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.     

A thermal method for the determination of tissue blood flow.

An isothermal flowmeter for the determination of local tissue blood flow is described. Flow is determined by the measurement of the thermal conductivity of the tissue in the vicinity of a heated thermistor maintained at a fixed temperature difference above a reference thermistor. Direct heating of the thermistor is utilized to eliminate the need for specially constructed indirectly heated thermistors. This design results in a device with a voltage output directly proportional to tissue thermal conductivity and to tissue blood flow. The device is shown to be adequate for the qualitative measurement of myocardial blood flow under various situations. Construction is simplified and the size of the circuit reduced by the use of readily available integrated circuits.     

Steady-state heat distribution in epidermis,dermis and subdermal tissues

Steady-state temperature distribution is investigated in human skin and subdermal tissue exposed to a dry and cool environment with negligible insensible perspiration. The mathematical model incorporates the effect of blood mass flow and metabolic heat generation. The rates of the two and the tissue thermal conductivity are assumed to have different values in all the three parts, namely epidermis, dermis and subdermal tissues. A simple variational finite element approach is used to find numerical values of the interface temperatures for a wide range of the values of skin surface temperature and for different thicknesses of the above parts. These values are used to obtain approximate temperature profiles in the whole region. The biological and physical implications of the results are also discussed.     

Finite element thermal analysis of bone cement for joint replacements

A finite element technique was developed to investigate the thermal behavior of bone cement in joint replacement procedures. Thermal tests were designed and performed to provide the parameters in a kinetic model of bone cement exothermic polymerization. The kinetic model was then coupled with an energy balance equation using a finite element formulation to predict the temperature history and polymerization development in the bone-cement-prosthesis system. Based on the temperature history, the possibility of the thermal bone necrosis was then evaluated. As a demonstration, the effect of cement mantle thickness on the thermal behavior of the system was investigated. The temperature profiles in the bone-cement-prosthesis system have shown that the thicker the cement, the higher the peak temperature in the bone. In the 7 mm thick cement case, a peak temperature of over 55 degrees C was predicted. These high temperatures occurred in a small region near the bone/cement interface. No damage was predicted in the 3 mm and 5 mm cement mantle thickness cases. Although thermal damage was predicted in the bone for the 7 mm mantle thickness case, the amount of thermal necrosis predicted was minimal. If more cement is used in the surgical procedure, more heat will be generated and the potential for thermal bone damage may rise. The systems should be carefully selected to reduce thermal tissue damage when more cement is used. The methodology developed in this paper provides a numerical tool for the quantitative simulation of the thermal behavior of bone-cement-prosthesis designs.     

Decreasing the Effective Thermal Conductivity in Glass Supported Thermoelectric Layers

As thermoelectric devices begin to make their way into commercial applications, the emphasis is put on decreasing the thermal conductivity. In this purely theoretical study, finite element analysis is used to determine the effect of a supporting material on the thermal conductivity of a thermoelectric module. The simulations illustrate the heat transfer along a sample, consisting from Cu, Cu₂O and PbTe thermoelectric layers on a 1 mm thick Pyrex glass substrate. The influence of two different types of heating, at a constant temperature and at a constant heat flux, is also investigated. It is revealed that the presence of a supporting material plays an important role on lowering the effective thermal conductivity of the layer-substrate ensemble. By using thinner thermoelectric layers the effective thermal conductivity is further reduced, almost down to the value of the glass substrate. As a result, the temperature gradient becomes steeper for a fixed heating temperature, which allows the production of devices with improved performance under certain conditions. Based on the simulation results, we also propose a model for a robust thin film thermoelectric device. With this suggestion, we invite the thermoelectric community to prove the applicability of the presented concept for practical purposes.     

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.     

Transient bioheat simulation of the laser-tissue interaction in human skin using hybrid finite element formulation

This paper presents a hybrid finite element model for describing quantitatively the thermal responses of skin tissue under laser irradiation. The model is based on the boundary integral-based finite element method and the Pennes bioheat transfer equation. In this study, temporal discretization of the bioheat system is first performed and leads to the well-known modified Helmholtz equation. A radial basis function approach and the boundary integral based finite element method are employed to obtain particular and homogeneous solutions of the laser-tissue interaction problem. In the boundary integral based finite element formulation, two independent fields are assumed: intra-element field and frame field. The intra-element field is approximated through a linear combination of fundamental solutions at a number of source points outside the element domain. The frame temperature field is expressed in terms of nodal temperature and the corresponding shape function. Numerical examples are considered to verify and assess the proposed numerical model. Sensitivity analysis is performed to explore the thermal effects of various control parameters on tissue temperature and to identify the degree of burn injury due to laser heating.     

