U.S. patent application number 14/027804 was filed with the patent office on 2014-01-16 for noninvasive, continuous in vitro simultaneous measurement of turbidity and concentration.
This patent application is currently assigned to SYRACUSE UNIVERSITY. The applicant listed for this patent is Joseph Chaiken, Jerry Goodisman. Invention is credited to Joseph Chaiken, Jerry Goodisman.
Application Number | 20140016117 14/027804 |
Document ID | / |
Family ID | 49913749 |
Filed Date | 2014-01-16 |
United States Patent
Application |
20140016117 |
Kind Code |
A1 |
Chaiken; Joseph ; et
al. |
January 16, 2014 |
NONINVASIVE, CONTINUOUS IN VITRO SIMULTANEOUS MEASUREMENT OF
TURBIDITY AND CONCENTRATION
Abstract
The invention provides a method of determining turbidity and
concentration simultaneously a sample by irradiating the sample
with a single incident wavelength and simultaneously measuring
wavelength shifted (IE) and unshifted (EE) light emitted. A
relative volume of light emitted from two phases may be determined,
wherein the two phases comprise a first Rayleigh and Mie scattering
and fluorescent phase associated with suspended particles, and a
second, non-scattering but fluorescent phase associated with
suspending solution. Volumes of the phases and/or concentrations of
specific fluorophores or Raman active species are calculated from
the volume of light emitted by the first phase relative to the
total volume of light emitted from the first and second phases.
Inventors: |
Chaiken; Joseph;
(Fayetteville, NY) ; Goodisman; Jerry; (Syracuse,
NY) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Chaiken; Joseph
Goodisman; Jerry |
Fayetteville
Syracuse |
NY
NY |
US
US |
|
|
Assignee: |
SYRACUSE UNIVERSITY
Syracuse
NY
|
Family ID: |
49913749 |
Appl. No.: |
14/027804 |
Filed: |
September 16, 2013 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
12889396 |
Sep 23, 2010 |
8538499 |
|
|
14027804 |
|
|
|
|
61245020 |
Sep 23, 2009 |
|
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Current U.S.
Class: |
356/51 ; 250/574;
356/72 |
Current CPC
Class: |
A61B 5/14535 20130101;
A61B 5/1455 20130101; G01N 21/49 20130101; G01N 21/6486 20130101;
A61B 5/14532 20130101 |
Class at
Publication: |
356/51 ; 356/72;
250/574 |
International
Class: |
G01N 21/49 20060101
G01N021/49; G01N 21/64 20060101 G01N021/64 |
Claims
1. A method of simultaneously obtaining a turbidity and
concentration from an in vitro sample comprising: irradiating the
sample with a single incident wavelength on a sample having a fluid
and particles suspended in the fluid; simultaneously measuring
wavelength shifted (IE) and unshifted (EE) light emitted from the
tissue; and determining a relative volume of light emitted from two
phases, wherein the two phases comprise a first Rayleigh and Mie
scattering and fluorescent phase associated with suspended
particles, and a second, non-scattering phase associated with the
fluid, wherein the percentage of suspended particles is calculated
from the volume of light emitted by the first phase (.PHI.r)
relative to the total volume of light emitted from the first and
second phases (.PHI.r+.PHI.p), wherein the determining comprises
calculating: .phi. r / ( .phi. r + .phi. p ) [ 5 ] .phi. r = a + (
b EE EE 0 ) + ( c IE IE 0 ) wherein [ 8 ] .phi. p = d + ( e EE EE 0
) + ( f IE IE 0 ) [ 9 ] EE = 1 + 2 .phi. p + 3 .phi. r [ 6 ] IE = 4
+ 5 .phi. p + 6 .phi. r [ 7 ] ##EQU00004## and wherein EE is total
elastically (unshifted) emitted light, IE is total inelastically
(shifted) emitted light, .sub.1 and .sub.4 are the fractions of EE
and IE, respectively, from the background; .sub.2 and .sub.5 are
the fractions of EE and IE, respectively, from the fluid; .sub.3
and .sub.6 are the fractions of EE and IE, respectively, from the
suspended particles; and .sub.1-6 are calculated numerically using
the radiative transport equation (RTE) to determine EE and IE as a
function of .phi..sub.r and .phi..sub.p; wherein EE.sub.o and
IE.sub.o are average values of EE and IE over a calibration time
period; and wherein a-f are obtained by inverting equations [6] and
[7] to express .phi..sub.r and .phi..sub.p in terms of EE and
IE.
