Mechanical Analysis of Single Myocyte Contraction in a 3-D Elastic Matrix

John Shaw,Leighton Izu,Ye Chen-Izu,Laszlo Csernoch

doi:10.1371/journal.pone.0075492

John Shaw, Leighton Izu + Show 2 more

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https://doi.org/10.1371/journal.pone.0075492

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Abstract

BackgroundCardiac myocytes experience mechanical stress during each heartbeat. Excessive mechanical stresses under pathological conditions cause functional and structural remodeling that lead to heart diseases, yet the precise mechanisms are still incompletely understood. To study the cellular and molecular level mechanotransduction mechanisms, we developed a new ‘cell-in-gel’ experimental system to exert multiaxial (3-D) stresses on a single myocyte during active contraction.MethodsIsolated myocytes are embedded in an elastic hydrogel to simulate the mechanical environment in myocardium (afterload). When electrically stimulated, the in-gel myocyte contracts while the matrix resists shortening and broadening of the cell, exerting normal and shear stresses on the cell. Here we provide a mechanical analysis, based on the Eshelby inclusion problem, of the 3-D strain and stress inside and outside the single myocyte during contraction in an elastic matrix.Results(1) The fractional shortening of the myocyte depends on the cell’s geometric dimensions and the relative stiffness of the cell to the gel. A slender or softer cell has less fractional shortening. A myocyte of typical dimensions embedded in a gel of similar elastic stiffness can contract only 20% of its load-free value. (2) The longitudinal stress inside the cell is about 15 times the transverse stress level. (3) The traction on the cell surface is highly non-uniform, with a maximum near its ends, showing ‘hot spots’ at the location of intercalated disks. (4) The mechanical energy expenditure of the myocyte increases with the matrix stiffness in a monotonic and nonlinear manner.ConclusionOur mechanical analyses provide analytic solutions that readily lend themselves to parametric studies. The resulting 3-D mapping of the strain and stress states serve to analyze and interpret ongoing cell-in-gel experiments, and the mathematical model provides an essential tool to decipher and quantify mechanotransduction mechanisms in cardiac myocytes.

Highlights

Cardiac muscle contraction generates mechanical force to pump blood, so the muscle cell experiences mechanical stress during each heartbeat
Excessive mechanical stress associated with pathological conditions, such as hypertension, volume overload, infarction, and asynchronous contraction, can result in cardiac remodeling and heart disease development [1]
Investigation of the mechanotransduction mechanisms has been hindered by lack of techniques to control the mechanical load at single cell level, especially in the case of live adult cardiac myocytes

Summary

Methods

Eshelby Inclusion Theory Of interest is the boundary value problem of a single beating cardiomyocyte embedded in an elastic hydrogel of infinite extent (see Fig. 1). The stresses in the inclusion and matrix are, in general, sIij. The approach is to introduce a fictitious transformation strain (bÃij), or ‘‘eigenstrain’’, to simulate the perturbed elastic fields due to the inhomogeniety. Equation (43b) is the strain energy in the matrix, which is just the mechanical work done on the gel by the cell Both results are valid for the homogeneous and inhomogeneous inclusions, where bÃij would be used in the calculation of sIij and eIij, but the actual transformation strain bij would still multiply the stress in eq (43a)

Conclusion

Introduction

Results and Discussion

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