- Email: [email protected]
Microminiaturized thermistor arrays for temperature gradient, flow and perfusion measurements
Sens.ws
and Actuators
A,
25-27
(1991)
641
6414545
Microminiaturized Thermistor Arrays for Temperature Gradient, Flow and Perfusion Measurements H. KUTTNER, L.
G. URBAN,
Boltmann-Institut
University
Vienna,
ftir
A. JACHIMOWICZ,
biomedizinische
Gwhaussrrasse
Mikrotechnik
F. KOHL, F. OLCAYTUG und Institut
jitir ollgemeke
and P. GOISER Elektrotechnik
und Elektronik,
Technical
27-29, A- 1040 Vienna (Austria)
Abstract This work reports first experiments on novel probes for measuring mass flow, heat conductivity, perfusion and local temperature gradient. Arrays of high quality microminiaturized thin-film thermistors were used. The outstanding features of these thermistors are the high temperature resolution, the small tracking error between the sensors and the small size of a single thermistor, which allows the use of minimized substrate sizes. The results of our experiments to measure mass flow and perfusion with the heat clearance method are very encouraging. The suitability is good, especially for low mass flow in a micro-channel and on-line blood-flow measurements in physiological matter. Further experiments with the heat clearance device show the probe is also feasible for vacuum measurements.
with interdistances of 0.4 mm and have a sensitive area of 0.014mm2 each. The 90% response time of the sensor is typically 3 ms. The miniaturized probe shown in Fig. 1 enables one to take measurements in physiological matter without serious destruction of tissue. A six-site temperature probe was designed on a flat, needle-shaped glass substrate, which was originally intended for the investigation of biological temperature fields with high spatial resolution [4]. Due to the features mentioned above, the same thermistor arrangement can serve for studies of perfusion in biological tissue, using the heat clearance method [5]. Further experiments in the laboratory showed that the use of this probe is feasible for the construction of sensitive mass-flow meters for liquid media
161. With a modified arrangement of the thermistors it is also possible to measure the
1. Methods Amorphous Ge films are used as the thermistor material [ 11. The temperature dependence of the conductivity (TCR) of the evaporated Ge films used is 2%/K at room temperature and a temperature resolution of 0.1 mK has been obtained at 303 K. The tracking error between two sensor elements is only 0.2% over the measurement range 273335 K. The structures of the probe are insulated by a 3 pm thick PeCVD silicon nitride layer [2, 31. The thermistors are arranged in a row
Fig. 1. Miniaturized thermistor array on a glass substrate.
Elsevier Sequoia/Printed in The Netherlands
642
thermal conductivity of several materials very easily. For flow and perfusion determination the thermistor arrays are used to detect the mass flow of a fluid with the heat-clearance method [5]. This system uses at least two thermistors of the sensor array. One of these measures the ambient temperature, whereas the other thermistor is kept at a temperature above the ambient value. The constant temperature difference is maintained by an electronic control circuit whose output power is dissipated by the heated thermistor. This power is closely related to the mass flow of a is specific medium. Power dissipation confined to the active thermistor material due to the high electrical resistance of the Ge film compared to that of the thin-film connection lines. Additionally this allows simple twowire measuring circuitry to be used. Figure 2 shows the scheme of the flow and perfusion measurement unit. In the case of flow measurements in a small tube it is advantageous to use a geometrical design where the heated and unheated probe are located on different substrates. This gives rise to a minimized parasitic heat flow between the two probes. For use as a perfusion measurement system, the heated and unheated probes must be located at the same substrate
to minimize tissue damage and to ensure a fixed interdistance between the two probes. Measurements in a miniaturized flow channel were taken as well as perfusion and temperature gradient records in the cerebral cortex of rabbits.
2. Characterization
of the Probe
2.1. Thermal Resistance The thermal resistance of the active thermistor area against the environment was determined for different media and in vacuum at a pressure of 10 Pascal. Table 1 shows the values of the thermal resistance of the thermistor located at the top of the needle-type sensor. The other probes on the substrate have only slightly different values except for in vacuum. That is caused by the low thermal energy flow along the substrate compared to the heat flow into the medium through the 3 pm thick silicon nitride layer. 2.2. Transient Characteristics
There are two major effects which determine the response time of one thermistor during a measurement. 2.2.1. The passive and active thermal response time
If the sensor is used as a passive ambient temperature measuring unit, the transient time depends on how fast the substrate has equilibrated its temperature with the medium. This characteristic has a value of less than 3 ms [7]. The active thermal time constant occurs if the substrate already has the same temperaTABLE 1. Thermal resistance of one thermistor on the probe
U,, = f(per
fI)
Fig. 2. Scheme of the flow and perfusion measurement unit.
