Three-dimensional numerical simulation of the effects of fractal vascular trees on tissue temperature and intracelluar ice formation during combined cancer therapy of cryosurgery and hyperthermia

A three-dimensional cell-to-tissue multiscale model for quantitative evaluation of the influences of vascular network on the treatment outcome of combined cancer therapy of cryosurgery and hyperthermia was developed, where the bioheat transfer equation was used to predict the thermal history in both the tumor and normal tissues, the Navier-Stokes equations were used to calculate the temperature and flow fields in the vascular network generated using fractal theory based on MRI images, and the thermal and cryo damage functions together with the injury caused by intracellular ice formation were used for evaluating the killing effect. The effects of the vascular tree on both the thermal history and intracellular ice formation in the tissues were investigated. For a tumor located at the first level of vascular network, the vascular network is significant only when the distance between the tumor and blood vessel is less than three times of the radius (R) of the tumor and this critical distance decreases to 2R for the second level of the vascular tree. For a fixed distance between tumor and blood vessel, the first level of vascular network was found to be thermally significant while the third or lower levels of vascular tree are not.