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Claims  |
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What is claimed is:
1. A method for quantifying cellular damage in a tissue sample, comprising:
measuring average sodium ion concentration in the entire tissue sample
([Na].sub.t);
measuring average potassium ion concentration in the entire tissue sample
([K].sub.t);
obtaining a value equal to [Na].sub.t -[K].sub.t ; and
comparing said value to the value of [Na].sub.t -[K].sub.t in normal
tissue,
whereby the degree of deviation from normal values is a quantitative
indication of cellular damage.
2. The method according to claim 1, wherein the tissue is brain tissue.
3. The method according to claim 1, wherein the sodium and potassium ion
concentrations are measured using nuclear magnetic resonance spectroscopy.
4. The method according to claim 1, wherein the sodium and potassium ion
concentrations are measured by atomic absorption or emission
spectrophotometry.
5. The method according to claim 1, wherein the sodium and potassium ion
concentrations are measured by ion-selective electrodes.
6. A method according to claim 1, wherein said measured sodium ion
concentration is [Na].sub.t.sbsb.m and said measured potassium ion
concentration is [K].sub.t.sbsb.m and further including, prior to said
obtaining step, calculating normalized values of sodium ion concentration
([Na].sub.t) and potassium ion concentration ([K].sub.t) by:
measuring the sodium ion concentration in a blood plasma sample
([Na].sub.p);
measuring the potassium ion concentration in a blood plasma sample
([K].sub.p); and
multiplying the measured values of [Na].sub.t.sbsb.m and [K].sub.t.sbsb.m
by a proportionality factor equal to ([Na].sub.t.sbsb.m)/([Na].sub.p
+[K].sub.p) to obtain normalized [Na].sub.t and [K].sub.t.
7. A method for determination of kind of tissue, comprising:
measuring sodium ion concentration in the total tissue sample ([Na].sub.t);
measuring potassium ion concentration in the total tissue sample
([K].sub.t);
obtaining a value equal to [Na].sub.t -[K].sub.t ; and
comparing said value to the value of [Na].sub.t -[K].sub.t in tissue of
known type,
whereby obtaining a value equal to that of tissue of known kind is an
indication that the tissue sample comprises tissue of that known kind.
8. The method according to claim 6, wherein the sodium and potassium ion
concentrations are measured using nuclear magnetic resonance spectroscopy.
9. The method according to claim 6, wherein the sodium and potassium ion
concentrations are measured by atomic absorption or emission
spectrophotometry.
10. The method according to claim 6, wherein the sodium and potassium ion
concentrations are measured by ion-selective electrodes.
11. A method according to claim 6, wherein said measured sodium ion
concentration is [Na].sub.t.sbsb.m and said measured potassium ion
concentration is [K].sub.t.sbsb.m and further including, prior to said
obtaining step, calculating normalized values of sodium ion concentration
([Na].sub.t) and potassium ion concentration ([K].sub.t) by:
measuring the sodium ion concentration in a blood plasma sample ([Na].sub.p
;
measuring the potassium ion concentration in a blood plasma sample
([K].sub.p); and
multiplying the measured values of [Na].sub.t.sbsb.m and [K].sub.t.sbsb.m
by a proportionality factor equal to ([Na].sub.t.sbsb.m
+[K].sub.t.sbsb.m)/([Na].sub.p +[K].sub.p) to obtain a normalized
[Na].sub.t and [K].sub.t.
12. A method for monitoring neural activity in an undamaged portion of
brain tissue, comprising:
measuring average a sodium ion concentration in the portion of brain tissue
being studied ([Na].sub.t) at predetermined intervals of time;
measuring average potassium ion concentration in the portion of brain
tissue being studied ([K].sub.t) at the same predetermined intervals of
time;
obtaining a value equal to [Na].sub.t -[K].sub.t at each said time
interval; and
comparing said values obtained over time,
whereby variation of said values over time is an indication of neural
activity in the brain tissue being studied.
13. The method according to claim 12, wherein the sodium and potassium ion
concentrations are measured using nuclear magnetic resonance spectroscopy.
14. A method according to claim 12, wherein said measured sodium ion
concentration is [Na].sub.t.sbsb.m and said measured potassium ion
concentration is [K].sub.t.sbsb.m and further including, prior to said
obtaining step, calculating normalized values of sodium ion concentration
([Na].sub.t) and potassium ion concentration ([K].sub.t) by:
measuring the sodium ion concentration in a blood plasma sample
([Na].sub.p);
measuring the potassium ion concentration in a blood plasma sample
([K].sub.p); and
multiplying the measured values of [Na].sub.t.sbsb.m and [K].sub.t.sbsb.m
by a proportionality factor equal to ([Na].sub.t.sbsb.m
+[K].sub.t.sbsb.m)/([Na].sub.p +[K].sub.p) to obtain a normalized
[Na].sub.t and [K].sub.t.
