Multi-scale modeling of hemodynamics in the cardiovascular system

The human cardiovascular system is a closed-loop and complex vascular network with multi-scaled heterogeneous hemodynamic phenomena. Here, we give a selective review of recent progress in macro-hemodynamic modeling, with a focus on geometrical multi-scale modeling of the vascular network, micro-hemodynamic modeling of microcirculation, as well as blood cellular, subcellular, endothelial biomechanics, and their interaction with arterial vessel mechanics. We describe in detail the methodology of hemodynamic modeling and its potential applications in cardiovascular research and clinical practice. In addition, we present major topics for future study: recent progress of patient-specific hemodynamic modeling in clinical applications, micro-hemodynamic modeling in capillaries and blood cells, and the importance and potential of the multi-scale hemodynamic modeling.Graphical AbstractHere we give a selective review of recent progress in macro-hemodynamic modeling, with a focus on geometrical multi-scale modeling of the vascular network, micro-hemodynamic modeling of microcirculation, as well as blood cellular, subcellular, endothelial biomechanics, and their interaction with arterial vessel mechanics. We describe in detail the methodology of hemodynamic modeling and its potential applications in cardiovascular research and clinical practice. In addition, we present major topics for future study: recent progress of patient-specific hemodynamic modeling in clinical applications, micro-hemodynamic modeling in capillaries and blood cells, and the importance and potential of the multi-scale hemodynamic modeling.

[1]  Hao Gao,et al.  Atherosclerosis Plaque Stress Analysis: A Review , 2014 .

[2]  Taiji Adachi,et al.  Three-dimensional modulation of cortical plasticity during pseudopodial protrusion of mouse leukocytes. , 2013, Biochemical and biophysical research communications.

[3]  A. Pries,et al.  Origins of heterogeneity in tissue perfusion and metabolism. , 2009, Cardiovascular research.

[4]  Pablo J. Blanco,et al.  Partitioned Analysis for Dimensionally-Heterogeneous Hydraulic Networks , 2011, Multiscale Model. Simul..

[5]  M. Sackner,et al.  Low-amplitude pulses to the circulation through periodic acceleration induces endothelial-dependent vasodilatation. , 2009, Journal of applied physiology.

[6]  B. Sumpio,et al.  Endothelial cell response to different mechanical forces. , 2000, Journal of vascular surgery.

[7]  N. Stergiopulos,et al.  Total arterial inertance as the fourth element of the windkessel model. , 1999, American journal of physiology. Heart and circulatory physiology.

[8]  R. Skalak,et al.  Strain energy function of red blood cell membranes. , 1973, Biophysical journal.

[9]  Ryutaro Himeno,et al.  A computational model of the cardiovascular system coupled with an upper-arm oscillometric cuff and its application to studying the suprasystolic cuff oscillation wave, concerning its value in assessing arterial stiffness , 2013, Computer methods in biomechanics and biomedical engineering.

[10]  Taiji Adachi,et al.  Reversible network reconnection model for simulating large deformation in dynamic tissue morphogenesis , 2013, Biomechanics and modeling in mechanobiology.

[11]  Lucas O Müller,et al.  A global multiscale mathematical model for the human circulation with emphasis on the venous system , 2014, International journal for numerical methods in biomedical engineering.

[12]  B. Zweifach,et al.  Network analysis of microcirculation of cat mesentery. , 1974, Microvascular research.

[13]  D. Ingber.  Tensegrity II. How structural networks influence cellular information processing networks , 2003, Journal of Cell Science.

[14]  N. Bressloff,et al.  Blood flow in microvascular networks , 2009 .

[15]  G. Borisy,et al.  Cell Migration: Integrating Signals from Front to Back , 2003, Science.

[16]  Frank Moss,et al.  Experiments and simulations , 2009 .

[17]  O. Frank,et al.  Die grundform des arteriellen pulses , 1899 .

[18]  D. F. Young,et al.  Computer simulation of arterial flow with applications to arterial and aortic stenoses. , 1992, Journal of biomechanics.

[19]  Berend E. Westerhof,et al.  The arterial Windkessel , 2009, Medical & Biological Engineering & Computing.

[20]  Keith Burridge,et al.  α-Actinin: Immunofluorescent localization of a muscle structural protein in nonmuscle cells , 1975, Cell.

