U.S. patent application number 14/775998 was filed with the patent office on 2016-01-21 for cryopreservative compostions and methods.
The applicant listed for this patent is REGENTS OF THE UNIVERSITY OF MINNESOTA. Invention is credited to John C. BISCHOF, Jeunghwan CHOI, Michael L. ETHERIDGE.
Application Number | 20160015025 14/775998 |
Document ID | / |
Family ID | 50736156 |
Filed Date | 2016-01-21 |
United States Patent
Application |
20160015025 |
Kind Code |
A1 |
BISCHOF; John C. ; et
al. |
January 21, 2016 |
CRYOPRESERVATIVE COMPOSTIONS AND METHODS
Abstract
This disclosure describes compositions and methods related to
cryoprotection of biomaterial. Generally, the cryoprotective
composition includes a cryoprotective agent and magnetic
nanoparticles effective for thawing a cryopreserved specimen
comprising biomaterial with minimal biomaterial damage. In some
embodiments, the composition is effective for thawing a
cryopreserved specimen having a minimum dimension of 0.1 mm.
Generally, the method includes obtaining a biomaterial
cryopreserved with a cryoprotective composition as summarized
above, then subjecting the cryopreserved biomaterial to
electromagnetic energy of an intensity sufficient to excite the
magnetic nanoparticles and thaw the biomaterial.
Inventors: |
BISCHOF; John C.; (Saint
Paul, MN) ; ETHERIDGE; Michael L.; (St. Louis Park,
MN) ; CHOI; Jeunghwan; (Winterville, NC) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
REGENTS OF THE UNIVERSITY OF MINNESOTA |
Minneapolis |
MN |
US |
|
|
Family ID: |
50736156 |
Appl. No.: |
14/775998 |
Filed: |
March 14, 2014 |
PCT Filed: |
March 14, 2014 |
PCT NO: |
PCT/US2014/028166 |
371 Date: |
September 14, 2015 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61790410 |
Mar 15, 2013 |
|
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Current U.S.
Class: |
435/1.3 ;
435/173.9; 435/2; 435/374 |
Current CPC
Class: |
A01N 1/0284 20130101;
C12N 13/00 20130101; A01N 1/0242 20130101; A01N 1/0221 20130101;
A01N 1/0294 20130101 |
International
Class: |
A01N 1/02 20060101
A01N001/02; C12N 13/00 20060101 C12N013/00 |
Goverment Interests
GOVERNMENT FUNDING
[0002] This invention was made with government support under
CBET-1066343 awarded by the National Science Foundation. The
government has certain rights in the invention.
Claims
1. A cryoprotective composition comprising: a cryoprotective agent
and magnetic nanoparticles effective for thawing a cryopreserved
specimen comprising biomaterial with minimal biomaterial
damage.
2. The composition of claim 1 wherein the cryopreserved specimen
has a minimum dimension of 0.1 mm.
3. The composition of claim 1 wherein the cryoprotective agent has
a molarity of no more than 9 M.
4. The composition of claim 1 wherein the magnetic nanoparticles
comprise superparamagnetic nanoparticles.
5. The composition of claim 1 wherein the magnetic nanoparticles
comprise ferromagnetic nanoparticles.
6. The method of claim 1 wherein the total concentration of
magnetic nanoparticles comprises 0.01 mg Fe/mL to 100 mg Fe/mL.
7. The composition of claim 1 wherein the damage comprises
cracking
8. The composition of claim 1 wherein the damage comprises
devitrification.
9. The composition of claim 1 wherein minimal damage comprises
sufficiently minimal structural damage to the biomaterial that the
biomaterial is suitable for transplantation.
10. A composition comprising: a biomaterial perfused with a
cryoprotective composition comprising: a cryoprotective agent; and
magnetic nanoparticles effective for thawing a cryopreserved
specimen comprising biomaterial with minimal biomaterial
damage.
11. The composition of claim 10 wherein the biomaterial comprises
an organ or portion thereof, a tissue or portion thereof, or
cells.
12. A composition comprising: a biomaterial suspended in a
cryoprotective composition comprising: a cryoprotective agent; and
magnetic nanoparticles effective for thawing a cryopreserved
specimen comprising biomaterial with minimal biomaterial
damage.
13. The composition of claim 12 wherein the biomaterial comprises
an organ or portion thereof, a tissue or portion thereof, or
cells.
14. A method of thawing a cryopreserved biomaterial, the method
comprising: obtaining a biomaterial cryopreserved with a
cryoprotective composition comprising: a cryoprotective agent; and
magnetic nanoparticles effective for thawing a cryopreserved
specimen comprising biomaterial with minimal biomaterial damage;
and subjecting the cryopreserved biomaterial to electromagnetic
energy of an intensity sufficient to excite the magnetic
nanoparticles and thaw the biomaterial.
15. The method of claim 14 wherein the electromagnetic energy
comprises a radio frequency field, an alternating magnetic field,
or a rotating magnetic field.
16. The method of claim 15 wherein the radio frequency field,
alternating magnetic field, or rotating magnetic field comprises a
frequency of 0 kHz to 10 MHz.
17. The method of claim 14 wherein the cryopreserved biomaterial is
perfused with the cryoprotective composition.
18. The method of claim 14 wherein the cryopreserved biomaterial is
suspended in the cryoprotective composition.
19. The method of claim 14 wherein the cryopreserved biomaterial
has a volume with a minimum dimension of at least 0.1 mm.
20. The method of claim 14 wherein the cryopreserved biomaterial is
thawed with minimal damage.
21. The method of claim 20 wherein the damage comprises
devitrification.
22. The method of claim 20 wherein the damage comprises
cracking
23. The method of claim 14 wherein the cryopreserved biomaterial is
warmed at a rate of at least 10.degree. C./minute throughout.
24. The method of claim 14 wherein subjecting the cryopreserved
biomaterial to electromagnetic energy of an intensity sufficient to
thaw the cryopreserved biomaterial generates a thermal gradient of
no more than 1.degree. C./mm within the biomaterial.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application claims priority to U.S. Provisional Patent
Application Ser. No. 61/790,410, filed Mar. 15, 2013, which is
incorporated herein by reference.
SUMMARY
[0003] This disclosure describes, in one aspect, a cryoprotective
composition. Generally, the cryoprotective composition includes a
cryoprotective agent and magnetic nanoparticles effective for
thawing a cryopreserved specimen comprising biomaterial with
minimal biomaterial damage.
[0004] In some embodiments, the composition is effective for
thawing a cryopreserved specimen having a minimum dimension of 0.1
mm.
[0005] In some embodiments, the magnetic nanoparticles can include
superparamagnetic nanoparticles and/or ferromagnetic nanoparticles.
In some embodiments, the nanoparticles may be RF-susceptible
nanoparticles. In some embodiments, the total concentration of
magnetic nanoparticles can be 0.01 mg Fe/mL to 100 mg Fe/mL.
[0006] In some embodiments, the composition is effective for
thawing a cryopreserved specimen with minimal cracking and/or
minimal devitrification.
[0007] In some embodiments, the composition is effective for
thawing a biomaterial that is suitable for transplantation.
[0008] In another aspect, this disclosure describes a composition
that includes a biomaterial perfused with and/or suspended in the
cryoprotective composition summarized above.
[0009] In another aspect, this disclosure describes a method of
thawing a cryopreserved biomaterial. Generally, the method includes
obtaining a biomaterial cryopreserved with a cryoprotective
composition as summarized above, then subjecting the cryopreserved
biomaterial to electromagnetic energy of an intensity sufficient to
excite the magnetic nanoparticles and thaw the biomaterial.
[0010] In some embodiments, the electromagnetic energy can include
a radio frequency field, an alternating magnetic field, or a
rotating magnetic field.
[0011] In some embodiments, the biomaterial is perfused with and/or
suspended in the cryoprotective composition.
[0012] In some embodiments, the cryoprotective composition has a
volume with a minimum dimension of at least 1 mm.
[0013] In some embodiments, the biomaterial is thawed with minimal
devitrification and/or cracking.
[0014] In some embodiments, the biomaterial is warmed at a rate of
at least 10.degree. C./minute throughout.
[0015] In some embodiments, subjecting the cryopreserved
biomaterial to electromagnetic energy generates a thermal gradient
of no more than 1.degree. C./mm during within the biomaterial.
[0016] The above summary of the present invention is not intended
to describe each disclosed embodiment or every implementation of
the present invention. The description that follows more
particularly exemplifies illustrative embodiments. In several
places throughout the application, guidance is provided through
lists of examples, which examples can be used in various
combinations. In each instance, the recited list serves only as a
representative group and should not be interpreted as an exclusive
list.
BRIEF DESCRIPTION OF THE FIGURES
[0017] FIG. 1. (Left) Methods exist to successfully vitrify bulk
systems (organs and thin tissues). However, issues related to
devitrification and cracking during thawing of bulk-vitrified
samples (Middle) are rate limiting to the technology. (Right) Here
we present a new approach to thawing using radiofrequency heating
of magnetic nanoparticles (mNPs).
[0018] FIG. 2. (Left) Extended phase diagram modified from Fahy et
al. Cryobiology 21(4):407-426, 1984. (Right). Critical warming
versus cooling rates from 10 rabbit kidney samples permeated with
30% 2,3 butanediol (w/w) as described in Peyridieu et al.,
Cryobiology 33(4):436-446, 1996. The reference solution is also
given and shown to require a much higher cooling and warming rate
than in the tissue. Notice also that various parts of the kidney
have equilibrated differently to the same cryoprotective agent
yielding different critical rates.
[0019] FIG. 3. Enthaplic and cryomicroscopic events during freezing
and thawing of 6 M glycerol in 1X PBS without pre-nucleation, as
described in Choi, J., and J. C. Bischof. Int J of Heat and Mass
Transfer 51:640-649, 2007.
