Skip to main content
SpringerLink
Log in

A LabVIEW™ Model Incorporating an Open-Loop Arterial Impedance and a Closed-Loop Circulatory System

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

While numerous computer models exist for the circulatory system, many are limited in scope, contain unwanted features or incorporate complex components specific to unique experimental situations. Our purpose was to develop a basic, yet multifaceted, computer model of the left heart and systemic circulation in LabVIEW™ having universal appeal without sacrificing crucial physiologic features. The program we developed employs Windkessel-type impedance models in several open-loop configurations and a closed-loop model coupling a lumped impedance and ventricular pressure source. The open-loop impedance models demonstrate afterload effects on arbitrary aortic pressure/flow inputs. The closed-loop model catalogs the major circulatory waveforms with changes in afterload, preload, and left heart properties. Our model provides an avenue for expanding the use of the ventricular equations through closed-loop coupling that includes a basic coronary circuit. Tested values used for the afterload components and the effects of afterload parameter changes on various waveforms are consistent with published data. We conclude that this model offers the ability to alter several circulatory factors and digitally catalog the most salient features of the pressure/flow waveforms employing a user-friendly platform. These features make the model a useful instructional tool for students as well as a simple experimental tool for cardiovascular research.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alexander, J., K. Sunagawa, N. Chang, and K. Sagawa. Instantaneous pressure–volume relation of the ejecting canine left atrium. Circ. Res. 61(2):209–219, 1987.

    Google Scholar 

  2. Arnold, J. M. O., G. E. Marchiori, J. R. Imrie, G. L. Burton, P. W. Pflugfelder, and W. J. Kostuk. Large artery function in patients with chronic heart failure. Circulation 84:2418–2425, 1991.

    Google Scholar 

  3. Burkhoff, D., D. Kass, W. L. Maughan, and A. Kolandaivelu. CVSIM v1.5. http://oac.med.jhmi.edu/cvsim/; 1998.

  4. Chen, C.-W., Y.-W. R. Shau, and C.-P. Wu. Analog transmission line model for simulation of systemic circulation. IEEE Trans. Biomed. Eng. 44(1):90–94, 1997.

    Google Scholar 

  5. Chung, D. C., S. C. Niranjan, J. W. Clark, Jr., A. Bidani, W. E. Johnston, J. B. Zwischenberger, and D. L. Traber. A dynamic model of ventricular interaction and pericardial influence. Am. J. Physiol. 272:H2942–H2962, 1997 (Heart Circ. Physiol. 41).

    Google Scholar 

  6. Danielsen, M. Modeling of feedback mechanisms which control the heart function in a view to an implementation in cardiovascular models. In: Mathematics, 2nd ed. Roskilde: Roskilde University, 1998, p. 145.

  7. Danielsen, M., and J. T. Ottesen. Describing the pumping heart as a pressure source. J. Theor. Biol. 212:71–81, 2001.

    Article  Google Scholar 

  8. Danielsen, M., J. L. Palladino, and A. Noordergraaf. The left ventricular ejection effect. In: Mathematical Modeling in Medicine, edited by J. T. Ottesen and M. Danielsen. Netherlands: IOS Press, 2000, pp. 13–28.

  9. Dankelman, J., H. G. Stassen, and J. A. E. Spaan. Coronary circulation mechanics. In: Coronary Circulation: Basic Mechanism and Clinical Relevance, edited by F. Kajiya, G. A. Klassen, J. A. E. Spaan, and J. I. E. Hoffman, New York: Springer-Verlag, 1990, pp. 75–87.

  10. Davis, M. J., and R. W. Gore. Determinants of cardiac function: simulation of a dynamic cardiac pump for physiology instruction. Adv. Physiol. Educ. 25(1):13–35, 2001.

    Google Scholar 

  11. Elzinga, G., and N. Westerhof. Pressure and flow generated by the left ventricle against different impedances. Circ. Res. 32(2):178–186, 1973.

    Google Scholar 

  12. Ferrari, G., M. Kozarski, C. De Lazzari, F. Clemente, M. Merolli, G. Tosti, M. Guaragno, R. Mimmo, D. Ambrosi, and J. Glapinski. A hybrid (numerical-physical) model of the left ventricle. Int. J. Artif. Organs 24(7):456–462, 2001.

    Google Scholar 

  13. Finkelstein, S. M., J. N. Cohn, V. R. Collins, P. F. Carlyle, and W. J. Shelley. Vascular hemodynamic impedance in congestive heart failure. Am. J. Cardiol. 55:423–427, 1985.

