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The importance of the pericardium for cardiac biomechanics: from physiology to computational modeling

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Abstract

The human heart is enclosed in the pericardial cavity. The pericardium consists of a layered thin sac and is separated from the myocardium by a thin film of fluid. It provides a fixture in space and frictionless sliding of the myocardium. The influence of the pericardium is essential for predictive mechanical simulations of the heart. However, there is no consensus on physiologically correct and computationally tractable pericardial boundary conditions. Here, we propose to model the pericardial influence as a parallel spring and dashpot acting in normal direction to the epicardium. Using a four-chamber geometry, we compare a model with pericardial boundary conditions to a model with fixated apex. The influence of pericardial stiffness is demonstrated in a parametric study. Comparing simulation results to measurements from cine magnetic resonance imaging reveals that adding pericardial boundary conditions yields a better approximation with respect to atrioventricular plane displacement, atrial filling, and overall spatial approximation error. We demonstrate that this simple model of pericardial–myocardial interaction can correctly predict the pumping mechanisms of the heart as previously assessed in clinical studies. Utilizing a pericardial model not only can provide much more realistic cardiac mechanics simulations but also allows new insights into pericardial–myocardial interaction which cannot be assessed in clinical measurements yet.

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Authors and Affiliations

  1. Institute for Computational Mechanics, Technical University of Munich, Boltzmannstr. 15, 85748, Garching b. München, Germany

    Martin R. Pfaller, Julia M. Hörmann, Martina Weigl, Andreas Nagler & Wolfgang A. Wall

  2. Inria, Paris-Saclay University, Palaiseau, France

    Radomir Chabiniok

  3. LMS, Ecole Polytechnique, CNRS, Paris-Saclay University, Palaiseau, France

    Radomir Chabiniok

  4. School of Biomedical Engineering and Imaging Sciences (BMEIS), St Thomas’ Hospital, King’s College London, London, UK

    Radomir Chabiniok

  5. Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, Nijenborgh 9, 9747 AG, Groningen, The Netherlands

    Cristóbal Bertoglio

  6. Center for Mathematical Modeling, Universidad de Chile, Beaucheff 851, 8370456, Santiago, Chile

    Cristóbal Bertoglio

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  1. Martin R. Pfaller
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  2. Julia M. Hörmann
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  3. Martina Weigl
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  4. Andreas Nagler
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  5. Radomir Chabiniok
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  6. Cristóbal Bertoglio
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  7. Wolfgang A. Wall
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Cristóbal Bertoglio and Wolfgang A. Wall are joint last authors.

Appendix

Appendix

1.1 Comparison of spring formulations

We show in Sect. 2.1 how the pericardial boundary condition in case pericardium can be derived from adhesive sliding contact by introducing several simplifications. To justify the simplifications made by our pericardial boundary condition, we use a very simple geometry of a hollow half-ellipsoid with \(\pm 60^\circ \) fibers, which roughly represents the shape of the left ventricle, see Fig. 22a. It is able to show the consequences of each approach while being simple enough to isolate the effects of the boundary condition. The parameters of the ellipsoid model are given in Table 3. We use the same active stress model introduced in (8) to mimic cardiac contraction. All three simulations use the same contractility parameter.

Table 3 Overview of material parameters in ellipsoid model
Full size table

As in Sect. 3, case pericardium utilizes the pericardial boundary condition proposed in (5) using the gap (4). Additionally, we introduce case pseudo-contact, which uses the definition of the gap in (3) based on projection and the current normal vector to the epicardium. Case free has homogeneous zero Neumann boundary conditions on the whole epicardial surface.

The results of the contraction simulation are shown in Fig. 22b, c at end-systole. Displayed are the reference configuration and all three boundary condition cases for a cross section of the ellipsoid. Figure 22b shows in a frontal view the shortening of the ellipsoid with visible epi- and endocardial contours. While cases pericardium and pseudo-contact are very similar with little differences only in radial direction, case free exhibits much less longitudinal shortening. There is almost no longitudinal shortening but a translational movement of the whole geometry instead.

Figure 22b shows the epicardial contour of the ellipsoid in a top-down view to observe the twisting motion of the ellipsoid. All three boundary condition cases are very similar. This confirms that the normal springs in cases pericardium and pseudo-contact in fact allow tangential sliding and do not prohibit any rotational movement, as they are very similar to case free. Furthermore, the similarity of cases pericardium and pseudo-contact shows that the simplified spring formulation (4) in case pericardium is sufficient to represent the effects of the pericardium compared to the more detailed formulation (3) in case pseudo-contact.

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Pfaller, M.R., Hörmann, J.M., Weigl, M. et al. The importance of the pericardium for cardiac biomechanics: from physiology to computational modeling. Biomech Model Mechanobiol 18, 503–529 (2019). https://doi.org/10.1007/s10237-018-1098-4

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