[0020] FIG. 4. Computed tomography (CT) of cryoprotective agent
loading, freezing (including both crystallization and
vitrification) and mNP loading of solutions, as described in
Bischof et al. Ann Biomed Eng 35(2):292-304, 2007.
[0021] FIG. 5. Mass-normalized, field dependent heating
(SAR.sub.Fe) measured for Ferrotec (superparamagnetic) and Micromod
(ferromagnetic) mNPs (a,b) in dispersed, aqueous solution at room
temperature. For Ferrotec, the dispersed heating was also compared
to a highly aggregated case (destabilized in high concentration
phosphate-buffered saline and 1% agarose gel), where an almost 50%
drop is observed (c). However, in both cases, the volumetric
heating (SAR.sub.V) demonstrates a direct dependence on mNP
concentration. Importantly, for many field strengths and
frequencies tested Ferrotec heats more efficiently on a per
nanoparticle basis (2-10-fold as shown) (d).
[0022] FIG. 6. One mNP cryoprotective agent test bed.
[0023] FIG. 7. Observed heating rates in flash frozen, aqueous (a)
and [6M glycerol in 1.times.PBS] (b) mNP solutions subjected to a
20 kA/m and 370 kHz radio frequency field. The ambient losses and
volumetric radio frequency heating (SAR.sub.V) were also calculated
from the aqueous samples based on a lumped approximation (c).
[0024] FIG. 8. Simple "kidney" model results, where volumetric
radio frequency heating was calculated based on the experimentally
measured data (See FIG. 7(c)) and vitrified tissue thermal
properties estimated from cryoprotective agent loaded liver
properties as described in Choi, J., and J. C. Bischof. Cryobiology
57(2):79-83, 2008. The minimum heating rate at the glass transition
temperature does not vary with the size of the kidney for the
insulated radio frequency heated case (a) and the temperature
fields remain uniform (b, right) after 1 minute of heating (r=2 cm)
versus a convective boundary warming case (b, left) with h=50
W/m.sup.2-K and T.sub.env=37.degree. C.
[0025] FIG. 9. Cryomacroscopy. (Left) shows a successfully
vitrified sample: note grid visibility below sample. Failed samples
include: (Middle) with cracking in top of image; and (Right)
devitrification as noted by loss of transparency (i.e., grid is no
longer visible).
[0026] FIG. 10. Freeze-thaw behavior of mNP-cryoprotectant
solutions. The addition of nanoparticles in the 6M glycerol and
VS55 solutions appeared to have very little impact on the
freeze-thaw behavior of the solutions, as demonstrated by the DSC
thermal traces for heating at 150.degree. C/min after cooling at
-150.degree. C./min (a,b). The specific heat of VS55 was estimated
from the apparent specific heat measured by DSC, while the
remainder of the thermal property data was estimated, with
distilled water included as a standard reference (c, d). Cooling
below the critical rate for 6M glycerol required a liquid nitrogen
quench and the rapid (non-uniform) cooling resulted in significant
cracking in the samples (e). While the VS55 samples were still
cooled in a liquid nitrogen bath, several insulating layers
provided for a more controlled cooling rate (with an annealing
step), allowing the samples to be vitrified and cooled to
-192.degree. C. without cracking (f).
[0027] FIG. 11. Radiofrequency heating of mNP-cryoprotectant
solutions. The samples were heated from an initial temperature of
-192.degree. C. in an inductive coil (c). The cryoprotectant
solutions containing mNPs heated at rates up to 300.degree. C/min
(a,b,d); these rates were fast enough to reduce devitrification in
the 6M glycerol samples (d) and avoid it altogether in the VS55
samples (b).
[0028] FIG. 12. SAR for mNPs heating in the cryogenic regime.
Analysis of the heating data provided estimates of the SAR as a
function of temperature, demonstrating very complex behavior (a-c).
The observed heating may reflect the effects of nanoparticle
aggregation (b), suspending phase (c), and temperature-dependent
magnetic behavior (a).
[0029] FIG. 13. Modeling uniform radiofrequency heating of mNPs in
bulk vitrified biomaterials. While tissues and organs can feature a
variety of complex geometries, vitrification protocols will
typically involve submersion and cooling in more simplified
geometries. Here we compared the general case of a vitrified
cylindrical volume, which can apply to a broad spectrum of
cryopreservation applications (a). The cases of convective,
boundary warming and uniform heating generation (c) were compared
for a range of characteristic dimensions and the calculated minimum
heating rate (b) demonstrates the independence of this technique on
sample size. The thermal gradients which result from boundary
warming are also quite apparent for the convective case (d).
[0030] FIG. 14. Modeling the effects of non-uniform mNP
distribution. A one-dimensional model (a) demonstrates the effects
of non-uniform heat generation within the biomaterial on limiting
the minimum heating rate (b) and imposing thermal stresses (c).
Included in the plots are the critical warming rate (v.sub.crit)
and critical tensile stress (a.sub.tens,crit) for VS55. However,
the stresses imposed during heating (expansion) will be
compressive, so the critical stress is expected to be much higher
in compression.
[0031] FIG. 15. Estimation of baseline specific heat for VS55. The
baseline specific heat of VS55 was extracted from the measured
apparent specific heat as previously described in Choi, J., and J.
C. Bischof. Cryobiology 60:52-70, 2010; Choi, J. H., and J. C.
Bischof. Cryobiology 57:79-83, 2008; Choi, J. H., and J. C.
Bischof. Int. J. Heat Mass Transf. 51:640-649, 2008; and Etheridge
et al. J. Biomech. Eng. 135:021001: 1-10, 2013.
[0032] FIG. 16. Cooling protocol for VS55 samples. (a) The VS55
samples were cooled in a liquid nitrogen bath inside a series of
containers to provide insulating air gaps and control the cooling
rate. (b) An "annealing" step at the glass transition was also
included to help relax thermal stresses that might have built up
and avoid cracking.
[0033] FIG. 17. Measured RF interference in metallic thermocouples.
While a measurable temperature rise was observed for insulated
thermocouples in the RF field (a), the interference and offset were
negligible when compared in aqueous samples (b).
DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS
[0034] Cryopreservation is commonly used to protect biomaterials
such as, for example, a tissue, an organ (e.g., for
transplantation), a cell monolayer, or a cell suspension, but may
be constrained by the toxicity of cryoprotectant chemicals and/or
difficulty in uniformly and rapidly heating and cooling the
biomaterial. Adding magnetic nanoparticles to cryoprotectant
solutions can allow rapid heating using external radio frequency
fields. Since the resulting thawing is rapid and uniform, lower
concentrations of cryoprotectants are required and cracking due to
thermal stress can be reduced. This can result in lower toxicity
and improved viability of cryopreserved biomaterial.
[0035] Traditional cryopreservation is limited because of
constraints on freezing and thawing biomaterials. Many current
techniques allow for sufficiently rapid cooling (sometimes with the
addition of high pressure for bulk systems), but they do not allow
sufficiently rapid thawing after cryopreservation. The use of
cryoprotectant chemicals can decrease the negative effects of, for
example, ice crystals forming in the biomaterial during cooling
and/or non-uniform and slow thawing. However, cryoprotectants at
high concentrations can be toxic to biomaterials.
[0036] This disclosure describes methods and compositions involving
rapid and uniform heating of cryopreserved biomaterials. This
results in lower thermal stresses (e.g., avoiding cracks) and
little or no devitrification (e.g., avoiding crystals) on the
cryopreserved biomaterial, which can translate to improved
survival. Thus, the process may allow a significant reduction in
the concentration of cryoprotectants that are required in the
cryopreservation process. A reduced concentration of
cryoprotectants can extend the application of cryopreservation to
larger biomaterials such as, for example, tissue slices, heart
valves, and kidneys. The technology also can be used, for example,
to preserve blood samples, stem cells, and reproductive
biomaterials.
[0037] The cryopreservation method described herein uses a
cryoprotectant solution that includes magnetic nanoparticles to
preserve biomaterials. A biomaterial may be submerged in or
perfused with a cryoprotectant solution prior to rapid cooling to a
vitreous (a non-crystalline or amorphous) state. External radio
frequency fields can be applied for controlled interaction with the
magnetic nanoparticles, leading to the rapid generation of heat at
nanoparticle sites dispersed throughout the biomaterial. This rapid
generation of heat at dispersed sites results in quick and uniform
thawing of cryopreserved biomaterial. Traditional thawing processes
allow heating rates of only 1.degree. C.-10.degree. C./min for
sample sizes larger than 1 cm in characteristic size. In contrast,
the use of radio frequency fields in conjunction with magnetic
nanoparticles allows heating rates as high as 100.degree.
C.-10,000.degree. C./min (a hundred-to-thousand-fold increase in
the heating rate). This rapid thawing allows for the use of lower
concentration of cryoprotectant chemicals--e.g., 4 M or lower,
compared to current standard cryoprotectant concentrations of 8 M
needed for vitrification. Since only certain biomaterials can
resist toxic effects that can be caused by the higher 8M
concentration of cryoprotectants, the lower concentration of
cryoprotectant chemicals needed to protect biomaterials in the
methods described herein makes cryopreservation a viable option for
a broader scope of biomaterials than is currently possible with
vitrification approaches.
[0038] Although alternatives to slow boundary convection-based
heating (e.g., rapid microwave heating) exist, they have
limitations in the uniformity of heating. Spatial differences in
the thawing rate through the biomaterial can lead to thermal
stresses that can physically damage the biomaterial (e.g.,
cracking) Such damage may be unacceptable for biomaterials intended
for transplantation. The present protocol effectively enhances the
heat generation within the cryopreserved system, which
significantly improves the rapidity and uniformity of heating, and
therefore reduces the amount of cryoprotectant chemical necessary
to preserve the biomaterial and/or reduces damage and stress
experienced by the biomaterial during the thawing process. The more
rapid and more uniform heating and/or reducing the amount of
cryoprotectants necessary to preserve biomaterial can reduce the
likelihood and/or extent of damage to cryopreserved biomaterials
that currently constrain more widespread use of
cryopreservation.
