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We see here that three different scales are involved in the cardiovascular system response to preload variations: cellular, ventricular, and cardiovascular.
We can conclude from these observations that the FS mechanism is a multiscale and dynamical LDA-driven response to a change in preload. This response does not only manifest as an increase in produced cellular force, but also as an altered dynamic of contraction. We should note that this increased "ejecting-capacity" of the ventricle upon preload increase implies a secondary increase in afterload. This partially counterbalances the stroke volume increase.
In other words, an increase in blood volume ejection capacity actually increases the aortic pressure, as more blood is ejected into the aorta. The afterload thus increases and tends to lower the expected increase in stroke volume.
The schematic FS curve from Fig 1 is portrayed in many textbooks and in the literature, but the underlying explanation can be vague or even incorrect. First, the general context is not always clarified. The FS mechanism is a rapid response that occurs on a beat-to-beat basis when only the preload is varied, all other variables remaining constant.
Second, our results show that the increase in maximal force does not provide a sufficient and complete explanation of the stroke volume increase. Finally, there is a secondary increase in afterload following preload alteration.
Since all these observations are rarely taken into account regarding the FS mechanism definition, inconsistencies can be found regarding the proposed FS curves. On the other hand, obtaining such curves experimentally is very challenging. With our model, we could build an FS curve consistent with the definition of the FS mechanism, by performing several IIP protocols with different mitral flow increased or decreased values.
We show that stroke volume is an increasing and almost linear function of preload. As noted by Glower et al. It is worth noticing once again that all the proposed preload indices end-diastolic volume or pressure, atrial pressure have their limitations, and the cardiac fibers length prior to contraction is a challenging measure to obtain experimentally. The FS mechanism is often considered as a strong basis for fluid therapy. The general idea is to extend the transitory FS mechanism to a stabilized behavior.
From a clinical perspective, the aim of vascular filling is to increase and stabilize the preload so that the stroke volume increase can be maintained, and the cardiac output improved. Our analysis shows that it is delicate to associate the transitory FS response with a stabilized increased cardiac output. The misunderstanding may arise from the fact that both the FS mechanism and vascular filling therapy are based on the length-dependent properties of cardiac cells.
As we have shown in this study, LDA indeed underlies both phenomena, but this does not mean that the FS mechanism is linked to the vascular filling response. We propose to introduce instead the concept of length-dependent fluid response LDFR , which we define as the mechanism underlying the motivations for vascular filling therapy: as circulating blood volume increases, preload increases and a stabilized substantial increase in stroke volume is expected if the patient is fluid-responsive.
Upon vascular filling, there is a competition between an increased produced pressure and an increased resistance to blood ejection. Our results indicate that for high stressed blood volume values, the LDA-driven increase in pressure development is not strong enough to counterbalance the afterload increase.
This leads to a saturating ejection duration as well. As a global result, the stroke volume follows the same tendency and saturates for high stressed blood volume values.
LDFR is thus a multiscale phenomenon where cellular, cardiac, and hemodynamic variables determine the global CVS behavior. Like for the FS mechanism, we observe a complex, multiscale response to preload variations although the relative contribution of each scale is probably different than for the FS mechanism.
Our results suggest that attention should not be drawn only to the preload during fluid therapy, because the afterload is also altered and definitely involved in stroke volume changes. In these simulations, we defined afterload as the aortic pressure at aortic valve opening in order to quantify it.
But the resistance to ejection occurs throughout the whole ejection period, and this resistance increases with filling. Our results indicate that this leads to a saturating limit for vascular filling procedures. It is important to emphasize that the saturating part of the vascular filling curve is not equivalent to the saturating part of the schematic FS curve, as commonly assumed.
The former corresponds to a stabilized behavior while the latter is a rapid response. As explained above, the saturating part of the vascular filling curve occurs because the resistance to blood ejection increases highly, and even if the produced force and ventricular pressure also increase, a stroke volume saturation is observed.
