title: A non-discrete method for computation of residence time in fluid mechanics simulations.
abstract: 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.
authors.affiliation: Department of Mechanical and Aerospace Engineering, University of California, San Diego, California 92093-0411, USA.
authors.forename: Mahdi
authors.initials: M
authors.lastname: Esmaily-Moghadam
authors.forename: Tain-Yen
authors.initials: TY
authors.lastname: Hsia
authors.forename: Alison L
authors.initials: AL
authors.lastname: Marsden
references.citation: J Artif Organs. 2005;8(1):56-62
references.pmid: 15951982
references.citation: Circulation. 2004 Oct 26;110(17):2747-71
references.pmid: 15505111
references.citation: J Biomech Eng. 2012 May;134(5):051002
references.pmid: 22757490
references.citation: Annu Rev Biomed Eng. 2009;11:109-34
references.pmid: 19400706
references.citation: Ann Biomed Eng. 1997 Mar-Apr;25(2):344-56
references.pmid: 9084839
references.citation: J R Soc Interface. 2008 Jul 6;5(24):705-22
references.pmid: 17925274
references.citation: Ann Biomed Eng. 2011 May;39(5):1423-37
references.pmid: 21203844
references.citation: Teratology. 1994 Aug;50(2):112-7
references.pmid: 7801298
references.citation: J Biomech Eng. 2010 Aug;132(8):081013
references.pmid: 20670062
references.citation: Am J Physiol Heart Circ Physiol. 2004 May;286(5):H1916-22
references.pmid: 14715506
references.citation: Environ Pollut. 2002;116(1):75-84
references.pmid: 11817363
references.citation: Am J Physiol Heart Circ Physiol. 2001 May;280(5):H2076-86
references.pmid: 11299209
references.citation: Thromb Res. 2011 Mar;127(3):235-41
references.pmid: 21172720
references.citation: Ann Biomed Eng. 2012 Oct;40(10):2228-42
references.pmid: 22539149
references.citation: Birth Defects Res A Clin Mol Teratol. 2006 Nov;76(11):747-56
references.pmid: 17051527
references.citation: Ann Biomed Eng. 2011 Feb;39(2):864-83
references.pmid: 21103933
references.citation: Arterioscler Thromb Vasc Biol. 1997 Apr;17(4):646-53
references.pmid: 9108776
references.citation: J Biomech. 2005 May;38(5):1129-41
references.pmid: 15797594
references.citation: J Am Coll Cardiol. 2009 Nov 17;54(21):1911-20
references.pmid: 19909870
references.citation: Ann Biomed Eng. 2010 Oct;38(10):3195-209
references.pmid: 20559732
references.citation: Thromb Res. 1998 Dec 15;92(6 Suppl 2):S25-31
references.pmid: 9886907
references.citation: Thromb Haemost. 1995 Sep;74(3):916-22
references.pmid: 8571321
references.citation: Ann Biomed Eng. 2010 Oct;38(10):3058-69
references.pmid: 20499185
references.citation: Stroke. 2007 Jun;38(6):1924-31
references.pmid: 17495215
references.citation: Biomech Model Mechanobiol. 2012 Jul;11(6):915-32
references.pmid: 22120599
references.citation: Proc IEEE Inst Electr Electron Eng. 2008 Aug 1;96(8):1266
references.pmid: 20107615
references.citation: J Biomech Eng. 1996 May;118(2):158-64
references.pmid: 8738779
references.citation: Cardiovasc Eng. 2010 Jun;10(2):84-90
references.pmid: 20514553