[0039] Vitrification, the freezing to a "glassy" rather than
crystalline phase, is a form of cryopreservation and an important
enabling approach for cellular and regenerative medicine.
Vitrification offers the ability to store and transport cells,
tissues, and/or organs for a great variety of biomedical uses. Our
protocol is based on uniform heat generation within the biomaterial
and is therefore not dependent on size or convective boundary
condition and, therefore, overcomes fundamental limitations
experienced with protocols that involve boundary convection or
microwave heating. Thus, our protocol can allow one to use
cryopreservation for larger volumes of samples that include
biomaterials, where devitrification and/or cracking routinely
result in preservation failures using conventional cryopreservation
methods. Moreover, faster thaw rates may allow one to reduce the
amount of potentially toxic cryoprotective agents needed to avoid
devitrification.
[0040] In one aspect, this disclosure describes a new approach for
rapidly and uniformly heating vitrified biospecimens through the
use of radio frequency (<1 MHz) excited magnetic nanoparticles
(mNPs). This technique can increase heating rates by two-to-three
orders of magnitude or more over conventional boundary heating and
does not depend on the size of the sample. Radio frequency thawing
of biomaterials perfused with or incubated in cryoprotective agents
that include magnetic nanoparticles decreases devitrification in
cryoprotective agents (6 M glycerol in 1X PBS) magnetic
nanoparticle solutions (FIG. 1 and FIG. 7). While existing methods
include the use of magnetic nanoparticles in cryoprotective
solutions in small dimensions, the challenges described above with
respect to uniformity of heating throughout a sample or specimen of
larger dimension (e.g., minimum dimension of at least 1 mm (e.g.,
at least 1-10 mm) have limited the application of the existing
methods.
[0041] In some embodiments, the mNP can include a combination of
nanoparticles (e.g., a superparamagnetic nanoparticle and a
ferromagnetic nanoparticle) to heat in two different cryoprotective
agent solutions (glycerol and VS55 (Fahy et al. Cryobiology
21(4):407-426, 1984)) under a range of applied fields which can
scale to larger systems. Glycerol alone is considered a suboptimal
cryoprotective agent because it requires one of the highest
critical warming rates to avoid devitrification in 50% w/w
cryoprotective agent on thaw (Boutron P. Cryobiology 21(2):183-191,
1984). VS 55 can require slower warming and has offered successful
vitrification for a number of tissue systems (Table 1).
TABLE-US-00001 TABLE 1 Examples of successfully vitrified
biomaterials. Cryoprotective Cool/Thaw Rate System Agent (.degree.
C./mm) Method Note Cite Embryo VS1 >20/>300 > rates best
(a) Vein VS55 43/225 Annealing < Tg (b) Artery VS55 >70/175
Annealing < Tg (c) Kidney VS55 10/300{circumflex over ( )} 1000
atm used (d, e) VS1 is very similar to VS55 developed by Fahy
(Cryobiology 21(4): 407-426, 1984) and studied by DSC by Mehl
(Cryobiology 30(5): 509-518, 1993). {circumflex over (
)}300.degree. C./min suggested for EM warming (Ruggera et al.
Cryobiology 27(5): 465-478, 1990). Importantly, the kidney can be
vitrified, but cannot be thawed successfully at present because
300.degree. C./min cannot be achieved in a large mammalian kidney
using boundary thawing. (a) Rail W F, Fahy G M. Nature. 1985;
313(6003): 573-575; (b) Song Y C, Khirabadi B S, Lightfoot F,
Brockbank K G, Taylor M J. Nature biotechnology. 2000; 18(3):
296-299; (c) Baicu S, Taylor M J, Chen Z, Rabin Y. Cell
preservation technology. 2006; 4(4): 236-244; (d) Fahy G M,
MacFarlane D R, Angell C A, Meryman H T. Cryobiology. 1984; 21(4):
407-426; (e) Fahy G M, Wowk B, Wu J, Phan J, Rasch C, Chang A, et
al. Cryobiology. 2004; 48(2): 157-178.
[0042] Thus, the use of mNP can extend the abilities of almost any
cryopreservation solution currently in use. Cryopreservation
requires that the biomaterial undergo controlled rate freezing
procedures that can damage and potentially destroy cells in
suspension, monolayers, or within a tissue or organ. At the
cellular level, this injury can involve dehydration and/or
intracellular ice formation. These factors are oppositely dependent
on the cooling rate: slow cooling can lead to dehydration, fast
cooling can produce intracellular ice formation. When taken to
extremes, both of these factors are known to reduce cell viability
in suspension, but by adding a sufficient molarity of
cryoprotective agent, these biophysical processes can be reduced,
and in some cases eliminated, through vitrification.
[0043] In simple terms vitrification relies on loading a high
enough concentration of cryoprotective agent (often 50% or more
w/w) and cooling rapidly enough to reach below the glass transition
temperature (T.sub.g) while minimizing or avoiding nucleation of
ice (T.sub.h) (FIG. 2a). Once below the glass transition
temperature, the biomaterial is stable and can be stored. To thaw,
one faces a similar challenge in reverse, which is to pass through
the devitrification temperature (T.sub.d) without allowing crystals
to grow. Avoiding ice growth as one moves through the
devitrification and liquidus temperatures (T.sub.d and T.sub.m) can
be achieved by increasing both cryoprotective agent concentration
and/or thawing rates. Our efforts address the successful thaw from
the vitrified state.
[0044] The cooling and thawing rates necessary to achieve
vitrification and avoid devitrification of small tissue samples
have been studied previously. (e.g., Peyridieu et al. Cryobiology
33(4):436-46, 1996). Cooling rates to achieve vitrification during
freezing are typically one to two orders of magnitude less than the
thawing rates needed to avoid devitrification upon subsequent
thawing (See FIG. 2b). For instance, cryoprotective agent (30%
butanediol w/w) can be added to kidney tissue and cooled at
10.degree. C./min to 100.degree. C./min to achieve vitrification
followed by thawing at rates 10-fold faster to avoid
devitrification (100.degree. C./min to 1000 .degree. C./min) (FIG.
2b). As one typically forms some small nuclei upon cooling, one
typically thaws the biomaterial more rapidly than the typical cool
rate in order to "rescue" the sample from the cooling-initiated
nuclei. These warming rates and cooling rates can be studied, for
example, in small pieces of kidney since the necessary warming and
cooling rates are unachievable in bulk systems using conventional
methods.
[0045] Differential Scanning calorimetry (DSC) may be used to
quantify the relative amounts of crystallization versus
vitrification and the critical cooling rates, and the critical
thawing rates in representative smaller volumes of tissues and
solution. FIG. 3 shows DSC heat release signatures due to
crystallization, vitrification, devitrification (i.e.,
crystallization upon thaw), and melting in glycerol. Controlled
cooling and thawing rates that are accessible by the machine are
typically less than 320.degree. C./min and the sample size is
usually .ltoreq.10 mg in order to avoid thermal lag and allow
proper calibration (Choi, J., and J. C. Bischof. Int J of Heat and
Mass Transfer 51:640-649, 2007; Choi, J., and J. C. Bischof.
Cryobiology 57(2):79-83, 2008). Thus, the DSC sample pan is
typically small and the sample is typically completely contained
within a volatile sample pan--i.e., the lid is crimped shut such
that no sample loss is possible due to evaporation or
volatilization of the sample. As shown in FIG. 3, one can measure
crystallization, vitrification (T.sub.g), devitrification (T.sub.d)
and melting (T.sub.m).
[0046] Imaging and microscopy methods also can be used to generate
complementary information to DSC such as, for example,
cryomicroscopy (FIG. 3), freeze-substitution (FIG. 1), and computed
tomography (FIG. 4). In the case of cryomicroscopy, one can observe
the crystalline versus amorphous material directly and compare the
results to DSC. In the case of freeze-substitution, one can
directly substitute for the ice using an organic solvent in the
cryogenic regime. Finally, one can calibrate the Hounsfield Unit to
the crystalline (or amorphous) phase within frozen biomaterials.
There can be a roughly 50 HU change between cryoprotective agent
loaded and frozen vs. loaded and vitrified material (i.e. the HU
change indicates whether the bulk material is vitrified or
crystallized).
[0047] As both cooling and heating depend at least in part on
thermal properties of the materials, one can measure the
temperature-dependent thermal properties of the system.
Specifically, thermal conductivity can be measured by, for example,
pulse decay (Choi, J., and J. C. Bischof. Int J of Heat and Mass
Transfer 51:640-649, 2007; Choi, J., and J. C. Bischof. Cryobiology
57(2):79-83, 2008) or "3 omega" technique (Lubner S D, Choi J W,
Hasegawa Y, Fong A, Bischof J C, Dames C, editors. Measurement of
the thermal conductivity of sub-millimeter biological tissues. ASME
IMECE; 2012; Houston: ASME). Using VS55 as a cryoprotective agent
may alter the thermal properties somewhat compared to, for example,
glycerol. Because magnetic nanoparticles can be a very small
percentage of the sample (<1% by volume), they are unlikely to
dramatically alter thermal properties of the cryoprotective
agent.
Heating Approaches
[0048] Rapid thawing of cellular systems can often be realized by
reducing the size of the sample, increasing the conductivity of the
sample holder, and/or creating a highly convective environment
(e.g., a heated water bath). This has been achieved for sperm, ova,
embryos, drosophila embryos, and many smaller systems that can be
placed in small containers that are amenable to boundary cooling
and thawing (See Table 1 for exemplary sample systems). However,
uniform and fast cooling or thawing from the boundary for larger
samples (beyond several mm in characteristic dimension) is not
possible due to heat transport limitations using conventional
techniques (Karlsson J O, Toner M. Biomaterials 17(3):243-256,
1996).
