductivity of the tissue,
E is the electric field in V/cm, and .phi. is the electrical
potential (Edd and Davalos, 2007). Boundaries along the tissue in
contact with the energized electrode were defined as .phi.=V.sub.o,
and boundaries at the interface of the other electrode were set to
ground. The applied voltages were manipulated to ensure that the
voltage-to-distance ratios (W) corresponded to those in Table 1.
The remaining boundaries were treated as electrically insulating,
.differential..phi./.differential.n=0.
[0173] The analyzed domain extends far enough from the area of
interest (i.e. the area near the electrodes) that the electrically
insulating boundaries at the edges of the domain do not
significantly influence the results in the treatment zone. The
physics-controlled finer mesh with .about.100,000 elements was
used. The numerical models have been adapted to account for a
dynamic tissue conductivity that occurs as a result of
electroporation, which is described by an asymmetrical Gompertz
curve for renal porcine tissue (Neal et al., 2012):
.sigma.(|E|)=.sigma..sub.o+(.sigma..sub.max-.sigma..sub.o)exp[-Aexp[-BE]
(2)
[0174] where .sigma..sub.o is the non-electroporated tissue
conductivity and .sigma..sub.max is the maximum conductivity for
thoroughly permeabilized cells, A and B are coefficients for the
displacement and growth rate of the curve, respectively. Here, it
is assumed that .sigma..sub.o=0.1 S/m but this value can be scaled
by a factor to match any other non-electroporated tissue
conductivity or material as determined by a pre-treatment pulse. In
this work the effect of the ratio of maximum conductivity to
baseline conductivity in the resulting electric current was
examined using the 50-.mu.s pulse parameters (A=3.05271; B=0.00233)
reported by Neal et al. (Neal et. al., 2012). The asymmetrical
Gompertz function showing the tissue electric conductivity as a
function of electric field is, for example, shown in FIG. 5.
[0175] The current density was integrated over the surface of the
ground electrode to determine the total current delivered. A
regression analysis on the resulting current was performed to
determine the effect of the parameters investigated and their
interactions using the NonlinearModelFit function in Wolfram
Mathematica 8.0. Current data from the numerical simulations were
fit to a mathematical expression that accounted for all possible
interactions between the parameters:
I=factor[aW+bX+cY+dZ+e(W-W)(X-X)+f(W-W)(Y-Y)+g(W-W)(Z-Z)+h(X-X)(Y-Y)+i(X-
-X)(Z-Z)+j(Y-Y)(Z-Z)+k(W-W)(X-X)(Y-Y)+l(X-X)(Y-Y)(Z-Z)+m(W-W)(Y-Y)(Z-Z)+n(-
W-W)(X-X)(Z-Z)+o(W-W)(X-X)(Y-Y)(Z-Z)+p] (3)
[0176] where I is the current in amps, W is the voltage-to-distance
ratio [V/cm], X is the edge-to-edge distance [cm], Y is the
exposure length [cm], and Z is the unitless ratio
.sigma..sub.max/.sigma..sub.o. The W, X, Y, and Z are means for
each of their corresponding parameters (Table 1) and the
coefficients (a, b, c, . . . , n, o, p) were determined from the
regression analysis (Table 2).
[0177] Results.
[0178] A method to determine electric conductivity change following
treatment based on current measurements and electrode configuration
is provided. The best-fit statistical (numerical) model between the
W, X, Y, and Z parameters resulted in Eqn. 3 with the coefficients
in Table 2 (R.sup.2=0.999646). Every coefficient and their
interactions had statistical significant effects on the resulting
current (P<0.0001). With this equation one can predict the
current for any combination of the W, Y, X, Z parameters studied
within their ranges (500 V/cm.ltoreq.W.ltoreq.3000 V/cm, 0.5
cm.ltoreq.X.ltoreq.2.5 cm, 0.5 cm.ltoreq.Y.ltoreq.3.0 cm, and
1.0.ltoreq.Z.ltoreq.6.0). Additionally, by using the linear results
(Z=1), the baseline tissue conductivity can be extrapolated for any
blunt-tip electrode configuration by delivering and measuring the
current of a non-electroporating pre-treatment pulse. The
techniques described in this specification could also be used to
determine the conductivity of other materials, such as
non-biological materials, or phantoms.
TABLE-US-00002 TABLE 2 Coefficients (P < 0.0001*) from the Least
Square analysis using the NonlinearModelFit function in
Mathematica. ESTIMATE a .fwdarw. 0.00820 b .fwdarw. 7.18533 c
.fwdarw. 5.80997 d .fwdarw. 3.73939 e .fwdarw. 0.00459 f .fwdarw.
0.00390 g .fwdarw. 0.00271 h .fwdarw. 3.05537 i .fwdarw. 2.18763 j
.fwdarw. 1.73269 k .fwdarw. 0.00201 l .fwdarw. 0.92272 m .fwdarw.
0.00129 n .fwdarw. 0.00152 o .fwdarw. 0.00067 p .fwdarw.
-33.92640
[0179] FIG. 6 shows a representative case in which the effect of
the W and Z are studied for electroporation-based therapies with
2.0 cm electrodes separated by 1.5 cm. The 3D plot corroborates the
quality of the model which shows every data point from the
numerical simulation (green spheres) being intersected by the
best-fit statistical (numerical) model. This 3D plot also shows
that when Z is kept constant, the current increases linearly with
the voltage-to-distance ratio (W). Similarly, the current increases
linearly with Z when the voltage-to-distance ratio is constant.
However, for all the other scenarios there is a non-linear response
in the current that becomes more drastic with simultaneous
increases in W and Z.
[0180] In order to fully understand the predictive capability of
the statistical (numerical) model, two cases in which the current
is presented as a function of the exposure length and electrode
separation are provided. FIG. 7A shows the linear case (Z=1) in
which the current can be scaled to predict any other combination of
pulse parameters as long as the pulses do not achieve
electroporation. For example, one can deliver a non-electroporation
pulse (.about.50 V/cm) and measure current. The current can then be
scaled to match one of the W values investigated in this study. By
using Eqn. 3 and solving for the factor, the baseline electric
conductivity of the tissue can be determined and used for treatment
planning. FIG. 7B is the case in which the maximum electric
conductivity was 0.4 S/m (Z=4) after electroporation. The trends
are similar to the ones described in FIG. 5 in that if exposure
length is constant, the current increases linearly with increasing
electrode separation and vice versa. However, even though the
conductivity within the treated region increases by a factor of 4,
the current increases non-linearly only by a factor of 3. This can
be seen by comparing the contours in FIG. 7A with those in FIG. 7B
which consistently show that the curves are increased by a factor
of 3.
Example 2. Determining the Relationship Between Blunt Tip Electrode
Configuration and Resulting Current after IRE Treatment
[0181] Model Assumptions:
[0182] Gompertz Conductivity: Pulse duration=50 .mu.s, Ex-vivo
kidney tissue
[0183] Baseline Conductivity: .sigma.=0.1 S/m
[0184] Spherical Domain: diameter=10 cm
[0185] Applied Voltage: Voltage=1000 V
[0186] Parametric Study:
[0187] Total Combinations: 720 models
[0188] Maximum Conductivity: 1.0.times., 1.25.times., 1.5.times.,
2.times., 3.times., 4.times., 5.times., 6.times. the baseline
[0189] Edge-to-edge Distance: 5, 10, 15, 20, 25 mm
[0190] Electrode Exposure: 5, 10, 15, 20, 25, 30 mm
[0191] Electrode Radius: 0.5, 0.75, 1.0 mm
[0192] The output of statistical analysis software (JMP 9.0) used
to fit model and determine the coefficients for all parameter
combinations is shown in the tables of FIGS. 8A and 8B and the plot
of FIG. 8C.
[0193] Parameters of Best Fit for Dynamic Conductivity Changes
Between 1.times.-6.times. the Baseline Conductivity
(R.sup.2=0.96):
[0194] a=-1.428057; (*Intercept Estimate*)
[0195] b=-0.168944; (*Gap Estimate*)
[0196] c=2.1250608; (*Radius Estimate*)
[0197] d=0.2101464; (*Exposure Estimate*)
[0198] e=1.1114726; (*Factor Estimate*)
[0199] f=-0.115352; (*Gap-Radius Estimate*)
[0200] g=-0.010131; (*Gap-Exposure Estimate*)
[0201] h=-0.067208; (*Gap-Factor*)
[0202] i=0.0822932; (*Radius-Exposure Estimate*)
[0203] j=0.4364513; (*Radius-Factor Estimate*)
[0204] k=0.0493234; (*Exposure-Factor Estimate*)
[0205] l=-0.006104; (*Gap-Radius-Exposure Estimate*)
[0206] m=0.0165237; (*Radius-Exposure-Factor Estimate*)*)
[0207] n=-0.003861; (*Gap-Exposure-Factor Estimate*)
[0208] o=-0.041303; (*Gap-Radius-Factor Estimate*)
[0209] p=-0.002042; (*Gap-Radius-Exposure-Factor Estimate*)
[0210] Analytical Function for Dynamic Conductivity Changes Between
1.times.-6.times. the Baseline Conductivity (R.sup.2=0.96):
[0211] 5 mm<gap=x<25 mm, 0.5 mm<radius=y<1.0 mm,
[0212] 5 mm<exposure=z<30 mm, 1<factor=w<6
[0213] Default conductivity of 0.1 S/m and 1000 V which can be
scaled for dynamic conductivities. The function is a linear
combination of all iterations examined in the parametric study:
Current(w,x,y,z)=a+bx+cy+dz+ew+f(x+bb)(y+cc)+g(x+bb)(z+dd)+h(x+bb)(w+e
e)+i(y+cc)(z+dd)+j(y+cc)(w+ee)+k(z+dd)(w+ee)+l(x+bb)(y+cc)+m(y+cc)(z+dd)(-
w+ee)+n(x+bb)(z+dd)(w+ee)+o(x+bb)(y+cc)(w+ee)+p(x+bb)(y+cc)(z+dd)(w+ee)
[0214] FIGS. 9A-9E show the representative (15 mm gap) correlation
between current vs. exposure length and electrode radius for
maximum conductivities (1.times.-6.times., respectively).
[0215] FIGS. 10A and 10B are tables showing experimental validation
of the code for determining the tissue/potato dynamic conductivity
from in vitro measurements.
[0216] Determining the Relationship Between Blunt Tip Electrode
Configuration and e-Field Distribution after IRE Treatment
[0217] Model Assumptions:
[0218] Gompertz Conductivity: Pulse duration=50 .mu.s, Ex-vivo
kidney tissue
[0219] Baseline Conductivity: .sigma.=0.1 S/m
[0220] Spherical Domain: diameter=10 cm
[0221] Electrode Radius: r=0.5 mm
[0222] Parametric Study:
[0223] Total Combinations: 1440 models
[0224] Maximum Conductivity: 1.0.times., 1.25.times., 1.5.times.,
2.times., 3.times., 4.times., 5.times., 6.times. the baseline
[0225] Edge-to-edge Distance: 5, 10, 15, 20, 25 mm
[0226] Electrode Exposure: 5, 10, 15, 20, 25, 30 mm
[0227] Voltage-to-distance Ratio: 500, 1000, 1500, 2000, 2500, 3000
V/cm
Example 3
[0228] Comparison of analytical solutions with statistical
(numerical) model to calculate current and explanation of procedure
that results in 3D IRE volume.
