Morphological Analysis of Articular Cartilage Using Multiphoton Microscopy as Input for Constitutive Modeling: Experiment and Mathematical Implementation

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The 3D structure of collagen fibers in chicken cartilage was quantified using multiphoton microscopy. Samples of fresh chicken cartilage were sectioned in three orthogonal planes using a vibratome. The sections were imaged using multiphoton microscopy, specifically imaging the collagen fibers using the second harmonic signal. Employing image analysis techniques based on Fourier analysis, the primary direction and anisotropy of the collagen fibers were extracted for the superficial layer resulting in a 3D map of the collagen fiber fabric. In the middle layer, image analysis using objective thresholding techniques was employed to extract the volume fraction occupied by extracellular matrix, the rest being occupied by the lacunae and residing chondrocytes.

To implement these imaging data in a computational setting, we propose a new, 3D large strain constitutive model for articular cartilage, focused on the essential load-bearing morphology: an inhomogeneous, visco-poroelastic solid matrix reinforced by an anisotropic, viscoelastic dispersed fiber fabric which is saturated by an incompressible fluid residing in strain-dependent pores of the collagen-proteoglycan solid matrix.

High-fidelity models, combining advanced imaging and computational biomechanics, will allow us to consider complex problems in structure-function relationships and provide insight to microphysical (mechanobiological) cellular stimuli.