Three-dimensional architecture of the left ventricular myocardium



Concepts for ventricular function tend to assume that the majority of the myocardial cells are aligned with their long axes parallel to the epicardial ventricular surface. We aimed to validate the existence of aggregates of myocardial cells orientated with their long axis intruding obliquely between the ventricular epicardial and endocardial surfaces and to quantitate their amount and angulation. To compensate for the changing angle of the long axis of the myocytes relative to the equatorial plane of the ventricles with varying depths within the ventricular walls, the so-called helical angle, we used pairs of cylindrical knives of different diameters to punch semicircular slices from the left ventricular wall of pigs, the slices extending from the epicardium to the endocardium. The slices were pinned flat, fixed in formaldehyde, embedded in paraffin, sectioned, stained with azan or hematoxilin and eosin, and analyzed by a new semiautomatic procedure. We made use of new techniques in informatics to determine the number and angulation of the aggregates of myocardial cells cut in their long axis. The alignment of the myocytes cut longitudinally varied markedly between the epicardium and the endocardium. Populations of myocytes, arranged in strands, diverge by varying angles from the epicardial surface. When paired knives of decreasing diameter were used to cut the slices, the inclination of the diagonal created by the arrays increases, while the lengths of the array of cells cut axially decreases. The visualization of the size, shape, and alignment of the myocytic arrays at any side of the ventricular wall is determined by the radius of the knives used, the range of helical angles subtended by the alignment of the myocytes throughout the thickness of the wall, and their angulation relative to the epicardial surface. Far from the majority of the ventricular myocytes being aligned at angles more or less tangential to the epicardial lining, we found that three-fifths of the myocardial cells had their long axes diverging at angles between 7.5 and 37.5° from an alignment parallel to the epicardium. This arrangement, with the individual myocytes supported by connective tissue, might control the cyclic rearrangement of the myocardial fibers. This could serve as an important control of both ventricular mural thickening and intracavitary shape. Anat Rec Part A 288A:565–578, 2006. © 2006 Wiley-Liss, Inc.

The ventricular myocardium is well recognized to be a mesh (Humphrey and McCulloch, 2003), with the individual myocytes attached to each other within a supporting matrix of collagenous fibrous tissue (Lev and Simkins, 1956; Grant, 1965; Goldsmith et al., 2004). Investigations using confocal microscopy have shown that each individual myocyte is linked to its neighbors, not only in end-to-end but also in end-to-side fashion (Canny, 1986). When considered in two dimensions, the effect is to produce endless sequences of myocytes, splitting in the fashion of railway lines, with some of the branches moving discernibly away from the orientation of the main line. Unlike railway lines, however, the myocardial cells branch in three dimensions, producing a contractile spatial mesh. There is no beginning and ending of the contractile chains thus formed, as is seen in skeletal muscle. Histologic sectioning (Mall, 1911; Feneis, 1943–1944; Hort, 1960; Streeter, 1979; LeGrice et al., 1995), as well as anatomic dissection (Mall, 1911; Anderson and Becker, 1980; Torrent-Guasp, 1980; Greenbaum et al., 1981; Sanchez-Quintana et al., 1990), makes it possible to discern the predominant orientation of the groups of individual myocytes aggregated together within the mesh, albeit there is ongoing disagreement concerning their specific arrangement. In part, this represents the fact that, because of their frequent branching, the myocytes, unless cut parallel to their long axis, have markedly variable shapes. If the orientation of these aggregates of individual myocytes is accurately to be determined, histological sections are required that expose a representative number sectioned parallel to their long axis, with the cut taken over sufficiently long distances to permit measurements of their alignment relative to the epicardial and endocardial surfaces of the ventricular wall. This is difficult to achieve when blocks of the ventricular wall are simply sectioned in their individual orthogonal planes. Previous studies of cubes of myocardium have shown that the alignment of the aggregated myocytes relative to the equatorial plane of the ventricles varies in characteristic fashion. When the mesh making up the wall is traced from epicardium to endocardium, the measured long axes of the cells rotate around a radial axis, with the degree of rotation being described as the helical angle (Hort, 1960; Streeter, 1979). Debate continues, however, concerning the extent of variability in alignment relative to the tangential plane (Hort, 1960; Streeter, 1979; Lunkenheimer et al., 2004). So as to provide more information on this aspect of ventricular architecture, we have sectioned the ventricular wall using circular knives, the technique being designed to permit us to assess the longitudinal orientation of the myocardial aggregates within the various levels of the transmural sections. Our findings reveal order in the way that the myocytes are assembled within the supporting fibrous matrix, the arrangement being best described as a nonuniform anisotropic three-dimensional mesh that coheres not only in the longitudinal plane of the ventricular wall, but also transversely from epicardium to endocardium.