[0229] The process of backing-out the electrical conductivity using
the analytical solutions and the one proposed in the "Towards a
Predictive Model of Electroporation-Based Therapies using Pre-Pulse
Electrical Measurements" abstract presented in the IEEE Engineering
in Medicine and Biology Conference in Aug. 28, 2012 in San Diego,
Calif. were compared. A method to determine the predictive power of
the equations to calculate current is analyzing the residuals of
the 1440 combinations of parameters examined. In the context of
this specification, a residual is the difference between the
predicted current and the actual current. As can be seen in FIGS.
11A and 11B with increasing non-linear change in conductivity due
to electroporation and increasing applied electric field there is
an increase in the residual for both cases. The main message though
is that using the shape factor (analytical) method the maximum
residual is 11.3502 A and with the statistical (numerical) model
the maximum is 1.55583 A. This analysis suggests that the shape
factor method may be inadequate to predict the non-linear changes
in current that occur during electroporation and for reliable
predictions the statistical (numerical) method may be better.
[0230] In terms of the prediction of the volume treated a
representative method is to map out the electric field 5 cm in the
directions along the (x,0,0), (0,y,0), and (0,0,z) axes from the
origin. In addition, the electric field can be extracted along a
line that starts at the origin and ends at 3 cm along each of the
axes. These plots contain the information for determining the
distances at which a particular IRE threshold occurs. In
embodiments, 1440 different parameter combinations were simulated
that resulted in data sets of 28,692 (x-direction), 20,538
(y-direction), 27,306 (z-direction), and 25,116 (xyz-direction) for
homogeneous conductivity. Even though these simulations only
include dynamic conductivity changes due to electroporation, it is
believed that an identical analysis for simulations that also
include the changes in conductivity due to temperature could also
be performed. In this manner, it would be possible to determine
irreversible electroporation thresholds as a function of
temperature and electroporation. Manipulating these large data sets
is challenging but it provides all the necessary information to
study the effect of electrode separation, electrode length, dynamic
conductivity factor, and voltage-to-distance ratio for any position
along the described paths. In order to be able to manipulate the
data and extract the distance for different IRE thresholds, the
function NonlinearModelFit (Mathematica) was used in order to come
up with analytical expressions that would closely match the
electric field. A different function was used for each of the
directions studied in the positive directions along the Cartesian
coordinate system. The Micheilis Menten function was used along the
x-direction (R.sup.2=0.978978), the analytical solution to the
Laplace equation along the y-direction (R.sup.2=0.993262), and the
Logistic equation in the z-direction (R.sup.2=0.983204). Each of
those functions was scaled by a 3rd order polynomial function that
enabled the fit to incorporate the electrode separation and
electrode exposure as well. Even though the described functions
were used to fit the data from the numerical data, there might be
other functions that are also appropriate and this will be explored
further in order to use the most reliable fit. In FIGS. 12A-12C
provided are representative contour plots of the electric field
strength at 1.0 cm from the origin using an edge-to-edge
voltage-to-distance ratio of 1500 V/cm assuming a z=1 which is the
case for non-electroporated electrical conductivity. It is
important to note that in this case the y and z data are starting
from (0, 0, 0) and the x-data starts outside the external
electrode-tissue boundary. One representative case is presented,
but any of the 1440 parameters combinations that were disclosed in
the conference proceeding could be plotted as well.
[0231] The following functions describe the electric field [V/cm]
distributions along the x-axis (E.sub.x), y-axis (E.sub.y), and
z-axis (E.sub.7) as a function of voltage-to-distance (W),
edge-to-edge separation between the electrodes (X), exposure length
(Y), maximum conductivity to baseline conductivity (Z), and
distance in the x-direction (xx), y-direction (yy), and z-direction
(zz).
[0232] Micheilis Menten Equation (Electric Field in the
x-Direction)
E.sub.x(W,X,Y,Z,xx)=W*(a*Exp[-bxx]+c)*(dX.sup.3+eX.sup.2fX+gY.sup.3hY.su-
p.2+iY+j)+k
[0233] The coefficients for the NonlinearModelFit are given
below:
[0234] a=-0.447392, b=8.98279, c=-0.0156167, d=-0.0654974,
e=0.468234, f=-6.17716, g=0.326307, h=-2.33953, I=5.90586,
j=-4.83018, k-9.44083
[0235] Laplace Equation (Electric Field in the y-Direction)
E y .function. ( W , X , Y , Z , yy ) = a + ( X 3 + x 2 + bX + cY 3
+ dY 2 + eY + f ) * ( h + ( gWXZ ) 2 * ( 1 Log .function. [ X + 0.1
0.05 ] ) * ) * Abs [ 1 yy - X 2 - 0.05 - 1 yy + X 2 + 0.05 ] )
##EQU00005##
[0236] The coefficients for the NonlinearModelFit are given
below:
[0237] a=-56.6597, b=-42.9322, c=6.66389, d=-50.8391, e=141.263,
f=138.934, g=0.00417123, h=0.184109
[0238] Logistic Equation (Electric Field in the z-Direction)
E z .function. ( W , X , Y , Z , zz ) = a + bWZ 1 + c Exp
.function. [ d ( 2 .times. zz y - e ) ] ( fX 3 + gX 2 + hX + i ) (
jY 3 + kY 2 + lY + m ) ##EQU00006##
[0239] The coefficients for the NonlinearModelFit are given
below:
[0240] a=49.0995, b=-0.00309563, c=1.39341, d=4.02546, e=1.24714,
f=0.276404, g=-1.84076, h=4.93473, I=-9.13219, j=0.699588,
k=-5.0242, I=12.8624, m=19.9113.
[0241] In order to visualize the predicted IRE shape the equation
of an ellipsoid was used and the semi-axes were forced to intersect
with the locations at which the IRE threshold wants to be examined.
Therefore, the provided functions can be adjusted in real-time to
display the IRE volume for any electric field threshold. This is
important since different tissues have different IRE thresholds
that depend on the temperature, dielectric properties of the
tissue, the electrode configuration, and the pulse parameters used.
Once again, even though the equation for an ellipsoid is used to
represent the IRE volume, other functions may be evaluated that may
also be appropriate to replicate the morphology of the zones of
ablation being achieved experimentally such as the Cassini curve. A
1500 V/cm was used as the voltage-to-distance ratio, electrode
exposure 2 cm, and electrode separation 1.5 cm to generate 3
different IRE zones using 1000 V/cm, 750 V/cm, and 500 V/cm as the
IRE thresholds with z=1.
[0242] From the 3D plots representing the zones of ablation shown
in FIGS. 13A-13C it can be seen that if the IRE threshold is
reduced from 1000 V/cm to either 750 V/cm or 500 V/cm, the volume
becomes larger. This is representative of how different tissues may
have different thresholds and this code may provide the ability to
simulate the fields in a broad/generic manner that can then be
applied to any tissue. Incorporating the xyz-data that was
extracted from the parametric study will help modify the
"roundness" of the current depictions of the zone of IRE ablation
in order to more realistically replicate the experimental results.
However, to the best of the inventors' knowledge there is no such
adaptable code currently available to provide a 3D IRE volume as a
function of measured current, electrode length, electrode exposure,
applied voltage-to-distance ratio, and customizable electric field
threshold so it is believed that this will greatly help the medical
community in planning and verifying the clinical treatments of
patients being treated with the IRE technology.
Example 4
[0243] Specific Conductivity
[0244] Specific conductivity can be important in embodiments for
treatment planning of irreversible electroporation (IRE). For many
applications, especially when treating tumors in the brain, the
volume (area) of IRE should be predicted to maximize the ablation
of the tumorous tissue while minimizing the damage to surrounding
healthy tissue. The specific electrical conductivity of tissue
during an irreversible electroporation (IRE) procedure allows the
physicians to: determine the current threshold; minimize the
electric current dose; decrease the Joule heating; and reduce
damage to surrounding healthy tissue. To measure the specific
conductivity of tissue prior to an IRE procedure the physician
typically performs one or more of the following: establishes the
electrode geometry (shape factor); determines the physical
dimensions of the tissue; applies a small excitation AC voltage
signal (1 to 10 mV); measures the AC current response; calculates
the specific conductivity (.sigma.) using results from the prior
steps. This procedure tends to not generate tissue damage (low
amplitude AC signals) and will supply the physician (software) with
the required information to optimize IRE treatment planning,
especially in sensitive organs like the brain which is susceptible
to high electrical currents and temperatures. Thus, the IRE
procedure is well monitored and can also serve as a feedback system
in between series of pulses and even after the treatment to
evaluate the area of ablation.
[0245] Special Cases for electrode geometry
[0246] Nomenclature (units in brackets):
[0247] V.sub.e=voltage on the hot electrode (the highest voltage),
[V]
[0248] G=electroporation voltage gradient (required for
electroporation), [V/m]
[0249] R.sub.1=radius of electrode with highest voltage (inner
radius), [m]
[0250] R.sub.2=radius at which the outer electrodes are arranged
(outer radius), [m]
[0251] i=total current, [A]
[0252] L=length of cylindrical electrode, [m]
[0253] A=area of plate electrode, [m.sup.2]
[0254] .sigma.=electrical conductivity of tissue, [S/m]
[0255] .rho.=density
[0256] c=heat capacity
[0257] Case 1
[0258] Electrical conduction between a two-cylinder (needle)
arrangement of length L in an infinite medium (tissue). It is
important to note that this formulation is most accurate when
L>>R.sub.1,R.sub.2 and L>>w. The electrical
conductivity can be calculated from,
.sigma. = i S V e ##EQU00007##
[0259] where the shape factor (S) corresponding to the electrode
dimensions and configuration is given by,
2 .pi. L cosh - 1 .function. ( 4 w 2 - ( 2 R 1 ) 2 - ( 2 R 2 ) 2 8
R 1 R 2 ) ##EQU00008##
[0260] Case 2
[0261] Cylindrical arrangement in which the central electrode is a
cylinder (needle) with radius R.sub.1 and the outer electrodes are
arranged in a cylindrical shell with a shell radius of R.sub.2 (not
the radius of the electrodes). The voltage on the central electrode
is V.sub.e. The voltage distribution in the tissue may be
determined as a function of radius, r:
V = V e .times. ln .times. r R 2 ln .times. R 1 R 2
##EQU00009##
[0262] The required voltage on the central electrode to achieve
IRE:
V e = GR 2 .times. ln .times. R 2 R 1 ##EQU00010##
[0263] The required current on the central electrode:
i = 2 .times. .pi. .times. .times. L .times. .times. .sigma.
.times. .times. V e ln .times. R 2 R 1 ##EQU00011##
[0264] The specific conductivity (a) of the tissue can be
calculated since the voltage signal (V.sub.e) and the current
responses (i) are known.
[0265] Explanation of electrical concepts.
