[Urodynamic paradigms: from renaissance fibrilar theory to current Doppler-flowmetry].

Unlabelled: To perform a historical introduction and a review of the mathematical model, emphasizing that our mathematical model may be the solution to the viscoelastic model. It is evident that the same experiment has been repeated over half a century, with similar results in all cases. We also show one of the projects we are working on: the electro-vesicogram for the evaluation of the filling phase, and Doppler uroflowmetry for the study of the voiding phase.

[The bases of urodynamics: analysis of stability of the solutions for the equation defining detrusor behaviour].

Objectives: In this article we develop the analysis of stability of the solution(s) of the differential equation describing detrusor behaviour as a forced and overcushioned tensor. We followed the theories of Lyapunov about stability. Therefore, we used a matricial method which is more didactical and also analytically more graphic.

[Rationale of Doppler urodynamics and urodynamics. What does Doppler contribute to urodynamics?].

Objectives: To make an analysis of the usefulness of urodynamic tests and what can be obtained from them.

Methods: We also perform and analytical deduction of those parameters that define detrusor behavior, such as the constant defining bladder compliance, the bladder elastic constant, in its tensile properties, and we found the expression of resistances and calculate the abdominal pressure formula; therefore we don't need to introduce a rectal catheter to know the value of those parameters that define bladder dynamics.

Results: Although they are provisional, they allow foreseeing a promising future for this application of a well-known device.