A novel framework for fluid/structure interaction in rapid subject-specific simulations of blood flow in coronary artery bifurcations

Milan Blagojević; Aleksandar Nikolić; Miroslav Živković; Milorad Živković; Goran Stanković

doi:10.2298/2792

Milan Blagojević Faculty of Engineering, University of Kragujevac, Kragujevac, Serbia
Aleksandar Nikolić Faculty of Engineering, University of Kragujevac, Kragujevac, Serbia
Miroslav Živković Faculty of Engineering, University of Kragujevac, Kragujevac, Serbia
Milorad Živković Faculty of Medicine, University of Belgrade, Belgrade, Serbia
Goran Stanković Faculty of Medicine, University of Belgrade, Belgrade, Serbia

DOI: https://doi.org/10.2298/2792

Keywords: models, theoretical, computer simulation, coronary vessels, blood flow velocity, atherosclerosis, risk factors,

Abstract

Background/Aim. Practical difficulties, particularly long model development time, have limited the types and applicability of computational fluid dynamics simulations in numerical modeling of blood flow in serial manner. In these simulations, the most revealing flow parameters are the endothelial shear stress distribution and oscillatory shear index. The aim of this study was analyze their role in the diagnosis of the occurrence and prognosis of plaque development in coronary artery bifurcations. Methods. We developed a novel modeling technique for rapid cardiovascular hemodynamic simulations taking into account interactions between fluid domain (blood) and solid domain (artery wall). Two numerical models that represent the observed subdomains of an arbitrary patient-specific coronary artery bifurcation were created using multi-slice computed tomography (MSCT) coronagraphy and ultrasound measurements of blood velocity. Coronary flow using an in-house finite element solver PAK-FS was solved. Results. Overall behavior of coronary artery bifurcation during one cardiac cycle is described by: velocity, pressure, endothelial shear stress, oscillatory shear index, stress in arterial wall and nodal displacements. The places where (a) endothelial shear stress is less than 1.5, and (b) oscillatory shear index is very small (close or equal to 0) are prone to plaque genesis. Conclusion. Finite element simulation of ﬂuid–structure interaction was used to investigate patient-specific ﬂow dynamics and wall mechanics at coronary artery bifurcations. Simulation model revealed that lateral walls of the main branch and lateral walls distal to the carina are exposed to low endothelial shear stress which is a predilection site for development of atherosclerosis. This conclusion is confirmed by the low values of oscillatory shear index in those places.

References

Zarins CK, Giddens DP, Bharadvaj BK, Sottiurai VS, Mabon RF, Glagov S. Carotid bifurcation atherosclerosis. Quantitative cor-relation of plaque localization with flow velocity profiles and wall shear stress. Circ Res 1983; 53(4): 502−14.

Nakazawa G, Yazdani SK, Finn AV, Vorpahl M, Kolodgie FD, Virmani R. Pathological findings at bifurcation lesions: the im-pact of flow distribution on atherosclerosis and arterial healing after stent implantation. J Am Coll Cardiol 2010; 55(16): 1679−87.

Ku DN, Giddens DP, Zarins CK, Glagov S. Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive cor-relation between plaque location and low oscillating shear stress. Arteriosclerosis 1985; 5(3): 293−302.

Moore JE, Xu C, Glagov S, Zarins CK, Ku DN. Fluid wall shear stress measurements in a model of the human abdominal aorta: oscillatory behavior and relationship to atherosclerosis. Atherosclerosis 1994; 110(2): 225−40.

Chatzizisis YS, Coskun AU, Jonas M, Edelman ER, Feldman CL, Stone PH. Role of endothelial shear stress in the natural history of coronary atherosclerosis and vascular remodeling: molecu-lar, cellular, and vascular behavior. J Am Coll Cardiol 2007; 49(25): 2379−93.

Gambillara V, Chambaz C, Montorzi G, Roy S, Stergiopulos N, Si-lacci P. Plaque-prone hemodynamics impair endothelial func-tion in pig carotid arteries. Am J Physiol Heart Circ Physiol 2006; 290(6): H2320−8.

Samady H, Eshtehardi P, McDaniel MC, Suo J, Dhawan SS, May-nard C, et al. Coronary artery wall shear stress is associated with progression and transformation of atherosclerotic plaque and arterial remodeling in patients with coronary artery dis-ease. Circulation 2011; 124(7): 779−88.

Giannoglou GD, Antoniadis AP, Koskinas KC, Chatzizisis YS. Flow and atherosclerosis in coronary bifurcations. EuroIntervention 2010; 6(Suppl J): J16−23.

Kung EO, Les AS, Figueroa AC, Medina F, Arcaute K, Wicker RB, et al. In vitro validation of finite element analysis of blood flow in deformable models. Ann Biomed Eng 2011; 39(7): 1947−60.

Stepanović Ž, Živković M, Vulović S, Aćimović L, Ristić B, Matić A, et al. High, open wedge tibial osteotomy: Finite element analysis of five internal fixation modalities. Vojnosanit Pregl 2011; 68(10): 867−71. (Serbian)

Mariūnas M, Kuzborska Z. Influence of load magnitude and du-ration on the relationship between human arterial blood pres-sure and flow rate. Acta Bioeng Biomech 2011; 13(2): 67−72.

Kim H, Vignon-Clementel I, Figueroa C, Jansen K, Taylor C. Devel-oping computational methods for three-dimensional finite element simulations of coronary blood flow. Finite Elem Anal Des 2010; 46(6): 514−25.

Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE. Com-puter modeling of cardiovascular fluid-structure interactions with the deforming-spatial-domain/stabilized space-time for-mulation. Comput Methods Appl Mech Eng 2006; 195: 1885–95.

Bazilevs Y, Hsu MC, Zhang Y, Wang W, Liang X, Kvamsdal T, et al. A fully-coupled fluid-structure interaction simulation of cerebral aneurysms. Comput Mech 2010; 46(1): 3−16.

Weydahl ES, Moore JE. Dynamic curvature strongly affects wall shear rates in a coronary artery bifurcation model. J Biomech 2001; 34(9): 1189−96.

Nichols WW, Orourke MF. McDonalds blood flow in arteries: Theoretica, experimental and clinical principles. 5th ed. Lon-don: A Hodder Arnold Publicatio; 2005.

Slager CJ, Wentzel JJ, Gijsen FJ, Schuurbiers JC, Wal AC, Steen AF, et al. The role of shear stress in the generation of rupture-prone vulnerable plaques. Nat Clin Pract Cardiovasc Med 2005; 2(8): 401−7.

Malek AM, Alper SL, Izumo S. Hemodynamic shear stress and its role in atherosclerosis. JAMA 1999; 282(21): 2035−42.

Gimbrone MA, Topper JN, Nagel T, Anderson KR, Garcia-Cardeña G. Endothelial dysfunction, hemodynamic forces, and athero-genesis. Ann N Y Acad Sci 2000; 902: 230−9; discussion 9−40.

Stone PH, Coskun AU, Kinlay S, Clark ME, Sonka M, Wahle A, et al. Effect of endothelial shear stress on the progression of coronary artery disease, vascular remodeling, and in-stent restenosis in humans: in vivo 6-month follow-up study. Circu-lation 2003; 108(4): 438−44.

Ku DN. Blood flow in arteries. Annu Rev Fluid Mech 1997; 29(1): 399−434.

Soulis JV, Giannoglou GD, Chatzizisis YS, Farmakis TM, Gian-nakoulas GA, Parcharidis GE, et al. Spatial and phasic oscillation of non-Newtonian wall shear stress in human left coronary artery bifurcation: an insight to atherogenesis. Coron Artery Dis 2006; 17(4): 351−8.

Younis HF, Kaazempur-Mofrad MR, Chan RC, Isasi AG, Hinton DP, Chau AH, et al. Hemodynamics and wall mechanics in human carotid bifurcation and its consequences for athero-genesis: investigation of inter-individual variation. Biomech Model Mechanobiol 2004; 3(1): 17−32.

Kojić M, Filipović N, Stojanović B, Kojić N. Computer Modeling in Bioengineering: Theoretical background, examples and soft-ware. Chichester: John Wiley & Sons; 2008.

Bathe K. Finite element procedures in engineering analysis. Englewood Cliffs, NJ: Prentice Hall; 1996.

Kojic M, Slavkovic R, Zivkovic M, Grujovic N. The finite element method: Linear analysis. Kragujevac: Faculty of Mechanical Engineering of Kragujevac; 1998. (Serbian)

Živković M. Department: Department for applied mechanics and automatic control. Kragujevac: Faculty of Engineering, University of Kragujevac; 2004.

Zhao SZ, Ariff B, Long Q, Hughes AD, Thom SA, Stanton AV, Xu XY. Inter-individual variations in wall shear stress and me-chanical stress distributions at the carotid artery bifurcation of healthy humans. J Biomech 2002; 35(10): 1367−77.

Soulis JV, Farmakis TM, Giannoglou GD, Louridas GE. Wall shear stress in normal left coronary artery tree. J Biomech 2006; 39(4): 742−9.

Nguyen KT, Clark CD, Chancellor TJ, Papavassiliou DV. Carotid geometry effects on blood flow and on risk for vascular dis-ease. J Biomech 2008; 41(1): 11−9.

Goubergrits L, Affeld K, Fernandez-Brittoy J, Falcon L. Investigation of geometry and atherosclerosis in the human carotid bi-furcations. J Mech Med Biol 2003; 3(1): 31−48.

Zhang YJ, Bajaj C. Adaptive and quality quadrilat-eral/hexahedral meshing from volumetric data. Comput Methods Appl Mech Engrg 2006; 195: 942−60.

de Santis G, de Beule M, van Canneyt K, Segers P, Verdonck P, Ver-hegghe B. Full-hexahedral structured meshing for image-based computational vascular modeling. Med Eng Phys 2011; 33(10): 1318−25.

Shirsat A, Gupta S, Shevare GR. Generation of multi-block to-pology for discretisation of three-dimensional domains. Com-put Graph 1999; 23(1): 45−57.

Yuan C, Yih N. A transfinite interpolation method of grid generation based on multipoints. J Sci Comp 1998; 13(1): 105−14.

Perktold K, Resch M, Florian H. Pulsatile non-Newtonian flow characteristics in a three-dimensional human carotid bifurca-tion model. J Biomech Eng 1991; 113(4): 464−75.

Perktold K, Resch M, Peter RO. Three-dimensional numerical analysis of pulsatile flow and wall shear stress in the carotid ar-tery bifurcation. J Biomech 1991; 24(6): 409−20.

Stone PH, Feldman CL. In vivo assessment of the risk profile of evolving individual coronary plaques: a step closer. Circula-tion 2011; 124(7): 763−5.