A sensitivity analysis of acoustic wave propagation through the ankle joint space.

Abstract

Ultrasound imaging is known to be non-invasive, fast, and cost-effective. However, a drawback is its reflection on bone. Therefore, an alternative acoustic wave propagating technique is being developed that eventually should be able to diagnose osteochondral defects (OCDs) that are now often missed with conventional imaging techniques. A novel technique is proposed that consists of acoustic wave propagation through the ankle joint space. The identification of OCDs is based on a presumed deviation between a reference signal (from a predicted model of the patient specific healthy ankle joint space) and a measured signal including the OCD in de ankle joint space. For the identification of OCDs, the diagnostic technique should be robust enough to cope with variation in acoustic parameters. To assess the influence of acoustic parameters, two dimensional finite-difference time-domain models of the ankle joint space were generated. A sensitivity analysis was performed to indicate the effect of variation in acoustic parameters of bone, the presence of soft tissues on acoustic wave propagation and the identification of OCDs. The minimal, maximal and mean values of the density, the Lamé’s constants, shear and bulk viscosity of bone were variated step by step. The values of acoustic bone parameters were derived from literature, those of the Achilles tendon and skin were determined experimentally. The output signals from the receiver that was placed on the outside of the ankle joint space were of main interest during present study. The output signals of the receiver in the middle and the anterior side of the ankle joint space were assessed to gain more insight in the behaviour of the acoustic waves within the ankle joint space. Variation in acoustic parameters of bone made noticeable alterations to the reference signal: variation in density resulted in normalized root mean square error (NRMSE) from 10%-16%, variation in the Lamé’s constants resulted in NRMSE from 8% -13% and variation in the bulk and shear viscosity ranged from 6% -10%. In comparison the NRMSE as a result of an OCD of 5 mm wide and 5 mm deep in the middle of the talus ranged from 5% to 7%. The receiver that was placed in the middle of the ankle joint space showed larger differences in amplitude and time shift between the healthy and defected ankle condition. The NRMSE caused by the variation in acoustic parameters of bone ranged from 1% - 10%, whereas the NRMSE caused by the presence of an OCD ranged from 10%-12%. The detectability of an OCD increases with the presence of Achilles tendon and skin. A slight difference in NRMSE and NMCC, the missing time shift and the least influence on the amplitude by the bulk and shear viscosity implies that acoustic wave propagation is less sensitive to variation in the shear and bulk viscosity than in density and Lamé’s constants. It is advised that the acoustic parameters of bone and soft tissues are estimated precisely when models of the ankle joint space for OCD identification purposes are developed.