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Annals of Biomedical Engineering

, Volume 44, Issue 9, pp 2642–2660 | Cite as

Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention

  • Yanhang Zhang
  • Victor H. Barocas
  • Scott A. Berceli
  • Colleen E. Clancy
  • David M. Eckmann
  • Marc Garbey
  • Ghassan S. Kassab
  • Donna R. Lochner
  • Andrew D. McCulloch
  • Roger Tran-Son-Tay
  • Natalia A. Trayanova
Multi-Scale Modeling in the Clinic

Abstract

Cardiovascular diseases (CVDs) are the leading cause of death in the western world. With the current development of clinical diagnostics to more accurately measure the extent and specifics of CVDs, a laudable goal is a better understanding of the structure–function relation in the cardiovascular system. Much of this fundamental understanding comes from the development and study of models that integrate biology, medicine, imaging, and biomechanics. Information from these models provides guidance for developing diagnostics, and implementation of these diagnostics to the clinical setting, in turn, provides data for refining the models. In this review, we introduce multi-scale and multi-physical models for understanding disease development, progression, and designing clinical interventions. We begin with multi-scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, personalized and precision medicine in cardiology with examples in arrhythmia and heart failure. We then introduce computational models of vasculature mechanics and associated mechanical forces for understanding vascular disease progression, designing clinical interventions, and elucidating mechanisms that underlie diverse vascular conditions. We conclude with a discussion of barriers that must be overcome to provide enhanced insights, predictions, and decisions in pre-clinical and clinical applications.

Keywords

Cardiac mechanics Electrophysiological modeling Cardiovascular fluid mechanics Vascular mechanics Extracellular matrix Mechanical forces Pathway network analysis Constitutive model Multi-scale modeling 

Abbreviations

2PEF

Two-photon excitation fluorescence

3-D

Three-dimensional

ABM

Agent-based model

APD

Action potential duration

ATP

Adenosine triphosphate

CARS

Coherent anti-stokes Raman scattering

CT

Computerized tomography

CV

Conduction velocity

CVD

Cardiovascular disease

DENSE

Displacement encoding with stimulated echoes

EADs

Early afterdepolarizations

ECG

Electrocardiogram

ECM

Extracellular matrix

HARP

Harmonic phase

IVUS

Intravascular ultrasound

MRI

Magnetic resonance imaging

NO

Nitric oxide

OCT

Optical coherence tomography

ODE

Ordinary differential equation

PDE

Partial differential equation

PET

Positron emission tomography

SHG

Second harmonic generation

SR

Sarcoplasmic reticulum

Notes

Acknowledgement

The authors acknowledge funding supports from National Science Foundation IUCRC CYBHOR NSF 106022 (Garbey); NSF CMMI 1463390 and CMMI 0954825 (Zhang), National Institute of Health U01EB016638 (Barocas); U01 EB016027 and R01 EB006818 (Eckmann); U01HL119178-01 (Berceli, Garbey, Tran Son Tay); R01HL117990 (Kassab) and U01 HL118738 (Beard and Kassab); P50 GM094503 (Beard), P41 GM103426-19 (Amaro), R01HL105242, and R01HL121754 (McCulloch); and R01HL098028 (Zhang), and FDA Critical Path Initiative (Lochner).

