Mathematical modeling of cardiovascular system dynamics using a lumped parameter method

Japanese Journal of Physiology

Volumn 54, Issue 6, 2004, Pages 545-553

  Shim, Eun Bo ^a   Sah, Jong Youb ^b   Youn, Chan Hyun ^c  

^a Kangwon National University   (South Korea)

^b Yeungnam University   (South Korea)

^c Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Autonomic nerve control; Dynamics of the cardiovascular system; Lumped parameter model

Indexed keywords

AUTONOMIC NERVE; BLOOD FLOW VELOCITY; BLOOD PRESSURE; CARDIOVASCULAR FUNCTION; FEEDBACK SYSTEM; HEMODYNAMICS; HYPOTENSION; HYPOVOLEMIA; LUNG CIRCULATION; MATHEMATICAL MODEL; MICROCIRCULATION; PRESSORECEPTOR REFLEX; PRESSURE VOLUME CURVE; REVIEW;

ANIMALS; AUTONOMIC NERVOUS SYSTEM; CARDIOVASCULAR PHYSIOLOGY; CARDIOVASCULAR SYSTEM; MODELS, CARDIOVASCULAR;

EID: 15744371403     PISSN: 0021521X     EISSN: None     Source Type: Journal    
DOI: 10.2170/jjphysiol.54.545     Document Type: Review

References (56)

