Computational analysis of the myocardial structure: Adaptation of cardiac myofiber orientations through deformation

Abstract

Deformation and structure of the cardiac wall can be assessed non-invasively by imaging techniques such as magnetic resonance imaging. Understanding the (patho-)physiology that underlies the observed deformation and structure is critical for clinical diagnosis. However, much about the genesis of deformation and structure is unknown. In the present computational model study, we hypothesize that myofibers locally adapt their orientation to achieve minimal fiber-cross fiber shear strain during the cardiac cycle. This hypothesis was tested in a 3D finite element model of left ventricular (LV) mechanics by computation of tissue deformations and subsequent adaptation of initial myofiber orientations towards those in the deformed tissue. As a consequence of adaptation, local tissue peak stress, strain during ejection and stroke work density were all found to increase by at least 10%, as well as to become 50% more homogeneous throughout the wall. Global LV work (peak systolic pressure, stroke volume and stroke work) increased significantly as well (>9%). The model-predicted myofiber orientations were found to be similar to those in experiments. To the best of our knowledge the presented model is the first that is able to simultaneously predict a realistic myocardial structure as well as to account for the experimentally observed homogeneity in local mechanics.

Introduction

Deformation and structure of the cardiac wall can be assessed by magnetic resonance imaging techniques such as tagging (Axel, 1989) and diffusion tensor imaging (DTI) (Geerts et al., 2002, Helm et al., 2006), respectively. Understanding the (patho-)physiology that underlies the observed deformation and structure is critical for clinical diagnosis. However, much about the genesis of deformation and structure is unknown. In this study, we propose to use a computational model to test hypothesized processes involved in the genesis of the myocardial structure. A correct computational estimate of myocardial structure as obtained with DTI would substantiate a possible role for the hypothesized processes in real physiology.

An important observation is that the cardiac left ventricle adapts its cavity and wall volume in response to altered mechanical loading (Omens, 1998, Holmes, 2004, Donker et al., 2005). Furthermore, models of cardiac mechanics have demonstrated that the load distribution in the wall is highly dependent on the myofiber orientations, i.e. variation of the myofiber orientations within the range of experimental data resulted in significant differences in myofiber stresses and strains (Bovendeerd et al., 1992, Ubbink et al., 2006). Experimental data, however, show that myofiber shortening during ejection exhibits little heterogeneity throughout the wall (MacGowan et al., 1997). In addition, heterogeneity in metabolism and oxygen consumption is limited as well, which suggests that myocardial work is homogeneously distributed (van der Vusse et al., 1990). These observations suggest the existence of an additional adaptive process controlling myofiber orientation so that mechanical load is homogeneously distributed over the wall (Arts et al., 1994, Rijcken et al., 1999, Geerts et al., 2002).

Rijcken et al. (1999) hypothesized that myofiber orientations are such that myofiber shortening throughout the cardiac wall is distributed uniformly. In their study, a polynomial description of the spatial distribution of myofiber orientations was used. Subsequently, coefficients of the polynomial were optimized for minimal heterogeneity in myofiber shortening during ejection. At the minimum, the myofiber angles were found to be realistic, thus supporting the idea that myofiber directions are such that loading is homogeneously distributed. Translation of the model to physiology implies that heterogeneity can be sensed and that myofiber orientations can be adapted at a spatial scale larger than that of the individual myofiber. This is unlikely to be realistic. Instead, it is more likely that cells adjust their orientation locally in response to a local stimulus (Arts et al., 1994).

For collagenous tissues, models have been proposed for adaptation of local collagen fiber orientation in response to local tissue deformation (Baek et al., 2006, Driessen et al., 2004, Driessen et al., 2008, Wilson et al., 2006). Application to passively loaded tissues such as the aortic valve leaflet, the artery or articular cartilage, showed that alignment of collagen in between principal deformation directions results in a structure similar to that in the real tissue. However, in the actively contracting cardiac wall, principal directions of deformation do not correlate directly to the myofiber orientation (Azhari et al., 1993, MacGowan et al., 1997, Prinzen et al., 1984, Waldman et al., 1988). Consequently, an alternative hypothesis is needed for the myocardial tissue.

In this study, we build upon the hypothesis that the local myocardial structure is determined by local deformation and assume that myofibers locally adapt their orientation to achieve minimal shear strain during the cardiac cycle. It is known that the extra-cellular matrix (ECM) acts as an important regulator of the myocardial structure. For instance, a disease that affects the ECM integrity such as osteogenesis imperfecta was found to coincide with abnormal myofiber orientations (Weis et al., 2000). We assume that fiber-cross fiber shear deformation, as induced by systolic myofiber contraction, reflects mechanical load of the connections between the ECM and the myofibers. These forces locally affect the structural integrity of the myocardium (see Fig. 1). In the process of continuous ECM turnover, rearrangement of connections would lead to reduction of forces between the myofibers and the ECM. Eventually, a structure would appear with minimal fiber-cross fiber shear.

The above hypothesized mechanism was investigated in a finite element model of left ventricular mechanics (Kerckhoffs et al., 2003), extended with a closed-loop model of the circulation. The model-predicted structure was quantitatively compared with DTI data from literature. In addition, we analyzed the effect of adaptation of the myofiber orientations on local mechanics and global hemodynamics.