Biomedical subjects
Publications and source records attributed to Y Cherruault.
We propose a new method for solving numerically minimization problems involving any function of two variables. This method uses a reducing transformation, and is inspired by the Alienor method. We have used this reducing transformation for applications to microbiology problems. Identification of models are treated.
The decomposition method solves a wide class of nonlinear functional equations. This method uses a series solution with rapid convergence. This paper is intended as a useful review and clarification of related issues.
We propose a new method, DIVANU (Diminution of Variables Number), for numerically solving minimization problems involving any function of any variables. This method uses a reducing transformation. We have used this method for applications to biological problems. The identification of models is treated.
Many bio-medical models lead to differential systems where some parameters have to be identified from partial observation on the system's solution. For two- or three-compartment models parameters to be identified can be explicitly calculated (when uniqueness is ensured) from the algebraic relation obtained by using classical methods. However, when the number of compartments is greater than three, numerical techniques are necessary. In this work we propose new numerical methods based on Adomian's method for solving identification and optimal control problems associated to biomedical systems.
In this paper we suggest new ideas for studying convergence of decomposition methods. Then we apply these techniques to the identification and control of biological systems modelled by differential systems of equations.
We present practical formulae for the calculus of Adomian's polynomials. We also prove the convergence of the decomposition method. Furthermore, we propose a new method for solving identification problems.
In this paper we present a model for the histamine negative feedback on the human basophil degranulation and another one for the feed-forward of these basophils on the extra-cellular histamine. These two models allow us to suggest a characterisation of the incubation time.
In this paper human basophil activation is modelled by means of a system of differential equations. The resolution of this system allows the justification of the incubation period and the unwedging period existing between the human basophil degranulation and the liberation of histamine.
The first purpose of this paper is to present a neural net model of the visual cortex of higher vertebrates based on the electrophysiological properties of the ganglion cells. This model takes Hebb's law [1] as the physiological learning rule for synaptic modification. The model consists of 85 x 85 neurons forming a layer similar to the cortex. The neurones are massively connected via weights that are typically adapted. We simulate several input patterns and show that the model reproduces the pattern recognition, contours pictures and moving perception.
The present study deals with the identification of exchange parameters involved in a three-compartment open model with two time lags in which elimination occurs from the central compartment. Two different optimization methods have been used which involve the reduction of different unknowns to a single variable theta, with the help of Archimedes Spiral. Thus, the solution requires the global minimum of a functional of single variable theta. Results are compared with those obtained by the generalized least square method.
This paper is related to the identification of pharmacokinetic parameters of a four-compartment open model with first order absorption from plasma level data. The eigenvalues of the characteristic matrix of the given system are obtained by transforming them into a single variable and the solution involves the minimization of the sum of squares of deviation of the model-predicted values of the state variables from an experimentally obtained values. The distribution volume and the lag time are also identified. Finally, the unicity of the absorption rate constant is obtained by the minimum energy principle. The results obtained with present method are compared with those obtained by the generalized least squares method.
We first present a linear compartmental model describing human basophiol degranulation by means of an antigen concentration. Then we study an optimal control problem associated to this linear compartmental model in presence of high dilutions. For solving this control problem we used the LAPLACE transform.
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.