We used three pairs of cylindrical knives, having diameters of 68 and 58 mm, 40 and 30 mm, and 30 and 20 mm, respectively, to remove slices of 5 mm thickness from the left ventricular wall of 10 porcine hearts. All hearts were procured from the slaughterhouse within 2 hr after death, thus being in the state of rigor mortis. In each heart, we opened the left ventricle from base to apex, using a cut made parallel to the posterior descending coronary artery, having first removed the right ventricle, and then pinned the left ventricular wall flat with its epicardium uppermost. The knives prepared by our toolmaker (Fig. 1) were punched through the wall from epicardium to endocardium, thus producing transmural slices (Fig. 2). Sections taken across the atrioventricular groove were semicircular, while those taken more toward the apex approached closer to full circle.

Figure 1.

The three pairs of twin knives used to cut our sections. The diameters are 20 and 30 mm, upper left; 30 and 40 mm, upper right; and 58 and 68 mm for the lower set.

Figure 2.

The left-hand panels show the scheme of the various angulations of the long axis of the individual myocytes when assessed at increasing depth from the epicardium to the endocardium in the superior wall of the left ventricle (top), the position of a semicylindrical twin knife intruding the wall in normal direction to the epicardium (middle), and the resulting myocardial slice bent open to a flat specimen, and with the epicardium on top, the endocardium below, the septal end at the left and the region of the obtuse margin at the right hand (lower). We have then marked art-factually the reproducible arrangement of myocytes cut in parallel to their long axis, this being seen as the diagonal that crosses the ventricular wall from its epicardial to the endocardial surface. As is shown in the middle panel, the left side of the knife parallels the long axis of the subepicardial fibers, the midportion parallels the long axis of some circular fibers in the middle of the wall, while the right side of the knife cuts the subendocardial fibers in their long axis. The middle panels show the ventricular mass of a freshly excised porcine heart subsequent to the preparation of two semicircular sections cut with a pair of knives of 68 and 58 mm diameter. The slice obtained close to the atrioventricular junction (upper) has been cut with the concave part of the knife upward. The profile closest to the apex (lower) has been cut with the concave part of the knife pointing downward. The right panels show the same aspects of a porcine heart after heat denaturation by boiling, with subsequent peeling of fibers to expose the alignment of the myocytes as they change their longitudinal orientation, the so-called helical angle, when traced at increasing depth from the epicardium toward the endocardium.

The slices obtained were fixed in formaldehyde while sandwiched between stainless steel meshes, thus keeping them flat. The slices were labeled to show whether the convexity or concavity of the initial semicircle or circle pointed toward the atrioventricular groove. After dehydration, the slices were embedded in paraffin, cut at a thickness of 20 microns parallel to their long axes to produce transmural sections, and stained using azan or haematoxylin and eosin. We then analyzed the entirety of the sections microscopically at 100 times amplification, coloring artificially all those segments sectioned axially over a sufficiently long distance to permit accurate measurements of their transverse orientation relative to the epicardial plane.

Automatic Analysis of Orientation of Myocytes

We developed an automatic method to analyze the orientations of the myocytes. The method is based on techniques used in digital image processing (Fig. 3). These may not be familiar to many readers, so we have tried to summarize the approach in nontechnical fashion. The data are produced as a digitized picture consisting of an array of 768 × 574 pixels. With each pixel, we have three numbers, representing the intensities of the red, blue, and green components of the picture at that point. As in a digital photograph, these data are sufficient to reconstruct the picture (Fig. 3a). The first step of preprocessing is to combine the three color components at each pixel into one value, the so-called gray-scale value, which is interpreted as a black-white intensity, the value of one representing black and the value of zero representing white. This image is shown in Figure 3b. Care must be taken to choose the combination so as to preserve the contrast in the picture. In our example, shown in Figure 3a, the variation is predominately in the red component. Had we used only the green component to create the gray-scale image, the image would lose much of the detail.

Figure 3.

The steps involved in automatic processing. a shows the digitized color image with the inset marking the area which is amplified for image c. b shows the result after pre-procession. c shows extracted central lines with sampled color-coded orientations. d shows the histogram of the orientation (red bars) and the estimated distribution (blue dashed line).