2. The method of claim 1, wherein the incident wavelength is
280-2500 nm.
3. The method of claim 2, wherein the incident wavelength is 632,
405, 670, 450, 785, 805 or 830 nm.
4. The method of claim 1, wherein the step of simultaneously
measuring wavelength shifted (IE) and unshifted (EE) light emitted
from the background is at a shift of 500-1800 cm-1 relative to the
incident wavelength for shifted light, and at -30-+10 cm-1 for
unshifted light.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation-in-part of U.S.
application Ser. No. 12/889,396, filed on Sep. 23, 2010, which
claims the benefit of U.S. Provisional Application No. 61/245,020,
filed on Sep. 23, 2009, both of which are hereby incorporated by
reference in their entireties.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The present invention relates to the measurement of
suspended matter in a solution and, more particularity, to the
measurement of turbidity in an in vivo sample.
[0004] 2. Description of the Related Art
[0005] Algal biofuel production is a process that has received much
attention as a more environmentally friendly renewable energy
source. The algae growth starts with proliferation where the cells
multiply and ends with profusion by the production of fats which
can be generated into biofuels. The growth of the algae culture is
currently determined by removing an aliquot, which could
potentially contaminate the culture. Accordingly, there is a need
for a way to non-invasively measure the amount of suspended
material in a sample.
BRIEF SUMMARY OF THE INVENTION
[0006] The present invention provides a method of determining
turbidity in an in vitro sample. The method comprises irradiating a
sample with a single incident wavelength and simultaneously
measuring wavelength shifted (IE) and unshifted (EE) light emitted
from the sample. The method further comprises determining a
relative volume of light emitted from two phases, wherein the two
phases comprise a first Rayleigh and Mie scattering and fluorescent
phase associated with suspended particles, and a second,
non-scattering phase associated with the supporting solution. As an
example, the apparatus and algorithms disclosed in the parent
application measure hematocrit (Hct) and plasma volume (Op)
noninvasively in the blood in vivo and are thus being applied to
measuring turbidity in in vitro sample using the apparatus and
algorithms with or without some minor modifications.
[0007] In a typical embodiment, the incident wavelength is 280-2500
nm. In some embodiments, the incident wavelength is 785, 805 or 830
nm. The measuring is typically at 500-1800 cm.sup.-1 for Stokes
shifted light, and at -30-+10 cm.sup.-1 for unshifted light.
[0008] In one embodiment, the determining comprises calculating the
turbidity as:
.phi. r / ( .phi. r + .phi. p ) [ 5 ] wherein .phi. r = a + ( b EE
EE 0 ) + ( c IE IE 0 ) [ 8 ] .phi. p = d + ( e EE EE 0 ) + ( f IE
IE 0 ) [ 9 ] EE = 1 + 2 .phi. p + 3 .phi. r [ 6 ] IE = 4 + 5 .phi.
p + 6 .phi. r [ 7 ] ##EQU00001##
[0009] and wherein EE is total elastically (unshifted) emitted
light, IE is total inelastically (shifted) emitted light, .sub.1
and .sub.4 are the fractions of EE and IE, respectively, from
static tissue; .sub.2 and .sub.5 are the fractions of EE and IE,
respectively, from suspended particles, such a blood cells; .sub.3
and .sub.6 are the fractions of EE and IE, respectively, from the
supporting fluid, such as plasma; and .sub.1-6 are calculated
numerically using the radiative transport equation (RTE) using
optical and geometric parameters appropriate to the tissue and
instrumentation appropriate to the specific probing, to determine
EE and IE as a function of .phi..sub.r and .phi..sub.p; wherein
EE.sub.o and IE.sub.o are calculated or measured average values of
EE and IE over a calibration time period that depends on the laser
power and volume of tissue probed under a reference condition.
Values for a-f can be obtained by inverting equations [6] and [7]
to express .phi..sub.r and .phi..sub.p in terms of EE and IE.
