{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/modeling-the-mitral-valve","title":"Modeling the Mitral Valve","arxiv_id":"1902.00018","date":"2019-01-31","proceeding":null,"authors":["Alexander D. Kaiser","David M. McQueen","Charles S. Peskin"],"abstract":"This work is concerned with modeling and simulation of the mitral valve, one\nof the four valves in the human heart. The valve is composed of leaflets, the\nfree edges of which are supported by a system of chordae, which themselves are\nanchored to the papillary muscles inside the left ventricle. First, we examine\nvalve anatomy and present the results of original dissections. These display\nthe gross anatomy and information on fiber structure of the mitral valve. Next,\nwe build a model valve following a design-based methodology, meaning that we\nderive the model geometry and the forces that are needed to support a given\nload, and construct the model accordingly. We incorporate information from the\ndissections to specify the fiber topology of this model. We assume the valve\nachieves mechanical equilibrium while supporting a static pressure load. The\nsolution to the resulting differential equations determines the pressurized\nconfiguration of the valve model. To complete the model we then specify a\nconstitutive law based on a stress-strain relation consistent with experimental\ndata that achieves the necessary forces computed in previous steps. Finally,\nusing the immersed boundary method, we simulate the model valve in fluid in a\ncomputer test chamber. The model opens easily and closes without leak when\ndriven by physiological pressures over multiple beats. Further, its closure is\nrobust to driving pressures that lack atrial systole or are much lower or\nhigher than normal.","url_abs":"http://arxiv.org/abs/1902.00018v1","url_pdf":"http://arxiv.org/pdf/1902.00018v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"modeling-the-mitral-valve","repo_url":"https://github.com/alexkaiser/mitral_valve","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"modeling-the-mitral-valve","repo_url":"https://github.com/alexkaiser/heart_valves","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"anatomy","task_name":"Anatomy"},{"task_slug":"stress-strain-relation","task_name":"Stress-Strain Relation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}