The next step is to enhance the edges of the myocytes (Canny, 1986). If this was done by hand, we would first locate the edges of the individual myocytes. When performing this digitally, we begin by enhancing the edges in the image. The basic idea is that, at an edge, there is a rapid change in the density. At each pixel, we subtract the gray-scale intensity in the pixel from the intensity in the neighboring pixel to the right and call this δx. Pixels where δx is large are near edges running parallel to the vertical direction. To capture edges running parallel to the horizontal direction, we subtract the gray-scale intensity in the pixel from the intensity in the neighboring pixel immediately above and call this δy. Knowing both δx and δy, we can say that, if δx + δy is large at a pixel, then the pixel is near an edge, and the ratio of δx to δy tells us the slope of this edge. In technical terms, the two numbers δx and δy together are called the gradient vector at that pixel. In action, we use a slightly more sophisticated tool, called the Sobel operator, to compute δx and δy. This tool uses the values of intensity at a pixel and its eight immediate neighbors. Having enhanced the edges, we proceed to extract the midline. If we were processing the image shown in Figure 3b by hand then, after locating the edges of a myocyte, we could take cross-sections of the myocyte and thereby determine the midline of the myocyte as the curve joining the midpoints of the cross-sections.

Implementation by computer uses another idea, one that would be impractical by hand. As discussed above, the pair of numbers δx and δy tell us when an edge is near, and also the slope of any such edge. They tell us as well the direction in which the center of the myocyte lies. To understand this, consider a horizontal myocyte. Inside the myocyte the intensity is nearly zero, while outside it is nearly 1 (Fig. 3b). At the upper edge of the myocyte, δy is equal to 1 − 0, that is, 1, while at the lower edge, δy is equal to −1. So, if we start on an edge and move in the opposite direction to δy, that is, downward if δy is positive and upward if δy is negative, then we will move toward the center of the myocyte. This argument can be extended to the case when neither δx nor δy is zero, so that the edge of the myocyte is a sloping line.

Using this information, the implementation moves the edges toward the centers of their myocytes. Were we to do this by hand, we could continue until the edges coalesced. This would happen along the midlines of the myocytes. To understand the computer implementation, let us go back for a moment to the case of a horizontal myocyte discussed above. As we saw, δy is 1 at the upper edge and −1 at the lower edge. As the edges move toward one another, δy will change ever more abruptly near the midline. The implementation is based on this idea. The values of δx and δy are combined using a new operator, called the div operator, which produces a single number at each pixel, called the creaseness. If the myocyte is horizontal, then the creaseness is the difference between the values of δy at vertically adjacent pixels. The program computes the creaseness (López et al., 1998) at pixels that lie on the line at right angles to the edges. In Figure 3c, we have marked those pixels where the creaseness is largest. When computing the movement of the edges, we use different step lengths to take account of the different scales in the data, such as thin as opposed to thick myocytes. We use a sequence of different step lengths, taking precautions to ensure that the information is preserved as best possible. This part of the implementation is quite complicated. The interested reader should consult the references for details.

Having enhanced the edges of the myocytes and established their midline, we are in a position to compute a histogram of midline orientations (Fig. 3d). In Figure 3d, the axis is divided into intervals representing slope angles, while the height of a bar is the sum of the midline lengths whose slope angle falls within the corresponding interval. In the previous step, we marked those pixels where the creaseness was largest, and which therefore lay on or near the midlines of the myocytes. While moving the boundaries, we retained the directional information contained in δx and δy, so that we also know the slope of the midline at these marked pixels.

One approach would be to identify a set of adjacent marked pixels that seem to form a linear segment and then compute the length and slope of this segment. This approach has two drawbacks. First, we would have to identify the linear segments. Second, by using only the average slope of the linear segment, we would suppress the variation between the adjacent pixels. Once again, we take a different approach, the basic idea of which is that the contribution of each marked pixel is calculated separately. The calculation of the contribution is easy. The slope is known from δx and δy, and the length of the midline piece within the pixel follows from elementary geometry. One aspect requires care. If the midline is parallel to the x- or y-axis, the length of the midline piece within each pixel is simply the width of the pixel. If n marked pixels lie alongside one another, the total length is n × pixel width. But, if the midline is sloping, the marked pixels are likely to be scattered like a staircase around the midline segment, and the number of these pixels may be quite large. If so, the contribution of the midline segment will be overestimated at the expense of horizontal or vertical midline segments. We correct for this by resampling at a sequence of equidistant points.

