Regional and Epi- to Endocardial Differences in Transmural Angles of Left Ventricular Cardiomyocytes Measured in Ex Vivo Pig Hearts: Functional Implications



Recent studies point toward the existence of a significant population of cardiomyocytes that intrude transmurally, in addition to those aligned tangentially. Our aim was to investigate the extent of transmural angulation in the porcine left ventricle using diffusion tensor magnetic resonance imaging (DTMRI). Hearts from eight 15 kg pigs were arrested in diastole. The ventricles were filled with polymer to maintain the end-diastolic dimensions. All hearts were examined using DTMRI to assess the distribution of transmural angulation of the cardiomyocytes at 12 predetermined locations covering the entirety of the left ventricle. We found significant differences between the regions, as well as within the transmural subcomponents. In eight out of the 12 predetermined mural segments, the highest mean transmural angle was located sub-endocardially. The greatest mean transmural angles were found in the anterior basal region, specifically 14.9 ± 6.0-degree angle, with the greatest absolute value being 34.3-degree angle. This is the first study to show the significant heterogeneities in the distribution of helical and transmural angles within the entirety of the left ventricular walls, not only for different depths within the ventricular walls, but also between different ventricular regions. The results show unequivocally that not all the contractile elements are aligned exclusively in tangential fashion within the left ventricle. The main function of the transmurally intruding component is most likely to equalize and normalize shortening of the cardiomyocytes at all depths within the myocardium, but our findings also support the notion of antagonistic forces existing within the myocardial walls. Anat Rec, 296:1724–1734, 2013. © 2013 Wiley Periodicals, Inc.

The individual myocytes making up left ventricular walls are organized as an anisotropic three-dimensional mesh (Anderson et al., 2005; Dorri et al., 2006). Within this meshwork, most attention has been directed to the so-called helical angle, which documents the tangential alignment of the chains of cardiomyocytes relative to the equatorial ventricular plane (Streeter, 1966), albeit that more recent attention has focused on the angle of transmural orientation or intrusion, quantitating the angle from epicardium to endocardium relative to a plane at right angles to the epicardial surface (Lunkenheimer et al., 2006). According to traditional interpretations of ventricular cardiodynamics, all the cardiomyocytes were considered to be aligned in a strictly tangential fashion relative to the ventricular cavity, thus producing the constrictive force required for systolic ventricular ejection (Frank, 1901). Streeter and colleagues maintained that transmural deviations from the tangential alignment were no greater than 11-degree angle, with subsequent workers accepting this dogma. More recently, this notion has been challenged. By using a novel technique, using circular knives to remove transmural segments of the ventricular walls, Lunkenheimer et al. (2006) showed that up to three-fifths of the aggregated chains of cardiomyocytes intruded transmurally in epicardial to endocardial direction by angles as great as 40-degree angle, initially making their measurements from histological sections, but then validating the results using diffusion tensor magnetic resonance imaging (Schmid et al., 2007). We have now extended these results still further by showing that the preferential alignment of the chains of cardiomyocytes produces characteristic figure-of-eight-like patterns that encircle the cavities of both ventricles in a fashion that is highly reproducible from heart to heart (Fig. 1; Nielsen et al., 2009; Smerup et al., 2009). Importantly these patterns exhibit a smooth and continuous transmural course that changes in both the helical and transmural angles from epicardium to endocardium. We have recently shown, using a mathematical modeling approach, that this quality is crucial to achieve cardiomyocytic strains within the physiologic range (Smerup et al., 2013). The arrangement also underscores the possibility for antagonistic forces to act within the ventricular walls (Lunkenheimer et al., 2004). The aim of this study, therefore, was to examine further the three-dimensional makeup of the left ventricular walls, establishing the extent of regional variations in the transmural angulation of the aggregated chains from epicardium to endocardium.