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 damage prediction for collagenous tissues part I: a clinically relevant numerical simulation incorporating heating rate dependent denaturation

Subablative thermotherapy is frequently used for the treatment of joint instability related diseases. In this therapy, mechanically deformed collagenous tissues are thermally shrunk and the stability of the tissue is re-established. In this research, the thermal damage fields generated by three different clinical heating modalities (monopolar and bipolar radio frequency and Ho:YAG laser) are compared numerically using finite element analysis. The heating rate dependent denaturation characteristics of collagenous tissues are incorporated into the model using experimental data from in vitro experimentation with rabbit patellar tendons. It is shown that there are significant differences among the thermal damage profiles created by these modalities, explaining the main reason for the discrepancies reported in the literature in terms of the efficacy and safety of each modality. In the complementary paper, the accuracy of the model presented here is verified by in vitro experimentation with a model collagenous tissue and by quantifying the denaturation-induced birefringence change using Optical Coherence Tomography and Magnetic Resonance Imaging.     

Temperature evolution in tissues embedded with large blood vessels during photo-thermal heating

During laser-assisted photo-thermal therapy, the temperature of the heated tissue region must rise to the therapeutic value (e.g., 43 °C) for complete ablation of the target cells. Large blood vessels (larger than 500 micron in diameter) at or near the irradiated tissues have a considerable impact on the transient temperature distribution in the tissue. In this study, the cooling effects of large blood vessels on temperature distribution in tissues during laser irradiation are predicted using finite element based simulation. A uniform flow is assumed at the entrance and three-dimensional conjugate heat transfer equations in the tissue region and the blood region are simultaneously solved for different vascular models. A volumetric heat source term based on Beer–Lambert law is introduced into the energy equation to account for laser heating. The heating pattern is taken to depend on the absorption and scattering coefficients of the tissue medium. Experiments are also conducted on tissue mimics in the presence and absence of simulated blood vessels to validate the numerical model. The coupled heat transfer between thermally significant blood vessels and their surrounding tissue for three different tissue-vascular networks are analyzed keeping the laser irradiation constant. A surface temperature map is obtained for different vascular models and for the bare tissue (without blood vessels). The transient temperature distribution is seen to differ according to the nature of the vascular network, blood vessel size, flow rate, laser spot size, laser power and tissue blood perfusion rate. The simulations suggest that the blood flow through large blood vessels in the vicinity of the photothermally heated tissue can lead to inefficient heating of the target.     

Theoretical temperature distributions produced by an annular phased array-type system in CT-based patient models

Theoretical calculations for the specific absorption rate (SAR) and the resulting temperature distributions produced by an annular phased array (APA)-type system are made. The finite element numerical method is used in the formulation of both the electromagnetic (EM) and thermal boundary value problems. A number of detailed two-dimensional patient models based on CT-scan data from the pelvic, visceral, and thoracic regions are generated to simulate a variety of tumor locations and surrounding normal tissues. The SAR values from the EM solution are put into the bioheat transfer equation, and steady-state temperature distributions are calculated for a wide range of blood flow rates. Based on our theoretical modeling, the APA shows no preferential heating of superficial over deep-seated tumors. However, in most cases for all three regions of the human trunk only fair thermal profiles (therapeutic area near 60%) are obtained in tumors with little or no blood flow and poor temperature patterns (therapeutic area less than 50%) are found in tumors with moderate to high perfusion rates. These theoretical calculations should aid the clinician in the evaluation of the effectiveness of APA-type devices in heating tumors located in the trunk region.     

Local heating of molecular motors using single carbon nanotubes

Temperature globally affects all chemical processes and biomolecules in living cells. Elevating the temperature of an entire cell accelerates so many biomolecular reactions simultaneously that it is difficult to distinguish the various mechanisms involved. The ability to localize temperature changes to the nanometer range within a cell could provide a powerful new tool for regulating biomolecular activity at the level of individual molecules. The search for a nanoheater for biological research has prompted experiments with carbon nanotubes (CNTs), which have the highest conductivity of any known material. The adsorption of skeletal muscle myosin molecules along the length of single multi-walled CNTs (~10 μm) has allowed researchers to observe the ATP-driven sliding of fluorescently labeled actin filaments. In one study, red-laser irradiation focused on one end of a myosin-coated CNT was used to heat myosin motors locally without directly heating the surrounding water; this laser irradiation instantly accelerated the actin-filament sliding speeds from ~6 to ~12 μm/s in a reversible manner, indicating a local, real-time heating of myosin motors by approximately Δ12 K. Calculation of heat transfer using the finite element method, based on the estimated temperature along a single CNT with a diameter of 170 nm, indicated a high thermal conductivity of ~1540 Wm^?1K^?1 in solution, consistent with values measured in vacuum in earlier studies. Temperature distribution indicated by half-decrease distances was ~3660 nm along the length of the CNT and ~250 nm perpendicular to the length. These results suggest that single-CNT-based heating at the nanometer- or micrometer-range could be used to regulate various biomolecules in many areas of biological, physical, and chemical research.     