The final step is to estimate the parameters of distribution. Given the orientations as the values of observation, we estimate the major direction μ by inspecting the intervals holding half of these observations. More precisely, we set μ to be the center of the smallest interval I, in which half of the observed orientation, the noisy orientations in the whole domain [−90°, +90°], are estimated by 5 × n. σ characterizes the deviation of the myocytic orientations around the major direction μ. We choose σ to be the standard deviation of a specific Gaussian distribution, centered at μ. The characteristic, which uniquely defines this Gaussian N (μ, σ), is that, if we model the orientations as an accordant distributed random variable, we expect to get the same number of orientations in I as we observed.


In all, we obtained 35 myocardial slices from the left ventricular free walls and septum. In 29 of these, we discovered a repeating pattern of aggregation of the myocytes that had been sectioned parallel to their long axis. This pattern extended through the slice in diagonal fashion from epicardium to endocardium (Figs. 4–6). This continuum of longitudinally sectioned myocytic aggregates progressed through the wall while showing a variable tilt relative to the epicardial surface. Thus, rather than the myocardial wall representing a sequence of stacked strands of individual myocytes, with the long axis of each individual cell running consistently parallel to the epicardium, it is composed of collections of cells that merge at widely variable angles, yet are held together within their collagenous matrix, the overall arrangement being to produce a coherent spatial mesh. As seen in its entirety, the arrangement revealed by sectioning with circular knives of variable diameters resembles a fan, with the inclination of the leaves of the fan toward the endocardium increasing with reciprocally decreasing diameter of the knives used to remove the slices (Fig. 5). The length of the diagonal through the array, when measured along the epicardial surface, decreases concomitantly with decreasing diameters of the sets of knives (Figs. 4, 5, and 8, Tables 2–4). The orientation of the diagonal itself changes depending on whether the semicircular, or close to circular, section was taken with the convex or concave margin toward the plane of the atrioventricular groove (Fig. 6).

Figure 4.

This histological section, taken from a slice removed using a pair of knives 30 and 40 mm in diameter from the basal half of the left ventricle, has been investigated histologically at 100× amplification area per area to quantify the focal alignment of the axially cut chains of myocytes. Fourteen representative segments have been amplified 5× (below). Then the continuous array of axially cut fibers has been colored artificially to show its diagonal course across the ventricular wall (lower panel). The array extends from the subepicardium (upper lining) adjacent to the septum (right hand), to the subendocardium (lower lining) near the obtuse margin (left hand). Note the thick middle layer (b), whereas the subendocardial (a) and subepicardial (c) tails of the labeled array are thin. The section is stained with hematoxylin and eosin. Its size is 1.5 times the natural size.

Figure 5.

The three myocardial slices shown at the top were harvested from the superior aspect of the left ventricular base by using cylindrical twin knives of variable diameter, from top to bottom of 68 and 58, 40 and 30, and 30 and 20 mm diameter, respectively. The inclination of the resulting arrays of longitudinally cut fibers, which were artificially colored as shown in Figure 4, changes relative to the epicardium depending on the diameter of the knife used, as shown in the bottom panels. It is minimal when a pair of large knives has been used (top), but much steeper when the smallest knives have been used (bottom). The reason for this disparity is that the smallest pair of knives parallels the axial alignment of the myocytes with a smaller radius of curvature than any larger knife. In contrast, the angulation of the individual myocytes accumulated within the arrays was found to be independent of the sizes of the pairs of knives used. The length of the resulting slices, and likewise the length of the nest of axially sectioned myocytes, is shortest with the smallest pair of knives. For geometrical reasons, the shorter the nest of axially sectioned fibers stretched out between epicardium and endocardium, the steeper must be its angulation toward the endocardium.

Figure 6.

The two slices shown are obtained from the midportion of the superior wall of the left ventricle using the largest pair of knives, with the septal area at the right end and the inferior wall area at the left end. The lower slice, stained with azan, was sectioned using the knives with their concavities directed toward the base, while the upper one, stained with hemotoxylin and eosin, was cut with the concavities directed toward the apex. The alignment of the resulting diagonal arrays of fibers cut longitudinally is again shown by artificial coloring. Magnification, 1.5× natural size.


Figure 7.

This semicircular slice obtained from the superior base of the left ventricle displays one of the rare arrays composed of a truly intruding continuum of myocytes. Histological sectioning, and staining with hematoxylin and eosin, had revealed an oblique transmural alignment of a sequence of longitudinally cut fibers running from the subepicardium (upper right) near the septum to the subendocardium (lower left) near the obtuse margin. To evaluate the true obliquity of these aggregated myocytes, the inclined fiber continuum was displayed in segments. The distribution of angulation of the contained myocytes was assessed automatically. The distribution measured in the four segments amplified by six (upper line) is displayed in the lower histograms.

