Fast blood-flow simulation for large arterial trees containing thousands of vessels

Blood flow modelling has previously been successfully carried out in arterial trees to study pulse wave propagation using nonlinear or linear flow solvers. However, the number of vessels used in the simulations seldom grows over a few hundred. The aim of this work is to present a computationally efficient solver coupled with highly detailed arterial trees containing thousands of vessels. The core of the solver is based on a modified transmission line method, which exploits the analogy between electrical current in finite-length conductors and blood flow in vessels. The viscoelastic behaviour of the arterial-wall is taken into account using a complex elastic modulus. The flow is solved vessel by vessel in the frequency domain and the calculated output pressure is then used as an input boundary condition for daughter vessels. The computational results yield pulsatile blood pressure and flow rate for every segment in the tree. This solver is coupled with large arterial trees generated from a three-dimensional constrained constructive optimisation algorithm. The tree contains thousands of blood vessels with radii spanning ~1 mm in the root artery to ~30 μm in leaf vessels. The computation takes seconds to complete for a vasculature of 2048 vessels and less than 2 min for a vasculature of 4096 vessels on a desktop computer.