A mathematical model of the mechanical link between shortening of the cardiomyocytes and systolic deformation of the left ventricular myocardium

Abstract

Background:

Left ventricular myocytes are arranged in a complex three-dimensional mesh. Since all myocytes contract approximately to the same degree, mechanisms must exist to enable force transfer from each of these onto the framework as a whole, despite the transmural differences in deformation strain. This process has hitherto not been clarified in detail.

Objective:

To present a geometrical model that establishes a mechanical link between the three-dimensional architecture and the function of the left ventricular myocardium.

Methods:

The left ventricular equator was modeled as a cylindrical tube of deformable but incompressible material, composed of virtual cardiomyocytes with known diastolic helical and transmural angles. By imposing reference circumferential, longitudinal, and torsional strains onto the model, we created a three-dimensional deformation field to calculate passive shortening of the myocyte surrogates. We tested two diastolic architectures: 1) a simple model with longitudinal myocyte surrogates in the endo- and epicardium, and circular ones in the midwall, and 2) a more accurate architecture, with progressive helical angle distribution varying from −60° in the epicardium to 60° in the endocardium, with or without torsion and transmural cardiomyocyte angulation.

Results:

The simple model caused great transmural unevenness in cardiomyocyte shortening; longitudinal surrogates shortened by 15% at all depths equal to the imposed longitudinal strain, whereas circular surrogates exhibited a maximum shortening of 23.0%. The accurate model exhibited a smooth transmural distribution of cardiomyocyte shortening, with a mean (range) of 17.0 (13.2–20.8)%. Torsion caused a shortening of 17.0 (15.2–18.9)% and transmural angulation caused a shortening of 15.2 (12.4–18.2)%. Combining the effects of transmural angulation and torsion caused a change of 15.2 (13.2–16.5)%.

Conclusion:

A continuous transmural distribution of the helical angle is obligatory for smooth shortening of the cardiomyocytes, but a combination of torsional and transmural angulation changes is necessary to execute systolic mural thickening whilst keeping shortening of the cardiomyocytes within its physiological range.