Abstract
An edema monitor uses patient-specific measurements of tissue conductivity and tissue perfusion and an empirically developed perfusion coefficient of thermal conductivity to obtain tissue intravascular water and tissue extravacular water components of tissue total water. Edema is an excess of tissue extravacular water. A value for edema is obtained by deducting from the obtained value for tissue extravacular water a normal value for tissue extravacular water.
Claims
1. A system for determining a value for tissue extravascular water in living tissue comprising: a thermistor probe adapted to be inserted into living tissue for detecting in the volume of tissue surrounding the thermistor probe a thermal conductivity value indicative of the total water content of the volume of tissue; means for determining in the volume of tissue a value indicative of perfusion in the volume of tissue as a function of the detected thermal conductivity value; a model of the relationship in living tissue of perfusion and thermal conductivity obtained from multiple measurements of thermal conductivity and perfusion in a population of living subjects; means for calculating a second value for thermal conductivity indicative of tissue intravascular water in the volume of tissue using the detected thermal conductivity value, the determined value indicative of perfusion and a value representing the relationship of thermal conductivity in living tissue to perfusion in living tissue provided by said model; and means for determining a value indicative of tissue extravascular water in the volume of tissue using the detected thermal conductivity value and the calculated second value for thermal conductivity.
2. A method for determining a value for tissue extravascular water in a volume of living tissue comprising the steps of: introducing a thermistor probe into living tissue; heating the thermistor probe to a temperature above the baseline temperature of the surrounding tissue by means of a control circuit having a power source for energizing the thermistor probe, as a function of the power used by the heating step detecting in the volume of tissue a value for thermal conductivity indicative of the total tissue water in the volume of tissue; detecting in the volume of tissue a value for perfusion in the volume of tissue as a function of the detected value for conductivity in the volume of tissue; and calculating a second value for thermal conductivity indicative of tissue extravascular water in the volume of tissue using the detected value for thermal conductivity, the detected value for perfusion and a value for the relationship in living tissue between thermal conductivity and perfusion provided by an empirically developed model of the relationship of tissue perfusion values and tissue thermal conductivity values created from multiple measurements in living tissue of thermal conductivity and perfusion in a population of subjects.
3. A system for determining a value for tissue extravascular water in a volume of living brain tissue of a subject comprising: a thermistor probe for insertion into living brain tissue; a control circuit having a power source for energizing the thermistor probe to raise the temperature of tissue surrounding the thermistor probe; an empirical model of the relationship of perfusion in living brain tissue and thermal conductivity in living brain tissue; and means responsive to the power required to heat the thermistor probe and a value for the relationship of perfusion in living brain tissue and thermal conductivity in living brain tissue provided by the model for determining a value indicative of tissue extravascular water in the tissue surrounding the thermistor probe.
4. A system according to claim 3 wherein the empirical model is obtained from multiple measurements of thermal conductivity and perfusion in living brain tissue in a population of subjects.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) FIG. 1A is a plot showing the relationship of brain intravascular water and brain extravascular water.
(2) FIG. 1B is a second plot showing the relationship of brain intravascular water and brain extravascular water.
(3) FIGS. 2A and 2B are plots relating to the derivation of a perfusion coefficient of thermal conductivity.
(4) FIG. 3 is a contour plot of brain extravascular water.
(5) FIG. 4 shows three phases of edema development.
(6) FIG. 5 is a block diagram of one example of a system in which the disclosed techniques can be used.
(7) FIG. 6 shows a thermal probe located in the brain of a subject.
(8) FIG. 7 is a flow chart of one embodiment of a method for determining edema according to the present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
(9) Heat transfer in tissue consists of a thermally conductive component and a thermally convective component resulting from perfusion. These components must be separated mathematically to realize the most accurate and reproducible measurement of thermal conductivity and perfusion in absolute physiologic values. The present system uses a series of algorithms that permit reliable quantification of tissue perfusion by accurately determining the conductive properties of the tissue from the initial rate of propagation of the thermal field and separating this component from the total heat transfer to determine the thermal convection component (Valvano, J T Allen, and H F Bowman, The Simultaneous Measurement of Thermal Conductivity, Thermal Diffusivity, and Perfusion in Small Volumes of Tissue, ASME J. of Biomech. Eng., 106:192-197, August 1984.)
