APPLICATION OF APPROXIMATE BAYESIAN COMPUTATION FOR THE ESTIMATION OF PARAMETERS IN A MODEL FOR THE CALCIUM DYNAMICS IN NEURONS

Ionic transfer plays an important role in several processes in the human body, in special in the electrophysiology of neurons, where the most important ions are those of potassium, sodium and calcium. The models for the dynamics of potassium and sodium are classical and well established in the literature. On the other hand, several models were proposed for the dynamics of calcium ions, such as those of Dupont and Erneux , 1997and of Dupont and Goldbetter ,1993. In fact, none of the proposed models for calcium dynamics is widely accepted and general to represent phenomena characteristic of anomalous behaviors observed in neurons, related, for example, to epilepsy. Due to the nonlinear character of these models, the values of their parameters strongly affect the predicted responses, like the transient ion concentrations, as well as the dynamics of several state variables, including the electrical current responses in voltage clamp experiments. Approximate Bayesian Computation (ABC) methods have been conceived for inferring posterior distributions where likelihood functions are computationally intractable, too costly to evaluate or not exactly known. In this work, we apply an ABC algorithm based on the Monte Carlo method (Toni et al., 2009) for the estimation of parameters appearing in the Calcium model proposed by Dupont and Goldbetter, 1993. Simulated measurements of the concentration of calcium ions in the cytosol are used for the parameter estimation

The reciprocity function approach applied to the non-intrusive estimation of spatially varying internal heat transfer coefficients in ducts: Numerical and experimental results

This paper presents a methodology to estimate internal convective heat transfer coefficients in ducts, using only data available at an exterior boundary. The methodology is based on the reciprocity function approach, which does not require any intrusive measurements and it needs low computational resources because it avoids the use of iterative techniques. The unknown function can be estimated by solving a linear system, where the solution vector is composed of integrals of the boundary data. Numerical results are presented, where the stability of the method is tested against different functions, with high levels of noise. In the final part of the paper, for a real test case, using measurements taken by an infrared camera, the method is analyzed and compared with a traditional technique, showing very good results. The estimate can be performed in less than 3 s, using an inexpensive Raspberry Pi computer (less than US$28), equipped with a Broadcom BCM2835 system on a chip (SoC) processor