Cardiovascular simulations provide a promising means to predict risk of thrombosis in grafts, devices, and surgical anatomies in adult and pediatric patients. Although the pathways for platelet activation and clot formation are not yet fully understood, recent findings suggest that thrombosis risk is increased in regions of flow recirculation and high residence time (RT). Current approaches for calculating RT are typically based on releasing a finite number of Lagrangian particles into the flow field and calculating RT by tracking their positions. However, special care must be taken to achieve temporal and spatial convergence, often requiring repeated simulations. In this work, we introduce a non-discrete method in which RT is calculated in an Eulerian framework using the advection-diffusion equation. We first present the formulation for calculating residence time in a given region of interest using two alternate definitions. The physical significance and sensitivity of the two measures of RT are discussed and their mathematical relation is established. An extension to a point-wise value is also presented. The methods presented here are then applied in a 2D cavity and two representative clinical scenarios, involving shunt placement for single ventricle heart defects and Kawasaki disease. In the second case study, we explored the relationship between RT and wall shear stress, a parameter of particular importance in cardiovascular disease.
A non-discrete method for computation of residence time in fluid mechanics simulations
Part of the Modeling Of Congenital Hearts Alliance (MOCHA). MOCHA Investigators: Edward Bove, M.D. and Adam Dorfman, M.D. (University of Michigan, USA); Andrew Taylor, M.D., Alessandro Giardini, M.D., Sachin Khambadkone, M.D., Marc de Leval, M.D., Silvia Schievano, Ph.D., and T.-Y. Hsia, M.D. (Institute of Child Health, UK); G. Hamilton Baker, M.D. and Anthony Hlavacek (Medical University of South Carolina, USA); Francesco Migliavacca, Ph.D., Giancarlo Pennati, Ph.D., and Gabriele Dubini, Ph.D. (Politecnico di Milano, Italy); Richard Figliola, Ph.D. and John McGregor, Ph.D. (Clemson University, USA); Alison Marsden, Ph.D. (University of California, San Diego, USA); Irene Vignon-Clementel (National Institute of Research in Informatics and Automation, France).
Mahdi Esmaily-Moghadam, Tain-Yen Hsia, Alison L. Marsden; A non-discrete method for computation of residence time in fluid mechanics simulations. Physics of Fluids 1 November 2013; 25 (11): 110802. https://doi.org/10.1063/1.4819142
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