Flow in Healthy and Stenosed Arteries

Abstract

Mathematical and computational models for blood flow in normal and diseased arteries include vessel geometry, material properties, governing equations, and proper initial and boundary conditions. Models for stenosis, carotid, coronary, aorta, abdominal aortic aneurysm, pulmonary capillaries, graft, and stent are presented, with controlling factors and research focuses for each model discussed and proper references cited. Recent trends and potential applications for artery modeling are also discussed.

Image-based modeling for better understanding and assessment of atherosclerotic plaque progression and vulnerability: Data, modeling, validation, uncertainty and predictions

“…It should be emphasized that many items needed for modeling are hard or near impossible to obtain in vivo, and are often subject to large errors when obtainable. Model construction procedures based on in vivo data are considerably different from earlier models based on idealized geometry or ex vivo data (Tang et al, 2004; Tang, 2006; Yang et al, 2007). Residual stress and zero-stress plaque morphology need to be handled properly to get accurate stress/strain predictions (Ohayon et al, 2007; Huang et al, 2009; Speelman et al, 2011).…”

“…A shrink–stretch process is needed (see Fig. 1) (Tang, 2006; Huang et al, 2009) to (a) shrink in vivo plaque geometry to obtain a starting no-load geometry; and (b) apply pressure and axial stretch to recover original in vivo geometry with residual stress/strain computed. The shrinking rate in the axial direction and shrinkage rates of lumen and outer wall (which have to be different) were determined so that (1) mass conservation is satisfied; and (2) the contours of the plaque and its components after pressurization and axial stretch achieve the best match with the in vivo geometry from MRI.…”

“…Considerable progress has been made in recent years in medical imaging (Yuan et al, 2001a, 2001b; Underhill, et al, 2010), histopathological analysis (Stary et al, 1992, 1994, 1995; Virmani et al, 2000, 2006), biomechanical plaque material properties (Finet et al, 2004; Le Floc'h et al, 2012; Baldewsing et al, 2008), mechanical stress risk factors (Richardson et al, 1989; Arroyo and Lee, 1999; Ohayon et al, 2011; Loree et al, 1992). and computational models (Tang, 2006; Friedman et al, 2010) for better understanding of plaque progression, rupture and to develop possible better patient screening and plaque assessment schemes. Richardson's paper (2002) provided an excellent review for plaque biomechanical analysis, covering essential topics including plaque components, tissue, cap pathology, modeling, and rupture process.…”

Using In Vivo Cine and 3D Multi-Contrast MRI to Determine Human Atherosclerotic Carotid Artery Material Properties and Circumferential Shrinkage Rate and Their Impact on Stress/Strain Predictions

“…However, the errors in stress/strain predictions caused by models without proper shrinkage were normally demonstrated in previous publications using hypothetic shrinkage (normally 8-10%) and material properties (just one set of parameters for all patients in one paper) from the literature [25-27, 30]. Shrinkage is linked to material properties.…”

“…In their in vivo MRI-based fluid-structure interaction (FSI) plaque models, Tang et al and Yang et al introduced a shrink-stretch process to a) shrink the vessel both axially and circumferentially to obtain the “no-load” shape as the numerical starting geometry; and b) stretch and pressurize the vessel to recover its in vivo shape under pressure and stretch conditions [7,25-27]. The shrinkage in axial direction was 9% so that the vessel would regain its in vivo length with a 10% axial stretch.…”