Mechanical Characterization by Mesoscale Indentation: Advantages and Pitfalls for Tissue and Scaffolds

Abstract

Regenerative medicine and tissue engineering are hindered by the lack of consistent measurements and standards for the mechanical characterization of tissue and scaffolds. Indentation methods for soft matter are favored because of their compatibility with small, arbitrarily shaped samples, but contact mechanics models required to interpret data are often inappropriate for soft, viscous materials. In this study, we demonstrate indentation experiments on a variety of human biopsies, animal tissue, and engineered scaffolds, and we explore the complexities of fitting analytical models to these data. Although objections exist to using Hertz contact models for soft, viscoelastic biological materials since soft matter violates their original assumptions, we demonstrate the experimental conditions that enable consistency and comparability (regardless of arguable misappropriation). Appropriate experimental conditions involving sample hydration, the indentation depth, and the ratio of the probe size to sample thickness enable repeatable metrics that are valuable when comparing synthetic scaffolds and host tissue, and bounds on these parameters are carefully described and discussed. We have also identified a reliable quasistatic parameter that can be derived from indentation data to help researchers compare results across materials and experiments. Although Hertz contact mechanics and linear viscoelastic models may constitute oversimplification for biological materials, the reporting of such simple metrics alongside more complex models is expected to support researchers in tissue engineering and regenerative medicine by providing consistency across efforts to characterize soft matter.

Tunable methacrylated hyaluronic acid‐based hydrogels as scaffolds for soft tissue engineering applications

“…Samples were hydrated with PBS to decrease adhesion between the probe and the surface of the sample. Indentation rate was 10 μm/s and the relaxation phase was 20 s. A rearrangement of the Hertz contact model was used to obtain a transient modulus, and the relaxation stage was fit to the standard linear solid model to obtain the steady‐state modulus, the effective modulus after relaxation (Rubiano, Delitto, et al, ; Rubiano, Galitz, et al, ). For details and discussion of this method, see Rubiano, Galitz, et al ().…”

Endocytic proteins with prion-like domains form viscoelastic condensates that enable membrane remodeling

“…Here, we transpose these phenomena to the cytoplasm. As noted by Rubiano et al (66), interpretations of mesoscale indentations of soft tissues to infer mechanical properties can be made using Hertzian contact mechanics, providing care is taken to work in a regime of appropriate hydration levels, and the size scales for probe sizes versus sample thickness. Our use of Hertzian contact mechanics is also supported by its adoption for analyzing data from atomic force microscopy for systems with high water content including biological soft matter (67,68).…”

Elastic modulus distribution in poly(N-isopopylacrylamide) and oligo(ethylene glycol methacrylate)-based microgels studied by AFM

“…Due to viscoelastic and hydrodynamic effects, the stiffness of hydrogels increases at high loading rates. 43,44 In addition, the microgels were dried to immobilize them on the solid support. This may lead to an increase in network density even after rehydration since the network could stay partially adhered to the support.…”