    Article  Google Scholar 

  14. Goerke, J. Jon Goerke's Arterial Simulation. http:// hemodynamics.ucdavis.edu/.

  15. Grossman, W., E. Braunwald, and T. Mann. Contractile state of the left ventricle in man as evaluated from end-systolic pressure–volume relations. Circulation 56(5):845–852, 1977.

    Google Scholar 

  16. Guyton, A. C., and J. E. Hall. Textbook of Medical Physiology, 10th ed. Philadelphia: Saunders, 2000.

  17. Hoffman, J. I. E. Pressure–flow relationships of the coronary arteries. In: Coronary Circulation: Basic Mechanisms and Clinical Relevance, edited by F. Kajiya, G. A. Klassen, J. A. E. Spaan, and J. I. E. Hoffman. New York: Springer-Verlag, 1990, pp. 109–125.

  18. Kleinbaum, D. G., and L. L. Kupper. Applied Regression Analysis and Other Multivariable Methods. North Scituate, MA: Duxbury Press, Division of Wadsworth Publishing Company Inc., 1978.

  19. Laskey, W. K., and W. G. Kussmaul. Arterial wave reflection in heart failure. Circulation 75(4):711–722, 1987.

    Google Scholar 

  20. Liu, Z., F. Shen, and F. C. P. Yin. Impedance of arterial system simulated by viscoelastic t tubes terminated in windkessels. Am. J. Physiol. 256(4 Pt 2):H1087–H1099, 1989.

    Google Scholar 

  21. Lu, K., J. W. Clark, Jr., F. H. Ghorbel, C. S. Robertson, D. L. Ware, J. B. Zwischenberger, and A. Bidani. Cerebral autoregulation and gas exchange studied using a human cardiopulmonary model. Am. J. Physiol. 286:H584–H601, 2003 (Heart Circ. Physiol.).

    Google Scholar 

  22. Lucas, C. L. Fluid mechanics of the pulmonary circulation. CRC Crit. Rev. Biomed. Eng. 10(4):317–392, 1984.

    Google Scholar 

  23. Mantero, S., R. Pietrabissa, and R. Fumero. The coronary bed and its role in the cardiovascular system: A review and an introductory single-branch model. J. Biomed. Eng. 14:109–116, 1992.

    Google Scholar 

  24. Maruyama, Y., and T. Takishima. Effect of ventricular and extraventricular pressure on the coronary artery pressure–flow relationship. In: Coronary Circulation: Basic Mechanisms and Clinical Relevance, edited by F. Kajiya, G. A. Klassen, J. A. E. Spaan, and J. I. E. Hoffman. New York: Springer-Verlag, 1990, pp. 127–138.

  25. Maughan, W. L., and K. Sunagawa. Factors affecting the end-systolic pressure–volume relationship. Fed. Proc. 43(9):2408–2410, 1984.

    Google Scholar 

  26. Maughan, W. L., K. Sunagawa, D. Burkhoff, and K. Sagawa. Effect of arterial impedance changes on end-systolic pressure–volume relation. Circ. Res. 54(5):595–602, 1984.

    Google Scholar 

  27. Mulier, J. P. Ventricular pressure as a function of volume and flow. University of Leuven, Belgium, 1994.

  28. Murgo, J. P., N. Westerhof, J. P. Giolma, and S. A. Altobelli. Aortic input impedance in normal man: Relationship to pressure wave forms. Circulation 62(1):105–116, 1980.

    Google Scholar 

  29. Murgo, J. P., N. Westerhof, J. P. Giolma, and S. A. Altobelli. Effects of exercise on aortic input impedance and pressure wave forms in normal humans. Circ. Res. 48(3):334–343, 1981.

    Google Scholar 

  30. Nichols, W. W., C. R. Conti, W. E. Walker, and W. R. Milnor. Input impedance of the systemic circulation in man. Circ. Res. 40(5):451–458, 1977.

    Google Scholar 

  31. Nichols, W. W., M. F. O'Rourke, and C. Hartley. McDonald's blood flow in arteries: Theoretical, experimental and clinical principles, 4th ed. London: Arnold, 1998.

  32. Nishioka, O., Y. Maruyama, K. Ashikawa, S. Isoyama, S. Satoh, J. Watanabe, Y. Shimizu, and T. Takishima. Load dependency of end-systolic pressure–volume relations in isolated, ejecting canine hearts. Jpn. Heart J. 29(5):709–722, 1988.

    Google Scholar 

  33. Noble, M. I. Left ventricular load, arterial impedance and their interrelationship. Cardiovasc. Res. 13(4):183–198, 1979.