References

  1. 1.
    Aletti, F., E. Lanzarone, M. L. Costantino, and G. Baselli. Simulation study of autoregulation responses of peripheral circulation to systemic pulsatility. Nonlinear Biomed. Phys. 3:7, 2009.PubMedPubMedCentralCrossRefGoogle Scholar
  2. 2.
    Amanfu, R. K., and J. J. Saucerman. Cardiac models in drug discovery and development: a review. Crit. Rev. Biomed. Eng. 39:379–395, 2011.PubMedPubMedCentralCrossRefGoogle Scholar
  3. 3.
    Ambrosi, D., G. Ateshian, E. Arruda, S. Cowin, J. Dumais, A. Goriely, G. A. Holzapfel, J. Humphrey, R. Kemkemer, and E. Kuhl. Perspectives on biological growth and remodeling. J. Mech. Phys. Solids 59:863–883, 2011.PubMedPubMedCentralCrossRefGoogle Scholar
  4. 4.
    An, G., Q. Mi, J. Dutta-Moscato, and Y. Vodovotz. Agent-based models in translational systems biology. Wiley Interdiscip. Rev. 1:159–171, 2009.Google Scholar
  5. 5.
    Arevalo, H., G. Plank, P. Helm, H. Halperin, and N. Trayanova. Tachycardia in post-infarction hearts: insights from 3d image-based ventricular models. PLoS ONE 8:e68872, 2013.PubMedPubMedCentralCrossRefGoogle Scholar
  6. 6.
    Arts, T., W. C. Hunter, A. Douglas, A. M. Muijtjens, and R. S. Reneman. Description of the deformation of the left ventricle by a kinematic model. J. Biomech. 25:1119–1127, 1992.PubMedCrossRefGoogle Scholar
  7. 7.
    Ashikaga, H., H. Arevalo, F. Vadakkumpadan, R. C. Blake, J. D. Bayer, S. Nazarian, M. M. Zviman, H. Tandri, R. D. Berger, H. Calkins, D. A. Herzka, N. A. Trayanova, and H. R. Halperin. Feasibility of image-based simulation to estimate ablation target in human ventricular arrhythmia. Heart Rhythm 10:1109–1116, 2013.PubMedPubMedCentralCrossRefGoogle Scholar
  8. 8.
    Ateshian, G., and J. Humphrey. Continuum mixture models of biological growth and remodeling: past successes and future opportunities. Annu. Rev. Biomed. Eng. 14:97–111, 2012.PubMedCrossRefGoogle Scholar
  9. 9.
    Augustin, C. M., G. A. Holzapfel, and O. Steinbach. Classical and all-floating FETI methods for the simulation of arterial tissues. Int. J. Numer. Meth. Eng. 99:290–312, 2014.CrossRefGoogle Scholar
  10. 10.
    Berceli, S. A., R. Tran-Son-Tay, M. Garbey, and Z. Jiang. Hemodynamically driven vein graft remodeling: a systems biology approach. Vascular 17:S2–S9, 2009.PubMedPubMedCentralCrossRefGoogle Scholar
  11. 11.
    Bers, D. M., and E. Grandi. Human atrial fibrillation: insights from computational electrophysiological models. Trends Cardiovasc. Med. 21:145–150, 2011.PubMedPubMedCentralCrossRefGoogle Scholar
  12. 12.
    Boekhoven, R. W., M. C. Rutten, M. R. van Sambeek, F. N. van de Vosse, and R. G. Lopata. Echo-computed tomography strain imaging of healthy and diseased carotid specimens. Ultrasound Med. Biol. 40:1329–1342, 2014.PubMedCrossRefGoogle Scholar
  13. 13.
    Buehler, M. J. Nature designs tough collagen: explaining the nanostructure of collagen fibrils. Proc. Natl. Acad. Sci. 103:12285–12290, 2006.PubMedPubMedCentralCrossRefGoogle Scholar
  14. 14.
    Bueno-Orovio, A., C. Sanchez, E. Pueyo, and B. Rodriguez. Na/K pump regulation of cardiac repolarization: insights from a systems biology approach. Pflugers Arch. 466:183–193, 2014.PubMedCrossRefGoogle Scholar
  15. 15.
    Caiazzo, A., D. Evans, J.-L. Falcone, J. Hegewald, E. Lorenz, B. Stahl, D. Wang, J. Bernsdorf, B. Chopard, and J. Gunn. A complex automata approach for in-stent restenosis: two-dimensional multiscale modelling and simulations. J. Comput. Sci. 2:9–17, 2011.CrossRefGoogle Scholar
  16. 16.
    Campbell, S. G., S. N. Flaim, C. H. Leem, and A. D. McCulloch. Mechanisms of transmurally varying myocyte electromechanics in an integrated computational model. Philos. Trans. A 366:3361–3380, 2008.CrossRefGoogle Scholar
  17. 17.
    Castañeda, P. P. Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. J. Mech. Phys. Solids 44:827–862, 1996.CrossRefGoogle Scholar
  18. 18.
    Castañeda P. P. and J. Willis. Variational second-order estimates for nonlinear composites. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, 1999, p. 1799–1811Google Scholar
  19. 19.
    Chen, H., Y. Liu, M. N. Slipchenko, X. Zhao, J.-X. Cheng, and G. S. Kassab. The layered structure of coronary adventitia under mechanical load. Biophys. J. 101:2555–2562, 2011.PubMedPubMedCentralCrossRefGoogle Scholar
  20. 20.
    Chen, H., Y. Liu, X. Zhao, Y. Lanir, and G. S. Kassab. A micromechanics finite-strain constitutive model of fibrous tissue. J. Mech. Phys. Solids 59:1823–1837, 2011.PubMedPubMedCentralCrossRefGoogle Scholar
  21. 21.
    Chen, H., T. Luo, X. Zhao, X. Lu, Y. Huo, and G. S. Kassab. Microstructural constitutive model of active coronary media. Biomaterials 34:7575–7583, 2013.PubMedPubMedCentralCrossRefGoogle Scholar
  22. 22.
    Chen, H., M. N. Slipchenko, Y. Liu, X. Zhao, J.-X. Cheng, Y. Lanir, and G. S. Kassab. Biaxial deformation of collagen and elastin fibers in coronary adventitia. J. Appl. Physiol. 115:1683–1693, 2013.PubMedPubMedCentralCrossRefGoogle Scholar
  23. 23.
    Chen, H., X. Zhao, X. Lu, and G. Kassab. Non-linear micromechanics of soft tissues. Int. J. Non Linear Mech. 56:79–85, 2013.CrossRefGoogle Scholar
  24. 24.
    Cheng, Y., S. Lindert, P. Kekenes-Huskey, V. S. Rao, R. J. Solaro, P. R. Rosevear, R. Amaro, A. D. McCulloch, J. A. McCammon, and M. Regnier. Computational studies of the effect of the S23D/S24D troponin I mutation on cardiac troponin structural dynamics. Biophys. J. 107:1675–1685, 2014.PubMedPubMedCentralCrossRefGoogle Scholar
  25. 25.
    Chow, M.-J., M. Choi, S. H. Yun, and Y. Zhang. The effect of static stretch on elastin degradation in arteries. PloS One 8:e81951, 2013.PubMedPubMedCentralCrossRefGoogle Scholar
  26. 26.
    Chow, M.-J., R. Turcotte, C. P. Lin, and Y. Zhang. Arterial extracellular matrix: a mechanobiological study of the contributions and interactions of elastin and collagen. Biophys. J. 106:2684–2692, 2014.PubMedPubMedCentralCrossRefGoogle Scholar
  27. 27.
    Clark, A. R., M. H. Tawhai, E. A. Hoffman, and K. S. Burrowes. The interdependent contributions of gravitational and structural features to perfusion distribution in a multiscale model of the pulmonary circulation. J. Appl. Physiol. 110:943–955, 2011.PubMedPubMedCentralCrossRefGoogle Scholar
  28. 28.
    Conway, D. E., M. T. Breckenridge, E. Hinde, E. Gratton, C. S. Chen, and M. A. Schwartz. Fluid shear stress on endothelial cells modulates mechanical tension across VE-cadherin and PECAM-1. Curr. Biol. 23:1024–1030, 2013.PubMedPubMedCentralCrossRefGoogle Scholar
  29. 29.
    Costa, K. D., Y. Takayama, A. D. McCulloch, and J. W. Covell. Laminar fiber architecture and three-dimensional systolic mechanics in canine ventricular myocardium. Am. J. Physiol. 276:H595–607, 1999.PubMedGoogle Scholar
  30. 30.
    Cowin, S. C. Tissue growth and remodeling. Annu. Rev. Biomed. Eng. 6:77–107, 2004.PubMedCrossRefGoogle Scholar
  31. 31.
