Posters

David Morselli

Title: Agent-based and continuum models for spatial dynamics of infection by oncolytic viruses.

Abstract: The spatial dynamics between cancer cells and oncolytic viruses is still poorly understood. We present here a stochastic agent-based model describing infected and uninfected cells for solid tumours, which interact with viruses in the absence of an immune response. Two kinds of movement, namely undirected random and pressure-driven movements, are considered: the continuum limit of the models is derived and a systematic comparison between the systems of partial differential equations and the individual-based model, in one and two dimensions, is carried out. Furthermore, we study the one-dimensional traveling waves of the two populations, with the uninfected proliferative cells trying to escape from the infected cells. In the case of undirected movement, a good agreement between agent-based simulations and the numerical and analytical results for the continuum model is possible. For pressure-driven motion, instead, we observe a wide parameter range in which the infection of the agents remains confined to the center of the tumour, even though the continuum model shows traveling waves of infection; outcomes appear to be more sensitive to stochasticity and uninfected regions appear harder to invade, giving rise to irregular, unpredictable growth patterns. The agreement between the discrete and continuum models can be recovered by increasing the number of agents, but this may compromise the biological meaning of the parameters. Our results suggest that the presence of spatial constraints in tumours’ microenvironments limiting free expansion has a very significant impact on virotherapy. Some of these situations allow us to qualitatively reproduce patterns observed in experiments in vitro, suggesting that stochastic events may play a central role in the use of oncolytic virotherapy.

Carles Falco

Title: Dynamics of growth, collision, and cell division in epithelial monolayers.

Abstract: Although tissues are typically studied in isolation, such situations rarely occur in biology, as cells, tissues, and organs coexist and interact across various scales, shaping both form and function. In this study, we adopt a quantitative approach that combines recent experimental data, mathematical modelling, and Bayesian parameter inference to describe the dynamics of freely expanding and colliding epithelial monolayers. Two simple and extensively studied continuum models are employed, where cells move either randomly or in response to population pressure gradients. Following appropriate calibration, both models successfully replicate the primary features of individual tissue expansions. However, our findings demonstrate that when tissues are not isolated and interactions become relevant, assuming random cell motion can lead to unrealistic behaviour. In such cases, a model that considers population pressure from different cell populations proves more suitable and facilitates comparison with experimental measurements. Additionally, we investigate the dynamics of cell division within epithelial monolayers and demonstrate how a combination of minimal modelling and Bayesian inference can capture mechanical checkpoints in cell-cycle progression.

Chiara Villa

Title: Evolutionary dynamics of glucose-deprived cancer cells: Insights from experimentally-informed mathematical modelling.

Abstract: Glucose is a primary energy source for cancer cells. Several lines of evidence support the idea that monocarboxylate transporters, such as MCT1, elicit metabolic reprogramming of cancer cells in glucose-poor environments, allowing them to reuse lactate, a byproduct of glucose metabolism, as an alternative energy source with serious consequences for disease progression. We employed a synergistic experimental and mathematical modelling approach to explore the evolutionary processes at the root of cancer cell adaptation to glucose deprivation. Data from in vitro experiments on breast cancer cells were used to inform and calibrate a mathematical model that comprises a partial integro-differential equation for the dynamics of a population of cancer cells structured by the level of MCT1 expression.  The analytical and numerical results of the calibrated model provide biological insights on the mechanisms underlying the increase in MCT1 expression observed in glucose-deprived aggressive cancer cells.

Kairui Li

Title: Quantifying Cytoskeletal Dynamics and Remodeling from Live-imaging Microscopy Data.

Abstract: The shape of biological cells emerges from dynamic remodeling of the cell’s internal scaffolding, the cytoskeleton. Hence, correct cytoskeletal regulation is crucial for the control of cell behaviour, such as cell division and migration. A main component of the cytoskeleton is actin. Interlinked actin filaments span the body of the cell and contribute to a cell’s stiffness. The molecular motor myosin can induce constriction of the cell by moving actin filaments against each other. Capturing and quantifying these interactions between myosin and actin in living cells is an ongoing challenge. For example, live-imaging microscopy can be used to study the dynamic changes of actin and myosin density in deforming cells. These imaging data can be quantified using Optical Flow algorithms, which locally assign velocities of cytoskeletal movement to the data. Extended Optical Flow algorithms also quantify actin polymerization and depolymerization. Here, we use in silico data to understand conditions under which Optical Flow is applicable. We found the condition to guarantee the method performs well is that the displacement has to be in a proper proportion as the object size. We test our methods using data on actin densities in larval epithelial cells of Drosophila pupae. The development of our Optical Flow method will be a starting point for identifying differences in cytoskeletal movement and remodeling under experimental perturbations. 

