Integrated Multidisciplinary Approaches in the Study and Care of the Human Eye

The human eye offers the extraordinary possibility to visualize and monitor non-invasively, in vivo, in humans, many morphological and haemodynamical features. Therefore, a large amount of data on ocular structures and macro- and micro-circulation can be obtained in a clinical setting during a patient’s visit. However, the interpretation of these data remains a very challenging task, since the understanding of the physiology, bio-mechanics and fluid-dynamics of the human eye remains scarce. This unmet gap between the availability of imaging data and their elusive clinical interpretation hinders the advancement of therapeutic strategies and clinical management for many ocular diseases, including glaucoma, diabetic retinopathy and age-related macula degeneration. Mathematical models can aid the interpretation of clinical data by providing quantitative representations of the bio-mechanics and fluid-dynamics of the eye and their relationship with systemic conditions. Acting as a virtual lab, mathematical models can simulate the independent contributions of structural, vascular, metabolic, and systemic factors to the pathophysiology of ocular diseases, allowing for a low-cost and low time-consuming analysis of this multimodal complex system. Even though ocular mechanics has received considerable attention over the last decade, the development of mathematical models capable of unraveling the interplay between ocular mechanics, haemodynamics and metabolism is still at its early stages. This is due to the fact that the mechanic/haemodynamic/metabolic coupling is a very arduous, and very much needed, scientific endeavor, which requires sophisticated mathematical techniques, including multi-scale analysis, dynamics of coupled systems, and partial differential equations of mixed type, which are still open areas of research in mathematics. This workshop has brought together in a fertile environment clinicians, engineers and applied mathematicians to promote the communication and cross-fertilization among these different disciplines and shape a new paradigm of scientific approach for the study of ocular diseases, based on the integration of clinical data and mathematical modeling predictions. The response of the scientific and medical community has been prompt and passionate. The spectrum of the talks has been wide and complementary, as it has included topics from the etiology and management of ocular diseases, nanotechnology for artificial retinas, and mathematics of blood flow and deformable structures. We envision a great future for integrated multidisciplinary approaches in the study and care of the human eye and we thank all the scientists and the sponsors who enthusiastically joined this ground-breaking adventure.

P. Causin, G. Guidoboni, A. Harris and R. Sacco

Foreword

Clinical Experience and Mathematical Modeling in
Eye Surgery

Introduction
Giovanna Guidoboni and Alon Harris
1 Mathematical Modeling in Eye Surgery
Rodolfo Repetto, Jennifer H. Siggers and Julia Meskauskas
2. Fluid Mechanics of the Vitreous Chamber
Rodolfo Repetto, Jennifer H. Siggers and Julia Meskauskas
3. Effect of Trabeculectomy on Retinal Hemodynamics: Mathematical Modeling of Clinical Data
Simone Cassani, Giovanna Guidoboni, Ingrida Januleviciene, Lucia Carichino, Brent A. Siesky, Leslie A. Tobe, Annahita Amireskandari, Daiva-Paulaviciute Baikstiene and Alon Harris

Clinical Experience and Mathematical Modeling in Ocular Haemodynamics

Introduction
Giovanna Guidoboni and Alon Harris
4. Modeling Blood Flow Autoregulation in the Retina
Julia Arciero
5. Effect Of Intraocular Pressure and Cerebrospinal Fluid Pressure on the Blood Flow in the Central Retinal Vessels
Lucia Carichino, Giovanna Guidoboni, Brent A. Siesky, Annahita Amireskandari, Ingrida Januleviciene and Alon Harris
6. Open-Angle Glaucoma and Blood Flow
Joshua Park, Annahita Amireskandari, Giovanna Guidoboni, Brent A. Siesky and Alon Harris

Diagnostic Techniques and Management of Ocular Diseases

Introduction
Alon Harris
7. Social and Economic Burden of Retinopathies
Costantino Bianchi
8. Statistical Methods for the Analysis of Stochastic Fiber Processes
Alessandra Micheletti and Vincenzo Capasso
9. Glaucoma Disease: Pathophysiology, Risks Factors and Clinical Perspectives
Noa Geffen

Emerging Techniques in Artificial Vision

Introduction
Alon Harris and Riccardo Sacco
10. Emerging Technologies in Retinal Prosthetics
Maria R. Antognazza, Matteo Porro, Diego Ghezzi, Fabio Benfenati and Guglielmo Lanzani

Multiscale Mathematical Modeling of Biological Tissues

Introduction
Paola Causin
11. Poro-Elastic Modeling for Biological Tissues and Human Eye: Recent Advances and Future Perspectives
Raimondo Penta and Davide Ambrosi
12. Mathematical Modeling of Retinal Microcirculation and Oxygen Delivery
Paola Causin, Giovanna Guidoboni, Francesca Malgaroli, Riccardo Sacco and Alon Harris
13. A Computational Model for the Retinal Vascular Network: The Dynamics of the Endothelial Tip Cell Filopodia
Giacomo Aletti and Giovanni Naldi