15. A method for determining the volume fraction of cells in a tissue
sample, comprising:
measuring potassium ion concentration or total potassium weight present in
the tissue sample ([K].sub.t);
measuring or assuming extracellular potassium ion concentration
([K].sub.e); and
using a predetermined value for the ionic gradient across cell membranes
(G) in the tissue sample, calculating cell volume fraction (V.sub.i
/V.sub.t), using the formula V.sub.i /V.sub.t =([K].sub.e -[K].sub.t)/G.
16. A method in accordance with claim 15, wherein said tissue sample is a
blood sample and said volume fraction of cells in the blood sample is the
hematocrit, and wherein said step of measuring or assuming [K].sub.e
comprises measuring the potassium ion concentration or the total potassium
weight present in the cell-free blood plasma ([K].sub.p) and using said
value of [K].sub.p as [K].sub.e.
17. An apparatus for determining and displaying a value representative of
the amount of cellular damage in a tissue sample or the tissue type of a
non-necrotic tissue sample, comprising:
first measuring means for measuring the total tissue sodium ion
concentration in the tissue sample;
second measuring means for measuring the total tissue potassium ion
concentration in the tissue sample;
processor means for subtracting the measured value of potassium ion
concentration obtained from said second measuring means, from the measured
value of sodium ion concentration obtained from said first measuring
means, to obtain a value for the calculated difference; and
display means for displaying the calculated difference obtained by said
processor means.
18. An apparatus in accordance with claim 17, further including removal
means for removing a tissue sample from a source of tissue and delivering
the tissue to said first and second measuring means.
19. An apparatus in accordance with claim 17, wherein said first and second
measuring means include an atomic absorption or emission
spectrophotometer.
20. An apparatus in accordance with claim 17, wherein said first and second
measuring means include a nuclear magnetic resonance spectrometer with a
probe double tuned to .sup.23 Na and .sup.39 K.
21. An apparatus in accordance with claim 17, wherein said first and second
measuring means include sodium and potassium ion sensitive electrodes.
22. An apparatus in accordance with claim 18, wherein said removal means
comprises a surgical aspirator.
23. An apparatus for determining the volume fraction of cells in a tissue
sample, comprising:
potassium measurement means for determining the total potassium content or
potassium ion concentration of a tissue or fluid sample;
calculator means connected to said potassium measurement means, for
calculating cellular volume fraction from the values obtained by said
potassium measurement means; and
output means connected to said calculator means, for outputting the
calculated values of cellular volume fraction.
24. An apparatus in accordance with claim 23 for determining the cellular
volume fraction (hematocrit) in a blood sample wherein said potassium
measurement means is for determining the total potassium content or
potassium ion concentration of a whole blood or cell-free plasma sample.
25. An apparatus in accordance with claim 24 and further including sodium
measurement means for determining the total sodium content or potassium
ion concentration of a whole blood or cell-free plasma sample and wherein
said calculator means is further connected to said sodium measurement
means and is further for calculating cellular volume fractions from the
values obtained by said potassium measurement means and said sodium
measurement means.
26. An apparatus in accordance with claim 24 which can also determine the
value of blood cell membrane ionic gradient (G), further including sodium
measurement means, connected to said calculator means, for determining the
total sodium content or sodium ion concentration of a blood or plasma
sample, wherein said calculator means is also for calculating G from the
values obtained by said potassium measurement means and said sodium
measurement means, and wherein said output means is further for outputting
the calculated value of G.
27. An apparatus in accordance with claim 23 and further including sodium
measurement means for determining the total sodium content or potassium
ion concentration of a tissue or fluid sample and wherein said calculator
means is further connected to said sodium measurement means and is further
for calculating cellular volume fractions from the values obtained by said
potassium measurement means and said sodium measurement means.
28. An apparatus in accordance with claim 27, wherein said sodium
measurement means comprises a sodium selective electrode and wherein said
potassium measurement means comprises a potassium selective electrode.
29. An apparatus in accordance with claim 27, wherein said calculator means
and said output means are packaged in a single portable calculator and
wherein said sodium and potassium measurement means are sodium and
potassium ion selective electrodes, respectively, each of which are
directly connected to said calculator.
