where Et ¼total effective elastic modulus as a function of time, Ess ¼steady state elastic modulus after complete relaxation, Ea ¼apparent strain-rate-dependent contribution to initial elastic modulus, and τ ¼η/Ea with η ¼viscosity. Special care needs to be taken when selecting an appropriate relaxation time for the exponential regression to result in positive, real number values for the three properties. Long relaxation times can cause viscosity values to be imaginary, while insufficient time can return inaccurate values for both elastic moduli. Additionally, all data points used to obtain SLS coefficients must reside within the relaxation portion of the elastic modulus function for the viscosity to be accurate and positive. Soft Matter Handling and Testing. A variety of soft matter samples have been used with this system, including synthetic hydrogels like polydimethylsiloxane and polyacrylamide, biomaterials like collagen gels and decellularized tissue scaffolds, and excised tissue from animals and humans. Maintaining in vitro sample stability and hydration and quantifying sample thickness are paramount concerns for successful characterization. Tissue samples are typically received from the operating room 1–2 h after excision, during which time they are stored on ice. Upon receipt, we transfer to a humid container lined with water-soaked tissues to maintain hydration and continue to store on ice. Characterization of fully submerged samples is complicated by buoyancy forces on the large probe tip, so for hydrogels, we typically constrain sample in custom silicone wells or on high friction surface (e.g. sandpaper) and surround sample with room temperature saline. Consistency of indentation data relies on indents approximately 10 % of sample thickness, so quantification of sample thickness is also important. For large (centimeter-scale) samples, we typically section them to known thickness with a matrix slicer (e.g. Ted Pella or Zivic). For smaller or awkwardly shaped samples, we measure the distance between the surface holding the sample and the top of the sample by using the encoded piezostage for thin (<800 μm) sections and the manual z-stage vernier scale for thicker samples. 14.3 Results Operation of MSI. Through appropriate cantilever design, we are able to apply normal loads of less than 10 μN. Our chosen cantilever and capacitive probe combination can measure forces with uncertainties ~25 μN and resolution ~0.5 μN. Real-time monitoring using a graphical user interface in LabVIEW allows visualization of indentations and estimation of uncertainty in calculated force (Fig. 14.3). Our current configuration has enabled characterization of the steady-state modulus for hydrogels (0.1–100 kPa), human pancreas (500 Pa–20 kPa), rat small intestine and colon (1–10 kPa), rat, mouse, and human brain tissue (500 Pa–4 kPa), and rat hearts (5–50 kPa). Details on select results are below. While we have chosen to fit our force-displacement indentation data to a viscoelastic model, the system can be configured for unconfined or porous-platen compression and fit a variety of different material models. By controlling the piezoelectric stage through LabVIEW, arbitrary profiles can be created to satisfy test conditions for many constitutive models. Cross-Linking of Collagen Hydrogels. In the body, collagen concentration and the mechanical properties of tissues are correlated. By creating a tunable range of moduli over different collagen concentrations, it is possible to isolate one variable from the other and study the effects of the mechanical microenvironment on cell behavior. In our system, stiffness can be controlled using different conditions of collagen concentration and glutaraldehyde crosslinking that result in overlapping values of elastic moduli (Fig. 14.4). Figure 14.4 also demonstrates custom silicone holder designed for efficient handling of soft biomaterials. Mechanical Properties of Normal and Malignant Brain Tissue. This indentation system has been used to characterize changes in health and disease of tissues [2]. For example, brain tissue from mice with xenograft human tumors demonstrated significant differences in mechanical properties between normal and tumor regions (Fig. 14.5). Results from such characterizations are critical to designing relevant biomimetic microenvironments in which to test cancer cells for proliferation, migration, and chemoresistance. 14.4 Conclusion While many groups have characterized the elastic properties of common tissues such as hearts, pancreas, and intestine, they vary widely in indentation methods. These variations in methods and material models obfuscate comparisons among the data. Reported data on the elastic modulus of heart muscle, for example, range from common accepted values for brain tissue 14 Custom Indentation System for Mechanical Characterization of Soft Matter 97
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