Figure 8.

The cartoon shows three semicircular section planes, 25, 35, and 63 mm, which represent the sections obtained from slices punched by the pairs of circular knives of 20 and 30, 30 and 40, and 58 and 68 mm, respectively. The main grain of myocytic orientation is shown in the subepicardium, the midportion of the ventricular wall, and the subendocardium. The sections illustrated are those taken from the left ventricular base, with the superior septum on the left, the inferior septum on the right, and the base on top. The gray zones A, B, and C indicate the areas in which the knives cut the myocytes parallel to their long axis. Those zones increase in width concomitant with the increase in varied angulation of the myocytes relative to the epicardium. In the cartoon, the axially coupled myocytes are shown as being aligned as strictly parallel straight lines. In reality, the chains of myocytes are aligned like branching railways, which deviate substantially from the straight course (Table 1). The arch A-B-C is the length of the array that contains myocytes sectioned axially. Note that the length of this array is determined primarily by the diameter of the pair of circular knives used to produce the slices. The length of the array increases further in mural segments in which the turn of the grain as subtended from the epicardium to the endocardium also increases, while it gets shorter in those segments in which the turn of the bordering myocardial layers is less pronounced. Because of this, there is marked variation in the figures given in Table 2 to 4 for the measured length of the arrays.

Table 1. Percent distribution of angles of deviation of the segments relative to the epicardial lining in 46 histological scans
ISCNoμ (°)σ (°)−45° equation image −37.5°37.5° equation image −30°−30° equation image −22.5°−22.5° equation image −15°−15° equation image −7.5°−7.5° equation image −0°equation image 7.5°7.5° equation image 15°15° equation image 22.5°22.5° equation image 30°30° equation image 37.5°37.5° equation image 45°
  1. μ, mean orientation of all segments measured within the scan; π, standard deviation of the segments from the mean orientation; ISC, number of identification of the histological scans; No, number of measured orientations/scan.

Outer-mid border               
Mid-inner border               
SD2835  0.691.432.724.805.966.496.196.547.834.451.830.68
Table 2. Alignment and dimension of the arrays of axially sectioned myocardial fibres obtained with the pair of smallest circular knives (diameters 20 and 40 mm)
Site of biopsy272829313230353433Mean values
Orientation of the knives' convexity to apexOrientation of the knives' convexity to base
BaseMidportionMidportion basalBaseMidportionApexBaseMidportionApex
  1. For the angle of intrusion in most cases two figures are given, because intrusion was generally less pronounced in the subepicardial halfs of the sections than in the subendocardial ones.

Angle of intrusion24/4130/3420/5215/4618/423219/4316/5830/4822.6 ± 6.5/45.5 ± 7.3
Length [mm] of array43273845423532353436.78 ± 5.8
Smooth continuum++ ++     
Segmented  +++++++ 
Thickness of the array of axially sectioned myocytes (Number of fibres piled up)
Subepi44125140110568030555677.3 ± 38.8
Mid286280350100260600180360170278.3 ± 145
Subendo3584190358962251269682.4 ± 52.3
True intrusion + + + ++ 
Table 3. Alignment and dimensions of the arrays of axially sectioned myocardial fibres obtained with the pair of mid-size knives (diameters 30 and 40 mm)
Site of biopsy1011121314202117161522192423Mean value
Orientation of the knives' convexity to apexOrientation of the knives' convexity to base
SuperiorSeptumInferiorSuperiorSuperior + inferiorSeptumInferior
  1. For the angle of intrusion in most cases two figures are given, because intrusion was generally less pronounced in the subepicardial halfs of the section than in the subendocardial ones.

Angle of intrusion22/562018/5318/2218/2534/4226/?18/2815/2810/24713/362213/1818.1 ± 8.3/30.5 ± 7.0
Length [mm] of array623942446838606262808758436557.86 ± 15.1
Smooth continuum++ +++++++++++ 
Segmented  +            
Thickness of the array of axially sectioned myocytes (Number of fibres piled up)
Subepi20809368795031605056 95953557 ± 21.4
Mid240160253198136170226190280156140180280155181.4 ± 46.1
Subendo43123616289140687810025 1104213993.6 ± 38.1
True intrusion ++    +       
Table 4. Alignment and dimensions of the arrays of axially sectioned myocardial fibres obtained with the pair of largest circular knives (diameters 58 and 68 mm)
Site of biopsy25126756Mean values
Orientation of the knives' convexity to apexOrientation of the knives' convexity to base
BaseSubbasalMidportionBasalMidportion 1Midportion 2
  1. For the angle of intrusion in most cases two figures are given, because intrusion was generally less pronounced in the subepicardial halfs of the section than in the subendocardial ones.

