In this study, we propose and validate a simple agent-based model to study cell-cell interactions and cell migration during in vitro scratch assays in the context of cutaneous fibrosis (keloid). For model parametrization, we collect data from in vitro experiments performed with healthy or keloid fibroblasts treated (or not) with type 1 or 2 macrophages secretome to mimic specific in vivo environments. All experiments were performed with mitomycin to inhibit cell proliferation, and subsequently isolate the sole contribution of migration to wound filling over time. The scratch assays are modeled within the cellular Potts model framework. The calibration process, via Levenberg-Maquart algorithm, gives a mean error of 4.53 ± 0.77% across the four modalities (healthy, control, M1 and M2 secretum) and the evaluation dataset gives a mean error of 10.55 ± 0.77%. With the help of this model, we test whether the hypothesis of contact inhibition of locomotion (CIL) can explain the movement of keloid fibroblasts. The simulation results and their comparison with the experimental data suggest that CIL might not characterize the movement of keloid fibroblasts, which is in contrast to the importance of CIL for the movement of healthy fibroblasts.

Many physiological processes rely on cellular communication through ligand mediated signalling, where ligands secreted by cells diffuse through the extracellular space and bind to receptors to trigger downstream responses. Although reaction diffusion models capture these dynamics, parameter calibration often lags behind model development due to limited data that reflect the biological microenvironment and the lack of a unified framework for integrating such data into mechanistic models. We propose that single cell RNA sequencing and spatial transcriptomics provide a rich, abundant, and underused source of information for calibrating such models at tissue scale. We develop a computational pipeline that integrates these data to infer model parameters, combining finite volume solvers with bioinformatics preprocessing, Approximate Bayesian Computation (ABC), and gradient based optimization. Using two open source human skin datasets as case studies, we calibrate parameters governing the isoforms of Transforming Growth Factor Beta, a key regulator of tissue repair and fibrosis, and compare the resulting spatial concentration fields with local cell type distributions. Benchmarking on synthetic datasets helps evaluate the inference accuracy and shows the benefits of combining ABC with gradient based methods. Overall, the pipeline provides a flexible and rigorous approach for calibrating tissue level mechanistic models using modern transcriptomics data.

In this work, we investigate the condition number for a system of coupled non-local reaction-diffusion-advection equations developed in the context of modelling normal and abnormal wound healing. Following a finite element discretisation of the coupled non-local system, we establish bounds for this condition number. We further discuss how model parameter choices affect the conditioning of the system. Finally, we discuss how the step size of the chosen time-stepping scheme and the spatial grid size of the finite element methods affect the bound for the condition number, while also suggesting possible parameter ranges that could keep the model well conditioned.

Background/Objectives: Misdiagnosing skin disorders leads to the administration of wrong treatments, sometimes with life-impacting consequences. Deep learning algorithms are becoming more and more used for diagnosis. While many skin cancer/lesion image classification studies focus on datasets containing dermatoscopic images and do not include keloid images, in this study, we focus on diagnosing keloid disorders amongst other skin lesions and combine two publicly available datasets containing non-dermatoscopic images: one dataset with keloid images and one with images of other various benign and malignant skin lesions (melanoma, basal cell carcinoma, squamous cell carcinoma, actinic keratosis, seborrheic keratosis, and nevus). Methods: Different Convolution Neural Network (CNN) models are used to classify these disorders as either malignant or benign, to differentiate keloids amongst different benign skin disorders, and furthermore to differentiate keloids among other similar-looking malignant lesions. To this end, we use the transfer learning technique applied to nine different base models: the VGG16, MobileNet, InceptionV3, DenseNet121, EfficientNetB0, Xception, InceptionRNV2, EfficientNetV2L, and NASNetLarge. We explore and compare the results of these models using performance metrics such as accuracy, precision, recall, F1score, and AUC-ROC. Results: We show that the VGG16 model (after fine-tuning) performs the best in classifying keloid images among other benign and malignant skin lesion images, with the following keloid class performance: an accuracy of 0.985, precision of 1.0, recall of 0.857, F1 score of 0.922 and AUC-ROC value of 0.996. VGG16 also has the best overall average performance (over all classes) in terms of the AUC-ROC and the other performance metrics. Using this model, we further attempt to predict the identification of three new non-dermatoscopic anonymised clinical images, classifying them as either malignant, benign, or keloid, and in the process, we identify some issues related to the collection and processing of such images. Finally, we also show that the DenseNet121 model has the best performance when differentiating keloids from other malignant disorders that have similar clinical presentations. Conclusions: The study emphasised the potential use of deep learning algorithms (and their drawbacks), to identify and classify benign skin disorders such as keloids, which are not usually investigated via these approaches (as opposed to cancers), mainly due to lack of available data.

