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The velocity-strain relationship

Application in normal and abnormal left ventricular function

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Abstract

Left-ventricular dimensions were measured during a complete cardiac cycle from one-plane cineangiograms and used to calculate the circumferential fiber velocity (V CF) and circumferential fiber strain (ε). A velocity-strain (V CF·ε) loop was then constructed for 39 patients. Characteristics of theV CF·ε loop included: peak systolicV CF(+V CF), ε at +V CFS), systolic time constant τS, absolute peak diastolicV CF (|−V CF|), ε at |−V CF| (εD), diastolic time constant τD,V CF≤|−V CF|, 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: +V CF≤|−V CF| 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. TheV CF·ε loop is independent of pressure, making it possible to acquire noninvasively.

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Abbreviations

M :

Percentage change of minor axis

l CF :

Midwall circumferential fiber length

M D :

Minor axis at end-diastole

W D :

Wall thickness at end-diastole

ε:

Circumferential fiber strain

εmax :

Maximum circumferential fiber strain

εD :

Diastolic circumferential fiber strain at |−V CF|

εS :

Systolic circumferential fiber strain at +V CF

ΔεD :

Change in diastolic strain

V CF :

Circumferential fiber velocity

+V CF :

Peak systolicV CF

|−V CF|:

Absolute value of peak diastolicV CF

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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Phillips, C.A. The velocity-strain relationship. Ann Biomed Eng 5, 329–342 (1977). https://doi.org/10.1007/BF02367313

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  • DOI: https://doi.org/10.1007/BF02367313

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