(10) Measured brain tissue thermal conductivity (k.sub.m), an intrinsic property, is equivalent to the sum of the thermal conductivities of the brain constituents (i.e., dry brain tissue (k.sub.bt=1.95 mW/cm- K) and water (k.sub.H2O=6.23 mW/cm- K)) in their volumetric proportion. If total brain water (BW) is the percent of the brain that is water, then:
(11)
(12) Rearranging (3) to calculate total brain water (in percent), yields:
(13)
(14) Total brain water (BW) consists of brain intravascular water (BIW) associated with perfusion and brain extravascular water (BEW), which in excess is edema. That is:
BW=BIW+BEW(5)
(15) Brain intravascular water is a function of perfusion; increasing perfusion increases vascular volume and total brain water, and therefore the measured thermal conductivity. Consequently, k.sub.m is parsed into two components, one linearly proportional to intravascular flow (i.e.: m.sub.) and the remaining portion (i.e.: k.sub.mm.sub.) associated with extravascular water. That is,
k.sub.m=f()+(k.sub.mf())
where is perfusion. Here we employ a linear model (as supported by the data shown in FIGS. 2(a) and 2(b))) in which the intravascular component is linearly proportional to flow (i.e.: f()=m.sub.)). Thus, the partitioning of k.sub.m as shown in FIGS. 1A and 1B is expressed as:
k.sub.m=(m.sub.)+(k.sub.mm.sub.)(6)
where m.sub. is an empirically derived perfusion coefficient of thermal conductivity.
(16) FIGS. 1A and 1B are for illustrative purposes. These figures illustrate the calculation of edema from measured thermal conductivity and perfusion values and the perfusion coefficient of thermal conductivity m.sub.. The specific values of conductivity and tissue water content shown along the Y axes are for illustration purposes and are not necessarily precise. For example, the value 1.95 mw/cm- C. represents the thermal conductivity of dry brain tissue and the value 6.2 mw/cm- C. represents the thermal conductivity of pure water at 37 C. (The vertical scale extends from 0% water to 100% water as seen on the right vertical axis representing percent water content.) While 1.95 mw/cm- C. is a published value for the thermal conductivity of dry brain tissue, the true value may be considered to be slight variants up or down of this value. Also, a more precise value for the thermal conductivity of pure water at 37 C. is 6.23 mw/cm- C. Further, by way of explanation, perfusion is shown in units of 0 ml/100 g-min to 100 ml/100 g-min, that is from a no flow condition to a condition well above normal levels of perfusion in brain white matter. A perfusion range of 20 ml/100 g-min to 40 ml/100 g-min is illustrative of the normal range of white matter perfusion.
(17) In the example shown in FIG. 1A, the measured k.sub.m and are shown, respectively, as 6 mw/cm- C. and 40 ml/100 g-min. The perfusion coefficient of thermal conductivity m.sub. is shown in FIG. 1A as the diagonal line extending from the measured value of k.sub.m on the Y axis and having a negative slope of 0.005, passing through the line indicating measured . (Determination of the slope is described hereafter in connection with FIGS. 2A and 2B.) The intercept between the line representing the perfusion coefficient of thermal conductivity and the line representing measured a) defines the separation of brain intravascular water and brain extravascular water.
(18) In FIG. 1A a plot of thermal conductivity (k.sub.m) and total brain water (BW) versus perfusion () illustrates the two additive contributors to thermal conductivity and their associated contributions to total brain water. Edema can be considered the excess extravascular water in the tissue above a normal value of extravascular water (69.6%1%) or above a value within a range of values considered normal (67-73%). The normal value of tissue water can be modeled by a chosen value supplied by a memory chip or by an expression that captures a range of values.
