%0 Journal Article
%T Numerical and Analytical Study of Bladder-Collapse Flow
%A M. Tziannaros
%A F. T. Smith
%J International Journal of Differential Equations
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/453467
%X Understanding and quantifying more of the workings of the human bladder motivates the present industry-supported study. The bladder performance in terms of the urinary velocities produced tends to be dominated by the internal fluid dynamics involved, in the sense that the bladder wall moves in a body-prescribed way. The enclosed urine flow responds to this wall movement, and there is relatively little feedback on the wall movement. Combined computational work and special-configuration analysis are applied over a range of configurations including computational and analytical results for the circle and sphere as basic cases; models of more realistic bladder shapes; the end stage of the micturition process where the bladder is relatively squashed down near the urethral sphincter and localised peak speeds arise. The combination of approaches above can be extended to allow for interaction between wall shape and flow properties such as internal pressure if necessary. 1. Introduction The investigation here involves industrial motivation and support with a biomedical setting which is strongly affected by fluid dynamics and is treated by computations along with analysis including matched asymptotic expansions. Industry with a view to incontinence devices in particular wishes to know of the induced velocities and pressures in a bladder, wishes for more mathematical approaches, and wishes eventually to understand more of realistic three-dimensional dynamics. The workings of the human lower urinary tract¡ªof which a diagram is shown in Figure 1¡ªare clearly of much interest. Relevant background material and some studies are in [1¨C6]. Yet scant attention has been paid to increased understanding and quantitative prediction for the bladder particularly. The bladder wall tends to move in a body-prescribed way, the enclosed urine flow responds to this wall movement, and there is comparatively little feedback from the flow behaviour on the wall movement. Computational results are obtained below by use of a relatively simple approach [7] which has the benefits of wide application allied with accuracy. Special-configuration analysis also proves a valuable and insightful approach applying over a wide range of configurations. Figure 1: Diagram taken from [ 8] of sections through the urinary tract and more specifically the ureters, parts of the bladder and the urethra. Around 15% of women and 7% of men suffer from incontinence, while benign prostatic hyperplasia occurs in more than 80% of men aged 75 [1]. A recent statistic published by Astellas Pharma shows that, in the UK
%U http://www.hindawi.com/journals/ijde/2012/453467/