Transport-dominated partial differential equation models have been used extensively over the past two decades to describe various collective migration phenomena in cell biology and ecology. To understand the behaviour of these models (and the biological systems they describe) different analytical and numerical approaches have been used. While the analytical approaches have been discussed by different recent review studies, the numerical approaches are still facing different open problems, and thus are being employed on a rather ad-hoc basis for each developed non-local model. The goal of this review is to summarise the basic ideas behind these transport-dominated non-local models, to discuss the current numerical approaches used to simulate these models, and finally to discuss some open problems related to the applications of these numerical methods, in particular the finite element method. This allows us to emphasize the opportunities offered by this numerical method to advance the research in this field. In addition, we present in detail some numerical schemes that we used to discretize these non-local equations; in particular a new semi-implicit scheme we introduced to stabilize the oscillations obtained with classical schemes.

All physiological processes fundamentally rely on continuous cellular cross-talk to maintain organization and ensure proper function. Among the various modes of cellular communication, ligand-mediated chemical signaling, in which a ligand is secreted by one cell, diffuses through the extracellular environment, and binds to a receptor on another (or the same) cell to elicit a downstream response, is arguably the most ubiquitous and foundational. Given its importance, numerous mathematical models have been developed to describe this reaction-diffusion mechanism, capturing ligand secretion, diffusion, decay, and binding under both normal and pathological conditions. However, parameter calibration for such models often lags behind model development. This is due to limited data that faithfully represent the biological microenvironment, as well as due to the absence of a robust, rigorous framework to integrate available data into the mathematical model. To address this gap, we propose that transcriptomics (gene expression) data, namely the combination of single-cell RNA sequencing and spatial transcriptomics, provide a rich, increasingly abundant, and underutilized source of information that can be used to calibrate the parameters of the cellular reaction-diffusion models at the larger mesoscopic scale. To this end, we develop a computational pipeline that leverages these data to extract parameter values for reaction-diffusion models, and illustrate its application through two human wound-healing case studies. Using open-source transcriptomics data, we calibrate the reaction-diffusion model parameters of the isoforms of Transforming Growth Factor Beta (TGF β ), a signaling molecule central to tissue repair and development as well as to pathological processes such as cancer and fibrosis. Our pipeline integrates traditional numerical (finite volume) solvers for the ligand concentration fields with bioinformatics, machine learning, and Bayesian inference methods, combining existing and novel computational tools into a single framework for a physiologically informed, data-driven parameter calibration process. The pipeline is modular, allowing easy extension or adjustment depending on user needs. Overall, this framework facilitates rigorous model calibration, an essential step toward ensuring that mathematical models have meaningful research and potential translational utility. ### Competing Interest Statement The authors have declared no competing interest. Agence Nationale de la Recherche, ANR-21-CE45-0025-01

