A Phenomenological Approach Toward Patient-Specific Computational Modeling of Articular Cartilage Including Collagen Fiber Tracking

Abstract

To model the cartilage morphology and the material response, a phenomenological and patient-specific simulation approach incorporating the collagen fiber fabric is proposed. Cartilage tissue response is nearly isochoric and time-dependent under physiological pressure levels. Hence, a viscoelastic constitutive model capable of reproducing finite strains is employed, while the time-dependent deformation change is purely isochoric. The model incorporates seven material parameters, which all have a physical interpretation. To calibrate the model and facilitate further analysis, five human cartilage specimens underwent a number of tests. A series of magnetic resonance imaging (MRI) sequences is taken, next the cartilage surface is imaged, then mechanical indentation tests are completed at 2–7 different locations per sample, resulting in force/displacement data over time, and finally, the underlying bone surface is imaged. Imaging and mechanical testing are performed with a custom-built robotics-based testing device. Stereo reconstruction of the cartilage and subchondral bone surface is employed, which, together with the proposed constitutive model, led to specimen-specific finite element simulations of the mechanical indentation tests. The force-time response of 23 such indentation experiment simulations is optimized to estimate the mean material parameters and corresponding standard deviations. The model is capable of reproducing the deformation behavior of human articular cartilage in the physiological loading domain, as demonstrated by the good agreement between the experiment and numerical results (R2=0.95±0.03, mean±standard deviation of force-time response for 23 indentation tests). To address validation, a sevenfold cross-validation experiment is performed on the 21 experiments representing healthy cartilage. To quantify the predictive error, the mean of the absolute force differences and Pearson’s correlation coefficient are both calculated. Deviations in the mean absolute difference, normalized by the peak force, range from 4% to 90%, with 40±25%(M±SD). The correlation coefficients across all predictions have a minimum of 0.939, and a maximum of 0.993 with 0.975±0.013(M±SD), which demonstrates an excellent match of the decay characteristics. A novel feature of the proposed method is 3D sample-specific numerical tracking of the fiber fabric deformation under general loading. This feature is demonstrated by comparing the estimated fiber fabric deformation with recently published experimental data determined by diffusion tensor MRI. The proposed approach is efficient enough to enable large-scale 3D contact simulations of knee joint loading in simulations with accurate joint geometries.