[0010] The invention provides an apparatus for measuring turbidity
in a sample. The apparatus comprises a means for irradiating the
sample with a single incident wavelength; a means for
simultaneously measuring wavelength shifted and unshifted light
emitted from the sample; and means for determining a relative
volume of light emitted from two phases, wherein the two phases
comprise a first predominantly Rayleigh and Mie scattering and
fluorescent phase associated with suspended particles, and a
second, non-scattering fluorescent phase associated with the fluid
medium. Typically, the apparatus also includes means for
calculating a volume fraction of suspended particles relative to
the total volume of suspended parties and fluid medium.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)
[0011] The present invention will be more fully understood and
appreciated by reading the following Detailed Description in
conjunction with the accompanying drawings, in which:
[0012] FIG. 1 is a graph of intensity verses frequency showing the
EE and IE regions regions;
[0013] FIG. 2 is a series of graphs showing the linear relationship
with respect to quarts spheres in an Example of the present
invention;
[0014] FIG. 3 is a series of graphs showing the relationship with
respect to porphyrin in an Example of the present invention;
[0015] FIG. 4 is a graph showing IE dependence on the volume
fraction of quartz spheres at various concentrations of porphyrin
and the fit [P] and .phi..sub.Q are compared to the expected values
from FIGS. 2 and 3;
[0016] FIG. 5 is a graphs showing EE dependence on the
concentration of porphyrin at various volume fractions of quartz
spheres with the expected values compared to the fitted values
calculated from equations [10] and [11];
[0017] FIG. 6 is a series of graphs showing a comparison between
the expected and the calculated values of A) .phi..sub.Q and B)
[P];
[0018] FIG. 7 is a series of images of quartz spheres settling with
0.0111% v/v spheres and 9.92E.sup.-5M porphyrin`
[0019] FIG. 8 is a series of images of sample 2 quartz spheres
settling with 0.00185% v/v spheres and 9.92E.sup.-5 M porphyrin
[0020] FIG. 9 is a series sample 3 quartz spheres settling with
0.0111% v/v spheres and 1.488E.sup.-4 M porphyrin;
[0021] FIG. 10 is a series of graphs showing A) IE and B) EE
measurements over time as the quartz spheres settle out of the
probed region;
[0022] FIG. 11 is a series of graphs showing calculated A)
.quadrature.Q and B) [P] over time as the quartz spheres settled
out of the probed region.
DETAILED DESCRIPTION OF THE INVENTION
[0023] Referring now to the drawings, wherein like reference
numerals refer to like parts throughout, the present invention
comprises the apparatus and algorithm of U.S. application Ser. No.
12/889,396, hereby incorporated by reference, which was used to
accurately determine hematocrit in vivo. The apparatus and
algorithm of present invention may also be used to evaluate certain
in vitro measurements, such as turbidity.
[0024] The present invention involves apparatus and a mathematical
algorithm to take measurements produced by the apparatus and report
the relative fractions of two phases present in a system. The
phases are distinguished by differing indices of refraction,
densities, light absorption and emission characteristsics and
chemical constitution. The apparatus includes a laser that shines
one color into a sample as well as optics to collect the light that
is remitted by the sample. Preferably, the apparatus of the present
invention comprises a source for delivering an incident wavelength
of about 280-2500 nm. In some embodiments, the incident wavelength
may be 405, 450, 632, 670, 785, 805 830, or 940 nm. The collected
light must be separated into two parts, one part having the same
color as the incident laser and the other having a different color.
Thus, the optics detector must be capable of measuring at about
500-1800 cm.sup.-1 for shifted light, and at about -30-+10 cm
.sup.-1 for unshifted light. The basic principle is that the amount
of same color emitted light is strongly affected by the presence of
physical objects that scatter the light without changing color and
the amount of color shifted light produced depends on the presence
of some chemical species and spectroscopic processes that depend on
the internal energy levels of one or more molecules.
