A Numerical Approach to Solving an Inverse Heat Conduction Problem Using the Levenberg‐Marquardt Algorithm

Tao, Min; Chen, Xing; Sun, Yuan; Huang, Qiang

doi:10.1155/2014/626037

Cited by 4 publications

(1 citation statement)

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“…In this work, the inverse heat transfer for estimating the values of the simulation parameters is performed using a least-square norm estimation procedure. The Levenberg-Marquardt algorithm, originally developed for nonlinear parameter estimation problems 23,24 , has been successfully applied to the solution of the ill conditioned inverse heat conduction problem 25,26 . Its combination of steepest descent and the Gauss-Newton method increases robustness and the likelihood for convergence.…”

Section: Adaptive Pennes' Bioheat Simulationmentioning

confidence: 99%

Adaptive simulation of 3D thermometry maps for interventional MR-guided tumor ablation using Pennes’ bioheat equation and isotherms

Alpers

Rötzer

Gutberlet

et al. 2022

Sci Rep

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Minimally-invasive thermal ablation procedures have become clinically accepted treatment options for tumors and metastases. Continuous and reliable monitoring of volumetric heat distribution promises to be an important condition for successful outcomes. In this work, an adaptive bioheat transfer simulation of 3D thermometry maps is presented. Pennes’ equation model is updated according to temperature maps generated by uniformly distributed 2D MR phase images rotated around the main axis of the applicator. The volumetric heat diffusion and the resulting shape of the ablation zone can be modelled accurately without introducing a specific heat source term. Filtering the temperature maps by extracting isotherms reduces artefacts and noise, compresses information of the measured data and adds physical a priori knowledge. The inverse heat transfer for estimating values of the simulated tissue and heating parameters is done by reducing the sum squared error between these isotherms and the 3D simulation. The approach is evaluated on data sets consisting of 13 ex vivo bio protein phantoms, including six perfusion phantoms with simulated heat sink effects. Results show an overall average Dice score of 0.89 ± 0.04 (SEM < 0.01). The optimization of the parameters takes 1.05 ± 0.26 s for each acquired image. Future steps should consider the local optimization of the simulation parameters instead of a global one to better detect heat sinks without a priori knowledge. In addition, the use of a proper Kalman filter might increase robustness and accuracy if combined with our method.

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