[21]  Shigeo Wada,et al.  Elastic behavior of a red blood cell with the membrane’s nonuniform natural state: equilibrium shape, motion transition under shear flow, and elongation during tank-treading motion , 2014, Biomechanics and modeling in mechanobiology.

[22]  S. Sherwin,et al.  Lumped parameter outflow models for 1-D blood flow simulations: Effect on pulse waves and parameter estimation , 2008 .

[23]  Michael P. O'Neil,et al.  Pulsatile versus nonpulsatile flow during cardiopulmonary bypass: microcirculatory and systemic effects. , 2012, The Annals of thoracic surgery.

[24]  S. Suresha,et al.  Mechanics of the human red blood cell deformed by optical tweezers , 2003 .

[25]  Yasuhiko Sugii,et al.  Measurement of red cell velocity in microvessels using particle image velocimetry (PIV). , 2003, Clinical hemorheology and microcirculation.

[26]  Ken-ichi Tsubota,et al.  Elastic force of red blood cell membrane during tank-treading motion: Consideration of the membrane's natural state , 2010 .

[27]  A Noordergraaf,et al.  Analog studies of the human systemic arterial tree. , 1969, Journal of biomechanics.

[28]  Charles A. Taylor,et al.  A coupled momentum method for modeling blood flow in three-dimensional deformable arteries , 2006 .

[29]  Nikos Stergiopulos,et al.  Pulse Wave Propagation in the Arterial Tree , 2011 .

[30]  F. N. Vosse,et al.  A wave propagation model of blood flow in large vessels using an approximate velocity profile function , 2007, Journal of Fluid Mechanics.

[31]  Giancarlo Pennati,et al.  Use of Mathematical Modeling to Compare and Predict Hemodynamic Effects Between Hybrid and Surgical Norwood Palliations for Hypoplastic Left Heart Syndrome , 2011, Circulation.

[32]  T. Ishikawa,et al.  A three‐dimensional particle simulation of the formation and collapse of a primary thrombus , 2010 .

[33]  Rolf Rannacher,et al.  ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER–STOKES EQUATIONS , 1996 .

[34]  G S Kassab,et al.  Analysis of blood flow in the entire coronary arterial tree. , 2005, American journal of physiology. Heart and circulatory physiology.

[35]  A. Pries,et al.  Biophysical aspects of blood flow in the microvasculature. , 1996, Cardiovascular research.

[36]  L. Formaggia,et al.  On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations , 2007 .

[37]  R. Glowinski,et al.  A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow , 2001 .

[38]  K. Rottner,et al.  Assembling an actin cytoskeleton for cell attachment and movement. , 1998, Biochimica et biophysica acta.

[39]  Peng Zhao,et al.  Blood Flow in the Circle of Willis: Modeling and Calibration , 2008, Multiscale Model. Simul..

[40]  A. Pries,et al.  Blood flow in microvascular networks. Experiments and simulation. , 1990, Circulation research.

[41]  Jing Zheng,et al.  Effects of Pulsatile Shear Stress on Nitric Oxide Production and Endothelial Cell Nitric Oxide Synthase Expression by Ovine Fetoplacental Artery Endothelial Cells1 , 2003, Biology of reproduction.

[42]  Y. Iwasa,et al.  Growth Based Morphogenesis of Vertebrate Limb Bud , 2008, Bulletin of mathematical biology.

[43]  M Intaglietta,et al.  Blood pressure fluctuations in human nailfold capillaries. , 1979, The American journal of physiology.

[44]  Hao Liu,et al.  Simulation of hemodynamic responses to the valsalva maneuver: an integrative computational model of the cardiovascular system and the autonomic nervous system. , 2006, The journal of physiological sciences : JPS.

[45]  Paolo Crosetto,et al.  Physiological simulation of blood flow in the aorta: comparison of hemodynamic indices as predicted by 3-D FSI, 3-D rigid wall and 1-D models. , 2013, Medical engineering & physics.

[46]  Kaoru Sugimura,et al.  Bayesian inference of force dynamics during morphogenesis. , 2012, Journal of theoretical biology.

[47]  Klemens Rottner,et al.  The lamellipodium: where motility begins. , 2002, Trends in cell biology.

[48]  T. Ishikawa,et al.  Computational study on effect of stenosis on primary thrombus formation. , 2011, Biorheology.

[49]  A. Pries,et al.  Generalization of the Fahraeus principle for microvessel networks. , 1986, The American journal of physiology.