[0025] Because both shifted and unshifted light can be collected
simultaneously, two pieces of independent information are obtained
about the sample. There are two equations in the algorithm from
classical radiation transfer theory that relate the presence of the
two phases to the two pieces of information. As a result, the
invention includes two independent equations having two variables
that are inverted to give the two volume fractions for the two
phases. Knowledge of the two volume fractions constitutes the end
product of the invention, which can in turn be used to accomplish
many useful tasks, such as measuring hemocrit in vivo or turbidity
in an in vitro sample.
[0026] The algorithm of the present invention comprises calculating
the turbidity as:
.phi. r / ( .phi. r + .phi. p ) [ 5 ] wherein .phi. r = a + ( b EE
EE 0 ) + ( c IE IE 0 ) [ 8 ] .phi. p = d + ( e EE EE 0 ) + ( f IE
IE 0 ) [ 9 ] EE = 1 + 2 .phi. p + 3 .phi. r [ 6 ] IE = 4 + 5 .phi.
p + 6 .phi. r [ 7 ] ##EQU00002##
[0027] and wherein EE is total elastically (unshifted) emitted
light, IE is total inelastically (shifted) emitted light, .sub.1
and .sub.4 are the fractions of EE and IE, respectively, from
static tissue; .sub.2 and .sub.5 are the fractions of EE and IE,
respectively, from suspended particles, such as red blood cells;
.sub.3 and .sub.6 are the fractions of EE and IE, respectively,
from the supporting fluid, such as plasma; and .sub.1-6 are
calculated numerically using the radiative transport equation (RTE)
using optical and geometric parameters appropriate to the tissue
and instrumentation appropriate to the specific probing, to
determine EE and IE as a function of .phi..sub.r and .phi..sub.p;
wherein EE.sub.o and IE.sub.o are calculated or measured average
values of EE and IE over a calibration time period that depends on
the laser power and volume of sample probed under a reference
condition. Values for a-f can be obtained by inverting equations
[6] and [7] to express .phi..sub.r and .phi..sub.p in terms of EE
and IE.
[0028] As seen in FIG. 1, Raman spectroscopy measures the change in
energy between light entering the sample and the light that is
emitted. Light emitted with the same energy is elastically
scattered (EE) whereas light emitted with a different energy is
inelastically scattered (IE). The EE and IE can be analyzed as
independent simultaneous measurements due to being caused by
fundamentally different processes. FIG. 1 demonstrates a typical
spectrum and defines the regions of the spectrum corresponding to
EE and IE.
[0029] In U.S. application Ser. No. 12/889,396, the present
invention was used to determine hemocrit based on the intensity of
scattered radiation from all three phases that is detected outside
the skin, given volume fractions, absorption coefficients, and
scattering coefficients for the three phases. The present invention
also accounts for the variation in detected intensity with
geometric parameters (placement of source and detector, etc.) and
changes in volume fractions.
[0030] For example, based on experiences with a range of actual
skin types and a specific experimental apparatus, for the base
calculation, geometric parameters are used as follows: The dome
formed when the fingertip is brought into registration with the
0.21 mm diameter optical aperture is assumed to be a spherical cap
with radius 0.1 cm and height 0.005 cm. The origin of coordinates
is in the center, 0.005 cm below the top of the dome. The angle
between the direction of the incoming beam and the vertical is
0.980 radians, and the origin of the beam is chosen so that the
center of the beam crosses the skin surface at the top of the dome
(actually at x=.quadrature.0.0025404 cm, y=0.004997 cm). The
detector center is at x=0.015 cm, y=0.013 cm.
[0031] The values of the parameters characterizing the skin for the
simulations are given in Tables 1 and 2. The parameters used in
calibrating the algorithm in this description are given in Table 3
and are somewhat different from those in Table 2. The differences
were based on the original authors' indications of the effect of
isolating the tissues from their normal in vivo setting and were
needed to obtain agreement with empirical observations. It should
not be assumed that the parameters given are necessarily
optimized.
[0032] The volume fractions in Table 1 are based on estimates of
the average capillary density, dimensions and a hematocrit of 0.10
for the blood in the most vascularized second layer. The third
layer was given 10% of the total blood fraction of the second
layer, i.e. from the top of the capillary loops down to the
superficial dermal plexus, consistent with medium to deep dermis.