Animal Experiments

We studied eight Danish landrace female pigs, each weighing 15 kg. Animal handling prior to the experiments, the anesthetic procedures, and surgical procurement of the hearts have all been described previously (Nielsen et al., 2009; Smerup et al., 2009). So as to secure diastolic proportions of the flaccid hearts after cardioplegic arrest, we injected a polymer (Histomer) into the ventricles via the atrioventricular valvar orifices, allowing surplus polymer to escape through the pulmonary and aortic valvar orifices, and thus avoiding excess dilation. After solidification of the polymer, the coronary arteries were perfused with Lillie's fluid, containing formalin at pH 7.4. After 1–3 days, the hearts were perfused with phosphate-buffered solution, and stored at 4°C.

Diffusion Tensor Magnetic Resonance Imaging

Imaging was performed in a Philips Intera, 1.5 T scanner (Philips Medical, Best, Netherlands), equipped with PowerTrack 6000 Gradients and Software release 2.1.3. Positioning and imaging were done as previously described (Smerup et al., 2009). Specifically, the number of signal averages was one. The scan time was from 12 to 16 hr for each heart, depending on its size. We used 32 isotropically distributed diffusion directions with the b-factor equal to 1270 s/mm2 and one with b = 0 s/mm2, 46–54 slices with 1.33 mm slice thickness and no gap, field-of-view 170 × 100 mm2 and a voxel size of 1.33 × 1.33 × 1.33 mm3. Note, that DTI was acquired with a standard spin-echo sequence in order to reduce artifacts usually occurring in echo-planar-imaging sequences. This results in artifact-free images, but disadvantage is a relatively long acquisition time.

Quantitative Measurements

The primary diffusion eigenvectors of each voxel were calculated as previously described (Nielsen et al., 2009; Smerup et al., 2009). In brief, we used a custom-made algorithm to track the manner of aggregation of the cardiomyocytes. Initially, for each voxel, the 33 symmetrically positive tensor matrix was calculated using multivariate linear fitting. After diagonalization, the eigenvectors and eigenvalues were calculated. The eigenvector corresponding to the largest eigenvalue was taken to be an indication for local cardiomyocyte orientation. The non-tangential orientation of the cardiomyocytes across the ventricular wall from epicardium to endocardium has been investigated experimentally (Geerts et al., 2002), as well as in theoretical finite elements studies (Bovendeerd et al., 2009). This aspect has also recently been examined in isolated human hearts (Lombaert et al., 2012) in terms of the so-called transverse angle, which is the difference as measured in the horizontal, or circumferential-radial, plane between the direction of the aggregated cardiomyocytes and the tangent to the local epicardial surface also lying in this plane. This value ranges from −90-degree angle to +90-degree angle, where a negative value signifies that the measured cardiomyocytes are pointing toward the endocardium, and a positive value signifies an inclination toward the epicardium. A value of 0-degree angle means that the aggregated cardiomyocytes are tangentially orientated. We showed in a previous mathematical study (Smerup et al., 2013) that non-tangential orientation of the cardiomyocytes, added onto the effects of helical angulation and ventricular torsion, might provide a means of equalization of strains across the ventricular wall from epi- to endocardium. The determining factor in this respect is the deviation from the tangential orientation itself, rather than the alignment of the cardiomyocytes toward the epicardium as opposed to the endocardium. In this study, therefore, we define a transmural angle rather than a transverse angle. The transmural angle is the absolute value of the acute angle between the primary eigenvector and its projection onto the tangential epicardial plane. We show the difference between the transverse and transmural angles in the lower panel of Figure 2. These two parameters would be identical if the cardiomyocytes were aggregated in exclusively circular fashion; in other words, in the middle of the wall. In contrast, the absolute value of the transverse angle will always exceed that of the transmural angle toward the epi- and endocardial boundaries of the ventricular walls. The transmural angle, therefore, cannot have a sign, since it is not described in relation to any geometrical entity apart from the epicardial tangent plane. In our current study, we determined the epicardial tangent plane empirically, using best squares fit from a number, at least three, sample points on the epicardial surface surrounding the radial sampling axis (E1 to E3 in Fig. 2, upper panel). Next, the long-axis LLV was determined from a point in the apex and a point in the aorto-mitral membrane. The line LNEt that is normal to the local epicardial tangent plane and intersects with LLV was now used to sample the voxels of interest through the myocardial wall; tensor values from the intersected voxels and their immediate neighbors in a three by three manner were used. The lines LH and LL are the horizontal and longitudinal tangents to the epicardium, lying in the epicardial tangent plane. The transmural angle was then defined as the angle between the primary diffusion vector and its projection onto the epicardial tangent plane regardless of the helical angle. The helical angle (not used in this study) is defined as the (positive) angle between the projection of the primary diffusion vector onto the epicardial tangent plane and the local horizontal line LH. LH is defined as a line lying on the epicardial tangent plane, and which is orthogonal to the long-axis LLV. Again, it follows that the epicardial tangent plane and the longitudinal–circumferential plane, coalesce only near the equator of the left ventricle, where the epicardial tangent in the longitudinal direction is parallel with the long axis of the ventricle. By using the epicardial tangent plane as our reference for measurements of the orientation of the aggregated cardiomyocytes, we account for any errors introduced by either the turn of the helical angle from the epicardial to the endocardial zones, or the curvature of the left myocardium. We measured transmural angles in 12 predetermined locations in the left ventricular walls, describing the heart as positioned on its apex, and with the septum in the sagittal plane. These represented the lateral, anterior, septal, and posterior walls of the ventricle at the level of the equator, and at levels halfway between the apex and the equator, and halfway between the equator and the ventricular base. More precisely, we defined the anterior, or superior, region as situated between the junction of the anterior right and left ventricular free walls, and the anterior aspect of the antero-lateral papillary muscle. The lateral or free wall region is placed between the papillary muscles. The posterior, or inferior, region is placed between the posterior aspect of the postero-medial papillary muscle and the posterior junction of the right and left ventricular free walls. The septum makes up the remainder of the mural extent between the anterior and the posterior junctions of the two ventricles. We placed our sampling points in the middle aspect of each of these regions in order to obtain a very evenly spaced distribution. This approach ensures that we are not sampling from inherently irregular regions, such as the ventricular junctions or the bases of the papillary muscles. Because of the fixed size of the voxels, and the varying thickness of the ventricular walls at these sites, the number of sampling voxels varied from 5 to 7 between animals, and between mural segments.