[50]  S. Chien.  Effects of Disturbed Flow on Endothelial Cells , 2008, Annals of Biomedical Engineering.

[51]  G Plank,et al.  Computational tools for modeling electrical activity in cardiac tissue. , 2003, Journal of electrocardiology.

[52]  Charles A. Taylor,et al.  Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries , 2006 .

[53]  Y Sezai,et al.  The role of pulsatility in end-organ microcirculation after cardiogenic shock. , 1996, ASAIO journal.

[54]  T Saitoh,et al.  Renal circulation and cellular metabolism during left ventricular assisted circulation: comparison study of pulsatile and nonpulsatile assists. , 1997, Artificial organs.

[55]  M Intaglietta,et al.  Elastic Environment of the Capillary Bed , 1966, Circulation research.

[56]  Hao Liu,et al.  Blood flow dynamic improvement with aneurysm repair detected by a patient-specific model of multiple aortic aneurysms , 2014, Heart and Vessels.

[57]  W. Helfrich.  Elastic Properties of Lipid Bilayers: Theory and Possible Experiments , 1973, Zeitschrift fur Naturforschung. Teil C: Biochemie, Biophysik, Biologie, Virologie.

[58]  Gary G. Borisy,et al.  Arp2/3 Complex and Actin Depolymerizing Factor/Cofilin in Dendritic Organization and Treadmilling of Actin Filament Array in Lamellipodia , 1999, The Journal of cell biology.

[59]  G. Karniadakis,et al.  Modeling Blood Flow Circulation in Intracranial Arterial Networks: A Comparative 3D/1D Simulation Study , 2010, Annals of Biomedical Engineering.

[60]  B J B M Wolters,et al.  A patient-specific computational model of fluid-structure interaction in abdominal aortic aneurysms. , 2005, Medical engineering & physics.

[61]  A. Quarteroni,et al.  On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels , 2001 .

[62]  Jean-François Stoltz,et al.  Calcul numérique de la déformation mécanique d'un modèle de cellule endothéliale , 2000 .

[63]  J Lee,et al.  Development and application of a one-dimensional blood flow model for microvascular networks , 2008, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[64]  P. Blanco,et al.  On the potentialities of 3D-1D coupled models in hemodynamics simulations. , 2009, Journal of biomechanics.

[65]  H. Mellor,et al.  Actin stress fibres , 2007, Journal of Cell Science.

[66]  R. Himeno,et al.  Biomechanical characterization of ventricular-arterial coupling during aging: a multi-scale model study. , 2009, Journal of biomechanics.

[67]  Shigeo Wada,et al.  Simulation Study on Effects of Hematocrit on Blood Flow Properties Using Particle Method , 2006 .

[68]  Anne J. Ridley,et al.  Shear stress–induced endothelial cell polarization is mediated by Rho and Rac but not Cdc42 or PI 3-kinases , 2003, The Journal of cell biology.

[69]  P Ganesan,et al.  Modelling of pulsatile blood flow in arterial trees of retinal vasculature. , 2011, Medical engineering & physics.

[70]  S. Chien,et al.  Effects of disturbed flow on vascular endothelium: pathophysiological basis and clinical perspectives. , 2011, Physiological reviews.

[71]  Spencer J. Sherwin,et al.  Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system , 2003 .

[72]  F. Ghorbel,et al.  A human cardiopulmonary system model applied to the analysis of the Valsalva maneuver. , 2001, American journal of physiology. Heart and circulatory physiology.

[73]  T D Pollard,et al.  The interaction of Arp2/3 complex with actin: nucleation, high affinity pointed end capping, and formation of branching networks of filaments. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[74]  K Weber,et al.  Antibody to myosin: the specific visualization of myosin-containing filaments in nonmuscle cells. , 1974, Proceedings of the National Academy of Sciences of the United States of America.

[75]  F P T Baaijens,et al.  A three-dimensional computational analysis of fluid-structure interaction in the aortic valve. , 2003, Journal of biomechanics.

[76]  Charles A. Taylor,et al.  Patient-specific modeling of cardiovascular mechanics. , 2009, Annual review of biomedical engineering.

[77]  Ryutaro Himeno,et al.  Multi-scale modeling of the human cardiovascular system with applications to aortic valvular and arterial stenoses , 2009, Medical & Biological Engineering & Computing.