The calculations show that, for all three phases, the contribution
of layer c is much less than that of layers a and b, so that the
assumptions made for layer c are not critical. Even if the total
blood fraction is assumed to be as high as 0.05, the scattering
length is very long compared with the dimensions of the layers and
the single scattering limit is appropriate. For the calibration of
the algorithm given below, volume fractions used were consistent
Jacques' estimates for well perfused skin, as would be appropriate
to fingertips. The estimates in Table 1 are more appropriate of
forearm skin.
TABLE-US-00001 TABLE 1 Assumed volume fractions of the three phases
in the three layers Phase Layer a Layer b Layer c p = plasma 0.00
0.0072 0.001200 r = red blood cells 0.00 0.0008 0.000133 t = static
tissue 1.00 0.9920 0.998667
TABLE-US-00002 TABLE 2 Absorption and scattering coefficients for
the three phases Elastic Inelastic (Rayleigh) (fluorescence)
Absorption scattering scattering Phase coefficient coefficient
coefficient r = rbc .alpha..sub.r = 4.5 cm.sup.-1 .mu..sub.r = 300
cm.sup.-1 4.5 cm.sup.-1 p = plasma .alpha..sub.p = 0.3 cm.sup.-1
.mu..sub.p = 0.60 cm.sup.-1 0.30 cm.sup.-1 t = static tissue
.alpha..sub.t = 5 cm.sup.-1 .mu..sub.t = 12 cm.sup.-1 5
cm.sup.-1
[0033] In the present invention, the sum of the absorption and
inelastic scattering coefficients, weighted by phase volume
fractions, are added to give the attenuation coefficient for each
layer. The calculated elastic scattering intensity from each phase
is proportional to the corresponding elastic scattering
coefficient, and the inelastic scattering intensity is proportional
to the inelastic scattering coefficient times a quantum yield. The
volume fractions (see Table 1) add up to unity, implying that there
are no voids.
[0034] This is summarized in equations [1] and [2] using .phi. for
each of the volume fractions, i.e. RBCs, plasma and static
tissue.
1=.phi..sub.r+.phi..sub.p+.phi..sub.s [1]
0=d.phi..sub.r+d.phi..sub.p+d.phi..sub.s [2]
[0035] Good agreement between theory and experiment was obtained by
summing the contributions from each phase and each layer.
Obviously, one can measure only the total elastic and inelastic
scattering, but one can calculate the separate contributions, as
shown below. It is clear that, because of the increased path length
and attenuation, the contribution of layer c is unimportant. The
calculations show that the scattering from any phase is a linear
function of the volume fraction of that phase in layer b. Thus, it
is the blood volume fractions in layer b that are measured; the
hematocrit involves volume fractions in layer b.
Hct=.phi..sub.r/(.phi..sub.r+.phi..sub.p) [3]
[0036] Based on the results of many calculations with the model, it
is assumed that the observed elastic and inelastic scattering
intensities are linear functions of the volume fractions of the
three phases in layer b. Using [1], one may write this as
EE=.sub.1+.sub.2.phi..sub.p+.sub.3.phi..sub.r [4]
IE=.sub.4+.sub.5.phi..sub.p+.sub.6.phi..sub.r [5]
[0037] The linear dependence is both direct (the amount of
scattering from any phase at any point is proportional to the
volume fraction of that phase at that point) and indirect (the
scattering is proportional to the incident light intensity, which
is determined by the attenuation, and the light reaching the
detector is attenuated as well). It is important to note that the
observed values of EE and IE depend on how they are measured and
geometrical parameters of the system. In particular, the yield of
measured scattered photons depends on the probed volume, the
frequency range considered, and the incident laser flux. However,
relations between the first three .sub.j and relations between the
second three .sub.j can be obtained from the model
calculations.
[0038] A series of calculations using the model were performed to
obtain elastic and inelastic scattering with values of .phi..sub.r
and .phi..sub.p centered around 0.004 and 0.036 respectively.
