Special Session 102: Mathematics of Cancer and Cardiovascular Dynamics: From High-Fidelity Simulation to Data-Driven Methods

Data Driven Modeling of Pseudopalisade Pattern Formation

Sandesh Athni Hiremath Rhinelandpfalz Technical University Germany Co-Author(s):    Christina Surulescu

Abstract: Pseudopalisading is an interesting phenomenon where cancer cells arrange themselves to form a dense garland-like pattern. Unlike the palisade structure, a similar type of pattern first observed in schwannomas by pathologist J.J. Verocay, pseudopalisades are less organized and associated with a necrotic region at their core. These structures are mainly found in glioblastoma (GBM), a grade IV brain tumor, and provide a way to assess the aggressiveness of the tumor. Identification of the exact bio-mechanism responsible for the formation of pseudopalisades is a difficult task, mainly because pseudopalisades seem to be a consequence of complex nonlinear dynamics within the tumor. In this paper we propose a data-driven methodology to gain insight into the formation of different types of pseudopalisade structures. To this end, we start from a state of the art macroscopic model for the dynamics of GBM, that is coupled with the dynamics of extracellular pH, and formulate a terminal value optimal control problem. Thus, given a specific, observed pseudopalisade pattern, we determine the evolution of parameters (bio-mechanisms) that are responsible for its emergence. Random histological images exhibiting pseudopalisade-like structures are chosen to serve as target pattern. Having identified the optimal model parameters that generate the specified target pattern, we then formulate two different types of pattern counteracting ansatzes in order to determine possible ways to impair or obstruct the process of pseudopalisade formation. This provides the basis for designing active or live control of malignant GBM. Furthermore, we also provide a simple, yet insightful, mechanism to synthesize new pseudopalisade patterns by linearly combining the optimal model parameters responsible for generating different known target patterns. This particularly provides a hint that complex pseudopalisade patterns could be synthesized by a linear combination of parameters responsible for generating simple patterns. Going even further, we ask ourselves if complex therapy approaches can be conceived, such that some linear combination thereof is able to reverse or disrupt simple pseudopalisade patterns; this is investigated with the help of numerical simulations.

Hybrid PINN-FEM framework for tumor growth models with stabilization

Suleyman Cengizci Antalya Bilim University Turkey Co-Author(s):

Abstract: This study presents a hybrid computational framework integrating physics-informed neural networks (PINNs) with stabilized finite element methods for simulating haptotaxis-driven cancer invasion dynamics. The governing equations consist of time-dependent, nonlinear, coupled partial differential equations describing cancer cell density, extracellular matrix (ECM) degradation, and matrix-degrading enzyme concentration. In convection-dominated regimes, standard Galerkin finite element methods produce spurious oscillations and nonphysical negative densities. To address this, we employ the streamline-upwind/Petrov--Galerkin (SUPG) formulation augmented with the YZ$\beta$ discontinuity-capturing technique to generate numerically stable reference solutions. A multi-phase adaptive PINN training strategy is then proposed, progressively transitioning from data-dominant learning using SUPG--YZ$\beta$ solutions to physics-informed refinement through selective enforcement of governing equations. The neural network architecture incorporates Fourier feature embeddings and deep residual blocks to capture sharp tumor invasion fronts. Numerical experiments on benchmark haptotaxis models demonstrate that the hybrid approach eliminates nonphysical oscillations while achieving enhanced accuracy compared to standalone stabilized FEM, effectively resolving steep gradients characteristic of invasive tumor boundaries. The framework is implemented using FEniCS and PyTorch with GPU acceleration, providing a flexible tool for mathematical oncology applications.

Computational investigation of the interactions between oncolytic viruses and tumour-associated macrophages

Raluca EFTIMIE University Marie and Louis Pasteur France Co-Author(s):

Abstract: The interactions between oncolytic viruses (OVs) and innate immunity are crucial for the success of oncolytic therapies. Here we focus on a heterogeneous and plastic population of innate immune cells, the tumour-associated macrophages, that can be involved in the elimination of OVs, as well as in the replication of OVs and their spread across tumour tissue. Computational approaches are used to investigate the importance of different biological mechanisms in the faster spread of OVs, as helped/hindered by different macrophage phenotypes.

