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We present our continuous efforts from a modeling and numerical viewpoint to develop a powerful and flexible mathematical and computational framework called Ocular Mathematical Virtual Simulator (OMVS). The OMVS aims to solve problems arising in biomechanics and hemodynamics within the human eye. We discuss our contribution towards improving the reliability and reproducibility of computational studies by performing a thorough validation of the numerical predictions against experimental data. The OMVS proved capable of simulating complex multiphysics and multiscale scenarios motivated by the study of glaucoma. Furthermore, its modular design allows the continuous integration of new models and methods as the research moves forward, and supports the utilization of the OMVS as a promising non‐invasive clinical investigation tool for personalized research in ophthalmology. [ABSTRACT FROM AUTHOR]

In this paper, we address the study of elliptic boundary value problems in presence of a boundary condition of integral type (IBC) where the potential is an unknown constant and the flux (the integral of the flux density) over a portion of the boundary is given by a value or a coupling condition. We first motivate our work with realistic examples from nano-electronics, high field magnets and ophthalmology. We then define a general framework stemming from the Hybridizable Discontinuous Galerkin method that accounts naturally for the IBC and we provide a complete analysis at continuous and discrete levels. The implementation in the Feel++framework is then detailed and the convergence and scalability properties are verified. Finally, numerical experiments performed on the real-life motivating applications are used to illustrate our methodology. [ABSTRACT FROM AUTHOR]

Altitude affects intraocular pressure (IOP); however, the underlying mechanisms involved and its relationship with ocular hemodynamics remain unknown. Herein, a validated mathematical modeling approach was used for a physiology-enhanced (pe-) analysis of the Mont Blanc study (MBS), estimating the effects of altitude on IOP, blood pressure (BP), and retinal hemodynamics. In the MBS, IOP and BP were measured in 33 healthy volunteers at 77 and 3466 m above sea level. Pe-retinal hemodynamics analysis predicted a statistically significant increase (p < 0.001) in the model predicted blood flow and pressure within the retinal vasculature following increases in systemic BP with altitude measured in the MBS. Decreased IOP with altitude led to a non-monotonic behavior of the model predicted retinal vascular resistances, with significant decreases in the resistance of the central retinal artery (p < 0.001) and retinal venules (p = 0.003) and a non-significant increase in the resistance in the central retinal vein (p = 0.253). Pe-aqueous humor analysis showed that a decrease in osmotic pressure difference (OPD) may underlie the difference in IOP measured at different altitudes in the MBS. Our analysis suggests that venules bear the significant portion of the IOP pressure load within the ocular vasculature, and that OPD plays an important role in regulating IOP with changes in altitude. [ABSTRACT FROM AUTHOR]

Neurodegenerative disorders (NDD) such as Alzheimer's and Parkinson's diseases are significant causes of morbidity and mortality worldwide. The pathophysiology of NDD is still debated, and there is an urgent need to understand the mechanisms behind the onset and progression of these heterogenous diseases. The eye represents a unique window to the brain that can be easily assessed via non-invasive ocular imaging. As such, ocular measurements have been recently considered as potential sources of biomarkers for the early detection and management of NDD. However, the current use of ocular biomarkers in the clinical management of NDD patients is particularly challenging. Specifically, many ocular biomarkers are influenced by local and systemic factors that exhibit significant variation among individuals. In addition, there is a lack of methodology available for interpreting the outcomes of ocular examinations in NDD. Recently, mathematical modeling has emerged as an important tool capable of shedding light on the pathophysiology of multifactorial diseases and enhancing analysis and interpretation of clinical results. In this article, we review and discuss the clinical evidence of the relationship between NDD in the brain and in the eye and explore the potential use of mathematical modeling to facilitate NDD diagnosis and management based upon ocular biomarkers. [ABSTRACT FROM AUTHOR]

