Gilbert, Robert P.Shoushani, Michael2022-04-202022-04-202022-03-18Gilbert, RP, Shoushani, M. Decomposition of transmitted ultrasound wave through a 2-D muscle–bone system. Math Meth Appl Sci. 2022; 1- 15. doi:10.1002/mma.81911099-1476https://udspace.udel.edu/handle/19716/30793This is the peer reviewed version of the following article: Gilbert, RP, Shoushani, M. Decomposition of transmitted ultrasound wave through a 2-D muscle–bone system. Math Meth Appl Sci. 2022; 1- 15. doi:10.1002/mma.8191, which has been published in final form at https://doi.org/10.1002/mma.8191. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited. This article will be embargoed until 03/18/2023.In this paper, we investigate ultrasound waves passing through a skeletal muscle segment of a specimen. The model is solved using an extension of a method due to Ilya Vekua. An ansatz is made that a solution to a partial differential equation can be found in a form resembling the ansatz of Vekua. It is shown that this is indeed possible. This method is used continuously throughout the paper to find simple representations of the acoustic equations in the different muscle and bone regions.en-USacousticscalcified tissuepartial differential equationsVekua decompositionArticle