Arthur Ghigo (UBC) - Towards a multi-model cardiovascular simulation framework: from 1D to 3D models

Cardiovascular pathologies are now one of the leading causes of death and disability in Europe and North
America. Unfortunately, these pathologies very often lay dormant until they reach a critical state, after which
treatment is difficult. Furthermore, their pathogenesis is a complex multiscale and multifactor process, difficult to
detect using punctual non-invasive measurements and medical imaging.
Recently, a wide-spread of connected devices have become available and offer continuous health monitoring in
the hopes of improving the detection and prevention of cardiovascular pathologies. While these devices
essentially monitor heart rate, could they provide more valuable insights, how, and to what degree of accuracy?
As hemodynamics play a major role in the development of cardiovascular pathologies, there is now widespread
recognition that cardiovascular mathematical models and numerical simulations can help predict blood flow and
better understand pathogenesis. In fact, these models are now being progressively integrated into modern
cardiovascular medicine ( https://www.heartflow.com/ ). They could also be used in future connected devices to go
beyond heart rate monitoring.
Cardiovascular blood flow models must account for the multiscale architecture of the cardiovascular system.
Indeed, arteries and veins (0.1 to 10 mm in diameter), organized in arborescent structures, constitute the
macroscopic and mesoscopic scales. Capillaries (4 to 10 μm), arranged in a dense and space-filling mesh,
connect at the microscopic scale the arteries and veins. While blood flow at each of these scales could be solved
using the 3D Navier-Stokes equations coupled to fluid-structure interaction algorithms, the resulting modeling and
computational costs would be too high. A multi-model framework is therefore necessary to efficiently compute the
hemodynamics at each of these scales in order to provide valuable insights to clinicians in a reasonable time
frame.
In the first part of this presentation, I will talk about my PhD work on simplified 1D and 2D numerical models
designed to solve blood flow at the macroscopic and mesoscopic cardiovascular scales. These simplified models,
similar to the Saint-Venant and hydrostatic multilayer equations, are derived under the long-wave hypothesis and
are capable of describing the wavelike evolution of pressure and flow rate at reduced computational costs. As an
example, I will present an application of the 1D model to bypass graft surgery. I will then rapidly discuss ideas
developed by the group of D.R. CNRS Sylvie Lorthois at IMFT (Toulouse, France) on modeling blood flow,
oxygen, and nutrient exchanges at the microscopic scale using both a network and a porous media approach.
In the second part of this presentation, I will talk about my current work in the group of Prof. Anthony Wachs on
the development of a Cartersion embedded boundary method (cut-cell method) for moving rigid bodies in 3D
incompressible Newtonian flows. The method is implemented in the software Basilisk
( http://basilisk.dalembert.upmc.fr/ ) and is compatible with adaptive mesh refinement. This framework allows us to
efficiently solve with second-order accuracy incompressible flows around bodies of arbitrary shape. In the near
future, we will use this method to efficiently describe interactions between rigid particles (drugs) and deformable
red blood cells to gain a better understanding of the mechanisms involved in, for example, drug delivery.