End-systolic Pressure–Volume Relation, Ejection Fraction, and Heart Failure: Theoretical Aspect and Clinical Applications

Shoucri, Rachad M.

doi:10.4137/cmc.s18740

Cited by 4 publications

(7 citation statements)

References 38 publications

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“…When the point D on the ESPVR moves on the curve BDC, the stroke work SW ≈ Pm SV reaches its maximum value SWx when the derivative d(SW)/dVm is zero. Simple calculation as in [8] gives Experimental verification of these results can be found for the LV in [4,5], and for the right ventricle in [6]. Figure 3 shows some clinical results verifying the results of the preceding discussion.…”

Section: Criteria Of LV Performancesupporting

confidence: 76%

“…The left ventricle is represented as a thick-walled cylinder contracting symmetrically [8][9][10] (see Fig. 1).…”

Section: Mathematical Formalismmentioning

confidence: 99%

“…The mathematical model used in this study has been derived in previous publications [8][9][10], it is based on the theory of large elastic deformation of the myocardium. An interesting feature of this model is the introduction of the peak active force generated by the myocardium in the mathematical formalism describing the non-linear ESPVR.…”

Section: Introductionmentioning

confidence: 99%

“…">IntroductionThe end-systolic pressure-volume relation (ESPVR) is the relation between pressure and volume in the left or right ventricle when the myocardium reaches its maximum state of activation during the contraction phase, possible clinical application of this relation has been extensively studied [1][2][3][4][5][6][7][8][9][10]. The mathematical model used in this study has been derived in previous publications [8][9][10], it is based on the theory of large elastic deformation of the myocardium.…”

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confidence: 99%

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The Pressure Gradient across the Endocardium

Shoucri

2016

2016 Computing in Cardiology Conference (CinC)

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A mathematical formalism for the non-linear endsystolic pressure-volume relation (ESPVR) in the heart ventricles has the interesting feature that the peak active pressure generated by the myocardium ( IntroductionThe end-systolic pressure-volume relation (ESPVR) is the relation between pressure and volume in the left or right ventricle when the myocardium reaches its maximum state of activation during the contraction phase, possible clinical application of this relation has been extensively studied [1][2][3][4][5][6][7][8][9][10]. The mathematical model used in this study has been derived in previous publications [8][9][10], it is based on the theory of large elastic deformation of the myocardium. An interesting feature of this model is the introduction of the peak active force generated by the myocardium in the mathematical formalism describing the non-linear ESPVR. When inertia forces and viscous forces are neglected, the peak active force generated by the myocardium can be equated to the peak isovolumic pressure Pisom generated by the myocardium in a non-ejecting contraction. Non-invasive calculation of the ratio (Pisom -Pm)/Pm is possible with the mathematical formalism used, and in this study we show how this ratio can be used for the purpose of segregation and classification of different clinical groups. This index can be related to the study of the problem of heart failure (HF) with normal or preserved ejection (HFpEF) as will be indicated, HFpEF is defined as HF with EF > 0.5 [7].In what follows we first review the mathematical formalism used, then we present some applications to clinical data published in the literature [11][12][13][14] Mathematical formalismThe left ventricle is represented as a thick-walled cylinder contracting symmetrically [8-10] (see Fig. 1). During the contraction phase, the myocardium generates a radial active force per unit volume of the myocardium designated by Dr, which force will develop an active pressure ∫a b Dr dr ≈ Piso on the inner surface of the myocardium (endocardium), a = inner radius, b = outer radius, h = b -a = thickness of the myocardium. In a quasi-static approximation (inertia and viscous forces neglected), the equilibrium of forces on the endocardium can be expressed in the form Piso -P = E2 (Ved -V)P is the LV pressure, V the LV volume and it is indicated as Ved at end-diastole (when dV/dt = 0), E2 is an elastance coefficient that relates the difference of pressures Piso -P to the difference of volumes Ved -V. Near end-systole when the myocardium reaches its maximum state of activation, Eq. (1) can be expressed in the formVm ≈ Ves (Ves the end-systolic volume when dV/dt = 0), Pisom, Pm, and Vm are as defined in Eq. (1) but measured at the moment when the myocardium reaches its maximum state of activation. Figure 2 represents a non-linear ESPVR shown as the curve BDC, it is the relation obtained when Pm and Vm are varied and the peak isovolumic pressure Pisom is kept constant (as if a balloon is inflated against a constant Pisom). From Fig.2, E2m = ...

