The importance of the pericardium for cardiac biomechanics: From physiology to computational modeling Martin Pfaller, Julia Hoermann, Martina Weigl, Andreas Nagler, Radomir Chabiniok, Cristóbal Bertoglio, Wolfgang Wall To cite this version: Martin Pfaller, Julia Hoermann, Martina Weigl, Andreas Nagler, Radomir Chabiniok, et al.. The importance of the pericardium for cardiac biomechanics: From physiology to computational modeling. Biomechanics and Modeling in Mechanobiology, Springer Verlag, In press. hal-01941544 HAL Id: hal-01941544 https://hal.inria.fr/hal-01941544 Submitted on 1 Dec 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Biomechanics and Modeling in Mechanobiology manuscript No. (will be inserted by the editor) The importance of the pericardium for cardiac biomechanics From physiology to computational modeling Martin R. Pfaller1 · Julia M. H¨ormann1 · Martina Weigl1 · Andreas Nagler1 · Radomir Chabiniok2;3;4 · Crist´obalBertoglio5∗ · Wolfgang A. Wall1∗ Received: date / Accepted: date Abstract The human heart is enclosed in the pericar- action can correctly predict the pumping mechanisms of dial cavity. The pericardium consists of a layered thin the heart as previously assessed in clinical studies. Uti- sac and is separated from the myocardium by a thin lizing a pericardial model can not only provide much film of fluid. It provides a fixture in space and friction- more realistic cardiac mechanics simulations but also less sliding of the myocardium. The influence of the allows new insights into pericardial-myocardial interac- pericardium is essential for predictive mechanical simu- tion which cannot be assessed in clinical measurements lations of the heart. However, there is no consensus on yet. physiologically correct and computationally tractable Keywords Cardiac mechanical modeling · Peri- pericardial boundary conditions. Here we propose to cardium · Boundary conditions · Finite element model the pericardial influence as a parallel spring and simulation 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 1 Introduction fixated apex. The influence of pericardial stiffness is demonstrated in a parametric study. Comparing simu- 1.1 Motivation lation results to measurements from cine magnetic reso- nance imaging reveals that adding pericardial boundary Cardiac mechanics simulations consist of solving a non- conditions yields a better approximation with respect linear elastodynamic boundary value problem [2]. Phys- to atrioventricular plane displacement, atrial filling, and iological boundary conditions are essential to achieve overall spatial approximation error. We demonstrate predictive results for any clinical purposes. The bound- that this simple model of pericardial-myocardial inter- ary conditions on the structure field of the myocardium are mainly governed by two physiological aspects: Blood M. R. Pfaller flow within the chambers near the inside surface of the [email protected] myocardium (endocardium) and the pericardial sac on arXiv:1810.05451v1 [cs.CE] 12 Oct 2018 1 Institute for Computational Mechanics, Technical Uni- the outside surface (epicardium), see figure 1a. There versity of Munich, Boltzmannstr. 15, 85748 Garching b. M¨unchen, Germany are many applications for simulating heart blood flow [3]. However, for many relevant questions the exact fluid 2 Inria, Paris-Saclay University, Palaiseau, France dynamics of blood within the heart or a resolved fluid- 3 LMS, Ecole Polytechnique, CNRS, Paris-Saclay University, solid interaction simulation are often not needed for Palaiseau, France simulating the myocardium. Instead, a realistic pressure- 4 School of Biomedical Engineering & Imaging Sciences flow relationship stemming from the circulatory system (BMEIS), St Thomas' Hospital, King's College London, UK is sufficient, which is commonly represented by lumped- 5 Bernoulli Institute for Mathematics, Computer Science and parameter fluid models that provide the correct normal Artificial Intelligence, University of Groningen, Nijenborgh 9, pressure to the endocardial wall [4]. 