arXiv subjects

Giovanna Guidoboni

Publications and source records attributed to Giovanna Guidoboni.

9 recordsLinked to original sources

arXiv2026

Stresses and fluid flow in lamina cribrosa through anisotropic poroelasticty

To investigate the mechanical correlations between intraocular pressure (IOP) variations and glaucoma, this study presents a linear transversely isotropic poroelastic model of the lamina cribrosa (LC) based on Reissner-Mindlin plate theory. A key feature of the proposed framework is its analytical tractability, which allows the governing poroelastic equations to be solved in closed form under appropriate mechanical and hydraulic boundary conditions. Within this setting, linearity is used to capture the reversible component of the tissue response, providing a baseline description of the coupled solid-fluid feedback on which more complex time-dependent phenomena, such as viscoelastic effects and remodelling, may build.The results indicate that both strain and stress measures (in the form of shear strain and deviatoric stress measures) peak in the peripheral region of the LC, which is currently suspected to be the initial site of glaucomatous damage. These quantities increase with IOP, suggesting a pressure-dependent mechanical insult to the retinal ganglion cell (RGC) axons. In parallel, the model predicts a monotonic reduction in fluid content as IOP rises, which may contribute to ischemic phenomena and disc haemorrhages. The influence of material anisotropy was also examined, revealing that isotropic assumptions tend to overestimate the fluid content while underestimating shear strain. Given the current experimental challenges in measuring blood flow within the LC, the proposed model provides a valuable framework for exploring the coupled mechanical-hemodynamic behavior of the tissue and for inverse estimation of its mechanical parameters, such as the stiffness of the opening for the central retinal vessels.

physics.flu-dyn↗

arXiv2025

Tubular Curvature Filter: Pointwise Curvature Calculation for Tubular Objects in Images

Purpose: Accurate estimation of blood vessel tortuosity from medical images is an extremely important and challenging task. It is particularly relevant in the context of retinopathy of prematurity (ROP), where the staging of disease severity and consequent therapeutic approaches are heavily informed by the presence and prominence of vessel tortuosity. Existing methods based on centerline or skeleton curvature fail to capture curvature gradients across a rotating tubular structure, thereby limiting their effectiveness in the case of ROP. Methods: This paper defines local tubular curvature and presents the Tubular Curvature Filter (TCF) method, which locally calculates the acceleration of curve bundles traversing a tubular object parallel to its centerline. This is achieved by examining the directional rate of change in the eigenvectors of the Hessian matrix of a tubular intensity function in space. TCF implicitly calculates the local tubular curvature without the need to explicitly segment or extracting the centerline of the tubular object. Results: Experimental results demonstrate that TCF provides accurate estimates of local curvature at any point inside tubular structures. Results on 2D and 3D images show that TCF discerns curvature differences between the inner and outer sides of curved tubular objects, while centerline-based approaches cannot. Conclusion: Our findings highlight that TCF's ability to discern between the inner and outer sides of curved tubular objects is particularly useful in medical fields that require vasculature curvature analysis from images, especially where vascular structures often have non-uniform diameters, such as in ROP.

eess.IV↗

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↗

arXiv2021

Cubature Kalman Filter Based Training of Hybrid Differential Equation Recurrent Neural Network Physiological Dynamic Models

Modeling biological dynamical systems is challenging due to the interdependence of different system components, some of which are not fully understood. To fill existing gaps in our ability to mechanistically model physiological systems, we propose to combine neural networks with physics-based models. Specifically, we demonstrate how we can approximate missing ordinary differential equations (ODEs) coupled with known ODEs using Bayesian filtering techniques to train the model parameters and simultaneously estimate dynamic state variables. As a study case we leverage a well-understood model for blood circulation in the human retina and replace one of its core ODEs with a neural network approximation, representing the case where we have incomplete knowledge of the physiological state dynamics. Results demonstrate that state dynamics corresponding to the missing ODEs can be approximated well using a neural network trained using a recursive Bayesian filtering approach in a fashion coupled with the known state dynamic differential equations. This demonstrates that dynamics and impact of missing state variables can be captured through joint state estimation and model parameter estimation within a recursive Bayesian state estimation (RBSE) framework. Results also indicate that this RBSE approach to training the NN parameters yields better outcomes (measurement/state estimation accuracy) than training the neural network with backpropagation through time in the same setting.

