Abstract
The planning of drug therapy for heart failure should involve both the diagnostic analysis of the patient’s defective state and a prediction of the drug effects on the identified state. We have devised a mathematical model of cardiovascular system mechanics, on which both quantitative diagnosis and evaluation of drug effects can be made. The model was composed of systemic and pulmonary circulatory networks including the dynamics of the left and right ventricles. The model of the ventricles can represent both systolic and diastolic problems in heart failure through the parameters of ventricular contractility and diastolic stiffness. Each vascular network was composed of arterial and venous resistances and total vascular capacitance. Patient’s ventricular and vascular parameters were estimated simultaneously from the clinically measurable haemodynamic variables based on the model. Despite the simplicity of the model, the results showed good agreement with clinical and experimental data. The clinically significant haemodynamic classification of heart failure by Forrester et al. (Forrester et al., 1977) was simulated well by the model. This model provides a useful basis for analysing pathophysiological states in heart failure and evaluating drug effects on the disease.
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References
Amoore, J. N., andSantamore, W. P. (1989): ‘Model studies of the contribution of ventricular interdependence to the transient changes in ventricular function with respiratory efforts’,Cardiovasc. Res.23 pp. 683–94
Avanzolini, G., Barbini, P., Cappello, A. andMassai, M. R. (1989): ‘Sensitivity analysis of the systemic circulation with a view to computer simulation and parameter estimation’,J. Biomed. Eng.,11, pp. 43–7
Barnea, O., Moore, T. W., andJaron, D. (1990): ‘Computer simulation of the mechanically-assisted failing canine circulation’,Ann. Biomed. Eng.18, pp. 263–83
Barnea, O., Moore, T. W., Dubin, S. E., andJaron, D. (1990): ‘Cardiac energy considerations during intraaortic balloon pumping’,IEEE Trans.,BME-37, pp. 170–81
Berman, J., O’Benar, J. D., andBellamy, R. F. (1987): ‘A computer model of hemorrhagic shock in domestic swine’,Circ. Shock,21, pp. 85–96
Beyar, R., andSideman, S. (1984): ‘A computer study of the left ventricular performance based on fiber structure, sarcomere dynamics, and transmural electrical propagation velocity’,Circ. Res.,55, pp. 358–75
Beyar, R., andGoldstein, Y. (1987): ‘Model studies of the effects of the thoracic pressure on the circulation’,Ann. Biomed. Eng.,15, pp. 373–83
Brodie, B. R., Grossman, W., Mann, T., andMcLaurin, P. (1977): ‘Effects of sodium nitroprusside on left ventricular diastolic pressure-volume relations’,J. Clin. Invest.,59, pp. 59–68
Burkhoff, D., Sugiura, S., David, T. Y., andSagawa, K. (1987): ‘Contractility-dependent curvilinearity of end-systolic pressure-volume relations’,Am. J. Physiol.,252, H1218–1227.