(19) Thermal conductivity is an intrinsic property of the material (e.g.: tissue or brain tissue) and is proportional to total brain water (BW). Total brain water (BW) is the sum of brain intravascular water (BIW) and brain extravascular water (BEW). Brain intravascular water is proportional to perfusion (). Brain extravascular water is obtained by subtracting brain intravascular water from total brain water. Brain extravascular water above normal levels or values is considered edema. (Brain extravascular water includes intracellular water and extracellular water.)
(20) FIGS. 2A and 2B graph an empirical derivation and modeling of the perfusion coefficient of thermal conductivity (m.sub.) (i.e., the increase in thermal conductivity per unit of perfusion). In FIG. 2A more than 6500 raw clinical data points (200) relating brain thermal conductivity to perfusion level are plotted. The large dataset (>6500 measurements) from a variety of clinical recordings (data points 200 in FIG. 2A) were grouped into bins of perfusion (in increments of 5 ml/100 g-min); the mean thermal conductivity taken for each bin was plotted (points 202 in FIGS. 2A and 2B). This data suggests a linear association between conductivity and perfusion in the observed range of flow.
(21) Since little data was available at high perfusion levels (>60 ml/100 g-min), that data is excluded from the analysis to determine m.sub.. For data at very low perfusion levels (<10 ml/100 gm/min), the increased conductivity is believed to be due to edema (and not intravascular fluid) in swelling-induced, compromised-flow states; thus it does not represent normal physiology and is also excluded from the analysis to determine m.sub..
(22) In FIGS. 2A and 2B the line 204 connects the mean thermal conductivity points 202 and suggests a linear fit. In FIG. 2B the linear fit 214 between conductivity and perfusion (k.sub.m=5.140+0.005, R.sub.sq=0.07, p<0.001) is shown in the range of flow (10-60 ml/100 g-min). Also shown in FIG. 2B are the mean values of conductivity 202 for each perfusion bin, the first standard deviation 210 and the second standard deviation 212.
(23) In FIG. 2B, the line 204 connecting mean values (202), the linear fit (214) and standard deviations 1 (210) and 2 (212) of the data are plotted for the values in the 10-60 ml/100 g-min range (k.sub.m=5.140+0.005; R.sub.wq=0.07, p<0.001). The slope is found to be 0.005. Consequently, from the empirical the data, the perfusion coefficient of thermal conductivity (m.sub.) is determined to be 0.005, the slope of linear fit 214. The linear fit 214 between conductivity and perfusion models the perfusion coefficient of conductivity (m.sub.) which model appears in FIGS. 1A and 1B as the sloped line.
(24) Substituting the perfusion-specific expression for thermal conductivity (6) into the equation for total brain water (5) yields BIW and BEW as the left and right terms in the resultant expression:
(25)
where BW is total tissue water, BIW is tissue intravascular water, BEW is tissue extravascular water, m.sub. is the perfusion coefficient of thermal conductivity, is tissue perfusion, k.sub.m is measured tissue thermal conductivity, k.sub.bt is the thermal conductivity of dry brain tissue and k.sub.H2O is the conductivity of water.
(26) The plot of brain extravascular water in FIG. 3 illustrates how independent changes in thermal conductivity and perfusion impact brain extravascular water, the clinically relevant factor for monitoring edema. FIG. 3 is a Contour Plot of Brain Extravascular Water (leftward diagonal bands being associated with higher water content) as a function of thermal conductivity (k.sub.m) and perfusion (). Relative changes in Brain Intravascular Water (BIW) are indicated by the size of the circles 302, 304 and 306 (which is not drawn to scale.) Examples 1-3 demonstrate changes in brain intravascular water (BM) and brain extravascular water (BEW) for three clinical scenarios. (Perfusion and thermal conductivity values are approximate; in each example the beginning perfusion value is 20 ml/100 gm-min and beginning thermal conductivity is 4.74 mw/cm- K.) (Example 1) Conductivity increasing to 5.64 mw/cm- K with constant perfusion (circle 302) is associated with increased BW, constant BIW and increased BEW. (Example 2) Conductivity increasing to 5.90 mw/cm- K and perfusion increasing to 50 ml/100 gm-min (circle 304) is associated with increased BW, increased BIW and increased BEW. (Example 3) Constant conductivity with an increase in perfusion to 80 ml/100 gm-min (circle 306) is associated with constant BW, increased BIW and decreased BEW.