cs.LG↗

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

A Stabilized Dual Mixed Hybrid Finite Element Method with Lagrange multipliers for Three-Dimensional Problems with Internal Interfaces

This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective interface. We propose a novel approach for the numerical approximation of such heterogeneous systems combining, for the first time: (1) a dual mixed hybrid (DMH) finite element method (FEM) based on the lowest order Raviart-Thomas space (RT0); (2) a Three-Field (3F) formulation; and (3) a Streamline Upwind/Petrov-Galerkin (SUPG) stabilization method. Using the abstract theory for generalized saddle-point problems and their approximation, we show that the weak formulation of the proposed method and its numerical counterpart are both uniquely solvable and that the resulting finite element scheme enjoys optimal convergence properties with respect to the discretization parameter. In addition, an efficient implementation of the proposed formulation is presented. The implementation is based on a systematic use of static condensation which reduces the method to a nonconforming finite element approach on a grid made by three-dimensional simplices. Extensive computational tests demonstrate the theoretical conclusions and indicate that the proposed DMH-RT0 FEM scheme is accurate and stable even in the presence of marked interface jump discontinuities in the solution and its associated normal flux. Results also show that in the case of strongly dominating advective terms, the proposed method with the SUPG stabilization is capable of resolving accurately steep boundary and/or interior layers without introducing spurious unphysical oscillations or excessive smearing of the solution front.

math.NA↗

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

A Theoretical Study of Aqueous Humor Secretion Based on a Continuum Model Coupling Electrochemical and Fluid-Dynamical Transmembrane Mechanisms

Intraocular pressure, resulting from the balance of aqueous humor (AH) production and drainage, is the only approved treatable risk factor in glaucoma. AH production is determined by the concurrent function of ionic pumps and aquaporins in the ciliary processes but their individual contribution is difficult to characterize experimentally. In this work, we propose a novel unified modeling and computational framework for the finite element simulation of the role of the main ionic pumps involved in AH secretion, namely, the sodium potassium pump, the calcium-sodium pump, the anion channel and the hydrogenate-sodium pump. The theoretical model is developed at the cellular scale and is based on the coupling between electrochemical and fluid-dynamical transmembrane mechanisms characterized by a novel description of the electric pressure exerted by the ions on the intrachannel fluid that includes electrochemical and osmotic corrections. Considering a realistic geometry of the ionic pumps, the proposed model is demonstrated to correctly predict their functionality as a function of (1) the permanent electric charge density over the channel pump surface; (2) the osmotic gradient coefficient; (3) the stoichiometric ratio between the ionic pump currents enforced at the inlet and outlet sections of the channel. In particular, theoretical predictions of the transepithelial membrane potential for each simulated pump/channel allow us to perform a first significant model comparison with experimental data for monkeys. This is a significant step for future multidisciplinary studies on the action of molecules on AH production.

q-bio.QM↗

arXiv2017

The role of structural viscoelasticity in deformable porous media with incompressible constituents: applications in biomechanics

The main goal of this work is to clarify and quantify, by means of mathematical analysis, the role of structural viscoelasticity in the biomechanical response of deformable porous media with incompressible constituents to sudden changes in external applied loads. Models of deformable porous media with incompressible constituents are often utilized to describe the behavior of biological tissues, such as cartilages, bones and engineered tissue scaffolds, where viscoelastic properties may change with age, disease or by design. Here, for the first time, we show that the fluid velocity within the medium could increase tremendously, even up to infinity, should the external applied load experience sudden changes in time and the structural viscoelasticity be too small. In particular, we consider a one-dimensional poro-visco-elastic model for which we derive explicit solutions in the cases where the external applied load is characterized by a step pulse or a trapezoidal pulse in time. By means of dimensional analysis, we identify some dimensionless parameters that can aid the design of structural properties and/or experimental conditions as to ensure that the fluid velocity within the medium remains bounded below a certain given threshold, thereby preventing potential tissue damage. The application to confined compression tests for biological tissues is discussed in detail. Interestingly, the loss of viscoelastic tissue properties has been associated with various disease conditions, such as atherosclerosis, Alzheimer's disease and glaucoma. Thus, the findings of this work may be relevant to many applications in biology and medicine.

math.AP↗