[0049] One alternative to boundary cooling and thawing involves
volumetric heating, in which the rates of thawing are related
directly to the applied heat generation (u''' or specific
absorption rate (SAR), W/m.sup.3):
.GAMMA. t = u m .rho. c p and u m = SAR y ~ [ W m 3 ] ( 1 )
##EQU00001##
where T is temperature, t is time, .rho. is density and c.sub.p is
specific heat. Heating rate (dT/dt) can be constant through the
biomaterial when, for example, heat generation is itself uniform
throughout and no heat transfer is occurring at the boundary--e.g.,
in an insulated container. One way of attempting to achieve uniform
heat generation involves microwave rewarming (e.g., Wusteman et al.
Cryobiology 48(2):179-189, 2004; Han et al. Microwave and Optical
Technology Letters 46(3):201-205, 2005). These high frequency
fields cannot be applied uniformly within bulk systems, resulting
in "hot spots" due at least in part to skin effects, attenuation of
the field, and/or variations in the temperature-dependent
dielectric constants within the sample. The resulting
non-uniformity in thawing can lead to thermal stresses within the
frozen sample that can produce cracking and differential viability,
fundamentally limiting its applicability. In short, volumetric
heating of bulk tissue systems has been explored for more than 30
years, but these fundamental limitations have not been
overcome.
[0050] Magnetic nanoparticle RF heating can circumvent the issues
in microwave warming. Although previous attempts using microwave
(100 s of MHz to GHz) thawing have produced heating rates up to
hundreds of .degree. C./min, they also demonstrate the inherent
limitation to heating at these high frequency fields in
biomaterials, which is non-uniformity. More specifically, microwave
heating at high frequencies is due to dielectric coupling of the
field with polar molecules. Although this is an effective means to
deposit energy into biomaterials with high water content,
inhomogeneity will occur even with the use of uniform fields due to
variations in the dielectric properties, attenuation of the field
(e.g., caused by skin depth), and/or the shape of the sample (Evans
S. Cryobiology 40(2):126-138, 2000; Burdette E C, Karow A M.
Cryobiology 15(2):142-151, 1978; Burdette et al. Cryobiology
17(4):393-402, 1980; Robinson et al. Phys. Med. Biol.
47(13):2311-2325, 2002). This can result in hot spots forming,
which are then compounded by "thermal runaway," where the local
heating accentuates the mismatch in the temperature-dependent
dielectric properties.
[0051] However, at lower radiofrequencies (<1 MHz), alternating
magnetic fields (AMFs) can uniformly penetrate biomaterials without
attenuation and negligible dielectric coupling (Atkinson et al.
IEEE Trans on Biomedical Engineering 31(1):70-75, 1984). Coupling
through induction of non-uniform Eddy currents may still occur, but
these are not typically significant given the low electrical
conductivities of vitrified solutions. Although these low frequency
fields are typically unable to rapidly heat biomaterial on their
own, they are able to produce significant losses in distributed
magnetic nanoparticles. The mechanisms of heating for magnetic
nanoparticles under an AMF may differ based on the particles'
magnetic behavior. Superparamagnetic nanoparticles (single-domain
crystals typically less than 20 nm) only exhibit magnetization
under an applied magnetic field. Under these conditions they may
heat due to Neelian (i.e., individual atomic moment relaxation) and
Brownian (i.e., physical particle rotation) mechanisms (Etheridge M
L, Bischof J C. Ann. Biomed. Eng. 41(1):78-88, 2013; Jordan et al.
International Journal of Hyperthermia 9(1):51-68, 1993; Rosensweig
R E. Journal of Magnetism and Magnetic Materials 252:370-374,
2002). On the other hand, larger mNPs are able to maintain remnant
magnetization in the absence of an applied field (ferro- or
ferrimagnetic behavior) and can heat through hysteresis behavior.
Although the physical mechanisms differ, the dynamic heating
process for magnetic nanoparticles is described by:
u.sup.w=SAR.sub.V=[.pi..mu..sub.gfH.sup.u]*X'' (2)
where SAR.sub.V is the heating in a nanoparticle loaded volume,
.mu..sub.0 is the permeability of free space, f is the applied
frequency, H is the applied field strength and x'' is the
out-of-phase component of magnetic susceptibility. This expression
can be viewed as two terms--the power density (term in brackets,
W/m.sup.3) and susceptibility. This essentially represents the
incident power and the nanoparticles' efficiency in converting the
incident field to heat energy. The incident power is a function of
frequency and field strength only, whereas the susceptibility
depends strongly on the magnetic nanoparticles' properties, in
addition to the suspending environment and applied field. Also,
SAR.sub.V can be normalized to the nanoparticle mass (SAR.sub.Fe,
W/mg Fe) (SAR.sub.V=SAR.sub.Fe*[mNP]). Both embodiments--using
superparamagnetic nanoparticles and using ferromagnetic
nanoparticles--are reflected in this disclosure.
[0052] Both fundamental nanoparticle types (superparamagnetic and
ferromagnetic) have demonstrated significant levels of heating in
the field ranges of interest (FIGS. 5(a) and 5(b)). Referring back
to Eqn. 2, the incident power can depend on the square of the
applied field and depend directly on the applied frequency. Thus,
optimal heating can be achieved at increased field strengths, but
the applied field will also affect the magnetic nanoparticles'
susceptibility. While the superparamagnetic nanoparticles
demonstrate higher heating below 20 kA/m, ferromagnetic
nanoparticles may experience significant increases in heating at
higher applied fields. FIG. 5(c) shows that magnetic nanoparticle
aggregation and confinement can lead to changes in heating behavior
(up to a 50% reduction for the superparamagnetic nanoparticles).
While ferromagnetic nanoparticles (60-80 nm core, Micromod
Partikeltechnologie GmbH, Rostock, Germany) can heat much better on
a per nanoparticle basis than superparamagnetic nanoparticles (10
nm core, Ferrotec Corp., Santa Clara, Calif.) due to their larger
volume of iron oxide, the superparamagnetic nanoparticles may heat
better on a per mass basis (FIG. 5(d)). This may be important when
delivery and distribution of the magnetic nanoparticles within the
biomaterial are considered. Finally, magnetic behavior is known to
vary with temperature, where a significant increase in
magnetization is typically observed at very low temperatures in
bulk materials. This trend has also been observed for iron oxide
mNPs (43) and may lead to some increase in heating in the cryogenic
regime.
[0053] Systems capable of applying uniform alternating magnetic
fields in the range of interest have been demonstrated and so the
uniformity in heating may depend mainly on the magnetic
nanoparticle distribution, where volumetric heating is directly
proportional to the local magnetic nanoparticle concentration (FIG.
5(c)). One feature of nanoparticles in biomedical applications is
their ability to achieve unique biodistributions due the particles'
small relative size to that of microscopic tissue structures (Kim
et al. New Eng. J. Med 2010;363(25):2434-2443, 2010; Etheridge et
al. Nanomedicine: Nanotechnology, Biology and Medicine 9(1):1-14,
2013). Biomaterials with larger cavities such as, for example,
cardiac chambers or large arteries, also may demonstrate sufficient
internal loading and heat transfer that full biomaterial perfusion
is not necessary.
[0054] The ability to vitrify larger biomaterials typically
involves loading the biomaterial with a cryoprotective agent such
as, for example, VS55. In order to reduce the critical cooling
rates necessary, up to 1000 atm of pressure is used during cooling.
Successful thawing in bulk systems after achieving this vitrified
state, however, remains a barrier to use of the technology.
Specifically, these larger biomaterials can be damaged by
devitrification during thawing at suboptimal rates and/or thermal
cracking due to non-uniformity of the thaw. Thermal stress can
yield cracks, but annealing around the glass transition temperature
helps. This idea was subsequently pursued using VS 55 (See Table
1).
[0055] To avoid loss of structural integrity, preserved materials
must avoid cracking during freezing or thawing. Cracking may be
driven by thermal stress and/or strain within the sample.
Specifically, when a body sustains changes in temperature and is
subjected to tensile stress in a single direction, its strain
(deformation) is the sum of these contributions:
= .beta..DELTA. T + .sigma. E ( 3 ) ##EQU00002##
where .epsilon. is the strain, .beta. is the thermal expansion
coefficient, .DELTA.T is temperature change, .sigma. is the stress
and E is the Young's modulus. The thermal expansion coefficient has
been tabulated for water, tissue components, and various
cryoprotective agents in water. The differences in .beta. within
sub-domains of the tissue, compounded with the temperature changes
across a bulk system, can easily create sufficient stress within
frozen systems during thawing that lead to cracks (FIG. 1).
[0056] This disclosure describes a new approach for rapidly and
uniformly heating vitrified biomaterials through the use of
radiofrequency-excited magnetic nanoparticles. The addition of
magnetic nanoparticles in two well-known cryoprotectants is shown
to have negligible effects on their freeze-thaw behavior through
differential scanning calorimetry measurements. We then demonstrate
the ability of these mNPs to generate heating rates as high
300.degree. C./min, reducing or altogether avoiding devitrification
in the vitrified cryoprotectant samples. Finally, the
experimentally characterized heating is used to model thawing
across several length scales to demonstrate the ability of this
approach to provide rapid and uniform heating, independent of
sample size or shape.
[0057] Two exemplary cryoprotectant solutions were investigated.
Glycerol was one of the earliest cryoprotectants studied, but is
also considered fairly inefficient by today's standards. Here we
look at a 6M mixture of glycerol in 1.times. phosphate buffered
saline (PBS) (hereafter referred to as "6M glycerol"). In contrast,
"VS55" is an optimized cryoprotectant cocktail that has
demonstrated successful vitrification of many biological systems.
