Simulation of Heat Transfer in the “Biological Tissue - Thermoelectric Sensor - Environment” System for the Diagnosis of Inflammatory and Destructive Processes
DOI:
https://doi.org/10.63527/1607-8829-2026-3-91-117Keywords:
thermoelectricity, heat flux density, thermoelectric sensor, bismuth telluride, Pennes bioheat equation, blood perfusion, computer simulation, control volume method, medical diagnostics, inflammation, tumour, ischaemiaAbstract
The paper presents a physical and mathematical model of the complete measuring system formed by multilayer biological tissue, a contact thermoelectric heat flux sensor and the environment. The model is based on the Pennes bioheat equation, which accounts for blood perfusion and metabolic heat generation, and it includes the sensor itself as a set of thermally resistive layers, so that the perturbation introduced by the instrument into the quantity it measures can be evaluated quantitatively. Pathological states are described by local changes of two physiological parameters only: the volumetric blood perfusion rate and the specific metabolic heat generation. The boundary value problems were solved by the control volume method implemented in Python with the NumPy and SciPy scientific libraries; the implementation was verified against an analytical solution, by grid convergence and by cross-comparison of independent one- and two-dimensional formulations. It is shown that under standardized conditions the undisturbed heat flux density from the skin surface is 13.5 mW/cm², and that blood perfusion is the dominant physiological driver of this flux - about thirty times more influential than volumetric metabolic heat generation (26.7 % against 0.8 % of the flux, switch-off test) - so that a pure-conduction model is inadmissible for this class of problems. For a pathological region extending laterally under the whole sensor the flux changes by up to +24 % (inflammation), +42 % (proliferating tumour, Gautherie relation) and −20 % (ischaemia); for a realistic localized focus of 8 mm radius the tumour signal is smaller and depth-dependent, from +15.9 % at 1 mm depth to +3.0 % at 9 mm. Heat flux measurement is shown to be markedly more sensitive to these pathological changes than surface thermometry, whose useful signal (1.9-2.3 °C) is only a few times the resolution of clinical thermography, whereas the flux changes above are five to eight times the instrument’s own passport error. The methodical error of a contact sensor of 14×14×3 mm - arising in comparable measure from the thermal resistance of its own layer stack, from the emissivity mismatch between its top face and skin, and, to the smallest extent, from the lateral bypass of flux around it - is −4.6 % under ideal contact and grows to −12.5 % for poor thermal contact; the sensor settling time is 1.5–2 min. The results define the physical limits of thermoelectric heat flux diagnostics and justify the requirements to sensor design and measurement procedure.
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