Acta Scientific Clinical Case Reports

Review ArticleVolume 3 Issue 4

Some Results Related to the Application of the ESPVR to the Study of Cardiac Mechanics

Rachad Mounir Shoucri*

Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Canada

*Corresponding Author: Rachad Mounir Shoucri, Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Canada.

Received: February 14, 2022; Published: March 31, 2022


Relations previously derived between the ejection fraction (EF) and the parameters describing the linear model of the end-systolic pressure-volume relation (ESPVR) of the left-ventricle of the heart have been used to derive indexes that can be used to study the mechanics of cardiac contraction and some aspects of heart failure (HF). The present study presents further applications of these indexes to clinical data published in the medical literature in a way to show the consistency of the mathematical formalism used. An important aspect of this mathematical formalism is the introduction of the peak active pressure generated by the myocardium during an ejecting contraction (also called isovolumic pressure Pisom by physiologists) in the mathematical formalism describing the ESPVR. The link between the change of volume of the left-ventricle and the pressures acting on the myocardium is given by two parameters, the slope Emax of the ESPVR, and the intercept Vom of the ESPVR with the horizontal volume-axis. It is observed that no one index gives perfect segregation between all clinical groups, some indexes are better than others depending on the clinical groups considered. It is also observed that bivariate (or multivariate) analysis of data gives better classification of clinical data than univariate analysis (like using only EF).

Keywords: Ejection Fraction; ESPVR; Heart Failure


  1. Frank O. “Die Grundform des arteriellen Pulses”. Zeit für Biol 37 (1899): 483-526.
  2. Kuhtz-Buschbeck JP., et al. “Rediscovery of Otto Frank’s contribution to science”. Journal of Molecular and Cellular Cardiology 119 (2018): 96-103.
  3. Kjorstad KE., et al. “Pressure-volume based single-beat estimation cannot predict left ventricular contractility in vivo”. American Journal of Physiology 282 (2002): H1739-H1750.
  4. Burkhoff D., et al. “Assessment of systolic and diastolic ventricular properties via pressure-volume analysis: A guide for clinical, translational, and basic researchers”. American Journal of Physiology 289 (2005): H501-H512.
  5. Suga H., et al. “Mechanical efficiency of the left ventricle as a function of preload, afterload, and contractility”. Heart and Vessels 1 (1985): 3-8.
  6. Carabello BA. “The role of end-systolic pressure-volume analysis in clinical assessment of ventricular function”. Trends in Cardiovascular Medicine 1 (1991): 337-341.
  7. Mehmel HC., et al. “The linearity of the end-systolic pressure-volume relationship in man and its sensitivity for assessment of ventricular function”. Circulation 63 (1981): 1216-1222.
  8. Shoucri RM. “The pressure-volume relation and the mechanics of left ventricular contraction”. Japanese Heart Journal 31 (1991): 713-729.
  9. Shoucri RM. “Theoretical study of the pressure-volume relation in left ventricle”. American Journal of Physiology-Heart and Circulatory Physiology 260 (1991): H282-H291.
  10. Shoucri RM. “Mathematical aspects of the mechanics of left ventricular contraction”. International Journal of Design and Nature and Ecodynamics2 (2010): 173-188.
  11. Shoucri RM. “Studying the mechanics of left ventricular contraction”. IEEE Engineering in Medicine and Biology Magazine 17 (1998): 95-101.
  12. Shoucri RM. “Ejection fraction and ESPVR, A study from a theoretical perspective”. International Heart Journal 54 (2013): 318-327.
  13. Shoucri RM. “Basic relations between ejection fraction and ESPVR”. Austin Journal of Clinical Cardiology 1 (2014): 1-6.
  14. Shoucri RM. “End-systolic pressure-volume relation, ejection fraction, and heart failure: Theoretical aspect and clinical applications”. Clinical Medicine Insights: Cardiology 9 (2015): 1-10.
  15. Shoucri RM. “Ejection fraction and ESPVR: A study in the mechanics of left ventricular contraction”. Cardiology Open Access (Austin)1 (2020): 37-47.
  16. Shoucri RM. “Clinical applications of the areas under ESPVR: A review”. in: Highlights on Medicine and Medical Research, vol. 10, chap. 2, editor: Dr John Yahya I. Elshimali (BP International) (2021): 10-15.
  17. Shoucri RM. “A Basic Look at Ventricular Function and Cardiac Mechanics”. in: Recent Development in Medicine and Medical Research, vol 4, chap. 5, editor: Naseem A. Qurashi (BP International) (2021): 31-45.
  18. Kitzman DW., et al. “Exercise intolerance in patients with heart failure and preserved left ventricular systolic function: Failure of the Frank-Starling mechanism”. Journal of the American College of Cardiology5 (1991): 1065-1072.
  19. Burkhoff D., et al. “Heart failure with a normal ejection fraction: Is it really a disorder of diastolic function?” Circulation 107 (2003): 656-658.
  20. Sanderson JE. “Heart failure with a normal ejection fraction”. Heart 93 (2007): 155-158.
  21. Little WC. “Hypertension, heart failure, and ejection fraction”. Circulation 118 (2008): 2223-2224.
  22. Marwick TH. “Ejection fraction pros and cons”. Journal of the American College of Cardiology3 (2018): 736-742.
  23. Naing P., et al. “Heart failure with preserved ejection fraction, a growing global epidemic”. Australian Journal of General Practice 48 (2019): 465-471.
  24. Sasayama S and Asanoi H. “Coupling between the heart and arterial system in heart failure”. The American Journal of Medicine 90 (1991): 14-18.
  25. Shoucri RM. “ESPVR, Ejection Fraction and Heart Failure”. Cardiovascular Engineering 11 (2010): 207-212.
  26. Maughan WL., et al. “Instantaneous pressure-volume relationship of the canine right ventricle”. Circulation Research 44 (1979): 309-315.
  27. Shoucri RM. “Pressure-volume relation in the right ventricle”. Journal of Biomedical Engineering 15 (1993): 167-169.
  28. Brimioulle S., et al. “Single-beat estimation of the right ventricular end-systolic pressure-volume relationship”. American Journal of Physiology-Heart and Circulatory Physiology 284 (2003): 1625-1630.
  29. Asanoi H., et al. “Ventriculo-arterial coupling in normal and failing heart in Humans”. Circulation Research 65 (1989): 483-493.
  30. Shoucri RM. “Possible clinical applications of the external work reserve of the myocardium”. Japanese Heart Journal 6 (1994): 771-787.
  31. Shoucri RM. “Theoretical study related to left ventricular energetics”. Japanese Heart Journal 4 (1993): 403-417.
  32. Burkhoff D and Sagawa K. “Ventricular efficiency predicted by an analytical model”. American Journal of Physiology 250 (1986): R1021-R1027.
  33. da Mota JPGF. “Intelligent modeling to predict ejection fraction from Echocardiographic reports”. MSc thesis in Mechaniical Engineering, IST Técnico Lisboa, Portugal (2013).
  34. Suga H. “Cardiac energetic: from Emax to pressure-volume area”. Clinical and Experimental Pharmacology and Physiology 30 (2003): 580-585.
  35. Shoucri RM. “Calculation of parameters of end-systolic pressure-volume relation in the ventricles”. Mathematical and Computer Modelling 54 (2011): 1638-1643.

Citation: Rachad Mounir Shoucri. “Some Results Related to the Application of the ESPVR to the Study of Cardiac Mechanics". Acta Scientific Clinical Case Reports 3.4 (2022): 75-89.

Copyright: © 2022 Rachad Mounir Shoucri. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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