VS55 solution is composed of 3.1M dimethyl sulfoxide (DMSO), 2.2M
propylene glycol, and 3.1M formamide in a base Euro-Collins
solution, for a total of 8.4M. These choices of cryoprotectant
solutions should bracket a range of potential behaviors which could
be observed for cryoprotectants used in the field. Distilled water
is also included as a control reference.
[0058] The studies were conducted with commercially available
EMG-308 solution (Ferrotec Corp., Santa Clara, Calif.) composed of
10.+-.2.5 nm-diameter superparamagnetic magnetite (Fe.sub.3O.sub.4)
nanoparticles coated with an anionic surfactant in aqueous
suspension. This system has been previously shown to heat
reproducibly, providing a convenient model for study. The stock
solution was diluted in the cryoprotectant solutions to provide a
concentration of 10 mg Fe/ml. The cryoprotectant-mNP mixtures were
formulated to account for the volume of aqueous mNP solution, such
that the final mixtures were at 6M glycerol in 1.times. PBS or 8.4M
VS55 in Euro-Collins.
[0059] Both 6M glycerol and VS55 solutions have been previously
characterized through differential scanning calorimetry (DSC) and
some of the important values are summarized in Table 2.
TABLE-US-00002 TABLE 2 Thermal behavior parameters for exemplary
cryoprotectant solutions 6M Glycerol VS55 Melt Temperature
-26.degree. C. -38.degree. C. Glass Transition near -100.degree. C.
-123.degree. C. Temperature Critical Cooling Rate -85.degree.
C./min -2.5.degree. C./min Critical Warming Rate 3.2 .times.
10.sup.4.degree. C./min 50.degree. C./min
FIG. 10(a) and FIG. 10(b) illustrate a thermal trace on heating for
the two vitrified solutions, with and without nanoparticles. Two
things are apparent. First, the nanoparticles appear to have
negligible impact on the freeze-thaw behavior of the
solutions--i.e., the mNPs do not produce a significant shift in the
phase transitions experienced by each solution. Differences between
the two solutions with respect to vitrified behavior are apparent,
however. Both solutions experience a glass transition, but the
absence of any additional latent heat in the VS55 thermal trace
indicates that the solution maintained the amorphous phase without
crystallization. In contrast, the 6M glycerol solution experiences
a significant heat release during devitrification and latent heat
during melting. These heat traces were performed at a heating rate
of 150.degree. C./min, which is well above the critical warming
rate for VS55. In contrast, heating rates on the order of
10.sup.4.degree. C./min would be required to avoid devitrification
in 6M glycerol. FIG. 10(c) and FIG. 10(d) illustrate the specific
heat and densities for 6M glycerol and VS55, based on these DSC
studies or literature (Choi, J. H., and J. C. Bischof. Cryobiology
57:79-83, 2008; Choi, J. H., and J. C. Bischof. Int. J. Heat Mass
Transf. 51:640-649, 2008; Harvey, A. H. Properties of Ice and
Supercooled Water. In: CRC Handbook of Chemistry and Physics
2012-2013. Boca Raton, Fla.: CRC Press, 2012, pp. 6-12; Jimenez
Rios, J. L., and Y. Rabin. Cryobiology 52:269-283, 2006; Rios, J.
L. J., and Y. Rabin. Cryobiology 52:284-294, 2006). These values
will be important in the subsequent analysis and modeling of
heating.
[0060] Aqueous, 6M glycerol, and VS55 solutions with or without
magnetic nanoparticles were heated in a radiofrequency alternating
magnetic field (AMF) at 22.8 kA/m (peak, volume-averaged field
strength) and 360 kHz (FIG. 11(a)). The cryoprotectant solutions
were cooled down to -192.degree. C. at sufficient rates to produce
vitrification (FIG. 10(e) and FIG. 10(f)) and then quickly
transferred into the inductive coil for immediate heating inside of
a sealed plastic vial, to lessen direct losses to the environment
(FIG. 11(c)). Fine thermocouples (40-gauge, OMEGA Engineering,
Inc., Stamford, Conn.) were embedded in the samples prior to
cooling and provided continuous temperature monitoring in
conjunction with a NI-DAQ data acquisition system (National
Instruments Corp., Austin, Tex.). RF fields are expected to produce
interference in metallic thermocouples, but this was characterized
and found to be negligible in the ultrafine gauge thermocouples
used.
[0061] The sample temperature data from the control and RF heated
samples were used to estimate two values as a function of
temperature: the heating rate and the mNP SAR. The sample
temperature was acquired at a frequency of 1 Hz, so the heating
rate was calculated from the temperature difference between each
measurement point, divided by the elapsed time; and the temperature
was then taken as the average between those two points. The heating
rates (as a function of temperature) for the aqueous, glycerol, and
VS55 samples are included in FIG. 11(a-c). While losses to the
ambient, room temperature surroundings resulted in some heating in
the control samples, the RF field did not induce any additional
heating in the samples without nanoparticles. Importantly, however,
heating rates on the order of 100s.degree. C./min were achieved in
the mNP-laden samples. These heating rates were high enough to
significantly reduce devitrification in the glycerol samples (FIG.
11(b)) and avoid it in the case of VS55 (FIG. 11(c)).
[0062] To better understand IONP heating for this application, SAR
was also estimated from an energy balance on the samples,
following.sup.11:
c p ( T s ) p ( T s ) * T t ( T s ) = hA ( T s ) * ( T s - T a ) +
SAR V ( T s ) ( 4 ) ##EQU00003##
where T.sub.s is the sample temperature (f(T.sub.s) indicates a
function of sample temperature), c.sub.p and .rho. are the specific
heat and density of the solution, dT/dt is the measured heating
rate, hA is an estimated ambient loss coefficient, T.sub.a is the
ambient room temperature, and SAR.sub.V is the volumetric heating
due to the IONPs (equivalent to q''' in a typical energy balance).
The ambient loss coefficient was estimated from the control samples
by assuming SAR.sub.V=0 and solving for hA at each sample
temperature. The SAR.sub.V could then be estimated for each
radiofrequency heating case, as a function of sample temperature.
The estimated SAR for a number of cases is compared in FIG.
12(a-c).
[0063] Without wishing to be bound by any particular theory, these
results can be explained by three factors: (1) IONP aggregation,
(2) suspending phase, and/or (3) material magnetization. First,
aggregation and confinement can lead to reductions in heating at
room temperature for the magnetic nanoparticles studied.
Significant aggregation was visually observed on mixing of the
magnetic nanoparticles with the VS55 solution and this accounts for
the drop in heating observed for the room temperature VS55
suspensions (FIG. 12(b)). However, if one concentrates on the phase
transitions encountered during heating (FIG. 12(c), the
solid-liquid transition in the aqueous sample and the glass
transition in the glycerol and VS55 samples), it appears the IONPs
heat less efficiently in the more rigid phases. The IONPs heat
nearly 70% less in -5.degree. C. crystalline ice than they do
suspended in liquid water at room temperature. And while not as
significant, there also appears to be a reduction in heating
observed between the glass and liquid phases in glycerol. Finally,
IONP magnetization can influence heating, with significant heating
increases correlating with increases in material magnetization.
(Hergt et al. Magn. IEEE Trans. On 34:3745-3754, 1998; Rosensweig,
R. E. J. Magn. Magn. Mater. 252:370-374, 2002). It is also common
for the magnetization of materials to increase at lower
temperatures and this has been shown to hold true for iron oxide
nanoparticles. (O'Handley, R. C. Modern magnetic materials:
principles and applications. New York, N.Y.: Wiley, 2000, 740 pp.;
Roca et al. Nanotechnology 17:2783, 2006) This may cause the
increasing trend in heating observed at lowering temperatures
observed in some of the phases (FIG. 11(d)).
[0064] One phenomenon observed for the crystallized ice and glassy
VS55 phases is the apparent increase in SAR.sub.Fe for the 10 mg
Fe/ml case over the 5 mg Fe/ml case (FIG. 12(a)). In the absence of
interparticle interactions, SAR.sub.Fe is expected to be
independent of magnetic nanoparticle concentration. However, the
increase in SAR.sub.Fe with increased magnetic nanoparticle
concentration might suggest an inverse trend to the aggregation
effects observed at room temperature. Thus, the interacting effects
of aggregation, structure of the suspending phase, and/or
temperature-dependent magnetic behavior may be quite
complicated.
[0065] COMSOL MULTIPHYSICS (COMSOL Inc., Burlington, Mass.) was
used to compare the case of uniform volumetric heating to
convective boundary warming. A cylindrical volume was chosen as a
representative case. While this is a rather generic geometry, these
results are generally applicable to a wide range of tissue systems.
While organ geometries can vary, cryopreservation protocols are
typically performed with the organ submersed in a volume of
cryoprotectant held in a container, which is often cylindrical
(FIG. 13(a)). The cylindrical volume was simulated by a 2D
axisymmetric case where the height was equal to two times the
radius. This radius was scaled from 0.2 cm to 3 cm to demonstrate
the effects of sample size on heating. Two heating cases were
compared in a transient, conductive heat transfer simulation. For
the traditional warming case, a convective heat transfer
coefficient of h=25 W/m.sup.2-K and ambient temperature of
T.sub.a=37.degree. C. were applied to the boundary of the simulated
volume, representative of, for example, a hot water bath. For the
magnetic nanoparticle thaw case, it was assumed that the boundaries
of the volume were insulated (adiabatic, .theta.T/.theta.n=0), but
that a uniform heat generation rate (q'''=SAR.sub.V) was applied
throughout the volume. SAR.sub.V was applied based on the data in
FIG. 11 for concentrations of 5 mg Fe/ml or 10 mg Fe/ml
(SAR.sub.V=SAR.sub.Fe X [Fe]). In all cases, the volume was
initially assumed to be at -196.degree. C. and the
temperature-dependent specific heat and density were applied as
interpolation functions, based on the data for VS55 in FIG. 10. The
default "Extremely Fine" mesh settings were used and the number of
elements depended on the size of the volume simulated. The default
transient solver conditions were used.