Medium
Thermal resistance [ lo3 K/WI sensor # 1 [top)
Hz0 Glycerine Atm. air Vacuum
x30/27 “C 4.5 127 “C 35/23 “C, 1015 hPa IO/O.1Pa
ture as the surrounding medium and the probe is used as a self-heating thermistor. After a sudden change of the supplied power it takes a few ns until the probe reaches 90% of the total temperature change [l]. The arrangement used for flow measurements as described above has a response time of approximately 300 ms until the heating power is settled. This duration corresponds to the establishment of the temperature field in the medium around the probe. 22.2. The electrical response time If the thermistor is connected to an electrical circuit, the output signal settling time is limited in general by an RC time constant. The minimal parasitic capacitance (without connecting cables) of one sensor on the substrate is approximately 100 pF. With the electrical resistance of the sensors between 300 kQ and 600 kQ, the RC time constant is below 60 ps. An important consequence of the large RC time constant compared to the active thermal response time is that heatpulse measuring techniques are not feasible. 2.3. Stability and Hysteresis
A long-term drift of the thermistor leads to an error of 0.25 K per year. The resolution and short time stability allow temperature differences of the order of 0.1 mK at 300 K to be measured. If the probe is cycled from 280 K to 330 K and back, a slight hysteresis is observed which would limit the accuracy. In this case the maximum temperature deviation is about 30 to 50 mK. This error disappears if the sensor is held in a small temperature range. Another way to reduce this hysteresis effect is to cycle the temperature over the whole range several ( >6) times. After this procedure, the hysteresis of the output signal is less than 10 mK.
3. Results 3.1. Measurement of Mass Flow Several measurements were taken inside a Plexiglass channel of 1.8 mm diameter using
m Yuutun:
c
1 [xl
; B !!I 3m 2:
; 108 3106 t3 t 104 X ,: 102 L 100
643
Pa Se g
*,=
0
0.2
0.4
0.6
0.8 hlr.
ZBC
1
:a ji
1.2
[mm/s1
Fig. 3. Relative power dissipation on the thermistor vs. flow velocity.
glycerine as flow medium. The heating power in relation to the mass flow is in good correlation with a theoretical model [8]. The usable measuring range corresponds to a flow velocity range of 0.05 mm/s up to 0.8 mm/s in glycerine. The temperature difference due to probe heating can be chosen between 300 mK and 2 K. The power dissipation on the probe increases non-linearly with the flow velocity. Up to a value of 250 pm/s, the output increases nearly linearly with the flow. Beyond this range the signal rise decreases because a higher velocity only causes a slightly increased heat flow over the boundary layer. Therefore for higher flow rates the accuracy of the measurement decreases and the useful measuring range is limited to 0.8 mm/s. Figure 3 shows the relative power dissipation versus flow velocity with glycerine as flow medium in a channel of 1.8 mm diameter. One advantage of glycerine as flow medium is its thermal properties and high viscosity. Low microconvection around the heated thermistor, and therefore small fluctuation of the output signal, result from this. 3.2.. Measurement of Regional Cerebral Blood Flow (r CBF) The probe equipped with six temperature sensors was mounted on a printed circuit board acting as mechanical and electrical support. Rabbits were anaesthetized initially with 20 mg/kg Thiopental. After a tracheotomy, animals were artificially ventilated with oxygen and anaesthesia was continued with 0.4% Halothane. Alloferin@ was used as muscle
644
-
Fig. 4. Variation of rCBF with 5% CO, breathing gas component.