    Criscione, J. C., A. D. McCulloch, and W. C. Hunter. Constitutive framework optimized for myocardium and other high-strain, laminar materials reinforced with one family of fibers. J. Mech. Phys. Solids 50:1681–1702, 2002.CrossRefGoogle Scholar
  32. 32.
    Cristini, V., and J. Lowengrub. Multiscale Modeling of Cancer: An Integrated Experimental and Mathematical Modeling Approach. Cambridge: Cambridge University Press, 2010.CrossRefGoogle Scholar
  33. 33.
    Das, T., and M. Hoshijima. Adding a new dimension to cardiac nano-architecture using electron microscopy: coupling membrane excitation to calcium signaling. J. Mol. Cell. Cardiol. 58:5–12, 2013.PubMedCrossRefGoogle Scholar
  34. 34.
    Davies, P. F., J. A. Spaan, and R. Krams. Shear stress biology of the endothelium. Ann. Biomed. Eng. 33:1714–1718, 2005.PubMedCrossRefGoogle Scholar
  35. 35.
    DeSart, K. M., K. Butler, K. A. O’Malley, Z. Jiang, and S. A. Berceli. Time and flow-dependent changes in the p27 kip1 gene network drive maladaptive vascular remodeling. J. Vasc. Surg. 62:1296, 2014.PubMedCrossRefGoogle Scholar
  36. 36.
    Dharmashankar, K., and M. E. Widlansky. Vascular endothelial function and hypertension: insights and directions. Curr. Hypertens. Rep. 12:448–455, 2010.PubMedPubMedCentralCrossRefGoogle Scholar
  37. 37.
    Dumaine, R., J. A. Towbin, P. Brugada, M. Vatta, D. V. Nesterenko, V. V. Nesterenko, J. Brugada, R. Brugada, and C. Antzelevitch. Ionic mechanisms responsible for the electrocardiographic phenotype of the Brugada syndrome are temperature dependent. Circ. Res. 85:803–809, 1999.PubMedCrossRefGoogle Scholar
  38. 38.
    Fan, R., and M. S. Sacks. Simulation of planar soft tissues using a structural constitutive model: finite element implementation and validation. J. Biomech. 47:2043–2054, 2014.PubMedPubMedCentralCrossRefGoogle Scholar
  39. 39.
    Fata, B., C. A. Carruthers, G. Gibson, S. C. Watkins, D. Gottlieb, J. E. Mayer, and M. S. Sacks. Regional structural and biomechanical alterations of the ovine main pulmonary artery during postnatal growth. J. Biomech. Eng. 135:021022, 2013.PubMedCrossRefGoogle Scholar
  40. 40.
    Fonseca, C. G., M. Backhaus, D. A. Bluemke, R. D. Britten, J. D. Chung, B. R. Cowan, I. D. Dinov, J. P. Finn, P. J. Hunter, A. H. Kadish, D. C. Lee, J. A. Lima, P. Medrano-Gracia, K. Shivkumar, A. Suinesiaputra, W. Tao, and A. A. Young. The Cardiac Atlas Project–an imaging database for computational modeling and statistical atlases of the heart. Bioinformatics 27:2288–2295, 2011.PubMedPubMedCentralCrossRefGoogle Scholar
  41. 41.
    Formaggia, L., F. Nobile, A. Quarteroni, and A. Veneziani. Multiscale modelling of the circulatory system: a preliminary analysis. Comput. Vis. Sci. 2:75–83, 1999.CrossRefGoogle Scholar
  42. 42.
    Garbey, M., and S. A. Berceli. A dynamical system that describes vein graft adaptation and failure. J. Theor. Biol. 336:209–220, 2013.PubMedCrossRefGoogle Scholar
  43. 43.
    Garbey, M., M. Rahman, and S. Berceli. A multiscale computational framework to understand vascular adaptation. J. Comput. Sci. 8:32–47, 2015.PubMedPubMedCentralCrossRefGoogle Scholar
  44. 44.
    Gima, K., and Y. Rudy. Ionic current basis of electrocardiographic waveforms: a model study. Circ. Res. 90:889–896, 2002.PubMedPubMedCentralCrossRefGoogle Scholar
  45. 45.
    Goldhaber, J. I., Z. L. Qu, A. Garfinkel, T. Duong, and J. N. Weiss. Determinants of action potential duration restitution in isolated ventricular myocytes. Circulation 96:3756–3756, 1997.CrossRefGoogle Scholar
  46. 46.
    Guccione, J. M., A. D. McCulloch, and L. K. Waldman. Passive material properties of intact ventricular myocardium determined from a cylindrical model. J. Biomech. Eng. 113:42–55, 1991.PubMedCrossRefGoogle Scholar
  47. 47.
    Hake, J., A. G. Edwards, Z. Yu, P. M. Kekenes-Huskey, A. P. Michailova, J. A. McCammon, M. J. Holst, M. Hoshijima, and A. D. McCulloch. Modelling cardiac calcium sparks in a three-dimensional reconstruction of a calcium release unit. J. Physiol. 590:4403–4422, 2012.PubMedPubMedCentralCrossRefGoogle Scholar
  48. 48.
    Hake, J., P. M. Kekenes-Huskey, and A. D. McCulloch. Computational modeling of subcellular transport and signaling. Curr. Opin. Struct. Biol. 25:92–97, 2014.PubMedCrossRefGoogle Scholar
  49. 49.
    Hald, E. S., K. E. Steucke, J. A. Reeves, Z. Win, and P. W. Alford. Long-term vascular contractility assay using genipin-modified muscular thin films. Biofabrication 6:045005, 2014.PubMedCrossRefGoogle Scholar
  50. 50.
    Hashambhoy, Y. L., J. C. Chappell, S. M. Peirce, V. L. Bautch, and F. MacGabhann. Computational modeling of interacting VEGF and soluble VEGF receptor concentration gradients. Front. Physiol. 2:62, 2011.PubMedPubMedCentralCrossRefGoogle Scholar
  51. 51.
    Haumann, J., R. K. Dash, D. F. Stowe, A. D. Boelens, D. A. Beard, and A. K. Camara. Mitochondrial free [Ca2+] increases during ATP/ADP antiport and ADP phosphorylation: exploration of mechanisms. Biophys. J. 99:997–1006, 2010.PubMedPubMedCentralCrossRefGoogle Scholar
  52. 52.
    Heijman, J., P. G. Volders, R. L. Westra, and Y. Rudy. Local control of beta-adrenergic stimulation: effects on ventricular myocyte electrophysiology and Ca(2+)-transient. J. Mol. Cell. Cardiol. 50:863–871, 2011.PubMedPubMedCentralCrossRefGoogle Scholar
  53. 53.
    Helm, P., M. F. Beg, M. I. Miller, and R. L. Winslow. Measuring and mapping cardiac fiber and laminar architecture using diffusion tensor MR imaging. Ann. N. Y. Acad. Sci. 296–307:2005, 1047.Google Scholar
  54. 54.
    Henriquez, C. S. A brief history of tissue models for cardiac electrophysiology. IEEE Trans. Biomed. Eng. 61:1457–1465, 2014.PubMedCrossRefGoogle Scholar
  55. 55.
    Higashi, Y., and M. Yoshizumi. New methods to evaluate endothelial function: method for assessing endothelial function in humans using a strain-gauge plethysmography: nitric oxide-dependent and-independent vasodilation. J. Pharmacol. Sci. 93:399–404, 2003.PubMedCrossRefGoogle Scholar
  56. 56.
    Hill, M. R., X. Duan, G. A. Gibson, S. Watkins, and A. M. Robertson. A theoretical and non-destructive experimental approach for direct inclusion of measured collagen orientation and recruitment into mechanical models of the artery wall. J. Biomech. 45:762–771, 2012.PubMedCrossRefGoogle Scholar
  57. 57.
    Hinch, R., J. L. Greenstein, A. J. Tanskanen, L. Xu, and R. L. Winslow. A simplified local control model of calcium-induced calcium release in cardiac ventricular myocytes. Biophys. J. 87:3723–3736, 2004.PubMedPubMedCentralCrossRefGoogle Scholar
  58. 58.
    Hollander, Y., D. Durban, X. Lu, G. S. Kassab, and Y. Lanir. Constitutive modeling of coronary arterial media—comparison of three model classes. J. Biomech. Eng. 133:061008, 2011.PubMedPubMedCentralCrossRefGoogle Scholar
  59. 59.
    Holzapfel, G. A., T. C. Gasser, and R. W. Ogden. A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elast. Phys. Sci. Solids 61:1–48, 2000.CrossRefGoogle Scholar
  60. 60.
    Hund, T. J., and P. J. Mohler. Role of CaMKII in cardiac arrhythmias. Trends Cardiovasc. Med. 25:392–397, 2015.PubMedCrossRefGoogle Scholar
