My research activities synergistically combine my expertise in engineering, mathematics and ophthalmology to study fluid flows in deformable domains and their application in life sciences and engineering. This includes fluid-structure interaction, such as the interaction between blood flow and vessel walls in the cardiovascular system, and flows through poro-visco-elastic media, such as fluid flows through tissues. Some ongoing research projects are described below.

Mathematical and computational properties of partial and ordinary differential equations arising in fluid-structure interaction and poro-visco-elasticity problems

This project focuses on the analytical and numerical investigation of system of partial and ordinary differential equations describing the interaction between the flow of a viscous fluid and the motion of a deformable structure. The mixed hyperbolic-parabolic nature of the system guides the design of efficient numerical methods for the approximate solution of this type of problems. Existence, uniqueness and continuous dependence on data are studied from the theoretical viewpoint, while assessing their impact on real-world applications.

For example, our recent theoretical study on poro-elatic and poro-visco-elastic models (Bociu et al (2016) Archives for Rational Mechanics and Analysis) led to formulate a clinical hypothesis, namely: based on the results from the analysis, reduced tissue viscoelasticity may increase the susceptibility of ischemic damage when the boundary and/or volumetric sources of momentum experience sudden changes in time. The clinical assessment of this hypothesis is now under investigation for its relevance in ophthalmology.

Figure: schematic of fluid-structure interactions and poro-visco-elastic models arising in ophthalmology (Prada et al (2016) Annual Meeting of ARVO).

This research has been supported by the National Science Foundation.

Fluid-dynamics, hemodynamics, biomechanics and metabolism in the eye:
mathematical modeling and clinical applications

This project focuses on the mathematical and computational modeling of various aspects of ocular biophysics, including blood flow, blood flow regulation, oxygen transport and delivery, flow of aqueous humor and tissue deformations induced by intraocular pressure (IOP) and cerebrospinal fluid pressure (CSFp). The goal of this project is to provide quantitative assessments of interplaying mechanisms in health and disease, thereby aiding the interpretation of clinical data, the formulation of new hypotheses on disease pathophysiology and, ultimately, the design of new management and therapeutic strategies.

We recently utilized this interdisciplinary approach in a pilot study to show that the clinically observed increase in retinal venous oxygen saturation can be explained by decreased oxygen demand in high-pressure glaucoma patients, but not in low-tension glaucoma patients. Further, biophysical modeling was used to investigate the complex interaction between blood pressure, IOP and perfusion pressure in health and disease and to quantify how vascular regulation and venous collapsibility influence this relationship. These differential results could not be achieved by simple statistical analysis, and the complexity of glaucoma risk factors likely masks many synergies of risk that modeling can identify. Therefore modeling of clinical and demographic risk factors holds great promise for improved diagnostic and tailored individualized treatment target identification.

Figure: schematic of blood flow in the ocular posterior segment (Gross et al (2016) Expert Reviews in Ophthalmology).

This research has been supported by the National Science Foundation, the Office of Vice President for Research at Indiana University, the Cercle Gutenberg of the Region Alsace (France), the Labex IRMIA of the University of Strasbourg (France) and the French Embassy in the United States.

Eye2Brain: Multiscale modeling of fluid-dynamical and metabolic connections between eye and brain

Thanks to its special connection to the brain and its accessibility to measurements, the eye provides a unique window on the brain, thereby offering non-invasive access to a large set of potential biomarkers that might help in the early diagnosis and clinical care of Neuro Degenerative Diseases (NDD). However, characterizing ocular biomarkers as surrogates of cerebral or systemic vascular status is far from trivial. Clinical measurements are influenced by many factors that vary among individuals and cannot be isolated in vivo, thereby posing serious challenges for the interpretation of such measurements.
Figure: simulation of blood flow in the cerebral veins (Chabannes et al (2015) Journal of Coupled Systems and Multiscale Dynamics).
This difficult, yet extremely appealing, opportunity of using the eye as a window on the brain provides the main rationale of our contribution to the project, which, more specifically, stems from the basic ideas that: (i) an ocular measurement per se does not allow to draw any conclusion on what might be the fluid-dynamical and/or metabolic status of the brain in a given patient, unless some other factors specific to that patient are properly taken into account; (ii) mathematical modeling can provide quantitative tools to help accounting for patient-specific factors when interpreting potential ocular biomarkers. We are motivated by the need of mathematical and computational methods to study the Eye Brain system (we call it Eye2Brain) and aid the interpretation of ocular measurements as biomarkers for the brain status. We currently are developing a reliable and efficient computational framework of the Eye2Brain system allowing for computer-aided interpretations of the clinical data. To this end, mathematical models parametrized with patient-specific data are required to quantitatively describe the fluid-dynamical and metabolic connections between the eye and the brain and to identify the main factors that influence these connections. The complexity of this Eye2Brain system calls for a multiscale modeling approach. Network based models allow to capture the main dynamics of complex systems at relatively low computational costs, whereas detailed 3d models allow to interface with clinical data that are 3d in nature, e.g. MRI maps and FD-OCT images.

This research has been supported by the National Science Foundation, the Office of Vice President for Research at Indiana University, the Cercle Gutenberg of the Region Alsace (France), the Labex IRMIA of the University of Strasbourg (France) and the French Embassy in the United States.

Graduate Students:
Daniele Prada, IUPUI, USA
Lorenzo Sala, IRMA, Strasbourg (France)

Former Graduate Students:
Lucia Carichino, currently Post-Doctoral Scholar at Worchester Polytechnic Institute, MA, USA
Simone Cassani, currently Post-Doctoral Scholar at Worchester Polytechnic Institute, MA, USA

Current Address: Department of Mathematical Sciences, 402 N. Blackford St., LD270 | Indianapolis, IN 46202-3267
Phone: (317) 274-6936 - Fax: (317) 274-3460