# Elucidation of extracellular matrix mechanics from muscle fibers and fiber bundles

*Entry by Angelo Mao, AP 225, Fall 2010*

**Title:** Elucidation of extracellular matrix mechanics from muscle fibers and fiber bundles

**Authors:** Gretchen A. Meyer, Richard L. Lieber

**Journal:** Journal of Biomechanics

**Year:** 2010

## Summary

The researchers invent and apply a novel method for testing the mechanical properties of muscle fibers and their surrounding extracellular matrix. They were able to conclude from measuring the quadratic moduli that the moduli of fibers was linear, while the modulus of the extracellular matrix was nonlinear.

*soft matter keywords*: elastic modulus, extracellular matrix

## Methods and Results

Attempts to determine the quadratic modulus (which is similar to the elastic modulus in principle, except that the unites are nor pressure per length, but pressure per area) of muscles and its respective components, especially the extracellular matrix, were complicated by the difficulty in completely digesting away the muscle cells so that the remaining matrix structure could be mechanically tested. The effects of digestion on matrix mechanical properties were also obstacles. The authors developed a method of removing the extracellular matrix from the muscle bundles instead of removing the muscle cells. This left behind fibers that, in principle, by comparing to unmodified muscle bundles, could reveal the contribution of the extracellular matrix.

The equation the researchers used for calculating the modulus is as follows:

- <math>E_m = \frac{E_c - E_f(1-A_m)}{A_m}</math>

in which <math>E_m</math> is the module for the extracellular matrix, <math>E_f</math> is the module for the fiber, and <math>A_m</math> is the cross-sectional area.

Figure 1 shows the results of measuring individual fibers (green), which have had the extracellular matrix removed. Because the net quadratic modulus is nonlinear, the researchers posited that this is due to a nonlinear component from the extracellular matrix (1A), or from the syncopated arrangement of individual fibers (1B).

To determine whether it was the arrangement of fibers or the contribution of the extracellular matrix that introduced a nonlinear component to the modulus of the muscle as a whole, the researchers conducted mechanical testing on muscle and muscle fibers in different arrangements. They found that the modulus of fibers with varied arrangements was much less than that of the muscle as a whole. From this, they concluded that the primary contribution of nonlinearity to muscle must be from the elastic modulus.

## Discussion

The researchers' justification that a weak modulus from muscle fiber groups indicates that nonlinearity was produced by the extracellular matrix seems a little thin. Some simulation with elucidation of a limit of the variability in fiber arrangement with regards to contribution to nonlinearity would seem to bolster the researchers' claims. Moreover, it seems that studying the anatomy of the muscle would solve the problem. In the context of soft matter, muscle and the extracellular matrix fall somewhat to the "hard" side of soft matter. However, the principles of elastic moduli play an important role in defining whether matter is elastic, viscoelastic, or viscous.