Figure 1.

The figure shows myocardial pathways which are tracked from the equatorial level of the sub-endocardium in the septum (blue) and in the free wall (red). As the pathways evolve they are seen to change both helical and transmural angles so that the sub-endocardial tracks extrude and the sub-epicardial tracks intrude through the myocardium.

Figure 2.

The figure shows how the transmural angles were calculated and describes the difference between the transmural angle and the transverse angle. See text for details.

Statistical Analysis

All data are presented as mean values with 95% confidence intervals. The variability in the transmural angle from epicardium to endocardium across the ventricular walls is shown by presenting these values as a function of the corresponding mural depth. By following this protocol, we produced a distribution for each of the 12 investigated mural segments. We then divided each distribution into sub-endocardial, mid-mural, and sub-epicardial components, using a depth range of 33%–66% of the mural thickness to delineate the mid-mural segment, and thus yielding a total of 36 sub-components. An overall ANOVA with a level of significance of 5% was then used to compare the means of the transmural angles between these 36 sub-components. In those instances shown to be statistically significant, we then performed similar ANOVAs to test differences within each of the 12 designated mural segments. Stata™ 8.0© 1984–2003 Statistics/Data Analysis package (Stata Corporation, 4905 Lakeway Drive, College Station, TX) was used for statistical analysis of data.

Ethical Considerations

All animal experiments were conducted after approval from the Danish Inspectorate of Animal Experimentation. The guidelines from this institution comply with “NIH publication No. 86-23, regarding principles of laboratory animal care (revised 1985). The authors had full access to the data and take responsibility for its integrity. All authors have read and agree to the manuscript as written.