[0066] A parametric study was used to solve each warming case for
cylindrical radii varying from 0.2 cm to 3 cm (in 0.2 cm
increments) and the minimum warming rates were compared. The
greatest risk of devitrification is around -85.degree. C. (Mehl, P.
M. Cryobiology 30:509-518, 1993; Rabin et al. Cell Preserv.
Technol. 3:169-183, 2005) and, based on diffusive mechanisms, the
slowest warming rate is typically at the center of the sample.
Therefore, the minimum warming rates are compared for the spatial
and temporal point when the center of the sample reaches
-85.degree. C. The calculated minimum warming rates are illustrated
in FIG. 13(b). While convective warming is able to produce fairly
high rates for radii dimensions on the order of 1 mm, the warming
rates are slowed dramatically for geometries that have a radius
greater than about 5 mm. In contrast, the uniform heat generation
for the magnetic nanoparticle thaw case is independent of sample
size (and shape), providing for rapid heating rates even in bulk
samples. The other benefit of uniform heat generation is
illustrated in FIG. 13(d). While a uniform temperature field is
demonstrated for the magnetic nanoparticle thaw case, significant
temperature gradients exist for the convective case, which can
produce thermal stresses.
[0067] The idealized case of uniform heat generation implies a
sufficiently uniform distribution of nanoparticles. However, there
are many cases where the magnetic nanoparticle distribution may not
be perfectly uniform. To investigate the application's sensitivity
to non-uniform particle distribution, we looked at a
one-dimensional planar case (FIG. 14(a)) where a section of tissue
with thickness L without heat generation is contained within a
semi-infinite medium subjected to a heat generation term
(SAR.sub.V). This case is analogous to an unloaded thin tissue
being submersed in a mNP-cryoprotectant solution or incomplete
perfusion of magnetic nanoparticles within a cryoprotectant-loaded
bulk tissue. Symmetry was applied along the tissue's centerline and
semi-infinite behavior was approximated by simulating the domain
out to 50.times.L, where an adiabatic boundary was applied. The
transient heat equation was then solved in MATHEMATICA (Wolfram
Research, Inc., Champaign, Ill.), for thicknesses ranging between 1
mm and 15 mm. The SAR.sub.V was calculated as above for a magnetic
nanoparticle concentration of 10 mg Fe/ml and the
temperature-dependent specific heat and density were input from an
interpolation function based on the data in FIG. 10.
[0068] The minimum heating rates were again calculated for each
case when the center reached -85.degree. C. In addition, since the
heat generation was no longer uniform, the imposed temperature
gradients produce thermal stress in the biomaterial. This was
approximated based on a modification to the "thermal shock"
equation, following:
.sigma. T = g * ( E .beta..DELTA. T 1 - v ) ( 5 ) ##EQU00004##
(Manson, S. S. NACA Rep. 1170:317-350, 1954; Steif et al. Cell
Preserv. Technol. 5:104-115, 2007) where .sigma..sub.T is the
thermal stress, g is a geometric coefficient (estimated as 0.33), E
is the modulus of elasticity (estimated as 1 GPa), .beta. is the
coefficient of thermal expansion (calculated as a function of
temperature based on data in Jimenez et al. Cryobiology 52:269-283,
2006), .DELTA.T is the maximum temperature difference in the
material, and v is Poisson's ratio (estimated as 0.2). The greatest
risk of fracture is generally around the glass transition
temperature, below which elastic behavior dominates. Thus, the
thermal stress analysis focused on temperatures below about
-123.degree. C. Above this point, the viscosity begins to decrease
dramatically and so nucleation becomes a significant challenge.
[0069] Significant additional thermal stresses induced during
cooling can exist in the vitrified biomaterial, but these are a
product of the cooling protocol and the current analysis is focused
on rewarming. More detailed thermal stress analyses can account for
thermal stress that results from cooling, but the stresses
calculated in Equation (5) should be viewed as an additional
thermal stress that results from rewarming the vitrified
material.
[0070] The minimum heating rate and thermal stress approximations
as a function of unloaded thickness (L) are included in FIG. 14(b)
and FIG. 14(c). While the non-uniformity in heating induces some
thermal stress, the material is expands upon heating and these
stresses will be compressive, so the magnitude of stress
experienced is reduced to acceptable levels. In contrast, the
minimum heating rate again appears to be the limiting factor. For
thicknesses above about 5 mm, the heating rate at the centerline
drops below the critical warming rate and some devitrification can
occur. The 5 mm thickness threshold is large enough, however, to
accommodate many thin tissues such as, for example, luminal tissues
(e.g., veins and arteries) that are typically smaller than 5 mm in
thickness. The 5 mm thickness threshold also assumes a worst case
loading. Rewarming protocols generally can allow equilibration with
not only the cryoprotectant, but allow distribution of magnetic
nanoparticles as well, so these limitations will be relaxed further
as the magnetic nanoparticles permeate even partially into the
tissue.
[0071] The present study provides data and modeling in support of a
new approach for magnetic nanoparticle thawing of cryopreserved
tissues. The use of magnetic nanoparticles for rewarming a
cryopreserved biospecimen can provide faster, more uniform heating
rates that can, in turn, reduce devitrification and/or other
detrimental effects on cryopreserved biospecimens. Further, the use
of magnetic nanoparticle to rewarm a cryopreserved biospecimen may
facilitate cryopreservation of larger systems with lower molarity
cryoprotectants, thereby reducing toxicity issues. In addition, it
is known that magnetic nanoparticle design and the applied RF field
are factors in the level of heating achieved. The magnetic
nanoparticles studied demonstrated complex behavior while heating
in the cryogenic regime. Finally, the basic experiments in
cryoprotectant solutions can be expanded to include study of the
impact on biological systems, including cellular suspensions and
simple tissue systems. This will include a characterization of
heating in these systems, as well as the effects on viability,
structure, and function.
[0072] Thus, in one aspect, this disclosure describes a
cryoprotective composition that includes a cryoprotective agent and
magnetic nanoparticles effective for thawing a cryopreserved
specimen that includes biomaterial with minimal damage to the
biomaterial. The cryoprotective agent can include any material
suitable for the cryopreservation of biomaterials. Exemplary
suitable cryoprotective agents include, for example, combinations
of alcohols, sugars, polymers and ice blocking molecules that alter
the phase diagram of water and allow a glass to be formed more
easily (and/or at higher temperatures) while also reducing the
likelihood of ice nucleation and growth during cooling or thawing.
In most cases, cryopreservative agents are not used alone, but in
cocktails. In the case of vitrification solutions, exemplary
cryopreservative cocktails are reviewed in Fahy et al. Cryobiology
48(1):22-35, 2004.
[0073] In some embodiments, the cryoprotective agent may be present
in the composition at a molarity of no more the 6 M such as, for
example, no more than 5 M, no more than 4 M, no more than 3 M, no
more than 2 M, no more than 1 M, no more than 900 mM, no more than
800 mM, no more than 700 mM, no more than 600 mM, no more than 500
mM, or no more than 250 mM.
[0074] The magnetic nanoparticles may be any magnetic nanoparticles
excitable by a radio frequency (i.e., RF susceptible
nanoparticles), including, without limitation, alternating magnetic
frequencies, or rotating magnetic frequencies, and as described
below. The magnetic nanoparticles can include one or more magnetic
elements such as, for example, iron, nickel and/or cobalt, and
compounds containing one or more atoms of a magnetic element. As
used herein, a particle may be considered a nanoparticle if it
possesses a maximum diameter of no more than one micrometer
(.mu.m), but may be incorporated as part of a structure--e.g., an
aggregate--with characteristic dimensions larger than one
micrometer. The dimensions provided herein refer to dimensions of
the nanoparticle, not the dimension of the larger structure. Thus,
the maximum diameter of a nanoparticle can be, for example, no more
than 800 nanometers (nm), no more than 700 nm, no more than 600 nm,
no more than 500 nm, no more than 450 nm, no more than 400 nm, no
more than 350 nm, no more than 300 nm, no more than 250 nm, no more
than 200 nm, no more than 150 nm, no more than 100 nm, no more than
90 nm, no more than 80 nm, no more than 70 nm, no more than 60 nm,
no more than 50 nm, no more than 40 nm, no more than 30 nm, no more
than 25 nm, no more than 20 nm, no more than 15 nm, or no more than
10 nm. A particle can be considered a nanoparticle if it possesses
a minimum diameter of at least 1 nm such as, for example, at least
2 nm, at least 3 nm, at least 4 nm, at least 5 nm, at least 6 nm,
at least 7 nm, at least 8 nm, at least 9 nm, at least 10 nm, at
least 25 nm, at least 50 nm, at least 100 nm, at least 250 nm, or
at least 500 nm. In some embodiments, the size of the magnetic
nanoparticles may include a range with endpoints defined by any
maximum diameter listed above and any minimum diameter listed above
that is smaller than the maximum diameter.
[0075] In some embodiments, the magnetic nanoparticles can include
superparamagnetic nanoparticles. In other embodiments, the magnetic
nanoparticles can include ferromagnetic nanoparticles. The
nanoparticles can have any suitable shape such as, for example,
spherical, cubical, pyramidal, etc. In some embodiments, the
magnetic nanoparticles can include a combination of any two or more
types of magnetic nanoparticles. In some embodiments, as noted
briefly above, the magnetic nanoparticles can aggregate. In such
embodiments, the magnetic nanoparticles can interact with one
another. In some of these embodiments, one can tune the aggregation
of nanoparticles to enhance or diminish the heating rate in a
particular application, as desired.
