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Conceived and designed the experiments: ACR TD. Performed the experiments: ACR TD. Analyzed the data: MP WK PHMB TD. Contributed reagents/materials/analysis tools: WK PHMB. Wrote the paper: MP TD PHMB WK ACR.

The authors have declared that no competing interests exist.

The left ventricle (LV) of mammals with Situs Solitus (SS, normal organ arrangement) displays hardly any interindividual variation in myofiber pattern and experimentally determined torsion. SS LV myofiber pattern has been suggested to result from adaptive myofiber reorientation, in turn leading to efficient pump and myofiber function. Limited data from the Situs Inversus Totalis (SIT, a complete mirror image of organ anatomy and position) LV demonstrated an essential different myofiber pattern, being normal at the apex but mirrored at the base. Considerable differences in torsion patterns in between human SIT LVs even suggest variation in myofiber pattern among SIT LVs themselves. We addressed whether different myofiber patterns in the SIT LV can be predicted by adaptive myofiber reorientation and whether they yield similar pump and myofiber function as in the SS LV. With a mathematical model of LV mechanics including shear induced myofiber reorientation, we predicted myofiber patterns of one SS and three different SIT LVs. Initial conditions for SIT were based on scarce information on the helix angle. The transverse angle was set to zero. During reorientation, a non-zero transverse angle developed, pump function increased, and myofiber function increased and became more homogeneous. Three continuous SIT structures emerged with a different location of transition between normal and mirrored myofiber orientation pattern. Predicted SIT torsion patterns matched experimentally determined ones. Pump and myofiber function in SIT and SS LVs are similar, despite essential differences in myocardial structure. SS and SIT LV structure and function may originate from same processes of adaptive myofiber reorientation.

Deciphering the structure-function relation in healthy hearts is important to understand cardiac pathologies. In the structure-function relation, the myofiber orientation patterns play a central role. Between people with normal organ arrangement (Situs Solitus, SS) this pattern is strikingly similar. Such consistency in myocardial structure might be the result of an adaptation process to accommodate for homogeneous distribution of myofiber strain across the wall and for optimal pump function. The heart of people with a mirror-imaged position of their organs (Situs Inversus Totalis, SIT) has a modified myofiber orientation pattern with respect to SS: normal at the LV apex, but mirrored at the base. Hence, studying SIT hearts provides a unique possibility 1) for understanding adaptation mechanisms related to myofiber orientation and mechanical load, and 2) to gain additional insights into the structure-function relations of the LV. Through mathematical modeling of LV mechanics, we have found that myofiber orientation pattern in both SS and SIT may originate from same processes of adaptive myofiber reorientation. After reorientation, pump and local myofiber function were found to be similar between SS and SIT as well: a remarkable finding when considering the large difference in myofiber orientation pattern.

The myofiber orientation pattern in the cardiac left ventricular wall has an invariant nature among mammals, including humans, with a normal organ arrangement (Situs Solitus, SS)

SS LVs not only display an invariant myofiber pattern, but also a large similarity in experimentally determined measures of deformation, such as torsion

Several model studies demonstrated that myofiber orientation pattern is a major determinant of strain distribution in the cardiac wall

Scarce experimental and anatomical studies demonstrated that in individuals with Situs Inversus Totalis (SIT), i.e., a complete mirror image of their organ anatomy and position, the myofiber orientation pattern of the LV is not a complete mirror image of the pattern in the SS LV

As can be expected considering the dependency of cardiac deformation on myofiber orientation pattern, torsion in the SIT LV was found to differ from that in the SS LV. At the apex, torsion patterns of SS and SIT coincide, whereas at the base an inverted torsion pattern is observed in SIT when compared to SS (

In this study, we addressed the question whether variations in myofiber patterns of the SIT LV can be predicted by adaptive reorientation of myofibers, and whether these various outcomes yield similar pump and myofiber function as in the SS LV. To investigate this, we employ a mathematical model of LV mechanics

In all simulations, local and global LV function increased significantly during the adaptation process as indicated by the increase in 1) myofiber shortening (decrease of myofiber strain) during ejection

Local function is presented by means and standard deviations (SD) of variables natural myofiber strain during isovolumic contraction

After 15 adaptation cycles, function parameter values are not significantly different between the SIT simulations. Neither are the values in the SIT simulations significantly different in comparison to the SS simulation (

Mean values and standard deviation (SD) of local function parameters are presented left, values of global parameters right. Differences between simulations are not significant.

Local myocardial function in simulation

Myofiber Cauchy stress-natural strain loops are analyzed in the nodes indicated in the LV mesh (right) before (− −) and after (−) reorientation. The location of the transition zone before reorientation is also indicated in the LV mesh.

