State-space Analysis of a Myocybernetic Model of the Lower Urinary Tract

Urge Incontinence and the Nervous System

“…Smooth muscle electrical activity is related to relaxation and contraction both [13], which has been largely neglected. A better understanding of sphincter function and of the myo-cybernetic requirements of the lower urinary tract by mathematical models is needed [10,11,35,36]. Therefore, main focus should be on fundamental research, in order to understand the reasons behind the symptom of incontinence, followed by an effective translation of the results into clinical applications [37,38].…”

Mathematical modeling of the lower urinary tract: A review

“…10 The most common method for modeling the fluid dynamics of the bladder utilizes a lumped model that considers how its fluid volume V B changes with time. [11][12][13][14][15] From the principle of conservation of mass and fixed fluid density, we obtain the relation…”

“…16 Different SLS models and variations, including the addition of an active element that models detrusor contraction, have been used in modeling the bladder. [11][12][13]17,18 The biomechanics of the bladder is often simplified by representing the bladder as a spherical shell of thickness h B , internal radius R B , and internal fluid volume V B , [11][12][13][14][15]19 as illustrated in Figure 2. This assumption has a very important implication: the validity of Laplace law that states that the tension T B of the bladder walls is proportional to the transmural pressure difference…”

“…The most common method for modeling the fluid dynamics of the bladder utilizes a lumped model that considers how its fluid volume $${V}_{B}$$ changes with time 11–15 . From the principle of conservation of mass and fixed fluid density, we obtain the relation $$$\frac{d{V}_{B}}{{dt}}={Q}_{{in}}-{Q}_{{out}},$$$where $${Q}_{{in}}$$ denotes the net flow rate of fluid into the bladder (either due to the inflow of urine from the kidneys or artificially infused fluid by experiments) and $${Q}_{{out}}$$ denotes the flow rate of urine from the bladder into the urethra.…”

Mathematical models in urinary system mechanics (review)

“…In one of these [87,88,[95][96][97][98] the problem was reduced [87] to a system of three equations for the bladder volume V and the muscle activation parameters ψ b and ψ u for the bladder and urethra, respectively. In this group of studies, attention was concentrated on the neural control of the mechanical processes, not the processes themselves.…”