(27) A plot to investigate and quantify edema of a typical patient with very low perfusion and concomitant edema is shown in FIG. 4. Note the inverted relationship between conductivity (K) and perfusion (), demonstrating the pathophysiology associated with the onset and partial resolution of edema. (Normally, conductivity increases with perfusion as demonstrated in FIG. 1A.) Given that normal white matter can be considered to contain 69.61% extravascular water (illustrated as 70% in FIG. 4), we can define a clinically edematous region if brain extravascular water (BEW) exceeds that value. Also, we could define a clinically edematous region if brain extravascular water (BEW) exceeds the higher limit of the range of normal water content values or if BEW exceeds a selected value from within the range of normal water content values. In the example of FIG. 4, the patient course traversed three phases over 6 days: (Phase 1) a rapid increase in edema (i.e.: BEW) with a concomitant decrease in perfusion, presumably due to increased intracranial pressure with brain swelling; (Phase 2) an initial reduction in edema and sustained low perfusion, presumably because swelling continued to compromise flow; and (Phase 3) a continued reduction in edema at a rate similar as in Phase 2 with improvement in perfusion, presumably because reduced swelling enabled increased flow. This third phase is of interest because the reduction in extravascular water was offset with an increase in intravascular water that kept total brain water (i.e., thermal conductivity) relatively constant. In a clinical setting, this data would be available to the clinical team in real time for evaluation of brain water content and its constituent components, allowing for a more rapid response to a patient's condition. In this example (Phase 3), the ability to resolve total brain Water into its components, brain intravascular water (BIW) and brain extravascular water (BEW), helps clinicians confirm the continued progressive impact of the therapy to reduce edema (which is associated with BEW and not BIW) in spite of the relatively constant total brain water (BEW+BIW).
(28) FIG. 1B shows the same relationship model as FIG. 1A wherein the patient-specific measured values for conductivity (k) and perfusion () are respectively 5.60 mw/cm- C. and 30 ml/100 g-min. The perfusion coefficient of thermal conductivity (m.sub.) is plotted as the downwardly sloped line (slope=0.005) intersecting the conductivity axis at the point of measured conductivity (i.e.: the conductivity value of 5.60 mw/cm- C.). The intercept of the sloped line representing the perfusion coefficient of thermal conductivity (m.sub.=0.005) and the ordinate line representing the measured perfusion value (30 ml/100 g-min) determines a second (i.e.: computed) value of conductivity of 5.45 mw/cm- C. The measured conductivity of 5.60 mw/cm- C. corresponds to the total brain water (BW) value of 85%; the calculated conductivity of 5.45 mw/cm- C. corresponds to the brain extravascular water (BEW) value of 81.25%. To obtain the value for edema corresponding to the patient's current assessment (i.e.: measured k=5.60; measured co=30) a value selected from the normal range of BEW values (the normal range being shown in FIG. 1B as 67%-73%) is subtracted from the BEW value of 81.25%. In the example of FIG. 1B the value selected from the normal range is the upper limit of the normal range or 73.00%. The resulting edema value is the difference between 81.25% and 73.00% or 8.25%.
(29) The above described determination of brain extravascular water utilizes a population-based perfusion coefficient of thermal conductivity. Perfusion and conductivity data gained in use of the edema monitor can be the basis of a real-time reassessment of the perfusion coefficient of thermal conductivity to develop a patient-specific perfusion coefficient or to fine tune the population-based perfusion coefficient. Enhanced perfusion coefficient values can form the basis of a revised and, in some circumstances, improved algorithm.
