Cartilage morphology is both an indicator of tissue health, and an important biomechanical determinant of internal joint mechanics. However, direct measurement of cartilage morphology and joint loading is not feasible. Thus, it is necessary to develop computational imaging and modeling tools to investigate the relationship between cartilage morphology and knee mechanics during human movement. Such tools are relevant clinically for tracking changes in morphology that can arise secondary to injury, surgical treatment and rehabilitation. Further, computational biomechanical modeling tools are beneficial in research for predicting the influence that interventions can have on joint loading patterns. The overall goal of this work was to develop, validate and use new computational approaches to accurately characterize in vivo cartilage morphology from MRI images and simulate tibiofemoral cartilage loading patterns during human walking. This goal was achieved by completing the following four objectives.

Objective 1. Develop an Accurate and Repeatable Semi-Automated Segmentation Algorithm for Reconstructing Articular Cartilage Morphology from Magnetic Resonance Images

Cartilage morphology is a vital indicator of tissue health. For example, in osteoarthritis, cartilage tissue is observed to undergo thickening in the early stages of the disease followed by thinning in the later stages. Advances in magnetic resonance (MR) imaging sequences can be used to obtain high resolution images of cartilage morphology that are useful for assessing subtle changes in cartilage thickness. However, segmenting out the entire cartilage volume from stacks of images remains a time-consuming task due to the inherent challenge in automatically identifying tissue boundaries. Further, the anatomical accuracy and repeatability of 3D cartilage models based on manual segmentation have been questioned. We introduce a semi-automated cartilage segmentation algorithm for creating 3D cartilage geometry models from MR images within a few seconds. The algorithm first uses region growing to segment out the bone tissue, edge detection to delineate tissue boundaries and then a novel radial projection scheme to identify the inner and outer surface of the cartilage. This sequence is repeated across a stack of MR image slices, resulting in a 3D reconstruction of the entire cartilage volume. We validated the segmentation algorithm by showing it produced unbiased porcine knee cartilage thickness estimates that were within 0.4mm of direct cartilage thickness measures obtained via a laser scanner. The segmentation algorithm was also successfully used to segment tibia and femoral articular cartilage surfaces from MR images collected on human subjects. Good computational performance was achieved with the automated algorithm requiring a couple orders of magnitude less time than a manual segmentation approach.

Objective 2. Introduce a Computationally Efficient Collision Detection Algorithm to enable the Calculation of Complex Cartilage Contact Pressure Patterns within Biomechanical Simulations of Movement

The location and magnitude of knee joint articular contact pressure are important factors that can affect the long-term health of cartilage tissue. The objective of the study was to develop a computationally efficient discrete element analysis (DEA) algorithm that would allow for surface pressure to be computed based on the depth of penetration between two articulating elastic surfaces. The primary computational challenge in using DEA with complex geometries involves determining the regions of surface overlap, a process that involves finding the face on a target surface that is intersected by a ray cast from a face on the parent surface. We accelerated the collision detection process by using a hierarchical bounding volume approach, in which the target surface was successively subdivided into regions that fit within tight fitting bounding boxes. Ray-box intersection tests then allowed us to quickly traverse the surface and identify the leaf node containing the triangle intersected by a ray. The parallelized algorithm was subsequently implemented on a graphics processor unit (GPU), providing nearly 10 fold increase in computation speed when high resolution cartilage surface meshes were used. The collision detection algorithm was shown to be sufficiently fast to enable simulations of tibiofemoral contact loading patterns within a multibody dynamic simulation of walking.

Objective 3. Investigate the Accuracy of Simulated Tibiofemoral Contact Loads Obtained via the Co-Simulation of Neuromuscular Dynamics and Knee Mechanics

This study introduced a framework for co-simulating neuromuscular dynamics and knee joint mechanics during gait. A knee model was developed that included 17 ligament bundles and a representation of the distributed contact between a femoral component and tibial insert surface. The knee was incorporated into a forward dynamics musculoskeletal model of the lower extremity. A computed muscle control algorithm was then used to modulate the muscle excitations to drive the model to closely track measured hip, knee, and ankle angle trajectories of a subject walking overground with an instrumented knee replacement. The resulting simulations predicted the muscle forces, ligament forces, secondary knee kinematics, and tibiofemoral contact loads. Model-predicted tibiofemoral contact forces were of comparable magnitudes to experimental measurements, with peak medial (1.95 body weight (BW)) and total (2.76 BW) contact forces within 4–17% of measured values. Average root-mean-square errors over a gait cycle were 0.26, 0.42, and 0.51 BW for the medial, lateral, and total contact forces, respectively.

Objective 4. Investigate the Influence of Cartilage Thickness on Simulated Tibiofemoral Contact Pressure Patterns during Normal Human Walking

Cartilage has a spatially varying micro- and macro-structural arrangement that is well adapted to the loading seen in vivo. It is believed that injury- and surgery-induced changes in knee mechanics may disrupt this loading and subsequently lead to cartilage thinning. This degenerative process may be cumulative, with changes in cartilage morphology affecting tissue loads in a way that exacerbates the problem. This pilot study was undertaken to investigate the influence that cartilage thickness can have on cartilage pressure patterns in human walking. Gait simulations were performed with combined tibiofemoral cartilage thickness ranging from 2 to 10 mm. Peak tibia plateau contact pressures increased nonlinearly with cartilage thinning, with a 51% increase in pressure predicted in the thin cartilage condition (2mm of total contact cartilage thickness) compared to the nominal cartilage model (6mm of total contact cartilage thickness). As a result, net contact areas decreased substantially with cartilage thinning, by 43% in the thin cartilage condition relative to the nominal condition.

The computational tools developed in this study will enable future investigations of cartilage loading on heterogenous cartilage thickness maps derived from images on individual subjects. Such studies are important for understanding and treating biomechanical factors that can contribute to cartilage tissue degeneration.