1. Grodins FS: Integrative cardiovascular physiology: A mathematical synthesis of cardiac and blood vessel hemodynamics. Q Rev Biol 34: 93-116, 1959
2. Attinger EO, and Anne A: Simulation of the cardiovascular system. Ann NY Acad Sci 128: 810-829, 1966
3. Avolio AP: Multi-branched model of the human arterial system. Med Biol Eng Comput 18: 709-718, 1980
4. Dagen J: Pulsatile mechanical and mathematical model of the cardiovascular system. Med Biol Eng Comput 20: 601-607, 1982
5. Hardy HH, Collins RE, and Calvert RE: A digital computer model of the human circulatory system. Med Biol Eng Comput 20: 550-564, 1982
6. LaCourse JR, Mohankrishnan G, and Sivaprasad K: Simulations of arterial pressure pulses using a transmission model. J Biomech 19: 771-780, 1986
7. Sud VK, and Sekhon GS: Analysis of blood flow through a model of the human arterial system under periodic body acceleration. J Biomech 19: 929-941, 1986
8. Ursino M: Interaction between carotid baroregulation and the pulsating heart: a mathematical model. Am J Physiol 275(5 Pt 2): H1733-H1747, 1988
9. Boyers DG., Cuthbertson JG, and Leutscher JA: Simulation of the human cardiovascular system: a model with normal responses to change of posture, blood loss, transfusion, and autonomic blockade. Simulation 18: 197-205, 1972
10. Croston RC, Rummel JA, and Kay FJ: Computer model of cardiovascular control system responses to exercise. J Dynamic Systems Measurement Control 95: 301-307, 1973
11. Ejaz T, Takemae T, Kosugi Y, and Hongo M: The high zero-flow pressure phenomenon in coronary circulation: a simulation study. Front Med Biol Eng 11: 335-340, 2002
12. Kresh JY, Fox M, Brockman SK, and Noordergraaf A: Model-based analysis of transmural vessel impedance and myocardial circulation dynamics. Am J Physiol 258 (1 Pt 2): H262-H276, 1990
13. Schreiner W, Neumann F, and Mohl W: Simulation of coronary circulation with special regard to the venous bed and coronary sinus occlusion. J Biomed Eng 12: 429-443, 1990
14. Magosso E, and Ursino M: Modelling study of the acute cardiovascular response to hypocapnic hypoxia in healthy and anaemic subjects. Med Biol Eng Comput 42: 158-166, 2004
15. Ursino M, Magosso E, and Avanzolini G: An integrated model of the human ventilatory control system: the response to hypoxia. Clin Physiol 21: 465-477, 2001
16. Jager GN, Westerhof N, and Noordergraaf A: Oscillatory flow impedance in electrical analog of arterial system: representation of sleeve effect and non-Newtonian properties of blood. Circ Res 16: 121-133, 1965
17. Porenta G, Young DF, and Rogge DR: A finite element model of blood flow in arteries including taper, branches, and obstructions. J Biomech 108: 161-167, 1986
18. Li X, Bai J, Cui S, and Wang S: Simulation study of the cardiovascular functional status in hypertensive situation. Comput Biol Med 32: 345-362, 2002
19. Masuzawa T, Fukui Y, and Smith NT: Cardiovascular simulation using a multiple modeling method on a digital computer-simulation of interaction between the cardiovascular system and angiotensin II. J Clin Monit 8: 50-58, 1992
20. Jaron D, Moore DW, and Chu CL: Cardiovascular model for studying impairment of cerebral function during +Gz stress. Aviat Space Environ Med 55: 24-31, 1984
21. Campbell K, Zeglen M, Kagehiro T, and Rigas H: A pulsatile cardiovascular computer model for teaching heart-blood vessel interaction. Physiologist 25: 155-162, 1982
22. Sunagawa K, and Sagawa K: Models of ventricular contraction based on time-varying elastance. Crit Rev Biomed Eng 7: 193-228, 1982
23. Heldt T, Shim EB, Kamm RD, and Mark RG: Computational modeling of cardiovascular response to orthostatic stress. J Appl Physiol 92: 1239-1254, 2002
24. Shim EB, Heldt T, Kamm RD, Mark RG, and Youn CH: Computational Modeling of the Cardiovascular System After Fontan Procedure. Lecture Notes in Computer Science 2526: 105-114, 2002
25. Melchior FM, Srinivasan RS, and Charles JB: Mathematical modeling of human cardiovascular system for simulation of orthostatic response. Am J Physiol 262(6 Pt 2): H1920-H1933, 1992
26. Mirsky I: Elastic Properties of the Myocardium: A quantitative approach with physiological and clinical applications. In: Handbook of Physiology (The Cardiovascular System), ed. Berne RM, American Physiological Society, Bethesda, pp 497-431, 1979
27. Dell'Italia LJ, and Walsh RA: Application of a time varying elastance model of right ventricular performance in man. Cardiovasc Res 22: 864-874, 1988
28. Senzaki H, Chen CH, and Kass D: Single-beat estimation of end-systolic pressure-volume relation in humans: a new method with the potential for non-invasive application. Circulation 94: 2497-2506, 1996
