Sum of Exponentials Approach for the Fractional Derivative Discretization in a Coronary Blood Flow Model

In this work, we utilize a sum of exponentials approach for the approximation of the Caputo fractional derivative in application to the one-dimensional coronary blood flow model. Numerical experiments were carried out to compare the computational efficiency of the utilized approach with the conventional L1-approximation of fractional derivative in zero-dimensional and one-dimensional models settings. It was shown that the sum of exponentials approach allows to obtain a noticeable speedup in computing fractional flow reserve in coronary vessels network up to 7 times compared to the approach with the L1-approximation, with the difference of computed values being negligibly small.