A mathematical model for the proliferation of bacteria in the urinary bladder due to enlarged prostate

Urinary retention due to enlargement of the prostate (prostate hypertrophy) leads to increased proliferation of bacteria in the bladder. This in turn increases the infection rate. The reason is that the enlarged prostate presses on the urine channel and tends to close it. Thus the out flux of the bladder consists of repeatedly small amounts of fluid during a day. A mathematical dynamic model with differential equations is developed for the proliferation of bacteria in the urinary bladder (vesica urinary). The model accounts for how this proliferation is associated with varying amounts of mass of urine within the bladder. Parameters are estimated from published data and analytical and numerical results are presented. The relationships between the proliferation of bacteria within the bladder and the type of urinal out flux from the bladder are examined. The proliferation is shown to depend on the amount of mass of urine and the out flux of urine from the bladder. In the normal situation the bladder is drained successfully which also drains the bacteria. In the abnormal situation the bladder drains only partly. Despite frequent urination, substantial urine mass in the bladder on the average allows bacteria to proliferate and increase in number through time. The simulations depend on the numerical values of the parameters which again depend on the prostate condition of each male adult under scrutiny. By determining the parameters for each male, the dynamic model can be used as a powerful tool by which the proliferation of bacteria in the bladder can be studied and controlled by different means. Three clinical advices are provided. First, try to achieve that the proliferation rate of bacteria in the bladder is as small as possible, e.g. through altering the pH or chemical composition within the bladder. Second, try to achieve that the out flux of urine from the bladder is substantial, through sufficient drinking. Third, try to achieve that the mass of urine in the bladder is as small as possible, through sufficient urination. The intrinsic parameters for each male can be used to pinpoint the actual out flux during a day necessary to keep the number of bacteria in the bladder low. Suggestions for how to test the model are briefly presented.