The impact of uncertainty on shape optimization of idealized bypass graft models in unsteady flow

Abstract

It is well known that the fluid mechanics of bypass grafts impacts biomechanical responses and is linked to intimal thickening and plaque deposition on the vessel wall. In spite of this, quantitative information about the fluid mechanics is not currently incorporated into surgical planning and bypass graft design. In this work, we use a derivative-free optimization technique for performing systematic design of bypass grafts. The optimization method is coupled to a three-dimensional pulsatile Navier-Stokes solver. We systematically account for inevitable uncertainties that arise in cardiovascular simulations, owing to noise in medical image data, variable physiologic conditions, and surgical implementation. Uncertainties in the simulation input parameters as well as shape design variables are accounted for using the adaptive stochastic collocation technique. The derivative-free optimization framework is coupled with a stochastic response surface technique to make the problem computationally tractable. Two idealized numerical examples, an end-to-side anastomosis, and a bypass graft around a stenosis, demonstrate that accounting for uncertainty significantly changes the optimal graft design. Results show that small changes in the design variables from their optimal values should be accounted for in surgical planning. Changes in the downstream ͑distal͒ graft angle resulted in greater sensitivity of the wall-shear stress compared to changes in the upstream ͑proximal͒ angle. The impact of cost function choice on the optimal solution was explored. Additionally, this work represents the first use of the stochastic surrogate management framework method for robust shape optimization in a fully three-dimensional unsteady Navier-Stokes design problem.

Computational Simulation of the Adaptive Capacity of Vein Grafts in Response to Increased Pressure

“…The SMF has been used successfully in a variety of complex problems, including unsteady fluid mechanics [30][31][32], helicopter rotor blade design [33,34], quantifying uncertainity in bypass graft models [35] and identifying arterial G&R parameters [36]. The SMF method was originally developed for computationally expensive simulations and can be applied to discontinuous functions and problems with nonlinear constraints [37].…”

Optimization of computationally expensive simulations with Gaussian processes and parameter uncertainty: Application to cardiovascular surgery

“…This problem is studied in [3], which uses the stochastic collocation technique to incorporate and study the effects of input uncertainties, and applies a derivative-free optimization method to perform robust shape design.…”

“…This method has the ability to converge to a mesh local optima for Lipschitz continuous functions. [3] demonstrated that accounting for implementation and measurement uncertainties affects the optimal graft attachment angle.…”

“…Our goal in using simulation is to compute the optimal graft attachment angles that minimize the area of low wall-shear stress (WSS). Previously, non-Bayesian methods (surrogate management framework SMF) [1] were used to perform robust shape optimization in cardiovascular simulations [2], [3], [4]. To account for uncertainties, a stochastic collocation method [4] was coupled with the SMF framework.…”

A reduced computational and geometrical framework for inverse problems in hemodynamics

“…On the other hand, whenever some parameters are uncertain, we aim at inferring their values (and/or distributions) from indirect observations (and/or measures) by solving an inverse problem: given an observed output, can we deduce the value of the parameters that resulted in this output? Such problems are often encountered in cardiovascular mathematics as problems of parameter identification [7,70], variational data assimilation [13,50,63,66], or shape optimization [1,44,51,64]. Computational inverse problems are characterized by two main difficulties:…”