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Electro-Chemo-Mechanical Modeling of the Artery Myogenic Response

Published online by Cambridge University Press:  17 June 2014

Yali Li  and
Nakhiah Goulbourne
Yali Li
Affiliation:
Aerospace engineering department, University of Michigan, Ann Arbor, MI 48109, U.S.A.
Nakhiah Goulbourne
Affiliation:
Aerospace engineering department, University of Michigan, Ann Arbor, MI 48109, U.S.A.
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Abstract

Active contraction of smooth muscle results in the myogenic response and vasomotion of arteries, which adjusts the blood flow and nutrient supply of the organism. It involves coupled electrobiochemical and chemomechanical processes. This paper presents a new constitutive model to describe the myogenic response of the artery wall under different transmural pressures. The model includes two major components: a cell-level model for the electrobiochemical process, and a tissue-level model for the chemomechanical coupling. The electrochemical model is a lumped Hodgkin-Huxley-type cell membrane model for the nanoscopic ionic currents: calcium, sodium, and potassium. The calculated calcium concentration serves as input for the chemomechanical portion of the model; its molecular binding and the reactions with other enzymes cause the relative sliding of thin and thick filaments of the contractile unit. In the chemomechanical model, a new nonlinear viscoelastic model is introduced to describe the time varying behavior of the smooth muscle. Specifically, this model captures the filament overlap effect, active stress evolution, initial velocity, and elastic recoil in the media layer. Using the proposed constitutive model and a thin-walled equilibrium equation, the myogenic response is calculated for different transmural pressures. The integrated model is able to capture the pressure-diameter relationship incorporating fewer parameters than previous work and with clear physical meanings.

Keywords

biomaterialsimulationstress/strain relationship
Type
Articles
Information
MRS Online Proceedings Library (OPL) , Volume 1685: Symposium U – Soft Nanomaterials , 2014 , mrss14-1685-u10-03
Copyright
Copyright © Materials Research Society 2014 

