Mathematical models are powerful tools for investigating and understanding complex systems. Their use must be guided by knowledge of their potentialities and limitations and a well-based approach to the modelling process. Such is embodied in an integrated methodology for model formulation, identification and validation which has emerged from practical modelling as well as historical studies. The methodology in operation is illustrated by application to the formulation of a model of the human cardiovascular system, its neural control and the effect of drugs. The derivation of the model is described in depth and a complete model listing is given. The companion paper develops a validation methodology and applies it to the cardiovascular model.
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References
1.
Al-Dahan, M., Rajkumar, N., Pullen, H.E., Finkelstein, L., Hill, D.W. and Carson, E.R.1979. 'Mathematical modelling of the human cardiovascular system' , Research Memorandum DSS/MAD-NR-HEP-LF-DWH-ERC/188, The City University, London.
2.
Atkins, G.L.1969. Multicompartmental models in biological systems , Methuen, London.
3.
Beneken, J.E.W.1975. 'A mathematical approach to cardiovascular function ', Technical Report No 2-4-516, Institute of Medical Physics, TNO , Utrecht, Netherlands.
4.
Beneken, J.E.W. and De Wit, B.1967. 'A physical approach to haemodynamic aspects of the human cardiovascular system', in Physical bases of circulatory transport , E. B. Reeve and A. C. Guyton (eds), W. B. Saunders, Philadelphia.
5.
Beneken, J.E.W. and Rideout, V.C.1968. 'The use of multiple models in cardiovascular system studies: transport and perturbation', IEEE Trans Biomed Eng , BME-15, 281-289.
6.
Bowers, D.A., Mitchell, C.R. and Webb, K.1981. 'Modelling bi-communal conflict: 3. Simulation and validatican ', Futures, 13,115-127.
7.
Carson, E.R., Cobelli, C. and Finkelstein. L.1983. Mathematical modeling of metabolic and endocrine systems , John Wiley & Sons, Inc, New York.
8.
Dick, D.E. and Rideout, V.C.1965. 'Analog simulation of left heart and arterial dynamics' , Proc 18th ACEMB, Philadelphia .
9.
Guyton, A.C.1955. 'Determination of cardiac output by equating venous return curves with cardiac output curves', Physiol Rev, 35,123-129.
10.
Guytom, A.C. and Coleman; T. G. 1967. 'Long-term regulation of the circulation: interrelationships with body fluid volume' in Physical bases of circulatory transport, E. B. Reeve and A. C. Guyton (eds), 170-201, W. B. Saunders, Philadelphia.
11.
Guyton, A.C., Coleman, T.G. and Granger, H.J.1972. 'Circulation: Overall regulation', Am RevPhysiol, 34, 13-46.
12.
Harvey, W.1628. Excertatio de motu cordis et sanguinis in animalibus , (translated by K. J. Franklin, Movement of the heart and blood in animals , Blackwell Scientific Publications, Oxford, 1957).
13.
Hull, C.J.1982. Pharmacodynamics of non-depolarizing neuromuscular blocking agents', Brit J Anaesthesia, 54, 169-182.
14.
Hyndman, P.W.1970. A digital simulation of the human cardiovascular system and its use in the study of sinus arrythmia. PhD Thesis, Imperial College, University of London.
15.
Katona, P.G., Barnet, O. and Jackson, W.D.1967. 'Computer simulation of the blood pressure control of heart period', in Baroreceptors and hypertension, P. Kezdi (ed), Pergamon, Oxford, pp 191-199.
16.
Leaning, M.S.1980. The validity and validation of mathematical models, PhD Thesis, The City University, London .
17.
Learning, M.S., Uttamsingh, R.J., Carson, E.R., Cobelli, C. and Finkelstein, L.1982. 'Methodological aspects of model validation: a model of the human renal - artificial kidney system', in A general survey of systems methodology, (Proc. 26th Annual Meeting of the SGSR), L. Troncale (ed), Society for General Systems Research, Louisville, Kentucky , pp 508-516.
18.
Mihram, G.A.1972. 'The modeling process', IEEE Trans Sys Man & Cybern, SMC-2, 621-629.
19.
Monin, A.S.1972. Weather forecasting as a problem in physics, MIT Press.
20.
Pullen, H.E.1976. Studies in the modelling and simulation of the human cardiovascular system with application to the effect of drugs, PhD Thesis , The City University, London.
21.
Rajkumar, N.1978. Reduction of a mathematical model of the human cardiovascular system, MSc Thesis, The City University , London.
22.
Simon, H.A.1969. The sciences of the artificial, (2nd edn, 1981), MIT Press.
23.
Snyder, M.F. and Rideout, V.C.1969. 'Computer simulation studies of the venous circulation' , IEEE Trans Biomed Eng, BME-16, 325-334.