The random scatter-plots shown in Figures 3-5 depict the transmural angles of the aggregated chains of cardiomyocytes as a function of their mural depth in the 12 predetermined left ventricular mural regions. Specifically, Figure 3 shows the transmural angles in the basal regions, Figure 4 shows the angles in the equatorial regions, and Figure 5 shows the angles in the apical regions. For clarity, we have also listed the mean transmural angles (Table 1). As shown in the figures and in the table, there are great differences between the regional distributions, as well as within the transmural subcomponents. This is reflected in the analysis of the mean transmural angles. The overall MANOVA, with P < 0.0001, indicates these differences to be highly significant. Thus, the transmural angle differed with respect to myocardial depth in the anterior basal (P < 0.0001), and equatorial (P < 0.0001) walls. the free wall basal (P < 0.0001), and apical (P < 0.23) walls, the posterior apical wall (P< 0.26), and the septal basal (P < 0.001) and equatorial (P < 0.0001) walls. The greatest mean transmural angles were found in the anterior basal region, where the measured value was 14.4 ± 5.4-degree angle. The greatest absolute value, measured at 28.6-degree angle, was found in the posterior apical wall (Table 2). In eight out of the 12 predetermined mural segments, the highest mean transmural angle was located in the sub-endocardial regions; the basal region exhibiting the highest mean sub-endocardial transmural angles followed by the equatorial, and the apical regions.

Figure 3.

The figure shows the transmural angle plotted against the myocardial depth in % for the four wall regions at the basal level. The horizontal stippled line delineates transmural angles above and below 7.5-degree angle (see text for details), and the vertical stippled lines delineates the mid-wall segment between 33% and 66% depth.

Figure 4.

The figure shows the transmural angle plotted against the myocardial depth for the four wall regions at the equatorial level. The horizontal stippled line delineates transmural angles above and below 7.5-degree angle (see text for details), and the vertical stippled lines delineates the mid-wall segment between 33% and 66% depth.

Figure 5.

The figure shows the transmural angle plotted against the myocardial depth for the four wall regions at the apical level. The horizontal stippled line delineates transmural angles above and below 7.5-degree angle (see text for details), and the vertical stippled lines delineates the mid-wall between 33% and 66% depth.

Table 1. Mean transmural angles in diastole across the left ventricular myocardial wall
 Anterior wallFree wallPosterior wallSeptum
  1. Mean transmural angles ± standard deviation in the 12 left ventricular wall regions. Overall MANOVA P < 0.0001. Separate MANOVA P-values below five percent indicate differences in mean transmural angles between the sub-endocardial, the mid-wall, and the sub-epicardial myocardium

BasicsSub-endocardium14.4 ± 5.4°Sub-endocardium6.2 ± 4.7°Sub-endocardium7.5 ± 4.9°Sub-endocardium7.2 ± 6.7°
Midwall11.9 ±3.5°Midwall4.8 ± 3.5°Midwall7.2 ± 4.5°Midwall6.4 ± 4.8°
Sub-epicardium9.5 ± 3.5°Sub-epicardium4.1 ± 3.2°Sub-epicardium7.8 ± 4.8°Sub-epicardium5.0 ± 3.2°
ANOVAp 0.0001ANOVAp 0.0001ANOVAp = 0.56ANOVAp = 0.001
EquatorSub-endocardium7.9 ± 4.7°Sub-endocardium5.5 ± 5.2°Sub-endocardium8.9 ± 5.8°Sub-endocardium8.1 ± 5.7°
Midwall4.7 ± 3.5°Midwall4.1 ± 3.2°Midwall8.0 ± 4.7°Midwall8.4 ± 5.8°
Sub-epicardium3.9 ± 2.8°Sub-epicardium4.7 ± 4.3°Sub-epicardium7.2 ± 7.2°Sub-epicardium5.3 ± 3.9°
ANOVAp < 0.0001ANOVAp = 0.08ANOVAp = 0.09ANOVAp < 0.0001
ApexSub-endocardium5.6 ± 4.2°Sub-endocardium5.7 ± 4.6°Sub-endocardium7.6 ± 6.3°Sub-endocardium5.2 ± 4.3°
Midwall6.3 ± 4.4Midwall5.9 ± 3.9Midwall5.5 ± 3.7Midwall5.4 ± 4.2
Sub-epicardium5.9 ± 4.4°Sub-epicardium4.6 ±3.1°Sub-epicardium5.5 ± 8.1°Sub-epicardium5.7 ± 4.3°
ANOVAp = 5.9


p = 0.023ANOVAp = 0.026ANOVAp = 0.78
Table 2. Maximum transmural angles in diastole