  61. 61.
    Hunter, P., and P. Nielsen. A strategy for integrative computational physiology. Physiology 20:316–325, 2005.PubMedCrossRefGoogle Scholar
  62. 62.
    Hunter, P. J., A. J. Pullan, and B. H. Smaill. Modeling total heart function. Annu. Rev. Biomed. Eng. 5:147–177, 2003.PubMedCrossRefGoogle Scholar
  63. 63.
    Huxley, A. F. Muscle structure and theories of contraction. Prog. Biophys. Chem. 7:255–318, 1957.Google Scholar
  64. 64.
    Hwang, M., M. Garbey, S. A. Berceli, R. Wu, Z. Jiang, and R. Tran-Son-Tay. Rule-based model of vein graft remodeling. PLoS ONE 8:e57822, 2013.PubMedPubMedCentralCrossRefGoogle Scholar
  65. 65.
    Ibragimov, A., C. McNeal, L. Ritter, and J. Walton. A mathematical model of atherogenesis as an inflammatory response. Math. Med. Biol. 22:305–333, 2005.PubMedCrossRefGoogle Scholar
  66. 66.
    Kapela A., A. Bezerianos and N. Tsoukias. Integrative mathematical modeling for analysis of microcirculatory function. In: Biological and Medical Data Analysis. Springer, 2006, pp. 161–171Google Scholar
  67. 67.
    Kerckhoffs, R. C., S. G. Campbell, S. N. Flaim, E. J. Howard, J. Sierra-Aguado, L. J. Mulligan, and A. D. McCulloch. Multi-scale modeling of excitation-contraction coupling in the normal and failing heart. Conf. Proc. IEEE Eng. Med. Biol. Soc. 4281–4282:2009, 2009.Google Scholar
  68. 68.
    Kerckhoffs, R. C., M. L. Neal, Q. Gu, J. B. Bassingthwaighte, J. H. Omens, and A. D. McCulloch. Coupling of a 3D finite element model of cardiac ventricular mechanics to lumped systems models of the systemic and pulmonic circulation. Ann. Biomed. Eng. 35:1–18, 2007.PubMedCrossRefGoogle Scholar
  69. 69.
    Kerckhoffs, R. C., J. Omens, and A. D. McCulloch. A single strain-based growth law predicts concentric and eccentric cardiac growth during pressure and volume overload. Mech. Res. Commun. 42:40–50, 2012.PubMedCrossRefGoogle Scholar
  70. 70.
    Kraeutler, M. J., A. R. Soltis, and J. J. Saucerman. Modeling cardiac beta-adrenergic signaling with normalized-Hill differential equations: comparison with a biochemical model. BMC Syst. Biol. 4:157, 2010.PubMedPubMedCentralCrossRefGoogle Scholar
  71. 71.
    Krishnamurthy, A., C. T. Villongco, J. Chuang, L. R. Frank, V. Nigam, E. Belezzuoli, P. Stark, D. E. Krummen, S. Narayan, J. H. Omens, A. D. McCulloch, and R. C. Kerckhoffs. Patient-specific models of cardiac biomechanics. J. Comput. Phys. 244:4–21, 2013.PubMedCrossRefGoogle Scholar
  72. 72.
    Lai, V. K., M. F. Hadi, R. T. Tranquillo, and V. H. Barocas. A multiscale approach to modeling the passive mechanical contribution of cells in tissues. J. Biomech. Eng. 135:071007, 2013.CrossRefGoogle Scholar
  73. 73.
    Lanir, Y. A structural theory for the homogeneous biaxial stress-strain relationships in flat collagenous tissues. J. Biomech. 12:423–436, 1979.PubMedCrossRefGoogle Scholar
  74. 74.
    Lanir, Y. Constitutive equations for fibrous connective tissues. J. Biomech. 16:1–12, 1983.PubMedCrossRefGoogle Scholar
  75. 75.
    Lanzarone, E., P. Liani, G. Baselli, and M. Costantino. Model of arterial tree and peripheral control for the study of physiological and assisted circulation. Med. Eng. Phys. 29:542–555, 2007.PubMedCrossRefGoogle Scholar
  76. 76.
    Lee, L. C., M. Genet, A. B. Dang, L. Ge, J. M. Guccione, and M. B. Ratcliffe. Applications of computational modeling in cardiac surgery. J. Card. Surg. 29:293–302, 2014.PubMedPubMedCentralCrossRefGoogle Scholar
  77. 77.
    Lee L. C., J. Sundnes, M. Genet, J. F. Wenk and S. T. Wall. An integrated electromechanical-growth heart model for simulating cardiac therapies. Biomech. Model. Mechanobiol. 2015. doi: 10.1007/s10237-015-0723-8.
  78. 78.
    LeGrice, I. J., Y. Takayama, and J. W. Covell. Transverse shear along myocardial cleavage planes provides a mechanism for normal systolic wall thickening. Circ. Res. 77:182–193, 1995.PubMedCrossRefGoogle Scholar
  79. 79.
    Li, Y.-S. J., J. H. Haga, and S. Chien. Molecular basis of the effects of shear stress on vascular endothelial cells. J. Biomech. 38:1949–1971, 2005.PubMedCrossRefGoogle Scholar
  80. 80.
    Liu, D.-W., G. A. Gintant, and C. Antzelevitch. Ionic bases for electrophysiological distinctions among epicardial, midmyocardial, and endocardial myocytes from the free wall of the canine left ventricle. Circ. Res. 72:671–687, 1993.PubMedCrossRefGoogle Scholar
  81. 81.
    Löhner, R., J. Cebral, O. Soto, P. Yim, and J. E. Burgess. Applications of patient-specific CFD in medicine and life sciences. Int. J. Numer. Methods Fluids 43:637–650, 2003.CrossRefGoogle Scholar
  82. 82.
    Lu, X., J. Yang, J. Zhao, H. Gregersen, and G. Kassab. Shear modulus of porcine coronary artery: contributions of media and adventitia. Am. J. Physiol. Heart Circ. Physiol. 285:H1966–H1975, 2003.PubMedCrossRefGoogle Scholar
  83. 83.
    Luo, T., T. Wischgoll, B. K. Koo, Y. Huo, G. S. Kassab, and T. W. Secomb. IVUS validation of patient coronary artery lumen area obtained from CT images. PLoS ONE 9:e86949, 2014.PubMedPubMedCentralCrossRefGoogle Scholar
  84. 84.
    MacKenna, D. A., S. M. Vaplon, and A. D. McCulloch. Microstructural model of perimysial collagen fibers for resting myocardial mechanics during ventricular filling. Am. J. Physiol. 273:H1576–1586, 1997.PubMedGoogle Scholar
  85. 85.
    Matsumoto, T., and K. Nagayama. Tensile properties of vascular smooth muscle cells: bridging vascular and cellular biomechanics. J. Biomech. 45:745–755, 2012.PubMedCrossRefGoogle Scholar
  86. 86.
    McDowell, K. S., F. Vadakkumpadan, R. Blake, J. Blauer, G. Plank, R. S. MacLeod, and N. A. Trayanova. Methodology for patient-specific modeling of atrial fibrosis as a substrate for atrial fibrillation. J. Electrocardiol. 45:640–645, 2012.PubMedPubMedCentralCrossRefGoogle Scholar
  87. 87.
    McDowell, K. S., S. Zahid, F. Vadakkumpadan, J. Blauer, R. S. MacLeod, and N. A. Trayanova. Virtual electrophysiological study of atrial fibrillation in fibrotic remodeling. PLoS ONE 10:e0117110, 2015.PubMedPubMedCentralCrossRefGoogle Scholar
  88. 88.
    Menzel, A., and E. Kuhl. Frontiers in growth and remodeling. Mech. Res. Commun. 42:1–14, 2012.PubMedPubMedCentralCrossRefGoogle Scholar
  89. 89.
    Meoli, A., E. Cutrì, A. Krishnamurthy, G. Dubini, F. Migliavacca, T.-Y. Hsia, and G. Pennati. A multiscale model for the study of cardiac biomechanics in single-ventricle surgeries: a clinical case. Interface Focus 5:20140079, 2015.PubMedPubMedCentralCrossRefGoogle Scholar
  90. 90.
    Migliavacca, F., F. Gervaso, M. Prosi, P. Zunino, S. Minisini, L. Formaggia, and G. Dubini. Expansion and drug elution model of a coronary stent. Comput. Methods Biomech. Biomed. Eng. 10:63–73, 2007.CrossRefGoogle Scholar
  91. 91.
    Moreno, J. D., and C. E. Clancy. Pathophysiology of the cardiac late Na current and its potential as a drug target. J. Mol. Cell. Cardiol. 52:608–619, 2012.PubMedCrossRefGoogle Scholar
  92. 92.