Malaria is an infectious and communicable disease, caused by one or more species of Plasmodium parasites. There are five species of parasites responsible for malaria in humans, of which two, Plasmodium Falciparum and Plasmodium Vivax, are the most dangerous. In Djibouti, the two species of Plasmodium are present in different proportions in the infected population: 77% of P. Falciparum and 33% of P. Vivax. In this study we present a new mathematical model describing the temporal dynamics of Plasmodium Falciparum and Plasmodium Vivax co-infection. We focus briefly on the well posedness of this model and on the calculation of the basic reproductive numbers for the infections with each Plasmodium species that help us understand the long-term dynamics of this model (i.e., existence and stability of various eqiuilibria). Then we use computational approaches to: (a) identify model parameters using real data on malaria infections in Djibouti; (b) illustrate the influence of different estimated parameters on the basic reproduction numbers; (c) perform global sensitivity and uncertainty analysis for the impact of various model parameters on the transient dynamics of infectious mosquitoes and infected humans, for infections with each of the Plasmodium species. The originality of this research stems from employing the FAST method and the LHS method to identify the key factors influencing the progression of the disease within the population of Djibouti. In addition, sensitivity analysis identified the most influential parameter for Falciparium and Vivax reproduction rates. Finally, the uncertainty analysis enabled us to understand the variability of certain parameters on the infected compartments.

This paper presents a critical analysis of the literature and perspective research ideas for modeling the epidemics caused by the SARS-CoV-2 virus. It goes beyond deterministic population dynamics to consider several key complexity features of the system under consideration. In particular, the multiscale features of the dynamics from contagion to the subsequent dynamics of competition between the immune system and the proliferating virus. Other topics addressed in this work include the propagation of epidemics in a territory, taking into account local transportation networks, the heterogeneity of the population and the study of social and economic problems in populations involved in the spread of epidemics. The overall content aims to show how new mathematical tools can be developed to address the above topics and how mathematical models and simulations can contribute to the decision making of crisis managers.

Significance: Glioblastoma (GBM) is a rare but deadly form of brain tumor with a low median survival rate of 14.6 months, due to its resistance to treatment. An independent simulation of the INtraoperative photoDYnamic therapy for GliOblastoma (INDYGO) trial, a clinical trial aiming to treat the GBM resection cavity with photodynamic therapy (PDT) via a laser coupled balloon device, is demonstrated. Aim: To develop a framework providing increased understanding for the PDT treatment, its parameters, and their impact on the clinical outcome. Approach We use Monte Carlo radiative transport techniques within a computational brain model containing a GBM to simulate light path and PDT effects. Treatment parameters (laser power, photosensitizer concentration, and irradiation time) are considered, as well as PDT's impact on brain tissue temperature. Results: The simulation suggests that 39% of post-resection GBM cells are killed at the end of treatment when using the standard INDYGO trial protocol (light fluence = 200 J/cm2 at balloon wall) and assuming an initial photosensitizer concentration of 5 mu M. Increases in treatment time and light power (light fluence = 400 J/cm(2) at balloon wall) result in further cell kill but increase brain cell temperature, which potentially affects treatment safety. Increasing the p hotosensitizer concentration produces the most significant increase in cell kill, with 61% of GBM cells killed when doubling concentration to 10 mu M and keeping the treatment time and power the same. According to these simulations, the standard trial protocol is reasonably well optimized with improvements in cell kill difficult to achieve without potentially dangerous increases in temperature. To improve treatment outcome, focus should be placed on improving the photosensitizer. Conclusions: With further development and optimization, the simulation could have potential clinical benefit and be used to help plan and optimize intraoperative PDT treatment for GBM.

We consider a one-dimensional nonlocal hyperbolic model introduced to describe the formation and movement of self-organizing collectives of animals in homogeneous 1D environments. Previous research has shown that this model exhibits a large number of complex spatial and spatiotemporal aggregation patterns, as evidenced by numerical simulations and weakly nonlinear analysis. In this study, we focus on a particular type of localised patterns with odd/even/no symmetries (which are usually part of snaking solution branches with different symmetries that form complex bifurcation structures called snake-and-ladder bifurcations). To numerically investigate the bifurcating solution branches (to eventually construct the full bifurcating structures), we first need to understand the numerical issues that could appear when using different numerical schemes. To this end, in this study, we consider ten different numerical schemes (the upwind scheme, the MacCormack scheme, the Fractional-Step method, and the Quasi-Steady Wave-Propagation algorithm, combining them with high-resolution methods), while paying attention to the preservation of the solution symmetries with all these schemes. We show several numerical issues: first, we observe the presence of two distinct types of numerical solutions (with different symmetries) that exhibit very small errors; second, in some cases, none of the investigated numerical schemes converge, posing a challenge for the development of numerical continuation algorithms for nonlocal hyperbolic systems; lastly, the choice of the numerical schemes, as well as their corresponding parameters such as time-space steps, exert a significant influence on the type and symmetry of bifurcating solutions.

