Análisis cualitativo de un modelo matemático aplicable a la absorción gástrica de una droga.

AGUIRRE CRISTINA; ARMENDARIZ MIRTA; RIGALLI ALFREDO; PUCHE RODOLFO

Rosario

Congreso; . VII Congreso. XXV Reunión Anual de la sociedad de Biología de Rosario; 2005

Sociedad de Biologia de Rosario

QUALITATIVE ANALYSIS OF A MATHEMATICAL MODEL APPLICABLE TO THE GASTRIC ABSORPTION OF ONE DRUGS María. Aguirre(1);Mirta Armendariz(1);Alfredo Rigalli(2);Rodolfo Puche(2)  (1)Área Matemática Fac. de Cs Bioq. y Far. U.N.R (2) Laboratorio de Biología Osea. Fac. de Cs Medicas. U.N.R. The sodium monofluorophosphate (MFP) given orally is hydrolyzed into fluoride (F)   in the intestine. At gastric level, the MFP is fully absorbed without undergoing hydrolysis. This determines the existence of two different forms of fluorides in plasma: the ionic fluoride and the MFP. The gastric MFPg is absorbed with a rate absorption kg. The analysis is restricted to the variable MFP concentration at plasma. The following differential equation system is set out with initial conditions dMFPp/dt = kg MFPg – ke MFPp  ;  dMFPg/dt = -kg MFPg   ;  MFPg(0) = MFP0   ;   MFPp(0) = 0 where MFP0 is the orally given dose and MFP(0) is the MFP concentration at plasma at 0 time The qualitative analysis of the system has been accomplished determining the point of balance and the trajectories of the phase plane. The phase portrait show the declination of the MFPg concentration as well as the variation of the MFPp. It is also observed that the disturbed system tends to retakes its estate of balance as time passes. In this cases, in which the system solutions are already known, its main features are verified through the qualitative analysis of equations. In complex pharmacokinetic or biological processes mathematical scheduled by  equations systems whose solutions can’t be expounded, the qualitative analysis allows us to get information about the behaviors of the variables involved in this process.