Of course, our vascular filling simulations do not consider other regulatory mechanisms that would take place in reaction to fluid infusion, but they highlighted the importance of monitoring afterload and not only preload to predict fluid responsiveness.
For instance, we may expect different fluid responsiveness curves from patients with heart failure or with dilated or hypertrophic cardiomyopathies. Our CVS model presents several limitations that must be addressed. Regarding the cell model, we used a myofilament-based LDA that does not take into account the OFF state of myosin [ 29 ], nor the length-dependent changes in calcium transient [ 56 ].
However, this model still correctly reproduces the length-tension relationship Fig 4 and could be used to link this cellular property to the organ and system scales. The ventricular model is rather simple, as it does not take into the complex, three-dimensional contraction of the ventricular chamber. However, force and pressure are still connected through geometrical laws see S1 Appendix , and thus a geometrical effect is still accounted for in our model.
In other words, there is still a physiological link between force and pressure in our model, but the ventricular response to preload changes would be better quantified with a more accurate model for the ventricular cavity.
Also, it should be noted that the atria were not considered in the circulation model. However, as the ventricles hold the major role in ejecting the blood through the systemic and pulmonary circulations, adding atrial contraction in the circulation model should not qualitatively change our results. Despite these modeling simplifications, the model correctly reproduces baseline results and can help investigating multiscale questions.
We performed a simple study to untangle the nature of the relationship between the FS mechanism global behavior and LDA cellular property. We could then challenge the assumed link between the FS mechanism and vascular filling therapy. Of course, our model could be improved with a more accurate depiction of LDA at the sarcomere scale by adding the myosin OFF state, for instance and a better description of the ventricular geometry at the organ scale.
However, we believe that a more accurate model would not challenge our qualitative results or question the multiscale nature of the studied phenomena. But of course, more precise models would provide better quantitative predictions about the relationship between LDA and the FS or fluid responsiveness mechanisms. The heart is a complex multiphysics and multiscale system.
Microscopic events at the subcellular level generate emergent properties at the organ scale [ 47 , 48 ]. For instance, the length-dependent activation, a property of cardiac cells, appears to underlie two important cardiac regulation mechanisms. The first one is the Frank-Starling mechanism, a rapid response to preload changes that occurs on a beat-to-beat basis. The second one is the length-dependent fluid response, a slower response to vascular filling.
However, some misconceptions may occur in cardiology books or scientific literature and lead to a distorted understanding of the phenomena. In particular, the FS mechanism is sometimes presented as the underlying cause of vascular filling responses. It is true that both mechanisms share the same cellular origin, which is LDA.
Furthermore, they both represent a complex, multiscale response to preload variations. But this is not enough to state that one mechanism causes the other. Our in silico multiscale study aimed to untangle those three concepts FS mechanism, vascular filling therapy, and LDA and provided a formal framework to characterize them. We emphasized that the three cellular, ventricular and cardiovascular scales participate truly in the global system behavior, and we showed that the roles of these three scales were different in the FS mechanism and in the vascular filling therapy.
For instance, the aortic pressure at aortic valve opening changes as a function of preload for the vascular filling simulations, and not for the FS mechanism simulations. Thus, the positive response to vascular filling cannot always be linked to a positive response to an acute preload increase, as the complex interactions taking place are different in the two situations. A visual representation of our conclusions is shown in Fig As our knowledge on cardiac function grows, we believe it is important to avoid misconceptions and keep a strict structure for defining cardiac concepts and properties.
This contributes to a more comprehensive knowledge of the sophisticated length-dependent properties of cardiac muscle. 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.
Table A. Electrophysiological parameters. Table B. Mechanical parameters. Table C. Hemodynamic parameters. Table D: Standard values of hemodynamic quantities corresponding to a healthy subject that are used in the parameter identification procedure. Table E. Standard values of hemodynamic quantities corresponding to a healthy subject that are used in the 9-parameter identification procedure.