[78]  R. Ogden,et al.  Constitutive modelling of arteries , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[79]  P. Verdonck,et al.  Modeling Hemodynamics in Vascular Networks Using a Geometrical Multiscale Approach: Numerical Aspects , 2013, Annals of Biomedical Engineering.

[80]  T. Wei,et al.  Experiments show importance of flow-induced pressure on endothelial cell shape and alignment , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[81]  Can Ince,et al.  Editorial Microcirculation , 2012 .

[82]  G Pasterkamp,et al.  Arterial Remodeling: Mechanisms and Clinical Implications , 2000 .

[83]  P. Davies,et al.  Mechanical stress mechanisms and the cell. An endothelial paradigm. , 1993, Circulation research.

[84]  J Seki,et al.  Flow pulsation and network structure in mesenteric microvasculature of rats. , 1994, The American journal of physiology.

[85]  N. Stergiopulos,et al.  Validation of a one-dimensional model of the systemic arterial tree. , 2009, American journal of physiology. Heart and circulatory physiology.

[86]  T D Pollard,et al.  Molecular mechanisms controlling actin filament dynamics in nonmuscle cells. , 2000, Annual review of biophysics and biomolecular structure.

[87]  Guolong Cai,et al.  A one-dimensional mathematical model for studying the pulsatile flow in microvascular networks. , 2014, Journal of biomechanical engineering.

[88]  Yoshihiro Morishita,et al.  Bayesian inference of whole-organ deformation dynamics from limited space-time point data. , 2014, Journal of theoretical biology.

[89]  K Perktold,et al.  Mathematical modeling of arterial blood flow and correlation to atherosclerosis. , 1995, Technology and health care : official journal of the European Society for Engineering and Medicine.

[90]  Matthew C Barker,et al.  Microvascular oxygen tension in the rat mesentery. , 2008, American journal of physiology. Heart and circulatory physiology.

[91]  Pablo J. Blanco,et al.  Iterative strong coupling of dimensionally heterogeneous models , 2009 .

[92]  D E Ingber,et al.  Cellular control lies in the balance of forces. , 1998, Current opinion in cell biology.

[93]  T J Pedley,et al.  Vascular endothelial cells minimize the total force on their nuclei. , 2000, Biophysical journal.

[94]  L. Formaggia,et al.  Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart , 2006, Computer methods in biomechanics and biomedical engineering.

[95]  R Tominaga,et al.  Pulsatile flow enhances endothelium-derived nitric oxide release in the peripheral vasculature. , 2000, American journal of physiology. Heart and circulatory physiology.

[96]  P. Yim,et al.  Characterization of shear stress on the wall of the carotid artery using magnetic resonance imaging and computational fluid dynamics. , 2005, Studies in health technology and informatics.

[97]  Ken-ichi Tsubota,et al.  Effect of the natural state of an elastic cellular membrane on tank-treading and tumbling motions of a single red blood cell. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[98]  Y C Fung,et al.  On measuring the third dimension of cultured endothelial cells in shear flow. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[99]  Y. Huo,et al.  A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree. , 2007, American journal of physiology. Heart and circulatory physiology.

[100]  S. Sherwin,et al.  Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows. , 2007, Journal of biomechanics.

[101]  C. Monaco,et al.  Biomechanical factors and macrophages in plaque stability. , 2013, Cardiovascular research.

[102]  P. S. Ramalho.  Microcirculation and hemorheology. , 1983, Acta medica portuguesa.

[103]  H. Higgs,et al.  The many faces of actin: matching assembly factors with cellular structures , 2007, Nature Cell Biology.

[104]  C. Peskin.  The immersed boundary method , 2002, Acta Numerica.

[105]  R. Lal,et al.  Shear stress-induced reorganization of the surface topography of living endothelial cells imaged by atomic force microscopy. , 1994, Circulation research.

[106]  Yubing Shi,et al.  Review of Zero-D and 1-D Models of Blood Flow in the Cardiovascular System , 2011, Biomedical engineering online.

[107]  Pekka Lappalainen,et al.  Stress fibers are generated by two distinct actin assembly mechanisms in motile cells , 2006, The Journal of cell biology.

[108]  M. Olufsen,et al.  Numerical Simulation and Experimental Validation of Blood Flow in Arteries with Structured-Tree Outflow Conditions , 2000, Annals of Biomedical Engineering.

[109]  Ken-ichi Tsubota,et al.  Short note on the bending models for a membrane in capsule mechanics: Comparison between continuum and discrete models , 2014, J. Comput. Phys..