(.mu..sub.t=25, .alpha..sub.r=150, quantum yield=1E-5). It was
verified that both calculated elastic and calculated inelastic
scatterings were linear in the volume fractions
(r.sup.2.gtoreq.0.999). The best bilinear fits were (C indicates
calculated quantities):
EC=0.0.313583-0.108563.phi..sub.r+0.0452094.phi..sub.p
IE=(0.631030+14.83102.phi..sub.r4+0.263197.phi..sub.p).times.10.sup.-5
[0039] Since EE is proportional to EC and IE is proportional to IC,
the ratios of .sub.2 and .sub.3 to .sub.1, and the ratios of .sub.5
and .sub.6 to .sub.4 are now known. One can thus write;
EE=.sub.1(1+0.144427346202.phi..sub.p-0.346202.phi..sub.r) [6]
IE=.sub.4(1-2.298501.phi..sub.p+20.889993.phi..sub.r) [7]
[0040] And that leaves only two parameters to be determined. These
are essentially normalizing parameters. Since the calculations
refer to .phi..sub.r=0.0040 and 100 .sub.p=0.0360,
.sub.1=EE.sub.0/1.003815 and .sub.4=IE.sub.0/1.000814, where
EE.sub.0 and IE.sub.0 are measured at some reference point with
respect to the measurement conditions, i.e. a particular applied
pressure relative to the test subject's diastolic and systolic
blood pressures or perhaps a particular temporal position with
respect to the cardiac pulse. Any choice should be based on
measurement conditions that actually produce the assumed set of
volume fractions defining the model calculation.
[0041] Solving [6] and [7] for the volume fractions gives
.phi. r = 1.034740 ( 1.003815 EE EE 0 - 1 ) + 0.065018 ( 1.000814
IE IE 0 - 1 ) [ 8 ] .phi. p = 9.404260 ( 1.003815 EE EE 0 - 1 ) +
0.1558538 ( 1.000814 IE IE 0 - 1 ) [ 9 ] ##EQU00003##
[0042] The Hct is then given by [3]. Note that if IE=IE.sub.0 and
EE=EE.sub.0 these equations yield .phi..sub.r=0.0040,
.phi..sub.p=0.0360. Thus one can calculate the two volume
fractions, .phi..sub.r and .phi..sub.p, from measured quantities,
and then obtain the hematocrit.
[0043] In the Example below, this algorithm is being applied to
quartz spheres suspended in a porphyrin solution in aqueous CsCIl
for adjustable density, and in a particular experimental
arrangement that by its nature produces a background signal
[0044] The in vitro experiment was designed with varying
concentrations of both quartz spheres and porphyrin, keeping a
constant volume for each sample. It is important for both variables
i.e. the .phi..sub.p and .phi..sub.r or their analogues to
demonstrate a linear relationship with respect to both EE and IE to
fit the data. FIG. 2 displays the linear relationship with respect
to quarts spheres and FIG. 3 the relationship with respect to
porphyrin.
[0045] Having demonstrated linear relationships with respect to IE
and EE for both variables independently, the system can be fitted
to the hematocrit algorithm yielding equations [8] and [9],
ch=a+b(EE)+c(IE) [8]
[P]=d+e(EE)+f(1E) [9]
where .phi.Q is the volume fraction of quartz spheres and [P] is
the concentration of porphyrin in molarity. Since the total volume
in this case is the focal volume of the laser inside the fluid in
the cuvette, the volume fraction of the quartz determines the
volume fraction of the remaining fluid phase. However, the
fluorescence and Raman emission produced by the fluid phase is a
function of the concentration of any fluorophores or Raman active
species thereby by providing the other independent variable needed
to characterize the IE in this intentionally turbid system. Thus a
volume fraction of the fluid phase can be replaced with the
concentration of the active species and the units will be reflected
in the units of the parameters a-f. Thus with appropriate choices
the closure relations analogous to equations 1 and 2 are implicitly
satisfied in this in vitro analogue.
[0046] These only serve as constraints to be satisfied when
optimizing the parameters a-f for the in vivo system. For the Hct
measurement i.e. the in vivo system there is homeostasis that
defines the EE.sub.0 and IE.sub.0 however, this is not the case for
the present experiment. Thus, equations [8] and [9] only utilize
the raw measurements of both EE and IE. The only requirement for
the algorithm to be applicable is for the IE and EE to be linearly
independent measurements because a two equation system in two
unknowns can always be inverted.