Fig A. Vertical bars indicate intervals for the four phases of the cardiac cycle. Abstract The Frank-Starling mechanism is a fundamental regulatory property which underlies the cardiac output adaptation to venous filling. Author summary It is commonly admitted that the length-dependent activation is the cellular property underlying the Frank-Starling mechanism. Funding: The author s received no specific funding for this work.
Introduction The Frank-Starling FS mechanism [ 1 , 2 ] is an important cardiac property addressed in every cardiology book. Download: PPT.
Fig 1. Length-dependent activation, the Frank-Starling mechanism and vascular filling therapy. Methods 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.
Fig 2. Fig 4. Length-tension relationship obtained with the half-sarcomere model. Instantaneous increase in preload 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. Vascular filling In the CVS model, the stressed blood volume is an adjusted parameter that characterizes the total amount of circulating blood volume responsible for a non-zero pressure inside the system.
The Frank-Starling mechanism Within the modeling framework described in the previous section, we can now challenge the nature of the relationship between LDA and the FS mechanism. Fig 7. Table 1. Vascular filling The results describing the vascular filling simulations are presented in Figs 10 — Fig Blood ejection duration during vascular filling simulations.
Discussion The FS mechanism is a rapid response induced by an acute increase in preload, which results in an increased stroke volume. We showed that: As preload increases, both the maximal force and pressure increase, but not to the same extent. The maximal force is not a reliable predictor for stroke volume variations upon IIP. Instead of force, pressure should be considered. Those concepts are not interchangeable, as developed pressure also depends on ventricular geometry.
An altered preload sets new initial conditions at the beginning of contraction. As a consequence, the whole dynamics of force and pressure development is altered. The aortic flow reaches a higher amplitude, and the ejection duration is extended. This leads to an increased stroke volume. Conclusion The heart is a complex multiphysics and multiscale system. Supporting information.
S1 Appendix. Model equations and parameters. S2 Appendix. Analysis of the time evolution of the system during an IIP protocol. References 1. Frank O. On the dynamics of cardiac muscle. Am Heart J. View Article Google Scholar 2. Starling EH. View Article Google Scholar 3. Sarnoff SJ, Berglund E. Ventricular function. Sarnoff SJ. Physiol Rev. J Clin Invest. Left ventricular function in man.
Gleason WL, Braunwald E. Relationships between left ventricular enddiatolic volume and stroke volume in man with observations on the mechanism of pulsus alternans. Ross J, Braunwald E. Braunwald E. The Control of Ventricular Function in Man. Br Heart J. Berlin DA, Bakker J. Starling curves and central venous pressure. Crit Care. In this expression, R vao is the aortic valve resistance, P lv is the left ventricular pressure and P ao is the aortic pressure.
The latter is a major component of afterload, which opposes blood ejection. The time evolutions of P lv and P ao are shown in Fig 8A. The aortic valve opens when P lv gets greater than P ao , and blood ejection begins. Upon IIP, the aortic valve opens roughly at the same time and for the same value of P ao than for the BL case, but P lv reaches higher values during the ejection.
An increase in stroke volume is thus expected. But, as more blood is indeed ejected through the aorta, P ao increases and further opposes blood ejection. This participates in a reduction of stroke volume. However, the net result is actually an increase in stroke volume, as can be seen from the aortic flow shown in Fig 8B stroke volume is basically given by the area under the aortic flow. Indeed, we observe that not only does the Q ao amplitude increase upon IIP, but the ejection period also lasts longer black arrow.
The ejection ends when the aortic valve closes, which occurs once P lv gets lower than P ao. An increased ejection duration thus means that the preload variations modified the whole dynamics of left ventricular and aortic pressures developments. This point will be developed further in the discussion section. Both effects finally lead to an increased stroke volume upon IIP.