30. An apparatus in accordance with claim 23 wherein said potassium
measurement means comprises a potassium selective electrode.
31. An apparatus in accordance with claim 23 wherein said output means is
for displaying the calculated values of cellular volume fraction.
32. An apparatus in accordance with claim 23, which can also determine the
average Na and K gradient across cellular membranes (G) in tissues which
have been removed from the body, further including sodium measurement
means, connected to said calculator means, for determining the total
sodium content or sodium ion concentration of a tissue or fluid sample,
wherein said calculator means is also for calculating G from the values
obtained by said potassium measurement means and said sodium measurement
means, and wherein said output means is further for outputting the
calculated value of G.
33. An apparatus in accordance with claim 32, wherein said calculator means
further includes input means for inputting estimated or assumed values and
said calculator means is further for calculating G from the values
obtained by said potassium measurement means and/or said sodium
measurement means as well as from values inputted through said input
means.
34. An apparatus in accordance with claim 23 which can also determine the
average Na and K gradient across cellular membranes (G) in tissues which
have been removed from the body, further including input means connected
to said calculator means, for inputting estimated or assumed values,
wherein said calculator means is also for calculating G from the values
obtained by said potassium measurement means and from values inputted
through said input means, and wherein said output means is further for
outputting the calculated value of G.
35. An apparatus in accordance with claim 23, wherein said calculator means
and said output means are packaged in a single portable calculator and
wherein said potassium measurement means is a potassium ion selective
electrode directly connected to said calculator.
36. A method for measuring the average Na and K gradient across cellular
membranes (G) in tissues that have been removed from the body, comprising:
measuring or estimating the cell volume fraction (V.sub.i /V.sub.t) of the
tissue sample;
measuring the potassium ion concentration in the tissue sample ([K].sub.t);
measuring the sodium ion concentration in the tissue sample ([Na].sub.t);
measuring or assuming a value of extracellular potassium ion concentration
([K].sub.e);
measuring or assuming a value of extracellular sodium ion concentration
([Na].sub.e); and
calculating G using the formula:
G=(([Na].sub.t -[K].sub.t)-([Na].sub.e -[K].sub.e))/2.multidot.(V.sub.i
/V.sub.t). |
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Claims |
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Description |
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FIELD OF THE INVENTION
The present invention relates to methods for quantifying tissue damage,
determining tissue type or monitoring neural activity by analyzing the
concentrations of sodium ion and potassium ion in tissue, determining the
cell volume of blood (hematocrit), and determining extent of blood loss
and dehydration. The present invention further relates to methods and
apparatus for measuring the relative sodium and potassium ion
concentration of tissue.
BACKGROUND OF THE INVENTION
Biologists and clinicians are constantly faced with the problem of
assessing tissue damage; currently available methods are cumbersome and
often not accurate. Pathologists devote a great deal of time to examining
the histology of tissues, counting cells, and estimating tissue damage
from the subjective appearance of cells. Radiologists spend a majority of
their time trying to find pathological changes on X-rays or magnetic
resonance images which would indicate tissue damage. Surgeons rely
primarily on visual clues to judge what tissues to remove and what tissues
to save, which is not an accurate method of assessing damage, as living
tissues often look dead. Additionally, surgeons currently cannot be
certain that all diseased tissue is removed during a surgical procedure,
which presents a great problem when malignant tissue is being removed.
Even in the laboratory, there is no reliable method for quantifying tissue
damage. Investigators spend millions of dollars on tracers and spend
months counting cells to measure tissue damage. In order to save time,
many investigators simply measure gross areas of necrosis. Since it is not
always possible to determine visually which cells are living and which
cells are dead, nor the extent of tissue damage to an organ, the currently
available methods can be described as crude, at best.
The relative sizes of extracellular and intracellular space in tissue is a
valid estimation of the amount of tissue damage in the total space
measured. Normal brain tissue, for example, generally has an intracellular
volume fraction of about 90%. If tissue is damaged, the intracellular
compartments of the dead cells equilibrate with the extracellular space
and thus the intracellular volume fraction will drop. The smaller the
intracellular volume fraction, the greater the amount of damage in the
sample.
The relative sizes of extracellular and intracellular space in brain
tissues have been the focus of many scientific studies. Many ingenious
methods have been devised to make this determination. In the 1960's, two
methods were dominant. One method involved passing an electric current
through brain tissues. Because the cells are relatively impervious to
electrical currents, the impedance of the brain tissues gave a rough
indication of the relative size of the extracellular space. The second
method involved the use of macromolecular tracers, including soaking
tissue in solutions of these tracers and then measuring the concentration
of the substance in the tissue. The ratio of the tissue concentration to
the medium was then determined to indicate the space occupied by the
tracer.
