A self-heated thermistor technique to measure effective thermal properties from the tissue surface

A microcomputer based instrument to measure effective thermal conductivity and diffusivity at the surface of a tissue has been developed. Self-heated spherical thermistors, partially embedded in an insulator, are used to simultaneously heat tissue and measure the resulting temperature rise. The temperature increase of the thermistor for a given applied power is a function of the combined thermal properties of the insulator, the thermistor, and the tissue. Once the probe is calibrated, the instrument accurately measures the thermal properties of tissue. Conductivity measurements are accurate to 2 percent and diffusivity measurements are accurate to 4 percent. A simplified bioheat equation is used which assumes the effective tissue thermal conductivity is a linear function of perfusion. Since tissue blood flow strongly affects heat transfer, the surface thermistor probe is quite sensitive to perfusion.     

Steady-state analysis of self-heated thermistors using finite elements

The purpose of this work is to validate, using numerical, finite element methods, the thermal assumptions made in the analytical analysis of a coupled thermistor probe-tissue model upon which a thermal conductivity measurement scheme has been based. Analytic, closed form temperature profiles generated by the self-heated thermistors can be found if three simplifying assumptions are made: the thermistor is spherical; heat is generated in all regions of the bead; and heat is generated uniformly in the bead. This analytic solution is used to derive a linear relationship between tissue thermal conductivity and the ratio of thermistor temperature rise over electrical power required to maintain that temperature rise. This derived, linear relationship is used to determine thermal conductivity from the observed experimental data. However, in reality, the thermistor bead is a prolate spheroid surrounded by a passive shell, and the heating pattern in the bead is highly nonuniform. In the physical system, the exact relationship between the tissue thermal conductivity and parameters measured by the thermistor is not known. The finite element method was used to calculate the steady-state temperature profiles generated by thermistor beads with realistic geometry and heating patterns. The results of the finite element analysis show that the empirical, linear relationship remains valid when all three simplified assumptions are significantly relaxed.     

Predicting effects of blood flow rate and size of vessels in a vasculature on hyperthermia treatments using computer simulation

Background

Pennes Bio Heat Transfer Equation (PBHTE) has been widely used to approximate the overall temperature distribution in tissue using a perfusion parameter term in the equation during hyperthermia treatment. In the similar modeling, effective thermal conductivity (K_eff) model uses thermal conductivity as a parameter to predict temperatures. However the equations do not describe the thermal contribution of blood vessels. A countercurrent vascular network model which represents a more fundamental approach to modeling temperatures in tissue than do the generally used approximate equations such as the Pennes BHTE or effective thermal conductivity equations was presented in 1996. This type of model is capable of calculating the blood temperature in vessels and describing a vasculature in the tissue regions.

Methods

In this paper, a countercurrent blood vessel network (CBVN) model for calculating tissue temperatures has been developed for studying hyperthermia cancer treatment. We use a systematic approach to reveal the impact of a vasculature of blood vessels against a single vessel which most studies have presented. A vasculature illustrates branching vessels at the periphery of the tumor volume. The general trends present in this vascular model are similar to those shown for physiological systems in Green and Whitmore. The 3-D temperature distributions are obtained by solving the conduction equation in the tissue and the convective energy equation with specified Nusselt number in the vessels.

Results

This paper investigates effects of size of blood vessels in the CBVN model on total absorbed power in the treated region and blood flow rates (or perfusion rate) in the CBVN on temperature distributions during hyperthermia cancer treatment. Also, the same optimized power distribution during hyperthermia treatment is used to illustrate the differences between PBHTE and CBVN models. K_eff (effective thermal conductivity model) delivers the same difference as compared to the CBVN model. The optimization used here is adjusting power based on the local temperature in the treated region in an attempt to reach the ideal therapeutic temperature of 43°C. The scheme can be used (or adapted) in a non-invasive power supply application such as high-intensity focused ultrasound (HIFU). Results show that, for low perfusion rates in CBVN model vessels, impacts on tissue temperature becomes insignificant. Uniform temperature in the treated region is obtained.