[0266] By using the bipolar electrode described previously in US
Patent Application Publication No. 2010/0030211 A1, one can apply a
small excitation AC voltage signal (for example from about 1 to 10
mV),
V(t)=V.sub.0 Sin(.omega.t)
[0267] where V(t) is the potential at time t, V.sub.0 is the
amplitude of the excitation signal and w is the frequency in
radians/s. The reason for using a small excitation signal is to get
a response that is pseudo-linear since in this manner the value for
the impedance can be determined indicating the ability of a system
(tissue) to resist the flow of electrical current. The measured AC
current (response) that is generated by the excitation signal is
described by
I(t)=I.sub.0 Sin(.omega.t+.theta.)
[0268] where I(t) is the response signal, I.sub.0 is the amplitude
of the response (I.sub.0.noteq.V.sub.0) and .theta. is the phase
shift of the signal. The impedance (Z) of the system (tissue) is
described by,
Z=(V(t))/(I(t))=(V.sub.0 Sin(.omega.t))/(I.sub.0
Sin(.omega.t+.theta.))=Z.sub.0(Sin(.omega.t))/(Sin(.omega.t+.theta.))
[0269] It is important to note that the measurement of the response
is at the same excitation frequency as the AC voltage signal to
prevent interfering signals that could compromise the results. The
magnitude of the impedance |Z.sub.0| is the electrical resistance
of the tissue. The electrical resistivity (.OMEGA. m) can be
determined from the resistance and the physical dimensions of the
tissue in addition to the electrode geometry (shape factor). The
reciprocal of the electrical resistivity is the electrical
conductivity (S/m). Therefore, after deriving the electrical
resistivity from the methods described above, the conductivity may
be determined.
[0270] As described in U.S. Patent Application No. 61/694,144 the
analytical solution (Table 4) assumes that the length of the
electrodes is much larger than the electrode radius or separation
distance between the electrodes. Additionally, the analytical
solution is not capable of capturing the non-linear electrical
response of the tissue during electroporation procedures. The
proposed statistical algorithm (Table 3) is preferably used in
order to capture the response in treatments that are being
conducted clinically and show how the analytical overestimates the
baseline and maximum current that uses the experimental data.
TABLE-US-00003 TABLE 3 Determination of conductivity using the
statistical model and in vivo data from pre-pulse and IRE pulses in
canine kidney tissue using identical electrode configuration that
the experimental one described below. Current Voltage Volt-2-Dist
Conductivity Z = [A] [V] [V/cm] [S/m]
.sigma..sub.max/.sigma..sub.min Pre-Pulse 0.258 48 53 0.365 --
IRE-Pulse 20.6 1758 1953 1.037 2.841 IRE-Pulse 23.7 1758 1953 1.212
3.320 IRE-Pulse 23.6 1758 1953 1.207 3.305 Avg. IRE 22.6 1758 1953
1.150 3.150 IRE-Pulse 10.4 1259 1399 0.727 1.990 IRE-Pulse 11.1
1257 1397 0.789 2.162 IRE-Pulse 11 1257 1397 0.781 2.138 Avg. IRE
10.8 1257 1397 0.763 2.090 Pre-Pulse 0.343 73.3 52 0.341 --
IRE-Pulse 23.6 2262 1616 1.007 2.952 IRE-Pulse 24.3 2262 1616 1.041
3.051 IRE-Pulse 25.4 2262 1616 1.094 3.207 Avg. IRE 24.5 2262 1616
1.050 3.080
TABLE-US-00004 TABLE 4 Determination of conductivity using the
analytical model and in vivo data from pre-pulse and IRE pulses in
canine kidney tissue using identical electrode configuration than
the experimental one described below. Assumption: Length >>
radius, Length >> width, 2 cylindrical electrodes in an
infinite medium. Current Voltage Volt-2-Dist Shape Factor
Conductivity [A] [V] [V/cm] [m] [S/m] Pre-Pulse 0.258 48 53 0.01050
0.512 IRE-Pulse 20.6 1758 1953 0.01050 1.116 IRE-Pulse 23.7 1758
1953 0.01050 1.284 IRE-Pulse 23.6 1758 1953 0.01050 1.279 Avg. IRE
22.6 1758 1953 0.01050 1.225 IRE-Pulse 10.4 1259 1399 0.01050 0.787
IRE-Pulse 11.1 1257 1397 0.01050 0.841 IRE-Pulse 11 1257 1397
0.01050 0.834 Avg. IRE 10.8 1257 1397 0.01050 0.819 Pre-Pulse 0.343
73.3 52 0.00924 0.506 IRE-Pulse 23.6 2262 1616 0.00924 1.129
IRE-Pulse 24.3 2262 1616 0.00924 1.163 IRE-Pulse 25.4 2262 1616
0.00924 1.215 Avg. IRE 24.5 2262 1616 0.00924 1.172
Example 5
[0271] In Vivo Experiments
[0272] 1) Animals.
[0273] IRE ablations were performed in canine kidneys in a
procedure approved by the local animal ethics committee. Male
canines weighing approximately 30 kg were premedicated with
acetylpromazine (0.1 mg/kg), atropine (0.05 mg/kg), and morphine
(0.2 mg/kg) prior to general anesthesia induced with propofol (6
mg/kg, then 0.5 mg/kg/min) and maintained with inhaled isofluorane
(1-2%). Anesthetic depth was monitored by bispectral index
monitoring (Covidien, Dublin, Ireland) of EEG brain activity. After
ensuring adequate anesthesia, a midline incision was made and
mesenchymal tissue was maneuvered to access the kidney. Pancuronium
was delivered intravenously to mitigate electrically mediated
muscle contraction, with an initial dose of 0.2 mg/kg, and adjusted
if contractions increased.
[0274] 2) Experimental Procedure.
[0275] Two modified 18 gauge needle electrodes (1.0 mm diameter and
1.0 cm in exposure) were inserted as pairs into the superior,
middle, or inferior lobe of the kidney, with lobes being randomly
selected. A BTX ECM830 pulse generator (Harvard Apparatus,
Cambridge, Mass.) was used to deliver an initial 100 .mu.s
pre-pulse of 50 V/cm voltage-to-distance ratio (center-to-center)
between the electrodes to get an initial current able to be used to
determine baseline conductivity. Electrical current was measured
with a Tektronix TCP305 electromagnetic induction current probe
connected to a TCPA300 amplifier (both Tektronix, Beaverton,
Oreg.). A Protek DSO-2090 USB computer-interface oscilloscope
provided current measurements on a laptop using the included
DSO-2090 software (both GS Instruments, Incheon, Korea). A
schematic of the experimental setup can be found in FIG. 14A.
Following the pre-pulse, a series of 100 pulses, each 100 us long,
at a rate of 1 pulse per second was delivered, reversing polarity
after 50 pulses. A five second pause was encountered after pulses
10 and 50 to save data. A schematic diagram showing dimension
labeling conventions is shown in FIG. 14B. Representative current
waveforms from a pre-pulse and experimental pulse can be found in
FIGS. 14C and 14D, respectively. Electrode exposure lengths were
set to 1 cm for all trials. The separation distance between
electrodes and applied voltage may be found in Table 5. After
completing pulse delivery, the electrodes were removed. Two
additional ablations were performed in the remaining lobes before
repeating the procedure on the contralateral kidney, resulting in a
total of three ablations per kidney and six per canine.
TABLE-US-00005 TABLE 5 KIDNEY EXPERIMENT PROTOCOLS IN CANINE
SUBJECTS Voltage- Separation, Distance Setup cm Voltage, V Ratio,
V/cm n 1 1 1250 1250 4 2 1 1750 1750 4 3 1.5 2250 1500 6
[0276] 3) Kidney Segmentation and 3D Reconstruction.
[0277] Numerical models provide an advantageous platform for
predicting electroporation treatment effects by simulating electric
field, electrical conductivity, and temperature distributions. By
understanding the electric field distribution, one can apply an
effective lethal electric field threshold for IRE, E.sub.IRE, to
predict ablation lesion dimensions under varying pulse protocols
(electrode arrangements and applied voltages). However, in order to
do so, these models should first be calibrated with experimental
data. Here, the numerical simulation algorithm developed from
porcine kidneys was expanded that accounts for conductivity changes
using an asymmetrical sigmoid function (R. E. Neal, 2nd, et al.,
"Experimental characterization and numerical modeling of tissue
electrical conductivity during pulsed electric fields for
irreversible electroporation treatment planning," IEEE Trans Biomed
Eng., vol. 59, pp. 1076-85. Epub 2012 Jan. 6, 2012 ("R. E. Neal,
2.sup.nd, et al., 2012")). The model is calibrated to the
experimental lesions to determine an effective electric field
threshold under the three experimental setups used. In addition,
static and linear conductivity functions are also correlated to the
lesion dimensions. The three functions are used to evaluate which
numerical technique will result in better accuracy in matching
lesion shapes and resulting current from actual IRE ablations in
mammalian tissue, particularly for kidney.
[0278] The imaging-based computational model domains were
constructed from a magnetic resonance imaging (MRI) scan of a
kidney from a canine subject of similar size to those in the study.
The scans were scaled by 1.21 times in all directions to better
match the experimental kidney dimensions while maintaining the
anatomical characteristics. Mimics 14.1 image analysis software
(Materialise, Leuven, BG) was used to segment the kidney geometry
from the surrounding tissues. The kidney was traced in each of the
two-dimensional (2D) MRI axial slices, which were then integrated
into a three-dimensional (3D) solid representation of the kidney
volume which was refined and exported to 3-matic version 6.1
(Materialise, Leuven, BG) to generate a volumetric mesh compatible
with Comsol Multiphysics finite element modeling software (Comsol
Multiphysics, v.4.2a, Stockholm, Sweden).
[0279] Electrodes were simulated as paired cylinders, each 1 cm
long and 1 mm in diameter, and separated by 1 or 1.5 cm to
represent the two experimental conditions. The pairs were inserted
into the 3D kidney mesh in two configurations, representing both
experimental approaches that used either the superior/inferior
(vertical) or middle (horizontal) lobe of the kidney, both with
tips 1.5 cm deep. The finite element model simulated the electric
field distribution in the kidney, which was used to determine cell
death EIRE by correlating the electric field values with the
average in vivo lesion height and width dimensions.
[0280] 4) Electric Field Distribution and Lethal E.sub.IRE
Determination.
[0281] The electric field distribution is determined according
to
-.gradient.(.sigma.(|E|).gradient..PHI.)=0 (1)
[0282] where .sigma. is the electrical conductivity of the tissue,
E is the electric field in V/cm, and .PHI. is the electrical
potential. Tissue-electrode boundaries for the cathode and anode
were defined as .PHI.=V.sub.o and ground, respectively. The
remaining boundaries were treated as electrically insulating,
d.PHI./dn=0, since the kidneys were isolated from the surrounding
mesenchymal tissue during the experimental procedures. The current
density was integrated over a mid-plane parallel to both electrodes
to determine simulated electric current.
