چکیده

In this paper we try to investigate and solve a bio heat conduction problem related to perfusion coefficient using location and time dependent temperature calculations. To solve this we first start with a given initial value q0. Having this value in the conditions of the bio heat equation we encounter a direct heat transfer problem. We discretize and solve this problem using Crank-Nicholson method to obtain the initial temperature answer at all points of the range. The problem of obtaining q or the perfusion coefficient is an inverse heat transfer problem and we know that the inverse heat transfer problems are ill-posed. Because small errors in the measured temperature cause large errors in the output perfusion coefficient due to the numerical differentiation of noisy data involved which represents an unstable procedure. Here by solving the sensitivity and adjoint equations and using the conjugate gradient method we reach the next values q1 q2 ... in the next iterations. Many researchers have worked in this field and have recorded results in this regard. The results of coding the equations obtained in the MATLAB program show that with more repetitions and increasing area points of the conjugate gradient method the amount of error calculated between the exact value and the estimate value is greatly reduced. And the value of the least squares function is minimized.

کليدواژه ها

Inverse problem bio-heat equation ill-posed problem conjugate gradient method perfusion coefficient

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ابراهیم طهماسبی سولگانی , 1400 , حل عددی یک مساله انتقال حرارت زیستی با استفاده از روش گرادیان مزدوج , اولین کنفرانس بین المللی ریاضیات و کاربردها