{"title":"A Model of the Deformations of a Cross-Section of the Spinal Cord Due to Periodic Pressure Loadings","authors":"Paul J. Harris, Jenny Venton","doi":"10.1002/mma.10666","DOIUrl":null,"url":null,"abstract":"<p>Changes in the pressure of the cerebrospinal fluid that surrounds the spinal cord can cause deformations of the spinal cord, which, in turn, may lead to the cord being damaged. In addition, the changes in the pressure of the surrounding cerebrospinal fluid can cause changes to the pressure of the extracellular fluid which saturates the spinal cord. The finite element method can be used to solve the differential equations, which describe both how the cord deforms and changes in the pressure of the extracellular fluid but often this requires a large number of time-steps to obtain an accurate and stable numerical solution. We present an alternative approach that uses a Fourier series method that avoids the need for using a time-stepping scheme and that can model how a pressure pulse affects the spinal cord.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6222-6229"},"PeriodicalIF":2.1000,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10666","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10666","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Changes in the pressure of the cerebrospinal fluid that surrounds the spinal cord can cause deformations of the spinal cord, which, in turn, may lead to the cord being damaged. In addition, the changes in the pressure of the surrounding cerebrospinal fluid can cause changes to the pressure of the extracellular fluid which saturates the spinal cord. The finite element method can be used to solve the differential equations, which describe both how the cord deforms and changes in the pressure of the extracellular fluid but often this requires a large number of time-steps to obtain an accurate and stable numerical solution. We present an alternative approach that uses a Fourier series method that avoids the need for using a time-stepping scheme and that can model how a pressure pulse affects the spinal cord.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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