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Section: Criteria Of LV Performancesupporting

confidence: 76%

“…The left ventricle is represented as a thick-walled cylinder contracting symmetrically [8][9][10] (see Fig. 1).…”

Section: Mathematical Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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The Pressure Gradient across the Endocardium

Shoucri

2016

2016 Computing in Cardiology Conference (CinC)

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“…Then relations between EF, the parameters describing the ESPVR and the areas under the ESPVR are derived and discussed, they give new insight into the mechanics of ventricular contraction. Applications to experimental and clinical data published in the literature shows the consistency of the mathematical formalism used [8][9][10][11][12][13][47][48][49][50][51][52][53][54][55][56]. The mathematical formalism to be discussed in what follows can be applied to the four chambers of the heart, this study is limited to applications to the left ventricle [57][58][59].…”

Section: Introductionmentioning

confidence: 99%

Ejection Fraction and Espvr: A Study in the Mechanics of Left Ventricular Contraction

2020

COA

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The end-systolic pressure-volume relation (ESPVR) is the relation between pressure Pm and volume Vm in the heart left ventricle when the myocardium reaches its maximum state of activation during contraction near end-systole. Relations between the ejection fraction (EF), parameters describing the ESPVR and the areas under the ESPVR are derived in this study for a linear model of the ESPVR. An important feature of the model is the inclusion of the active pressure generated by the myocardium during an ejecting contraction (also called isovolumic pressure Piso) in the mathematical expression of the linear ESPVR. Criteria that can help in understanding the problem of heart failure with normal or preserved ejection fraction (HFpEF) are discussed. Applications to clinical data published in the literature are presented, the applications show the consistency of the mathematical formalism used. When ratios of pressures are used, the calculation can be carried out with clinical data measured in a non-invasive way (the ratio of pressures can be calculated). This study shows that the EF is just one index of several indexes that can be derived from the ESPVR for the assessment of the ventricular function, and that using bivariate (or multivariate) analysis of data is superior to univariate analysis for the purpose of classification and segregation between different clinical groups.

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Efficient approximation of cardiac mechanics through reduced‐order modeling with deep learning‐based operator approximation

Cicci,

Fresca,

Manzoni

et al. 2023

Numer Methods Biomed Eng

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Reducing the computational time required by high‐fidelity, full‐order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient‐specific simulations into clinical practice. Indeed, while FOMs, such as those based on the finite element method, provide valuable information on the cardiac mechanical function, accurate numerical results can be obtained at the price of very fine spatio‐temporal discretizations. As a matter of fact, simulating even just a few heartbeats can require up to hours of wall time on high‐performance computing architectures. In addition, cardiac models usually depend on a set of input parameters that are calibrated in order to explore multiple virtual scenarios. To compute reliable solutions at a greatly reduced computational cost, we rely on a reduced basis method empowered with a new deep learning‐based operator approximation, which we refer to as Deep‐HyROMnet technique. Our strategy combines a projection‐based POD‐Galerkin method with deep neural networks for the approximation of (reduced) nonlinear operators, overcoming the typical computational bottleneck associated with standard hyper‐reduction techniques employed in reduced‐order models (ROMs) for nonlinear parametrized systems. This method can provide extremely accurate approximations to parametrized cardiac mechanics problems, such as in the case of the complete cardiac cycle in a patient‐specific left ventricle geometry. In this respect, a 3D model for tissue mechanics is coupled with a 0D model for external blood circulation; active force generation is provided through an adjustable parameter‐dependent surrogate model as input to the tissue 3D model. The proposed strategy is shown to outperform classical projection‐based ROMs, in terms of orders of magnitude of computational speed‐up, and to return accurate pressure‐volume loops in both physiological and pathological cases. Finally, an application to a forward uncertainty quantification analysis, unaffordable if relying on a FOM, is considered, involving output quantities of interest such as, for example, the ejection fraction or the maximal rate of change in pressure in the left ventricle.

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End-systolic Pressure–Volume Relation, Ejection Fraction, and Heart Failure: Theoretical Aspect and Clinical Applications

Cited by 4 publications

References 38 publications

The Pressure Gradient across the Endocardium

The Pressure Gradient across the Endocardium

Ejection Fraction and Espvr: A Study in the Mechanics of Left Ventricular Contraction

Efficient approximation of cardiac mechanics through reduced‐order modeling with deep learning‐based operator approximation

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