Mixing neural networks, continuation and symbolic computation to solve parametric systems of non linear equations.

We consider a square non linear parametric equations system F(P,X) = 0 which is constituted of n non differential equations in the n unknowns {x1,…,xn} that are the components of X while P={p1,…,pm} is a set of m parameters that play a role in the definition of the equations F. We assume that P is restricted to lie in a bounded region and we are interested in developing a solver for obtaining all real solutions exactly (a notion that is defined in the paper) for any parameter values within the bounded region. The starting point of the proposed approach is that we assume that a numerical methods has allowed us to determine the real solutions (but not necessarily all of them) for a very limited number of fixed P called the initial solution set. Starting from this set we show that we can create multiple pairs (parameters, solution) and that these pairs may be structured into coherent learning sets that will be used to train multi-layer perceptrons (MLP). The training process is specific: although it still uses a decrease of a loss function its main objective is to maximize the success rate i.e. the number of occurrences, expressed in percentage of number of samples of the training set, for which the Newton scheme, initialized with the MLP prediction, converges toward the expected solution. We then show that for a sufficiently large number of MLPs we may obtain a 100% success rate for all learning sets. The solver is obtained by running a set of local solvers each of which is based on a specific MLP whose prediction may lead to an exact solution of the system. This solver is tested on verification sets i.e. set of samples constituted of parameter values (all different from the samples in the learning set) and all the solutions of the corresponding system. We show that these sets may be automatically generated and that they may also be used in a self-learning process for improving the performance of the solver established from the initial solution set. This approach is illustrated on two engineering problems in robotics and chemistry and it is shown that the solver provides all solutions for any instance of P with a high probability although we cannot guarantee it. The time required to design the final solver is large but the solving time is extremely low so that this approach should be used when the system has to be solved for a sufficient number of occurrences of the P. Furthermore we will show that the computation time required for establishing the solver may be drastically reduced by using a distributed implementation.

[Pharmacokinetic and clinical evaluation of rectal hydrophilic gel of methohexital in pediatric surgery]. / Evaluation pharmacocinétique et clinique d'un gel rectal hydrophile de méthohexital en chirurgie pédiatrique.

The purpose of the study was to develop and to test a new form of rectal systemic gel for methohexitone administration in children undergoing minor surgery. Pharmacokinetics of methohexitone were determined in children following intravenous or intrarectal administration either at low or therapeutic dosage. Anaesthesic efficacy of this gel was performed in 11 patients receiving a therapeutic dosage (25 mg/kg). Pharmacokinetics of methohexitone appears independent of both dosage and route of administration in children. The bioavailability of the rectal gel appears sufficient to provide efficient clinical plasmatic concentrations. As a consequence of the rapid and good resorption of methohexitone from rectal lumen and of the low variability of plasmatic concentrations, a rapid and reliable sedation was observed in all patients. The clinical anaesthesic efficacy of the rectal hydrophilic gel associated with the absence of an apparent local intolerance and important side effects, make this new form suitable for methohexitone administration in children.

[Isolation of tubular proximal cells of the human kidney by affinity chromatography using Lotus tetragonolobus lectin]. / Isolement de cellules tubulaires proximales de reins humains par chromatographie d'affinité grâce à la lectine de Lotus tetragonolobus.

An affinity chromatography technique, using a lectin issued from Lotus tetragonolobus as ligand, and coupled to Sepharose 6MB support, has been chosen to enrich a cellular population in tubular proximal cells. Cell desorption was obtained with a competitive sugar, L Fucose. Intensive enzymatic brush border activity, shown in selected cells compared with initial cellular mixture, evidenced an enrichment in proximal tubular cells. These results prove that lectin use as ligand in affinity chromatography permits the separation of renal cell populations and presents the advantage that the bound cells can be recovered by a gentle competitive elution for further cultures.

[Morphologic and enzymatic characteristics of healthy human kidney epithelial tubular cells in culture]. / Caractéristiques morphologiques et enzymatiques de cellules épithéliales tubulaires de rein humain sain en culture.

The present study defines morphological and enzymatic characteristics of human healthy renal tubular cells in primary culture, and during three passages. The results confirm the ability to culture human renal tubular cells and to quantitatively evaluate the activity of specific tubular enzymes in the cells and in the culture medium. Such determinations can be compared to similar enzyme activity research in renal biopsies or in urines, to investigate human renal cell functions, in clinical, pharmacological or toxicological approaches.

[Effect of cisplatin on healthy human renal tubular cells and cancerous cells in culture]. / Effet du cis-platine sur des cellules tubulaires rénales humaines saines et cancéreuses en culture.

An in vitro comparative cis-platin cytotoxicity was evidenced in human renal normal and tumoral cultured cells. Cytotoxic effect was estimated at membrane level by intracellular enzymatic markers release into culture medium and nuclear level by ADN synthesis inhibition after 3H thymidine incorporation. These results show a more intensive activity of cis-platin in normal tubular cells than in tumoral ones.

An in vitro test for measuring cytotoxicity of mercuric chloride to human kidney epithelial cells by specific enzyme release.

Mercuric compound toxicity is well documented in animals and man for practically all organs. The recent development of cell culture techniques appeared as a novel fruitful tool in toxicology, especially in renal toxicology. Heavy metal induced renal cell alterations can be evaluated by membrane permeability damages.The present study evaluates mercuric chloride nephrotoxic effect in human kidney epithelial cells by measuring the release of two specific nephrotoxicity marker enzymes, Gamma Glutamyl Transferase (GGT) and Alkaline Phosphatase (ALP) in the culture medium. Cultured kidney epithelial cells were exposed to different HgCl(2) concentrations (5, 10, 20, and 50 µg). Cultures were examined after 6 and 24 hours exposure. A good correlation between mercury dose and toxic effect, and exposure time and toxic effect was found. Enzymes were significantly released into the culture medium for 5 µg and 10 µg HgCl(2)/ml after 6 hours exposure; and after 24 hours exposure, enzymes were released for 5 µg/ml only.It appears that the specific tubular enzyme release in the culture medium is a good in vitro test for quantification of specific tubular damage.