ECM mechanical function 12

Understanding and describing native tissue mechanical properties is important in determining how physiologic forces are transmitted through the multi-scale ECM to the level of the cell to regulate function. These same properties can serve as benchmarks in the development and validation of novel biomaterials or engineered replacement tissues, especially in the case of load bearing tissues. Important properties to understand in this context are the elastic modulus, anisotropy, non-linearity and viscoelasticity of a given

tissue. These mechanical properties of the ECM can be quantified and described using solid mechanics (Gurtin 1981).

Elastic Deformations:

When force is applied to a tissue, it elongates in the direction of force application. In some cases, this deformation is instantaneous and increases linearly as the load is increased, following Hooke’s law, which can be used to describe many elastic materials:

𝐹

𝐴= 𝜎=𝐸𝜀 = 𝐸

𝑙+Δ𝑙

𝑙

Where 𝜎 is the stress (force over area) and 𝜀 is the strain (normalized elongation) in the material. This relationship can be used to determine the material property E, known as the Young’s modulus of the material (Figure 2-2A). In elastic materials, the applied deformation can be fully reversed when the load is removed. Under normal physiologic loading, some tissues act as elastic materials, and recover completely from the applied deformation when the load is removed. Often, these tissues also display deformation in the unloaded directions. That is, when a tensile load is applied in one direction, there is a contraction in the directions perpendicular to that, resulting in a decrease in the cross- sectional area of the tissue. This behavior is known as the Poisson effect and the relative magnitude of these perpendicular strains is referred to as the Poisson’s ratio (νxy) (Figure

2-2D), another material property that is likely important not only for tissue function but for facilitating the cellular response within a tissue. Tissues that are required to withstand very large loads in one direction, such as tendons and ligaments, tend to display a very large Poisson’s ratio because of the highly aligned and crimped ECM structure that is

required to withstand this intense uniaxial loading (Reese, Maas et al. 2010). This itself is yet another important mechanical characteristic of tissues and is referred to as anisotropy.

Figure 2-2: Mechanical attributes important for tissue function. Tissues that are loaded heavily in a single direction, often display anisotropy (A), or preferential alignment of ECM molecules in one direction. This results in mechanical properties that are significantly higher in one direction such that the ratio of stress to strain (modulus, E) is higher in that direction. Fibrous tissues also often display non- linearity (B) such that the ratio of stress to strain is not constant. Viscoelasticity is a common characteristic of hydrated tissues that are exposed to large compressive loads (C) and results in a time dependent stress-strain response. Another

This is defined as the ratio of strains in the perpendicular vs. applied strain direction. Some tissues stretch while showing very little compression in the transverse direction. Other tissues, that possess a high degree of anisotropy, can display very large lateral compressive strains that surpass the applied strain.

Isotropy vs. Anisotropy:

Tissues with a very high degree of alignment in one direction are referred to as mechanically anisotropic, meaning that they have direction dependent mechanical properties (Figure 2-2A). In the case of a single fiber direction, these tissues are referred to as transversely isotropic, meaning they have equal mechanical properties in any plane transverse to the fiber direction but display different mechanical properties in the fiber direction. Higher orders of anisotropy also exist in some tissues, with some displaying multiple levels of transverse isotropy and others displaying distinct mechanical properties in each direction. Other tissues, which display equal properties in all directions, are referred to as isotropic. This isotropy or anisotropy is governed by the organization of the ECM molecules within the tissue and can range from very anisotropic to almost perfectly isotropic. This organization is important for the mechanical function of a tissue and can influence the mechanical cues seen by cells. Often this organization can be altered with increased tissue deformation resulting in strain dependent mechanical properties, referred to as non-linearity.

Non-Linearity:

Highly aligned tissues often display a crimped or wavy structure in their unloaded configuration, where the collagen fibers undulate with a defined periodicity. During early phases of deformation of such tissues, these crimped fibers straighten, followed by

a phase in which the straightened fibers elongate. This gives rise to a stress versus strain curve that has two distinct regions (Figure 2-2B). The first region is referred to as the ‘toe’ region that has a lower elastic modulus while the second ‘linear’ region has a higher elastic modulus. This crimp structure, along with the associated non-linear stress-strain response is an essential mechanical characteristic that enables tissue to undergo low force deformations (so that energy expenditures can be minimized) while at the same time providing for a higher modulus at greater strains (protecting the tissue from undue deformations).

Viscoelasticity:

Another structural feature of tissues that can regulate the stress-strain response is the viscoelasticity. Biologic tissues are highly hydrated and often contain fixed negative charges that are covalently bound to the ECM, especially in the case of proteoglycan rich tissues such as cartilage. Solids are capable of displaying perfectly elastic material properties, in that load immediately induces a strain and that this strain is recovered immediately following the release of load. Tissues however, especially those rich in water and fixed charges, display time-dependent strain in response to a step load, due to their viscous water component (Figure 2-2C). Thus, most tissues are referred to as viscoelastic, displaying properties of both an elastic material and a viscous fluid. The combination of water and fixed charge in biologic tissues also induces a hydrostatic pressure within the tissue that can play a critical mechanical role, but also regulates the cellular deformations within a tissue in a time dependent manner (Screen, Toorani et al. 2013).