A One Dimensional Mathematical Model for Urodynamics

Millions of people in the world suffer from urinary incontinence and overactive bladder with the major causes for the symptoms being stress, urge, overflow and functional incontinence. For a more effective treatment of these ailments, a detailed understanding of the urinary flow dynamics is required. This challenging task is not easy to achieve due to the complexity of the problem and the lack of tools to study the underlying mechanisms of the urination process. Theoretical models can help find a better solution for the various disorders of the lower urinary tract, including urinary incontinence, through simulating the interaction between various components involved in the continence mechanism. Using a lumped parameter analysis, a one-dimensional, transient mathematical model was built to simulate a complete cycle of filling and voiding of the bladder. Both the voluntary and involuntary contraction of the bladder walls is modeled along with the transient response of both the internal and external sphincters which dynamically control the urination process. The model also includes the effects signals from the bladder outlet (urethral sphincter, pelvic floor muscles and fascia), the muscles involved in evacuation of the urinary bladder (detrusor muscle) as well as the abdominal wall musculature. The necessary geometrical parameters of the urodynamics model were obtained from the 3D visualization data based on the visible human project. Preliminary results show good agreement with the experimental results found in the literature. The current model could be used as a diagnostic tool for detecting incontinence and simulating possible scenarios for the circumstances leading to incontinence. INTRODUCTION Urinary incontinence has been reported to affect 35% of American women over 50 years of age an almost 15% who have leakage on a daily basis [1]. The common types of incontinence are (1) Stress incontinence (2) Urge incontinence (3) Overflow incontinence and (4) Functional incontinence. Approximately 60% of women with incontinence will have stress incontinence [2] where the urethral sphincter is not able to hold urine due to weakened pelvic muscles that support the bladder, or malfunction of the urethral sphincter [3]. Urge incontinence is also a storage problem in which the bladder muscle contracts regardless of the amount of urine in the bladder. Urge incontinence may occur without a recognizable prior disease or may result from neurological injuries, neurological diseases, infection, bladder cancer, bladder stones, bladder inflammation, or bladder outlet obstruction [4]. Overflow incontinence happens when there is an impediment to the normal flow of urine out of the bladder and the bladder cannot empty completely. Patients with functional incontinence have mental or physical disabilities that impair urination, although the urinary system itself is normal [5]. In order to understand and simulate the various incontinence mechanisms we intend to build a mathematical model to describe the hydrodynamic processes in the urinary tract. We first present the anatomy of the human urinary tract. The lower part of the urinary tract consists of a sack like muscular storage organ called the bladder, that is found in the pelvis behind the pelvic bone (pubic symphysis) and a drainage tube, called the urethra, that exits to the outside of the body. The bladder is an organ where the urine filtered by kidneys is stored. The kidneys filter approximately 160 liters of blood a day in order to maintain the necessary fluid balance. Water makes up approximately 95 percent of the total volume of urine, with the remaining 5 percent consisting of dissolved solutes or wastes (i.e. urea, creatinine, uric acid and several electrolytes). Urine is steadily excreted from the kidneys then pumped down to the ureters to the bladder by means of muscle contractions and the force of gravity (Figure 1). Once in the