To the best of our knowledge, ours is the first investigation to study in detail the transmural angles of the myocytes from epicardium to endocardium for the entirety of the ventricular mass. Interestingly, in a recent study, Lombaert et al. (2012) used diffusion tensor magnetic resonance imaging to construct a statistical atlas of the helical and transverse angles covering the 17 American Heart Association segments of the human left ventricular myocardium. As we have discussed in “Materials and Methods” section and as is further elaborated below, the transverse and the transmural angles both describe the non-tangential orientation of the cardiomyocytes, but they differ in their geometrical definitions. In our opinion, it is the transmural angle that is best suited for the mechanistic assessment of the implication of non-tangentiality for equalization of myocyte strains. In this study, therefore, we used a novel algorithm for analysis, which accounts for the curvature of the myocardial wall, and the depth-related variation of the helical angle, to reveal the marked spatial variability of the transmural angle. This analysis revealed significant heterogeneities in the distribution of angles, not only for different depths within the ventricular walls, but also between different ventricular regions. The results show unequivocally that, when the left ventricle is considered in its entirety, not all the contractile elements are aligned exclusively in tangential fashion. Subsequent to the emergence of the concept of Frank (1901), those seeking to explain cardiodynamics tended to discount the mere existence of cardiomyocytes aligned with non-tangential orientation, the emphasis being placed on the changing helical angulation of the perceived tangentially aligned cardiomyocytes (Streeter, 1966; Streeter et al., 1969). Streeter and colleagues had recognized the existence of some myocytes aligned in non-circumferential fashion, but claimed that the transmural angulation across the wall from epicardium to endocardium, which they termed the angle of imbrication, was no greater than 11-degree angle on average. This assertion was later endorsed by Geerts et al. (2002). In contrast, Lunkenheimer et al. (2004) used a circular knife technique to reveal the existence of a significant population of non-tangential cardiomyocytes (Lunkenheimer et al., 2006; Schmid et al., 2007). Their data reveals that up to two-fifths of the cardiomyocytes diverge by more than 7.5-degree angle from the tangential orientation. These results are in good agreement with our current findings. We found that, dependent upon myocardial region, between approximately one half to one fifth of the measured voxels displayed transmural angles greater than 7.5-degree angle (Figs. 3-5). Furthermore, we found mean values ranging from approximately 6–15-degree angle in the endocardial zones (Table 1) while maximal values for transmural angulations during diastole varied in the range of 17–29-degree angle for the various myocardial regions (Table 2). These results are in accordance with our recent mathematical model study, which shows that transmural angulation of the cardiomyocytes is crucial for equalization and normalization of myocytic strains to retain physiologic values around 15% at all depths within the myocardial wall during systolic mural deformation (Smerup et al., 2013). The arrangement may also point toward the existence of intrinsic myocardial antagonism.

Importance of the Transmurally Intruding Netting Component for Normal Ventricular Function