    Moreno, J. D., Z. I. Zhu, P. C. Yang, J. R. Bankston, M. T. Jeng, C. Kang, L. Wang, J. D. Bayer, D. J. Christini, N. A. Trayanova, C. M. Ripplinger, R. S. Kass, and C. E. Clancy. A computational model to predict the effects of class I anti-arrhythmic drugs on ventricular rhythms. Sci. Transl. Med. 3:98ra83, 2011.PubMedPubMedCentralCrossRefGoogle Scholar
  93. 93.
    Murfee, W. L., R. S. Sweat, K.-i. Tsubota, F. M. Gabhann, D. Khismatullin, and S. M. Peirce. Applications of computational models to better understand microvascular remodelling: a focus on biomechanical integration across scales. Interface Focus 5:20140077, 2015.PubMedPubMedCentralCrossRefGoogle Scholar
  94. 94.
    Nagaraja, S., A. Kapela, and N. M. Tsoukias. Intercellular communication in the vascular wall: a modeling perspective. Microcirculation 19:391–402, 2012.PubMedPubMedCentralCrossRefGoogle Scholar
  95. 95.
    Nielsen, P. M. F., I. J. Le Grice, B. H. Smaill, and P. J. Hunter. Mathematical model of geometry and fibrous structure of the heart. Am. J. Physiol. 260:H1365–H1378, 1991.PubMedGoogle Scholar
  96. 96.
    Okada, J.-I., T. Yoshinaga, J. Kurokawa, T. Washio, T. Furukawa, K. Sawada, S. Sugiura, and T. Hisada. Screening system for drug-induced arrhythmogenic risk combining a patch clamp and heart simulator. Sci. Adv. 1:e1400142, 2015.PubMedPubMedCentralCrossRefGoogle Scholar
  97. 97.
    Onishi, Y., K. Aoki, K. Amaya, T. Shimizu, H. Isoda, Y. Takehara, H. Sakahara, and T. Kosugi. Accurate determination of patient-specific boundary conditions in computational vascular hemodynamics using 3D cine phase-contrast MRI. Int. J. Numer. Methods Biomed. Eng. 29:1089–1103, 2013.CrossRefGoogle Scholar
  98. 98.
    Pandit, A., X. Lu, C. Wang, and G. S. Kassab. Biaxial elastic material properties of porcine coronary media and adventitia. Am. J. Physiol. Heart Circ. Physiol. 288:H2581–H2587, 2005.PubMedCrossRefGoogle Scholar
  99. 99.
    Peskin, C. S. The immersed boundary method. Acta Numer. 11:479–517, 2002.CrossRefGoogle Scholar
  100. 100.
    Polzer, S., T. C. Gasser, C. Forsell, H. Druckmüllerova, M. Tichy, R. Staffa, R. Vlachovsky, and J. Bursa. Automatic identification and validation of planar collagen organization in the aorta wall with application to abdominal aortic aneurysm. Microsc. Microanal. 19:1395–1404, 2013.PubMedCrossRefGoogle Scholar
  101. 101.
    Ponzini, R., M. Lemma, U. Morbiducci, F. M. Montevecchi, and A. Redaelli. Doppler derived quantitative flow estimate in coronary artery bypass graft: a computational multiscale model for the evaluation of the current clinical procedure. Med. Eng. Phys. 30:809–816, 2008.PubMedCrossRefGoogle Scholar
  102. 102.
    Prakosa, A., P. Malamas, S. Zhang, E. Pashakhanloo, H. Arevalo, D. A. Herzka, A. Lardo, H. Halperin, E. McVeigh, N. Trayanova, and F. Vadakkumpadan. Methodology for image-based reconstruction of ventricular geometry for patient-specific modeling of cardiac electrophysiology. Prog. Biophys. Mol. Biol. 115:226–234, 2014.PubMedPubMedCentralCrossRefGoogle Scholar
  103. 103.
    Quail, M. A., and A. M. Taylor. Computer modeling to tailor therapy for congenital heart disease. Curr. Cardiol. Rep. 15:395, 2013.PubMedCrossRefGoogle Scholar
  104. 104.
    Quarteroni, A., and A. Veneziani. Analysis of a geometrical multiscale model based on the coupling of ODE and PDE for blood flow simulations. Multiscale Model. Simul. 1:173–195, 2003.CrossRefGoogle Scholar
  105. 105.
    Quarteroni, A., A. Veneziani, and P. Zunino. Mathematical and numerical modeling of solute dynamics in blood flow and arterial walls. SIAM J. Numer. Anal. 39:1488–1511, 2002.CrossRefGoogle Scholar
  106. 106.
    Ramachandra, A. B., S. Sankaran, J. D. Humphrey, and A. L. Marsden. Computational simulation of the adaptive capacity of vein grafts in response to increased pressure. J. Biomech. Eng. 137:031009, 2015.CrossRefGoogle Scholar
  107. 107.
    Rantner, L. J., F. Vadakkumpadan, P. J. Spevak, J. E. Crosson, and N. A. Trayanova. Placement of implantable cardioverter-defibrillators in paediatric and congenital heart defect patients: a pipeline for model generation and simulation prediction of optimal configurations. J. Physiol. Lond. 591:4321–4334, 2013.PubMedPubMedCentralCrossRefGoogle Scholar
  108. 108.
    Rausch, M. K., W. Bothe, J.-P. E. Kvitting, J. C. Swanson, N. B. Ingels, Jr, D. C. Miller, and E. Kuhl. Characterization of mitral valve annular dynamics in the beating heart. Ann. Biomed. Eng. 39:1690–1702, 2011.PubMedCrossRefGoogle Scholar
  109. 109.
    Rezakhaniha, R., A. Agianniotis, J. T. C. Schrauwen, A. Griffa, D. Sage, C. Bouten, F. Van de Vosse, M. Unser, and N. Stergiopulos. Experimental investigation of collagen waviness and orientation in the arterial adventitia using confocal laser scanning microscopy. Biomech. Model. Mechanobiol. 11:461–473, 2012.PubMedCrossRefGoogle Scholar
  110. 110.
    Roberts, B. N., P. C. Yang, S. B. Behrens, J. D. Moreno, and C. E. Clancy. Computational approaches to understand cardiac electrophysiology and arrhythmias. Am. J. Physiol. Heart Circ. Physiol. 303:H766–783, 2012.PubMedPubMedCentralCrossRefGoogle Scholar
  111. 111.
    Rodriguez, E. K., A. Hoger, and A. D. McCulloch. Stress-dependent finite growth in soft elastic tissues. J. Biomech. 27:455–467, 1994.PubMedCrossRefGoogle Scholar
  112. 112.
    Rodriguez, M. L., P. J. McGarry, and N. J. Sniadecki. Review on cell mechanics: experimental and modeling approaches. Appl. Mech. Rev. 65:060801, 2013.CrossRefGoogle Scholar
  113. 113.
    Rodriguez, B., N. Trayanova, and D. Noble. Modeling cardiac ischemia. Ann. N. Y. Acad. Sci. 395–414:1080, 2006.Google Scholar
  114. 114.
    Rouillard, A. D., and J. W. Holmes. Coupled agent-based and finite-element models for predicting scar structure following myocardial infarction. Prog. Biophys. Mol. Biol. 115:235–243, 2014.PubMedCrossRefGoogle Scholar
  115. 115.
    Ryall, K. A., D. O. Holland, K. A. Delaney, M. J. Kraeutler, A. J. Parker, and J. J. Saucerman. Network reconstruction and systems analysis of cardiac myocyte hypertrophy signaling. J. Biol. Chem. 287:42259–42268, 2012.PubMedPubMedCentralCrossRefGoogle Scholar
  116. 116.
    Sacks, M. S., D. B. Smith, and E. D. Hiester. A small angle light scattering device for planar connective tissue microstructural analysis. Ann. Biomed. Eng. 25:678–689, 1997.PubMedCrossRefGoogle Scholar
  117. 117.
    Salven, P., S. Mustjoki, R. Alitalo, K. Alitalo, and S. Rafii. VEGFR-3 and CD133 identify a population of CD34+ lymphatic/vascular endothelial precursor cells. Blood 101:168–172, 2003.PubMedCrossRefGoogle Scholar
  118. 118.
    Sato, D., D. C. Bartos, K. S. Ginsburg, and D. M. Bers. Depolarization of cardiac membrane potential synchronizes calcium sparks and waves in tissue. Biophys. J. 107:1313–1317, 2014.PubMedPubMedCentralCrossRefGoogle Scholar
  119. 119.
    Saucerman, J. J., L. L. Brunton, A. P. Michailova, and A. D. McCulloch. Modeling beta-adrenergic control of cardiac myocyte contractility in silico. J. Biol. Chem. 278:47997–48003, 2003.PubMedCrossRefGoogle Scholar
