Towards efficient design optimization of a miniaturized thermoelectric generator for electrically active implants via model order reduction and submodeling technique

Abstract

Thermoelectric generators (TEG) convert the thermal energy into electrical energy and are under investigation as a power supply for medical implants. To improve the performance of TEG, the design optimization process through finite element model simulation is preferred by biomedical engineers. This paper aims to provide an efficient method of speeding up the design optimization process of TEG. A three-dimensional realistic human torso model incorporating the TEG is investigated, where the internal heat transfer in human tissue is characterized by Pennes bioheat equation. In addition, convection, radiation, and evaporation effects at the skin surface are applied to identify the heat transfer effects between the human body and the environment. To speed up finite element simulation of the large-scale human torso model, projectionbased model order reduction (MOR) is applied for generation of a compact but highly accurate model. Parametric MOR (pMOR) further enables generating a parameter-independent compact model. For an efficient design optimization of TEG, this compact human torso model is applied within a thermal submodeling approach. Its temperature distribution results are back-projected and used as boundary conditions for the TEG submodel. The achieved speed-up in simulation time, demonstrated in this work, clearly indicates that the design optimization process of TEG is more efficient with the combination of MOR and submodeling techniques.bioheat modeling, energy harvesting, finite element method, implantable biomedical devices, model order reduction, thermoelectric generator ABBREVIATIONS: MOR, model order reduction; pMOR, parametric model order reduction; TEG, thermoelectric generator.

The Effect of Different Parameters on the Amount of Obtained Power the Thermoelectric Generator Placed in the Human Living Tissue

“…The energy obtained from the temperature difference between the thermocouple legs is due to the Seebeck effect. For this reason the output voltage varies depending on the temperatures difference (C. Yuan et al, 2020). The following equations are used to calculate the output power (Jaziri et al, 2020).…”

Efficient design optimization of a miniaturized thermoelectric generator for electrically active implants based on parametric model order reduction

“…Meanwhile, on the surface of the skin layer, the convection, radiation and evaporation effects were considered to be the external heat transfer effects to balance the heat generated inside. Based on the research of Yuan et al 26 the temperature‐dependent perfusion, radiation, and evaporation effects were transformed and a linear thermal tissue model was obtained for the convenience of pMOR. The temperature dependent effects in Equations (1) and (2) can be modeled as follows: where the blood perfusion heat generation Q b is transformed as a convective heat transfer boundary condition q b .…”

“…When load resistance is below 0.4 Ω, an obvious error in power output can be observed, which we attribute to the limited accuracy of the resistor. In this section, the multivariate moment-matching pMOR method, which has been demonstrated to be successful in linear models, 38,39,25,26,31,32 was applied to generate highly accurate but compact surrogates with preservation of the main features of the original large-scale system to speed up the simulations of the thermoelectric and thermal models introduced in Section 2. In the pROMs of the thermoelectric and thermal models, the effective thermal conductivity of the representative thermopile, the heat transfer coefficient and the ambient temperature in convection boundary conditions were set as the parameters, which can be changed in the reduced model.…”

“…To provide realistic human thermal environments, the bioheat human tissue model illustrated in Section 2.1 was developed based on the research work of Yuan et al 26 Tissue properties from the IT'IS database 34 were applied. Pennes' bioheat equation, 35 which accounts for heat conduction, metabolic heat generation, and perfusion effects, was applied to describe the time transient heat transfer within human tissue as follows: where T is the temperature distribution in human tissue.…”

“…To speed up the simulations, Jadhav et al 23 applied model order reduction (MOR) method 24 on the finite element model of TEG to obtain a highly accurate but low-dimensional model. Afterwards, to investigate the impact of the environmental conditions on TEG and to avoid the need to regenerate the new reducedorder model with each change of the parameters, Yuan et al 25,26 constructed a TEG reduced model preserving the parameters in convection boundary conditions through the multi-moment matching parametric model order reduction (pMOR) method. 27,28,29,30 Furthermore, Yuan et al 31,32 extracted the fill factor of thermopiles as an optimization parameter by parameterizing the equivalent thermal conductivity of a thermal dummy model.…”