Mathematical Model of Anal Canal for Anal Fistula Surgery

Abstract

Abstract: Purpose: Surgery is necessary for the treatment of an anal fistula. However, excision of some sphincter muscle would compromise sphincter integrity or function, which is the cause of a reduced success rate in the long term. In order to develop an appropriate surgical plan, a mathematical model that describes the relationship between the internal pressure of the anal canal and the structure of anal sphincters is required. Methods: The anatomical structure of the anal canal and the corresponding sphincter pressure can be measured by endoanal ultrasound (EAUS) imaging and manometry, respectively. Length-tension relationships for skeletal and smooth muscles, two major components of the external and internal anal sphincter, respectively, were reviewed first. Results: Based on the information about the internal and external sphincters, two mathematical models, the thick-wall cylinder model and the two-layer model, have been created, from which the influence of complete or partial excision of the sphincter muscle can be estimated. Conclusions: The proposed thick-wall cylinder and two-layer models could describe the relationship between the internal anal canal pressure and the structure of anal sphincters, from which the influence of complete or partial excision of the sphincter muscle may be estimated.