  120. 120.
    Saucerman, J. J., and A. D. McCulloch. Computational modeling of PKA-mediated phosphoregulation of cardiac excitation-contraction coupling. Biophys. J. 86:107a, 2004.Google Scholar
  121. 121.
    Schmidt, A., K. Brixius, and W. Bloch. Endothelial precursor cell migration during vasculogenesis. Circ. Res. 101:125–136, 2007.PubMedCrossRefGoogle Scholar
  122. 122.
    Schoenberg, M. Geometrical factors influencing muscle force development. II. Radial forces. Biophys. J. 30:69–77, 1980.PubMedPubMedCentralCrossRefGoogle Scholar
  123. 123.
    Schriefl, A. J., H. Wolinski, P. Regitnig, S. D. Kohlwein, and G. A. Holzapfel. An automated approach for three-dimensional quantification of fibrillar structures in optically cleared soft biological tissues. J. R. Soc. Interface 10:20120760, 2013.PubMedPubMedCentralCrossRefGoogle Scholar
  124. 124.
    Selimovic, A., Y. Ventikos, and P. N. Watton. Modelling the evolution of cerebral aneurysms: biomechanics, mechanobiology and multiscale modelling. Procedia IUTAM 10:396–409, 2014.CrossRefGoogle Scholar
  125. 125.
    Sheidaei, A., S. Hunley, S. Zeinali-Davarani, L. Raguin, and S. Baek. Simulation of abdominal aortic aneurysm growth with updating hemodynamic loads using a realistic geometry. Med. Eng. Phys. 33:80–88, 2011.PubMedCrossRefGoogle Scholar
  126. 126.
    Shen, Z. L., M. R. Dodge, H. Kahn, R. Ballarini, and S. J. Eppell. Stress-strain experiments on individual collagen fibrils. Biophys. J. 95:3956–3963, 2008.PubMedPubMedCentralCrossRefGoogle Scholar
  127. 127.
    Shibuya, M. Structure and function of VEGF/VEGF-receptor system involved in angiogenesis. Cell Struct. Funct. 26:25–35, 2001.PubMedCrossRefGoogle Scholar
  128. 128.
    Smith, N. P., A. J. Pullan, and P. J. Hunter. Generation of an anatomically based geometric coronary model. Ann. Biomed. Eng. 28:14–25, 2000.PubMedCrossRefGoogle Scholar
  129. 129.
    Soeller, C., and D. Baddeley. Super-resolution imaging of EC coupling protein distribution in the heart. J. Mol. Cell. Cardiol. 58:32–40, 2013.PubMedCrossRefGoogle Scholar
  130. 130.
    Soeller, C., M. D. Jacobs, K. T. Jones, G. C. Ellis-Davies, P. J. Donaldson, and M. B. Cannell. Application of two-photon flash photolysis to reveal intercellular communication and intracellular Ca2+ movements. J. Biomed. Opt. 8:418–427, 2003.PubMedCrossRefGoogle Scholar
  131. 131.
    Soltis, A. R., and J. J. Saucerman. Synergy between CaMKII substrates and beta-adrenergic signaling in regulation of cardiac myocyte Ca(2+) handling. Biophys. J. 99:2038–2047, 2010.PubMedPubMedCentralCrossRefGoogle Scholar
  132. 132.
    Starmer, C. F. How antiarrhythmic drugs increase the rate of sudden cardiac death. Int. Bifurc. Chaos 12:1953–1968, 2002.CrossRefGoogle Scholar
  133. 133.
    Starmer, C. F., V. N. Biktashev, D. N. Romashko, M. R. Stepanov, O. N. Makarova, and V. I. Krinsky. Vulnerability in an excitable medium—analytical and numerical-studies of initiating unidirectional propagation. Biophys. J. 65:1775–1787, 1993.PubMedPubMedCentralCrossRefGoogle Scholar
  134. 134.
    Starmer, C. F., A. A. Lastra, V. V. Nesterenko, and A. O. Grant. Proarrhythmic response to sodium-channel blockade—theoretical-model and numerical experiments. Circulation 84:1364–1377, 1991.PubMedCrossRefGoogle Scholar
  135. 135.
    Stern, M. D., L. S. Song, H. Cheng, J. S. Sham, H. T. Yang, K. R. Boheler, and E. Rios. Local control models of cardiac excitation-contraction coupling. A possible role for allosteric interactions between ryanodine receptors. J. Gen. Physiol. 113:469–489, 1999.PubMedPubMedCentralCrossRefGoogle Scholar
  136. 136.
    Sugiura, S., T. Washio, A. Hatano, J. Okada, H. Watanabe, and T. Hisada. Multi-scale simulations of cardiac electrophysiology and mechanics using the University of Tokyo heart simulator. Prog. Biophys. Mol. Biol. 110:380–389, 2012.PubMedCrossRefGoogle Scholar
  137. 137.
    Tangney, J. R., J. S. Chuang, M. S. Janssen, A. Krishnamurthy, P. Liao, M. Hoshijima, X. Wu, G. A. Meininger, M. Muthuchamy, A. Zemljic-Harpf, R. S. Ross, L. R. Frank, A. D. McCulloch, and J. H. Omens. Novel role for vinculin in ventricular myocyte mechanics and dysfunction. Biophys. J. 104:1623–1633, 2013.PubMedPubMedCentralCrossRefGoogle Scholar
  138. 138.
    Taylor, C. A., and C. Figueroa. Patient-specific modeling of cardiovascular mechanics. Annu. Rev. Biomed. Eng. 11:109–134, 2009.PubMedPubMedCentralCrossRefGoogle Scholar
  139. 139.
    Taylor, C. A., and J. Humphrey. Open problems in computational vascular biomechanics: hemodynamics and arterial wall mechanics. Comput. Methods Appl. Mech. Eng. 198:3514–3523, 2009.PubMedPubMedCentralCrossRefGoogle Scholar
  140. 140.
    Taylor, C. A., and D. A. Steinman. Image-based modeling of blood flow and vessel wall dynamics: applications, methods and future directions. Ann. Biomed. Eng. 38:1188–1203, 2010.PubMedCrossRefGoogle Scholar
  141. 141.
    ter Keurs, H. E. Heart failure and Starling’s Law of the heart. Can. J. Cardiol. 12:1047–1057, 1996.PubMedGoogle Scholar
  142. 142.
    Timmins, L. H., Q. Wu, A. T. Yeh, J. E. Moore, and S. E. Greenwald. Structural inhomogeneity and fiber orientation in the inner arterial media. Am. J. Physiol. Heart Circ. Physiol. 298:H1537–H1545, 2010.PubMedCrossRefGoogle Scholar
  143. 143.
    Tran, K., N. P. Smith, D. S. Loiselle, and E. J. Crampin. A metabolite-sensitive, thermodynamically constrained model of cardiac cross-bridge cycling: implications for force development during ischemia. Biophys. J. 98:267–276, 2010.PubMedPubMedCentralCrossRefGoogle Scholar
  144. 144.
    Trayanova, N. A. Mathematical approaches to understanding and imaging atrial fibrillation: significance for mechanisms and management. Circ. Res. 114:1516–1531, 2014.PubMedPubMedCentralCrossRefGoogle Scholar
  145. 145.
    Trayanova, N. A., and P. M. Boyle. Advances in modeling ventricular arrhythmias: from mechanisms to the clinic. Wiley Interdiscip Rev Syst Biol Med 6:209–224, 2014.PubMedCrossRefGoogle Scholar
  146. 146.
    Trayanova, N. A., P. M. Boyle, H. J. Arevalo, and S. Zahid. Exploring susceptibility to atrial and ventricular arrhythmias resulting from remodeling of the passive electrical properties in the heart: a simulation approach. Front. Physiol. 5:435, 2014.PubMedPubMedCentralCrossRefGoogle Scholar
  147. 147.
    Trayanova, N. A., J. Constantino, and V. Gurev. Electromechanical models of the ventricles. Am. J. Physiol. Heart Circ. Physiol. 301:H279–286, 2011.PubMedPubMedCentralCrossRefGoogle Scholar
  148. 148.
    Ukwatta, E., J. Yuan, W. Qiu, K. C. Wu, N. Trayanova, and F. Vadakkumpadan. Myocardial infarct segmentation and reconstruction from 2D late-gadolinium enhanced magnetic resonance images. Med. Image Comput. Comput. Assist. Interv. 17:554–561, 2014.PubMedPubMedCentralGoogle Scholar
  149. 149.
