arXiv subjects

Chiara Giverso

Publications and source records attributed to Chiara Giverso.

8 recordsLinked to original sources

arXiv2026

Modeling tumor growth with variable mass and angiogenesis-driven perfusion through a 3D-1D coupled framework

Tumor growth beyond a critical size relies on the development of a functional vascular network, which ensures adequate oxygen and nutrient supply. In this work, we present a modeling framework based on an optimization-based 3D-1D coupling strategy to simulate perfusion in a tumoral tissue with growing mass, interacting with a dynamically evolving capillary network. The tumor is described as a multiphase system including tumor cells and interstitial fluid, governed by a non-linear PDE system for cell volume fraction, pressure, oxygen, and VEGF, and discretized via finite elements. Capillary growth is tackled using a continuous-discrete hybrid tip-tracking approach. The vascular geometry is updated over time according to angiogenic signals, and coupled to the tissue model through a constrained optimization formulation that enforces fluid and nutrient exchange via interface variables. A sensitivity analysis using the Morris elementary effect method identifies key parameters influencing system behavior. Results highlight the critical role of vascular development in regulating tissue perfusion and tumor progression. Overall, the proposed numerical approach provides a versatile tool for investigating tumor-vascular interactions and can support further quantitative analysis of angiogenesis and tumor perfusion dynamics.

math.NA↗

arXiv2025

From Brain Scans to Therapy Response: PDE Modelling of Immunotherapy for Glioblastoma

Glioblastoma Multiforme (GBM) is a highly aggressive brain tumour with limited therapeutic options and poor prognosis. This study presents a mathematical framework to investigate the efficacy of immunotherapy strategies based on cytotoxic T-lymphocyte (CTL) infusion. The model couples tumour and immune dynamics through a system of partial differential equations (PDEs), incorporating cell proliferation, diffusion, and chemotactic migration in response to TGF-$\beta$, a tumour-secreted signalling molecule. A reduced ordinary differential equation (ODE) model is first analysed to derive threshold conditions for tumour eradication, identifying critical infusion levels consistent with clinical data. Numerical bifurcation analysis explores the impact of parameter variations. The full PDE model is solved using the finite element method on simplified 2D domains, followed by sensitivity analyses to quantify parameter influence on tumour mass and volume. The model is then applied to a realistic 3D brain geometry reconstructed from patient-specific MRI and DTI data, accounting for anatomical anisotropy and tissue heterogeneity. Therapeutic scenarios are simulated with spatially localised lymphocyte infusion. Results highlight spatial variations in tumour growth and treatment response, with infusion intensity and tumour location critically influencing therapeutic outcomes. These findings emphasise the importance of personalised, spatially informed modelling in optimising immunotherapy protocols for GBM.

q-bio.PE↗

arXiv2025

The mechanics of anisotropic active plates with applications to cell alignment on curved substrates

We develop a continuum mechanics framework for active anisotropic plates within the F\"oppl-von K\'arm\'an limit, incorporating a preferential direction and inelastic active contractions in geometrically nonlinear plate theory. Through asymptotic expansion, we derive coupled equilibrium equations for plates with transversely isotropic and possibly inhomogeneous reinforcement undergoing spatially varying active contractions through their thickness. The framework highlights the coupling between material anisotropy and active deformations, with target curvatures that compete with geometric constraints. To demonstrate its capabilities, we apply the model to curvature-induced cell alignment, where substrate geometry, cytoskeletal anisotropy, and contractility interact to determine orientation. For cylindrical substrates, the model predicts a supercritical bifurcation in preferred orientation, from perpendicular to parallel through an oblique orientation, governed by the ratio of active contractility to substrate curvature. For ellipsoidal geometries, we capture stable parallel, perpendicular, and oblique configurations set by principal curvatures, whereas spherical substrates show no preferred alignment. These predictions qualitatively reproduce experimental observations across cell types, providing a mechanistic interpretation of the distinct behaviors of contractile epithelial cells and stiffer fibroblasts. As a further illustration, we analyze the buckling of active anisotropic rings, showing how reinforcement and contractility jointly modulate the instability threshold. More broadly, the model applies to thin fiber-reinforced active structures arising in soft robotics, morphogenesis, and tissue engineering.

