Author + information
- Thomas M. Stokke, MD,
- Kristina H. Haugaa, MD, PhD,
- Otto A. Smiseth, MD, PhD,
- Thor Edvardsen, MD, PhD and
- Espen W. Remme, MSc, Dr Ing∗ ()
- ↵∗Institute for Surgical Research, Oslo University Hospital, Rikshospitalet, Postboks 4950 Nydalen, 0424 Oslo, Norway
We appreciate the comments from Dr. van Dalen and colleagues and agree that twist may increase as a result of pathologies, which reduce contractility of subendocardial fibers with oppositely oblique orientation to the subepicardial fibers.
The main reason a relatively small fiber shortening is transformed to a high ejection fraction (EF) is that the fibers encapsulate a 3-dimensional volume which amplifies the 1D fiber shortening to a power of 3. This may be illustrated by inspecting the volume of a box, in which volume = width × length × height. As each of these dimensions are reduced by, for example, 17%, the fraction of the original volume is 0.833 = 0.57, i.e., EF = 43%. Note that this box is a shell without wall thickening contributing to EF. In our model (1), EF = 60% with 1-cm wall thickness, 5-cm short-axis diameter and global circumferential strain = global longitudinal strain = −17% at the midwall, without twisting. Nevertheless, twist may have other beneficial effects on myocardial mechanics as it has been suggested to equalize fiber shortening and stress across the wall (2).
Ejection is caused by a reduction of the long- and short-axis diameters, which are linked to longitudinal and circumferential shortening as well as to wall thickening. If both longitudinal and circumferential shortenings are reduced, their contributions to shortening the diameters will be reduced, and also their contributions to wall thickening through the Poisson ratio effect. All these factors decrease EF. This raises the question how can increased twist compensate? Potentially, shear strains could contribute to reduce the cavity diameter by increasing wall thickening. There are 3 independent shear strains where circumferential longitudinal shear strain (twist) is one. Radial circumferential shear strain is also seen as the subendocardial region twists more than the subepicardial region (3), which seems counterintuitive but may possibly be attributed to a transmural fiber angle component in the basal and apical regions (3,4). Furthermore, shear deformation of fiber sheet cleavage planes in the subendocardium (approximately corresponding to radial longitudinal shear strain) may also contribute to some of the wall thickening (5). Future studies will likely provide new insights of this complex myofiber sheet microstructure and deformations including how various shear strains may contribute to ejection. The intent of our study was to explain EF’s geometric relationship with longitudinal and circumferential shortening and wall thickness and short-axis diameter. The resulting model is highly simplified, but interestingly, it still seems to determine EF well, suggesting that these factors are the main determinants of EF.
Please note: The authors have reported that they have no relationships relevant to the contents of this paper to disclose.
- 2018 American College of Cardiology Foundation
- Stokke T.M.,
- Hasselberg N.E.,
- Smedsrud M.K.,
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