Development of an Inverse Approach for the Characterization of In Vivo Mechanical Properties of the Lower Limb Muscles

Abstract

The purpose of this study was to develop an inverse method, coupling imaging techniques with numerical methods, to identify the muscle mechanical behavior. A finite element model updating (FEMU) was developed in three main interdependent steps. First, a 2D FE modeling, parameterized by a Neo-Hookean behavior (C10 and D), was developed from a segmented thigh muscle 1.5T MRI (magnetic resonance imaging). Thus, a displacement field was simulated for different static loadings (contention, compression, and indentation). Subsequently, the optimal mechanical test was determined from a sensitivity analysis. Second, ultrasound parameters (gain, dynamic, and frequency) were optimized on the thigh muscles in order to apply the digital image correlation (DIC), allowing the measurement of an experimental displacement field. Third, an inverse method was developed to identify the Neo-Hookean parameters (C10 and D) by performing a minimization of the distance between the simulated and measured displacement fields. To replace the experimental data and to quantify the identification error, a numerical example was developed. The result of the sensitivity analysis showed that the compression test was more adapted to identify the Neo-Hookean parameters. Ultrasound images were recorded with a frequency, gain, and dynamic of 9 MHz, 34 dB, 42 dB, respectively. In addition, the experimental noise on displacement field measurement was estimated to be 0.2 mm. The identification performed on the numerical example revealed a low error for the C10 (<3%) and D (<7%) parameters with the experimental noise. This methodology could have an impact in the scientific and medical fields. A better knowledge of the muscle behavior will help to follow treatment and to ensure accurate medical procedures during the use of robotic devices.