Larger changes are observed between initial and final distributions of

In

In this study, different SIT LV structures were estimated using a finite element (FE) model of LV mechanics

In

As a consequence of myofiber reorientation, local and global LV function increased significantly in all simulations. This suggests that, as in the SS LV, mechanical work could indeed be distributed homogeneously in the SIT LV too. Moreover, the location of the transition from a normal myofiber orientation pattern at the apex to an inverted pattern at the base had no influence on the local and global SIT LV function. Finally, SIT LV function was comparable to SS LV function, which is in agreement with the finding that SIT individuals display no cardiac complaints

The choice of simulations with fixed

The additional simulations were performed with a variation on simulation

This finding seems to contradict the finding of our previous study in the SS LV, where we concluded that the effect of the initial condition of the helix angle disappeared upon adaptation

In

Because of relaxation of spins in the magnetized tissue, the strength of the MR signal decreases over time. This makes tracking of the tags more difficult at the end of the filling phase. The decrease in reliability of the estimation of torsion towards the end of the cardiac cycle is evident from the non-zero values of torsion amplitude: considering the cyclic deformation of the myocardium, these values are expected to return to zero.

The maximum amplitude of torsion occurred earlier in the model than in the experiment. This observation indicates that the timing of increase and decrease of active stress development in the model is not entirely realistic. However, the difference in timing had no influence on the increase in homogeneity in function nor on the gradient in torsion amplitude, which was developed in the SIT simulations after reorientation.

The results of the shear-induced adaptation may have been influenced by the absence of sheets in the constitutive model of the tissue. Sheets are predominantly oriented in transmural direction, facilitating thickening of the wall

As mentioned before, other adaptation mechanisms are likely to be active as well. Clinically, one of the most evident examples of adaptation is the change in LV wall mass and cavity volume in response to pressure and volume overload, respectively. In addition, in reality the externally unloaded LV exhibits a transmural gradient in sarcomere length with epicardial sarcomeres being longer than endocardial ones

In this study, torsional deformation was used to compare results of model and experiment. We also compared model predictions of the deformation mode circumferential-radial shear to experimental data. Similar to our previous study for SS

Our cardiac mechanics model has several limitations. For example, the onset of contraction was assumed to be homogeneous, despite the fact that there is a delay in electrical activation of about

Geometry and structure of the LV were assumed rotationally symmetric, while interaction of the LV with the right ventricle (RV) was not taken into account. Myofiber orientations show differences between septum and LV free wall

In this study, we have found that local and global LV function in SIT and SS were similar, despite essential differences in myocardial structure. Using the same processes of shear-induced myofiber reorientation, both SS and SIT LV structures were estimated by this adaptation mechanism and the structures were continuous. The space of feasible solutions predicted by the model turned out to be larger than the experimentally found variation in structures. This suggests that additional physiological mechanisms exist that regulate myofiber orientation. Large agreement in torsion data between model and experiment suggests that measured interindividual differences in torsion pattern could originate from different locations of the transition from a normal myofiber orientation pattern at the apex to an inverted pattern at the base.

All subjects gave informed consent prior to enrolment in the study, in accordance to the joint ethical committee of Maastricht University and Academic Hospital Maastricht.

Tissue deformations during the cardiac cycle are calculated with a generic finite element (FE) model of LV mechanics. With respect to geometry, material properties and the circulation in which the LV is embedded, this FE model is identical to the model presented in

In the passive stress-free state, a thick-walled geometry is assumed (

Myocardial tissue Cauchy stress

Active stress

In the model, the quasi-static equations of conservation of linear momentum are solved:

The equilibrium equations (3) are solved numerically with a Galerkin type finite element method using 27-noded hexahedral elements with a tri-quadratic interpolation of the displacement field. Because the model is rotationally symmetric, tissue displacements are described in a right-handed cylindrical coordinate system {

The myofiber orientation

We simulated myofiber reorientation with the model by Kroon

One SS simulation and three SIT simulations were performed. In all simulations, the first 10 consecutive cardiac cycles were used to reach a hemodynamic steady state and myofiber reorientation was not included. In subsequent cycles myofiber reorientation was simulated throughout the whole LV.

At the start of the adaptation process, the transmural distribution of

In both SS and SIT the parameterized description of fiber orientation is abandoned during adaption, and myofiber orientation is adapted per node.

According to anatomical data of SIT LVs, the helix angle

In this study, the location of the transition zone

Local function was quantified by changes in mean and standard deviation (SD) of four parameters quantifying mechanical tissue load: stroke work density

Left ventricular torsion