The left ventricle is an amazing structure, capable of ejecting ≥60% of its contents at high pressure, then filling at very low pressure in a fraction of a second. Remarkably, this high ejection fraction can be accomplished despite the fact that each myocyte is capable of contracting by only about 15%, no matter where it is in the myocardium. Yet, this uniform 15% myocyte shortening leads to ≥20% shortening in the longitudinal and circumferential directions and 40% to 50% wall thickening radially. The ellipsoidal shape of the ventricle also dictates a tremendous (up to fourfold) transmural gradient in longitudinal and circumferential shortening. The only way that sarcomeric shortening can be uniform in such a geometry is not by myocytes’ working in isolation but by their being organized into sheets going from the endocardium to the epicardium (see Costa et al . for details). This type of organization, through sheet thinning and between-sheet slippage and radial tilting, enables subendocardial circumferential and longitudinal strain to be significantly higher in magnitude than the actual myocyte shortening in the same area. One of the unsolved tasks in cardiovascular imaging is to use macroscopic imaging to tease out what is happening on the microscopic scale within the myocardium. In this issue of JASE , Pedrizzetti et al . demonstrate important, though incremental, progress in this quest.
To understand the novelty and limitations of the investigators’ findings, we need a brief review of strain, a measure of deformation in a physical body. If one squeezes a stress-relief ball, it decreases in the two dimensions in which the hand squeezes (negative strain) but increases in the opposite one. Physicists refer to these as normal strains, meaning that they are deformations perpendicular to the surface, but to avoid confusion with the clinical meaning of the word normal , we will call them linear strains, usually expressed as percentages. Please note that if the tissue is incompressible (as the myocardium almost is, the exception being the small change in blood volume ), one cannot have all three linear strains as either positive or negative; there must be two of one sign and one of the other so that they sum (approximately, for small strains) to zero. There is a second kind of strain. If one places (softly) a hand on a cube of gelatin and moves the upper surface relative to the lower one, it will produce a tangential deformation, termed shear strain, which can be expressed either as a percentage or as an angle.
In real life, force usually acts on a body at some angle, causing both linear (three components) and shear (three more components) strain. The easiest way one can conceptualize this is to imagine a cube: one can measure the linear strains occurring between front and back surfaces, left and right surfaces, and top and bottom surfaces and shear strains occurring between each pair of adjoining orthogonal surfaces. In a heart, three linear strains are longitudinal, circumferential, and radial. Three shear strains are radial-circumferential, radial-longitudinal, and circumferential-longitudinal. Shear strains of the heart are usually not measured, the exception being circumferential-longitudinal shear strain, which is estimated indirectly through torsion measurement.
A third “type” of strain is called principal strain. If both linear and shear forces act on a body, it is possible to find a local coordinate system in which shear strains disappear while linear strain increases to its maximum value (see Figure 1 in Pedrizzetti et al . ). In an incompressible three-dimensional body, there are three principal strains, all perpendicular to one another, and oriented with specific angles relative to the initial coordinate system. In a heart, the largest principal strain is positive and roughly aligned to the radial direction, while at the midwall, the two smaller orthogonal principal strains are negative and oriented off the long axis, with the larger one oriented along the left-handed helix of the epicardial fibers (see the excellent report by Moore et al . ).
If one had complete understanding of all the linear and shear components of the myocardium throughout the heart, one could use standard linear algebra to calculate the principal strains and their angles relative to the standard cardiac geometry. And if one additionally had complete knowledge of the fiber and sheet architecture throughout the heart, one could in theory relate the principal strains and angles to the local fiber direction and derive true myocyte shortening, a factor that might be very helpful in the diagnosis and treatment of heart failure. This appears to be the overarching long-term goal of Pedrizzetti et al .’s work, but the limits of cardiac imaging in 2014 mandate several key points of compromise.