Corresponding aortic flows. This is shown in Fig 9 , where stroke volume is reported as a function of preload preload is calculated as the maximal half-sarcomere length. Obtaining an FS curve experimentally is very challenging for a few reasons.
First of all, the length of cardiac fibers is not measurable in vivo , and preload indices are used instead. Second, changing the preload while keeping all the other variables constant is hardly manageable in practice. With our model, however, we can easily build an FS curve which is consistent with the FS mechanism definition, by performing IIP protocols for different Q mt increase or decrease values.
We see that stroke volume is an increasing, and almost linear function of preload, and we do not observe the commonly assumed curvilinear shape or the plateau phase for high preloads see Fig 1. One possible explanation for this is that the shape of the experimental FS curves actually depends on the chosen preload index [ 14 ]. For instance, a saturating portion of the curve may be expected if the end-diastolic pressure is chosen as the preload index, given the non-linear compliance of the ventricle.
The absence of a plateau phase may also be related to the model limitations see [ 49 ] and the Discussion section below. The important thing to note here is that, when drawing a FS curve, it is essential to explicitly state which preload-increase protocol is applied, and which preload index is measured.
The red filled circle on the curves always corresponds to the baseline situation introduced above normal hemodynamics conditions as shown in Fig 5. Points located at the right side of the baseline red filled circle correspond to vascular filling. In Fig 10 , we see that stroke volume increases with filling, up to a certain limit where it saturates. Since we know that the competition between P lv and P ao actually dictates the stroke volume see Eq 7 , maximal P lv is shown as a function of stressed blood volume in Fig 11A.
We see that it increases with filling but does not reach a plateau phase. P ao at aortic valve opening, which we use to quantify afterload, is shown in Fig 11B. It also increases with filling, without any plateau phase either.
Finally, the ejection duration is plotted in Fig 12 , and a saturation is observed for high stressed blood volume values.
This means that, even if the left ventricular pressure development is enhanced with vascular filling, for high stressed blood volume values it is counterbalanced by the increase in afterload. This leads to a saturated ejection duration and a saturated stroke volume. Stroke volume increases with filling, up to a saturating plateau. The red filled circle corresponds to the BL case normal hemodynamics conditions.
Maximal left ventricular pressure during vascular filling simulations. Aortic pressure at valve opening during vascular filling simulations. The latter is used to quantify the afterload. Maximal left ventricular force with blue curve and without red curve LDA. Maximal left ventricular pressure with blue curve and without red curve LDA. Afterload with blue curve and without red curve LDA. Stroke volume with blue curve and without red curve LDA. Indeed, maximal produced force and pressure increase more marginally with filling once LDA is turned off see Fig 13A and 13B.
This is not enough to counterbalance the increase in afterload Fig 13C , and thus stroke volume decreases for high stressed blood volume values see Fig 13D. The FS mechanism is a rapid response induced by an acute increase in preload, which results in an increased stroke volume. The common given explanation of this phenomenon is that, as preload increases, LDA is triggered and the maximal produced force increases, and so does the stroke volume.
It is important to remember that LDA is essentially highlighted and defined in isometric cellular experiments, while cardiac fibers actually undergo auxotonic contractions in a beating heart.
This is why we developed a model where the dependence on the length values is switched off, while the dependence on the length variations velocity-dependence is unchanged. Then, to investigate the nature of the relationship between LDA and the FS mechanism, which is hard to study experimentally, we proposed an Instantaneous Increase in Preload protocol performed on a multiscale model of the human CVS.
We showed that:. As preload increases, both the maximal force and pressure increase, but not to the same extent. The maximal force is not a reliable predictor for stroke volume variations upon IIP. Instead of force, pressure should be considered. Those concepts are not interchangeable, as developed pressure also depends on ventricular geometry. An altered preload sets new initial conditions at the beginning of contraction. As a consequence, the whole dynamics of force and pressure development is altered.
