Numerical Simulation of a Physiological Mathematical Model of Energy Consumption in a Sarcomere

Simulation of a sarcomere

  • Kathia Gabriela Flores Rodríguez Universidad Autónoma de Nuevo León
  • David Edel Pérez Garza Servicios de Salud de Nuevo León
  • Griselda Quiroz Universidad Autónoma de Nuevo León
Keywords: mathematical modelling, sarcomere, skeletal muscle, energy consumption.


Systems Biology of (SB) offers a platform for analyzing biological processes from the perspective of systems theory based on qualitative knowledge of the biological sciences to generate quantitative knowledge. The area of SB devoted to human health is called Systems Medicine. It studies physiological processes, pathological conditions, and recommended treatments with the goal of providing quantitative elements for optimizing medical treatments. Two analytical tools of SB are mathematical modelling and numerical simulation. The first offers a quantitative abstraction of processes; the second involves implementing computer-based models to reproduce and visualize the variables for purposes of prediction. This article presents a case of the application of mathematical modelling and numerical simulation to the physiological process of energy consumption in the sarcomere of skeletal muscle. It proposes a model that includes activation of the contractile cycle based on the action potential that reaches the neuromuscular union, calcium release into the sarcoplasm, the mechanical response, and quantification of the energy that the sarcomere requires to perform mechanical work.


Wiener N. Cybernetics: or control and communication in the animal and the machine. Cambridge: The MIT Press; 1961. 352 p.

Kitano H. Computational systems biology. Nature [Internet]. 2002;420(6912):206–10. Available from:

Kitano H. Systems Biology: A Brief Overview. Science [Internet]. 2002;295(5560):1662–4. Available from:

Vogt H, Hofmann B, Getz L. The new holism: P4 systems medicine and the medicalization of health and life itself. Med Health Care Philos [Internet]. 2016;19(2):307–23. Available from:

Verboven K, Hansen D. Critical Reappraisal of the Role and Importance of Exercise Intervention in the Treatment of Obesity in Adults. Sport Med [Internet]. 2021;51(3):379–89. Available from:

Brychta R, Wohlers E, Moon J, Chen K. Energy Expenditure: Measurement of Human Metabolism. IEEE Eng Med Biol [Internet]. 2010;29(1):42–7. Available from:

Tortora GJ, Derrickson BH. Principles of Anatomy and Physiology. 12th ed. NJ: John Wiley & Sons; 2009. 299 p.

Dao TT, Ho Ba Tho M-C. A Systematic Review of Continuum Modeling of Skeletal Muscles: Current Trends, Limitations, and Recommendations. Appl Bionics Biomech [Internet]. 2018;2018:7631818. Available from:

Rodrigo S, García I, Franco M, Alonso-Vázquez A, et al. Energy expenditure during human gait. I-An optimized model. In: 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology [Internet]. Buenos Aires: IEEE; 2010: 4254–7. Available from:

Böl M, Reese S. Micromechanical modelling of skeletal muscles based on the finite element method. Comput Methods Biomech Biomed Engin [Internet]. 2008;11(5):489–504.

Landesberg A, Sideman S. Mechanical regulation of cardiac muscle by coupling calcium kinetics with cross-bridge cycling: a dynamic model. Am J Physiol Circ Physiol [Internet]. 1994;267(2):H779–95. Available from:

Sugiura S, Washio T, Hatano A, Okada J, et al. Multi-scale simulations of cardiac electrophysiology and mechanics using the University of Tokyo heart simulator. Prog Biophys Mol Biol [Internet]. 2012;110(2–3):380–9. Available from:

Regazzoni F, Dedè L, Quarteroni A. Biophysically detailed mathematical models of multiscale cardiac active mechanics. PLoS Comput Biol [Internet]. 2020;16(10):e1008294. Available from:

Kügler P. Modelling and Simulation for Preclinical Cardiac Safety Assessment of Drugs with Human iPSC-Derived Cardiomyocytes. Jahresber Dtsch Math Ver [Internet]. 2020;122(4):209–57. Available from:

Tchaicheeyan O, Landesberg A. Regulation of energy liberation during steady sarcomere shortening. Am J Physiol Heart Circ Physiol [Internet]. 2005;289(5):2176–82. Available from:

Gams A, Petric T, Debevec T, Babic J. Effects of robotic knee exoskeleton on human energy expenditure. IEEE Trans Biomed Eng [Internet]. 2013;60(6): 1636-44. Available from:

Landesberg A, Sideman S. Force-velocity relationship and biochemical-to-mechanical energy conversion by the sarcomere. Am J Physiol Heart Circ Physiol [Internet]. 2000;278(4):H1274–84. Available from:

Hill AV. The heat of shortening and the dynamic constants of muscle. Proc. R. Soc. Lond. B [Internet]. 1938;126(843):136–95. Available from:

Yaniv Y, Sivan R, Landesberg A. Stability, controllability, and observability of the “four state” model for the sarcomeric control of contraction. Ann Biomed Eng [Internet]. 2006;34(5):778-89. Available from:

Brenner B, Eisenberg E. Rate of force generation in muscle: correlation with actomyosin ATPase activity in solution. Proc Natl Acad Sci U S A[Internet]. 1986;83(10):3542–6. Available from:

Chalovich JM, Eisenberg E. The effect of troponin-tropomyosin on the binding of heavy meromyosin to actin in the presence of ATP. J Biol Chem [Internet]. 1986;261(11):5088–93. Available from:

Beuckelmann DJ, Näbauer M, Erdmann E. Intracellular calcium handling in isolated ventricular myocytes from patients with terminal heart failure. Circulation [Internet]. 1992;85(3):1046–55. Available from:

Yaniv Y, Sivan R, Landesberg A. Analysis of hystereses in force length and force calcium relations. Am J Physiol Circ Physiol [Internet]. 2005;288(1):H389–99. Available from:

Edman KAP. Contractile properties of mouse single muscle fibers, a comparison with amphibian muscle fibers. J Exp Biol [Internet]. 2005;208(10):1905–13. Available from:

Ma S, Zahalak GI. Activation dynamics for a distribution-moment model of skeletal muscle. Math Comput Model [Internet]. 1988;11:778–82. Available from:

Gollapudi SK. Modeling temperature dependent dynamic contractile properties in human skeletal muscle fibers using crossbridge models [Ph.D.'s thesis]. [Washington]: Washington State University, 2011.

Stienen GJ, Kiers JL, Bottinelli R, Reggiani C. Myofibrillar ATPase activity in skinned human skeletal muscle fibres: Fibre type and temperature dependence. J Physiol [Internet]. 1996;493(2):299–307. Available from:

Marcucci L, Reggiani C, Natali AN, Pavan PG. From single muscle fiber to whole muscle mechanics: a finite element model of a muscle bundle with fast and slow fibers. Biomech Model Mechanobiol [Internet]. 2017;16(6):1833–43. Available from:

How to Cite
Flores Rodríguez, K. G., Pérez Garza, D. E., & Quiroz, G. (2021). Numerical Simulation of a Physiological Mathematical Model of Energy Consumption in a Sarcomere: Simulation of a sarcomere. Mexican Journal of Biomedical Engineering, 42(2), 104-118. Retrieved from
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