Active opening out of the urethra questions the basis of the Valentini–Besson–Nelson mathematical model

Abstract

Dear Editor, The mechanics of micturition are an important step in the understanding and therefore, potential treatment of micturition dysfunctions. Mathematical models such as the Valentini– Besson–Nelson (VBN) mathematical model are an important step in this process [1]. This is a field that has also occupied our attention for some years. We are concerned at a singular omission from the VBN model, the active opening out of the urethra by external striated muscle forces (Fig. 1). Active opening out of the urethra would have major effects on the VBN model. It is clear from Fig. 1 that the anterior vaginal wall, and therefore the urethra, is stretched backwards, extending urethral elasticity, a pre-requisite for obtaining a smooth surface for urine flow. In this context, urethral elasticity ceases to be a dominant factor in the calculation. It is likely that the rhabdosphincter would relax during micturition. Whether it does or not, our radiological micturition studies show no urethral compression at the midurethra. On the contrary, they clearly demonstrate opening out of the whole urethral tube, often to double the original diameter. Therefore, this element of the VBN equation must also be questioned. Our modelling of the anatomical structures of the urethral wall indicates that the pressure generated by detrusor contraction is nowhere near sufficient to expel urine in the absence of this external striated mechanism [2], mathematically confirming our observations of active opening. Active opening must also confound the detrusor element of the VBN equation, as the pressure measured is a function of the urethral resistance and in turn, the radius. This is obvious when one considers that paraplegic patients cannot urinate spontaneously and have to be catheterized. We were not able to check reference [3]. Our bench and computer modelling indicate that intraurethral resistance is exponentially related, inversely to the 5th power of the urethral radius [4].