Elixir
Modeling blood flow and especially the propagation of the pulse wave in systemic arteries is a topic that is interesting to the medical society since the shape of the pressure profiles has diagnostic significance. We build a package that can simulate blood flow and pressure in large arteries by solving a nonlinear onedimensional model based on the incompressible Navier-Stokes equations for a Newtonian fluid in an elastic tube. Our method, however, does not require the usage of discretized methods for solving differential equations such as the popular Lax-Wendroff method (LW) but instead uses automatic differentiation to achieve a similar result.
Modeling blood flow and pressure in the systemic arteries has been a topic of interest both to theoretical and clinical investigators. Thus, research in this area has a vital interdisciplinary aspect. This project aims to develop a package capable of performing such simulations using the models we develop to treat cardiovascular diseases better. This is important since most deaths in developed countries result from cardiovascular diseases, mostly associated with abnormal flow in the arteries.
The original project's inspiration arose from previous and present efforts to develop an anaesthesia simulator based on mathematical models. An important part of which is having a good model for the cardiovascular system. However, as stated previously, the traditional focus of such projects generally is developing a good model.
The choice of the method to be used to solve the associated equations generally comes from a standard list of such methods.
We present a new method that, unlike its predecessors, offers a continuous solution, along with other benefits such as GPU support, a massive community, and such like.
Usage
Please refer to the instruction manual for instructions on how to set up and use the python package.
Paper
Please refer to the abstract for information regarding the theory and implementational details of the project.
Watch our video that highlights the fundamental idea of the project.
