A simple model for shear stress mediated lumen reduction in blood vessels

The goal of this paper is to qualitatively describe the dominant flow characteristics associated with shear stress mediated lumen reduction due to atherosclerotic plaque growth. The approach is to develop rate equations for the reduction of the lumen as a function of the shear stress near the intima wall. Elementary, qualitative, models for fully developed laminar and turbulent flows are employed, leading to nonlinear ordinary differential equations. The model provides a qualitative description of one aspect of the long-term reduction, perhaps taking years, of the lumen due to wall growth. This is useful because of the extreme complexity of long-term experiments.

[1]  K. Hayashi.  Cardiovascular solid mechanics. Cells, tissues, and organs , 2003 .

[2]  P. Shah.  Plaque Disruption and Coronary Thrombosis: New Insight into Pathogenesis and Prevention , 1997, Clinical cardiology.

[3]  A E Becker,et al.  Atherosclerotic plaque rupture--pathologic basis of plaque stability and instability. , 1999, Cardiovascular research.

[4]  S. Berger,et al.  Numerical Simulation of the Flow in the Carotid Bifurcation , 1998 .

[5]  T. Zohdi.  An adaptive‐recursive staggering strategy for simulating multifield coupled processes in microheterogeneous solids , 2002 .

[6]  G. V. R. Born,et al.  INFLUENCE OF PLAQUE CONFIGURATION AND STRESS DISTRIBUTION ON FISSURING OF CORONARY ATHEROSCLEROTIC PLAQUES , 1989, The Lancet.

[7]  Corrosion Engineering,et al.  Corrosion engineering , 1979 .

[8]  P. Shah,et al.  The role of inflammation in plaque disruption and thrombosis. , 2001, Reviews in cardiovascular medicine.

[9]  D Saloner,et al.  Influence of stenosis morphology on flow through severely stenotic vessels: implications for plaque rupture. , 2000, Journal of biomechanics.

[10]  G. Holzapfel,et al.  A structural model for the viscoelastic behavior of arterial walls: Continuum formulation and finite element analysis , 2002 .

[11]  Gerhard A. Holzapfel,et al.  A Layer-Specific Three-Dimensional Model for the Simulation of Balloon Angioplasty using Magnetic Resonance Imaging and Mechanical Testing , 2002, Annals of Biomedical Engineering.

[12]  R. Ogden,et al.  A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models , 2000 .

[13]  S. Berger,et al.  Flows in Stenotic Vessels , 2000 .

[14]  J. Humphrey.  Cardiovascular solid mechanics , 2002 .

[15]  A phenomenological model for atherosclerotic plaque growth and rupture , 2004 .

[16]  D. Saloner,et al.  Numerical analysis of flow through a severely stenotic carotid artery bifurcation. , 2002, Journal of biomechanical engineering.

[17]  P. Libby,et al.  The Vascular Biology of Atherosclerosis , 2006 .

[18]  Tarek I. Zohdi,et al.  Modeling and simulation of a class of coupled thermo-chemo-mechanical processes in multiphase solids , 2004 .

[19]  Peter Libby,et al.  Current Concepts of the Pathogenesis of the Acute Coronary Syndromes , 2001, Circulation.

[20]  David Saloner,et al.  Physiological Flow Studies in Exact-Replica Atherosclerotic Carotid Bifurcations , 2003 .

[21]  M. Davies,et al.  Risk of thrombosis in human atherosclerotic plaques: role of extracellular lipid, macrophage, and smooth muscle cell content. , 1993, British heart journal.

[22]  G. Andros,et al.  Assessing and modifying the vulnerable atherosclerotic plaque: Valentin Fuster; Armonk, NY; 2002 Futura; 379 pages; $144.95 , 2004 .

[23]  Tarek I. Zohdi,et al.  A computational framework for agglomeration in thermochemically reacting granular flows , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[24]  D Saloner,et al.  Experimental flow studies in exact-replica phantoms of atherosclerotic carotid bifurcations under steady input conditions. , 2003, Journal of biomechanical engineering.

[25]  R D Kamm,et al.  Effects of fibrous cap thickness on peak circumferential stress in model atherosclerotic vessels. , 1992, Circulation research.