Dimitris Katsaounis

Title: Hybrid modelling for cancer invasion and metastasis.

Abstract: Cancer cells have the ability to interact with the tumour microenvironment and invade the surrounding tissue by reformulating the extracellular matrix (ECM). The coordinated actions of cancer cells, the ECM, cancer associated fibroblasts (CAFs), and the epithelial to mesenchymal transition (EMT) result to in the invasion of the tissue. In this talk, I will present a multiscale hybrid mathematical model which combines the macroscopic nature of the phenomenon, where solid tumours of epithelial-like cancer cells (ECCs) invade the tissue, as well as the microscopic individual based strategy of mesenchymal-like cancer cells (MCCs). The model consists of partial and stochastic differential equations that describe the evolution of the ECCs and the MCCs while accounting for the transitions between them. Numerical simulations of the proposed model will be presented.

Giulia Celora

Title: Emergent surface tension drives self-organised patterning in Dictyostelium group migration 

Abstract: Dictyostelium amoeba are widely studied for their collective cell migration. These cells can aggregate together and move as a cohesive multicellular structure (or swarm) in response to chemical signals. state-of-the-art imaging to visualise the complex spatio-temporal evolution of Dictyostelium cell swarms as they feed on a population of bacteria. Feeding and chemotaxis combine to cause the Dictyostelium swarms to move along a self-generated bacterial concentration gradient. Surprisingly, we observe that as the swarms move collectively, they periodically shed groups of cells at the rear. By representing the cell swarm as an active droplet, we have developed a novel continuum mathematical model to understand the biophysical mechanisms that drive the experimentally observed shedding dynamics. The model suggests that self-organised shedding is driven by the interplay between feeding, active movement and proliferation of cells, and an emergent surface tension. Our work reveals a novel mechanism for self-organised pattern formation in biological systems.

Rebecca Crossley

Title: Travelling waves in a volume-filling model for cell invasion into extracellular matrix

Abstract: Many reaction-diffusion models produce travelling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumour growth. These models have since been adapted to describe the interactions between cells and extracellular matrix (ECM), using various underlying assumptions. In this work, we derive a system of reaction-diffusion equations by coarse-graining an agent-based, volume-filling model of cell invasion into ECM. We study the resulting travelling wave solutions both numerically and analytically across various parameter regimes. Subsequently, we perform a systematic comparison between the population level behaviours observed in this model and those predicted by simpler models in the literature, which do not consider volume-filling effects in the same way. Our study justifies the use of some of these simpler, more analytically tractable models to reproduce the qualitative properties of the solutions in the limiting cases, as well as revealing some interesting properties caused by the introduction of cell and ECM volume-filling effects, where model simplifications might not be appropriate.

Elena Ambrogi

Title: Adaptation processes in the neural dynamics

Abstract: The presence of a slow adaptation current is one of the most prominent responsible for the interspike frequency adaptation in the neural activity. We give an overview on the analysis of its dynamic: existence, uniqueness and regularity of the steady solution and asymptotic convergence or divergence results in relation to the parameters. We also propose a structure preserving numerical scheme and qualitative rates of convergence.

Stéphanie Abo

Title: Synchronization by noise: A stochastic mean-field limit of coupled circadian neurons

Abstract: The suprachiasmatic nucleus (SCN), also known as the circadian master clock, consists of a large population of oscillator neurons. These neurons produce a coherent signal that drives the body’s circadian rhythms. We present a mean-field description of globally coupled neurons modeled as Goodwin oscillators with standard Gaussian noise. We study how the interaction between external noise and intercellular coupling affects the dynamics of the collective rhythm, and we provide a numerical description of the bifurcations resulting from the noise-induced transitions. 