[0283] The model was solved for the vertical and horizontal
electrode configurations, each considering three electrical
conductivity tissue responses. These responses included a
homogeneous static conductivity (.sigma..sub.0) as well as two that
accounted for electroporation based conductivity changes in tissue
that result from cell membrane permeabilization. The dynamic models
are based on a relationship between a minimum baseline and a
maximum conductivity. The static conductivity model was used to
determine the baseline conductivity, .sigma..sub.0, by matching
simulated electrical current with the pre-pulse experimental data,
where the field strength should be below that able to permeabilize
any cells in the tissue. The maximum conductivity, .sigma..sub.max,
occurs when the number of cells electroporated in the tissue has
saturated, and the cellular membranes no longer restrict the extent
of interstitial electrolyte mobility. The statistical model
discussed in (P. A. Garcia, et al., "Towards a predictive model of
electroporation-based therapies using pre-pulse electrical
measurements," Conf Proc IEEE Eng Med Biol Soc, vol. 2012, pp.
2575-8, 2012 ("P. A. Garcia, et al., 2012")) was used to predict
.sigma..sub.max from previously characterized tissue response to
pre-pulse .sigma..sub.0 and electrical data.
[0284] The .sigma..sub.0 and .sigma..sub.max values provide the
required parameters to define the electric field-dependent
conductivity, .sigma.(|E|), of renal tissue in vivo. One model
assumed a linear relationship that grew between the minimum and
maximum conductivities over a range from 200 to 2000 V/cm,
.sigma..sub.L|E|), and the second used an asymmetrical sigmoid
Gompertz curve, .sigma..sub.S(|E|), derived from the work described
in (R. E. Neal, 2nd, et al., 2012) using the equation:
.sigma..sub.s(|E|)=.sigma..sub.0+(.sigma..sub.max-.sigma..sub.0)exp[-Aex-
p(-BE)] (2)
[0285] where A and B are unitless coefficients that vary with pulse
length, t(s). This function was fit using curve parameters for a
100 .mu.s long pulse, where A=3.053 and B=0.00233 (R. E. Neal,
2.sup.nd, et al., 2012)
[0286] The electric field distribution along a width and height
projection based at the midpoint length of the electrodes was used
to determine the electric field magnitude that matched experimental
lesion dimensions. This was performed for all three conductivity
scenarios in all three experimental protocol setups in order to
determine which model best matched the IRE ablations, providing the
optimum conductivity modeling technique for mammalian tissue.
[0287] 5) Results: In Vivo Experiments.
[0288] Electrical Currents.
[0289] All animals survived the procedures without adverse event
until euthanasia. Electrical pre-pulse currents were 0.258.+-.0.036
A (mean.+-.SD) for the 1 cm electrode separation trials and
0.343.+-.0.050 A for the 1.5 cm separation trials. Electrical
currents from the trials for pulses 1-10, 40-50, and 90-100 are
reported in Table 6. Although currents are typically reported to
increase with consecutive pulses, there is no statistically
significant correlation between pulse number and measured current.
Therefore, all numerical calibrations to match electrical current
and determine .sigma..sub.max used the average current from all
captured pulses for each experimental setup.
TABLE-US-00006 TABLE 6 EXPERIMENTAL ELECTRIC CURRENTS TO CALIBRATE
NUMERICAL MODELS Separation, Average Delivered Pulse Average
Electric Setup cm Voltage, V Number Current, A* Pre 1 1 48 1750
0.258 (0.036) Pre 2 1.5 73 1250 0.343 (0.050) 1 1 1258 1-10 10.4
(1.7) 40-50 11.1 (1.1) 90-100 11.0 (1.7) 2 2 1758 1-10 20.6 (3.2)
40-50 23.7 (5.1) 90-100 23.6 (3.8) 3 1.5 2262 1-10 23.6 (1.47)
40-50 24.3 (3.25) 90-100 25.4 (3.27) *Currents given as "average
(standard deviation)"
[0290] 6) Determination of Dynamic Conductivity Function.
[0291] Pre-pulse electrical current was used to calculate the
baseline conductivity, .sigma..sub.0, used in the static numerical
simulation. In addition, the baseline and maximum, .sigma..sub.max,
electrical conductivities required for generating the asymmetrical
sigmoid and linear dynamic conductivity functions were calculated
according to the procedure outlined in (P. A. Garcia, et al., 2012)
and are provided in Table 7. The ratio between these conductivities
was calculated and demonstrates an increase in conductivity between
2.09 and 3.15 times, consistent with values determined in the
literature for other organs (N. Payselj, et al., "The course of
tissue permeabilization studied on a mathematical model of a
subcutaneous tumor in small animals," IEEE Trans Biomed Eng, vol.
52, pp. 1373-81, August 2005).
TABLE-US-00007 TABLE 7 BASELINE AND MAXIMUM ELECTRIC CONDUCTIVITIES
Gap, V/d Ratio, Setup cm V/cm .sigma..sub.0 .sigma..sub.max
.sigma..sub.max/.sigma..sub.0 1 1 1250 0.365 0.763 2.09 2 1 1750
0.365 1.150 3.15 3 1.5 1500 0.341 1.050 3.08
Example 6
[0292] How to Use the Ratio of Maximum Conductivity to Baseline
Conductivity in Modifying the Electric Field Distribution and Thus
the Cassini Oval Equation.
[0293] Irreversible electroporation (IRE) is a promising new method
for the focal ablation of undesirable tissue and tumors. The
minimally invasive procedure involves placing electrodes into the
region of interest and delivering a series of low energy electric
pulses to induce irrecoverable structural changes in cell
membranes, thus achieving tissue death. To achieve IRE, the
electric field in the region of interest needs to be above a
critical threshold, which is dependent on a variety of conditions
such as the physical properties of the tissue, electrode geometry
and pulse parameters. Additionally, the electric conductivity of
the tissue changes as a result of the pulses, redistributing the
electric field and thus the treatment area. The effect of a dynamic
conductivity around the electrodes where the highest electric
fields are generated was investigated in order to better predict
the IRE treatment for clinical use.
[0294] The electric field distribution associated with the electric
pulse is given by solving the governing Laplace equation,
.gradient.(.sigma..gradient..phi.)=0, where .sigma. is the tissue
electrical conductivity (baseline 0.2 S/m) and .phi. the electrical
potential (3000 V). The dynamic changes in electrical conductivity
due to electroporation were modeled with the flc2hs Heaviside
function within the finite element modeling software used in the
study (Comsol Multiphysics 3.5a, Stockholm, Sweden). The dynamic
conductivity factor ranged between 2.0-7.0 times the baseline value
in the regions exceeding 3000 V/cm. The total electrical current,
volumes, and lesion shapes from the IRE treatment were
evaluated.
[0295] FIGS. 15A and 15B display the electric field distributions
for the non-electroporated (baseline conductivity) and
electroporated (maximum/baseline conductivity) maps, respectively.
The electric field from using the baseline conductivity resulted in
a "peanut" shape distribution (FIG. 15A). By incorporating the
conductivity ratio between .sigma..sub.max/.sigma..sub.0, there is
a redistribution of the electric field and thus the volumes,
currents and lesion shapes are modified as well. The electric field
distribution for a 7.0.times. factor (FIG. 15B), shows a more
gradual dissipation of the electric field and a rounder predicted
IRE lesion.
[0296] A method to predict IRE lesions and incorporate the dynamic
changes in conductivity due to electroporation around the
electrodes is presented in this example. This procedure provides
additional tools to better approximate the electric field
distributions in tissue and thus help to generate more reliable IRE
treatment planning for clinical use using Finite Element Analysis
(FEA) models.
[0297] Specifically in order to adapt the Cassini Oval to match
experimental lesions or electric field distributions the following
procedure should be used:
[0298] In IRE treatments, the electric field distribution is the
primary factor for dictating defect formation and the resulting
volume of treated tissue (J. F. Edd and R. V. Davalos,
"Mathematical modeling of irreversible electroporation for
treatment planning," Technol Cancer Res Treat, vol. 6, pp. 275-286,
2007; D. Sel, et al., "Sequential finite element model of tissue
electropermeabilization," IEEE Trans Biomed Eng, vol. 52, pp.
816-27, May 2005; S. Mahnic-Kalamiza, et al., "Educational
application for visualization and analysis of electric field
strength in multiple electrode electroporation," BMC Med Educ, vol.
12, p. 102, 2012 ("S. Mahnic-Kalamiza, et al., 2012")). The
electric field is influenced by both the geometry and positioning
of the electrodes as well as the dielectric tissue properties.
Additionally, altered membrane permeability due to electroporation
influences the tissue conductivity in a non-linear manner.
Therefore numerical techniques are preferably used to account for
different electrode configurations and incorporate tissue-specific
functions relating the electrical conductivity to the electric
field distribution (i.e. extent of electroporation). The inventors
are currently using imaging-based computational models for IRE
treatment planning that use the physical properties of the tissue
and patient-specific 3D anatomical reconstructions to generate
electric field distributions (P. A. Garcia, et al., "Non-thermal
irreversible electroporation (N-TIRE) and adjuvant fractionated
radiotherapeutic multimodal therapy for intracranial malignant
glioma in a canine patient," Technol Cancer Res Treat, vol. 10, pp.
73-83, 2011 ("P. A. Garcia, et al, 2011")).
[0299] Oftentimes in clinical practice, there is need to rapidly
visualize the estimated zone of ablation without relying on complex
and time consuming numerical simulations. As an alternative,
analytical solutions are powerful techniques that provide valuable
insight and offer the ability to rapidly visualize electric field
distributions (S. Mahnic-Kalamiza, et al., 2012). However, these
analytical solutions assume infinitely long electrodes which are
not the case in clinical practice and do not incorporate the
non-linear changes in tissue conductivity due to electroporation.
Therefore, there is a need for simple, quick, and accurate methods
to provide physicians with predicted IRE zones of ablation during
surgery when one of the pulse parameters needs to be adjusted. To
this end, the inventors have adapted the Cassini curve in an effort
to provide researchers and physicians with a graphical
representation of IRE zones of ablation, for example, in in vivo
porcine liver. The goal of this work is to provide a correlation
between experimentally produced zones of ablations in in vivo
porcine liver tissue with the corresponding IRE pulse parameters
and electrode configuration. These Cassini curves are calibrated to
experimental IRE ablations, and incorporate the dynamic changes in
tissue conductivity, a limitation of the analytical approach.
[0300] The Cassini oval is a plane curve that derives its set of
values based on the distance of any given point, a, from the fixed
location of two foci, q.sub.1 and q.sub.2, located at (x.sub.1,
y.sub.1) and (x.sub.2, y.sub.2). The equation is similar to that of
an ellipse, except that it is based on the product of distances
from the foci, rather than the sum. This makes the equation for
such an oval
.left brkt-bot.(x.sub.1-a).sup.2+(y.sub.1-a).sup.2.right
brkt-bot..left brkt-bot.(x.sub.2-a).sup.2+(y.sub.2-a).sup.2.right
brkt-bot.=b.sup.4 (3)
[0301] where b.sup.4 is a scaling factor to determine the value at
any given point. For incorporation of this equation into shapes
that mimic the electric field distribution, it is assumed that the
two foci were equidistantly located on the x-axis at (.+-.x,0). The
flexibility of the Cassini curve is crucial since it allows for
fitting a wide range of shapes by adjusting the `a` and/or `b`
parameters from Equation 3 simultaneously and fitting them to the
experimental lesion dimensions or the locations at which a
particular electric field value results from the computational
simulations. The new approach in this analysis is that it is not
assumed that the parameter `a` is related to the separation
distance between the electrodes used in IRE treatments for example
but will be a second parameter to match the width/depth of any
distribution thus allowing for more flexibility between the shapes
achieved with the Cassini Oval as can be seen in FIGS. 16A and
16B.