:
35.0
:
/ I
2
J
/ f
Ll
40&m
relaxant. The skull was trepanized above the visual cortex (area 0~1). The printed circuit board was fixed to a stereotactic holder and placed above the visual cortex of the rabbits. The needle probe was carefully inserted vertically into the neocortex until the uppermost sensing area was located just beneath the cortical surface. After insertion of the needle, the trepanized region was covered with agar gel and the temperature was equilibrated within half an hour. The animals were placed on a temperature-regulated heating pad. Figure 4 shows the variation of regional cerebral blood flow evoked by the 5% CO2 component of the breathing gas. During 30 s inhalation a rise of perfusion after a delay time of 10 s was caused. The decrease of perfusion to the baseline takes place with a time constant of 4 min, which is longer than that for the perfusion increase. 3.3. Measurement of Temperature Fields Several recordings were taken in the cerebral cortex of rabbits to study the temperature in relation to changes of the composition of the anaesthetic gas. The preparation method of the rabbits was the same as that described in Section 3.2. As mentioned above, the covering of the prepared hole in the skull with agar gel was a very important requirement to get proper results. Figure 5 shows a typical temperature distribution and gradient within the cortical layer of a rabbit. The temperature decreases 2 K within a 2 mm layer. The temperature gradient shows a flat behaviour near the white matter as well as
: / 5
6
Nr.of swnh
spotIn4
Fig. 5. Typical temperature distribution and gradient in the cerebral cortex of a rabbit.
higher changes in the histological layers III to IV and an evident increase towards the surface. 3.4. Measurement of Thermal Resistance in Liquid Media
A different sensor arrangement was used to determine thermal resistance with the heat clearance control unit. The major difference in the sensor design was that two needles were used, one level with the other. The interdistance of two rows of thermistors was 2 mm. Similar to channel flow measurement, the heated and unheated probe are on these different substrates to minimize parasitic heating. The probe with the double needle was inserted into different liquid media in a 10 ml glass beaker. Due to the two thermistor measurements the ambient temperature does not effect the results of the measurement. The results of the experiments have a good reproducibility within a maximum tolerance of 2% and can be calibrated for estimation of the thermal conductivity.
4. Discussion
Various temperature-field, flow, perfusion and thermal resistance measurements were taken with good reproducibility. All of the above-mentioned measurements were taken with the standard thin-film layout. Neverthe-
645
less, it is possible to optimize the probe design for the different investigations. In most cases when the thermal resistance of the medium is lower than that of the substrate material, the temperature field around the probe will be only negligibly affected. As a result of the extremely high temperature resolution of the thermistor used, a very small temperature difference is required for sensitive mass-flow and perfusion measurements by the heat clearance device. Thus investigations of vulnerable matter like cortical tissue or thermal labile fluids can be performed. Due to the small size and the high quality of the sensor it was possible to get new results in some fields of investigation. Further expe rience gained with the standard structure also showed good feasibility for vacuum pressure measurement’ and for recording of chemical reaction enthalpy in a microcalorimetric device.
References 1 G. Urban, Hochauflosende Temperatursensoren fiir Medizin und Technik, Doctor’s Thesis, Institut fur
Allgemeine Elektrotechnik und Elektronik, Technical University, Vienna, Austria, 1985. 2 G. Rieder and F. Olcaytug, Preparation and dielectric properties of S&N, thin films, Thin Solid Films, 89 (1982) 95-99. 3 F. Olcaytug, K. Riedling and W. Fallmann, A low temperature process for the reactive formation of Si,N4 layers on InSb. Thin Solid Films. 67 (1980) 321-324. 4 G. Urban, A. Jachimowicz, F. Kohl, H. Kuttner, P.
Goiser, K. Lindner and H. Pockberger, High resolution multi-temperature sensors for biomedical application, Medical Progress through Technology, in press. 5 J. Kuttner, G. Urban, A. Jachimowicz, et al., Mikrominiaturisierter Mehrfach-Temperatursensor fiir Durchblutungsmessungen, Beitrug zum Band zur Jahrestagung der Gesallschaft ftirBiomedizische Technologie Iglsllnnsbncck, 1990.
6 H. Kuttner, Integrierte Wlrmeflusssensoren zur StrBmungsmessung, Diplomurbeit, Institut fur Allgemeine
Elektrotechnik, Technical University, Vienna, Austria, 1987. 7 G. Urban, A. Jachimowicz, F. Kohl, H. Kuttner, F. Olcaytug, H. Kamper, 0. Prohaska and M. Schonauer, High resolution thin-film temperature sensors for medical applications, Sensors and Actuators, A21 A23 (1990) 650-654. 8 L. Priebe, Heat transport and specific blood flow in
homogeneously and isotropically perfused tissue, in Hardy, Gagge et al. (eds), Physiological and Behavioral Temperature Regulation, Thomas, Springfield, IL, U.S.A., 1970.
and Actuators
A,
25-27
(1991)
641
6414545
Microminiaturized Thermistor Arrays for Temperature Gradient, Flow and Perfusion Measurements H. KUTTNER, L.
