Sensitivity analysis of one-dimensional heat transfer in tissue with temperature-dependent perfusion

Thermal safety considerations for implantable micro-coil design

Micro magnetic stimulation of the brain via implantable micro-coils is a promising novel technology for neuromodulation. Careful consideration of the thermodynamic profile of such devices is necessary for effective and safe designs.Objective.We seek to quantify the thermal profile of bent wire micro-coils in order to understand and mitigate thermal impacts of micro-coil stimulation.Approach. In this study, we use fine wire thermocouples and COMSOL finite element modeling to examine the profile of the thermal gradients generated near bent wire micro-coils submerged in a water bath during stimulation. We tested a range of stimulation parameters previously reported in the literature such as voltage amplitude, stimulus frequency, stimulus repetition rate and coil wire materials.Main results. We found temperature increases ranging from <1 °C to 8.4 °C depending upon the stimulation parameters tested and coil wire materials used. Numerical modeling of the thermodynamics identified hot spots of the highest temperatures along the micro-coil contributing to the thermal gradients and demonstrated that these thermal gradients can be mitigated by the choice of wire conductor material and construction geometry.Significance. ISO standard 14708-1 designates a thermal safety limit of 2 °C temperature increase for active implantable medical devices. By switching the coil wire material from platinum/iridium to gold, our study achieved a 5-6-fold decrease in the thermal impact of coil stimulation. The thermal gradients generated from the gold wire coil were measured below the 2 °C safety limit for all stimulation parameters tested.

Wearable Personal Core Body Temperature Measurement Considering Individual Differences and Dynamic Tissue Blood Perfusion

Accurate and continuous measurement of the human core body temperature by a wearable device is of great significance for human health care and disease monitoring. The current wearable thermometers ignore the physiological differences between individuals and the role of blood perfusion in thermoregulation, resulting in insufficient accuracy and limitations in terms of the measurement sites. This study proposed a novel personal model for measuring core body temperature by taking dynamic tissue blood perfusion and individual differences into consideration. The technique facilitates possible accurate core body temperature measurements from the skin surface of the wrist and forehead. First, the personal core body temperature model was established based on the thermal equilibrium between the human body and the measurement device, in which the tissue blood perfusion changes dynamically with tissue temperature. Then, the parameters of the personal model that imply individual physiological differences were obtained based on personal data collected daily. The results show that with the developed personal model, the accuracy of the measured body temperature from the wrist is close to that of the forehead model. The wrist model and the forehead model have a mean absolute error of 0.297 (SD=0.078) C and 0.224 (SD=0.071) C, respectively, which meets the accuracy and robustness requirements of practical applications. The personal models significantly improve the accuracy compared with that of the group model, especially for the wrist model.

Bioheat transfer model of transcutaneous spinal cord stimulation-induced temperature changes

Transcutaneous spinal cord stimulation (tSCS) has been extensively studied due to its promising application in motor function restoration. Many previous studies have explored both the essential mechanism of action and the methods for determining optimal stimulation parameters. In contrast, the bioheat transfer analysis of tSCS therapy has not been investigated to the same extent, despite widely existing, and being of great significance in assuring a stable and thermally safe treatment. In this paper, we concentrated on the thermal effects of tSCS using a finite element-based method. By coupling the electric field and bioheat field, systematic finite element simulations were performed on a human spinal cord model to survey the influence of anatomical structures, blood perfusion, and stimulation parameters on temperature changes for the first time. The results show that tSCS-induced temperature rise mainly occurs in the skin and fat layers and varies due to individual differences. The current density distribution along with the interactions of multiple biothermal effects synthetically determines the thermal status of the whole spinal cord model. Smaller stimulation electrodes have a higher risk of thermal damage when compared with larger electrodes. Increasing the stimulation intensity will result in more joule heat accumulation, hence an increase in the temperature. Among all configurations in this study that simulated the clinical tSCS protocols, the temperature rise could reach up to 9.4 °C on the skin surface depending on the stimulation parameters and tissue blood perfusion.

Transport lattice models of heat transport in skin with spatially heterogeneous, temperature-dependent perfusion

BACKGROUND

Investigation of bioheat transfer problems requires the evaluation of temporal and spatial distributions of temperature. This class of problems has been traditionally addressed using the Pennes bioheat equation. Transport of heat by conduction, and by temperature-dependent, spatially heterogeneous blood perfusion is modeled here using a transport lattice approach.

