Sensitivity Analysis in the Problem of the Impact of an External Heat Impulse on Oxygen Distribution in Biological Tissue

During the exposure of biological tissue to an external heat impulse (both controlled as in various types of thermotherapy and uncontrolled related to thermal burns), processes occur related to changes in its parameters, especially perfusion, and thus the transport of oxygen to the tissue. This paper presents a combined model of bioheat transfer and oxygen distribution in tissue. The latter was based on Krogh's cylinder concept, taking into account the Hill oxygen dissociation curve. The variable value of the perfusion coefficient is shown to affect the value of blood velocity in the capillary and, therefore, the distribution of partial pressure in the tissue. A sensitivity analysis was performed for the oxygen distribution model using the direct method for seven parameters present in its mathematical description. The results show that a 10% change in the values of all parameters leads to changes in the partial oxygen pressure exceeding 8 mmHg, and for the reduced value of the oxygen inlet pressure, the largest changes in the partial oxygen pressure within the Krogh cylinder model occur near the outlet capillary. In the stage of numerical realization, the finite difference method and the shooting method were used.