G. URBAN,
Boltmann-Institut
University
Vienna,
ftir
A. JACHIMOWICZ,
biomedizinische
Gwhaussrrasse
Mikrotechnik
F. KOHL, F. OLCAYTUG und Institut
jitir ollgemeke
and P. GOISER Elektrotechnik
und Elektronik,
Technical
27-29, A- 1040 Vienna (Austria)
Abstract This work reports first experiments on novel probes for measuring mass flow, heat conductivity, perfusion and local temperature gradient. Arrays of high quality microminiaturized thin-film thermistors were used. The outstanding features of these thermistors are the high temperature resolution, the small tracking error between the sensors and the small size of a single thermistor, which allows the use of minimized substrate sizes. The results of our experiments to measure mass flow and perfusion with the heat clearance method are very encouraging. The suitability is good, especially for low mass flow in a micro-channel and on-line blood-flow measurements in physiological matter. Further experiments with the heat clearance device show the probe is also feasible for vacuum measurements.
with interdistances of 0.4 mm and have a sensitive area of 0.014mm2 each. The 90% response time of the sensor is typically 3 ms. The miniaturized probe shown in Fig. 1 enables one to take measurements in physiological matter without serious destruction of tissue. A six-site temperature probe was designed on a flat, needle-shaped glass substrate, which was originally intended for the investigation of biological temperature fields with high spatial resolution [4]. Due to the features mentioned above, the same thermistor arrangement can serve for studies of perfusion in biological tissue, using the heat clearance method [5]. Further experiments in the laboratory showed that the use of this probe is feasible for the construction of sensitive mass-flow meters for liquid media
161. With a modified arrangement of the thermistors it is also possible to measure the
1. Methods Amorphous Ge films are used as the thermistor material [ 11. The temperature dependence of the conductivity (TCR) of the evaporated Ge films used is 2%/K at room temperature and a temperature resolution of 0.1 mK has been obtained at 303 K. The tracking error between two sensor elements is only 0.2% over the measurement range 273335 K. The structures of the probe are insulated by a 3 pm thick PeCVD silicon nitride layer [2, 31. The thermistors are arranged in a row
Fig. 1. Miniaturized thermistor array on a glass substrate.
Elsevier Sequoia/Printed in The Netherlands
642
thermal conductivity of several materials very easily. For flow and perfusion determination the thermistor arrays are used to detect the mass flow of a fluid with the heat-clearance method [5]. This system uses at least two thermistors of the sensor array. One of these measures the ambient temperature, whereas the other thermistor is kept at a temperature above the ambient value. The constant temperature difference is maintained by an electronic control circuit whose output power is dissipated by the heated thermistor. This power is closely related to the mass flow of a is specific medium. Power dissipation confined to the active thermistor material due to the high electrical resistance of the Ge film compared to that of the thin-film connection lines. Additionally this allows simple twowire measuring circuitry to be used. Figure 2 shows the scheme of the flow and perfusion measurement unit. In the case of flow measurements in a small tube it is advantageous to use a geometrical design where the heated and unheated probe are located on different substrates. This gives rise to a minimized parasitic heat flow between the two probes. For use as a perfusion measurement system, the heated and unheated probes must be located at the same substrate
to minimize tissue damage and to ensure a fixed interdistance between the two probes. Measurements in a miniaturized flow channel were taken as well as perfusion and temperature gradient records in the cerebral cortex of rabbits.
2. Characterization
of the Probe
2.1. Thermal Resistance The thermal resistance of the active thermistor area against the environment was determined for different media and in vacuum at a pressure of 10 Pascal. Table 1 shows the values of the thermal resistance of the thermistor located at the top of the needle-type sensor. The other probes on the substrate have only slightly different values except for in vacuum. That is caused by the low thermal energy flow along the substrate compared to the heat flow into the medium through the 3 pm thick silicon nitride layer. 2.2. Transient Characteristics
There are two major effects which determine the response time of one thermistor during a measurement. 2.2.1. The passive and active thermal response time
If the sensor is used as a passive ambient temperature measuring unit, the transient time depends on how fast the substrate has equilibrated its temperature with the medium. This characteristic has a value of less than 3 ms [7]. The active thermal time constant occurs if the substrate already has the same temperaTABLE 1. Thermal resistance of one thermistor on the probe
U,, = f(per
fI)
Fig. 2. Scheme of the flow and perfusion measurement unit.