    Article  MathSciNet  Google Scholar 

  34. O'Rourke, M. F. Arterial Function in Health and Disease. Edinburgh, NY: Churchill Livingstone, 1982.

  35. Olansen, J. B., J. W. Clark, D. Khoury, F. Ghorbel, and A. Bidani. A closed-loop model of the canine cardiovascular system that includes ventricular interaction. Comput. Biomed. Res. 33:260–295, 2000.

    Article  Google Scholar 

  36. Ottesen, J. T. Modelling of the baroreflex-feedback mechanism with time-delay. J. Math. Biol. 36:41–63, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  37. Ottesen, J. T. Nonlinearity of baroreceptor nerves. Surv. Math. Ind. 7:187–201, 1997.

    MATH  Google Scholar 

  38. Ottesen, J. T. Modelling the dynamical baroreflex-feedback control. Math. Comp. Model. 31:167–173, 2000.

    Google Scholar 

  39. Ottesen, J. T., and M. Danielsen. Modeling ventricular contraction with heart rate changes. J. Theor. Biol. 222:337–346, 2003.

    Article  MathSciNet  Google Scholar 

  40. Ottesen, J. T., M. S. Olufsen, and J. K. Larsen. Applied Mathematical Models in Human Physiology. Philadelphia: SIAM, 2004.

  41. Palladino, J. L., G. M. Drzewiecki, and A. Noordergraaf. Modeling strategies in physiology. In: The Biomedical Engineering Handbook, edited by J. D. Bronzino. Boca Raton, FL: CRC Press, IEEE Press, 1995, pp. 2367–2374.

  42. Palladino, J. L., J. P. Mulier, and A. Noordergraaf. Closed-loop circulation model based on the Frank mechanism. Surv. Math. Ind. 7:177–186, 1997.

    MATH  Google Scholar 

  43. Palladino, J. L., J. P. Mulier, F. Wu, M. Moser, T. Kenner, R. M. Baevsky, and A. Noordergraaf. Assessing the state of the circulatory system via parameters vs. variables. J. Cardiovasc. Diagnosis Procedures 13(2):131–139, 1996.

    Google Scholar 

  44. Palladino, J. L., and A. Noordergraaf. The changing view of the heart through the centuries. Stud. Health Technol. Inform. 71:3–11, 2000.

    Google Scholar 

  45. Palladino, J. L., L. C. Ribeiro, and A. Noordergraaf. Human circulatory system model based on Frank's mechanism. In: Mathematical Modeling in Medicine, edited by J. T. Ottesen and M. Danielsen. Thes Netherlands: IOS Press, 2000, pp. 29–40.

  46. Paulus, W. J., V. A. Claes, and D. L. Brutsaert. End-systolic pressure–volume relation estimated from physiologically loaded cat papillary muscle contractions. Circ. Res. 47(1):20–26, 1980.

    Google Scholar 

  47. Pepine, C. J., W. W. Nichols, and C. R. Conti. Aortic input impedance in heart failure. Circulation 58(3):460–465, 1978.

    Google Scholar 

  48. Pietrabissa, R., S. Mantero, T. Marotta, and L. Menicanti. A lumped parameter model to evaluate the fluid dynamics of different coronary bypasses. Med. Eng. Phys. 18:477–484, 1996.

    Article  Google Scholar 

  49. Rideout, V. C. Mathematical and Computer Modeling of Physiological Systems. Madison, WI: Medical Physics Publishing, 1991.

  50. Rose, W. C., and A. A. Shoukas. Two-port analysis of systemic venous and arterial impedances. Am. J. Physiol. 265:H1577–H1587, 1993 (Heart Circ. Physiol. 34).

    Google Scholar 

  51. Sagawa, K. The ventricular pressure–volume diagram revisited. Circ. Res. 43(5):677–687, 1978.

    Google Scholar 

  52. Sagawa, K. The end-systolic pressure–volume relation of the ventricle: Definition, modifications and clinical use. Circulation 63(6):1223–1227, 1981.

    Google Scholar 

  53. Sagawa, K., L. Maughan, H. Suga, and K. Sunagawa. Cardiac Contraction and the Pressure–Volume Relationship. New York: Oxford University Press, 1988.

  54. Stergiopulos, N., B. E. Westerhof, and N. Westerhof. Total arterial inertance as the fourth element of the windkessel model. Am. J. Physiol. 276(1 Pt 2):H81–H88, 1999.

    Google Scholar 

  55. Suga, H., and K. Sagawa. Instantaneous pressure–volume relationships and their ratio in the excised, supported canine left ventricle. Circ. Res. 35(1):117–126, 1974.

