arXiv subjects

Marcela Szopos

Publications and source records attributed to Marcela Szopos.

10 recordsLinked to original sources

arXiv2026

From flocking to jamming in collective cell dynamics: a Vicsek-like model including contact forces

The goal of the present work is to propose an agent-based model that originally combines classical Vicsek-like polarity alignments and contact forces, as implemented in the framework developed by Maury and Venel in [Maury, Venel, 2011]. The description additionally incorporates velocity feedback on polarity and soft attraction-repulsion interactions. After carefully studying the well posedness of the model, we introduce a suitable discretization and perform an extensive range of numerical experiments to assess the impact of different modeling ingredients. The dynamical system is capable of recovering the order-disorder phase transition of the flock, as well as the jamming effect in high density regimes. As such, the developed framework can be seen as a promising theoretical tool that could contribute to improving the understanding of complex collective cell dynamics and emerging tissue flows.

math.NA↗

arXiv2026

Mathematical modeling and simulation of coupled aqueous humor flow and temperature distribution in a realistic 3D human eye geometry

We present a comprehensive computational model to simulate the coupled dynamics of aqueous humor flow and heat transfer in the human eye. To manage the complexity of the model, we make significant efforts in meshing and efficient solution of the discrete problem using high-performance resources. The model accurately describes the dynamics of the aqueous humor in the anterior and posterior chambers and accounts for convective effects due to temperature variations. Results for fluid velocity, pressure, and temperature distribution are in good agreement with existing numerical results in the literature. Furthermore, the effects of postural changes and wall shear stress behavior are analyzed, providing new insights into the mechanical forces acting on ocular tissues. Overall, the present contribution provides a detailed three-dimensional simulation that enhances the understanding of ocular physiology and may contribute to further progress in clinical research and treatment optimization in ophthalmology.

math.AP↗

arXiv2025

Eye2Heart : a validated lumped-parameter model bridging cardiovascular and ocular dynamics

The cardiovascular and ocular systems are intricately connected, with hemodynamic interactions playing a crucial role in both physiological regulation and pathological conditions. However, existing models often treat these systems separately, limiting the understanding of their interdependence. In this study, we present the Eye2Heart model, a novel closed-loop mathematical framework that integrates cardiovascular and ocular dynamics. Using an electricalhydraulic analogy, the model describes the interactions between the heart and retinal circulation through a system of ordinary differential equations. The model is validated against clinical and experimental data, demonstrating its ability to reproduce key cardiovascular parameters (e.g., stroke volume, cardiac output) and ocular hemodynamics (e.g., retinal blood flow). Additionally, we explore in silico the effects of intraocular pressure (IOP) and left ventricular compliance on both local ocular and global systemic circulation, revealing critical dependencies between cardiovascular and ocular health. The results highlight the model's potential for studying cardiovascular diseases with ocular manifestations, paving the way for patient-specific data integration and expanding applications in personalized medicine.

physics.med-ph↗

arXiv2024

Model order reduction and sensitivity analysis for complex heat transfer simulations inside the human eyeball

Heat transfer in the human eyeball, a complex organ, is significantly influenced by various pathophysiological and external parameters. Particularly, heat transfer critically affects fluid behavior within the eye and ocular drug delivery processes. Overcoming the challenges of experimental analysis, this study introduces a comprehensive three-dimensional mathematical and computational model to simulate the heat transfer in a realistic geometry. Our work includes an extensive sensitivity analysis to address uncertainties and delineate the impact of different variables on heat distribution in ocular tissues. To manage the model's complexity, we employed a very fast model reduction technique with certified sharp error bounds, ensuring computational efficiency without compromising accuracy. Our results demonstrate remarkable consistency with experimental observations and align closely with existing numerical findings in the literature. Crucially, our findings underscore the significant role of blood flowand environmental conditions, particularly in the eye's internal tissues. Clinically, this model offers a promising tool for examining the temperature-related effects of various therapeutic interventions on the eye. Such insights are invaluable for optimizing treatment strategies in ophthalmology.