Conclusion

Therefore, any method that could decrease or prevent blood flow rates into the tumorous region is recommended as a pre-process to hyperthermia cancer treatment. Second, the size of vessels in vasculatures does not significantly affect on total power consumption during hyperthermia therapy when the total blood flow rate is constant. It is about 0.8% decreasing in total optimized absorbed power in the heated region as γ (the ratio of diameters of successive vessel generations) increases from 0.6 to 0.7, or from 0.7 to 0.8, or from 0.8 to 0.9. Last, in hyperthermia treatments, when the heated region consists of thermally significant vessels, much of absorbed power is required to heat the region and (provided that finer spatial power deposition exists) to heat vessels which could lead to higher blood temperatures than tissue temperatures when modeled them using PBHTE.     

Local heating of human skin by millimeter waves: effect of blood flow

We investigated the influence of blood perfusion on local heating of the forearm and middle finger skin following 42.25 GHz exposure with an open ended waveguide (WG) and with a YAV mm wave therapeutic device. Both sources had bell-shaped distributions of the incident power density (IPD) with peak intensities of 208 and 55 mW/cm(2), respectively. Blood perfusion was changed in two ways: by blood flow occlusion and by externally applied vasodilator (nonivamide/nicoboxil) cream to the skin. For thermal modeling, we used the bioheat transfer equation (BHTE) and the hybrid bioheat equation (HBHE) which combines the BHTE and the scalar effective thermal conductivity equation (ETCE). Under normal conditions with the 208 mW/cm(2) exposure, the cutaneous temperature elevation (DeltaT) in the finger (2.5 +/- 0.3 degrees C) having higher blood flow was notably smaller than the cutaneous DeltaT in the forearm (4.7 +/- 0.4 degrees C). However, heating of the forearm and finger skin with blood flow occluded was the same, indicating that the thermal conductivity of tissue in the absence of blood flow at both locations was also the same. The BHTE accurately predicted local hyperthermia in the forearm only at low blood flow. The HBHE made accurate predictions at both low and high perfusion rates. The relationship between blood flow and the effective thermal conductivity (k(eff)) was found to be linear. The heat dissipating effect of higher perfusion was mostly due to an apparent increase in k(eff). It was shown that mm wave exposure could result in steady state heating of tissue layers located much deeper than the penetration depth (0.56 mm). The surface DeltaT and heat penetration into tissue increased with enlarging the irradiating beam area and with increasing exposure duration. Thus, mm waves at sufficient intensities could thermally affect thermo-sensitive structures located in the skin and underlying tissue.     

Thermal pulse decay method for simultaneous measurement of local thermal conductivity and blood perfusion: a theoretical analysis

Presented here is a theoretical analysis of the recently developed thermal pulse decay (TPD) method for a simultaneous measurement of local tissue conductivity and blood perfusion rate. The paper describes the theoretical model upon which the TPD method is based and details its capabilities and limitations. The theoretical aspects that affected the development of the measurement protocol are also discussed. The performance of the method is demonstrated with an experimental example which compares the measurements of local kidney blood perfusion rates made using the TPD method with the total renal blood flow obtained coincidentally using a blood flowmeter, in an anesthetized dog.     

Calculation of thermally caused blood flow changes in a finger using thermographic skin temperature measurements (author's transl)]

The skin temperature changes of the third finger were registered with the help of an infrared camera during a cooling process of the hand and forearm of a male, 38-years-old subject. Using the system of formulae, explained in previous publications [4-7], it was possible to describe the blood flow changes in the finger. The results are: 1. A formula for the "pseudo thermal conductivity" (material constant of the thermal conductivity plus the convective contribution), which is similar to the formula used for theat release of the whole body [4], describes well the experimental results. The "pseudo thermal conductivity" is a measure for the specific blood flow and can be converted into it. 2. The "pseudo thermal conductivity" has a local maximum. 3. The position of the maximum is independent of the tissue temperature. The anatomical properties of the finger seem to determine the position of the maximum. 4. The maximum of the "pseudo thermal conductivity"--and therefore the maximal blood flow--increases stronger than linearly with the tissue temperature.     

