One-dimensional haemodynamic model of a vascular network with fractional-order viscoelasticity

We propose a computational framework for a one-dimensional haemodynamic model with the arterial walls described by the fractional-order viscoelastic material constitutive law. This framework is used to compare blood flow characteristics for simulations with elastic and fractional-order viscoelastic walls. We use three well-established benchmark tests: a single pulse wave in a long vessel, flow in a 37-segment network of elastic tubes, and flow in anatomically detailed arterial network consisting of 61 arterial segments. All results for elastic model are in a good agreement with analytical solutions, in vitro data and other well-established approaches. Fractional-order model demonstrates noticeable differences in pulse wave propagation speed and minor differences in pressure and flow profiles. Differences in profiles are negligible in major vessels, but more profound in vessels beyond the third or fourth generation.