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Force interval relationship (FIR) related to the global function of the left ventricle: a computer study

  • Biomechanics
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Abstract

A model which relates the left ventricular (LV) geometry, structure and sarcomere properties to its global function, recently proposed by the authors, is extended to account for contractility changes which are a function of the heart rate, prematurity of the beat and calcium transients within the cell. To characterise LV function and relate it to fibre function under varying rhythm conditions, a model of muscle force restitution, based on calcium kinetics, was used to calculate the maximum fibre stress at the optimum sarcomere length σ0 as the parameter which depends on the heart rate, the test pulse interval TPI, the action potential duration APD and the restitution time constant. The global LV force interval relationship FIR was then calculated, and by comparing the calculated FIR to the experimental measurement (in dogs) at the ventricular level, the constants of the restitution of force at the fibre level were derived. Based on these constants, the LV function under ejecting conditions at various rhythm disturbances was calculated and related to the local, distributed parameters. This approach provides a tool to describe ventricular function as well as transmural distribution of stress and sarcomere length at a wide variety of loading and rhythm conditions based on given ‘muscle level’ parameters.

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Abbreviations

a 1,a 2 :

constants, eqn. 1

APD :

action potential duration

b 1,b 2 :

constants, eqn. 3

c 1,c 2 :

constants, eqn. 5

C R max :

maximum(dp/dt) max assuming sufficient restitution time

(dp/dt) max :

maximum pressure/time derivative

(dp/dt) max, n :

normalised(dp/dt) max [=(dp/dt) max /(dp/dt) max, ss ]

(dp/dt) max, ss :

maximum pressure/time derivative at steady state

EF :

ejection fraction

E max :

maximum elastance

FIR:

force interval relationship

HR :

heart rate, min−1

SL :

sarcomere length

ss :

steady state

TC :

time of contraction, including systolic and relaxation durations

TDI :

time from end of depolarisation to beginning of next depolarisation wave

TPI :

time interval between the previous pulse and the test pulse

T es :

time to reach point of end systole

π0 :

maximum stress at optical sarcomere length

π0,n :

normalised maximum stress [=π0/π0,ss]

σ R max :

maximum stress at optimal sarcomere length assuming complete restitution of the contractility at the given basalHR

τ:

time constant for mechanical restitution of the LV system

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Authors and Affiliations

  1. Julius Silver Institute of Biomedical Engineering, Technion-Israel Institute of Technology, 32000, Technion City, Haifa, Israel

    R. Beyar & S. Sideman

  2. Department of Chemical Engineering, Technion-Israel Institute of Technology, 32000, Technion City, Haifa, Israel

    R. Beyar & S. Sideman

  3. Department of Biomedical Engineering, Johns Hopkins Medical School, 21218, Baltimore, MD, USA

    D. Burkhoff

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  1. R. Beyar
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  2. D. Burkhoff
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  3. S. Sideman
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Beyar, R., Burkhoff, D. & Sideman, S. Force interval relationship (FIR) related to the global function of the left ventricle: a computer study. Med. Biol. Eng. Comput. 28, 446–456 (1990). https://doi.org/10.1007/BF02441968

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  • DOI: https://doi.org/10.1007/BF02441968

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