Two-regime model of the perfusion measuring heated thermocouple probe

A theoretical analysis of the transient temperature responses of a heated thermocouple and its surroundingin vivo tissue is described. The model includes the effects of local blood perfusion, metabolic heat generation and blood pooling. The solutions presented are generalized for pulsed heating in the probe region. Inspection of these solutions reveals that for accurate experimental results precise knowledge of the tissue's thermal conductivity is necessary but that blood pooling around the probe may sometimes be regarded as an insignificant parameter.     

High-intensity static magnetic fields modulate skin microcirculation and temperature in vivo

We investigated the acute effect of static magnetic fields of up to 8 T on skin blood flow and body temperature in anesthetized rats. These variables were measured prior to, during, and following exposure to a magnetic field in a superconducting magnet with a horizontal bore. The dorsal skin was transversely incised for 1 cm to make a subcutaneous pocket. Probes of a laser Doppler flowmeter and a thermistor were inserted into the pocket and positioned at mid-dorsum to measure skin blood flow and temperature. Another thermistor probe was put into the rectum to monitor rectal temperature. After baseline measurement outside the magnet, the rat was inserted into the bore for 20 min so that mid-dorsum was exactly positioned at the center, where the magnetic field was nearly homogeneous. Post-exposure changes were then recorded for 20 min outside the bore. Sham-exposed animals were submitted to exactly the same conditions, except that the superconducting magnet was not energized. Skin blood flow and temperature decreased significantly during magnetic field exposure and recovered after removal of the animal from the magnet. The rectal temperature showed a tendency to decrease while the animal was in the magnet. The microcirculatory and thermal reactions in the present study were consistent and agreed with some of the predictions based on mathematical simulations and model experiments.     

A new technique utilizing thermistor probes for the measurement of thermal properties of biomaterials

The thermal limitations inherent with the use of invasive thermistor probes in the measurement of thermal properties of biomaterials have been investigated. An electronic temperature controller has been developed which provides a nearly instantaneous step rise in average probe resistance (temperature). The method of experimentally determining the heat rate required to maintain the average probe temperature constant and incorporation of that heat rate into the general heat diffusion equation provides a solution which allows the determination of both thermal conductivity and diffusivity values with improved accuracy. The method is general to all media which wet the surface of the probe; the need for calibrating media is avoided. The solution also predicts the minimum required sample size.     

树干自然温度梯度变化对热扩散法测算树干液流速率的影响

为了揭示树干自然温度梯度的变化规律及其对树干液流速率测算结果的影响,于2007年5月至10月利用改进的SF-L型热扩散式树液流测定装置,对北京低山区生长的油松和侧柏的树干自然温度梯度、加热温差和气象、土壤水分因子进行了连日同步监测。结果表明:(1)树干自然温度梯度对加热针温差的影响,侧柏大于油松。(2)树干自然温度梯度对液流速率计算结果的影响具有显著的统计意义(P0.01),平均误差大于30%,误差峰值出现在太阳高度角较小的时候。(3)影响树干自然温度梯度最重要的环境因子是光照强度,其次是空气温度。上述结果说明,树干自然温度梯度对热扩散法测定的液流速率的影响不可忽视,研究树木耗水机制时应予以充分考虑。光照强度和空气温度是影响树干自然温度梯度最重要的两个因子,但其影响机制仍需进一步研究。     

Heat transport mechanisms in vascular tissues: a model comparison

We have conducted a parametric comparison of three different vascular models for describing heat transport in tissue. Analytical and numerical methods were used to predict the gross temperature distribution throughout the tissue and the small-scale temperature gradients associated with thermally significant blood vessels. The models are: an array of unidirectional vessels, an array of countercurrent vessels, and a set of large vessels feeding small vessels which then drain into large vessels. We show that three continuum formulations of bioheat transfer (directed perfusion, effective conductivity, and a temperature-dependent heat sink) are limiting cases of the vascular models with respect to the thermal equilibration length of the vessels. When this length is comparable to the width of the heated region of tissue, the local temperature changes near the vessels can be comparable to the gross temperature elevation. These results are important to the use of thermal techniques used to measure the blood perfusion rate and in the treatment of cancer with local hyperthermia.     