The tracer methods suffered from several drawbacks. No tracer substance is
ideal, and all tracers penetrate into the cells to some degree. Different
tracers yield different values of extracellular space. Delivery of the
tracer into the tissue is problematical. If the tracer is administered
intravenously, its penetration into the brain tissues may be limited by
the blood-brain barrier. Blood flow also influences delivery. Therefore,
to interpret the data, multiple tracers are necessary: one to monitor
blood-brain barrier breakdown, one to measure blood flow, and one to
assess extracellular space.
C. Nicholson at New York University developed a method for measuring
extracellular volume fraction (V.sub.e /V.sub.t) by introducing a tracer
substance such as tetra-ethylammonium (TEA), which should not penetrate
the cells. If the extracellular volume increases or decreases, the
concentration of TEA changes. By measuring the concentration of TEA with
microelectrodes, it is possible to estimate V.sub.e /V.sub.t. The
intracellular volume, V.sub.i, divided by V.sub.t, is equal to 1-V.sub.e
/V.sub.t. This method also has several major disadvantages. First, it is
quite difficult to introduce tracer substances into tissues. The tracer
concentration in extracellular space must first be measured before a given
injurious event, and then the change must be observed. It is difficult to
ensure that the same amount of tracer is injected into the tissue. Second,
the method gives the extracellular volume fraction only in the immediate
vicinity of the microelectrode recording. Since the ratio of the
extracellular volume to the tissue volume may vary within the tissue, it
is necessary to sample many points of tissue in order to obtain a
representative average value. Thirdly, the ion-selective microelectrodes
required to measure the tracer concentrations are fragile and difficult to
make. Fourthly, the equations for calculating the extracellular volume
fraction require a factor called tortuosity, the convolutions of the
pathways through which the ions must diffuse. This factor is resolvable by
assuming that the tissue is anisotropic, i.e., that the diffusion of ions
is the same in all directions. This method is not accurate when applied to
tissues with oriented cellular structures, such as white matter. Because
of the complexity of this method, the measured values must be checked very
carefully, and errors can very easily arise.
Accordingly, a relatively simple and accurate method of determining
intracellular volume fraction has been long sought in order to quantify
the extent of tissue damage in any given tissue sample.
Another problem facing biologists and clinicians is obtaining accurate
imaging of different types of soft tissue. Existing imaging technology,
such as x-ray and NMR, depend on tissue density or differences in proton
relaxation rates to identify different tissue types. Both tissue density
and proton concentrations have one major drawback. Neither directly
reflect tissue damage or biological changes in the tissue. For example,
tissue density to x-rays depends on the concentration of x-ray absorbing
substances, such as calcium. Calcium concentrations do not change much in
acutely injured soft tissues and, if they do change, take place over a
period of days, weeks, or months. X-rays, therefore, are primarily useful
for visualizing bone and detecting chronic soft tissue injuries. Likewise,
magnetic resonance signals resulting from proton relaxation times in
tissues represent complex and yet poorly understood contributions from
hydrogen in water and organic substances. While magnetic resonance signals
do change relatively rapidly in injured tissue, thus allowing early
detection and imaging of tissue changes, the nature of the changes is not
well understood. Furthermore, the signal changes are relatively small and
not necessarily linearly related to known tissue variables. Thus, accurate
imaging and differentiation of tissue damage, tumors, and normal tissues
of different organs are limited with current technology.
The measurement of neural activity is a very important area of brain
research. Presently, this must be done with external or implanted
electrodes. There are many disadvantages to such techniques. A
non-invasive technique for imaging changes in neural activity in different
portions of the brain would be an invaluable research tool.
Probably the most common blood test utilized by clinicians and others is
the hematocrit or measurement of cell volume in blood. The present
techniques for measuring hematocrit are relatively crude and involve
centrifugation of whole blood in a glass capillary tube until the cells
are packed at the bottom. The ratio of the cells to total blood volume
represents the hematocrit. Most instruments measure hematocrit by
optically measuring the heights of the different phases of centrifuged
blood. Several disadvantages are associated with this procedure for
measuring hematocrits.
1. The instruments required for centrifugation of the capillary tubes and
optical measurements tend to be bulky and cannot be easily run on battery.
Therefore, portable hematocrit machines are not readily available.
