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:
- Cardiovascular and Cellular Engineering Laboratory at Ecole Polytechnique, France

MASS TRANSPORT AND DRUG DELIVERY PROCESSES IN BIOLOGICAL TISSUES

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 develop a mathematical model for describing the dissolution process of irregularly-shaped particles that can undergo solubility reduction due to phase transition induced by dissolution. The ensuing recrystallization process is also considered.
The main feature of the model consists in its simplicity as, whatever the particular solid surface morphology, only two coupled nonlinear ordinary differential equations are needed to describe the dissolution process. A model advantage lies on the possibility of determining its parameters by means of common independent techniques thus enabling the evaluation of the importance of solid wettability on the dissolution process. Several simulations are carried out over a variety of irregularly-shaped bodies to show the influence of roundness on the dissolution kinetics.