[0076] The magnetic nanoparticles can be present in the
cryoprotective composition in an amount sufficient to provide
minimum at least 0.01 mg of magnetic atoms per milliliter of the
vitrified tissue such as, for example, at least 1.0 mg/ml, at least
2.0 mg/ml, at least 3.0 mg/ml, at least 4.0 mg/ml, at least 5.0
mg/ml, at least 6.0 mg/ml, at least 7.0 mg/ml, at least 8.0 mg/ml,
at least 9.0 mg/ml, at least 10 mg/ml, at least 11 mg/ml, at least
12 mg/ml, at least 13 mg/ml, at least 14 mg/ml, at least 15 mg/ml,
at least 20 mg/ml, at least 25 mg/ml, or at least 50 mg/ml. In some
embodiments, the magnetic nanoparticles can be present in the
cryoprotective composition in an amount sufficient to provide a
maximum of no more than 100 mg/ml, no more than 75 mg/ml, no more
than 50 mg/ml, no more than 25 mg/ml, no more than 20 mg/ml, no
more than 15 mg/ml, no more than 10 mg/ml, no more than 9 mg/ml, no
more than 8 mg/ml, no more than 7 mg/ml, no more than 6 mg/ml, or
no more than 5 mg/ml. In some embodiments, the amount of the
magnetic nanoparticles in the cryoprotective composition may be
characterized as a range having endpoints defined by any minimum
amount listed above and any maximum amount listed above that is
smaller than the maximum amount.
[0077] The cryoprotective composition can be used in a method for
thawing a cryopreserved specimen that includes biomaterial with
minimal damage to the biomaterial. As used herein, "cryopreserved"
refers to a biomaterial--e.g., a tissue sample, organ, portion of
an organ, cell suspension, or cell monolayer--that has been
perfused with or suspended in a cryoprotective composition as
described herein and cooled as described in more detail below.
[0078] Also as used herein, "minimal damage" refers to an amount of
damage to the thawed biomaterial insubstantial enough so that the
biomaterial retains its desired biofunctionality when thawed. Thus,
minimal devitrification can allow for some degree of damage and the
permissible amount may vary depending upon the intended use of the
biomaterial after thawing. In this context, "damage" is a
collective term that generically refers to damage to biomaterial
that can commonly result in failed cryopreservation. Such damage
includes, for example, devitrification and/or cracking In
embodiments in which the biomaterial includes, for example, an
organ for transplantation, the thawed organ having "minimal damage"
may sustain some damage, but remains useful for transplantation
into a recipient. As another example, in embodiments in which the
biomaterial includes, for example, reproductive materials (e.g.,
ova, sperm, semen), the specimen having "minimal damage" may
include an acceptable percentage of non-viable cells while
retaining a useful percentage of viable cells.
[0079] In some embodiments, the cryopreserved biomaterial can
include biomaterial perfused with or suspended in a volume of the
cryoprotective composition having a smallest linear dimension of
0.1 mm. In some embodiments, the smallest linear dimension can be,
for example, at least 0.1 mm, at least 0.5 mm, at least 1 mm, at
least 2 mm, at least 5 mm, at least 1 cm, at least 2 cm, at least 5
cm, at least 10 cm, at least 25 cm, at least 50 cm, or at least 100
cm. In the embodiments in which the biomaterial is perfused with
the cryoprotective composition, the dimension listed above may be,
in effect, the dimension of the biomaterial. In embodiments in
which the biomaterial is suspended in a cryoprotective composition,
the dimension may reflect a vessel containing the cryopreserved
biomaterial and/or a vessel in which the cryopreserved biomaterial
was cooled.
[0080] In another aspect, this disclosure describes a biomaterial
such as, for example, an organ or a portion thereof that is
perfused with or suspended in a cryoprotective composition as
described herein. The perfused and/or suspended biomaterial may be
vitrified or thawed.
[0081] In another aspect, this disclosure describes a method of
cryopreserving a biomaterial. Generally, the method includes with a
cryoprotective composition as described herein and cooling the
perfused biomaterial to a suitable cryopreservative temperature.
Suitable cryopreservative temperatures can include, for example, a
temperature below the glass transition temperature of the
cryoprotective agent in the cryoprotective composition. As one
example, the glass transition temperature of 6 M glycerol is
-100.degree. C. Accordingly, the biomaterial may be cooled to a
maximum temperature of no more than 0.degree. C. such as, for
example, no more than -20.degree. C., no more than -40.degree. C.,
no more than -80.degree. C., no more than -100.degree. C., no more
than -120.degree. C., no more than -130.degree. C., no more than
-140.degree. C., no more than -150.degree. C., no more than
-160.degree. C., no more than -170.degree. C., no more than
-180.degree. C., no more than -190.degree. C., or no more than
-200.degree. C. In some embodiments, suitable cryopreservative
temperatures can include a minimum temperature of no less than
-220.degree. C., no less than -200.degree. C., or no less than
-150.degree. C. In some embodiments, suitable cryopreservative
temperatures can be characterized as a range having as endpoints
any maximum temperature listed above and any minimum temperature
listed above that is less than the maximum temperature. In some
embodiments, a suitable cryopreservative temperature may be the
boiling point of nitrogen, -196.degree. C. Our approach is
particularly useful in cryoprotective systems where the glass
transition is below 0.degree. C., when biomaterial may be subject
to devitrification during thawing.
[0082] The perfused biomaterial may be cooled to the
cryopreservative temperature at a rate effective for
cryopreservation. Cooling rates can promote vitrification of the
perfused biomaterial. In some embodiments, the perfused biomaterial
may be cooled at a minimum rate of at least 1.degree. C. per minute
(.degree. C./min) such as, for example, at least 2.degree. C./min,
at least 5.degree. C./min, at least 10.degree. C./min, at least
15.degree. C./min, at least 20.degree. C./min, at least 25.degree.
C./min, at least 30.degree. C./min, at least 40.degree. C./min, at
least 50.degree. C./min, at least 60.degree. C./min, at least
70.degree. C./min, at least 100.degree. C./min, at least
1000.degree. C./min, or multiple thousands .degree. C./min. In some
embodiments, the perfused biomaterial may be cooled at a maximum
rate of no more than 100.degree. C./min such as, for example, no
more than 80.degree. C./min, no more than 60.degree. C./min, no
more than 50.degree. C./min, no more than 40.degree. C./min, no
more than 30.degree. C./min, or no more than 20.degree. C./min. In
some embodiments, the cooling rate may be within a range of cooling
rate having endpoints defined by any minimum cooling rate listed
above and any maximum cooling rate listed above that is greater
than the minimum cooling rate. In embodiments involving larger
systems, the cooling process can involve use of a high pressure
freezing vial as described by Fahy et al. Cryobiology
48(2):157-178, 2004. Added pressure--e.g., up to 1000 atm--can
reduce the ability of ice to nucleate and grow within the sample
during cooling. However, samples cooled in this manner can require
rapid thawing to avoid devitrification and cracking.
[0083] In yet another aspect, this disclosure describes a method of
thawing a cryopreserved biomaterial. Generally, the method includes
obtaining a biomaterial cryopreserved with a cryopreservative
composition as described herein, and subjecting the cryopreserved
biomaterial to electromagnetic energy of an intensity, and for a
duration, effective to thaw the biomaterial. In some embodiments,
the biomaterial may exhibit minimal devitrification, as defined
herein, while being thawed.
[0084] In some embodiments, the electromagnetic energy can include
a radio frequency field, alternating magnetic field, or rotating
magnetic field. In such embodiments, the electromagnetic energy can
exhibit a minimum frequency of no more than 1 MHz such as, for
example, no more than 750 Hz, no more than 500 Hz, no more than 375
Hz, no more than 300 Hz, no more than 250 Hz, no more than 225 Hz,
no more than 200 Hz, no more than 175 Hz, no more than 150 Hz, no
more than 125 Hz, no more than 100 Hz, no more than 75 Hz, or no
more than 50 Hz. In some embodiments, the radio frequency field can
exhibit a maximum frequency of at least 1 Hz such as, for example,
at least 5 Hz, at least 10 Hz, at least 25 Hz, at least 50 Hz, at
least 75 Hz, at least 100 Hz, at least 125 Hz, at least 150 Hz, at
least 175 Hz, at least 200 Hz, at least 225 Hz, or at least 250 Hz.
In some embodiments, the radio frequency field may be characterized
by a range of frequencies having as endpoints any minimum frequency
listed above and any maximum frequency listed above that is greater
than the minimum frequency and may be time-dependent. In some
embodiments, for example, the radio frequency field may range from
about 175 Hz to about 375 Hz. In another particular example, the
radio frequency field may range from 100 Hz to about 500 Hz.
[0085] In some embodiments, the radio frequency field may have a
minimum strength of at least 1 kA/m such as, for example, at least
5 kA/m, at least 10 kA/m, at least 20 kA/m, at least 30 kA/m, at
least 50 kA/m, at least 75 kA/m, or at least 100 kA/m. In some
embodiments, the radio frequency filed may have a maximum strength
of no more than 200 kA/m such as, for example, no more than 150
kA/m, no more than 100 kA/m, no more than 80 kA/m, no more than 50
kA/m, or no more than 25 kA/m. In some embodiments, the strength of
the radio frequency field may be characterized as a range having as
endpoints any minimum strength listed above and any maximum
strength listed above that is greater than the minimum strength and
may be time-dependent. In some embodiments, the radio frequency
field may have a strength of from about 10 kA/m to about 100 kA/m.
In one particular embodiment, the radio frequency filed can have a
strength of 24 kA/m.