METHODS

We represent heat transport processes by using a lattice that represents the Pennes bioheat equation in perfused tissues, and diffusion in nonperfused regions. The three layer skin model has a nonperfused viable epidermis, and deeper regions of dermis and subcutaneous tissue with perfusion that is constant or temperature-dependent. Two cases are considered: (1) surface contact heating and (2) spatially distributed heating. The model is relevant to the prediction of the transient and steady state temperature rise for different methods of power deposition within the skin. Accumulated thermal damage is estimated by using an Arrhenius type rate equation at locations where viable tissue temperature exceeds 42 degrees C. Prediction of spatial temperature distributions is also illustrated with a two-dimensional model of skin created from a histological image.

RESULTS

The transport lattice approach was validated by comparison with an analytical solution for a slab with homogeneous thermal properties and spatially distributed uniform sink held at constant temperatures at the ends. For typical transcutaneous blood gas sensing conditions the estimated damage is small, even with prolonged skin contact to a 45 degrees C surface. Spatial heterogeneity in skin thermal properties leads to a non-uniform temperature distribution during a 10 GHz electromagnetic field exposure. A realistic two-dimensional model of the skin shows that tissue heterogeneity does not lead to a significant local temperature increase when heated by a hot wire tip.

CONCLUSIONS

The heat transport system model of the skin was solved by exploiting the mathematical analogy between local thermal models and local electrical (charge transport) models, thereby allowing robust, circuit simulation software to obtain solutions to Kirchhoff's laws for the system model. Transport lattices allow systematic introduction of realistic geometry and spatially heterogeneous heat transport mechanisms. Local representations for both simple, passive functions and more complex local models can be easily and intuitively included into the system model of a tissue.

Uncertainty analysis for temperature prediction of biological bodies subject to randomly spatial heating

An analytical solution to the Pennes bioheat transfer equation in three-dimensional geometry with practical hyperthermia boundary conditions and random heating was obtained in this paper. Uncertainties for the predicted temperatures of tissues due to approximate parameters were studied based on analyzing one-dimensional heat transfer in the biological bodies subject to a spatially decay heating. Contributions from each of the thermal parameters such as heat conductivity, blood perfusion rate, and metabolic rate of the tissues, the scattering coefficient and the surface power flux of the heating apparatus were compared and the uncertainty limit for temperature distribution in this case was estimated. The results are useful in a variety of clinical hyperthermia and biological thermal parameter measurement.

Temperature and perfusion responses of muscle and lung tissue during chronic heating in vivo

For the first time, both temperature and perfusion responses have been obtained from in vivo studies of chronically heated lung and muscle tissue of calves. In each tissue, the spatial temperature distribution was measured by thermistors placed in needles at several distances from an implanted heated disc. A perfusion parameter was defined for a bioheat transfer model that describes temperature dynamics with distance from the heated disc. Estimates of perfusion were obtained by a least-squares fit of the model output to a step change in heat flux. Except for short transient experiments several times a week, a constant heat flux of 0.04, 0.06 or 0.08 Wcm(-2) was maintained at the disc surface for up to seven weeks. At the higher heat fluxes, the steady-state tissue temperature decreased with heating duration. Also, the characteristic time constants of the tissues decreased with heating duration. Muscle perfusion showed a statistically significant increase during chronic heating. Tissue adapts to chronic heating above 42 degrees C by allowing more capillary blood flow that increases heat loss to reduce tissue temperature.

Parametric studies on the phase shift method to measure the blood perfusion of biological bodies

To better understand the phase shift method to non-invasively measure the blood perfusion of living tissues in vivo, the dual reciprocity boundary element method (DRBEM) was applied to numerically solve the transient and non-linear two-dimensional bio-heat transfer in biological bodies subject to a sinusoidal heat flux at the skin surface. The influences of the heating flux, the heating oscillation magnitude, the heating frequency, the blood vessel underneath the skin, and the space or temperature dependent blood perfusion to the temperature response and the phase shift between the heat flux and the temperature response at the skin surface were comprehensively examined. The effects of the heating area to the temperature response were also investigated. And a better understanding on the heat transfer behavior of biological bodies under sinusoidal heating was thus obtained. These results are expected to be valuable for constructing the practical instrumentation to non-invasively measure the blood perfusion of biological bodies.