[The bases of urodynamics: analysis of stability of the solutions for the equation defining detrusor behaviour].
OBJECTIVE
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. Solutions are placed in the Trace-Determinant (T-D) plane. This work represents a previous study to the one about detrusor as a dispersing system. And about which we would have to perform an analysis, first from the point of view of the Hamiltonian systems, then from the point of view of chaos.


RESULTS
We worked on the equation which has been widely described in previous articles in the series of publications titled "the bases of urodynamics". In previous articles, we gave results after applying other methods different from the ones that are usually employed to solve differential equations. We used the matricial method for the analysis of stability of solutions because of its greater didactical clarity.


CONCLUSIONS
We conclude that we are in an unstable balance until the moment right before to start voiding. Once voiding is initiated, we are in front of a system with a drain, which at the same time is a fountain. Then we pass from a Hamiltonian dispersing system to a chaotic one. But this is another question...
Benítez Navío
Julio
J
Servicio de Urología, Complejo Hospitalario de Ciudad Real, España.
Caballero Gómez
Pilar
P
Ruíz Martínez
Rafael
R
Pastor Sánchez
Carlos
C
Gallardo Alcañiz
Ma José
MJ
D006801:Humans; D008433:Mathematics; D009130:Muscle, Smooth / Q000502:physiology*; D001743:Urinary Bladder / Q000502:physiology*; D014563:Urodynamics