First blood: An efficient, hybrid one‐ and zero‐dimensional, modular hemodynamic solver

Low‐dimensional (1D or 0D) models can describe the whole human blood circulation, for example, 1D distributed parameter model for the arterial network and 0D concentrated models for the heart or other organs. This paper presents a combined 1D‐0D solver, called first_blood, that solves the governing equations of fluid dynamics to model low‐dimensional hemodynamic effects. An extended method of characteristics is applied here to solve the momentum, and mass conservation equations and the viscoelastic wall model equation, mimicking the material properties of arterial walls. The heart and the peripheral lumped models are solved with a general zero‐dimensional (0D) nonlinear solver. The model topology can be modular, that is, first_blood can solve any 1D‐0D hemodynamic model. To demonstrate the applicability of first_blood, the human arterial system, the heart and the peripherals are modelled using the solver. The simulation time of a heartbeat takes around 2 s, that is, first_blood requires only twice the real‐time for the simulation using an average PC, which highlights the computational efficiency. The source code is available on GitHub, that is, it is open source. The model parameters are based on the literature suggestions and on the validation of output data to obtain physiologically relevant results. Results in the arterial system from different locations showing the pressure (p), and the velocity (v) as a function of time (t) for one cycle. Red curves indicate the simulations from first_blood, and the blue lines come from the literature52 for qualitative validation of the pulse waves