[0047] As in the hematocrit algorithm, the parameters a-f can be
calculated based on a fit of the experimental data comprising FIGS.
2 and 3. To calculate a-c, a bilinear fit was applied with OQ as
the dependent variable and EE and IE as independent variables. For
d-f, [P] was the dependent variable keeping EE and IE as
independent variables. The calculated parameters are introduced
into equations [8] and [9] yielding equations [10] and [11].
.phi..sub.Q=0.0897+9.89413E.sup.-11(EE)-7.33145E.sup.-11(IE)
[10]
[P]=-0.001501+3.34025E.sup.-13(EE)+3.57857E.sup.-12(IE) [11]
[0048] The fit [P] and .phi.Q are compared to the expected values
from FIGS. 2 and 3, presented in FIGS. 4-6. The calculated values
of both [P] and .phi.Q match the experimental data very well at
lower concentrations. However, the fit begins to deviate from
linear behavior at higher concentrations of both porphyrin and
quartz spheres consistent with the curvature in FIGS. 2B and 3B.
This demonstrates that the higher concentrations are beginning to
deviate from the linear regime. A more accurate fit could be
refined if all of the concentrations stayed within the linear
region.
[0049] A verification of the calculated parameters can be
demonstrated by calculating the .phi.Q as the spheres settle out of
the solution as a function of time. The hypothesis is that as the
spheres settle out of the probed volume, the .phi.Q calculated by
the algorithm will be decreasing. For reference, images of the
sample cells over time are shown in FIGS. 7-9 demonstrating that
the settling of the spheres can be visually observed. The recorded
EE and IE are presented in FIG. 10 and the calculated .phi.Q and
[P] in FIG. 11.
[0050] The volume fraction of quartz spheres is calculated to
rapidly decrease at the start of the experiment then level off,
which is visually observed in FIGS. 7-9. A greater initial
concentration leads to quicker and more drastic changes from the
settling. The result of increasing porphyrin concentration was
initially surprising however, it is a logical outcome. In the
overall sample it can be assumed that the porphyrin is equally
dispersed throughout. Therefore, if the quartz spheres settle out
of the probed volume, that volume experiences an increase in
porphyrin containing solution giving an apparent rise in the
porphyrin concentration. That is, the volume fraction increases in
time as the porphyrin concentration is constant. Thus the model
accurately and simultaneosuly represents the effect of changing
concentrations and equal volumes as well as changing volumes with
equal concentrations.
[0051] The turbidity of biological samples cause a distortion in
the scattering, giving rise to a need for more accurate methods of
measurement. The Hct algorithm presented above utilizes
[0052] the measurement of both the inelastic and the elastic
scattering intensities to approach the scattering distortion issue.
The current work provides a validation of the algorithm by applying
the same concept to an in vitro system that is analogous to the
transcutaneous measurements. The measurement of EE and IE were
linear with respect to both .phi.Q and [P] allowing for a bilinear
fit providing the parameters a-f to fit the settling experiment.
The results match what is expected affording support for the
algorithm.
[0053] While the utility of this approach has been demonstrated,
the experiments should be repeated within the linear regime for
both EE and IE measurements. This data would give a more accurate
and precise fit. Because there are many particle systems that are
commercially available the present invention could be evaluated
with other particles, such as polystyrene particles in aqueous
glucose solution, to more thoroughly explore and probe this
approach.
[0054] Algal biofuel production is a process that has received much
attention as a more environmentally friendly renewable energy
source. The present invention could be used to measure the growth
of algae in a bulk solution before processing. A second application
of the present application could be the determination of the
viability of bacteria in a growing culture. The algae growth starts
with proliferation where the cells multiply and ends with profusion
by the production of fats which can be generated into biofuels. For
these applications, the algae would be analogous to the RBCs, the
nutrient solution would be analogous to plasma, and the background
signal to contributions to in vivo optical probing EE and IE
signals from the static tissue surrounding the intravascular
space.
[0055] The algorithm of the present invention could thus be applied
to the algae growth to measure both the proliferation and the
profusion as a function of time. The advantage of this approach
would be to measure the growth of the algae culture non-invasively
instead of removing an aliquot which could potentially contaminate
the culture.