Medium
Thermal resistance [ lo3 K/WI sensor # 1 [top)
Hz0 Glycerine Atm. air Vacuum
x30/27 “C 4.5 127 “C 35/23 “C, 1015 hPa IO/O.1Pa
ture as the surrounding medium and the probe is used as a self-heating thermistor. After a sudden change of the supplied power it takes a few ns until the probe reaches 90% of the total temperature change [l]. The arrangement used for flow measurements as described above has a response time of approximately 300 ms until the heating power is settled. This duration corresponds to the establishment of the temperature field in the medium around the probe. 22.2. The electrical response time If the thermistor is connected to an electrical circuit, the output signal settling time is limited in general by an RC time constant. The minimal parasitic capacitance (without connecting cables) of one sensor on the substrate is approximately 100 pF. With the electrical resistance of the sensors between 300 kQ and 600 kQ, the RC time constant is below 60 ps. An important consequence of the large RC time constant compared to the active thermal response time is that heatpulse measuring techniques are not feasible. 2.3. Stability and Hysteresis
A long-term drift of the thermistor leads to an error of 0.25 K per year. The resolution and short time stability allow temperature differences of the order of 0.1 mK at 300 K to be measured. If the probe is cycled from 280 K to 330 K and back, a slight hysteresis is observed which would limit the accuracy. In this case the maximum temperature deviation is about 30 to 50 mK. This error disappears if the sensor is held in a small temperature range. Another way to reduce this hysteresis effect is to cycle the temperature over the whole range several ( >6) times. After this procedure, the hysteresis of the output signal is less than 10 mK.
3. Results 3.1. Measurement of Mass Flow Several measurements were taken inside a Plexiglass channel of 1.8 mm diameter using
m Yuutun:
c
1 [xl
; B !!I 3m 2:
; 108 3106 t3 t 104 X ,: 102 L 100
643
Pa Se g
*,=
0
0.2
0.4
0.6
0.8 hlr.
ZBC
1
:a ji
1.2
[mm/s1
Fig. 3. Relative power dissipation on the thermistor vs. flow velocity.
glycerine as flow medium. The heating power in relation to the mass flow is in good correlation with a theoretical model [8]. The usable measuring range corresponds to a flow velocity range of 0.05 mm/s up to 0.8 mm/s in glycerine. The temperature difference due to probe heating can be chosen between 300 mK and 2 K. The power dissipation on the probe increases non-linearly with the flow velocity. Up to a value of 250 pm/s, the output increases nearly linearly with the flow. Beyond this range the signal rise decreases because a higher velocity only causes a slightly increased heat flow over the boundary layer. Therefore for higher flow rates the accuracy of the measurement decreases and the useful measuring range is limited to 0.8 mm/s. Figure 3 shows the relative power dissipation versus flow velocity with glycerine as flow medium in a channel of 1.8 mm diameter. One advantage of glycerine as flow medium is its thermal properties and high viscosity. Low microconvection around the heated thermistor, and therefore small fluctuation of the output signal, result from this. 3.2.. Measurement of Regional Cerebral Blood Flow (r CBF) The probe equipped with six temperature sensors was mounted on a printed circuit board acting as mechanical and electrical support. Rabbits were anaesthetized initially with 20 mg/kg Thiopental. After a tracheotomy, animals were artificially ventilated with oxygen and anaesthesia was continued with 0.4% Halothane. Alloferin@ was used as muscle
644
-
Fig. 4. Variation of rCBF with 5% CO, breathing gas component.
