Mathematical models predicting dynamical profiles are of interest for the clinicians because the shape of such variables are of diagnostic significance and their anomalies can be used to detect pathological states in vascular system.  A correct modelling and simulation of the wave propagation in vascular system is one of the primary objectives of this research.
Another key feature is local effect of the microcorrugations of the wall, due to the endothelial cells, that induces fluctuations of the wall shear stress. Furthermore, the endothelium is covered by a thin ciliate layer, called glycocalyx. Recent work has revealed a correlation between the flow-induced mechano-transduction, the stress-induced ATP release at the endothelium and its role in the atherosclerosis development.
Also, we model the red blood cells as immiscible droplets.  In particular, within a two-component fluid framework, red blood cells are fluid-filled vesicles enclosed by a deformable membrane subjected to interfacial tension, specified interface compressibility and bending rigidity. All these meso-microscopic aspects of blood flow are investigated  by means of a coarse-grained fluid model based on a lattice Boltzmann method.

This research is focused on:

- Stress-induced ATP-ADP release in microvessels
- Blood flow over a corrugated endothelium.
- Glycocalyx modelling.
- Red blood cells dynamics in a bi-component fluid flow.
- Lattice-Boltzmann methods for meso-microscopic hemodynamics and multiscale simulations.

Links to related international institution research projects:
Material and Engineering Resarch Institute, Sheffield Hallam University, UK

- Cardiovascular and Cellular Engineering Laboratory at Ecole Polytechnique, France


Mass transfer and diffusion processes of a therapeutic agent (typically a drug)  from a release device into a biological tissue is investigated.  We develop two-phase mathematical models to describe the dynamics of a substance between two or multi-layer porous coupled media of different properties and extents.
Local mass non-equilibrium and reversible binding-unbinding processes are addressed. Predictions of concentration profiles and of drug masses are useful  to estimate the transport parameters for an efficient  drug delivery and for an optimal design of  medical devices, such as drug-eluting stents, microcapsules or transdermal patches.

Applications to:

- Drug-eluting stents
- Transdermal drug delivery and transdermal patches
- Therapeutical lenses
- Drug release from microcapsules and liposomes
- Pharmacokinetics

Links to related international institution research projects:
Dept. of Biomedical Engineering, University of Glasgow, UK

Dept. of  Applied Mathematics, National University  Ireland, Galway


We investigate the phase separation (Cahn-Hilliard equation) in a  tube with and possible arrested coalescence when the typical size of the phase domains reaches the value of the diameter of the tube. The arrested state consists of an alternating sequence of  cylindrical domains, called “plugs”.
We also develop mathematical models describing the storage and dissolution of drug-polymer solid dispersions. The two-phase interaction  is modelled using Flory-Huggins theory  to identify regimes in the model parameter space that lead to stable, metastable and unstable storage behaviour.

(last update: july 2020)