The mechanical link between cardiomyocytic shortening and systolic left ventricular deformation, in terms of combined long-axis shortening, circumferential constriction and mural thickening, is not as straightforward as may at first be perceived. There is substantial evidence to suggest that all cardiomyocytes are constrained to shorten to approximately the same modest degree, namely from 14% to 16% (Halle and Wollenberger, 1970; Julian and Sollins, 1975; Krueger and Pollack, 1975; Lehto and Tirri, 1980; Rodriguez et al., 1992). Because of the hemi-ellipsoidal solid geometry of the left ventricular wall, circumferential strains increase with depth through the myocardium, whereas the longitudinal strains, for all practical purposes, remain constant (Arts et al., 1979; Sabbah et al., 1981; Arts et al., 1982; Gallagher et al., 1985). This means that, in the greater parts of the ventricular walls, apart from the outer zones, the circumferential strains are greater than the suggested myocytic strains of 14–16% (Bogaert and Rademakers, 2001). Or, in plain words, the myocardial wall seems to deform more than its contractile elements! Thus, if the cardiomyocytes were only oriented in circular fashion, they would be unable to transfer their systolic tension onto most of the myocardium. Until now, two related structural–functional features of the myocardium have been suggested to explain this paradox, and to normalize and equalize cardiomyocytic strains. These are, first, the counter-wound helical arrangement of the cardiomyocytes, and second, the associated functional ventricular torsion (Arts et al., 1979; Arts and Reneman, 1980; Arts et al., 1984; Hansen et al., 1987). The compensatory mechanism of the helical structure is a structurally based effect of the more longitudinal orientation of the endocardial and epicardial cardiomyocytes, which consequently do not have to produce large strains in the magnitude of the circumferential strains, but instead produce longitudinal strains in the order of 15% (Bogaert and Rademakers, 2001), which is within the normal physiological range of cardiomyocytic strains (Arts et al., 1979). The second compensatory effect, torsion, is a direct functional effect of the helical arrangement, since it is caused by the epicardial populations of cardiomyocytes aggregated with a left hand helical orientation, which cause the left ventricular apex to rotate counter clockwise during systole (Arts et al., 1984; Ingels et al., 1989). The rotation involves the entirety of the ventricular wall, and thus counteracts the potential net clockwise rotation of the endocardium, which consequently lowers cardiomyocytic strains in the endocardial zones. The combined effect of these two compensatory mechanisms, however, is insufficient to normalize the known values for shortening of the cardiomyocytes through the entirety of the ventricular myocardium (Streeter and Hanna, 1973; Arts et al., 1979; Chadwick, 1982; Rijcken et al., 1999; Bogaert and Rademakers, 2001; Stevens and Hunter, 2003; Dorri et al., 2006). In a recent model, we represented the left ventricle as a cylindrical tube containing the three-dimensional architecture of the myocardial mesh, including transmural angulation, and calculated deformations as governed by hydraulic principles (Smerup et al., 2013). The model confirmed the insufficient effect of the helical angle and the associated left ventricular torsion on equalization of cardiomyocytic strains. The addition of transmural angulation, in contrast, was able to equalize and normalize calculated strains to a mean of 15.3%, with a maximum of 16.7%, which is clearly within the physiological range. The results of this study, therefore, further substantiate the existence of the transmurally intruding population of aggregated cardiomyocytes, and stress the functional importance of this quality of the myocardial mesh for normal ventricular deformation during systole.

Great Transmural Angles may be the Structural Substrate for Myocardial Antagonism

The controversial notion of antagonistic forces existing within the myocardial walls was first suggested by Brachet (1813), who claimed the existence of radially oriented groups of cardiomyocytes which were capable of thinning the ventricular wall, as opposed to the majority of the tangentially oriented, and thus constrictive, cardiomyocytes. This concept was later refuted by studies from Pettigrew (1864), Streeter (1966), and Greenbaum et al. (1981) all of whom were able to show that the prevailing grain of cardiomyocytes was encircling the ventricular cavities, and thus seemingly did not hold the potential for the generation of dilatory forces. The concept of antagonistic forces, however, was revived by Lunkenheimer et al. (2004), who used needle force-transducers inserted into the ventricular walls to show the existence of two antagonistic signals in the myocardium, revealing the so-called unloading and auxotonic forces, with the structural substrate for intrinsic myocardial antagonism being transmurally angulated groups of cardiomyocytes.

In our recent mathematical model, we used transmural angles ranging linearly from 6-degree angle in the epicardium to 10-degree angle in the endocardium (Smerup et al., 2013). It is clear that these values coincide perfectly with the averaged mean transmural angles found in our present study (Table 1). Our present study, however, also revealed absolute values that greatly exceed these means (Table 2). The potential role for such deviation from the tangential orientation can also be elucidated with our mathematical approach. It can be calculated that cardiomyocytes with diastolic transmural angles greater than approximately 22-degree angle, depending upon mural depth, will not contribute to myocardial thickening. Instead, they potentially act antagonistically against the more tangentially oriented cardiomyocytes, due to the fact that they increase their transmural angle to more than 45-degree angle during systole, and hence are directed more radially than circumferentially at end-systole. It is likely, therefore, that cardiomyocytes with diastolic transmural angles ranging from 0 to approximately 20-degree angle act to normalize and equalize strains during systole, and therefore contribute to constriction of the ventricular cavities as discussed above. In contrast, cardiomyocytes with transmural angles greater than 20-degree angle may act partially to antagonize the constriction.

