An optimal control approach to determine resistance-type boundary conditions from in-vivo data for cardiovascular simulations

Abstract

The choice of appropriate boundary conditions is a fundamental step in computational fluid dynamics (CFD) simulations of the cardiovascular system. Boundary conditions, in fact, highly affect the computed pressure and flow rates, and consequently haemodynamic indicators such as wall shear stress, which are of clinical interest. Devising automated procedures for the selection of boundary conditions is vital to achieve repeatable simulations. However, the most common techniques do not automatically assimilate patient-specific data, relying instead on expensive and time-consuming manual tuning procedures. In this work, we propose a technique for the automated estimation of outlet boundary conditions based on optimal control. The values of resistive boundary conditions are set as control variables and optimized to match available patient-specific data. Experimental results on four aortic arches demonstrate that the proposed framework can assimilate 4D-Flow MRI data more accurately than two other common techniques based on Murray's law and Ohm's law.

Parameter estimation in fluid flow models from aliased velocity measurements

“…We defined two sets of experiments starting from different initial guesses for the physical parameters to estimate: 3 ) = (52 500, 52 500, 52 500) Recall that the target values are U = 75, (R d,1 , R d,2 , R d,3 ) = (7200, 11 520, 11 520) as detailed in section 2.3. Here, the velocity amplitude U is in cm s −1 and the distal resistances R d,i are in (dyn • s)/cm 5 .…”

“…In the context of 3D-0D coupled models, the personalization typically relies on estimating those 0D model parameters at each outlet boundary of the 3D model from velocity (and eventually pressure) data using non-linear least-squares approaches solved via variational [3] or sequential [4,5] methods.…”