Studies on the three-dimensional temperature transients in the canine prostate during transurethral microwave thermal therapy

Thermal therapy of benign prostatic hyperplasia requires accurate prediction of the temperature distribution induced by the heating within the prostatic tissue. In this study, the Pennes bioheat transfer equation was used to model the transient heat transfer inside the canine prostate during transurethral microwave thermal therapy. Incorporating the specific absorption rate of microwave energy in tissue, a closed-form analytical solution was obtained. Good agreement was found between the theoretical predictions and in-vivo experimental results. Effects of blood perfusion and the cooling at the urethral wall on the temperature rise were investigated within the prostate during heating. The peak intraprostatic temperatures attained by application of 5, 10, or 15 W microwave power were predicted to be 38 degrees C, 41 degrees C, and 44 degrees C. Results from this study will help optimize the thermal dose that can be applied to target tissue during the therapy.     

A parametric study of thermal therapy of skin tissue

A thermal therapy for cancer in skin tissue is numerically investigated using three bioheat conduction models, namely Pennes, thermal wave and dual-phase lag models. A laser is applied at the surface of the skin for cancer ablation, and the temperature and thermal damage distributions are predicted using the three bioheat models and two different modeling approaches of the laser effect. The first one is a prescribed surface heat flux, in which the tissue is assumed to be highly absorbent, while the second approach is a volumetric heat source, which is reasonable if the scattering and absorption skin effects are of similar magnitude. The finite volume method is applied to solve the governing bioheat equation. A parametric study is carried out to ascertain the effects of the thermophysical properties of the cancer on the thermal damage. The temperature distributions predicted by the three models exhibit significant differences, even though the temperature distributions are similar when the laser is turned off. The type of bioheat model has more influence on the predicted thermal damage than the type of modeling approach used for the laser. The phase lags of heat flux and temperature gradient have an important influence on the results, as well as the thermal conductivity of the cancer. In contrast, the uncertainty in the specific heat and blood perfusion rate has a minor influence on the thermal damage.     

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.     

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.     

The Effects of Thermal Radiation on an Unsteady MHD Axisymmetric Stagnation-Point Flow over a Shrinking Sheet in Presence of Temperature Dependent Thermal Conductivity with Navier Slip

In this paper, the magnetohydrodynamic (MHD) axisymmetric stagnation-point flow of an unsteady and electrically conducting incompressible viscous fluid in with temperature dependent thermal conductivity, thermal radiation and Navier slip is investigated. The flow is due to a shrinking surface that is shrunk axisymmetrically in its own plane with a linear velocity. The magnetic field is imposed normally to the sheet. The model equations that describe this fluid flow are solved by using the spectral relaxation method. Here, heat transfer processes are discussed for two different types of wall heating; (a) a prescribed surface temperature and (b) a prescribed surface heat flux. We discuss and evaluate how the various parameters affect the fluid flow, heat transfer and the temperature field with the aid of different graphical presentations and tabulated results.     

Heating of tissues by microwaves: A model analysis

We consider the thermal response times for heating of tissue subject to nonionizing (microwave or infrared) radiation. The analysis is based on a dimensionless form of the bioheat equation. The thermal response is governed by two time constants: one(τ₁) pertains to heat convection by blood flow, and is of the order of 20–30 min for physiologically normal perfusion rates; the second (τ₂) characterizes heat conduction and varies as the square of a distance that characterizes the spatial extent of the heating. Two idealized cases are examined. The first is a tissue block with an insulated surface, subject to irradiation with an exponentially decreasing specific absorption rate, which models a large surface area of tissue exposed to microwaves. The second is a hemispherical region of tissue exposed at a spatially uniform specific absorption rate, which models localized exposure. In both cases, the steady-state temperature increase can be written as the product of the incident power density and an effective time constant τ_eff, which is defined for each geometry as an appropriate function of τ₁ and τ₂. In appropriate limits of the ratio of these time constants, the local temperature rise is dominated by conductive or convective heat transport. Predictions of the block model agree well with recent data for the thresholds for perception of warmth or pain from exposure to microwave energy. Using these concepts, we developed a thermal averaging time that might be used in standards for human exposure to microwave radiation, to limit the temperature rise in tissue from radiation by pulsed sources. We compare the ANSI exposure standards for microwaves and infrared laser radiation with respect to the maximal increase in tissue temperature that would be allowed at the maximal permissible exposures. A historical appendix presents the origin of the 6-min averaging time used in the microwave standard. Bioelectromagnetics 19:420–428, 1998. © 1998 Wiley-Liss, Inc.     

A finite element model of cell deformation during magnetic bead twisting.

Magnetic twisting cytometry probes mechanical properties of an adherent cell by applying a torque to a magnetic bead that is tightly bound to the cell surface. Here we have used a three-dimensional finite element model of cell deformation to compute the relationships between the applied torque and resulting bead rotation and lateral bead translation. From the analysis, we computed two coefficients that allow the cell elastic modulus to be estimated from measurements of either bead rotation or lateral bead translation, respectively, if the degree of bead embedding and the cell height are known. Although computed strains in proximity of the bead can be large, the relationships between applied torque and bead rotation or translation remain virtually linear up to bead rotations of 15 degrees, above which geometrical nonlinearities become significant. This appreciable linear range stands in contrast to the intrinsically nonlinear force-displacement relationship that is observed when cells are indented during atomic force microscopy. Finally, these computations support the idea that adhesive forces are sufficient to keep the bead firmly attached to the cell surface throughout the range of working torques.