(30) This invention can be implemented by use of a system such as that illustrated schematically in FIG. 5. As explained in the patents referenced above and illustrated by FIG. 5, a probe 510 is immersed in a medium (e.g.: tissue) 511 and energized; the energized probe is heated by a heater voltage V.sub.h(t) supplied via control circuit 513. The sensed voltage V.sub.s(t) from probe 510 is supplied to A/D converter 515 for input to a data processor 514 in digital form for suitable processing in order to determine k (intrinsic thermal conductivity), (diffusivity), and (flow rate or perfusion). The values may be displayed in a display device 516.
(31) The system incorporates the mathematical model described herein and exemplified by FIGS. 1A and 1B. The data processor 514 includes the thermal property data processor 519 and thermal conductivity model 520. The thermal property data processor 519 receives input from the thermal conductivity model 520 (corresponding to the examples of FIGS. 1A and 1B) to solve the above expressions 7, 8 and 9. The data processor 514 computes brain intravascular water (BIW) from the measured values for tissue conductivity (6.0 m.sub./cm- C. in the example of FIG. 1A) and perfusion (40% in the example of FIG. 1A).
(32) Viewing FIG. 6, a thermal probe 610 (e.g.: thermistor) is introduced into the cranium and into the brain tissue 611 via a burr hole through the skull 620. It is held in place by a cranial bolt 618.
(33) Referring to FIG. 5, the probe 510 (which may be a self-heating thermistor) is immersed in a volume of tissue 511 and heated by a heater voltage V.sub.h(t) supplied via power source and control circuit 513. The temperature of the probe (i.e.: thermistor) is rapidly raised to a predetermined level above its initial equilibrium temperature, thus above the baseline temperature of the surrounding tissue, by the power source and control circuit 513. The heated probe causes the temperature of the surrounding volume of tissue to rise. The volume of tissue surrounding the probe 510 in which the temperature of the tissue is elevated to any substantial extent by the heated probe is considered the measurement field. The rate at which heat is transferred from the probe 510 is a function of the effective thermal conductivity of the tissue. The power used or dissipated in the probe 510 to maintain a predetermined elevated temperature level thus is also a function of the effective thermal conductivity of the surrounding tissue. The effective thermal conductivity of living tissue has two principal components, intrinsic thermal conductivity (k) of the tissue and tissue perfusion () (i.e.: the effect of convection in the tissue). Intrinsic thermal conductivity of tissue is a function of tissue water content. Therefore the rate of heat transfer from the probe 510 is also a function of tissue water content. The voltage V.sub.h(t) across the probe 510 provides a parameter from which a determination of the effective thermal conductivity is made. The sensed voltage V.sub.s(t) from probe 510 is supplied to A/D converter 515 for input to a data processor 514 in digital form suitable for processing. In the data processor 514 the thermal effect of intrinsic thermal conductivity (k) and the thermal effect of perfusion () are separated and determined. The determined values may be displayed in a display device 516. The intrinsic thermal conductivity value is used in the calculation of tissue water content.
(34) In the data processor 514, as mentioned above, the thermal property data processor 519 receives input from the thermal property model 520 to solve expressions 7, 8 and 9. The data processor 514 computes brain total water (BW) from the measured value of conductivity (k) and brain intravascular water (BIW) from the measured values of conductivity (k) and perfusion () and the perfusion coefficient of thermal conductivity (m.sub.). (See FIG. 1A or FIG. 1B.) Brain extravascular water (BEW) is the difference between the computed value of brain total water (BW) and the computed value of brain intravascular water (BIW). A value for edema is obtained by deducting from the resulting value for brain extravascular water (BEW) a selected tissue water content value within the normal range of tissue water values. The value for edema is displayed on the display device 516.
