B-spline-based Modulating Function Method for Arterial Blood Flow's Estimations

This paper considers the estimation problem of arterial blood flow by using a fractional model of arterial hemodynamics. This model has been introduced as an enhanced version of the conventional integer-order Windkessel model. This advanced model incorporates a fractional-order capacitor to characterize the intricate and the frequency-dependent arterial compliance. A recent algorithm that consists of modulating functions method combined with an iterative Newton approach has been proposed to solve this estimation problem. However, the method\x92s performance was highly dependent on the convergence of the Newton method. In addition, it was affected by the choice of the basis functions. In this paper, we present an enhanced version of this two-stage algorithm, which leverages modulating functions, genetic algorithms, and B-spline basis functions for the simultaneous estimation of both the model\x92s input (the blood flow) and the fractional differentiation order within a finite time frame. To validate the approach, in silico human data is employed, and its performance is compared with that of the former method. The outcomes demonstrate significant potential for accurate calibration of the fractional model and estimation of the blood flow.