Fig 1.
Length-dependent activation, the Frank-Starling mechanism and vascular filling therapy.
Length-dependent activation (LDA) is a cardiac cell property highlighted by the length-tension relationship (left). As the length of the cardiac cell increases, the peak force during an isometric twitch contraction increases. It is commonly admitted that LDA underlies the Frank-Starling (FS) mechanism, a property of the cardiac pump (right). As the length of cardiac fibers prior to contraction (namely, the preload) increases, the ejected blood volume (namely, the stroke volume) increases, up to physiological limits. The FS mechanism is also often assumed to be the basis for fluid therapy. If the patient is operating on the “ascending portion” of the FS curve, the patient is said to be “fluid-responsive”, as a substantial stroke volume increase should be observed upon vascular filling. In this study, we revisit the three concepts of LDA, FS mechanism, and vascular filling and we build a computational model of the human cardiovascular system to investigate thoroughly the true nature of the relationship between the latter.
Fig 2.
6-chamber lumped-parameter model of the cardiovascular system.
Ventricular contraction is described at the cellular scale. The left and right ventricles are assimilated to spheres, and the force and length of a half-sarcomere are connected to the pressure and volume within the ventricular chambers.
Fig 3.
The half-sarcomere model describes the total force Fm produced by an active contractile element of length L (A). The crossbridges kinetic cycle is described with a 5-state model (B). The states highlighted in red correspond to attached crossbridges. Two of the rate constants, f and gd, are functions of the half-sarcomere length L (see Eqs 2–3).
Fig 4.
Length-tension relationship obtained with the half-sarcomere model.
This curve is similar to Fig 11A from [51], as we use the same set of parameters for the crossbridge cycle rate constants. Force is normalized to the muscle cross-sectional area and is thus expressed in mN/mm2.
Fig 5.
Baseline results obtained with the CVS model.
These curves, that describe normal (healthy) hemodynamical conditions, are similar to Fig 5 from [49]. Time values on the PV loop indicate the beginning of each phase of the cardiac cycle for an 800 ms heartbeat.
Fig 6.
Half-sarcomere length LBL during a baseline heartbeat (normal hemodynamics conditions) (A). Associated attachment rate f (B) and irreversible detachment rate gd (C). These rates are used as input functions for the NO LDA model, in such a way that panels B and C also correspond to the attachment rate f and irreversible detachment rate gd for the NO LDA case.
Fig 7.
Left ventricular PV loops from the BL, IIP and IIP NO LDA simulations.
IIP starts during ventricular filling (black dot). PV loop for the baseline case (blue) corresponds to a stabilized behavior (each heartbeat leads to that same PV loop). On the other hand, the two PV loops for the IIP protocols (red dashed or solid lines) correspond to a transient response to a preload change. The behavior is not stabilized yet, as this would take several more heartbeats to return to the baseline state. Those PV loops are thus not closed, but this it cannot be seen in the picture.
Table 1.
Quantitative comparison of the BL, IIP and IIP NO LDA simulations.
See text for detailed explanations.
Fig 8.
A. Ventricular and aortic pressures during a BL (blue), IIP (red), and IIP NO LDA (dashed red) simulation protocol. B. Corresponding aortic flows. The aortic flow amplitude (inset) and ejection duration (black arrow) increase for the IIP protocol compared to the BL case, but not for the IIP NO LDA protocol.
Fig 9.
Frank-Starling curve obtained with the CVS model.
Fig 10.
Stroke volume increases with filling, up to a saturating plateau. The red filled circle corresponds to the BL case (normal hemodynamics conditions).
Fig 11.
A. Maximal left ventricular pressure during vascular filling simulations. B. Aortic pressure at valve opening during vascular filling simulations. The latter is used to quantify the afterload.
Fig 12.
Blood ejection duration during vascular filling simulations.
Fig 13.
A. Maximal left ventricular force with (blue curve) and without (red curve) LDA. B. Maximal left ventricular pressure with (blue curve) and without (red curve) LDA. C. Afterload with (blue curve) and without (red curve) LDA. D. Stroke volume with (blue curve) and without (red curve) LDA.
Fig 14.
Visual representation of the interplay between the FS mechanism, vascular filling, and LDA.
LDA, a cellular property, underlies the FS mechanism. The latter occurs at the organ scale on a beat-to-beat basis. LDA also underlies the motivation for vascular filling therapy. As vascular filling takes place, a new steady state is obtained after several heartbeats and a new stroke volume is achieved. Stroke volume, preload, and filling are variables which also impact or depend on cardiovascular-level variables, such as afterload. Each curve is a qualitative curve, as this figure is built from the qualitative conclusions of our study.