    Vadakkumpadan, F., H. Arevalo, C. Ceritoglu, M. Miller, and N. Trayanova. Image-based estimation of ventricular fiber orientations for personalized modeling of cardiac electrophysiology. IEEE Trans. Med. Imaging 31:1051–1060, 2012.PubMedPubMedCentralCrossRefGoogle Scholar
  150. 150.
    Vadakkumpadan, F., N. Trayanova, and K. C. Wu. Image-based left ventricular shape analysis for sudden cardiac death risk stratification. Heart Rhythm 11:1693–1700, 2014.PubMedPubMedCentralCrossRefGoogle Scholar
  151. 151.
    Valentin, A., J. D. Humphrey, and G. A. Holzapfel. A finite element-based constrained mixture implementation for arterial growth, remodeling, and adaptation: theory and numerical verification. Int. J. Numer. Method Biomed. Eng. 29:822–849, 2013.PubMedPubMedCentralCrossRefGoogle Scholar
  152. 152.
    Vankan, W. J., J. M. Huyghe, C. C. van Donkelaar, M. R. Drost, J. D. Janssen, and A. Huson. Mechanical blood-tissue interaction in contracting muscles: a model study. J. Biomech. 31:401–409, 1998.PubMedCrossRefGoogle Scholar
  153. 153.
    Veress A., G. Raymond, G. Gullberg and J. Bassingthwaighte. Multi-scale modeling of hypertension. In: 2009 IEEE Computers in Cardiology, 2009, p. 385–388.Google Scholar
  154. 154.
    Vignon-Clementel, I. E., C. Figueroa, K. Jansen, and C. Taylor. Outflow boundary conditions for 3D simulations of non-periodic blood flow and pressure fields in deformable arteries. Comput. Methods Biomech. Biomed. Eng. 13:625–640, 2010.CrossRefGoogle Scholar
  155. 155.
    Wagenseil, J. E., and R. P. Mecham. Vascular extracellular matrix and arterial mechanics. Physiol. Rev. 89:957–989, 2009.PubMedPubMedCentralCrossRefGoogle Scholar
  156. 156.
    Walker, D. C., and J. Southgate. The virtual cell—a candidate co-ordinator for ‘middle-out’modelling of biological systems. Brief. Bioinform. 2009. doi: 10.1093/bib/bbp010.PubMedGoogle Scholar
  157. 157.
    Walpole, J., J. A. Papin, and S. M. Peirce. Multiscale computational models of complex biological systems. Annu. Rev. Biomed. Eng. 15:137, 2013.PubMedPubMedCentralCrossRefGoogle Scholar
  158. 158.
    Wan, W., J. B. Dixon, and R. L. Gleason. Constitutive modeling of mouse carotid arteries using experimentally measured microstructural parameters. Biophys. J. 102:2916–2925, 2012.PubMedPubMedCentralCrossRefGoogle Scholar
  159. 159.
    Wan, J., F. He, Y. Zhao, H. Zhang, X. Zhou, and M. Wan. Non-invasive vascular radial/circumferential strain imaging and wall shear rate estimation using video images of diagnostic ultrasound. Ultrasound Med. Biol. 40:622–636, 2014.PubMedCrossRefGoogle Scholar
  160. 160.
    Wang, Y., S. Zeinali-Davarani, E. C. Davis, and Y. Zhang. Effect of glucose on the biomechanical function of arterial elastin. J. Mech. Behav. Biomed. Mater. 49:244–254, 2015.PubMedCrossRefGoogle Scholar
  161. 161.
    Wang, Y., S. Zeinali-Davarani, and Y. Zhang. Arterial mechanics considering the structural and mechanical contributions of ECM constituents. J. Biomech. 2016. doi: 10.1016/j.jbiomech.2016.02.027.PubMedCentralGoogle Scholar
  162. 162.
    Weafer, P., W. Ronan, S. Jarvis, and J. McGarry. Experimental and computational investigation of the role of stress fiber contractility in the resistance of osteoblasts to compression. Bull. Math. Biol. 75:1284–1303, 2013.PubMedCrossRefGoogle Scholar
  163. 163.
    Weinberg, E. J., D. Shahmirzadi, and M. R. K. Mofrad. On the multiscale modeling of heart valve biomechanics in health and disease. Biomech. Model. Mechanobiol. 9:373–387, 2010.PubMedCrossRefGoogle Scholar
  164. 164.
    Weiss, J. N., Z. Qu, P.-S. Chen, S.-F. Lin, H. S. Karagueuzian, H. Hayashi, A. Garfinkel, and A. Karma. The dynamics of cardiac fibrillation. Circulation 112:1232–1240, 2005.PubMedCrossRefGoogle Scholar
  165. 165.
    Wicker, B., H. Hutchens, Q. Wu, A. Yeh, and J. Humphrey. Normal basilar artery structure and biaxial mechanical behaviour. Comput. Methods Biomech. Biomed. Eng. 11:539–551, 2008.CrossRefGoogle Scholar
  166. 166.
    Win, Z., G. D. Vrla, K. E. Steucke, E. N. Sevcik, E. S. Hald, and P. W. Alford. Smooth muscle architecture within cell-dense vascular tissues influences functional contractility. Integr. Biol. 6:1201–1210, 2014.CrossRefGoogle Scholar
  167. 167.
    Wischgoll, T., J. S. Choy, and G. S. Kassab. Extraction of morphometry and branching angles of porcine coronary arterial tree from CT images. Am. J. Physiol. Heart Circ. Physiol. 297:H1949–H1955, 2009.PubMedPubMedCentralCrossRefGoogle Scholar
  168. 168.
    Wischgoll, T., J. Choy, E. Ritman, and G. Kassab. Validation of image-based extraction method for morphometry of coronary arteries. Ann. Biomed. Eng. 36:356–368, 2008.PubMedCrossRefGoogle Scholar
  169. 169.
    Yan, G.-X., and C. Antzelevitch. Cellular basis for the Brugada syndrome and other mechanisms of arrhythmogenesis associated with ST-segment elevation. Circulation 100:1660–1666, 1999.PubMedCrossRefGoogle Scholar
  170. 170.
    Yang, J., J. W. Clark, R. M. Bryan, and C. S. Robertson. Mathematical modeling of the nitric oxide/cGMP pathway in the vascular smooth muscle cell. Am. J. Physiol. Heart Circ. Physiol. 289:H886–H897, 2005.PubMedCrossRefGoogle Scholar
  171. 171.
    Yang, J. H., and J. J. Saucerman. Phospholemman is a negative feed-forward regulator of Ca2+ in beta-adrenergic signaling, accelerating beta-adrenergic inotropy. J. Mol. Cell. Cardiol. 52:1048–1055, 2012.PubMedPubMedCentralCrossRefGoogle Scholar
  172. 172.
    Zeinali-Davarani, S., M.-J. Chow, R. Turcotte, and Y. Zhang. Characterization of biaxial mechanical behavior of porcine aorta under gradual elastin degradation. Ann. Biomed. Eng. 41:1528–1538, 2013.PubMedPubMedCentralCrossRefGoogle Scholar
  173. 173.
    Zeinali-Davarani, S., Y. Wang, M.-J. Chow, R. Turcotte, and Y. Zhang. Contribution of collagen fiber undulation to regional biomechanical properties along porcine thoracic aorta. J. Biomech. Eng. 137:051001, 2015.PubMedCrossRefGoogle Scholar
  174. 174.
    Zhang, W., H. Y. Chen, and G. S. Kassab. A rate-insensitive linear viscoelastic model for soft tissues. Biomaterials 28:3579–3586, 2007.PubMedPubMedCentralCrossRefGoogle Scholar
  175. 175.
    Zhang, W., and G. S. Kassab. A bilinear stress–strain relationship for arteries. Biomaterials 28:1307–1315, 2007.PubMedCrossRefGoogle Scholar
  176. 176.
    Zhang, W., X. Lu, and G. S. Kassab. Shear modulus of porcine coronary artery in reference to a new strain measure. Biomaterials 28:4733–4738, 2007.PubMedCrossRefGoogle Scholar
  177. 177.
    Zhang, W., C. Wang, and G. S. Kassab. The mathematical formulation of a generalized Hooke’s law for blood vessels. Biomaterials 28:3569–3578, 2007.PubMedCrossRefGoogle Scholar
  178. 178.
    Zou, Y., and Y. Zhang. The orthotropic viscoelastic behavior of aortic elastin. Biomech. Model. Mechanobiol. 10:613–625, 2011.PubMedCrossRefGoogle Scholar
  179. 179.
    Zoumi, A., X. Lu, G. Kassab, and B. Tromberg. Selective imaging of coronary artery micro-structural components using multi-photon microscopy. Biophys. J. 87:2778–2786, 2004.PubMedPubMedCentralCrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2016

