Biomedical subjects
Publications and source records attributed to Y Cherruault.
We first present a global simulation model describing inhibition of human basophil degranulation by means of high dilutions. Then we study an optimal control problem associated to a non-linear compartmental model. This control is associated to an antigen concentration. For solving this control problem we used a dynamic programming method.
A mathematical model of the human fetal arterial circulation based on mass and momentum conservation for one-dimensional flow is presented. We simplified the fetal arterial vascular system from the heart to the placenta, defined 16 anatomical segments and studied the characteristics of the vascular system in relation to changes in morphology and hemodynamics. The two-step Lax-Wendroff finite difference scheme was used to solve the system of equations, after introducing the rheological constants, the diameter and length of the segments measured by two-dimensional imaging and the mean arterial velocity at the inlet segments obtained by pulsed Doppler. The model was validated by comparing the numerical results to our non-invasive ultrasound direct measurements and to previous published data.
A mathematical model is proposed for describing the mechanism of diffusion from gel (Tissucol) into the extracellular space. After diffusion of the antibiotic in one dimension, the gradient concentration was determined with microvoltametric electrodes. These microelectrodes measure the free diffusible form of electroactive antibiotics in the extracellular brain space. The aim of this study was to find simultaneously the coefficient of diffusion and extraction of some antibiotics (in our case the Fotemustin) using the Alienor Algorithm. These coefficients are useful for predicting the concentration gradient into abscesses, fibrin, etc.
In this paper we study the stability and bifurcation of partial differential equations derived from enzyme immobilisation modelling. Sufficient mathematical conditions ensuring stability and bifurcation are obtained.
Many drugs confer upon the body the characteristics of a four compartment model. This paper deals with the estimation of pharmacokinetic parameters of a four compartment model to study the distribution of strontium in the organism. The central compartment (where the introduction of the material takes place) is connected to two other compartments (which represent the organic fluids) and one of them is connected to the fourth compartment (which represents the fraction that can be exchanged in the bone). The elimination from the central compartment is through urine and the elimination from the third compartment is in the form of a non-exchangeable deposit. The method of solution involves an optimization method which provides the global minimum of delta, a single variable function. The model is tested for different sets of data and the results are compared with those obtained by the generalized least square method.
Studies are made for a four compartment model in which the central compartment is connected reversibly to three other compartments and the elimination occurs from the central compartment only. Identification of different distribution rate constants is made, with concentrations of drug in the central compartment at different times of observation being known. The solution depends on an optimization method in which the different unknowns are reduced to single variable with the help of Archimedes spiral. Thus, the solution requires the global minimum of a functional of single variable. Results are compared with those obtained by the generalized least square method.
Estulic [corrected] given orally without food after overnight fast produces a blood concentration curve with a pronounced second peak that does not appear when the drug is taken with food. A two-compartment open model involving two different time lags is used to study the pharmacokinetics of estulic [corrected] in humans after oral administration. The drug accumulates in a tissue or organ that is well perfused in the first pass transfer. The accumulation appears to occur by a competitive process. The second peak apparently is the result of a rapid release of drug and bioreversible drug compounds from the hepatic-biliary system with subsequent reabsorption. This release may occur spontaneously, but appears to be triggered by food intake. We use an optimization method to characterize the pharmacokinetic profiles of drug for this model. This technique which provides the global minimum of the deviation delta, from the given observations, leads to the optimization of a single variable function. The results are compared with those obtained from the generalized least squares method.
After a short review of the functional anatomy of the kidney, we express the usual hypotheses about the phenomena of reabsorption and filtration in the loop of Henle and the collecting duct. Starting from these hypotheses and the laws of biophysics, we formulate the equations of the model. This model accounts for the great increase in concentration of electrolyte and urea in the loop of Henle, the collecting duct and the interstitium, as we "go down" from the outer medullary area towards the inner areas, the active transportation of sodium in the loop of Henle being limited to the thick ascending limb.
The purpose of this pulmonary gas exchange model is to study the effect produced by an inhomogeneous distribution of the ventilation-perfusion (V A/Q) and diffusion-perfusion (D/Q) ratios on the oxygen transfer. We calculate partial pressures of oxygen and carbon dioxide in venous blood, in capillary blood and alveolar gas of each element as the unique solution of a non-linear system, the parameters of which are the local values of ventilation, perfusion and diffusion. We show that an inhomogeneous distribution of any ratio leads to a decrease of the mixed arterial concentration of oxygen and that the greater the inhomogeneity, the greater the decrease. We show by numerical stimulation that if two inhomogeneities (V A/Q) and (D/Q) are associated, the oxygen arterial concentration decrease is rather less important if the diffusion-ventilation ratio has a distribution almost homogeneous, i.e. if the V A/Q and D/Q inhomogeneities are almost identical.
A system of quadratic differential equations is proposed within the framework of 'non-linear mechanics', but also outside this framework in respect of certain features, and it is used with a view to formalising a feedback control system. The model helps to simulate states of balance or imbalance within an ago-antagonistic couple and to suggest methods for correcting the imbalances, which do not require modification of the parameter space. Its possibilities of synchronic or diachronic functioning are emphasised. The model may apparently be used for the construction of similar models which include several ago-antagonistic couples. Finally, the aims of such a model, which could be considered as an 'action' model, are defined; its place would be assigned midway between a black-box system and 'knowledge' models.
We propose two methods for solving numerically minimization problems involving non-linear functions of n variables. The first method is based on an approximation of a n variables function by a separated variables function. The second uses a reducing transformation (ALIENOR) allowing to approach a n variables function by a function of one variable. Applications to biomedical problems and specially to identification of models are given.