math.AP↗

arXiv2024

A coupled fluid-dynamics-heat transfer model for 3D simulations of the aqueous humor flow in the human eye

Understanding human eye behavior involves intricate interactions between physical phenomena such as heat transfer and fluid dynamics. Accurate computational models are vital for comprehending ocular diseases and therapeutic interventions.This work focuses on modeling and simulating aqueous humor flow in the anterior and posterior chambers of the eye, coupled with overall heat transfer.Aqueous humor dynamics regulates intraocular pressure, crucial for understanding conditions like glaucoma.Convective effects from temperature disparities also influence this flow.Extending prior research, this work develops a comprehensive three-dimensional computational model to simulate coupled fluid-dynamic-heat transfer model, thus contributing to the understanding of ocular physiology.

math.AP↗

arXiv2021

Uncertainty propagation and sensitivity analysis: results from the Ocular Mathematical Virtual Simulator

We propose an uncertainty propagation study and a sensitivity analysis with the Ocular Mathematical Virtual Simulator, a computational and mathematical model that predicts the hemodynamics and biomechanics within the human eye. In this contribution, we focus on the effect of intraocular pressure, retrolaminar tissue pressure and systemic blood pressure on the ocular posterior tissue vasculature. The combination of a physically-based model with experiments-based stochastic input allows us to gain a better understanding of the physiological system, accounting both for the driving mechanisms and the data variability.

math.NA↗

arXiv2019

Cardiovascular function and ballistocardiogram: a relationship interpreted via mathematical modeling

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 work provides a quantitative framework for the clinical interpretation of BCG signals and the optimization of BCG sensing devices. The present study considers an average human body and can potentially be extended to include variability among individuals.

physics.med-ph↗

arXiv2018

Energy-based operator splitting approach for the time discretization of coupled systems of partial and ordinary differential equations for fluid flows: The Stokes case

The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The proposed algorithm is based on a semi-discretization in time based on operator splitting, whose design is guided by the rationale of ensuring that the physical energy balance is maintained at the discrete level. As a result, unconditional stability with respect to the time step choice is ensured by the implicit treatment of interface conditions within the Stokes substeps, whereas the coupling between Stokes and ODE substeps is enforced via appropriate initial conditions for each substep. Notably, unconditional stability is attained without the need of subiterating between Stokes and ODE substeps. Stability and convergence properties of the proposed algorithm are tested on three specific examples for which analytical solutions are derived.

math.NA↗

arXiv2017

High order finite element simulations for fluid dynamics validated by experimental data from the fda benchmark nozzle model

The objective of the present work is to construct a sound mathematical, numerical and computational framework relevant to blood flow simulations and to assess it through a careful validation against experimental data. We perform simulations of a benchmark proposed by the FDA for fluid flow in an idealized medical device, under different flow regimes. The results are evaluated using metrics proposed in the literature and the findings are in very good agreement with the validation experiment.

math.AP↗

arXiv2010

On discretization in time in simulations of particulate flows

We propose a time discretization scheme for a class of ordinary differential equations arising in simulations of fluid/particle flows. The scheme is intended to work robustly in the lubrication regime when the distance between two particles immersed in the fluid or between a particle and the wall tends to zero. The idea consists in introducing a small threshold for the particle-wall distance below which the real trajectory of the particle is replaced by an approximated one where the distance is kept equal to the threshold value. The error of this approximation is estimated both theoretically and by numerical experiments. Our time marching scheme can be easily incorporated into a full simulation method where the velocity of the fluid is obtained by a numerical solution to Stokes or Navier-Stokes equations. We also provide a derivation of the asymptotic expansion for the lubrication force (used in our numerical experiments) acting on a disk immersed in a Newtonian fluid and approaching the wall. The method of this derivation is new and can be easily adapted to other cases.

math.NA↗