Greaser, Thomas C. Irving, and Pieter P. USA 8 , february 23, This research used resources of the Advanced Photon Source, a U. Toggle navigation BioCAT. When venous return is increased, there is increased filling of the ventricle along its passive pressure curve leading to an increase in end-diastolic volume see Figure. If the ventricle now contracts at this increased preload, and the afterload and inotropy are held constant, the ventricle empties to the same end-systolic volume, thereby increasing its stroke volume, which is defined as end-diastolic minus end-systolic volume.
The increased stroke volume is displayed as an increase in the width of the pressure-volume loop. The normal ventricle, therefore, is capable of increasing its stroke volume to match physiological increases in venous return. This is not, however, the case for ventricles that are in failure. Increased venous return increases the ventricular filling end-diastolic volume and therefore preload , which is the initial stretching of the cardiac myocytes prior to contraction. Myocyte stretching increases the sarcomere length , which causes an increase in force generation and enables the heart to eject the additional venous return, thereby increasing stroke volume.
This phenomenon can be described in mechanical terms by the length-tension and force-velocity relationships for cardiac muscle. Increasing preload increases the active tension developed by the muscle fiber and increases the velocity of fiber shortening at a given afterload and inotropic state. One mechanism to explain how preload influences contractile force is that increasing the sarcomere length increases troponin C calcium sensitivity, which increases the rate of cross-bridge attachment and detachment, and the amount of tension developed by the muscle fiber see Excitation-Contraction Coupling.
At the heart scale, it is commonly admitted that an increase in preload ventricular filling leads to an increased cellular force and an increased volume of ejected blood. This explanation also forms the basis for vascular filling therapy.
It is actually difficult to unravel the exact nature of the relationship between length-dependent activation and the Frank-Starling mechanism, as three different scales cellular, ventricular and cardiovascular are involved. Mathematical models are powerful tools to overcome these limitations.
In this study, we use a multiscale model of the cardiovascular system to untangle the three concepts length-dependent activation, Frank-Starling, and vascular filling. We first show that length-dependent activation is required to observe both the Frank-Starling mechanism and a positive response to high vascular fillings. Our results reveal a dynamical length dependent activation-driven response to changes in preload, which involves interactions between the cellular, ventricular and cardiovascular levels and thus highlights fundamentally multiscale behaviors.
We show however that the cellular force increase is not enough to explain the cardiac response to rapid changes in preload. We also show that the absence of fluid responsiveness is not related to a saturating Frank-Starling effect.
As it is challenging to study those multiscale phenomena experimentally, this computational approach contributes to a more comprehensive knowledge of the sophisticated length-dependent properties of cardiac muscle.
It is commonly admitted that the length-dependent activation is the cellular property underlying the Frank-Starling mechanism. However, it is challenging to assess the cardiac cell length in vivo , and to link it to system-level variables. In this study, we investigated the relationship between length-dependent activation LDA , the Frank-Starling mechanism, and vascular filling therapy using a multiscale model of the cardiovascular system.
We showed that the Frank-Starling mechanism is a multiscale, dynamical and LDA-driven phenomenon involving essential connections between the three cellular, ventricular and cardiovascular scales. We also demonstrated that the response to vascular filling therapy is similarly multiscale and LDA-driven, and that afterload is an important factor to account for when trying to predict the system fluid responsiveness.
Citation: Kosta S, Dauby PC Frank-Starling mechanism, fluid responsiveness, and length-dependent activation: Unravelling the multiscale behaviors with an in silico analysis. PLoS Comput Biol 17 10 : e This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Competing interests: The authors have declared that no competing interests exist. The Frank-Starling FS mechanism [ 1 , 2 ] is an important cardiac property addressed in every cardiology book.
It states that the heart is able to adapt the ejected blood volume to the venous return on a beat-to-beat basis see Fig 1. As more blood enters the ventricle, preload, defined as the length of cardiac fibers prior to contraction, increases. As a consequence, stroke volume increases up to physiological limits. 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. 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. 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. They came up with the idea of a "family of Starling curves".
For a fixed inotropic state, their studies indicate that there is always a direct relationship to be found between preload and cardiac output. Braunwald and colleagues studied the FS mechanism in human patients [ 5 — 9 ].
Working with a variety of protocols and measurements methods, they concluded that the FS mechanism is present in man. Actually, many studies confirmed this intrinsic ability of the heart to accommodate changes in preload [ 10 ], thus corroborating the early findings of Starling: "Within wide limits, the heart is able to increase its output in direct proportion to the inflow. It is important to note that different experimental protocols can be used to induce preload changes [ 6 — 8 , 12 — 17 ].