The heat transfer analysis of nanoparticle heat source in alanine tissue by molecular dynamics

The purpose of this study is to simulate the heat transfer problem when the 3-D Alanine tissue is heated by the gold nanoparticle in the field of molecular dynamics. In this paper, the Alanine molecule is adopted and its parameters are available in the GROMACS protein data bank. A computing algorithm is developed to evaluate the heat transfer phenomena in the nano-scale biological system based on the molecular dynamics and the protein data bank. The value of the thermal conductivity of Alanine is calculated from the autocorrelation function of the Green-Kubo formalism and this result has a roughly approximation with the bulk thermal conductivity reported by experimental data . Two kinds of problems are investigated in the paper. One is the Alanine tissue heated by the constant heat source and the other is by the time-varying heat source. The numerical results show that a temperature jump exists around the source and the temperature profiles drop to the environmental temperature within a very short distance. It concludes that only a small region around the nano-scale heat source is affected by the heated process. Therefore, the results of the nanoparticle-heated method could be applied to the clinical therapy of tumor, and the normal cells are destroyed only within a smaller region than those of chemotherapy or surgery.     

Perfused phantom models of microwave irradiated tissue

The theoretical basis, practical design considerations, and prototype testing of a perfused model suitable for simulation studies of microwave heated tissue are presented. A parallel tube heat exchanger configuration is used to simulate the internal convection effects of blood flow. The global thermal response of the phantom, on a scale of several tube spacings, is shown theoretically to be nearly identical to that predicted by Pennes' bioheat equation, which is known to give a reasonable representation of tissue under many conditions. A parametric study is provided for the relationships between the tube size, spacing and material properties and the simulated perfusion rate. A prototype with a physiologically reasonable perfusion rate was tested using a typical hyperthermia applicator. The measured thermal response of the phantom compares favorably with the numerical solution of the bioheat equation under the same irradiation conditions. This similarity sheds light on the unexpected success of the bioheat equation for modeling the thermal response of real tissue.     

Local Blood Flow in Human Leg Muscle Measured by a Transient Response Thermoelectric Method

The initial transient response of a Gibbs type thermoelectric probe embedded in human resting leg muscle was used for absolute quantitative measurement of local blood flow per unit tissue volume (local perfusion). The probe consisted of two thermistor-containing needles, one of which was heated by a constant electrical power input. The temperatures of both thermistors were recorded continuously on a two-channel, fast-response recorder. Upon sudden occlusion of the blood flow to the leg, each temperature vs. time record exhibited a change of slope. The change in slope of the temperature difference, divided by the temperature difference, (degrees/minute degree) was identified with the local perfusion (milliliters/minute milliliter) existing just before occlusion. The local perfusions determined agreed in range and mean with literature values of average perfusion by venous occlusion plethysmography. The nature of the local blood flow measured by the present method is discussed relative to that by other methods.     

Thermal property measurements on biological materials at subzero temperatures.

The self-heated thermistor technique was used to measure the thermal conductivity and thermal diffusivity of biomaterials at low temperatures. Thermal standards were selected to calibrate the system at temperatures from -10 degrees C to -70 degrees C. The thermal probes were constructed with a convection barrier which eliminates convection inside liquid samples of low viscosity, without affecting the conductivity and diffusivity results. Using this technique, the thermal conductivity and diffusivity of two organ perfusates (HP5 and HP5 + 2M glycerol), one kidney phantom (a low ionic strength gel), as well as rabbit kidney cortex have been measured from -10 degrees C to -70 degrees C.     