[0056] The most advantageous time in which to start processing the
grown algae could be anticipated granting maximum productivity.
When inducing bacteria to produce a protein of interest, the growth
of the culture can be measured by the change in optical density.
While this is helpful to measure the growth, it would be favorable
to measure the vitality of the bacteria. In this system, the
bacteria would be analogous to the red blood cells, the liquid
broth (LB) growth medium to plasma and the background signal to
contributions to in vivo optical probing EE and IE signals from the
static tissue surrounding the intravascular space. As live bacteria
may be able to move throughout the solution, but dead bacteria
would theoretically descend to the bottom at a constant rate. Thus,
the example of the quartz spheres settling could be applied to a
culture of bacteria to estimate the amount of dead bacteria. As the
results from experiments utilizing a culture of bacteria can often
take days to see the results, the present invention provides an
ability to determine the liveliness of a culture while it is
growing rather than realizing days later that the bacteria were not
producing the protein.
[0057] The present invention may thus be used for fluorescence
based immunoassays, nephalometry and turbidometry assays for
biofluids, quantitative protein analysis, bioreactor design,
process control, biofuel production, stem cell culturing, stem cell
production and cell viability testing.
EXAMPLE
[0058] The following materials were used without further
purification: Meso-tetra(4-Sulfonatophenyl)porphine dihydrochloride
from Frontier Scientific, Cesium chloride from Sigma-Aldrich, SiO2
Microspheres, 8 vm from Cospheric, and Inorganic Membrane Filters,
0.02 vm 25 mm from Whatman. A 0.00496 M stock solution of
Meso-tetra(4-Sulfonatophenyl)porphine dihydrochloride(porphyrin)
was prepared by dissolving 50 mg in 10 mL of deionized (DI) water.
A stock solution of cesium chloride was prepared by dissolving 12 g
of CsCI in 20 mL of DI water to give a solution with a density of
1.6 g/mL. The solutions with quartz spheres were made in serial
dilution. The first solution was prepared by adding 0.102 g quartz
spheres to 5.1 mL of the stock CsCI solution to give a 0.02 g/mL
solution. Dividing the 0.02 g/mL of quartz spheres by the density
of 1.8 g/mL gives a % volume/volume (% v/v) of 0.0111 quartz
spheres in solution for the most concentrated solution. This
solution was used to make serial dilutions to solutions with volume
fractions of 5.56E-.sup.3, 1.85E-.sup.3, 2.467E.sup.4,
8.22E-.sup.5, and 4.167E-5.
[0059] The Raman instrument uses a continuous wave external cavity
laser operating at 785 nm (Process Instruments, Salt Lake, Utah).
The laser delivers a maximum of 450 mW at the sample in a 1.5
cm-.sup.1 spectral bandwidth within a multimode spatial
distribution. The spot is roughly square and is focused to a spot
about 125 mm wide at the sample. Spectra were collected with an
exposure time of 0.02 seconds, accumulation time of 0.02 seconds
and 1500 accumulations. The spectra of each sample was collected
prior to porphyrin addition. Then, 30 .mu.L of the stock 0.00496 M
porphyrin solution was added to each solution, mixed thoroughly,
and spectra were collected with an identical experimental setup.
Following this same procedure, 30 .mu.L of stock porphyrin was
added then spectra were accumulated twice giving each quartz sphere
sample at four different porphyrin concentrations: 0 M (OP),
4.96E.sup.-5 M (30P), 9.92E.sup.-5 M (60P), and 1.488E.sup.-4 M
(90P). The raw data was transferred to Origin Lab 9.0 software for
analysis.
[0060] For the settling experiment, the same porphyrin and CsCI
stock solutions were used. Samples 1 and 3 were prepared with same
0.0111% v/v concentration as above and sample 2 was prepared with a
0.00185% v/v concentration. Samples 1 and 2 were given a
4.96E.sup.-5 M porphyrin concentration and sample 3 was given a
9.92E.sup.-5 M porphyrin concentration. The experimental setup was
the same as for the previous experiment, however, there were 30
consecutive acquisitions for samples 1 and 3 and 40 acquisitions
for sample 2 giving spectra every 30 seconds for 15 minutes and 20
minutes respectively.
* * * * *