However, measuring the preload that is, the length of cardiac fibers prior to contraction is not really achievable in vivo , so there is an experimental need for a preload index, i. Among the ventricular preload indices, we can cite the end-diastolic volume, the end-diastolic pressure, or the right atrial pressure. All these indices have however shown their limitations [ 10 , 18 — 21 ], and the search for an ideal preload index is still going on. Such curves are generally supposed to represent cardiac output variations upon change in preload, all other variables remaining constant.
Since this procedure is hard to obtain experimentally, such curves are built as an ideal representation of the FS mechanism, rather than on experimental data, and thus they are mainly qualitative. It is commonly admitted that the FS mechanism has a cellular origin, and that it arises from the length-dependent properties of the cardiac cells.
There is still a debate about the molecular mechanisms that are involved in LDA [ 27 , 28 ]. Myosins are recruited from this super-relaxed state during activation to contribute to cross-bridge cycling and force-production. Once activation ends, most myosins come back to the OFF state. Some authors suggest that the recruitment from the OFF state could be force-dependent and may explain the increase in isometric force upon cell lengthening via a mechanosensing mechanism [ 31 ].
Hence, the giant protein titin, responsible for the passive elastic properties of the sarcomere, could be driving the length-dependent properties of force production [ 32 ]. The myosin-binding protein C, an important regulator of cardiac function, has also been proposed as key modulator of LDA [ 33 ]. Even if the LDA molecular mechanisms are complex and not fully elucidated yet, the generally admitted explanation regarding the cellular origins of the FS mechanism goes as follows [ 25 , 34 ]: if cardiac cell length increases, then the maximal produced force increases signature of LDA , and so does the pressure and the amount of blood ejected by the ventricle.
Here a delicate point must be highlighted: LDA is a cellular property that is mainly studied and described in isometric cellular experiments, where the cell length is fixed. On the other hand, the FS mechanism occurs in vivo , where cell length changes during the cardiac cycle.
It has already been underlined that the length-tension relationship and the Starling Law could not directly be put in parallel [ 35 — 38 ]. It has also been shown that preload affects the velocity of shortening in isotonic experiments [ 39 ], and the timing and magnitude of contraction in auxotonic conditions [ 40 , 41 ].
The "positive effect of ejection" highlighted by Hunter [ 42 ] reveals how preload, among other parameters, may affect the whole dynamics of an ejecting beat [ 26 , 42 , 43 ]. These properties are rarely cited when discussing the cellular basis for the FS mechanism.
The latter is somehow always associated with an increase in peak force following an increase in fiber length. The impact of preload on the whole dynamics of cardiac contraction is more rarely discussed. It is especially important to investigate this question, as the FS mechanism is also assumed to be the basis for fluid therapy [ 20 , 44 — 46 ].
This therapy consists in intravenous administrations of fluid to a patient in order to restore their cardiac output. Indeed, an increase in circulating blood volume leads to an increase in preload and thus triggers the FS mechanism. As explained above, experimental difficulties may arise regarding the study of the FS mechanism. In particular, the connection between the FS mechanism and LDA or other cellular mechanisms is difficult to unravel experimentally, as three very different scales cellular, ventricular and cardiovascular are involved.
Mathematical modeling of biological system is a growing field that helps complement the experimental data. Once validated, a model can overcome the experimental limitations and become a powerful instrument, either for clinical purposes, or for broadening physiological knowledge [ 47 , 48 ].
Regarding the FS mechanism, a multiscale model of the cardiovascular system CVS would help link the cellular properties namely, LDA to the ventricular and cardiovascular observations namely, the stroke volume variations in response to preload variations , while providing a formal framework to integrate the experimental observations coming from the three scales. In this paper, such a multiscale model is described, and in silico protocols are proposed to analyze the FS mechanism in the left ventricle, its relationship with LDA and its relevance to fluid therapy.
In the following sections, our mathematical model of the CVS is described. Then vascular filling simulations are carried out to further analyze the LDA function in fluid responsiveness. Our multiscale model of the human cardiovascular system has already been described elsewhere, and the interested reader is referred to references [ 49 , 50 ] for all details and notations.
The whole model equations and parameters can be found in the supplementary material S1 Appendix , and it corresponds to the model presented in [ 50 ], where a few hemodynamical parameters were changed compared to [ 49 ] see Table C from S1 Appendix. Briefly, the CVS is represented as a 6-chamber lumped-parameter model see Fig 2. A simple thick sphere model for the left and right ventricles allows connecting the force and length produced by a half-sarcomere model [ 51 , 52 ] to the pressure and blood volume inside a spherical ventricle model [ 53 ].
