2-D finite difference time domain model of ultrasound reflection from normal and osteoarthritic human articular cartilage surface

Quantitative high-frequency ultrasonic evaluation of articular cartilage has shown a potential for the diagnosis of osteoarthritis, where the roughness of the surface, collagen and proteoglycan contents, and the density and mechanical properties of cartilage change concurrently. Experimentally, these factors are difficult to investigate individually and thus a numerical model is needed. The present study is the first one to use finite difference time domain modeling of pulse-echo measurements of articular cartilage. Ultrasound reflection from the surface was investigated with varying surface roughness, material parameters (Young's modulus, density, longitudinal, and transversal velocities) and inclination of the samples. The 2-D simulation results were compared with the results from experimental measurements of the same samples in an identical geometry. Both the roughness and the material parameters contributed significantly to the ultrasound reflection. The angular dependence of the ultrasound reflection was strong for a smooth cartilage surface but disappeared for the samples with a rougher surface. These results support the findings of previous experimental studies and indicate that ultrasound detects changes in the cartilage that are characteristic of osteoarthritis. In the present study there are differences between the results of the simulations and the experimental measurements. However, the systematic patterns in the experimental behavior are correctly reproduced by the model. In the future, our goal is to develop more realistic acoustic models incorporating inhomogeneity and anisotropy of the cartilage.