Simple Mathematical Model of CAR-T Cells Therapy for Glioblastoma

Urszula Forys University of Warsaw, Faculty of Mathematics, Informatics and Mechanics Poland Co-Author(s):    Juan Belmonte-Beitia, Marek Bodnar, Mariusz Bodzioch, Monika J. Piotrowska, Magdalena Szafra\`nska-\L{}\c{e}czycka

Abstract: CAR-T (chimeric antigen receptor T) cell therapy is a novel immunotherapy that oncologists are trying to adapt to various types of cancer, including glioblastomas - brain tumors of glial origin. We consider a generalisation of the mathematical model proposed by Le\`{o}n-Triana et al. (2021) describing the competition of CAR-T and glioblastoma tumour cells. We focus on the mathematical properties of the proposed model, analyzing the stability of steady states, and then discuss two different types of treatments: constant and periodic, comparing their effectiveness.

Discontinuous Galerkin methods on essentially arbitrarily shaped element meshes

Emmanouil Georgoulis National Technical University of Athens / Heriot-Watt University Greece Co-Author(s):

Abstract: We extend the applicability of the popular interior penalty discontinuous Galerkin (dG) method for discretising advection diffusion reaction problems to meshes comprising extremely general, essentially arbitrarily shaped elements. In particular, our analysis allows for curved element shapes without the use of iso-parametric elemental maps. The feasibility of the method relies on the definition of a suitable discontinuity penalisation parameter, which turns out to be essentially independent of the particular element shape. A priori error bounds for the resulting method are given under very mild structural assumptions restricting the magnitude of the local curvature of element boundaries. Numerical experiments are also presented, indicating the practicality of the proposed approach. This work generalises our earlier work detailed in the monograph.

Cancer invasion and metastasis across phenotypic scales

Dimitrios Katsaounis RWTH Aachen University Germany Co-Author(s):

Abstract: Cancer invasion and metastasis are inherently multiscale processes driven by complex interactions between cancer cells and the tumour microenvironment. A central mechanism underlying cancer heterogeneity is the epithelial-to-mesenchymal transition (EMT), through which proliferative epithelial-like cancer cells (ECCs), forming the bulk of solid tumours, progressively acquire migratory and invasive mesenchymal-like traits. Mesenchymal-like cancer cells (MCCs) can actively invade surrounding tissue and disseminate to distant organs via the vasculature. At secondary sites, they may undergo the reverse mesenchymal-to-epithelial transition (MET), enabling metastatic growth. Importantly, EMT is a continuous process that gives rise to intermediate hybrid phenotypes with increasing invasive potential. In this talk, we present a phenotype-dependent individual-based model together with its corresponding macroscopic formulation, incorporating continuous transitions along the epithelial-mesenchymal spectrum. This framework enables the study of the emergence and maintenance of phenotypic heterogeneity during tumour progression. Additionally, we investigate an individual-based model for MCC migration, focusing on the role of cell-cell adhesion in collective dynamics, informed by experimental data. In particular, we introduce a stochastic representation of N-cadherin-mediated adhesion, where bond lifetimes depend on the pulling force acting on the cells.

A Reduced Model of Aspiration Thrombectomy

Niklas Kolbe RWTH Aachen University Germany Co-Author(s):    Dimitrios Katsaounis, Agnese Lucchetti, Michael Neidlin

Abstract: Aspiration thrombectomy has emerged as a critical intervention for ischemic stroke caused by large vessel occlusions, wherein a catheter is navigated to the occlusion site and suction is applied to restore cerebral blood flow. To facilitate efficient computational analysis of this procedure, we present a new one-dimensional fluid-structure interaction model that captures the essential hemodynamics while decreasing computational cost compared over three-dimensional simulations. The model includes detailed constitutive modeling of the catheter material properties and accounts for viscoelastic effects in the blood flow through a Voigt-Kelvin pressure formulation. To address the resulting coupled hyperbolic system, we construct problem-suited nodal solvers based on hyperbolic relaxation, which are integrated into a splitting approach to derive an efficient numerical scheme capable of simulating realistic therapy scenarios. We validate the proposed 1D model against experimental measurements from an in-vitro physical model and demonstrate good agreement with fully resolved 3D CFD simulations, establishing the reduced model`s potential for clinical translation in thrombectomy planning.

