Annals of Biomedical Engineering

, Volume 5, Issue 4, pp 329–342 | Cite as

The velocity-strain relationship

Application in normal and abnormal left ventricular function
  • Chandler A. Phillips
Article

Abstract

Left-ventricular dimensions were measured during a complete cardiac cycle from one-plane cineangiograms and used to calculate the circumferential fiber velocity (VCF) and circumferential fiber strain (ε). A velocity-strain (VCF·ε) loop was then constructed for 39 patients. Characteristics of theVCF·ε loop included: peak systolicVCF(+VCF), ε at +VCFS), systolic time constant τS, absolute peak diastolicVCF (|−VCF|), ε at |−VCF| (εD), diastolic time constant τD,VCF≤|−VCF|, εD≤εS, and τD≤τS. The first two inequalities combined provided the best criterion of cardiac decompensation. Only 2 of 15 normal patients, 2 of 6 compensated volume overload patients, and 1 of 3 compensated pressure overload patients satisfied the double inequality. However, 6 of 9 decompensated volume overload patients and 5 of 6 congestive cardiomyopathy patients satisfied the double inequality. Physically, this would imply that with depressed cardiac function: +VCF≤|−VCF| due to a reduced ability of the ventricle to actively contract, εD≤εS (and τD≤τS) due to an increased viscoelastic stiffness of the ventricle. TheVCF·ε loop is independent of pressure, making it possible to acquire noninvasively.

Keywords

Cardiomyopathy Cardiac Cycle Pressure Overload Good Criterion Cardiac Decompensation 

List of Symbols

M

Percentage change of minor axis

lCF

Midwall circumferential fiber length

MD

Minor axis at end-diastole

WD

Wall thickness at end-diastole

ε

Circumferential fiber strain

εmax

Maximum circumferential fiber strain

εD

Diastolic circumferential fiber strain at |−VCF|

εS

Systolic circumferential fiber strain at +VCF

ΔεD

Change in diastolic strain

VCF

Circumferential fiber velocity

+VCF

Peak systolicVCF

|−VCF|

Absolute value of peak diastolicVCF

ΔM

Change in minor L.V. circumference

ΔW

Change in L.V. wall thickness

τ

Time constant

τD

Diastolic time constant

τS

Systolic time constant

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References

  1. Bass, H. The flow-volume loop: normal standards and abnormalities in chronic obstructive pulmonary disease.Chest 1973,62, 171–176.Google Scholar
  2. Doeblin, E. O.Dynamic analysis and feedback control. New York: McGraw-Hill, 1962.Google Scholar
  3. Falsetti, H. L., Mates, R. E., Grant, C., Green, D. G., and Bunnell, I. L. Left ventricular wall stress calculated from one-plane cineangiography.Circulation Research 1970,26, 71–83.PubMedGoogle Scholar
  4. Falsetti, H. L., Geraci, A. R., Bunnell, I. L., Greene, D. G., and Grant, C. Function of left ventricle and extent of coronary artery lesions: Failure of correlation in cineangiographic studies.Chest 1971a,59, 610–617.PubMedGoogle Scholar
  5. Falsetti, H. L., Mates, R. E., Greene, D. G., and Bunnell, I. L.V max as an index of contractile state in man.Circulation 1971b,43, 467–479.PubMedGoogle Scholar
  6. Gaasch, W. H., Bing, O. H. L., Phear, W. P., Clement, J., and Weinbraub, R. M. Relation between acute changes in left ventricular wall thickness and diastolic compliance.Circulation (Abstr.) 1976,54, II-154.Google Scholar
  7. Gault, J. H., Ross, J., Jr., and Braunwald, E. Contractile state of the left ventricle in man.Circulation Research 1968,22, 451–463.PubMedGoogle Scholar
  8. Gould, K. L., Lipscomb, K., Hamilton, G. W., and Kennedy, J. W. Relation of left ventricular shape, function and wall stress in man.American Journal of Cardiology 1974,34, 627–634.PubMedGoogle Scholar
  9. Greene, D. G., Carlisle, R., Grant, C., and Bunnell, I. L. Estimation of left ventricular volume by one-plane cineangiography.Circulation 1967,35, 61–69.PubMedGoogle Scholar
  10. Hammermeister, K. E., Brooks, R. C., and Warbasse, J. R. The rate of change of left ventricular volume in man.Circulation 1974,49, 729–738.PubMedGoogle Scholar
  11. Karliner, J. S., Gault, J. H., Eckberg, D., Mullins, C. B., and Ross, J., Jr. Mean velocity of fiber shortening.Circulation 1971,44, 323–333.PubMedGoogle Scholar
  12. Katz, A. M.V max as an index of contractile state in man: Letters to the editor.Circulation 1972,45, 925–927.PubMedGoogle Scholar
  13. Lewis, R. P., and Sandler, H., Relationship between changes in left ventricular dimensions and the ejection fraction in man.Circulation 1971,44, 548–557.PubMedGoogle Scholar
  14. Mack, C.Essentials of statistics for scientists and technologists. New York: Plenum, 1967.Google Scholar
  15. Mann, T., Brodie, B., and McLaurin, L. The effect of ischemia on the left ventricular diastolic pressure-volume relationship.Circulation (Abstr.) 1976,54, II-65.Google Scholar
  16. Mirsky, I., and Parmley, W. W. Evaluation of passive elastic stiffness for the left ventricle and isolated heart muscle. In I. Mirsky, D. Ghista, and H. Sandler (Eds.),Cardiac mechanics: Physiological, clinical and mathematical considerations. New York: Wiley, 1974. Pp. 331–358.Google Scholar
  17. Phillips, C. A., Grood, E. S., and Schuster, B.An energetic evaluation of cardiac contraction. University of Dayton Research Institute, Dayton, Ohio, UDRI-TR-74-54, 1974.Google Scholar
  18. Phillips, C. A., Grood, E. S., Mates, R. E., and Falsetti, H. L. Left ventricular area ratios: Comparison of the longitudinal and circumferential directions and correlation with left ventricular function.ASME Advances in Bioengineering 1977, in press.Google Scholar
  19. Rotman, H. H., Liss, H. P., and Weg, J. C. Diagnosis of upper airway obstruction by pulmonary function testing.Chest 1975,68, 796–799.PubMedGoogle Scholar

Copyright information

© Academic Press, Inc. 1977

Authors and Affiliations

  • Chandler A. Phillips
    • 1
  1. 1.The Departments of Engineering and PhysiologyWright State UniversityDayton

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