Blood flowing in a vessel is modelled using one-dimensional equations derived from the Navier-Stokes theory on the base of long pressure wavelength.The vessel wall is modelled as an initially highly prestressed elastic membrane, which slightly deforms under the blood pressure pulses. On the stressed configuration, the vessel wall undergoes, even in larger arteries, small deformation and its motion is linearized around such initial prestressed state. The mechanical fluid-wall interaction is expressed by a set of four partial differential equations. To account for a global circulation features, the distributed model is coupled with a six compartments lumped parameter model which provide the proper boundary conditions by reproducing the correct waveforms entering into the vessel and avoid unphysical reflections. The solution has been computed numerically: the space derivatives are discretized by a finite difference method on a staggered grid and a Runge-Kutta scheme is used to advance the solution in time. Numerical experiments show the role of the initial stresses in the flow dynamics and the wall deformation.

We present the numerical results of simulations of complex fluids under shear flow. We employ a mixed approach which combines the lattice Boltzmann method for solving the Navier-Stokes equation and a finite difference scheme for the convection-diffusion equation. The evolution in time of shear banding phenomenon is studied. This is allowed by the presented numerical model which takes into account the evolution of local structures and their effect on fluid flow.

A contrast enhanced dynamic Magnetic Resonance clinical exam produces a set of images displaying over time the concentration of a contrast agent in the blood stream of an organ. The portion of tissue represented by each pixel can be classified as normal, benign or malignant tumoral, according to the qualitative behavior of the contrast agent uptake associated to it. These responses can be considered as the noisy output of a pharmacokinetic distributed model whose parameters have an intrinsic diagnostic importance. Fundamental MR imaging characteristics force a compromise between the noise level and the spatial and temporal resolution of the dynamic sequence. This makes the identification of the pharmacokinetic parameters and the classification problem difficult especially if short computation time is required by physicians. In this paper, a fast method is proposed to solve simultaneously the parameter identification and the classification problems. The complexity of the algorithm is $O(N\cdot n_p)$ flops where $N$ is the number of pixels and $n_p$ is the number of pharmacokinetic parameters per pixel. A family of functions for the parameters and the classification labels is defined. Each function is the weighted sum, with unknown weights, of a coherence-to-data term, several terms which enforce a roughness penalty on the model parameters, a term measuring the distance between the parameters in each pixel and the expected parameters for each class and a term which enforces a roughness penalty on the classification labels. A constrained optimization problem is solved to choose a member of the family, i.e. to estimate the unknown weights, and to minimize it in order to jointly estimate the parameters and the classification labels. A tuning procedure have been also devised, which makes the algorithm fully automated. The performances of the method are illustrated on real data sets.

This paper deals with the numerical solution of optimal control problems for ODEs. The approach is based on the coupling between quadrature rules and continuous Runge-Kutta solvers and it lies in the framework of direct optimization methods and recursive discretization techniques. The analysis of discrete solution accuracy has been carried out and coupling criteria are established in order to have global methods featured by a given accuracy order. Consequently numerical schemes are built up to high orders. The effectiveness of the proposed schemes has been validated on several test problems arising in the field of economic applications. Results have been compared with the ones by classical Runge-Kutta methods, in terms of single function evaluations and average cpu time of the optimization process. The search for optimal solutions has been performed by standard algorithms in Matlab environment.