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. Now more details are provided regarding LDA inside the model [ 49 , 51 , 52 ]. The biochemistry of the half-sarcomere contraction is described with a calcium kinetic model as shown in Fig 3. Here the basic unit for the crossbridge cycling model is chosen to be a troponin system TS , defined as three adjacent troponin—tropomyosin regulatory units.
Note that this force is normalized to the muscle cross-sectional area, and is thus expressed in Newton per unit area. In the figures and equations of this paper, cellular force is always expressed with units of stress. The half-sarcomere model describes the total force F m 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 g d , are functions of the half-sarcomere length L see Eqs 2 — 3.
Two of the rate constants from Fig 3 , f and g d , are functions of the half-sarcomere length L : 2 3. Eq 2 describes a symmetrical CB attachment rate in the zone of overlap between thick and thin filaments.
Eq 3 describes an unsymmetrical and irreversible CB detachment rate. This equation represents the lattice spacing effect on the rate of CB detachment: g d decreases at larger length, where thick and thin filament are closer to each other. It is important to emphasize that these two equations actually define and describe LDA in our approach.
Note also that this model does not allow to discriminate between potential contributors to LDA, but it is enough to reproduce a vast range of experimental results [ 51 , 52 ], such as the length-tension curve shown in Fig 4 , or the tension-pCa curve, which are two typical effects of LDA in cardiac muscle. We have used the same set of parameters for the crossbridge cycle rate constants than in [ 52 ] as a way to ensure that our model correctly reproduced the length-dependent properties of the cardiac muscle.
In other words, this half-sarcomere contraction model is able to reproduce experimental data showing length-dependent activation. The model is also able to reproduce baseline behaviors of the CVS.
See for instance the left ventricle pressure-volume loop from Fig 5. In this figure, the force and length of the half-sarcomere model are also represented. The hemodynamical parameters were fitted so that the hemodynamical variables such as the mean ventricular pressure and the half-sarcomere lengths range between physiologically relevant values see details on the fitting procedure in S1 Appendix.
The multiscale feature allows for a translation of cellular properties to the organ level. The results presented in Fig 5 , among others published with this model [ 49 ], agree well with experimental observations and thus validate our modeling approach.
This curve is similar to Fig 11A from [ 51 ], as we use the same set of parameters for the crossbridge cycle rate constants. 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 ms heartbeat. Since the FS mechanism is actually a rapid response to an increase in preload, occurring within a single heartbeat, all other variables remaining constant, we propose the following protocol to study the FS mechanism in silico.
We want to induce a rapid increase in left ventricular preload. We thus artificially increase mitral blood flow which corresponds to the blood flow entering the left ventricle during the blood filling phase. This maneuver alters the blood volume distribution across the CVS so that more blood enters the left ventricle , but the total circulating blood volume is kept constant so no blood volume is artificially added to the circulation. This mitral blood flow increase is induced as a way to mimic a sudden increase in venous return, and thus preload, during ventricular filling this preload increase can occur when legs are raised, for instance.
Of course, the duration and amplitude of the mitral flow increase will dictate the end-diastolic volume. Hence an increase in preload is induced at the beginning of the cardiac cycle and the variations in stroke volume are recorded within the same heartbeat. This constitutes the instantaneous increase in preload IIP protocol. In order to investigate the role of LDA in the response to an IIP protocol, we need to introduce a modified model, in addition to our multiscale model of the CVS presented above.
It is also important to emphasize that the sarcomere length appears in many places in the equations that govern the CVS see all these equations in S1 Appendix and this variable thus plays a quite complex role in the behavior of the system.
The middle ground in detail is held by Fuchs which is a satisfying compromise of depth and breadth, but you'd have to buy Molecular Control Mechanisms in Striated Muscle Contraction in order to read it. Some effort has been made to melt these excellent works down into short memorable point-form statements, as below:. The main reason for this mechanism is the need to match the output of the heart to constant changes in the right and left cardiac output, and to adjust rapidly within one beat to sudden changes in preload conditions.
To illustrate the point, let us consider a preposterous scenario where there is no Frank-Starling mechanism. If the stroke volume remained the same irrespective of loading conditions, the ventricle would dilate hideously with increasing preload.
If the right heart were to increase its output but the left one did not , there would also be an accumulation of blood in the pulmonary circulation. Similarly, if the RV decreased its output, without adjusting to the change in pulmonary blood flow the left ventricle would rapidly empty the pulmonary circulation. Thus, in uncharacteristically laconic point form, the main functional significance of the Frank-Starling mechanism is:.
Jacob, R. Dierberger, and G. Zimmer, Heinz-Gerd. HP, Bowditch. Starling, E. B Visscher. Mann, Deepinder. Springer, Cham,
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