Califf, R. M., Bounous, P., Harrel, F. E., McAnts, B., Lee, K. L., McKinnis, R. A., andRosati, R. A. (1982): ‘The prognosis in the presence of coronary artery disease’,inBraunwald, E., Mock, M. B., andWatson, J. (Eds.): ‘Congestive heart failure’ (New York and London, Grune & Stratton) pp. 31–40
Carasso, S., Beyar, R., Rooke, A. G., andSideman, S. (1988): ‘Combining transmural left ventricular mechanics and energetics to predict oxygen demand’,Ann. Biomed. Eng.,16, pp. 495–513
Coleman, T. G. (1985): ‘Mathematical analysis of cardiovascular function’,IEEE Trans.,BME-32, pp. 289–294
Dagan, J., andLevi, U. (1978): ‘The cardiovascular system simulated mathematically for normal and defective states’,T.-I.-T. J. Life Sci.,8, pp. 47–53
Forrester, J. S., Diamond, G. A., andSwan, J. (1977): ‘Correlative classification of clinical and hemodynamic function after acute myocardial infarction’,Am. J. Cardiol.,39, pp. 137–145
Greenway, C. V. (1982): ‘Mechanisms and quantitative assessment of drug effects on cardiac output with a new model of the circulation’,Pharmacol. Rev.33, pp. 213–251
Grossman, W. (1982): ‘Hemodynamic evaluation of congestive heart failure’inBraunwald, E., Mock, M. B., andWatson, J. (Eds.), ‘Congestive heart failure’, (New York and London, Grune & Stratton) pp. 167–178
Guyton, A. C. (1963): ‘Venous return’inHamilton, W. F., andDow, P. (Eds.), ‘Handbook of physiology, Section 2: circulation’ (American Physiological Society, Washington) Vol. 2, pp. 1099–1133
Guyton, A. C. (1980): ‘Circulatory physiology III: arterial pressure and hypertension’ (WB Saunders, Philadelphia)
Haddy, F. J., andAlexander, R. S. (1971): ‘Compliance of the arteriovenous system: man and dog’inAltman, P. L. andDittmer, D. S. (Eds.): ‘Respiration and circulation’ (American Physiological Society, Bethesda, Maryland) pp. 391–395
Herndon, C., andSagawa, K. (1969): ‘Combined effects of aortic and right atrial pressures on aortic flow’,Am. J. Physiol.,217, pp 65–72
Hultgren, H. N., andFlamm, M. D. (1971): ‘Heart pressures: man’inAltman, P. L., andDittmer, D. S. (Eds.): ‘Respiration and circulation’ (American Physiological Society, Bethesda, Maryland) pp. 314–315
Levy, M. N. (1979): ‘The cardiac and vascular factors that determine systemic blood flow’,Circ. Res.,44, pp. 739–746
Lindsey, A. W., Banahan, B. F., Cannon, R. H., andGuyton, A. C. (1957): ‘Pulmonary blood volume of the dog and its changes in acute heart failure’,Am. J. Physiol.,190, pp. 45–48.
Low, L. R., Windham, J. P., Farison, J. B., andPotvin, W. J. (1989): ‘Computer model for simulation of first transit cardiac radionuclide curves—I’,IEEE Trans.BME-36, pp. 935–45
Maughan, W. L., Sunagawa, K., andSagawa, K. (1987): ‘Ventricular systolic interdependence: volume elastance model in isolated canine hearts’,Am. J. Physiol.253, H1381–1390
Meador, S. A. (1986): ‘Computer simulation of cardiopulmonary resuscitation: computer analysis of a simple electrical model of the circulation’,Resusc.,13, pp. 145–57
Metcalfe, J., andHeinz, B. (1971): ‘Arterial and venous blood gas comparison: man’inAltman, P. L., andDittmer, D. S. (Eds.): ‘Respiration and circulation’ (American Physiological Society, Bethesda, Maryland) pp. 140–141
Nose, Y., Tajimi, T., Watanabe, Y., Yokota, M., Akazawa, K. andNakamura, M. (1987): ‘A beat-to-beat calculator for the diastolic pressure time index and the tension time index’,Med. Inform.,12, pp. 223–30
Permutt, S., BrombergerBarnea, B., andBane, H. N. (1962): ‘Alveolar pressure, pulmonary venous pressure, and the vascular waterfall’,Med. Thorac.,19, pp. 239–260
Peskin, C. S., andTu, C. (1986): ‘Hemodynamics in congenital heart disease’,Comput. Biol. Med.,16, pp. 331–59
Peterson, N. S., andCampbell, K. B. (1985): ‘Teaching cardiovascular integrations with computer laboratories’,Physiol.,28, pp. 159–69