2. The accuracy of hematocrits depends critically on the absence of blood
clotting and lysis. If the blood cells were to clot or lyse, the
hematocrit becomes grossly inaccurate. Thus, it is essential that the
blood be relatively fresh, be placed in a container immediately with
anticoagulants, and be centrifuged under appropriate conditions.
3. Hematocrits are relatively imprecise. Most hematocrits measured by eye,
using a modified ruler scale, probably are no more accurate than .+-.5% of
the mean, e.g., 2% of the normal 40% hematocrit. Factors such as
centrifugation force and time, packing of the cells, etc., also may play a
role in the variability of measurements.
A quick and accurate test for determining hematocrit in any blood sample,
including clotted blood, lysed blood and even blood from corpses, which
can be implemented with a small portable device, would be a very valuable
addition to the hematological analytical array.
SUMMARY OF THE INVENTION
It is an object of the present invention to overcome the above-mentioned
deficiencies in the prior art.
It is another object of the present invention to provide a method for
determining the amount of living and/or dead tissue in a tissue sample and
quantifying the relative amount of damage in that sample.
It is yet another object of the present invention to provide a method for
distinguishing different types of living tissue.
A further object of the present invention is to provide a method to
determine neural activity in the central nervous system.
It is yet another object of the present invention to provide a method to
give substantially instant feedback to a surgeon as to the relative amount
of tissue damage or the type of tissue being removed as it is being
removed.
It is still another object of the present invention to provide a
non-invasive imaging technique to show the amount of tissue damage in the
tissue areas being scanned.
It is a further object of the present invention to provide a quick and
accurate test for determining hematocrit and extent of blood loss or
dehydration using small portable equipment.
It is yet a further object of the present invention to provide a direct
measure method for determining hematocrit which is easier and more precise
than the standard centrifugation approaches to determining hematocrit and
can be applied to any blood removed from the body even after it has
clotted and lysed.
It is a further object of the present invention to provide apparatus for
carrying out all of said methods.
According to the present invention, tissue damage may be quantified in
damaged tissue of the same type, tissue type can be determined in tissue
which is not necrotic, neural activity can be monitored, and blood
hematocrit can be determined, all by the simple expedient of measuring the
difference in the total sodium and potassium ion concentrations in the
tissue sample, sometimes with the additional expedient of measuring the
sodium and/or potassium ion concentrations in the extracellular fluid,
such as CSF or blood plasma. The present invention is based on the
realization of a mathematical formula which establishes that the
difference in the total sodium and potassium ion concentrations in tissues
is linearly related to the volume of cytoplasm in the tissue with a slope
reflecting the average transmembrane cationic gradient and a y-intercept
reflecting the difference in extracellular sodium and potassium
concentrations. Since the value of the average transmembrane cationic
gradient is relatively constant in a given tissue type, and this constant
value is known, the difference in the total sodium and potassium ion
concentrations in the tissue sample will be directly related to the
intracellular volume fraction. Thus, by merely measuring the total sodium
ion concentration and the total potassium ion concentration in a tissue
sample, one has a relative indication of intracellular volume fraction
which in turn is an accurate indication of the volume of living cells in
the tissue. By comparing to a normal control and assigning a constant
normal transmembrane cationic gradient for the particular tissue type
being examined, a special case of average intracellular volume fraction
can be accurately determined. In such a case, the difference in total
tissue sodium and potassium concentrations is linearly related to a value
of intracellular volume fraction representing the equivalent volume of
cytoplasm with normal transmembrane cationic gradient or the idealized
intracellular volume fraction of the tissue (IVF*). This idealized
intracellular volume fraction approximates the volume of living cells in
the tissue.
It is further known that cells of different tissue types or in different
states, such as normal cells versus malignant cells, or muscle cells
versus liver cells, etc., have substantially constant average
intracellular volume fractions but have different average cellular
transmembrane cationic gradients. If the intracellular volume fraction is
considered to be constant, changes in the difference between total sodium
and potassium ion concentrations will represent changes in the average
cellular transmembrane cationic gradients and, thus, changes in tissue
type. If the total tissue sodium and potassium ion concentrations are
measured by the device, such as, for example, by means of nuclear magnetic
resonance spectroscopy, the device will image areas of different average
cellular transmembrane cationic gradients. Measurements based on the
assumption of constant intracellular volume fraction will yield
differences in average transmembrane cationic gradients or G*.
Furthermore, in normal brain tissues over short time periods, where the
intracellular volume fraction and the transmembrane cationic gradient
remain relatively constant, differences in tissue sodium and potassium ion
concentration will reflect neural activity since brain activity causes
sodium and potassium movements and the difference in tissue sodium and
potassium concentrations will reflect these movements accordingly. Thus,
the device can be used to detect and measure neural activity.