9747 AG Groningen, The Netherlands However, there is no consensus on boundary condi- joint last authors ∗ tions to represent the effects of the pericardial sac. The 2 Martin R. Pfaller1 et al. Serous Pericardium Neighboring Tissue Fibrous Pericardium Parietal Pericardial Pericardium Cavity Serous and Fluid Pericardium Visceral Pericardium Myocardium Myocardium Fibrous Pericardium Blood (a) Dissected mediastinum with cut (b) Location of the heart with re- (c) Cross-sectional view of transmural layers pericardium and heart surface. Image spect to serous and fibrous peri- of heart and pericardium. Inspired by [1]. by G. M. Gruber, Medical University cardium. Inspired by [1]. of Vienna, Austria. Fig. 1: Heart and pericardium. goal of this work is twofold: (a) to provide a detailed simulation results and cine MRI. We close this work literature review of pericardial biomechanics, hence jus- with a discussion of the results, the limitations of our tifying its modeling using a computationally inexpen- study, future perspectives, and some conclusions in sec- sive viscoelastic model, and (b) to highlight the rele- tion 4. vance of such boundary conditions through a detailed quantitative analysis using a subject-specific cine MRI data set. We employ a four-chamber geometry includ- 1.2 The pericardium ing parts of the great vessels, as it provides us with ad- ditional options to asses the physiological correctness In the following, we review the anatomy of the peri- of our boundary condition, e.g. through the interplay cardium and its physiology, where we focus on the me- between ventricles and atria during ventricular systole. chanical interaction between the pericardium and the Note, however, that the pericardial boundary condition heart. Based on this review, we evaluate variants of is independent of the geometry and is meant to be ap- pericardial boundary conditions and propose a model plied to any kind of cardiac mechanics simulation that for pericardial-myocardial interaction. includes the epicardial surface. 1.2.1 Anatomy This work is structured as follows. Following a re- view of the anatomy and physiology of the pericardium As shown in figure 1a, the pericardium is a sac-like in section 1.2, we review pericadial boundary condi- structure with a combined thickness of 1-2 mm that tions currently used in cardiac mechanics simulations. contains the heart and parts of the great vessels [5]. We propose a model to represent the influence of the Figures 1b and 1c show a cross-sectional view of the pericardium by parallel springs and dashpots acting in myocardium and the layers of the pericardium. A com- normal direction to the epicardium in section 2. Fur- mon analogy for the location of the heart within the thermore, we summarize a three-dimensional elastody- pericardium is that of a fist pushed into an inflated namical continuum model for the myocardium which is balloon [6]. monolithically coupled to a zero-dimensional reduced- The fibrous pericardium consists of a fibrous layer order windkessel model for the circulatory system. We that forms a flask-like sac with a wavy collagenous struc- demonstrate the influence of the pericardial boundary ture of three interwoven main layers that are oriented condition in section 3 through a detailed quantitative 120◦ to each other [7]. It has a higher tensile stiff- comparison of simulation results to cine MRI. For that ness than the myocardium and is dominated by the we evaluate ventricular volume, atrioventricular-plane- viscoelastic behavior of extracellular collagen matrix displacement, atrioventricular interaction, and introduce and elastin fibers [8]. The fibrous pericardium is fixed a quantitative error measurement by calculating a dis- in space by a "three point cardiac seat belt" via the tance error at endo- and epicardial surfaces between pericardial ligaments to the sternum. Furthermore, it The importance of the pericardium for cardiac biomechanics 3 is thoroughly attached to the central tendon of the ing the volume of fluid within the pericardial cavity, thoracic diaphragm and additionally supported by the the pericardial liquid pressure remains constant until it coats of the great vessels [9]. The various tissues, the suddenly rises sharply. This led to the conclusion that fibrous pericardium is in contact with, can be seen in most of the fluid is contained in pericardial sinuses and figure 2. groves. This mostly empty space forms the so-called The fibrous pericardium contains a serous mem- pericardial reserve volume, acting as a buffer against brane, the serous pericardium, forming a closed sac. increasing pericardial liquid pressure. Only a small por- The serous pericardium is connected to the myocardium tion of the pericardial fluid remains as a thin film on (visceral pericardium) and the fibrous pericardium (pari- the interface between parietal and visceral pericardium. etal pericardium). The composite of fibrous and parietal