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

Kathia Gabriela Flores Rodríguez; David Edel Pérez Garza; Griselda Quiroz

doi:10.17488/RMIB.42.2.9

Autores/as

Kathia Gabriela Flores Rodríguez Universidad Autónoma de Nuevo León, México
David Edel Pérez Garza Servicios de Salud de Nuevo León, México
Griselda Quiroz Universidad Autónoma de Nuevo León, México https://orcid.org/0000-0002-4910-2521

DOI:

https://doi.org/10.17488/RMIB.42.2.9

Palabras clave:

Modelado matemático, Sacómero, Músculo esquelético, Consumo de energía

Resumen

La Biología de Sistemas (BS) ofrece una plataforma para el análisis de procesos biológicos desde la teoría de sistemas, partiendo del conocimiento cualitativo de las ciencias biológicas para generar conocimiento cuantitativo. El área de la BS dedicada a la salud humana es la Medicina de Sistemas, en donde se estudian los procesos fisiológicos, las condiciones patológicas y los tratamientos recomendados. Su objetivo es proporcionar elementos cuantitativos para la optimización de los tratamientos médicos. Dos de las herramientas de análisis de la BS son el modelamiento matemático y las simulaciones numéricas. La primera ofrece una abstracción cuantitativa del proceso, la segunda es la implementación computacional de modelos para reproducir y visualizar las variables, con fines de predicción. En este trabajo se muestra un caso de aplicación de modelado matemático y simulación numérica para el proceso fisiológico de consumo de energía en el sarcómero del músculo esquelético. Se propone un modelo que incluye la activación del ciclo de contracción a partir del potencial de acción que llega a la unión neuromuscular, la liberación de calcio en el sarcoplasma, la respuesta mecánica y la cuantificación de la energía, que requiere el sarcómero para realizar trabajo mecánico.

Descargas

Los datos de descargas todavía no están disponibles.

Citas

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: https://doi.org/10.1038/nature01254

Kitano H. Systems Biology: A Brief Overview. Science [Internet]. 2002;295(5560):1662–4. Available from: https://doi.org/10.1126/science.1069492

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: https://doi.org/10.1007/s11019-016-9683-8

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: https://doi.org/10.1007/s40279-020-01392-8

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: https://doi.org/10.1109/MEMB.2009.935463

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: https://doi.org/10.1155/2018/7631818

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: https://doi.org/10.1109/IEMBS.2010.5627174

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. https://doi.org/10.1080/10255840701771750

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: https://doi.org/10.1152/ajpheart.1994.267.2.h779

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: https://doi.org/10.1016/j.pbiomolbio.2012.07.001

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: https://doi.org/10.1371/journal.pcbi.1008294

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: https://doi.org/10.1365/s13291-020-00218-w

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: https://doi.org/10.1152/ajpheart.00124.2005

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: https://doi.org/10.1109/tbme.2013.2240682

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: https://doi.org/10.1152/ajpheart.2000.278.4.h1274

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: https://doi.org/10.1098/rspb.1938.0050

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: https://doi.org/10.1007/s10439-006-9093-9

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: https://doi.org/10.1073/pnas.83.10.3542

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: https://www.ncbi.nlm.nih.gov/pubmed/2937784

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: https://doi.org/10.1161/01.cir.85.3.1046

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: https://doi.org/10.1152/ajpheart.00722.2003

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: https://doi.org/10.1242/jeb.01573

Ma S, Zahalak GI. Activation dynamics for a distribution-moment model of skeletal muscle. Math Comput Model [Internet]. 1988;11:778–82. Available from: https://doi.org/10.1016/0895-7177(88)90599-7

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: https://doi.org/10.1113/jphysiol.1996.sp021384

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: https://doi.org/10.1007/s10237-017-0922-6