[0302] The in vivo experimental data in porcine liver was provided
from published studies performed at the Applied Radiology
Laboratory of Hadassah Hebrew University Medical Center (P. A.
Garcia, et al., 2011). All experiments were performed with
Institutional Animal Care and Use Committee approval from the
Hebrew University Medical Center. The treatments were performed
with a two-needle electrode configuration, 1.5 cm center-to-center
separation, 2.0 cm electrode exposure, and an applied voltage of
2250 V. In this paper we only evaluate the effect of pulse number
and pulse duration on the resulting `a` and `b` parameters required
to fit the IRE zones of ablation with the Cassini curve. The
NonlinearModelFit function in Wolfram Mathematica 9 was used to
determine the `a` and `b` parameters (average.+-.standard
deviation) for each pulse parameter resulting in three curves for
each condition. This same technique can be used to fit the `a` and
`b` parameters to match the electric field shape at any particular
electric field value as well thus providing an avenue to capture
the shape for any IRE lesion independent of the tissue or
patient.
[0303] The NonlinearModelFit results for the `a` and `b` parameters
to generate the Cassini curves are provided in FIG. 17. The `a`
parameter ranged from 0.75-1.04 and the `b` from 1.06-1.35 for the
average IRE zones of ablation in the in vivo porcine liver. From
these data it can be seen that each pulse parameter used results in
a unique `a` and `b` combination except for the twenty 100-.mu.s
pulses and ninety 20-.mu.s pulses which overlap since they had
identical IRE ablations. Therefore, consideration should be given
to pulse length and total number of pulses when planning treatments
to ensure maximum accuracy when using Cassini curves to rapidly
predict treatment zones.
[0304] FIG. 18 provides a representation of the average IRE zone of
ablation and also includes the experimentally achieved standard
deviations. This Cassini curve is the most clinically relevant as
ninety 100-.mu.s pulses is the recommended setting by the
manufacturer that is currently being used by physicians to treat
several types of cancer. The Cassini curves in FIG. 18 were
generated using two single needle electrodes with a=0.821.+-.0.062
and b=1.256.+-.0.079 that corresponded to IRE ablations that were
3.0.+-.0.2 cm in width and 1.9.+-.0.1 cm in depth (P. A. Garcia, et
al., 2011). The results suggest that the Cassini curve is a viable
method to represent experimentally achieved IRE zones of ablation.
These curves can be used to provide physicians with simple, quick,
and accurate prediction of IRE treatments. The parameters generated
in this study were achieved from porcine liver ablations data. The
parameters for other tissues and/or tumors can be determined in a
similar manner. Cassini curve parameters should be re-calibrated if
the pulse parameters or electrode configuration (i.e. separation or
exposure) deviate from the typical protocols in Ben-David et al.
Additionally, there is a need to calibrate these Cassini curves to
electric and temperature distributions in order to take advantage
of the relatively simple curves in representing simulated solutions
that account for other pulse parameters and electrode configuration
including different electrode separations, diameter, exposure, and
voltages. A method to represent IRE zones of ablation in a
computationally efficient manner and based on experimental data is
thus presented. Such methods can be used to predict IRE ablation in
liver in order to provide physicians with an immediate tool for
treatment planning.
[0305] FIG. 19 is a representation of the 3D Electric Field [V/cm]
Distribution in Non-Electroporated (Baseline) Tissue with 1.5-cm
Single Needle Electrodes at a Separation of 2.0 cm and 3000 V
applied.
[0306] FIGS. 20A-D are representations of the Electric Field [V/cm]
Distributions from the 3D Non-Electroporated (Baseline) Models with
1.5-cm Electrodes at a Separation of 2.0 cm and 3000 V
(cross-sections), wherein FIG. 20A is a representation of the x-y
plane mid-electrode length, FIG. 20B is a representation of the x-z
plane mid-electrode diameter, FIG. 20C is a representation of the
y-z plane mid electrode diameter, and FIG. 20D is a representation
of the y-z plane between electrodes.
[0307] FIG. 21 is a representation of the 3D Electric Field [V/cm]
Distribution in Electroporated Tissue with 1.5-cm Single Needle
Electrodes at a Separation of 2.0 cm and 3000 V applied assuming
.sigma..sub.max/.sigma..sub.0=3.6.
[0308] FIGS. 22A-22D are representations of the Electric Field
[V/cm] Distributions from the 3D Electroporated Models with 1.5-cm
Electrodes at a Separation of 2.0 cm and 3000 V (cross-sections)
assuming .sigma..sub.max/.sigma..sub.0=3.6, wherein FIG. 22A is a
representation of the x-y plane mid-electrode length, FIG. 22B is a
representation of the x-z plane mid-electrode diameter, FIG. 22C is
a representation of the y-z plane mid electrode diameter, and FIG.
22D is a representation of the y-z plane between electrodes.
Example 7: The Cassini Oval Equation
[0309] In mathematics, a Cassini oval is a set (or locus) of points
in the plane such that each point p on the oval bears a special
relation to two other, fixed points q.sub.1 and q.sub.2: the
product of the distance from p to q.sub.1 and the distance from p
to q.sub.2 is constant. That is, if the function dist(x,y) is
defined to be the distance from a point x to a point y, then all
points p on a Cassini oval satisfy the equation:
dist(q.sub.1,p).times.dist(q.sub.2,p)=b.sup.2 (2)
where b is a constant.
[0310] Nevertheless, in embodiments the `b` parameter can be
modified to manipulate the shape of the Cassini curve and
illustrate the desired electric field distribution. Therefore, the
`b` is a variable parameter that is determined based on the
specific location (distance) of a particular electric field
threshold to be displayed.
[0311] The points q.sub.1 and q.sub.2 are called the foci of the
oval.
[0312] Suppose q.sub.1 is the point (a,0), and q.sub.2 is the point
(-a,0). Then the points on the curve satisfy the equation:
((x-a).sup.2+y.sup.2)((x+a).sup.2+y.sup.2)=b.sup.4 (3)
[0313] The equivalent polar equation is:
r.sup.4-2a.sup.2r.sup.2 cos 2.theta.=b.sup.4-a.sup.4 (4)
[0314] The shape of the oval depends on the ratio b/a. When b/a is
greater than 1, the locus is a single, connected loop. When b/a is
less than 1, the locus comprises two disconnected loops. When b/a
is equal to 1, the locus is a lemniscate of Bernoulli.
[0315] The Cassini equation provides a very efficient algorithm for
plotting the boundary line of the treatment zone that was created
between two probes on grid 200. By taking pairs of probes for each
firing sequence, the first probe is set as qi being the point (a,0)
and the second probe is set as q.sub.2 being the point (-a,0). This
original Cassini oval formulation was revised by modifying the
assumption of the `a` parameter being related to the position of
the electrodes. In the revised formulation the `a` is a variable
parameter that is adjusted depending on the width and length of the
Cassini oval in order to intercept the zone of ablation in the x-
and y-directions.
[0316] In summary, the `a` and `b` variable parameters should be
determined in order to have the ability to generate a Cassini curve
that could fit the shape of any electric field isocontour.
Specifically from the electric field simulations or experimental
irreversible electroporation zones of ablation the user should
determine the distance along the x-axis and y-axis that the Cassini
curve should intersect.
[0317] For example in the case of a Finite Element Analysis (FEA)
simulation using two 1-mm in diameter electrodes, separated by a
center-to-center distance of 2.0 cm, 1.5 cm in exposure, and an
applied voltage of 3000 V to one electrode and ground to the other
electrode the distances from the point in between the electrodes to
a specific electric field contour is given below (Table 8 for the
baseline (non-electroporated) and .sigma..sub.max/.sigma..sub.0=3.6
(electroporated) models.
TABLE-US-00008 TABLE 8 E-field Baseline Baseline
.sigma..sub.max/.sigma..sub.0 = 3.6 .sigma..sub.max/.sigma..sub.0 =
3.6 [V/cm] (p.sub.1x, 0) [cm] (0, p.sub.2y) [cm] (p.sub.3x, 0) [cm]
(0, p.sub.4y) [cm] 300 1.97 0.92 2.38 1.39 400 1.81 0.69 2.17 1.18
500 1.70 0.49 1.99 1.01
[0318] Using the 500 V/cm electric field isocontour as an example
it can be determined that the Cassini oval using the baseline model
will intersect the points (1.70,0) and (0,0.49) and the model using
.sigma..sub.max/.sigma..sub.0=3.6 will intersect the point (1.99,0)
and (0,1.01). Using the two points that will be intersected by the
Cassini oval of each specific model type (non-electroporated vs.
electroporated) allows for determination of the `a` and `b`
variable parameter and still satisfy the mathematical condition
outlined above in the first paragraph of this section by way of
least square fits such as the NonlinearModelFit function in
Mathematica or via interpolation tables as the one presented
below.
[0319] The interpolation method involves assuming values for the
`a` parameter from 0.00 cm to 3.00 cm in steps of 0.01 cm and
calculating the `b` parameter using the specific points from the
previous paragraph. The distance and steps were arbitrarily chosen
and can vary depending on the specific Cassini oval that is being
developed. In the case of Table 9 the point p1x=(1.70 cm, 0 cm) and
the point p2y=(0 cm, 0.49 cm) and the corresponding distances to
either q1 (-a,0) or q2 (a,0) are calculated.
TABLE-US-00009 TABLE 9 `a` d (q1, p1x) = d1 d (q2, p1x) = d2 d1 *
d2 d (q1, p2y) = d3 d (q2, p2y) = d4 d3 * d4 d1 * d2/d3 * d4 1.04
0.66 2.74 1.808 1.150 1.150 1.322 1.37 1.05 0.65 2.75 1.788 1.159
1.159 1.343 1.33 1.06 0.64 2.76 1.766 1.168 1.168 1.364 1.30 1.07
0.63 2.77 1.745 1.177 1.177 1.385 1.26 1.08 0.62 2.78 1.724 1.186
1.186 1.407 1.23 1.09 0.61 2.79 1.702 1.195 1.195 1.428 1.19 1.1
0.60 2.80 1.680 1.204 1.204 1.450 1.16 1.11 0.59 2.81 1.658 1.213
1.213 1.472 1.13 1.12 0.58 2.82 1.636 1.222 1.222 1.495 1.09 1.13
0.57 2.83 1.613 1.232 1.232 1.517 1.06 1.14 0.56 2.84 1.590 1.241
1.241 1.540 1.03 1.15 0.55 2.85 1.568 1.250 1.250 1.563 1.00 1.16
0.54 2.86 1.544 1.259 1.259 1.586 0.97 1.17 0.53 2.87 1.521 1.268
1.268 1.609 0.95 1.18 0.52 2.88 1.498 1.278 1.278 1.633 0.92 1.19
0.51 2.89 1.474 1.287 1.287 1.656 0.89 1.2 0.50 2.90 1.450 1.296
1.296 1.680 0.86 1.21 0.49 2.91 1.426 1.305 1.305 1.704 0.84 1.22
0.48 2.92 1.402 1.315 1.315 1.729 0.81 1.23 0.47 2.93 1.377 1.324
1.324 1.753 0.79 1.24 0.46 2.94 1.352 1.333 1.333 1.778 0.76
[0320] In the baseline case analyzed above when the variable
parameter `a` was 1.15 cm the calculated b.sup.2 were 1.568 and
1.563 for the d1*d2 and d3*d4, respectively. The last column
calculates the ratio of both b.sup.2 values in order to determine
the location at which they are the same (or closest) which happens
when (d1*d2)/(d3*d4)=1.00.
