Simultaneous Wide-Field Planar Strain-Fiber Orientation Distribution Measurement Using Polarized Spatial Domain Imaging

Abstract

In the present study, we demonstrate that soft tissue fiber architectural maps captured using polarized spatial frequency domain imaging (pSFDI) can be utilized as an effective texture source for DIC-based planar surface strain analyses. Experimental planar biaxial mechanical studies were conducted using pericardium as the exemplar tissue, with simultaneous pSFDI measurements taken. From these measurements, the collagen fiber preferred direction [Formula: see text] was determined at the pixel level over the entire strain range using established methods ( https://doi.org/10.1007/s10439-019-02233-0 ). We then utilized these pixel-level [Formula: see text] maps as a texture source to quantify the deformation gradient tensor [Formula: see text] as a function of spatial position [Formula: see text] within the specimen at time t. Results indicted that that the pSFDI approach produced accurate deformation maps, as validated using both physical markers and conventional particle based method derived from the DIC analysis of the same specimens. We then extended the pSFDI technique to extract the fiber orientation distribution [Formula: see text] as a function of [Formula: see text] from the pSFDI intensity signal. This was accomplished by developing a calibration procedure to account for the optical behavior of the constituent fibers for the soft tissue being studied. We then demonstrated that the extracted [Formula: see text] was accurately computed in both the referential (i.e. unloaded) and deformed states. Moreover, we noted that the measured [Formula: see text] agreed well with affine kinematic deformation predictions. We also demonstrated this calibration approach could also be effectively used on electrospun biomaterials, underscoring the general utility of the approach. In a final step, using the ability to simultaneously quantify [Formula: see text] and [Formula: see text], we examined the effect of deformation and collagen structural measurements on the measurement region size. For pericardial tissues, we determined a critical length of [Formula: see text] 8 mm wherein the regional variations sufficiently dissipated. This result has immediate potential in the identification of optimal length scales for meso-scale strain measurement in soft tissues and fibrous biomaterials.

Keywords: Affine deformation; Fiber structure; Optical–mechanical–numerical methods; Soft tissue mechanics.