Objective: To develop quantitative methods for the clinical interpretation of the ballistocardiogram (BCG). Methods: A closed-loop mathematical model of the cardiovascular system is proposed to theoretically simulate the mechanisms generating the BCG signal, which is then compared with the signal acquired via accelerometry on a suspended bed. Results: Simulated arterial pressure waveforms and ventricular functions are in good qualitative and quantitative agreement with those reported in the clinical literature. Simulated BCG signals exhibit the typical I, J, K, L, M, and N peaks and show good qualitative and quantitative agreement with experimental measurements. Simulated BCG signals associated with reduced contractility and increased stiffness of the left ventricle exhibit different changes that are characteristic of the specific pathological condition. Conclusion: The proposed closed-loop model captures the predominant features of BCG signals and can predict pathological changes on the basis of fundamental mechanisms in cardiovascular physiology. Significance: This paper provides a quantitative framework for the clinical interpretation of BCG signals and the optimization of BCG sensing devices. The present paper considers an average human body and can potentially be extended to include variability among individuals. [ABSTRACT FROM AUTHOR]

This work aims at investigating the interactions between the flow of fluids in the eyes and the brain and their potential implications in structural and functional changes in the eyes of astronauts, a condition also known as spaceflight associated neuro-ocular syndrome (SANS). To this end, we propose a reduced (0-dimensional) mathematical model of fluid flow in the eyes and brain, which is embedded into a simplified whole-body circulation model. In particular, the model accounts for: (i) the flows of blood and aqueous humor in the eyes; (ii) the flows of blood, cerebrospinal fluid and interstitial fluid in the brain; and (iii) their interactions. The model is used to simulate variations in intraocular pressure, intracranial pressure and blood flow due to microgravity conditions, which are thought to be critical factors in SANS. Specifically, the model predicts that both intracranial and intraocular pressures increase in microgravity, even though their respective trends may be different. In such conditions, ocular blood flow is predicted to decrease in the choroid and ciliary body circulations, whereas retinal circulation is found to be less susceptible to microgravity-induced alterations, owing to a purely mechanical component in perfusion control associated with the venous segments. These findings indicate that the particular anatomical architecture of venous drainage in the retina may be one of the reasons why most of the SANS alterations are not observed in the retina but, rather, in other vascular beds, particularly the choroid. Thus, clinical assessment of ocular venous function may be considered as a determinant SANS factor, for which astronauts could be screened on earth and in-flight. [ABSTRACT FROM AUTHOR]

The development of a software platform incorporating all aspects, from medical imaging data, through three-dimensional reconstruction and suitable meshing, up to simulation of blood flow in patient-specific geometries, is a crucial challenge in biomedical engineering. In the present study, a fully three-dimensional blood flow simulation is carried out through a complete rigid macrovascular circuit, namely the intracranial venous network, instead of a reduced order simulation and partial vascular network. The biomechanical modeling step is carefully analyzed and leads to the description of the flow governed by the dimensionless Navier–Stokes equations for an incompressible viscous fluid. The equations are then numerically solved with a free finite element software using five meshes of a realistic geometry obtained from medical images to prove the feasibility of the pipeline. Some features of the intracranial venous circuit in the supine position such as asymmetric behavior in merging regions are discussed. [ABSTRACT FROM PUBLISHER]

We establish several linear and nonlinear inequalities of Korn's type for curves in the three-dimensional Euclidean space. These inequalities are obtained under weak regularity assumptions on the curve of reference. We also establish an infinitesimal rigid displacement lemma for curves. [ABSTRACT FROM AUTHOR]

The fundamental theorem of Riemannian geometry asserts that a connected and simply-connected Riemannian space ω of ℝp can be isometrically immersed into the Euclidean space ℝp+q if and only if there exist tensors satisfying the Gauss–Ricci–Codazzi equations, in which case these immersions are uniquely determined up to isometries in ℝp+q. In this fashion, we can define a mapping which associates with these prescribed tensors the reconstructed submanifold. The purpose of this paper is twofold: under a smoothness assumption on the boundary of ω, we first establish an analogous result for the existence and uniqueness of a submanifold "with boundary" and then show that the mapping constructed in this fashion is locally Lipschitz-continuous with respect to the topology of the Banach spaces $\mathcal{C}^l(\bar{\omega}), l\geq1$. [ABSTRACT FROM AUTHOR]

Presents a missing funding acknowledgment for Dr. Mihail Popescu in the above named paper. [ABSTRACT FROM AUTHOR]