[0321] Once it is determined that `a`=1.15 cm provides the closest
ratio to one, the average of the d1*d2 (1.568) and d3*d4 (1.563)
quantities is calculated and used to determine the corresponding
`b` parameter by taking the square root as shown in the equation
below.
b = ( d .times. .times. 1 * d .times. .times. 2 ) + ( d .times.
.times. 3 * d .times. .times. 4 ) 2 = 1.568 + 1.563 2 = 1.5655 =
1.2512 ( 5 ) ##EQU00012##
[0322] Once the `a` and `b` parameters are determined then any
plotting software can be used to illustrate the Cassini curve in
Cartesian coordinates using the modified equation
y = .+-. - a 2 - x 2 .+-. b 4 + 4 .times. a 2 .times. x 2 ( 6 )
##EQU00013##
[0323] The steps outlined in the previous paragraphs just above can
also be used to determine the `a` and `b` parameters using the same
methodology and with points p3x=(1.99 cm, 0 cm) and p4y=(0 cm, 1.01
cm) and results in `a`=1.21 cm and `b`=1.578 cm as the Cassini
parameters for the electroporated model when
.sigma..sub.max/.sigma..sub.0=3.6.
TABLE-US-00010 TABLE 10 `a` d (q1, p3x) = d5 d (q2, p3x) = d6 d5 *
d6 d (q1, p4y) = d7 d (q2, p4y) = d8 d7 * d8 d5 * d6/d7 * d8 1.1
0.89 3.09 2.750 1.493 1.493 2.230 1.23 1.11 0.88 3.10 2.728 1.501
1.501 2.252 1.21 1.12 0.87 3.11 2.706 1.508 1.508 2.275 1.19 1.13
0.86 3.12 2.683 1.516 1.516 2.297 1.17 1.14 0.85 3.13 2.661 1.523
1.523 2.320 1.15 1.15 0.84 3.14 2.638 1.531 1.531 2.343 1.13 1.16
0.83 3.15 2.615 1.538 1.538 2.366 1.11 1.17 0.82 3.16 2.591 1.546
1.546 2.389 1.08 1.18 0.81 3.17 2.568 1.553 1.553 2.413 1.06 1.19
0.80 3.18 2.544 1.561 1.561 2.436 1.04 1.2 0.79 3.19 2.520 1.568
1.568 2.460 1.02 1.21 0.78 3.20 2.496 1.576 1.576 2.484 1.00 1.22
0.77 3.21 2.472 1.584 1.584 2.509 0.99 1.23 0.76 3.22 2.447 1.592
1.592 2.533 0.97 1.24 0.75 3.23 2.423 1.599 1.599 2.558 0.95 1.25
0.74 3.24 2.398 1.607 1.607 2.583 0.93 1.26 0.73 3.25 2.373 1.615
1.615 2.608 0.91 1.27 0.72 3.26 2.347 1.623 1.623 2.633 0.89 1.28
0.71 3.27 2.322 1.630 1.630 2.659 0.87 1.29 0.70 3.28 2.296 1.638
1.638 2.684 0.86 1.3 0.69 3.29 2.270 1.646 1.646 2.710 0.84
[0324] In FIG. 23, it can be seen that with the implementation of
the pre-pulse concept to determine the ratio of maximum
conductivity to baseline conductivity one can derive a Cassini
curve representing zones of ablation. In this case the 500 V/cm
isocontour was specified but this technique could be used for any
other isocontour that perhaps could represent the lethal IRE
threshold for any other tissue/tumor type.
[0325] The polar equation for the Cassini curve could also be used
because since it provides an alternate method for computation. The
current Cartesian coordinate algorithm can work equally as well by
using the polar equation of the Cassini curve. By solving for
r.sup.2 from eq. (4) above, the following polar equation was
developed:
r.sup.2=a.sup.2 cos(2*theta)+/-sqrt(b.sup.4-a.sup.4
sin.sup.2(2*theta)) (5)
[0326] and the `a` and `b` parameters should be determined as
previously described in this application.
Example 8: Mapping of Electric Field and Thermal Contours Using a
Simplified Data Cross-Referencing Approach
[0327] This method can be used to identify the volume of tissue
which will be elevated above a specific temperature (e.g.
45.degree. C.) for specific treatment parameters. This contour can
then be correlated with electric field intensity. This data in turn
can be used to fit a contour using the Cassini oval software in the
NANOKNIFE.RTM. System.
[0328] Methods: A mathematical model was built with COMSOL
Multiphysics (Version 4.2a, Comsol Inc., Burlington, Mass., USA) to
estimate the temperature rise within tissue due to Joule heating
effects. The electric field distribution within the simulation
domain was solved using the Joule Heating module, as described by
the Laplace Equation:
.gradient..sup.2.PHI.=0
[0329] where .PHI. is the electric potential, this equation is
solved with boundary conditions:
[0330] {right arrow over (n)}{right arrow over (J)}=0 at the
boundaries
[0331] .PHI.=V.sub.in at the boundary of the first electrode
[0332] .PHI.=0 at the boundary of the second electrode
[0333] wherein {right arrow over (n)} is the normal vector to the
surface, {right arrow over (J)} is the electrical current and
V.sub.in is the electrical potential applied. Heat transfer in the
solid domain was calculated as:
.rho. .times. .times. C p .times. .differential. T .differential. t
= .gradient. ( k .times. .gradient. T ) + Q jh .function. [ W m 3 ]
##EQU00014##
[0334] where .rho. is the density, C.sub.p is the heat capacity, k
is the thermal conductivity, Q.sub.jh and are the resistive
losses
Q jh = J E .function. [ W m 3 ] ##EQU00015##
[0335] where J is the induced current density
J = .sigma. .times. .times. E .function. [ A m 2 ] ##EQU00016##
[0336] and .sigma. is the tissue conductivity and E is the electric
field
E = - .gradient. .PHI. .function. [ V m ] ##EQU00017##
[0337] To account for the pulsed nature of the applied electric
field, the Joule heating term in COMSOL was adjusted by adding in a
duty cycle term equal to 100.times.10-6, the pulse duration (100
.mu.s) (See P. A. Garcia, et al., "A Parametric Study Delineating
Irreversible Electroporation from Thermal Damage Based on a
Minimally Invasive Intracranial Procedure," Biomed Eng Online, vol.
10, p. 34, Apr. 30 2011).
[0338] In the Joule Heating Model equation view, the equation for
resistive losses was modified to:
jh.Qrh=((jh.Jix+jh.Jex)*duty_cycle*jh.Ex+(jh.Jiy+jh.Jey)*duty_cycle*jh.E-
y+(jh.Jiz+jh.Jez)*duty_cycle*jh.Ez)*)t<=90)+0*(t>90)
[0339] The resulting behavior was to calculate Joule heating only
for the first 90 seconds (Ninety pulses of 100 .mu.s each) of the
simulation, after which, heat was allowed to dissipate within the
tissue domain without additional heating. The parameters used in
the simulations are provided in Table 11 below.
TABLE-US-00011 TABLE 11 Parameters used in COMSOL finite element
model Parameter Value Unit Description r_e 0.0005 [m] electrode
radius l_e 0.15 [m] electrode length l_t 0.15 [m] tissue radius h_t
0.1 [m] tissue thickness gap 0.015 [m] center-to-center spacing
epsi_e 0 -- electrode permittivity epsi_i 0 -- insulation
permittivity epsi_t 0 -- tissue permittivity sigma_e 2.22E+06 [S/m]
electrode conductivity sigma_i 6.66E-16 [S/m] insulation
conductivity sigma_t 0.2 [S/m] tissue conductivity rho 1080 [kg/m3]
tissue density Cp 3890 [J/(kg * K)] tissue heat capacity k 0.547
[W/(m * K)] tissue thermal conductivity duty_cycle 1.00E-04 --
pulse duty cycle
[0340] Results: The COMSOL model was used to solve for temperature
distributions at times between 0 and 900 seconds (10 second
increment 0-100 s, 100 second increment 100-900 seconds). Electric
Field and Temperature distributions were exported along lines on
the x-(width) and y-axis (depth) with 100 micrometer spacing
between data points. These values were imported into Excel and used
as the basis for the Cassini oval calculations. FIGS. 24A-D shows
the temperature distributions determined in COMSOL at 90 seconds
(Ninety pulses of 100 .mu.s each) for 3000 V treatments with 1.0
cm, 1.5 cm, 2.0 cm, and 2.5 cm electrode spacing and an electrode
exposure of 1.5 cm. Contours on this figure show an approximate
electric field which corresponds to tissue temperatures greater
than 45.degree. C. Simulations of each parameter required
approximately 30 minutes to complete for a total computational
duration of 15 hours.
[0341] FIGS. 25A-D shows the Cassini oval approximations for the
temperature and electric field distributions based on the finite
element simulation results. Iso-contour lines correspond to the
tissue with temperature elevated above 45.degree. C. and electric
field above 500 V/cm, at the end of a 90 second IRE treatment
(Ninety pulses of 100 .mu.s).
[0342] The Cassini oval spreadsheet has been programmed so that the
user can plot contour lines for specified voltages (500, 1000,
1500, 2000, 2500, 3000 V), electrode separations (0.5, 1.0, 1.5,
2.0, 2.5 cm), Simulation times (0-900 seconds), Temperatures
(37-Tmax .degree. C.), and electric field intensities (0-infinity
V/cm). FIGS. 26A-D shows the temperature distributions for a 3000
V, 2.5 cm spacing treatment at 10, 40, 90, and 200 seconds. The
simulation accounts for Joule heating up to 90 seconds. After 90
seconds, Joule heating is no longer calculated and the temperature
dissipates over time since the ninety-pulse delivery is
completed.
[0343] The Cassini oval approximation can also be used to
investigate the contours of any temperature. FIG. 27A-D shows the
volumes of tissue that have been heated by at least 0.2, 3.0, 8.0,
and 13.0.degree. C. At 3000V, 1.5 cm exposure, and 2.5 cm electrode
spacing at a time=90 seconds (Ninety pulses of 100 .mu.s each),
only a very small volume of tissue outside the ablation zone (500
V/cm) experiences any temperature increase.