The aortic flow reaches a higher amplitude, and the ejection duration is extended. This leads to an increased stroke volume. We see here that three different scales are involved in the cardiovascular system response to preload variations: cellular, ventricular, and cardiovascular. We can conclude from these observations that the FS mechanism is a multiscale and dynamical LDA-driven response to a change in preload. This response does not only manifest as an increase in produced cellular force, but also as an altered dynamic of contraction.
We should note that this increased "ejecting-capacity" of the ventricle upon preload increase implies a secondary increase in afterload. This partially counterbalances the stroke volume increase. In other words, an increase in blood volume ejection capacity actually increases the aortic pressure, as more blood is ejected into the aorta.
The afterload thus increases and tends to lower the expected increase in stroke volume. The schematic FS curve from Fig 1 is portrayed in many textbooks and in the literature, but the underlying explanation can be vague or even incorrect.
First, the general context is not always clarified. The FS mechanism is a rapid response that occurs on a beat-to-beat basis when only the preload is varied, all other variables remaining constant. Second, our results show that the increase in maximal force does not provide a sufficient and complete explanation of the stroke volume increase. Finally, there is a secondary increase in afterload following preload alteration.
Since all these observations are rarely taken into account regarding the FS mechanism definition, inconsistencies can be found regarding the proposed FS curves. On the other hand, obtaining such curves experimentally is very challenging. With our model, we could build an FS curve consistent with the definition of the FS mechanism, by performing several IIP protocols with different mitral flow increased or decreased values.
We show that stroke volume is an increasing and almost linear function of preload. As noted by Glower et al. It is worth noticing once again that all the proposed preload indices end-diastolic volume or pressure, atrial pressure have their limitations, and the cardiac fibers length prior to contraction is a challenging measure to obtain experimentally.
The FS mechanism is often considered as a strong basis for fluid therapy. The general idea is to extend the transitory FS mechanism to a stabilized behavior. From a clinical perspective, the aim of vascular filling is to increase and stabilize the preload so that the stroke volume increase can be maintained, and the cardiac output improved.
Our analysis shows that it is delicate to associate the transitory FS response with a stabilized increased cardiac output. The misunderstanding may arise from the fact that both the FS mechanism and vascular filling therapy are based on the length-dependent properties of cardiac cells. As we have shown in this study, LDA indeed underlies both phenomena, but this does not mean that the FS mechanism is linked to the vascular filling response. We propose to introduce instead the concept of length-dependent fluid response LDFR , which we define as the mechanism underlying the motivations for vascular filling therapy: as circulating blood volume increases, preload increases and a stabilized substantial increase in stroke volume is expected if the patient is fluid-responsive.
Upon vascular filling, there is a competition between an increased produced pressure and an increased resistance to blood ejection.
Our results indicate that for high stressed blood volume values, the LDA-driven increase in pressure development is not strong enough to counterbalance the afterload increase. This leads to a saturating ejection duration as well. As a global result, the stroke volume follows the same tendency and saturates for high stressed blood volume values.
LDFR is thus a multiscale phenomenon where cellular, cardiac, and hemodynamic variables determine the global CVS behavior. Like for the FS mechanism, we observe a complex, multiscale response to preload variations although the relative contribution of each scale is probably different than for the FS mechanism.
Our results suggest that attention should not be drawn only to the preload during fluid therapy, because the afterload is also altered and definitely involved in stroke volume changes. In these simulations, we defined afterload as the aortic pressure at aortic valve opening in order to quantify it. But the resistance to ejection occurs throughout the whole ejection period, and this resistance increases with filling. Our results indicate that this leads to a saturating limit for vascular filling procedures.
It is important to emphasize that the saturating part of the vascular filling curve is not equivalent to the saturating part of the schematic FS curve, as commonly assumed. The former corresponds to a stabilized behavior while the latter is a rapid response. As explained above, the saturating part of the vascular filling curve occurs because the resistance to blood ejection increases highly, and even if the produced force and ventricular pressure also increase, a stroke volume saturation is observed.
