Strategies for Automated Extraction of Young's Moduli of Soft Materials from Afm Force Curves: Application to Cartilage

INTRODUCTION Articular cartilage is a highly inhomogeneous soft tissue with composition, structure, and mechanical properties that vary with depth and region. Its primary constituents (water, collagen II fibrils, and aggrecan proteoglycans) define its functional role as a load-bearing structure. An understanding of local structure-properties relationships in cartilage can help in identifying the link between mechanical stress and biochemical processes responsible for pathological conditions such as osteoarthritis. Although constitutive laws have been developed to describe the bulk behavior of cartilage [1, 2], there remains a lack of appropriate models to describe the mechanical and thermodynamic properties of inhomogeneous, gel-like systems. Researchers have thus relied on osmotic techniques [3] and the atomic force microscope (AFM) [4] to derive contributions of the collagen network or aggrecan macromolecules to cartilage mechanics. Our goal is to map the osmotic and mechanical properties of cartilage using a tissue osmometer [5] and the AFM. Due in large part to its versatility, the AFM has become prevalent as a tool for characterizing biological and biomimetic materials. Based on the small tip size and controlling of tip-sample interactions, it is a powerful technique for imaging surface topography with subnanometer resolution. Unlike electron microscopes, imaged samples can be immersed in liquid, allowing biological specimens to be maintained at or near their native conditions. The AFM is well suited for measuring the local elasticity of small, inhomogeneous samples. For example, it has been used to study the changes in the elastic modulus of cartilage along the articular surface [6]. Despite the advantages of the AFM, tip geometry and data processing issues hinder the consistency of elasticity measurements on soft biological tissues. Although improvements to experimental techniques and to the Hertzian model of contact can correct for finite sample thickness and different tip geometries [7], difficulties still arise in determining the contact point from the force curves. Here, we describe a strategy for optimizing and automating the data fitting procedure and present examples of the approach as applied to the testing of tissue-engineered cartilage.