Mechanical analysis of single myocyte contraction in a 3-D elastic matrix

Cardiac 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.

Isolated 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.

(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.

Our 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.