Angle of intrusion15/1818/5813/2816/3211/1812/1414.2 ± 2.6/28.0 ± 16.2
Length [mm] of the array90915996998987.33 ± 14.4
Smooth continuum++++++ 
Thickness of the array of axially sectioned myocytes (Number of fibres piled up)
Subepi25154840 3532.6 ± 12.9
Mid250280350190210210284.3 ± 59.5
Subendo659813516045110102.2 ± 42.8
True intrusion+  + + 

The diagonal array visualized within each section is seen as a continuous entity only because the curvature of the diameters of the knives used to remove the slice fits with the varying orientation of the long axes of the myocytes. This angle changes markedly with increasing depth in the wall from epicardium to endocardium. In those slices in which fixation did not provide a perfectly flattened wall, the array of cells sectioned longitudinally was fragmented, with short segments of cells sectioned longitudinally seen scattered within the wall between the epicardium and endocardium. We often observed such fragmented arrays in the slices prepared using the knives of smallest diameter (Fig. 5), which had the greatest curvature, and hence needed the most rigorous unbending to achieve flat fixation. Fragmentation was less prevalent in the slices produced with the knives of greater diameter (Fig. 6).

Directly adjacent to the array containing the aggregates of cells cut in longitudinal axis, a sharp transition is observed with the remaining greater part of the section, in which the myocardial cells were cut in their short axis. The resulting borders produced relatively straight lines within the transmural sections. In some slices, the array of cells cut in their long axis produced a staircase-like arrangement, with the steps readily discernible within the stairs, descending from the epicardial to endocardial surfaces (Fig. 4).

As shown by the measurements summarized in Table 1, a minority of cells is sectioned along their long axis with alignment over long distances directly parallel to the epicardium. Indeed, only two-fifths of the population deviate by mean angles of ±7.5°. The majority, three-fifths, are aggregated with their long axis at angles of ±7.5 and 45° from the epicardial surface. This distribution of angles varied within the sections, independent of the size of the pairs of circular knives used. The distribution of angles, furthermore, varied within the sections independent of the depth within the ventricular wall. Some individual fine strands of aggregated myocytes, not included in Table 1, intruded still more obliquely relative to the tangential plane and occasionally exceeded angles of 45°. These were found mostly in slices harvested from the basal parts of the left ventricular wall, from the ventricular apex, and from the portions of wall supporting the roots of the papillary muscles. In Tables 2 to 4, we have labeled the occurrence of these aggregates, found in 11 out of 33 slices, as “true intrusion” (Fig.