:
35.0
:
/ I
2
J
/ f
Ll
40&m
relaxant. The skull was trepanized above the visual cortex (area 0~1). The printed circuit board was fixed to a stereotactic holder and placed above the visual cortex of the rabbits. The needle probe was carefully inserted vertically into the neocortex until the uppermost sensing area was located just beneath the cortical surface. After insertion of the needle, the trepanized region was covered with agar gel and the temperature was equilibrated within half an hour. The animals were placed on a temperature-regulated heating pad. Figure 4 shows the variation of regional cerebral blood flow evoked by the 5% CO2 component of the breathing gas. During 30 s inhalation a rise of perfusion after a delay time of 10 s was caused. The decrease of perfusion to the baseline takes place with a time constant of 4 min, which is longer than that for the perfusion increase. 3.3. Measurement of Temperature Fields Several recordings were taken in the cerebral cortex of rabbits to study the temperature in relation to changes of the composition of the anaesthetic gas. The preparation method of the rabbits was the same as that described in Section 3.2. As mentioned above, the covering of the prepared hole in the skull with agar gel was a very important requirement to get proper results. Figure 5 shows a typical temperature distribution and gradient within the cortical layer of a rabbit. The temperature decreases 2 K within a 2 mm layer. The temperature gradient shows a flat behaviour near the white matter as well as
: / 5
6
Nr.of swnh
spotIn4
Fig. 5. Typical temperature distribution and gradient in the cerebral cortex of a rabbit.
higher changes in the histological layers III to IV and an evident increase towards the surface. 3.4. Measurement of Thermal Resistance in Liquid Media
A different sensor arrangement was used to determine thermal resistance with the heat clearance control unit. The major difference in the sensor design was that two needles were used, one level with the other. The interdistance of two rows of thermistors was 2 mm. Similar to channel flow measurement, the heated and unheated probe are on these different substrates to minimize parasitic heating. The probe with the double needle was inserted into different liquid media in a 10 ml glass beaker. Due to the two thermistor measurements the ambient temperature does not effect the results of the measurement. The results of the experiments have a good reproducibility within a maximum tolerance of 2% and can be calibrated for estimation of the thermal conductivity.
4. Discussion
Various temperature-field, flow, perfusion and thermal resistance measurements were taken with good reproducibility. All of the above-mentioned measurements were taken with the standard thin-film layout. Neverthe-
645
less, it is possible to optimize the probe design for the different investigations. In most cases when the thermal resistance of the medium is lower than that of the substrate material, the temperature field around the probe will be only negligibly affected. As a result of the extremely high temperature resolution of the thermistor used, a very small temperature difference is required for sensitive mass-flow and perfusion measurements by the heat clearance device. Thus investigations of vulnerable matter like cortical tissue or thermal labile fluids can be performed. Due to the small size and the high quality of the sensor it was possible to get new results in some fields of investigation. Further expe rience gained with the standard structure also showed good feasibility for vacuum pressure measurement’ and for recording of chemical reaction enthalpy in a microcalorimetric device.
References 1 G. Urban, Hochauflosende Temperatursensoren fiir Medizin und Technik, Doctor’s Thesis, Institut fur
Allgemeine Elektrotechnik und Elektronik, Technical University, Vienna, Austria, 1985. 2 G. Rieder and F. Olcaytug, Preparation and dielectric properties of S&N, thin films, Thin Solid Films, 89 (1982) 95-99. 3 F. Olcaytug, K. Riedling and W. Fallmann, A low temperature process for the reactive formation of Si,N4 layers on InSb. Thin Solid Films. 67 (1980) 321-324. 4 G. Urban, A. Jachimowicz, F. Kohl, H. Kuttner, P.
Goiser, K. Lindner and H. Pockberger, High resolution multi-temperature sensors for biomedical application, Medical Progress through Technology, in press. 5 J. Kuttner, G. Urban, A. Jachimowicz, et al., Mikrominiaturisierter Mehrfach-Temperatursensor fiir Durchblutungsmessungen, Beitrug zum Band zur Jahrestagung der Gesallschaft ftirBiomedizische Technologie Iglsllnnsbncck, 1990.
6 H. Kuttner, Integrierte Wlrmeflusssensoren zur StrBmungsmessung, Diplomurbeit, Institut fur Allgemeine
Elektrotechnik, Technical University, Vienna, Austria, 1987. 7 G. Urban, A. Jachimowicz, F. Kohl, H. Kuttner, F. Olcaytug, H. Kamper, 0. Prohaska and M. Schonauer, High resolution thin-film temperature sensors for medical applications, Sensors and Actuators, A21 A23 (1990) 650-654. 8 L. Priebe, Heat transport and specific blood flow in
homogeneously and isotropically perfused tissue, in Hardy, Gagge et al. (eds), Physiological and Behavioral Temperature Regulation, Thomas, Springfield, IL, U.S.A., 1970.