Abstarct: The brain is one of the most important organs in a biological body. With the interruption of cardiopulmonary circulation in many cardiac surgical procedures or accidental events leading to cerebral circulation arrest, an imbalance between energy production and consumption will occur. Meanwhile, the cooling function of the blood flow on the hot tissue will be stopped, while mextabolic heat generation in the tissues still keeps running for a while. Under such adverse situations, the potential for cerebral protection through hypothermia has been intensively investigated in clinics by lowering brain temperature to restrain the cerebral oxygen demands. In this paper, the conjugate gradient method, coupled with an adjoint equation approach, is used to solve the inverse
heat conduction problem using Pennes bio heat equation in the axisymmetric coordinate system and estimate the time-dependent
heat flux using temperature distribution at a point brain to achieve the temperature reduction about 5 degrees within 30 minutes. To solve this problem the general coordinate method is used. The obtained results for few selected examples show the good accuracy of the presented method. Also the solutions have good stability even if the input data includes noise.