Combining Displacement Field and Grip Force Information to Determine Mechanical Properties of Planar Tissue With Complicated Geometry

Soft-tissue characterization using planar biaxial testing and nominal stress–strain curves usually relies on certain conditions1: The sample should have a shape, (e.g., square or cruciform) that tends to produce homogeneous strain fields in the central region. If the sample is fibrous, the fiber orientation should be known and aligned with the axes of the test system. Strain should be measured far from any rigid boundary, such as a grip or attachment to bone. These criteria are often met (e.g., Refs. [3–9]), but for some tissue types, meeting one or more criteria is impossible. The tissue may, for example, be too small to allow isolation of a sample that is large enough for biaxial testing and is shaped to create a homogeneous strain region in the center. Aligning the material axes does not allow a biaxial test to generate planar shear strain [10]. Furthermore, if the material axes are improperly aligned, the variation in tissue response will increase, which could hinder elucidation of complex behaviors such as coupling between the two directions [10]. Other groups [e.g., Ref. 10] have used biaxial testing to good effect for off-axis fibrous samples. This is only effective, however, when the fiber orientation is known. When fiber orientation is unknown and/or the objective is to determine the fiber orientation, as in the current study, force-stretch data alone are insufficient. It also may be undesirable or even impossible to remove the tissue from bone, which restricts one's ability to align the tissue fiber direction with the testing apparatus and leads to inhomogeneity of the strain field. An example of these challenges is found in the AF of the intervertebral disk, particularly if one seeks to do single lamella experiments. Although some single lamella experiments have been performed in uniaxial [11–13] and biaxial modes [14–16], testing with intact bone [12–14,16] is attractive both because of direct relevance to in vivo loading and because of minimized tissue damage. Figure ​Figure11 shows a lamella of AF attached to axial vertebral bone. This geometry is not conducive to a homogeneous strain field, and the principal fiber direction does not align with the axes of the testing apparatus. Fig. 1 Lamella of the AF. The sample is attached to bone, labeled, and is anisotropic with fibers aligned 30 deg from the horizontal testing axis, along the dotted line. The dissected tissue is too small to be removed from the bone and cut to align the ... Sample geometries that produce inhomogeneous strain fields pose a considerable challenge to the investigator, but the advent of image-correlation-based methods for tracking motion over the entire tissue during testing [17–24] present new opportunities. The approach of simulating the experiment and then iterating over the model parameters to determine a best fit has been used in elastography [25,26] as well as indentation [27] and can be applied to tissue testing as well. In this study, we demonstrate the use of combined displacement field data, grip force-stretch data, and FE modeling to determine tissue properties from a biaxial test.