arXiv subjects

Giulia Pozzi

Publications and source records attributed to Giulia Pozzi.

3 recordsLinked to original sources

arXiv2025

On a phenotype-structured phase-field model of nutrient-limited tumour growth

Phase-field models of tumour growth have proved useful as theoretical tools to investigate cancer invasion. A key implicit assumption underlying mathematical models of this type which have so far been proposed, though, is that cells in the tumour are identical. This assumption ignores both the fact that cells in the same tumour may express different characteristics to different extents, exhibiting heterogeneous phenotypes, and the fact that cells may undergo phenotypic changes, with their characteristics evolving over time. To address such a limitation, in this paper we incorporate inter-cellular phenotypic heterogeneity and the evolution of cell phenotypes into the phase-field modelling framework. This is achieved by formulating a phenotype-structured phase-field model of nutrient-limited tumour growth. For this model, we first establish a well-posedness result under general assumptions on the model functions, which encompass a wide spectrum of biologically relevant scenarios. We then present a sample of numerical solutions to showcase key features of spatiotemporal and evolutionary cell dynamics predicted by the model. We conclude with a brief overview of modelling and analytical research perspectives.

math.AP↗

arXiv2025

Modeling the prion protein-mediated transport of extracellular vesicles on the neuron surface

Neurodegenerative diseases are among the leading causes of global mortality, characterized by the progressive deterioration of specific neuron populations, ultimately leading to cognitive decline and dementia. Extracellular vesicles (EVs) are believed to play a role in the early stages of these diseases, acting as carriers of pathogens and contributing to neuroinflammation and disease propagation. This study presents a mathematical model aimed at characterizing the movement of EVs bearing prion protein (PrP) on their surface along neuronal surfaces. The model, informed by experimental data, investigates the influence of PrP and actin polymerization on EV transport dynamics and explores the possible interplay between passive and active mechanisms. EVs isolated from non-human astrocytes were analyzed under three conditions: untreated control (Ctrl), neurons treated with Cytochalasin D (CytoD-HN), and EVs treated with Cytochalasin D (CytoD-EV). The mathematical model is data-driven, testing different hypotheses regarding the underlying transport mechanisms. In the CytoD-EV dataset, EV movement was modeled using a flashing Brownian ratchet to represent directed motion. For active transport in the CytoD-HN set, a symmetric periodic potential was used to describe EV rolling along the neuron surface. The Ctrl scenario incorporates both mechanisms, reflecting a more complex transport behavior. A sensitivity analysis and comparison between numerical predictions and experimental data suggest that the model effectively captures key features of EV motion, providing a quantitative framework to interpret different transport regimes. While some variability remains, the approach offers a promising basis for future investigations into the role of cytoskeletal dynamics in EV-mediated disease propagation.

physics.bio-ph↗

arXiv2024

Reconstruction of the local contractility of the cardiac muscle from deficient apparent kinematics

Active solids are a large class of materials, including both living soft tissues and artificial matter, that share the ability to undergo strain even in absence of external loads. While in engineered materials the actuation is typically designed a priori, in natural materials it is an unknown of the problem. In such a framework, the identification of inactive regions in active materials is of particular interest. An example of paramount relevance is cardiac mechanics and the assessment of regions of the cardiac muscle with impaired contractility. The impossibility to measure the local active forces directly suggests us to develop a novel methodology exploiting kinematic data from clinical images by a variational approach to reconstruct the local contractility of the cardiac muscle. By finding the stationary points of a suitable cost functional we recover the contractility map of the muscle. Numerical experiments, including severe conditions with added noise to model uncertainties, and data knowledge limited to the boundary, demonstrate the effectiveness of our approach. Unlike other methods, we provide a spatially continuous recovery of the contractility map without compromising the computational efficiency.

physics.med-ph↗