numerical solution a bio heat conduction transfer problem by conjugategradient method

In this paper, we try to investigate and solve a bio heat conduction problem relatedto perfusion coefficient using location and time dependent temperature calculations. to solvethis, we first start with a given initial valueq0. having this value in the conditions of the bioheat equation, we encounter a direct heat transfer problem. we discretize and solve thisproblem using crank-nicholson method to obtain the initial temperature answer at all pointsof the range. the problem of obtaining q or the perfusion coefficient is an inverse heat transferproblem, and we know that the inverse heat transfer problems are ill-posed. because smallerrors in the measured temperature cause large errors in the output perfusion coefficient due tothe 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 thisfield and have recorded results in this regard. the results of coding the equations obtained inthe matlab program show that with more repetitions and increasing area points of theconjugate gradient method, the amount of error calculated between the exact value and theestimate value is greatly reduced. and the value of the least squares function is minimized