Previously, the cellular volume fraction or hematocrit of blood was
determined by a centrifugation method using calibrated capillary tubes.
Data has now been obtained showing that a formula involving the
measurements of only whole blood potassium concentrations ([K].sub.t) and
extracellular or plasma potassium concentrations ([K].sub.e) is a robust
and accurate indicator of blood hematocrit. [K].sub.t and [K].sub.3
measurements are easier and more precise than the standard centrifugation
approaches to determining hematocrit and can be applied to any blood
removed from the body, even after it has clotted and lysed. In addition,
whole blood sodium concentration ([Na].sub.t) and [K].sub.t measurements
provide an estimate of blood ionic osmolarity, an important indicator of
dehydration which will aid interpretation of hematocrit and [Na].sub.t and
[K].sub.t changes. Finally, measuring hematocrit (in the standard manner),
and performing linear regression analysis of [Na].sub.t -[K].sub.t versus
hematocrit will provide a quantitative estimate of the difference between
extracellular sodium ([Na].sub.e) and [K] .sub.e from the y-intercept of
regression, as well as the average ionic gradient across blood cell
membranes (G) from the slope of the regression. This forms the basis of a
new method of measuring hematocrit that can be easily implemented in small
portable devices.
Sodium and potassium ion concentration can be measured by any applicable
technique. For example, potassium and sodium ion sensitive microelectrodes
can be used as can atomic absorption spectrophotometry, flame photometry,
ionic titration or nuclear magnetic resonance spectroscopy.
The present invention will be better understood from a consideration of the
following detailed description of the preferred embodiments and the brief
description of the drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows the procedure for measuring tissue sodium and potassium
concentrations in rat brains after cerebral ischemia produced by occlusion
of the middle cerebral artery.
FIG. 2 shows the mean differences in tissue sodium and potassium
concentrations in rat brains at 24 hours after middle cerebral artery
occlusion. [Na].sub.w and [K].sub.w represent wet tissue concentrations of
sodium and potassium, respectively, expressed in .mu.moles per gram wet
tissue weight. Concentration values expressed in .mu.mol/g W units
approximate millimolar concentration units since 1 g of wet tissue is
approximately 1 ml in volume.
FIGS. 3A and 3B show scatterplots of [Na].sub.w -[K].sub.w versus
[Na].sub.w in a frontal cortical slice at 6 and 24 hours after middle
cerebral artery occlusion, respectively.
FIG. 4 shows the mean values of [Na].sub.w -[K].sub.w in graded spinal cord
contusion.
FIG. 5 is a schematic diagram showing an apparatus in accordance with the
present invention including an ultrasonic surgical aspirator.
FIG. 6 is a schematic diagram showing an apparatus in accordance with the
present invention including a scanning NMR spectroscope.
FIG. 7 is a graph showing the relationship of [Na].sub.t -[K].sub.t with
hematocrit.
FIG. 8 is a graph showing the relationship of cell volume fraction with
hematocrit.
FIG. 9 is a graph showing the potassium volume fraction (KVF) versus
hematocrit. KVF was calculated from ([K].sub.t -5)/124.
FIG. 10 is a schematic diagram showing an apparatus in accordance with the
present invention for measuring hematocrit.
FIG. 11 is a schematic diagram showing an alternative embodiment of an
apparatus in accordance with the present invention for measuring
hematocrit, which can also measure the cationic gradient across the blood
cell membranes.
DETAILED DESCRIPTION OF THE INVENTION
Sodium and potassium ions constitute more than 98% of the positively
charged inorganic ions in mammalian tissues. Together, these ions account
for more than 99% of the osmotic activity of the tissue. Small cationic
gradients cause enormous osmotic forces. For example, a 10 mM difference
in Na+K concentrations will generate more than 1 atmosphere of pressure,
i.e., 760 mm Hg compared to only 100-200 mm Hg exerted by the blood
pressure. Water will shift to reduce osmotic gradients, due to pressures
that are generated. Therefore, we can reasonably assume that the sum of Na
and K concentrations in different compartments of tissue are equal, i.e.,
[Na].sub.t +[K].sub.t =[Na].sub.e +[K].sub.e =[Na].sub.i +[K].sub.i (1)
where [Na].sub.t and [K].sub.t are the tissue concentrations of sodium and
potassium, [Na].sub.e and [K].sub.e are the extracellular sodium and
potassium concentrations, and [Na].sub.i and [K].sub.i are the
intracellular concentrations of sodium and potassium, respectively.