[0344] The Cassini oval approximation tool provides a rapid method
for determining the temperature distribution expected for a given
set of treatment parameters (FIGS. 28 and 29). Voltage, Electrode
Spacing (Gap), Time, Temperature, and Electric Field can be
selected by moving the slider or editing values in the green boxes.
In embodiments, baseline conductivity of the target treatment area,
and/or a conductivity for a specific tissue type, and/or a change
in conductivity for the target treatment area can also, and/or
alternatively, be selected. Voltage is selectable in 500 V discrete
steps between 500 and 3000 V. Electrode Spacing (Gap) is selectable
in 5.0 mm discrete steps between 5.0 mm and 25 mm. Time is
selectable in 10 second discrete steps between 0 and 100 seconds
and 100 second discrete steps between 100 and 900 seconds. The
temperature contour line is selectable for any value between
37.degree. C. and T.sub.max, where T.sub.max is the maximum
temperature in the tissue at a given treatment time. Additionally,
the electric field distribution within the tissue can be set for
any value.
[0345] Additional examples of usage of the Cassini oval
approximation tool are shown in the following figures. FIGS. 30A-D
show temperature contour lines for 40.degree. C. (FIG. 30A),
45.degree. C. (FIG. 30B), 50.degree. C. (FIG. 30C), and 55.degree.
C. (FIG. 30D) for a 90 second IRE treatment (Ninety pulses of 100
.mu.s each) with a voltage of 3000 V and electrode spacing of 10
mm. An electric field contour line of 500 V/cm is shown for
comparison. As can be seen, the figures show a temperature gradient
that expectedly increases from the 500 V/cm contour line toward the
electrodes.
[0346] FIGS. 31A-D show contour lines representing a 40.degree. C.
temperature and a 500 V/cm electric field for a 90 second IRE
treatment (Ninety pulses of 100 .mu.s each) and electrode spacing
of 10 mm at different voltages (3000V (FIG. 31A), 2000V (FIG. 31B),
1500V (FIG. 31C), and 1000V (FIG. 31D)). The figures show that the
size of the electric field and heated area decreases in proportion
to the decrease in voltage.
[0347] FIGS. 32A-D show electric field contour lines for 500 V/cm
(FIG. 32A), 1000 V/cm (FIG. 32B), 1500 V/cm (FIG. 32C), and 2000
V/cm (FIG. 32D) for a 90 second IRE treatment (Ninety pulses of 100
.mu.s each) with a voltage of 3000 V and electrode spacing of 10
mm. As can be seen, the figures show an electric field gradient
that expectedly increases from the 40.degree. C. contour line
toward the electrodes.
[0348] FIGS. 33A-D show contour lines representing a 40.degree. C.
temperature and a 500 V/cm electric field for a 90 second IRE
treatment (Ninety pulses of 100 .mu.s each) and voltage of 3000V at
different electrode spacings (5 mm (FIG. 33A), 10 mm (FIG. 33B), 15
mm (FIG. 33C), 20 mm FIG. 33D)). As can be seen, increasing the
electrode distance up to 15 mm widens the electric field and
temperature contour. At an electrode distance of 20 mm, the
electric field contour line widens and narrows, but the area heated
to at least 40.degree. C. is limited to a radius around each
electrode.
[0349] FIGS. 34A-D show contour lines representing a 40.degree. C.
temperature and a 500 V/cm electric field for an IRE treatment of
3000V and an electrode spacing of 10 mm at different durations of
treatment (90 seconds (Ninety pulses of 100 .mu.s each) (FIG. 34A),
60 seconds (Sixty pulses of 100 .mu.s each) (FIG. 34B), 30 seconds
(Thirty pulses of 100 .mu.s each) (FIG. 34C), 10 seconds (Ten
pulses of 100 .mu.s each) (FIG. 34D)). The graphs show that
decreasing the durations of treatment reduces the area heated at
least 40.degree. C., but not the area of the electric field.
[0350] Model Limitations: This model was designed to give a rapid
approximation for the temperature distribution within a volume of
tissue without the need for complex finite element simulations. The
data used to fit the Cassini oval curves uses values calculated
assuming a constant conductivity of 0.2 S/m. This represents an
approximate conductivity of human tissue, though conductivities of
tissue vary between patients, tissue types, locations, and
pathologies. Changing conductivity due to temperature increases or
electroporation effects were not included. FIG. 35 shows the COMSOL
three-dimensional finite element domain mesh used to calculate the
electric field and temperature information to create the Cassini
Oval values and curves.
[0351] The effects of blood flow and perfusion through the tissue,
metabolic heat generation, or diffusion of heat at the tissue
domain boundaries were not considered. It is anticipated that these
effects will result in lower temperatures. Therefore, the
visualization tool provides a conservative (worst case scenario)
estimate as to the zones exposed to critical temperatures. The
effects of changing conductivity and conductivities other than 0.2
S/m were not considered. Elevated conductivities are anticipated to
result in higher temperatures within the tissue. Blood flow,
metabolic heat generation, tissue conductivity, and ratios of
changing conductivity are tissue type specific and will require the
inclusion of in-vivo derived data.
[0352] Conclusions: In this Example, a real time visualization
package plots the isocontour lines for an arbitrary temperature and
electric field based on applied voltage, electrode spacing, and
time. This data can be used to build intuition and instruct
clinicians on reasonable expectations of temperature increases to
prevent damage to critical structures of organs in the proximity of
the treatment.
Example 9: Visualization of Electric Field Distributions Using
Different Configurations of Bipolar Probes
[0353] FIGS. 36A-36C show a representation of a visualization tool
providing the 650 V/cm electric field distributions using different
configurations of bipolar probes and includes dynamic change
(3.6.times.) in electrical conductivity from the non-electroporated
baseline for runs 7, 8, and 9 of the visualization. FIG. 36D is a
table showing parameters of each run including electrode length,
separation distance (insulation), and applied voltage. FIG. 36E is
a table showing lesion dimensions for runs 7, 8, and 9. The results
show that as the length of the bipolar electrode increases, the
size of the zone of ablation increases.
Example 10: Determining the IRE Threshold for Different Tissues
According to Conductivity
[0354] In this Example, as shown in the following figures, the
"Goldberg" data (red-dashed line), is from pre-clinical data for a
particular treatment (2700V, 90 pulses, 100 .mu.s energized per
pulse). By adjusting one or more treatment parameters, a user can
determine the electric field threshold for these types of tissues
(black-solid line).
[0355] An important aspect of this model is that the tissue
conductivity is allowed to change as a function of electric field
to simulate what happens when the tissue becomes irreversibly
electroporated. This function is `sigmoidal` or `S` shaped and
increases from a baseline (non-electroporated) to a conductivity
multiplier (electroporated). This transition happens at a specific
electric field intensity.
[0356] In FIG. 37, the conductivity changes from 0.1 to 0.35 at an
electric field centered at 500 V/cm. A user can change/shift all of
the values in this curve to fit the experimental data. FIG. 38A is
a contour plot comparing the "Goldberg" data (red dashed line) with
a calculated threshold (solid black line) based on the parameters
shown in FIG. 38C, explained below. FIG. 38B is a contour plot
comparing the conductivity (blue dotted line) with a calculated
threshold (solid black line) based on the parameters shown in FIG.
38C.
[0357] IRE Threshold [V/cm]: This parameter is the electric field
at which the change in conductivity occurs for the sigmoidal curve.
By changing this value, the sigmoidal curve shifts to the left or
right. A value of 500 V/cm has been found to fit the data best.
[0358] Transition zone: This is the `width` of the transition zone.
By changing this value, the rate at which the conductivity increase
changes. In FIG. 37, this value is set to 0.49, the widest
transition possible. It has been found that a transition of 0.2
matches the experimental data best.
[0359] Sigma: This is the baseline conductivity before treatment.
It has been found that a value of 0.067 (or 0.1) works well.
[0360] Conductivity Multiplier: This is how much the conductivity
increases by when the tissue has been irreversibly electroporated.
A 3.6.times. increase has been found experimentally for liver and
fits the data well.
[0361] E-Field: This is the parameter that is adjusted to find the
in-vivo irreversible electroporation threshold. With the values set
for the other parameters above, it has been found that IRE should
occur at a threshold of 580 V/cm to match the lesions found
in-vivo.
[0362] The following figures show how modifying the conductivity of
the tissue changes the calculated zone of ablation. FIGS. 39A-39F
were performed according to the parameters in FIG. 38C, except the
conductivity of the tissue was modified. FIGS. 39A-39C show the
"Goldberg" data and calculated threshold and FIGS. 39D-39F show the
conductivity and calculated threshold for conductivity multipliers
of 2, 3, and 4, respectively. As can be seen, the calculated
ablation zone increases in comparison to the Goldberg preclinical
data as conductivity increases.
[0363] FIGS. 40A-40F were performed for an IRE Threshold of 600
V/cm, a transition zone of 0.4, a Voltage of 700 V, an E-Field of
700 V/cm, and a Sigma (electrical conductivity) of 0.20 S/m. FIGS.
40A-40C show the "Goldberg" data and calculated threshold and FIGS.
40D-40F show the conductivity and calculated threshold for
conductivity multipliers of 2, 3, and 4, respectively.
[0364] FIGS. 41A-41F were performed for an IRE Threshold of 1000
V/cm, a transition zone of 0.2, a Voltage of 2700 V, an E-Field of
700 V/cm, and a Sigma (electrical conductivity) of 0.20 S/m. FIGS.
41A-41C show the "Goldberg" data and calculated threshold and FIGS.
41D-41F show the conductivity and calculated threshold for
conductivity multipliers of 2, 3, and 4, respectively.
[0365] As can be seen, the calculated ablation zone increases in
comparison to the Goldberg preclinical data as the conductivity
multiplier increases.
Example 11: Correlating Experimental and Numerical IRE Lesions
Using the Bipolar Probe
[0366] Purpose: To establish a function that correlates
experimentally produced zones of ablations in in vivo porcine
tissue with the corresponding IRE pulse parameters (duration,
number, strength) and single needle electrode configuration.
[0367] A mathematical function was developed that captures the IRE
response in liver tissue as a function of applied voltage, pulse
number, and pulse duration for the bipolar electrode configuration.
It is important to note that the inventors used a rate equation
that was fit to the 1.5 cm.times.2.9 cm IRE zone of ablation but
this has not been validated experimentally (See Golberg, A. and B.
Rubinsky, A statistical model for multidimensional irreversible
electroporation cell death in tissue. Biomed Eng Online, 2010.
9(1): p. 13). The results below provide insight as to the effect of
different pulse parameters and electrode/insulation dimensions in
the resulting zone of IRE ablation in order to optimize the bipolar
probe electrode for clinical use. In order to perform a
computationally efficient study, the models were constructed in a
2-D axis-symmetric platform which generates results that are
representative of the 3-D space.