大鼠小肠肠系膜微血管血流随温度变化的光学检测

利用CCD显微成像技术和激光散斑技术,对局部加热（41℃-54℃,30min）下大鼠小肠肠系膜微血管的管径（直径约15μm-50μm)和血流速率的变化进行实时,在体监测,并由二者计算血流量的变化。结果表明：41℃,43℃,45℃,46℃各温度点30min的加热过程中,血流速度变化平缓,血管管径和血流量明显增加,最终均逐渐趋趋于恒定。49℃时,血流速率仅在前12min内增加,30min时已降至低于初始值,血管管径及血流量在14min时达最大后开始减小,加热停止时仍旧高于初始值。温度高于49℃时（51℃,54℃）血流速率,管径,血流量呈现先升高后下降的变化趋势,在30min时,三者均低于初始值,由此可知,加热时间为30min,大鼠肠系膜微血管的临界温度为49℃;在相同的时间条件下,热损伤速率随温度升高而增加。     

A technique for measuring the thermal conductivity and evaluating the "apparent conductivity" concept in biomaterials

A simple technique for measuring thermal conductivity of biomaterials is described. The method is based on depositing a pulse of heat into the material of choice, and fitting the subsequent local temperature decay to that predicted by a theoretical model. This transient method is most suitable in situations where frequent measurements of the thermal conductivity are desired. The method was evaluated by calculating the thermal conductivity of several inert materials. The measured conductivities compared well with published values. The developed technique was also used to examine the applicability of the "apparent conductivity" index to combine both conductive and blood-convective thermal effects in living, blood perfused tissues. Using both simulated and experimental results, it was shown that the changes in the apparent conductivity are highly correlated with changes in blood flow. However, quantitative application of this index must be restricted to conditions that are similar to those which existed at the time the apparent conductivity was measured.     

A quantitative analysis of the thermal properties of porcine liver with glycerol at subzero and cryogenic temperatures

There is a lack of information on the effect of cryoprotective agents (CPAs) on the thermal properties of biomaterials at cryobiologically relevant temperatures (i.e. <233.15 K, −40 °C). Thermal properties that are of most interest include: thermal conductivity, density, specific heat, and latent heat resulting from phase change in tissue systems. Availability of such information would be beneficial for accurate mathematical modeling of cryobiological applications. Recently, we reported these thermal properties in phosphate buffered saline (PBS) with varying concentrations of glycerol, a widely used cryoprotective agent. In this study we extend these results by assessing the effects of glycerol on the thermal properties of porcine liver at subzero temperatures. Differential scanning calorimeter (DSC) was used to measure the specific heat and the latent heat release of porcine liver immersed in PBS and varying concentrations of glycerol. The specific heat data obtained from the DSC experiments were also used to predict the bulk thermal conductivity. This was done using a transient heat transfer model with a thermistor probe technique. Results show that the introduction of glycerol significantly alters thermal properties from known values for H₂O and non-treated liver. Therefore, inaccuracies in thermal predictions can be expected due to the application of measured vs. predicted thermal properties such as from weight averaging. This supports the need for these and other measurements of biomaterial thermal properties, with and without CPA addition, in the cryogenic regime.     

Influence of blood flow and millimeter wave exposure on skin temperature in different thermal models

Recently we showed that the Pennes bioheat transfer equation was not adequate to quantify mm wave heating of the skin at high blood flow rates. To do so, it is necessary to incorporate an "effective" thermal conductivity to obtain a hybrid bioheat equation (HBHE). The main aim of this study was to determine the relationship between non-specific tissue blood flow in a homogeneous unilayer model and dermal blood flow in multilayer models providing that the skin surface temperatures before and following mm wave exposure were the same. This knowledge could be used to develop multilayer models based on the fitting parameters obtained with the homogeneous tissue models. We tested four tissue models consisting of 1-4 layers and applied the one-dimensional steady-state HBHE. To understand the role of the epidermis in skin models we added to the one- and three-layer models an external thin epidermal layer with no blood flow. Only the combination of models containing the epidermal layer was appropriate for determination of the relationship between non-specific tissue and dermal blood flows giving the same skin surface temperatures. In this case we obtained a linear relationship between non-specific tissue and dermal blood flows. The presence of the fat layer resulted in the appearance of a significant temperature gradient between the dermis and muscle layer which increased with the fat layer thickness.