Euler, Father of Hemodynamics
- 1 University of Sao Paulo, Sao Paulo, Brazil
Abstract
In 1742, Euler presented an essay on the “Principles for determining the motion of the blood through arteries”. This is the first known work on the mechanics of flows in elastic tubes, in which Euler applied his equations to analyze the flow of blood through arteries, driven by a piston pump simulating the heart. However, Euler did not recognize the wave nature of his equations, which led him to a dead end on trying to find a closed form solution. Nonetheless, it will be shown that the hemodynamic equations developed by Euler about 275 years ago, still undergird the most advanced numerical methods in use today for blood flow analysis in arterial networks. Therefore, Euler’s pioneering and seminal work in the area of blood flow justifies he be called the father of hemodynamics.
- Alastruey, J., Parker, K. H., & Sherwin, S. J. (2012). Arterial Pulse Wave Haemodynamics. In S. Anderson (Ed.), 11th International Conference on Pressure Surges (pp. 401-443). Lisbon: Virtual PiE Led t/a BHR Group.
- Boileau, E., et al. (2015). A Benchmark Study of Numerical Schemes for One-Dimensional Arterial Blood Flow Modelling. International Journal for Numerical Methods in Engineering, 31, Article ID: e02732. https://doi.org/10.1002/cnm.2732
- Cerny, L. C., & Walawender, W. P. (1974). Leonhardi Euleri’s Principia pro motu sanguinis per arterias determinando. Journal of Biological Physics, 2, 41-56. https://doi.org/10.1007/BF02309372
- D’Alembert, J. L. R. (1747). Recherches sur la courbe que forme une corde tendue mise en vibration. Histoire de l’Académie Royale des Sciences et Belles-Lettres de Berlin pour l’année, 1750, 214-219.
- Euler, L. (1754). E 206—Sur le mouvement de l’eau par des tuyaux de conduite. Mémoires de l’académie des sciences de Berlin, 8, 111-148. (Also in Opera Omnia: Series 2, Volume 15, pp. 219-250. According to C. G. J. Jacobi, a Treatise with This Title Was Presented to the Berlin Academy on October 23, 1749).
- Euler, L. (1759). E 305—De la propagation du son. Mém Acad Sci Berlin, 15, 185-209.
- Euler, L. (1862). E 855—Principia pro motu sanguinis per arterias determinando. Opera Postuma, 2, 814-823.
- Euler, L. (1979). E 855—Principia pro motu sanguinis per arterias determinando. Opera Omnia: Series 2, 16, 178-196.
- Hughes, T. J. R., & Lubliner, J. (1973). On the One-Dimensional Theory of Blood Flow in the Larger Vessels. Math Biosciences, 18, 161-170. https://doi.org/10.1016/0025-5564(73)90027-8
- Parker, K. H. (2009). A Brief History of Arterial Wave Mechanics. Medical & Biological Engineering & Computing, 47, 111-118. https://doi.org/10.1007/s11517-009-0440-5
- Saito, M., et al. (2011). One-Dimensional Model for Propagation of a Pressure Wave in a Model of the Human Arterial Network: Comparison of Theoretical and Experimental Results. Journal of Biomechanical Engineering, 133, Article ID: 121005. https://doi.org/10.1115/1.4005472
- Smith, N. P., Pullan, A. J., & Hunter, P. J. (2002). An Anatomically Based Model of Transient Coronary Blood Flow in the Heart. SIAM Journal on Applied Mathematics, 62, 990-1018. https://doi.org/10.1137/S0036139999355199
- Tijsseling, A. S., & Anderson, A. (2012). A Isebree Moens and DJ Korteweg: On the Speed of Propagation of Waves in Elastic Tubes [Keynote Paper]. http://www.win.tue.nl/~atijssel/pdf_files/CASA-12-42.pdf