[0368] Part 1: The work from Part 1 determined the electric field
threshold for 0.7 cm electrodes with a 0.8 cm insulation to be
572.8 V/cm assuming a static electric conductivity (Table 12). This
threshold is the average between the width (349.5 V/cm) and length
(795.1 V/cm) electric field thresholds that matched the
experimental lesion of 1.5 cm (width) by 2.9 cm (length). It is
important to note that due to the mismatch between the electric
field thresholds, the predicted width will be underestimated and
the predicted length will be overestimated when using the average
value of 572.8 V/cm. The model assumes an applied voltage of 2700
V, ninety 100-.mu.s pulses, at a repetition rate of 1 pulse per
second, and a viability value of 0.1% (S=0.001) as the complete
cell death due to IRE exposure (FIG. 42). The rate equation used in
the analysis is given by S=e.sup.-kEt where S is the cell viability
post-IRE, E is the electric field, t is the cumulative exposure
time, and k is the rate constant that dictates cell death.
Specifically during this Part, it was determined that k=1.33996
assuming an E=572.8 V/cm, S=0.001, and t=0.009 s
(90.times.100-.mu.s). The k parameter was scaled by the duty cycle
of the pulses (0.0001 s) in order to reflect the cell viability in
the time scale in which the pulses were delivered (i.e. one pulse
per second).
TABLE-US-00012 TABLE 12 Electric field thresholds for the static
modeling approach from experimental IRE lesions in liver. Lesion
E-field Average Threshold Conductivity Dimensions [V/cm] [V/cm]
[V/cm] Static - .sigma..sub.0 x = 1.5 cm 349.5 349.5 572.8 Static -
.sigma..sub.0 y = 2.9 cm (distal) 796.2 795.1 Static -
.sigma..sub.0 y = 2.9 cm 795.6 (proximal)
[0369] A parametric study was constructed in order to explore the
effect of electrode diameter (18 G=1.27 mm, 16 G=1.65 mm, 14 G=2.11
mm), electrode spacing (0.4 cm, 0.8 cm, 1.2 cm, 1.6 cm), and
electrode length (0.5 cm, 0.75 cm, 1.0 cm, 1.25 cm, and 1.5 cm). In
order to provide a comprehensive analysis of all iterations we
computed the volumes of tissue that would achieve a cell viability,
S<0.001, and these results are reported in the table of FIG.
48A-B. The results with the specific minimum and maximum parameters
from Part 1 are presented in Table 13 and demonstrate that with
increasing probe diameter and electrode length a larger area/volume
of IRE ablation is achieved for ninety 100-.mu.s pulses delivered
at 2700 V at a repetition rate of one pulse per second. FIGS. 43A-D
shows the predicted regions of post-IRE cell viability isocontour
levels with the solid white curve illustrating the 0.1%, 1.0%, and
10% cell viability levels. Of importance is the fact that if the
electrodes are spaced too far apart, the resulting IRE zone of
ablation is not contiguous and the treatment would fail between the
electrodes as shown with Runs 60 and 10, respectively.
TABLE-US-00013 TABLE 13 Predicted IRE lesion dimensions for the
min. and max. parameters investigated in Part 1. Spacing Length
Area Volume Run Diameter (cm) (cm) (cm.sup.2) (cm.sup.3) x (cm) y
(cm) x:y 60 14G = 2.11 mm 1.6 1.5 2.705 6.232 0.311 5.550 0.056 10
18G = 1.27 mm 1.6 0.5 1.042 1.689 0.227 3.390 0.067 49 18G = 1.27
mm 0.4 1.5 2.242 4.626 1.257 4.210 0.299 3 14G = 2.11 mm 0.4 0.5
1.120 2.241 1.221 2.190 0.558
[0370] In an effort to better understand the effects of the
electrode geometry on the ablation region an extra set of values
(Table 14) was generated. The closest outputs to a 1.5 cm.times.2.9
cm lesion size from parameters in Table 13 were modified to better
approximate the targeted lesion. Considering all 60 different runs,
number 15 is closest to the targeted values with a lesion geometry
of 1.301 cm.times.2.84 cm.
TABLE-US-00014 TABLE 14 Predicted IRE lesion dimensions for
parameters approximating a 1.5 cm .times. 2.9 cm ablation region.
Spacing Length Area Volume Run Diameter (cm) (cm) (cm.sup.2)
(cm.sup.3) x (cm) y (cm) x:y 3 14G = 2.11 mm 0.4 0.5 1.120 2.241
1.221 2.190 0.558 1 18G = 1.27 mm 0.4 0.5 0.943 1.590 1.037 2.170
0.478 15 14G = 2.11 mm 0.4 0.75 1.483 3.215 1.301 2.840 0.458 18
14G = 2.11 mm 0.8 0.75 1.680 3.652 1.181 3.250 0.363
[0371] Part 2: In Part 2 the electric field distribution assuming a
dynamic electric conductivity was used to determine the threshold
of cell death due to IRE exposure. Specifically during this Part, a
sigmoid function (FIG. 44) with a baseline (0.067 S/m) and maximum
(0.241 S/m) conductivity values was used (see Sel, D., et al.,
Sequential finite element model of tissue electropermeabilization.
IEEE Trans Biomed Eng, 2005. 52(5): p. 816-27). This published
function assumes that reversible electroporation starts at 460 V/cm
and is irreversible at 700 V/cm as reported by Sel. et al. Using
the dynamic conductivity function resulted in a more consistent
electric field threshold between the width (615.7 V/cm) and the
length (727.4 V/cm); therefore, using the average (670.1 V/cm)
provides a better prediction of the IRE lesions being achieved in
vivo versus the ones predicted in Part 1 that assume a static
conductivity (Table 15). The electric field threshold for IRE using
the dynamic conductivity approach resulted in a revised k=1.14539
assuming an E=670.1 V/cm, S=0.001, and t=0.009 s (90.times.100
.mu.s). The k parameter was scaled by the duty cycle of the pulses
(0.0001 s) in order to reflect the cell viability in the time scale
in which the pulses were delivered (i.e. one pulse per second).
TABLE-US-00015 TABLE 15 Electric field thresholds for the dynamic
modeling approach from experimental IRE lesions in liver. E-field
Threshold Conductivity IRE Dimension [V/cm] Average [V/cm] Dynamic
- x = 1.5 cm 615.7 615.7 670.1 .sigma.(E) Dynamic - y = 2.9 cm
(distal) 720.7 727.4 .sigma.(E) Dynamic - y = 2.9 cm 734.0
.sigma.(E) (proximal)
[0372] In Part 2, the effect of pulse strength (2000 V, 2250 V,
2500 V, 2750 V, 3000 V) and pulse number (20, 40, 60, 80, 100) was
explicitly investigated and the results of the parametric study are
provided in the table of FIG. 49 and a representative plot provided
in FIG. 45. The results with the specific minimum and maximum
parameters from Part 2 are presented in
[0373] Table 16 and demonstrate that with increasing pulse strength
and pulse number a larger volume of IRE ablation is achieved at a
repetition rate of one pulse per second (FIGS. 46A-D). In order to
compare the results to the electric field threshold, both
areas/volumes were computed and are provided as well. Similar to
the results from Part 1, the white solid curve represents the 0.1%,
1.0%, and 10% cell viability isocontour levels due to IRE. For all
voltages investigated, delivering one hundred 100-.mu.s pulses
covers a greater area/volume than the prediction by the 670.1 V/cm
electric field threshold assumed with the dynamic conductivity
function.
TABLE-US-00016 TABLE 16 Predicted lesion dimensions for the minimum
and maximum parameters investigated in Part 2. Voltage Area Volume
E-Field E-Field Run (V) Number (cm.sup.2) (cm.sup.3) (cm.sup.2)
(cm.sup.3) x (cm) y (cm) x:y 3 2000 20 0.080 0.050 0.970 1.575
0.216 2.350 0.092 6 2000 100 1.209 2.238 0.970 1.575 0.646 1.630
0.396 27 3000 20 0.209 0.170 1.493 3.171 0.221 1.800 0.123 30 3000
100 1.900 4.604 1.493 3.171 0.946 1.130 0.837
[0374] Part 3: In this Part the exposure of liver tissue to 300
(5.times.60) and 360 (4.times.90) pulses were simulated at an
applied voltage of 3000 V, 100-.mu.s pulses, at a repetition rate
of one pulse per second. From the cell viability plots in FIG.
47A-B it can be seen that with increasing number of pulses, larger
zones of IRE ablation are achieved with the corresponding areas and
volumes included in Table 17 and the table of FIG. 50. It is
important to note that in this case the simulation assumes that
there is sufficient thermal relaxation time between sets of pulses;
thus preventing any potential thermal damage from Joule heating
which is not simulated in this work.
TABLE-US-00017 TABLE 17 Predicted lesion dimensions for the 5
.times. 60 and 4 .times. 90 IRE pulses investigated in Part 3.
Voltage Area Volume E-Field E-Field Run (V) Number (cm.sup.2)
(cm.sup.3) (cm.sup.2) (cm.sup.3) x (cm) y (cm) x:y 16 3000 5
.times. 60 6.135 27.282 1.493 3.171 2.877 4.900 0.587 19 3000 4
.times. 90 6.950 33.202 1.493 3.171 3.287 5.540 0.593
[0375] Models with exploratory geometries were developed that
include multiple voltage sources and current diffusers (balloons).
FIGS. 51A-C present images of the raw geometries being tested and
FIGS. 51D-F show the corresponding electric field distribution. In
general, the most influential parameter remains the size of the
electrodes and insulation. According to the values generated from
these simulations, it seems like substantial helps to achieve more
spherical lesions.
TABLE-US-00018 TABLE 18 Predicted IRE lesion dimensions for
exploratory models in Appendix D. Length Area Volume Run Diameter
Spacing (cm) (cm) (cm.sup.2) (cm.sup.3) x (cm) y (cm) x:y 61 0.211
0.4 0.5 1.453 1.807 1.201 2.850 0.421 62 0.211 0.4 1 1.617 2.129
1.321 3.670 0.360 63 0.211 0.4 1 2.008 3.041 1.241 2.955 0.420 64
0.211 0.4 0.5 1.389 1.929 1.261 2.810 0.449 65 0.211 0.4 0.5 0.976
1.142 1.421 2.000 0.711
[0376] The present invention has been described with reference to
particular embodiments having various features. In light of the
disclosure provided, it will be apparent to those skilled in the
art that various modifications and variations can be made in the
practice of the present invention without departing from the scope
or spirit of the invention. One skilled in the art will recognize
that the disclosed features may be used singularly, in any
combination, or omitted based on the requirements and
specifications of a given application or design. Other embodiments
of the invention will be apparent to those skilled in the art from
consideration of the specification and practice of the
invention.
[0377] It is noted in particular that where a range of values is
provided in this specification, each value between the upper and
lower limits of that range is also specifically disclosed. The
upper and lower limits of these smaller ranges may independently be
included or excluded in the range as well. The singular forms "a,"
"an," and "the" include plural referents unless the context clearly
dictates otherwise. It is intended that the specification and
examples be considered as exemplary in nature and that variations
that do not depart from the essence of the invention fall within
the scope of the invention. In particular, for method embodiments,
the order of steps is merely exemplary and variations appreciated
by a skilled artisan are included in the scope of the invention.
Further, all of the references cited in this disclosure are each
individually incorporated by reference herein in their entireties
and as such are intended to provide an efficient way of
supplementing the enabling disclosure of this invention as well as
provide background detailing the level of ordinary skill in the
art.
* * * * *