Authors and Affiliations

  • Yanhang Zhang
    • 1
  • Victor H. Barocas
    • 2
  • Scott A. Berceli
    • 3
  • Colleen E. Clancy
    • 4
  • David M. Eckmann
    • 5
  • Marc Garbey
    • 6
  • Ghassan S. Kassab
    • 7
  • Donna R. Lochner
    • 8
  • Andrew D. McCulloch
    • 9
  • Roger Tran-Son-Tay
    • 10
  • Natalia A. Trayanova
    • 11
  1. 1.Departments of Mechanical Engineering and Biomedical EngineeringBoston UniversityBostonUSA
  2. 2.Department of Biomedical EngineeringUniversity of MinnesotaMinneapolisUSA
  3. 3.Department of SurgeryUniversity of FloridaGainesvilleUSA
  4. 4.Department of PharmacologyUniversity of CaliforniaDavisUSA
  5. 5.Department of Anesthesiology and Critical CareUniversity of PennsylvaniaPhiladelphiaUSA
  6. 6.Center for Computational SurgeryMethodist Hospital Research InstituteHoustonUSA
  7. 7.California Medical Innovations InstituteSan DiegoUSA
  8. 8.Office of Science and Engineering Laboratories, Center for Devices and Radiological HealthU.S. Food and Drug AdministrationSilver SpringUSA
  9. 9.Departments of Bioengineering and MedicineUniversity of CaliforniaSan DiegoUSA
  10. 10.Departments of Mechanical & Aerospace Engineering and Biomedical EngineeringUniversity of FloridaGainesvilleUSA
  11. 11.Department of Biomedical Engineering and Institute for Computational MedicineJohns Hopkins UniversityBaltimoreUSA

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