Methodological Considerations

Because of the complex three-dimensional arrangement of the aggregated cardiomyocytes, and specifically because of the depth-related changes in their helical angles, it is very difficult to assess the extent and angulation of intrusion of individual cells when using histological sections prepared in strictly planar fashion. In a transverse block cut across the ventricular wall, when examining, for example, histological slices made in the horizontal plane, the only true representation of the extent of cardiomyocytes intruding from epicardium to endocardium would be found in the center of the mid-mural component, where the helical angle is close to zero, and the long axis of the individual cells is more-or-less in plane with the section. It is possible, however, to compensate for the depth-related differences in the alignment of the cardiomyocytes by cutting the transmural myocardial block with circular knifes (Lunkenheimer et al., 2006; Schmid et al., 2007). But this technique itself is limited in that only discrete, and somewhat arbitrary, curved planar positions are investigated within the ventricular walls. The method, therefore, is not optimal for precise determination of spatial heterogeneities over the entirety of the ventricular mass.

In our current study, we used diffusion tensor imaging to investigate selected parts of the left ventricle, focusing on 12 sites so as to simplify the measurements. We used the inherent properties of the primary diffusion vector to assess the transmural angle across the wall from epicardium to endocardium. The angle is measured as the absolute difference between the projection of the primary diffusion vector onto the local epicardial tangential plane and the primary diffusion vector itself (Fig. 2). While similar methods have been employed by others to overcome the local curvature of the myocardial walls, these studies have measured the so-called transverse angles, rather than the transmural angles (Lombaert et al., 2012). As we have discussed briefly in our section dealing with our methodology, there are differences in their geometrical definition. Thus, the transverse angle is measured between the projection of the primary diffusion vector onto the horizontal plane, and the epicardial tangent also lying in this plane. While both parameters describe the deviation of the long axis of the cardiomyocytes away from their tangential orientation, it is our opinion that the functional implications might differ. The transverse angle directly describes the potential force vector relevant for circumferential–radial shear of the myocardium, or in other words, the phenomenon observed when the values of endocardial and epicardial systolic rotation are not equal (Bogaert and Rademakers, 2001). An important quality of the transverse angle, as opposed to the transmural angle used in our current study, is that it possesses both positive and negative values (Lombaert et al., 2012). Its distribution within a confined volume at any given myocardial depth is Gaussian, with a mean value which is close, but not equal, to zero. Most likely, therefore, there exists a force balance between the positively and negatively transversely angled cardiomyocytes that governs the process of circumferential–radial shear. Conversely, the transmural angle, as we have discussed above, is arguably more suited for the assessment of the ability to equalize strains in the cardiomyocytes across the depth of the ventricular wall. In this respect, our previous mathematical model revealed that this value was not influenced by the orientation of the cardiomyocytes toward or away from the endocardium (Smerup et al., 2013).

We recognize the limitations of our current study, in particular the lack of direct histological evaluation. The use of diffusion tensor magnetic resonance imaging, nonetheless, has been thoroughly validated by histology in previous studies (Hsu et al., 1998; Scollan et al., 1998). Another potential error of the technique is the fact that the sampled voxels each have a volume of approximately 1.3 × 1.3 × 1.3 mm3. Given the average size of a cardiomyocyte at 20 × 20 × 100 µm3, and recognizing the additional influence of the extracellular matrix in aggregating the individual cells, the primary eigenvector represents the mean direction in the chosen voxel of at least 25,000 cardiomyocytes. The angulations of some of these individual cardiomyocytes may diverge significantly from the measured alignment using diffusion tensor imaging in terms of greater or lesser angles relative to the tangential and equatorial planes of the cavities. Recent studies have shown that populations of individual cardiomyocytes diverge significantly from a tangential direction within the myocardium (Lunkenheimer et al., 2006). Such detailed geometry is not revealed with the present technique.