Of course, our vascular filling simulations do not consider other regulatory mechanisms that would take place in reaction to fluid infusion, but they highlighted the importance of monitoring afterload and not only preload to predict fluid responsiveness.
For instance, we may expect different fluid responsiveness curves from patients with heart failure or with dilated or hypertrophic cardiomyopathies. Our CVS model presents several limitations that must be addressed. Regarding the cell model, we used a myofilament-based LDA that does not take into account the OFF state of myosin [ 29 ], nor the length-dependent changes in calcium transient [ 56 ]. However, this model still correctly reproduces the length-tension relationship Fig 4 and could be used to link this cellular property to the organ and system scales.
The ventricular model is rather simple, as it does not take into the complex, three-dimensional contraction of the ventricular chamber. However, force and pressure are still connected through geometrical laws see S1 Appendix , and thus a geometrical effect is still accounted for in our model.
In other words, there is still a physiological link between force and pressure in our model, but the ventricular response to preload changes would be better quantified with a more accurate model for the ventricular cavity. Also, it should be noted that the atria were not considered in the circulation model.
However, as the ventricles hold the major role in ejecting the blood through the systemic and pulmonary circulations, adding atrial contraction in the circulation model should not qualitatively change our results. Despite these modeling simplifications, the model correctly reproduces baseline results and can help investigating multiscale questions. We performed a simple study to untangle the nature of the relationship between the FS mechanism global behavior and LDA cellular property.
We could then challenge the assumed link between the FS mechanism and vascular filling therapy. Of course, our model could be improved with a more accurate depiction of LDA at the sarcomere scale by adding the myosin OFF state, for instance and a better description of the ventricular geometry at the organ scale.
However, we believe that a more accurate model would not challenge our qualitative results or question the multiscale nature of the studied phenomena.
But of course, more precise models would provide better quantitative predictions about the relationship between LDA and the FS or fluid responsiveness mechanisms.
The heart is a complex multiphysics and multiscale system. Microscopic events at the subcellular level generate emergent properties at the organ scale [ 47 , 48 ]. For instance, the length-dependent activation, a property of cardiac cells, appears to underlie two important cardiac regulation mechanisms. The first one is the Frank-Starling mechanism, a rapid response to preload changes that occurs on a beat-to-beat basis.
The second one is the length-dependent fluid response, a slower response to vascular filling. However, some misconceptions may occur in cardiology books or scientific literature and lead to a distorted understanding of the phenomena.
In particular, the FS mechanism is sometimes presented as the underlying cause of vascular filling responses. It is true that both mechanisms share the same cellular origin, which is LDA. Furthermore, they both represent a complex, multiscale response to preload variations. But this is not enough to state that one mechanism causes the other. Our in silico multiscale study aimed to untangle those three concepts FS mechanism, vascular filling therapy, and LDA and provided a formal framework to characterize them.
We emphasized that the three cellular, ventricular and cardiovascular scales participate truly in the global system behavior, and we showed that the roles of these three scales were different in the FS mechanism and in the vascular filling therapy.
For instance, the aortic pressure at aortic valve opening changes as a function of preload for the vascular filling simulations, and not for the FS mechanism simulations. Thus, the positive response to vascular filling cannot always be linked to a positive response to an acute preload increase, as the complex interactions taking place are different in the two situations. A visual representation of our conclusions is shown in Fig As our knowledge on cardiac function grows, we believe it is important to avoid misconceptions and keep a strict structure for defining cardiac concepts and properties.
This contributes to a more comprehensive knowledge of the sophisticated length-dependent properties of cardiac muscle. 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. Table A. Electrophysiological parameters. Table B. Mechanical parameters. Table C. Hemodynamic parameters. Table D: Standard values of hemodynamic quantities corresponding to a healthy subject that are used in the parameter identification procedure.
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