Shifting these terms, we arrive at:
[Na].sub.i -[Na].sub.e =[K].sub.e -[K].sub.i =G (2)
where G represents the sodium and potassium cationic gradients across
cellular membranes. We know that the sum of cationic contents of
intracellular and extracellular compartments is equal to the total
cationic contents, i.e.,
[Na].sub.t .multidot.V.sub.t =[Na].sub.i .multidot.V.sub.i +[Na].sub.e
.multidot.V.sub.e (3)
and
[K].sub.t .multidot.V.sub.t =[K].sub.i .multidot.V.sub.i +[K].sub.e
.multidot.V.sub.e (4)
where V.sub.e, V.sub.i and V.sub.t are the volumes of the extracellular and
intracellular compartments and the total tissue volume, respectively.
Subtracting equation (4) from equation (3) gives:
([Na].sub.t -[K].sub.t).multidot.V.sub.t =([Na].sub.i
-[K].sub.i).multidot.V.sub.i +([Na].sub.e -[K].sub.e).multidot.V.sub.e (5)
From equation (2), it is known that [K].sub.i =[K].sub.e -G and [Na].sub.i
=G+[Na].sub.e. Substituting this into equation (5) gives:
([Na].sub.t -[K].sub.t).multidot.V.sub.t =([Na].sub.i
-[K].sub.i).multidot.(V.sub.i +V.sub.e)+2G.multidot.V.sub.i /V.sub.t(6)
Dividing both sides of the equation by V.sub.t and knowing that V.sub.t
=V.sub.i +V.sub.e, one can arrive at the following equation:
([Na].sub.t -[K].sub.t)=([Na].sub.e -[K].sub.e)+2G.multidot.V.sub.i
/V.sub.t (7)
By using equation (7) above, it can be seen that the difference between
tissue sodium and potassium concentrations relates linearly to the ratio
of intracellular to total tissue volumes (V.sub.i /V.sub.t) with a
y-intercept of ([Na].sub.e -[K].sub.e) and a slope that is twice the
cationic gradient across membranes (G). Since V.sub.i is the volume of the
intracellular compartment and V.sub.t is the tissue volume, V.sub.i
/V.sub.t is the intracellular volume fraction. G is the gradient of sodium
or potassium across the cellular membranes. [Na].sub.e and [K].sub.e can
be measured, e.g. with ion-selective microelectrodes, or can be assumed to
have equilibrated with plasma or cerebrospinal fluid. [Na].sub.e and
[K].sub.e should equilibrate with plasma values rapidly, within hours, due
to ionic diffusion. By assuming that [Na].sub.e -[K].sub.e is equal to
plasma [Na]-[K], either G or V.sub.i /V.sub.t can be estimated from the
equation. If G is measured or assumed to be normal, V.sub.i /V.sub.t can
be determined. Conversely, if V.sub.i /V.sub.t is measured or assumed to
be normal, G can be determined. Similarly, if [Na].sub.e -[K].sub.e and G
are substantially constant when [Na].sub.t -[K].sub.t is being measured,
such as in chronically injured tissues, [Na].sub.t -[K].sub.t is directly
related to V.sub.i /V.sub.t. If [Na].sub.e -[K].sub.e and V.sub.i /V.sub.t
are substantially constant when the [Na].sub.t -[K].sub.t changes are
being measured, as when there is no substantial cell loss in the tissue
and the tissue type is being determined, [Na].sub.t -[K].sub.t is directly
related to G.
The value of V.sub.i /V.sub.t is intracellular volume fraction.
Intracellular volume fraction should approximate the cellular volume
fraction, i.e., the volume of cells divided by total tissue volume. When
the "tissue" being studied is blood, the cellular volume fraction is also
known as the hematocrit of the blood. Solving equation (7) for V.sub.i
/V.sub.t gives the following equation:
V.sub.i /V.sub.t =(([Na].sub.t -[K].sub.t)-([Na].sub.e -[K].sub.e))/2G (8)
Thus, measurement of [Na].sub.t -[K].sub.t provides a value directly
related to the cellular volume fraction. In other words, there is a linear
relationship between the difference in total Na and K concentrations and
the cellular volume fraction.
The number of measurements necessary to solve equation (8) can be decreased
in view of the relationship of equation (1), i.e., [Na].sub.t +[K].sub.t
=[Na].sub.e +[K].sub.e. Solving for [Na].sub.e we arrive at:
[Na].sub.e =[Na].sub.t +[K].sub.t -[K].sub.e (9)
Substituting equation (9) into equation (8) yields a much simpler equation:
V.sub.i /V.sub.t =([K].sub.e -[K].sub.t)/G (10)
Thus, assuming a normal value for transmembrane ionic gradient (G), only
the potassium concentration of the total homogenized tissue and the
potassium concentration of the cell-free fluid need be measured to
determine a substantially accurate value for cellular volume fraction .