    Google Scholar 

  56. Sunagawa, K., W. L. Maughan, G. Friesinger, P. Guzman, M.-S. Chang, and K. Sagawa. Effects of coronary arterial pressure on left ventricular end-systolic pressure–volume relation of isolated canine heart. Circ. Res. 50(5):727–734, 1982.

    Google Scholar 

  57. Sunagawa, K., K. Sagawa, and W. L. Maughan. Ventricular interaction with the loading system. Ann. Biomed. Eng. 12(2):163–189, 1984.

    Google Scholar 

  58. Timmons, W. D. Cardiovascular models and control. In: The Biomedical Engineering Handbook, edited by J. D. Bronzino. Boca Raton, FL: CRC Press, IEEE Press, 1995, pp. 2386–2403.

  59. Tsitlik, J. E., H. R. Halperin, A. S. Popel, A. A. Shoukas, F. C. P. Yin, and N. Westerhof. Modeling the circulation with three-terminal electrical networks containing special non-linear capacitors. Ann. Biomed. Eng. 20:595–616, 1992.

    Google Scholar 

  60. Tsujioka, K., M. Goto, O. Hiramatsu, Y. Wada, Y. Ogasawara, and F. Kajiya. Functional characteristics of intramyocardial capacitance vessels and their effects on coronary arterial inflow and venous outflow. In: Coronary Circulation: Basic Mechanisms and Clinical Relevance, edited by F. Kajiya, G. A. Klassen, J. A. E. Spaan, and J. I. E. Hoffman. New York: Springer-Verlag, 1990, pp. 89–97.

  61. Ursino, M. Interaction between carotid baroregulation and the pulsating heart: A mathematical model. Am. J. Physiol. 275:H1733–H1747, 1998 (Heart Circ. Physiol. 44).

    Google Scholar 

  62. Ursino, M., M. Antonucci, and E. Belardinelli. Role of active changes in venous capacity by the carotid baroreflex: Analysis with a mathematical model. Am. J. Physiol. 267:H2531–H2546, 1994 (Heart Circ. Physiol. 36).

    Google Scholar 

  63. Watanabe, I., T. A. Johnson, C. L. Engle, C. Graebner, M. G. Jenkins, and L. S. Gettes. Effects of Verapamil and Propranolol on changes in extracellular K +, pH, and local activation during graded coronary flow in the pig. Circulation 79(4):939–947, 1989.

    Google Scholar 

  64. Watt, T. B., and C. S. Burrus. Arterial pressure contour analysis for estimating human vascular properties. J. Appl. Physiol. 40(2):171–176, 1976.

    Google Scholar 

  65. Westerhof, N. Arterial haemodynamics. In: The Physics of Heart and Circulation, edited by J. Strackee and N. Westerhof. Philadelphia: Institute of Physics Pub., 1993, pp. 355–381.

  66. Westerhof, N., and G. Elzinga. Normalized input impedance and arterial decay time over heart period are independent of animal size. Am. J. Physiol. 261(1 Pt 2):R126–R133, 1991.

    Google Scholar 

  67. Westerhof, N., G. Elzinga, and S. Pieter. An artificial system for pumping hearts. J. Appl. Physiol. 31(5):776–781, 1971.

    Google Scholar 

  68. Zamir, M. The Physics of Pulsatile Flow. New York: Springer-Verlag, 2000.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Biomedical Engineering, University of North Carolina at Chapel Hill, 150 MacNider Hall, Chapel Hill, NC, 27599

    R. T. Cole & C. L. Lucas

  2. Division of Cardiology, Department of Internal Medicine, The Brody School of Medicine, East Carolina University, Greenville, NC, 27834

    W. E. Cascio & T. A. Johnson PhD (Professor of Medicine)

  3. Division of Cardiology, Department of Internal Medicine, The Brody School of Medicine, East Carolina University, Brody 3E-116D, Greenville, NC, 27834

    T. A. Johnson PhD (Professor of Medicine)

Authors
  1. R. T. Cole
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. L. Lucas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. E. Cascio
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. T. A. Johnson PhD
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. A. Johnson PhD.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cole, R.T., Lucas, C.L., Cascio, W.E. et al. A LabVIEW™ Model Incorporating an Open-Loop Arterial Impedance and a Closed-Loop Circulatory System. Ann Biomed Eng 33, 1555–1573 (2005). https://doi.org/10.1007/s10439-005-7785-1

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-005-7785-1

Key Words

Search

Navigation