Pouleur, H., Covell, J. W., andRoss Jr.,J. (1980): ‘Effects of nitroprusside on venous return and central blood volume in the absence and presence of acute heart failure’,Circ.,61, pp. 328–337
Sagawa, K. (1967): ‘Analysis of the ventricular pumping capacity as a function of input and output pressure loads’inReeve, E. B., andGuyton, A. C. (Eds.): ‘Physical bases of circulatory transport’ (WB Saunders, Philadelphia) pp. 141–149
Sagawa, K., Suga, H., Shoukas, A. A., andBakalar, K. M. (1977): ‘End-systolic pressure/volume ratio: a new index of ventricular contractility’,Am. J. Cardiol.,40, pp. 748–753
Singer, R. B. (1971): ‘Blood gas variables, factors, and constants: man’inAltman, P. L., andDittmer, D. S. (Eds.): ‘Respiration and circulation’ (American Physiological Society, Bethesda, Maryland) pp. 139–140
Specht, P. C. (1988): ‘Computer graphics interface to a complex simulation’,P. R. Health Sci. J.,7, pp. 184–8
Suga, H., andSagawa, K. (1974): ‘Instantaneous pressure-volume relationships and their ratio in the excised, supported canine left ventricle’,Circ. Res.,35, pp. 117–126
Suga, H. (1979): ‘Driving energy of time-varying capacitance model of left ventricle and cardiac oxygen consumption’,Jpn. J. Med. Electron. Biol. Eng.,17, pp. 141–146
Suga, H., Kitabatake, A., andSagawa, K. (1979): ‘End-systolic pressure determines stroke volume from fixed end-diastolic volume in the isolated canine left ventricle under a constant contractile state’,Circ. Res.,44, pp. 238–249
Suga, H., Yasumura, Y., Nozawa, T., Futaki, S., Igarashi, Y., andGoto, Y. (1987): ‘Prospective prediction of O2 consumption from pressure-volume area in dog hearts’,Am. J. Physiol.,252, H1258–64
Suga, H. (1990): ‘Ventricular energetics’,Physiol. Rev.,70, pp. 247–277
Tsuruta, H., Sato, T., andIkeda, N. (1994): ‘Mathematical model of cardiovascular mechanics for diagnostic analysis and treatment of heart failure. Part 2: analysis of vasodilator therapy and planning of optimal drug therapy’,Med. Biol. Eng. Comput.,32, pp. 12–18
Yu, C., Roy, R. J., andKaufman, H. (1990): ‘A circulatory model for combined nitroprusside-dopamine therapy in acute heart failure’,Med. Prog. Through Technol.,16, pp. 77–88
Walker, J. R., andTraber, D. L. (1985): ‘A computer simulation of the interaction of drugs with cardiovascular reflexes’,Physiol.,28, pp. 454–5
Watanabe, Y., Shimada, R., Nose, Y., Yokota, M., Inoue, T., andNakamura, M. (1985): ‘Computer analysis of left ventricular pressure-volume relationships by echocardiography’,Med. Inform.,10, pp. 249–58
Weber, K. T., andJanicki, J. S. (1977): ‘Instantaneous force-velocity-length relations: experimental findings and clinical correlates’,Am. J. Cardiol.,40, pp. 740–747
Weber, K. T., Janicki, J. S., andFishman, A. P. (1982): ‘Respiratory gas exchange during exercise in the noninvasive evaluation of the severity of chronic heart failure’inBraunwald, E., Mock, M. B., andWatson, J. (Eds.) ‘Congestive heart failure’ (New York and London, Grune & Stratton) pp. 221–236
Weissler, A. M. (1971): ‘Systolic time intervals: man’inAltman, P. L., andDittmer, D. S. (Eds.) ‘Respiration and circulation’ (American Physiological Society, Bethesda, Maryland) p. 310
Woodard, J. C., Farrar, D. J., Chow, E., Santamore, W. P., Burkhoff, D., andHill, J. D. (1989): ‘Computer model of ventricular interaction during left ventricular circulatory support’,ASAIO Trans.,35, pp. 439–41
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Tsuruta, H., Sato, T., Shirataka, M. et al. Mathematical model of cardiovascular mechanics for diagnostic analysis and treatment of heart failure: Part 1 model description and theoretical analysis. Med. Biol. Eng. Comput. 32, 3–11 (1994). https://doi.org/10.1007/BF02512472
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DOI: https://doi.org/10.1007/BF02512472