Uncertainty analysis of Altantic salmon fish scale's acoustic impedance using 30 MHz C-Scan measurements

Understanding the biomechanics of fish scales is crucial for their survival and adaptation. Ultrasonic C-scan measurements offer a promising tool for non-invasive characterization, however, existing literature lacks uncertainty analysis while evaluating acoustic impedance. This article presents an innovative integration of uncertainty into the analytical framework for estimating stochastic specific acoustic impedance of salmon fish scale through ultrasonic C-scans. In this study, the various types of uncertainties arising due to variation in biological structures and aging, measurement errors, and analytical noises are combined together in the form of uncertain reflectance. This uncertain reflectance possesses a distribution which is derived using a theory of waves by assuming suitable stochasticity in wavenumber. This distribution helps in development of a stochastic-specific acoustic impedance map of the scales which demonstrates the possible deviations of impedance from mean value depending on uncertainties. Furthermore, maximal overlap discrete wavelet transform is employed for efficient time-frequency deconvolution and Kriging for spatial data interpolation to enhance the robustness of the impedance map, especially in scenarios with limited data. The framework is validated by accurately estimating the specific acoustic impedance of well-known materials like a pair of target medium (polyvinylidene fluoride) and reference medium (polyimide), achieving over 90% accuracy. Moreover, the accuracy of the framework is found superior when compared with an established approach in the literature. Applying the framework to salmon fish scales, we obtain an average specific acoustic impedance of 3.1 MRayl along with a stochastic map visualizing the potential variations arising from uncertainties. Overall, this work paves the way for more accurate and robust studies in fish scale biomechanics by incorporating a comprehensive uncertainty analysis framework.