[0086] In some embodiments, the biomaterial may be warmed at a
minimum rate of at least 50.degree. C./min such as, for example, at
least 75.degree. C./min, at least 100.degree. C./min, at least
125.degree. C./min, at least 150.degree. C./min, at least
175.degree. C./min, at least 200.degree. C./min, at least
225.degree. C./min, at least 250.degree. C./min, at least
275.degree. C./min, or at least 300.degree. C./min. In some
embodiments, the biomaterial may be warmed at a maximum rate of no
more than 100,000.degree. C./min such as, for example, no more than
1500.degree. C./min, no more than 1000.degree. C./min, no more than
750.degree. C./min, no more than 500.degree. C./min, no more than
400.degree. C./min, no more than 300.degree. C./min, no more than
250.degree. C./min, no more than 200.degree. C./min, no more than
175.degree. C./min, or no more than 150.degree. C./min. In some
embodiments, the biomaterial may be warmed at a rate within a range
having endpoints defined by any minimum rate listed above and any
maximum rate listed above that is greater than the minimum rate. In
certain embodiments, the biomaterial may be warmed at a rate of
about 300.degree. C./min. In other particular embodiments, the
biomaterial may be warmed at a rate of about 225.degree. C./min or
about 175.degree. C./min.
[0087] In some embodiments, the biomaterial may be warmed at a
constant rate throughout the biomaterial according to Equation (1),
above. As used herein, "constant rate throughout the biomaterial"
refers to a temperature gradient of no more than 1 .degree. C./m
across the biomaterial such as, for example, no more than 1.degree.
C./cm across the biomaterial or no more than 1.degree. C./mm across
the biomaterial.
[0088] In the preceding description, the term "and/or" means one or
all of the listed elements or a combination of any two or more of
the listed elements; the terms "comprises" and variations thereof
do not have a limiting meaning where these terms appear in the
description and claims; unless otherwise specified, "a," "an,"
"the," and "at least one" are used interchangeably and mean one or
more than one; and the recitations of numerical ranges by endpoints
include all numbers subsumed within that range (e.g., 1 to 5
includes 1, 1.5, 2, 2.75, 3, 3.80, 4, 5, etc.).
[0089] Also in the preceding description, particular embodiments
may be described in isolation for clarity. Unless otherwise
expressly specified that the features of a particular embodiment
are incompatible with the features of another embodiment, certain
embodiments can include a combination of compatible features
described herein in connection with one or more embodiments.
[0090] For any method disclosed herein that includes discrete
steps, the steps may be conducted in any feasible order. And, as
appropriate, any combination of two or more steps may be conducted
simultaneously.
[0091] Compositions and methods are illustrated by the preceding
description. It is to be understood that the particular examples,
materials, amounts, and procedures are to be interpreted broadly in
accordance with the scope and spirit of the invention as set forth
herein.
EXAMPLES
Differential Scanning Calorimetry Methods
[0092] The freeze-thaw behavior of 6M glycerol (Sigma-Aldrich, St.
Louis, Mo.) and VS55 Rall W F, Fahy G M. Nature 313(6003):573-575,
1985), both with and without the addition of 10 mg Fe/ml
nanoparticles, was measured with a Diamond differential scanning
calorimeter (PerkinElmer Inc., Waltham, Mass.) from -150.degree. C.
to 25.degree. C. Ten milligram samples were placed in aluminum
sample pans. Water, sapphire, and an empty sample pan were used as
calibration standards during each day of measurements. All
experimental measurements were repeated for n=3. The samples were
cooled at -150.degree. C./min to ensure complete vitrification of
the cryoprotectant samples.
[0093] Various warming rates were included in the preliminary
investigations (5.degree. C./min, 20.degree. C./min, 50.degree.
C./min, 100.degree. C./min, and 150.degree. C./min) to verify
previously observed freeze-thaw behaviors--i.e., phase transitions
and critical warming rates. The heat flows for heating rate and
cooling rate were calibrated for cyclohexane and n-decane. The DSC
protocols (Choi, J., and J. C. Bischof. Cryobiology 60:52-70, 2010;
Choi, J. H., and J. C. Bischof. Cryobiology 57:79-83, 2008; Choi,
J. H., and J. C. Bischof. Int. J. Heat Mass Transf. 51:640-649,
2008) included two-minute hold times at the end-point temperatures
between each ramping period. The specific heat for VS55 was
characterized between -150.degree. C. and 25.degree. C. for a
heating rate of 50.degree. C./min. The specific heats of pure
water/ice and pure glycerol also were measured following the same
protocol, to provide quantitative reference standards. The
measurement protocol demonstrated good agreement for both
standards.
[0094] The enthalpy measured by DSC included some latent heat
associated with the glass transition and a small amount of melting
(50.degree. C./min is just below the critical warming rate for
VS55). The baseline specific heat of VS55 was then extracted based
on methods previously described in Choi, J., and J. C. Bischof.
Cryobiology 60:52-70, 2010; Choi, J. H., and J. C. Bischof.
Cryobiology 57:79-83, 2008; Choi, J. H., and J. C. Bischof. Int. J.
Heat Mass Transf. 51:640-649, 2008; and Etheridge et al. J.
Biomech. Eng. 135:021001: 1-10, 2013. Results are shown in FIG. 15.
The density for VS55 included in FIG. 10(d) was estimated based on
the experimentally determined thermal expansion coefficient for
VS55, as a function of temperature, extrapolating from the room
temperature density measured at 1069 kg/m.sup.3, as described in
Jimenez Rios, J. L., and Y. Rabin. Cryobiology 52:269-283,
2006.
Cryoprotectant Cooling Protocols
[0095] The very high critical cooling rate required to vitrify 6M
glycerol (-85.degree. C./min) necessitated direct quenching in
liquid nitrogen. While this did provide rapid cooling, the extreme
gradients experienced also produced significant cracking in the
sample (FIG. 10(e)). The lower critical cooling limits for VS55
(-2.5.degree. C./min) allowed for a more nuanced approach. While
the samples were still cooled in a liquid nitrogen bath, they were
first placed in a series of containers which provided several
plastic and air barriers that insulated the cooling rate (FIG.
11(a)). In addition, the sample temperature was closely monitored
and when it reached the glass transition, the innermost sample
container was removed and held out in the room temperature air for
30 seconds, wiped of any frost that had formed (with a gloved
hand), and then returned to the cooling container. This process
repeatedly produced about a 10.degree. C. increase in the sample
temperature before cooling resumed (FIG. 16(b)). This should
produce an "annealing" effect in the sample, in which some of the
thermal stresses induced during cooling are relaxed. Through this
process, the VS55 samples were successfully cooled to -192.degree.
C. while maintaining an amorphous state without cracking (FIG.
10(f)).
Validation of Thermocouple Measurements
[0096] Fiber optic thermometry systems are typically used for RF
heating measurements, but the plastic probes used with these
devices are not rated for use down to cryogenic temperatures. It
was therefore necessary to use thermocouples in these studies.
However, the strong inductive fields used for heating the mNPs also
may produce significant coupling with metals, so we characterized
the interference produced in the (type T, copper-constantan)
thermocouples. Two investigations demonstrated negligible
interference with the ultrafine (40-gauge) thermocouples chosen
(OMEGA Engineering, Inc., Stamford, CT). The thermocouples were
calibrated at three phase transition temperatures before any
measurements were made (liquid nitrogen at -196.degree. C., ice
bath at 0.degree. C., and boiling water at 100.degree. C.).
[0097] First, metals in an inductive field were subjected to
heating. A thermocouple was sandwiched between two pieces of
insulation and the tip was centered in the inductive coil. While
the thermocouples did experience almost 6.degree. C. of heating
under these conditions (FIG. 17(a)), the thermal mass of the wires
is extremely low and so this equates to an energy of only about 0.5
millijoules. Under the actual experimental conditions, the heat
generated in the tip is quickly transferred into the surrounding
medium, where this small amount of energy has negligible impact on
the measured temperature.
[0098] Second, the electrical currents generated in the inductive
field also may interfere with the fundamental operation of the
thermocouples, which is based on changes in electrical potential.
To characterize this, the thermocouples were placed in an
uninsulated, 1 ml sample of room temperature water in a cryovial,
along with a fluoroptic temperature probe (Luxtron Inc., Santa
Clara, Calif.), and this was placed in the inductive coil. When the
field was activated, no noticeable increase in noise was observed
(FIG. 17(b)). While the fluoroptic probe did not indicate any
temperature change, a 0.2-0.3.degree. C. temperature offset was
observed for the thermocouples. This may be due, at least in part,
to a combination of the thermocouple heating and interference
effects. The practical impact, however, is negligible over the
large temperature range analyzed in these studies.
One-Dimensional, Non-Uniform Heating Analysis
[0099] The following system of partial differential equations was
solved numerically in MATHEMATICA (Wolfram Research, Inc.,
Champagne, Ill.) utilizing the NDSolve function, based on the
problem formulation presented in FIG. 14(a).
[0100] The complete disclosure of all patents, patent applications,
and publications, and electronically available material cited
herein are incorporated by reference in their entirety. In the
event that any inconsistency exists between the disclosure of the
present application and the disclosure(s) of any document
incorporated herein by reference, the disclosure of the present
application shall govern. The foregoing detailed description and
examples have been given for clarity of understanding only. No
unnecessary limitations are to be understood therefrom. The
invention is not limited to the exact details shown and described,
for variations obvious to one skilled in the art will be included
within the invention defined by the claims.
[0101] Unless otherwise indicated, all numbers expressing
quantities of components, molecular weights, and so forth used in
the specification and claims are to be understood as being modified
in all instances by the term "about." Accordingly, unless otherwise
indicated to the contrary, the numerical parameters set forth in
the specification and claims are approximations that may vary
depending upon the desired properties sought to be obtained by the
present invention. At the very least, and not as an attempt to
limit the doctrine of equivalents to the scope of the claims, each
numerical parameter should at least be construed in light of the
number of reported significant digits and by applying ordinary
rounding techniques.
[0102] Notwithstanding that the numerical ranges and parameters
setting forth the broad scope of the invention are approximations,
the numerical values set forth in the specific examples are
reported as precisely as possible. All numerical values, however,
inherently contain a range necessarily resulting from the standard
deviation found in their respective testing measurements.
[0103] All headings are for the convenience of the reader and
should not be used to limit the meaning of the text that follows
the heading, unless so specified.
* * * * *