(35) In the herein described embodiments for measuring edema the mathematical model is that described above, particularly that embodied by expressions (7), (8) and (9). The mathematical model is implemented in the data processor 514 to determine brain intravascular water (BIW) and brain extravascular water (BEW) components of total brain water (BW), which values along with the calculated value of edema may be displayed in the display device 516. The significance of BIW, BEW and BW is illustrated in the plots of FIG. 1A. In that example the patient's current assessment is shown at a measured conductivity (k) value of 6.0 mw/cm- C. and a measured perfusion () value of 40 ml/100 g-min. The measured conductivity value of 6.0 corresponds to total brain water (BW) of approximately 95%. The perfusion coefficient of thermal conductivity (m.sub.) is plotted as a downwardly sloped line intersecting the conductivity axis at the point of measured conductivity (i.e.: the value of 6.0). The locus of the intercept of the sloped line (i.e.: the perfusion coefficient of thermal conductivity, m.sub.) with the line representing the measured perfusion value (i.e.: the value of 40) defines the computed value of thermal conductivity. The computed value of thermal conductivity is indicative of the separate brain intravascular water and brain extravascular water components of total brain water. In FIG. 1A the computed value of thermal conductivity is 5.80 mw/cm- C.; that value corresponds to a brain extravascular water value of 90% and a brain intravascular water value of 5% (total brain water of 95% minus brain extravascular water of 90%). Edema is the portion of brain extravascular water in excess of the normal levels of brain extravascular water. The normal level of brain extravascular water is shown on the plot of FIG. 1A as 69.6%1%. Using the value of 69.6% for normal extravascular water, edema in the illustrated instance is 20.4% (brain extravascular water of 90% minus normal extravascular water of 69.6%). (The value for normal extravascular water can be any value selected from the range of normal values, shown in FIG. 1A as 67%-73%).
(36) In FIGS. 1A and 1B the slope of the plot representing the perfusion coefficient of thermal conductivity (m.sub.) is constant and its intercept with the conductivity axis is located at the measured value of conductivity. Accordingly, with changes in measured values of conductivity and measured values of perfusion the changed values of total brain water, brain intravascular water and brain extravascular water are reflected. Empirical data (FIGS. 2B and 2B) suggests a linear fit for the perfusion coefficient of thermal conductivity. This is reflected in linear slope of the plot of the perfusion coefficient of thermal conductivity in FIGS. 1A and 1B. It is possible that more data possibly could introduce a small non-linearity in the fit and thus in the plot.
(37) In one embodiment of this invention the method of quantifying edema includes the steps shown in the flow chart of FIG. 7. Living tissue is contacted with the thermistor and the thermistor is heated (700) to a level above the base temperature of the tissue. This causes the temperature of a volume of tissue surrounding the thermistor to rise. The rate at which heat dissipates from the thermistor is a function of the perfusion in the tissue and the thermal conductivity of the tissue. The thermal conductivity of the tissue is determined (710) and tissue perfusion is determined (720) as a function of the temperature rise of the thermistor and the power required to heat the thermistor. The model of tissue conductivity as a function of perfusion, referenced above in connection with FIGS. 1A and 1B, is accessed (730) and the data processor computes (740) a second, calculated, value of conductivity as a function of measured values of thermal conductivity and perfusion, the second value of conductivity being indicative of the extravascular water content. (Viewing FIGS. 1A and 1B, the second value of conductivity is the value of conductivity at the intercept of the vertical measured perfusion line with the sloped plot of the perfusion coefficient of thermal conductivity.) A normal value of thermal conductivity, that characteristic of a healthy subject, is accessed (750) and subtracted from the second conductivity value (760) to obtain the conductivity associated with patient edema (770).
(38) In one embodiment a method for quantifying edema in living tissue of a subject comprises the steps of:
(39) contacting living tissue with a thermal sensor at a site where edema is to be quantified;
(40) energizing the thermistor to cause the temperature of a volume of tissue to rise;
(41) as a function of the power used to energize the thermistor and the temperature rise of the thermistor determining thermal conductivity of the volume of tissue and perfusion in the volume of tissue;
(42) accessing a model relating the perfusion coefficient of thermal conductivity to the determined tissue conductivity and the determined tissue perfusion;
(43) determining a second value of conductivity indicative of tissue extravascular water using the determined value of conductivity, the determined value of perfusion and the conductivity model;
(44) accessing a value of conductivity typical of a healthy subject; and
(45) computing a value indicative of edema as a function of the difference between the second value of conductivity and the value of conductivity typical of a healthy subject.
(46) The invention is not to be deemed as limited to the herein described embodiments except as defined by the following claims.