First, although Pedrizzetti et al . speak of three-dimensional strain throughout their report, the analysis actually involved only the subendocardium, not the full thickness of the left ventricular wall. Second, in part because the focus was on the subendocardium, only two components of strain, longitudinal and circumferential, were calculated, not the radial component, which is actually the largest magnitude one. A consequence is that although the myocardium as a whole is incompressible, the subendocardium assuredly is not, as least in the sense that it is a two-dimensional surface that becomes smaller in area with contraction. Thus, one cannot use the incompressibility properties to double-check the consistency of the strain measurements by ensuring that the three components sum to approximately zero. A third limitation is that the fiber architecture used to relate to the strain patterns was not calculated for individual patients but rather was based on a single data set obtained by diffusion tensor magnetic resonance imaging on an explanted heart preserved in formaldehyde, not a particularly patient-friendly technique!
So with these caveats in mind, what actually was demonstrated in the study? From the subendocardial circumferential and longitudinal strains, the magnitude and direction of the principal strain was calculated. Interestingly, although one might assume that the greatest shortening would be along the local fiber direction, the investigators found that in normal subjects, for about 50% of the endocardium (mainly the septal, inferior, and lateral walls), the greatest shortening was perpendicular to the local fibers, lining up rather with the epicardial fibers. Perhaps the fiber sheets are organized differently in anterior and inferior walls, but with limited histologic data available, it is difficult to prove (or disprove) this hypothesis. It should be noted that this finding differs from the seminal study of MacGowan et al ., which showed that in both healthy subjects and patients with idiopathic dilated cardiomyopathy, subendocardial shortening is uniformly orthogonal to the subendocardial myocyte orientation. In Pedrizzetti et al .’s group of patients with hypertension (who were significantly older than the normal control subjects), significantly more of the endocardial shortening lined up with the epicardium, perhaps reflecting the greater wall thickness, giving the epicardial fibers an advantage in torque compared with those in the normal controls.
A second broad analysis in the study involved the calculation of global strain characteristics averaged throughout the endocardium. Overall, there was no difference in longitudinal, circumferential, or the first component principal strain between the normal controls and patients with hypertension. It was only the second component of the principal strain decomposition (GSS; directed perpendicular to the principal strain vector) that showed a difference between the two patient groups. Normal patients had slightly negative GSS, while in those with hypertension, GSS was slightly positive. Given the multiple numeric manipulations necessary to derive GSS and the fundamental limitation of using only two components of strain in deriving it, it is difficult to find much meaning in this finding. It also differs from data obtained at the midmyocardial level, where both global principal strain and GSS were significantly negative. Taken at face value, though, these findings demonstrate that the subendocardial surface does shrink, mostly in a single direction. This single direction varies but is generally perpendicular to the local fiber orientation. The accuracy of this finding, however, needs to be corroborated in future studies.
Another interesting finding is the relatively small shear in the subendocardial (circumferential-longitudinal) plane. It is known that shear strain in the subepicardial plane is several times larger than in the subendocardial plane and that left ventricular torsion is determined mostly by subepicardial myocardial fibers. Yet prior studies have shown that although subendocardial shear strain is relatively low (1%–5% ), it is still higher than the values reported by Pedrizzetti et al . This is somewhat difficult to reconcile with the large difference between principal strains and strains within local coordinates seen in the present study. Further studies are needed to assess this issue.
So where might the field move from here? Despite the many technical issues with this study and the ambiguities in interpreting the results, the investigators should be commended for pushing hard against the current limitations of myocardial imaging. We were particularly pleased to see a very detailed mathematical description of their methodology presented in an appendix. This may be understandable by but a handful of JASE readers (at most!), but for those few, it allows the possibility of replicating the methodology and extending the approach. And there is hope that future imaging breakthroughs will allow a full three-dimensional structure-function analysis of the left ventricle. For example, in vivo diffusion-tensor magnetic resonance imaging techniques are developing, allowing individual fiber architecture to be discerned. There are even approaches to measure fiber angle by echocardiography. Three-dimensional strain imaging is currently limited by relatively low spatial and temporal resolution, but these are improving by the year. No, we cannot increase the speed of sound, but with Moore’s law still providing a doubling of computing power every 18 months even 50 years after it was proposed, we can expect more and more data from echocardiography. When that happens, and with the help of investigators such as Pedrizzetti et al ., we can look forward to deeper insight into cardiac function with the promise of routine clinical application. Yes, there are many uncertainties as to the accuracy and true meaning of the findings shown in the present report. Still, this is a great step forward into a very exciting and poorly understood territory of regional cardiac mechanics, for which the authors should be commended.