cond-mat.soft↗

arXiv2025

A phenotype-structured reaction-diffusion model of avascular glioma growth

We consider a phenotype-structured reaction-diffusion model of avascular glioma growth. The model describes the interaction dynamics between tumour cells and oxygen, and takes into account anisotropic cell movement and oxygen diffusion related to structural anisotropy of the brain's extracellular environment. In this model, phenotypic heterogeneity of tumour cells is captured by a continuous phenotype-structuring variable, the value of which evolves due to phenotypic changes. We first analyse a one-dimensional version of the model and formally show, through a Hopf-Cole transformation, that it admits, in appropriate asymptotic regimes, phenotypically heterogeneous travelling wave solutions, wherein the locally prevailing cell phenotype varies across the wave due to the presence of oxygen gradients. This provides a mathematical formalisation for the emergence of intratumour phenotypic heterogeneity driven by differences in oxygen availability across the tumour. We then report on the results of both 1D simulations, which corroborate the results of formal asymptotic analyses, and 2D simulations, which also demonstrate the impact of anisotropy in cell movement and oxygen diffusion on tumour growth and on the phenotypic composition of the tumour edge. These results are complemented with additional results of 3D simulations, which are carried out on the geometry of the brain by using a hybrid finite difference-finite element method and integrating patient-specific magnetic resonance imaging data with diffusion tensor imaging data.

q-bio.PE↗

arXiv2022

The influence of nucleus mechanics in modelling adhesion-independent cell migration in structured and confined environments

Recent biological experiments have shown that certain types of cells are able to move in structured and confined environment even without the activation of focal adhesion. Focusing on this particular phenomenon and based on previous works, we derive a novel two-dimensional mechanical model, which relies on the following physical ingredients: the asymmetrical renewal of the actin cortex supporting the membrane, resulting in a backward flow of material; the mechanical description of the nucleus membrane and the inner nuclear material; the microtubule network guiding nucleus location; the contact interactions between the cell and the external environment. The resulting fourth order system of partial differential equations is then solved numerically to conduct a study of the qualitative effects of the model parameters, mainly those governing the mechanical properties of the nucleus and the geometry of the confining structure. Coherently with biological observations, we find that cells characterized by a stiff nucleus are unable to migrate in channels that can be crossed by cells with a softer nucleus. Regarding the geometry, cell velocity and ability to migrate are influenced by the width of the channel and the wavelength of the external structure. Even though still preliminary, these results can be potentially useful in determining the physical limit of cell migration in confined environment and in designing scaffold for tissue engineering.

math.AP↗

arXiv2022

An optimization based 3D-1D coupling strategy for tissue perfusion and chemical transport during tumor-induced angiogenesis

A new mathematical model and numerical approach are proposed for the simulation of fluid and chemical exchanges between a growing capillary network and the surrounding tissue, in the context of tumor-induced angiogenesis. Thanks to proper modeling assumptions the capillaries are reduced to their centerline: a well posed mathematical model is hence worked out, based on the coupling between a three-dimensional and a one-dimensional equation (3D-1D coupled problem). Also the application of a PDE-constrained optimization formulation is here proposed for the first time for angiogenesis simulations. Under this approach no mesh conformity is required, thus making the method particularly suitable for this kind of application, since no remeshing is required as the capillary network grows. In order to handle both the evolution of the quantities of interest and the changes in the geometry, a discrete-hybrid strategy is adopted, combining a continuous modeling of the tissue and of the chemicals with a discrete tip-tracking model to account for the vascular network growth. The tip-tracking strategy, together with some proper rules for branching and anastomosis, is able to provide a realistic representation of the capillary network.

q-bio.TO↗

arXiv2021

Effective interface conditions for continuum mechanical models describing the invasion of multiple cell populations through thin membranes

We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different proliferative abilities and mobility, which may vary from part to part of the tissue, as well as by different invasion potentials within the membranes. The original transmission problem, consisting of a set of mass balance equations for the volume fraction of cells of every population complemented with continuity of stresses and mass flux across the surfaces of the membranes, is then reduced to a limiting transmission problem whereby each thin membrane is replaced by an effective interface. In order to close the limiting problem, a set of biophysically-consistent transmission conditions is derived through a formal asymptotic method. Models based on such a limiting transmission problem may find fruitful application in a variety of research areas in the biological and medical sciences, including developmental biology, immunology and cancer growth and invasion.

math.AP↗

arXiv2019

Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes

We consider a continuum mechanical model of cell invasion through thin membranes. The model consists of a transmission problem for cell volume fraction complemented with continuity of stresses and mass flux across the surfaces of the membranes. We reduce the original problem to a limiting transmission problem whereby each thin membrane is replaced by an effective interface, and we develop a formal asymptotic method that enables the derivation of a set of biophysically consistent transmission conditions to close the limiting problem. The formal results obtained are validated via numerical simulations showing that the relative error between the solutions to the original transmission problem and the solutions to the limiting problem vanishes when the thickness of the membranes tends to zero. In order to show potential applications of our effective interface conditions, we employ the limiting transmission problem to model cancer cell invasion through the basement membrane and the metastatic spread of ovarian carcinoma.

q-bio.TO↗