Three-Dimensional Structure of Ventricular Walls

Our study has revealed aspects of ventricular structure that are foreign to concepts currently used by those studying ventricular mechanics (Rademakers et al., 1992; Costa et al., 1999; Stuber et al., 1999; Harrington et al., 2005). Thus, we have shown that the ventricular walls are made up of myocytes that merge with their neighbors in nonuniform anisotropic fashion, the overall effect being to produce a unitary meshwork of myocytes contained within a supporting collagenous matrix. The epicardial and the endocardial fibers of the ventricular wall are made up primarily of myocytes orientated with the angles of their long axes almost at 90° to each other when measured relative to the equatorial plane as represented by the ventricular groove. When these angulations relative to the equatorial plane are assessed at various depths within the wall, a gradation is seen in the angulation relative to the ventricular equator. This is the so-called helical angle, with the succeeding subendocardial portion ascending from the apex to the base anticlockwise as seen from the base, while the succeeding subepicardial fibers ascend in clockwise fashion (Hort, 1960; Streeter, 1979; Torrent-Guasp, 1980). It is well established that the midportion of the ventricular wall, particularly adjacent to the ventricular base, is made up primarily of myocardial cells orientated in circular fashion (Hort, 1960; Grant, 1965; Anderson and Becker, 1980; Sanchez-Quintana et al., 1990). These circular fibers seem at first sight to be aligned almost parallel to the epicardial and endocardial surfaces. Many of them nonetheless intrude obliquely between superjacent aggregates, although there is dispute concerning the extent and angulation of this intrusion (Streeter, 1979; Karlon et al., 1998; Costa et al., 1999; Lunkenheimer et al., 2004). Taking into account the acknowledged turn of the myocytes on a radial axis, we reasoned that, by cutting our slices of the ventricular wall with circular knives, at some point we would section the long axis of myocytes at all depths within the wall. Those in the epicardial and endocardial parts of the wall would be parallel to the curved ends of the slice cut by the knife. The cells making up the middle part of the wall, in contrast, would be cut in long axis by either the concave or convex part of the knife. As all myocytes, with increasing depth in the wall when assessed from the epicardium to the endocardium, are known to turn on a radial axis, one segment of each depth must be sectioned in its long axis in the slice removed by the circular knives. Our purpose in using the new technique was to identify and measure the extent to which those cells cut in their long axis deviated from the tangential alignment. By this means, we discriminated myocytes aligned in sequence, some close to parallel to the epicardial and the endocardial boundaries, along with others intruding markedly but at variable angles in the direction from epicardium to endocardium. All were merged as part of a continuous myocardial and fibrous spatial mesh. None of the observed chains of myocytes differed in size, thickness, or shape. In this respect, Torrent-Guasp (1980), albeit without any supporting histological evidence, had suggested that all myocytes deviating from a strictly tangential alignment served to transmit excitation, rather than contributing to ventricular emptying. We found no evidence to support this assertion. On the contrary, our findings, confirming previous histological studies (Feneis, 1943–1944; Hort, 1960; Streeter, 1979; Greenbaum et al., 1981; LeGrice et al., 1995), show that the components of the myocardial mesh share the same basic structure, with an essentially identical contractile potential prevailing in all regions of the ventricular mass.

Automatic Assessment of Angles of Intrusion

With respect to the methodology we used to measure automatically the orientation relative to the epicardial ventricular lining, our implementation may seem to be unnecessarily complicated, but the resulting computation is fully automatic. In our attempt to explain the method, we discussed the situation for an individual myocyte. The implementation, however, makes no attempt to identify individual myocytes and their midlines. It simply applies the chosen operators to all the pixels. Many of the techniques used in informatics are standard for the processing of digital images, and similar data from other sources could be processed in like fashion. Certain aspects have been optimized for our particular use. One example is the moving of the edges, since it is necessary to ensure that myocytes of different width are treated correctly. Furthermore, we found that better results could be obtained if some intermediate values were smoothed or cut off. We have not described these steps, because while they improved the results, they are not essential.

Shape and Orientation of Axially Sectioned Myocytes Identified Within Spatial Mesh

The most outstanding feature of the nest of axially cut myocytes is its S-like configuration, with subepicardial and subendocardial tails, and a wider midportion of variable length. This S-shape is determined by the slope of the rotation of the helical angles, which is rapid in the subepicardium and subendocardium, yet slow in the midportion of the wall. This dynamic also varies depending on the area of the ventricular wall from which the individual slice has been taken.

Because of the slow turn in the orientation in the midportion of the ventricular wall, the knives transect axially a greater number of cells in this region than in the subepicardial and subendocardial zones. The vertical extension of the array, therefore, is wide in its middle part, and thin at its subepicardial and subendocardial tails. In detail, as shown in Tables 2 to 4, the number of myocytes aggregated between the epicardium and endocardium in the three segments of the array differs markedly, amounting in the mean to 238.9 ± 82 in the midsegment, 92.7 ± 47.3 in the subendocardium, and 56.6 ± 37 in the subepicardium. The wide scatter of the figures is related to the pronounced variation of the local deviations of the myocytes from their purely tangential alignment (Table 1). For instance, some myocytes at a depth of 2 mm may be aligned exactly parallel to those myocytes forming the immediate subepicardium. Because of this, they will be cut axially with the same segment of the knives as the subepicardial myocytes. In this setting, the array of axially sectioned myocytes found in the segment is widened in vertical direction.

