Reconstruction of the Space- and Time-Dependent Blood Perfusion Coefficient in Bio-Heat Transfer

Abstract

The identification of the space- and time-dependent perfusion coefficient in the one-dimensional transient bio-heat conduction equation is investigated. While boundary and initial conditions are prescribed, additional temperature measurements are considered inside the solution domain. The problem is approached both from a global and a local perspective. In the global approach a Crank–Nicolson-type scheme is combined with the Tikhonov regularization method. In the local approach, we compute both the time first-order and space second-order derivatives by means of first kind integral equations. A comparison between the numerical results obtained using the two methods shows that the local approach is more accurate and stable than the global one.