29. Ursino M: Interaction between carotid baroregulation and the pulsating heart: a mathematical model. Am J Physiol 275(5 Pt 2): H1733-H1747, 1998
30. Ursino M, and Magosso E: Role of short-term cardiovascular regulation in heart period variability: a modeling study. Am J Physiol Heart Circ Physiol 284: H1479-H1493, 2003
31. Ursino M: A mathematical model of the carotid baroregulation in pulsating conditions. IEEE Trans Biomed Eng 46: 382-392, 1999
32. Burkhoff, DJ, Alexander, and Schipke K: Assessment of Windkessel as a model of aortic impedance. Am J Phys 255 (Heart Circ Physiol 24): H742-H753, 1988
33. Campbell K, Zeglen M, Kagehiro T, and Rigas H: A pulsatile cardiovascular model for teaching heart-blood vessel interaction. Physiologist 25: 155-162, 1982
34. Davis TL, and Mark RG: Teaching Physiology Through Simulation of Hemodynamics. Computers in Cardiology 1990, IEEE Computer Society
35. Davis TL: Teaching Physiology Through Interactive Simulation of Hemodynamics, in Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, 1991
36. Guyton AC, Coleman TG, Manning, Jr. Rd, and Hall JE: Some problems and solutions for modeling overall cardiovascular regulation. Math Biosci 72: 141-155, 1984
37. Kenner T: Physical and mathematical modeling in cardiovascular systems. In: Quantitative Cardiovascular Studies, University Park, Baltimore, MD, pp 41-109, 1979
38. White RJ, Fitzjerrell DG, and Croston RD: Fundamentals of Lumped Compartment Modelling of the Cardiovascular System, in Adv. Cardiovasc. Phys., Karger, Basel, pp 162-184, 1983
39. Braakman R, Sipkema P, and Westerhof N: A dynamic nonlinear lumped parameter model for skeletal muscle circulation. Ann Biomed Eng 17: 593-616, 1989
40. Rideout VC, and J Katra: Computer simulation study of the pulmonary circulation. Simulation 12: 239-245, 1969
41. Wang JZ, Tie B, Welkowitz W, Kostis J, and Semmlow J: Incremental network analogue model of the coronary artery. Med Biol Eng Comput 27: 416-422, 1989
42. Zagzoule M, and Marc-Vergnes JP: A global mathematical model of the cerebral circulation in man. J Biomech 19: 1015-1022, 1986
43. Stettler JC, Niederer P, and Anliker M: Theoretical analysis of arterial hemodynamics including the influence of bifurcations. Part I: mathematical models and prediction of normal pulse patterns. Ann Biomed Eng 9: 145-164, 1981
44. Xiao X, Ozawa ET, Huang Y, and Kamm RD: Model-based assessment of cardiovascular health from non-invasive measurements. Ann Biomed Eng 30: 612-623, 2002
45. Ursino M, Coli L, Brighenti C, Chiari L, de Pascalis A, and Avanzolini G: Prediction of solute kinetics, acid-base status, and blood volume changes during profiled hemodialysis. Ann Biomed Eng 28: 204-216, 2000
46. Coli L, Ursino M, De Pascalis A, Brighenti C, Dalmastri V, La Manna G, Isola E, Cianciolo G, Patrono D, Boni P, and Stefoni S: Evaluation of intradialytic solute and fluid kinetics. Setting up a predictive mathematical model. Blood Purif 18: 37-49, 2000
47. Coli L, Bonomini M, La Manna G, Dalmastri V, and Ursino M, Ivanovich P, and Bonomini V. Clinical use of profiled hemodialysis. Artif Organs 22: 724-730, 1998
48. Melchior FM, Srinivasan RS, Ossard G, and Clere J-M: A mathematical model of the cardiovascular response to +Gz acceleration. Physiologist 36 (1 Suppl): S62-S63, 1993
49. Beneken JEW, and DeWitt B: A physical approach to hemodynamic aspects of the human cardiovascular system. In Physical Bases of Circulatory Transport: Regulation and Exchange, Saunders, Philadelphia, pp 1-45, 1967
50. Snyder MF, and Rideout VC: Computer simulation studies of the venous circulation. IEEE Trans Bio-Med Eng 16: 325-334, 1969
51. Luo XY, and Pedley TJ: A numerical simulation of unsteady flow in a 2-D collapsible channel. J Fluid Mech 314: 191-225, 1996
52. Shim EB, and Kamm RD: Numerical simulation of steady flow in a compliant tube or channel with tapered wall thickness, J Fluids Struct 16: 1009-1027, 2002
53. Thomas JD, Zhou J, Greenberg N, Bibawy G, McCarthy PM, and Vandervoort PM: Physical and physiological determinants of pulmonary venous flow: numerical analysis. Am J Physiol 272(5 Pt 2): H2453-H2465, 1997
54. DeBoer RW, Karemaker JM, and Strackee J: Hemodynamic fluctuations and baroreflex sensitivity in humans: a beat- to-beat model. Am J Physiol 253(3 Pt 2): H680-H689, 1987
55. Melchior FM, Srinivasan RS, and Clere JM: Mathematical modeling of human cardiovascular response to LBNP. Physiologist 35 (1 Suppl): S204-S205, 1994
56. Ursino M, Coli L, Brighenti C, Chiari L, de Pascalis A, and Avanzolini G: Prediction of solute kinetics, acid-base status, and blood volume changes during profiled hemodialysis. Ann Biomed Eng 28: 204-216, 2000