This greatly simplifies the apparatus necessary to determine hematocrit
since only a potassium selective electrode need be present with no
measurement of sodium being necessary.
It is also possible to assume a normal value for [K].sub.e and thus obtain
a substantially accurate cellular volume fraction measurement by measuring
only the total potassium ion concentration. If [K].sub.e and (G) are
normal, i.e., 5 mM and -124 mM, respectively, then
V.sub.i /V.sub.t =(5-[K].sub.t)/-124=([K].sub.t -5)/124 (11)
[K].sub.e usually remains constant in biological tissues whereas [Na].sub.e
can vary greatly. Normal [Na].sub.e values vary within a range of 130-160
mM whereas [K].sub.e is always tightly controlled in the range of 3-5 mM.
The reason is because biological tissues cannot tolerate large
fluctuations of [K].sub.e. Furthermore small [K].sub.e changes have
profound effects on membrane potentials. Electrochemical potentials can be
calculated from the Nernst equation, where E.sub.m is the transmembrane
potential recorded with an electrode inserted into a cell (relative to a
reference electrode outside the cell), z is the valence of the ion, R is
the Universal Gas Constant, F is Faraday's constant and T is the
temperature in absolute (Kelvin) degrees:
##EQU1##
If G=-125mM, where [K].sub.e, [K].sub.i, [Na].sub.e, and [Na].sub.i are 4,
129, 150, and 25 mM respectively, the ionic gradients will have the
following Nernst potentials.
##EQU2##
Thus, a 5 mM increase in [K].sub.e, for example, produces a 25 mV change
in E.sub.k whereas a 5 mM increase in [Na].sub.e would change E.sub.N a by
<1 mV. [K].sub.e levels exceeding 10 mM are incompatible with neuronal,
muscle, and cardiac activity.
Since [K].sub.e stays within a narrow range in the tissues, we can
reasonably assume normal values of [K].sub.e in uninjured tissues or
injured tissues that have had time to equilibrate with plasma. In any
case, since [K].sub.e is usually much smaller than [K].sub.t, small
deviations of [K].sub.e from assumed values will introduce only minor
errors in the estimates of V.sub.i /V.sub.t. [K].sub.e can also be
approximated from measurement of cerebrospinal fluid or blood [K].sub.e.
The former can be imaged in the ventricles of the brain. [K].sub.e can be
easily determined by chemical analysis from both CSF and blood samples.
When dealing with blood, the sum of the sodium and potassium concentration
measurements provide an estimate of blood ionic osmolarity, an important
indicator of dehydration which will aid interpretation of hematocrit
changes.
Direct measurements of transmembrane ionic gradient are usually difficult
because intracellular ionic concentrations cannot be readily determined
with ion-selective microelectrodes or other means. Penetration of a cell,
for example, with a microelectrode will allow leakage of extracellular
fluids into the cells. Moreover, it is difficult to measure transmembrane
ionic gradients in a large number of cells. The following equation
provides a simple and easy method of estimating the average transmembrane
ionic gradients of cells in any given tissue.
##EQU3##
G can be accurately determined by measuring [Na].sub.t -[K].sub.t,
[Na].sub.e -[K].sub.e and V.sub.i /V.sub.t. G can also be estimated from
[Na].sub.t -[K].sub.t and V.sub.i /V.sub.t alone by use of linear
regression without measuring [Na].sub.e -[K].sub.e. The slope of
regression gives 2.multidot.G. G may be a useful clinical diagnostic
parameter.
It is important to accurately define the various terms used in the
above-described relationships, to assess sources of error in the
measurement thereof, and to control the extent of any such error as much
as possible. The equations refer to intracellular (V.sub.i), extracellular
(V.sub.e), and total tissue (V.sub.t) volumes. Because tissues are
inhomogeneous and may contain substantive non-aqueous (e.g., lipid)
compartments which have less or no ions, V.sub.t, V.sub.i, and V.sub.e may
not necessarily relate exactly to the actual volumes of two compartments
in the tissue. Furthermore, the ionic concentration terms are subject to
different definitions. Because Na and K may be bound and concentrations
can be expressed as a function of volume, tissue weight, or other
denominators, application of the equation may lead to misleading values of
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