Integrating mechanistic mathematical modelling and single-cell data to study cellular hierarchies in neural stem cells and glioblastoma

Anna Marciniak-Czochra Institute for Mathematics, Heidelberg University Germany Co-Author(s):

Abstract: Understanding how heterogeneous cellular populations evolve is central to uncovering the mechanisms of tissue regeneration and cancer progression. In healthy neural stem cell systems and glioblastoma, cellular hierarchies and stem-like states govern long-term dynamics, adaptation, and functional plasticity. In this talk, I will present mathematical approaches that integrate mechanistic modelling with single-cell omics data to study the evolution of cellular states in space and time. Different mathematical frameworks will be discussed, including compartmental and structured population models, as well as their generalisation to the evolution of measures, which describe the dynamics of cell populations in the high-dimensional state spaces revealed by single-cell data. These approaches provide insight into transitions between stemness and differentiation and into how cellular hierarchies emerge and evolve in regeneration and cancer. The work highlights the potential of combining single-cell data with mechanistic mathematical modelling to uncover principles governing heterogeneous cellular systems.

CAR-T cell therapy for glioblastoma

Magdalena Szafranska-Leczycka Doctoral School of Exact and Natural Sciences, University of Warsaw, Warsaw, Poland Poland Co-Author(s):    Z. Szyma\`{n}ska, M. J. Piotrowska, M. Bodnar and U. Fory\`{s}

Abstract: In this presentation, based on mathematical models incorporating tumor growth, delays in CAR-T cell proliferation, and the development of resistance mechanisms, we analyze treatment scenarios inspired by clinical trials targeting IL13Ralpha2, HER2, and EGFRvIII, as described in Migliorini et al. (2018). We focus on evaluating the effectiveness of different therapeutic protocols, including variations in dosing strategies and treatment scheduling. This approach allows us to compare how distinct treatment designs influence tumor dynamics and to identify which strategies lead to the most favorable outcomes. In addition, we perform sensitivity analysis to determine the key parameters that govern treatment success. This enables us to assess the relative importance of biological processes such as CAR-T expansion, tumor growth rate, and resistance development. The results provide deeper insights into the mechanisms underlying therapy efficacy and point to key factors that may limit or enhance the response to CAR-T cell treatment of glioblastoma multiforme.

Mathematical modelling of cancer invasion: Phenotypic transitioning provides insight into multifocal foci formation

Zuzanna Szymanska ICM, University of Warsaw Poland Co-Author(s):    Miros\l{}aw Lachowicz, Nikolaos Sfakianakis and Mark A.J. Chaplain

Abstract: The transition from the epithelial to mesenchymal phenotype and its reverse (from mesenchymal to epithelial) are crucial processes necessary for the progression and spread of cancer. We investigate how phenotypic switching at the cancer cell level impacts the behaviour at the tissue level, specifically on the emergence of isolated foci of the invading solid tumour mass, leading to a multifocal tumour. To this end, we propose a new mathematical model of cancer invasion that includes the influence of cancer cell phenotype on the rate of invasion and metastasis. The implications of the model are explored through numerical simulations, revealing that the plasticity of tumour cell phenotypes appears crucial for disease progression and local invasive spread. The computational simulations show the progression of the invasive spread of primary cancer reminiscent of in vivo multifocal breast carcinomas, where multiple, synchronous neoplastic foci are frequently observed and are associated with a poorer patient prognosis.