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References

REFERENCES

Huxley, H. and Hanson, J.. Changes in the cross-striations of muscle during contraction and stretch and their structural interpretation. Nature, 173(4412):973–976, 1954.CrossRefGoogle ScholarPubMed
Huxley, A. F. and Niedergerke, R.. Structural changes in muscle during contraction: Interference microscopy of living muscle fibres. Nature, 173(4412):971–973, 1954.CrossRefGoogle ScholarPubMed
Huxley, A. F.. Muscle structure and theories of contraction. Progress in biophysics and biophysical chemistry, 7:255–318, 1957.CrossRefGoogle ScholarPubMed
Huxley, A. F.. Muscular contraction. The Journal of Physiology, 243(1):1–43, 1974.CrossRefGoogle ScholarPubMed
Huxley, A. F.. Mechanics and models of the myosin motor. Philosophical Transactions of the Royal Society B: Biological Sciences, 355(1396):433–440, 2000.CrossRefGoogle ScholarPubMed
Huxley, H. E.. Fifty years of muscle and the sliding filament hypothesis. European Journal of Biochemistry, 271(8):14031415, 2004.CrossRefGoogle ScholarPubMed
Murphy, R. A., Herlihy, J. T., and Megerman, J.. Force-generating capacity and contractile protein content of arterial smooth muscle. J General Physiology, 64(6):691–705, 1974.CrossRefGoogle ScholarPubMed
Fajmut, A., Brumen, M., and Schuster, S.. Theoretical model of the interactions between Ca2+, calmodulin and myosin light chain kinase. FEBS Letters, 579(20):4361–4366, 2005.CrossRefGoogle ScholarPubMed
Hai, C. M. and Murphy, R. A.. Cross-bridge phosphorylation and regulation of latch state in smooth muscle. Am J physiology, 254(1 Pt 1):C99–106, 1988.CrossRefGoogle Scholar
Gestrelius, S. and Borgstrom, P.. A dynamic model of smooth muscle contraction. Biophysical Journal, 50(1):157–169, 1986.CrossRefGoogle ScholarPubMed
Wang, I., Politi, A. Z., Tania, N., Bai, Y., Sanderson, M. J., and Sneyd, J.. A mathematical model of airway and pulmonary arteriole smooth muscle. Biophysical Journal, 94(6):2053–2064, 2008.CrossRefGoogle ScholarPubMed
Maggio, C. D., Jennings, S. R., Robichaux, J.L., Stapor, P. C., and Hyman, J. M.. A modified Hai and Murphy model of uterine smooth muscle contraction. Bulletin of Mathematical Biology, 74(1):143–158, 2012.CrossRefGoogle ScholarPubMed
Hill, A. V.. The heat of shortening and the dynamic constants of muscle. Proceedings of the Royal Society of London. Series B, Biological Sciences, 126(843):136–195, 1938.Google Scholar
Fung, Y. C.. Mathematical representation of the mechanical properties of the heart muscle. Journal of Biomechanics, 3(4):381–404, 1970.CrossRefGoogle ScholarPubMed
Fung, Y. C.. Biomechanics: mechanical properties of living tissues. Springer-Verlag, New York, 1993.CrossRefGoogle Scholar
Murtada, S. C., Arner, A., and Holzapfel, G. A.. Experiments and mechanochemical modeling of smooth muscle contraction: Significance of filament overlap. J Theoretical Biology, 297:176–186, 2012.CrossRefGoogle ScholarPubMed
Yang, J., Clark, J. W. Jr., Bryan, R. M., and Robertson, C.. The myogenic response in isolated rat cerebrovascular arteries: smooth muscle cell model. Medical Engineering & Physics, 25(8):691–709, 2003.CrossRefGoogle ScholarPubMed
Stalhand, J., Klarbring, A., and Holzapfel, G.A.. Smooth muscle contraction: Mechanochemical formulation for homogeneous finite strains. Progress in Biophysics and Molecular Biology, 96(13): 465–481, 2008.CrossRefGoogle ScholarPubMed
Stalhand, J., Klarbring, A., and Holzapfel, G.A.. A mechanochemical 3D continuum model for smooth muscle contraction under finite strains. J Theoretical Biology, 268(1):120–130, 2011.CrossRefGoogle ScholarPubMed
Kroon, M.. A constitutive model for smooth muscle including active tone and passive viscoelastic behaviour. Mathematical Medicine and Biology, 27(2):129–155, 2010.CrossRefGoogle ScholarPubMed
Rachev, A. and Hayashi, K.. Theoretical study of the effects of vascular smooth muscle contraction on strain and stress distributions in arteries. Annals of Biomedical Engineering, 27(4):459–468, 1999.CrossRefGoogle ScholarPubMed
Zulliger, M. A., Rachev, A., and Stergiopulos, N.. A constitutive formulation of arterial mechanics including vascular smooth muscle tone. Am J Physiology Heart and Circulatory Physiology, 287(3):H1335–H1343, 2004.CrossRefGoogle ScholarPubMed
Holzapfel, G. A.. Nonlinear Solid Mechanics: A Continuum Approach for Engineering. John Wiley & Sons, 2000.Google Scholar
Gasser, T. C., Ogden, R. W., and Holzapfel, G. A.. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J The Royal Society Interface, 3(6):15–35, 2006.CrossRefGoogle ScholarPubMed
Warshaw, D. M., Desrosiers, J. M., Work, S. S., and Trybus, K. M.. Smooth muscle myosin cross-bridge interactions modulate actin lament sliding velocity in vitro. J Cell Biology, 111(2):453–463, 1990.CrossRefGoogle Scholar
Kamm, K. E., Gerthoffer, W. T., Murphy, R A, and Bohr, D F. Mechanical properties of carotid arteries from DOCA hypertensive swine. 1989.CrossRefGoogle Scholar
Herlihy, J. T. and Murphy, R. A.. Length-tension relationship of smooth muscle of the hog carotid artery. Circulation Research, 33(3):275–283, 1973.CrossRefGoogle ScholarPubMed
Dillon, P. F., Aksoy, M. O., Driska, S. P., and Murphy, R. A.. Myosin phosphorylation and the cross-bridge cycle in arterial smooth muscle. Science, 211(4481):495–497, 1981.CrossRefGoogle ScholarPubMed
Knot, H. J. and Nelson, M. T.. Regulation of arterial diameter and wall [Ca] in cerebral arteries of rat by membrane potential and intravascular pressure. J Physiol (Lond) 508(1): 199–209, 1998.CrossRefGoogle Scholar
Lindblad, D.S., Murphy, C.R., Clark, J. W., and Giles, W. R.. A model of the action potential and underlying membrane currents in rabbit atrial cell. Am J Physiol 271: H1666–H996, 1996.Google ScholarPubMed