The deviation of myocardial aggregates from a strictly tangential alignment measured in our previous study (Lunkenheimer et al., 2004) and confirmed in this study is far greater than was recognized by Streeter (1979). This deviation is a necessary feature of the frequent branching of the individual myocytes within the spatially contracting myocardial and fibrous mesh. The overall spatial netting guarantees that the individual myocytes are activated by the spread of the impulse from one cell to its neighbors. The distribution of angles is specific for a given segment of the myocardial wall, rather than being associated with the depth at which it is measured between epicardium and endocardium. It is impossible to reconcile this heterogeneous distribution of angles throughout the ventricular walls with concepts of preformed tertiary arrangements of the myocardium. Thus, there is no evidence to support the notion of tracts, or individual muscle bundles, coexisting within the ventricular walls (Torrent-Guasp, 1980), nor for fibrous lamellar structures packing the myocytes into orderly and repeating compartments extending from epicardium to endocardium (LeGrice et al., 1995). In this regard, it is generally assumed by those concerned with cardiodynamics that the visualized axis is the surrogate of the main direction of force engendered by the myocytes producing the image. This notion, however, takes no account of the linkages between adjacent myocytes, nor the extent of aggregates that deviate from purely tangential orientations. The extent of aggregates intruding obliquely as identified in our studies heralds a potentially significant interaction with the fibers aligned more tangentially.

Potential Role of Connective Tissue Scaffold

As estimated from our morphological findings, the measured deviation of the individual myocytes from the tangential alignment seems unlikely to be able to create an overall force vector acting in the radial direction significant enough to induce ventricular diastolic dilation, first because the angle of their inclination rarely exceeds 45°, and second because their contractile mass is too small relative to the remainder of the mural myocardium. Direct measurements nonetheless have revealed the existence of an auxotonic force signal measurable in circumscribed areas within the left ventricular wall of mammals, heralding some antagonistic activity within the normal heart (Lunkenheimer et al., 2004). The auxotonic signal, furthermore, is generated during the period of ejection, while the ventricular wall increases in thickness (Lunkenheimer et al., 2004). Such auxotonic signals, the activity of which outlasts that of tangential fibers, were found in only one-fifth of our sites of measurements in experimental mammals. In patients with chronic ischemic heart disease, known to be associated with marked fibrosis of the ventricular walls, auxotonic signals were produced in four-fifth of the impalements. From this, we infer that any transmission of force in radial direction requires the involvement of the connective tissue scaffold that supports the myocardial component of the mesh (Fig. 9) (Caulfield and Borg, 1979). When the myocardial fibers shorten during systole, even in the normal heart, then of necessity they also act on their supporting matrix of connective tissue. This scaffold then becomes part of the chain for transmission of spatial forces. Our experiments (Lunkenheimer et al., 2004) suggest that the scaffold might be able to increase the angle of transmission of force relative to the epicardium beyond 45° during ventricular systole, producing the force vector at endsytole which we measured in patients with coronary arterial disease that persisted up to 120 msec after the termination of ejection (Lunkenheimer et al., 2004). This force might effectively oppose, and eventually control, the thickening of the ventricular wall and hence promote ejection. In this way, the ventricular myocardium is able to sustain both constrictive and dilatory actions relative to the cavity. We speculate that such an antagonistic system might be critically enhanced in myocardial fibrosis (Weber et al., 1988).

Figure 9.

The cartoon shows the overall arrangement of the mesh of myocardial cells supported within a scaffold of connective tissue. The fibrous matrix consists of short struts, fixing myocytes to myocytes and the capillaries. A fine mesh of collagen also wraps each myocyte. The matrix of connective tissue determines the freedom of motion of the myocytes in all three spatial coordinates (x, y, and z in lower panel). As demonstrated by our current findings, however, this potential control of myocardial contractile function by connective tissue varies markedly within the ventricular mass, the alignment of myocytes within the matrix being far less regular than shown here.

Regulation of Ventricular Function by Heterogeneities in Structure

It was Brutsaert (1987) who focused attention on heterogeneities in myocardial function within the ventricular wall as a pivotal means of regulating global ventricular function. We suggest that one substrate of the postulated heterogeneity may be the presence of the intruding contractile pathways, acting in concert with the coordinated netting of the connective tissue scaffold. As we have shown by direct measurements (Lunkenheimer et al., 2004), loading, and hence shortening, of the myocardial aggregates varies throughout the ventricular wall, both in respect to their amount and time course, namely, in onset and termination. In accordance with Brutsaert's studies on isolated trabecular muscles (Brutsaert, 1987), we assume that each of these variables is a function of the spatial alignment and coupling of the myocardial cells. With respect to global ventricular function, this arrangement produces an antagonistic mechanism, which serves to stabilize ventricular shape and to terminate systolic mural thickening. We also speculate that the mechanism is able to harmonize ventricular emptying by controlling the time course and amount of regional wall thickening in a way that resistance to flow within the ventricular cavity is minimized.