Giulia Chiari

Title: A mathematical study of the impact of  hypoxia on cancer development and radiotherapy effectiveness

Abstract: In the study of cancer evolution and radiotherapy treatments, a key dynamic lies in the tumor-abiotic-factors interaction. In particular, oxygen concentration plays a central role in the determination of the phenotypic heterogeneity of the cancer cell population, both from a qualitative and geometric point of view. We present a continuous mathematical model to study the influence of hypoxia on the evolutionary dynamics of cancer cells. The model is settled in the mathematical framework of phenotype-structured population dynamics and it is formulated in terms of systems of coupled non-linear integro-differential equations. Numerical simulations are performed using Galerkin finite element methods with the aim to test and represent various biological situations. Then, the effects of radiotherapy treatment are included in the model to analyze the influence of the heterogeneity in oxygen concentration and phenotypic distribution of cancer cells on the treatment effectiveness. Various therapeutical protocols are considered. Simulations show that the geometric characterization of tumor niches differentiated by phenotypic characteristics determines a heterogeneous response to radiotherapy. The analysis of the study results provides suggestions about possible therapeutic strategies to optimize the radiotherapy protocol in light of the phenotypic and geometric inhomogeneities of the tumor. The study constitutes the first step in the development of a mathematical tool for the delineation of patient-specific protocols which, in the perspective of personalized medicine, aim not only at the eradication of the tumor mass, but also at the optimization, in case of relapse, of the phenotypic composition of the tumor so that resistance to subsequent treatments can be avoided as possible.

Francesca Cavallini

Title: Uncertainty Quantification for Neural Field equations with random data

Abstract: Neural field models are nonlinear integro-differential equations for the evolution of neuronal activity, and they are a prototypical large-scale, coarse-grained neuronal model in continuum cortices. Neural fields are often simulated heuristically and, in spite of their popularity in mathematical neuroscience, their numerical analysis is not yet fully established. On top of that, how uncertainty in parameters of the model plays a role in these equations a is still unexplored. Motivated by these considerations, we carry out an abstract analysis and propose a numerical scheme for neural fields with random data. We implement an algorithm using generic projection methods for deterministic neural fields and interpolation in the random parameter space, and derive a-priori error bounds for these schemes. We find that the error splits in two contributions, the first one coming from spatial projection and the second one from stochastic collocation (interpolation). We demonstrate optimal convergence of stochastic collocation analytically and present numerical results.

Alejandro Fernandez

Title: A gradient flow approach to study a family of Cahn-Hilliard equations

Abstract: On a recent work from Falcó, Baker, and Carrillo, they describe a new local model for cell-cell adhesion for two species,

Here, we focus on the one species model and study the problem,

We are able to express this equation with a gradient flow formulation. Therefore, using the JKO scheme we can prove existence of (very) weak solutions for 1≤ m<2+2/d (where d is the dimension). With the same technique we can extend the result to the system. The poster presents on-going work with J.A.Carrillo, A.Esposito, and C. Falcó.

Annachiara Colombi

Title: A hybrid PDE–ODE model for cancer-on-chip experiments: a global sensitivity analysis.

Abstract: The employment of mathematical models to study relevant biological phenomena as organogenesis, tissue repair, and tumor invasion, is widely diffusing. In this context, mathematical models able to capture complex and interconnected processes at the basis of these phenomena, may depend on a large number of parameters, or may involve parameters that are not directly measurable in vivo/vitro. In these cases, the parameter estimation may require strong efforts. In this respect, the global sensitivity analysis (GSA) offers useful instruments to support the identification of regions of the parameter space that results in feasible scenarios. Moreover, the GSA is able to highlight how the parameters affect the variability of the outputs of the models, thereby either validating the model or suggesting possible modelling improvements. In particular, in this work, we deal with the hybrid ODE-PDE model proposed in a recent work by G.Bretti et al. in [1] to reproduce Cancer-on-chip experiments where tumor cells, treated with chemotherapy drug, secrete chemical signals stimulating the response of immune cells. A global sensitivity analysis is performed by considering a series of target outputs, properly defined to characterize both the spatial distribution and the dynamics of immune cells.

[1] G. Bretti et al. Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment. Axioms,10(4),2021.