This paper deals with the modeling and simulation of the in-host dynamics of a virus. The modeling approach was developed according to the idea that mathematical models should go beyond deterministic single-scale population dynamics by taking into account the multiscale, heterogeneous features of the complex system under consideration. Here, we considered modeling the competition between the virus, the epithelial cells it infects, and the heterogeneous immune system with evolving activation states that induce a range of different effects on virus particles and infected cells. The subsequent numerical simulations showed different types of model outcomes: from virus elimination, to virus persistence and periodic relapse, to virus uncontrolled growth that triggers a blow-up in the fully activated immune response. The simulations also showed the existence of a threshold in the immune response that separates the regimes of higher re-infections from lower re-infections (compared to the magnitude of the first viral infection).

In this study we propose a novel agent-based model to reproduce and propose new hypotheses on the biological mechanisms of cell-cell interactions and cell migration from data obtained during scratch assay with healthy and keloid fibroblasts. The advantage of the agent-based model we propose in this paper lies in its simplicity: only three governing parameters. We conducted a parametric sensitivity analysis and we incorporated the evaluation of contact inhibition of locomotion, aligning with the observed loss during malignant invasion. To study invasion modalities, we conducted in vitro wound healing assays using healthy and pseudo-tumoral (keloid) fibroblasts under diverse conditions: control, macrophage type 1 secretome, and macrophage type 2 secretome. Mitomycin inhibition of proliferation isolated the contribution of migration to wound filling. Our agent-based mathematical model describes configurations based on our microscopy imaging and statistical data, which enables quantitative comparisons between our experimental and numerical results. Calibration and evaluation were performed on the same experiments, enriched by external datasets. With only three governing parameters, our model not only demonstrated good agreement (8.78% to 18.75% error) with external evaluation datasets for all experimental configurations but also provided us with a nuanced understanding of keloid fibroblast behavior during wound healing, especially regarding contact inhibition dynamics.### Competing Interest StatementThe authors have declared no competing interest.

Pattern formation in biological aggregations is a topic of great interest, due to the complex spatial structure of various aggregations of cells/bacteria/animals that can be observed in nature. While many such aggregations look similar at the macroscopic level, they might differ in their microscopic spatial structure. However, the complexity of the non-linear and sometimes non-local interactions among individuals inside these aggregations makes it difficult to investigate these spatial structures. In this study, we investigate numerically the transitions between different spatial patterns of animal aggregations with various symmetries (even, odd or no symmetry) that characterise the microscopic distribution of individuals inside these aggregations. To this end, we construct a bifurcation diagram starting with perturbations of spatially homogeneous solutions with low, medium, and high amplitudes. For perturbations with low amplitudes, the bifurcating structures show transitions among even-symmetric, odd-symmetric, and non-symmetric solutions. For perturbations with large amplitudes, there are wide parameter regions with non-convergent solutions, characterised by oscillatory transitions between different relatively similar solutions. These numerical results emphasize: (i) the effect of nonlinear and non-local interactions on the microscopically different symmetric/non-symmetric structures of macroscopically similar ecological aggregations; (ii) the difficulty of developing continuation algorithms for this class of non-local models.

. This study considers a non-local mathematical model for normal and abnormal wound healing described by four equations: an ordinary differential equation for the dynamics of extracellular matrix, and three partial differential equations for the dynamics of growth factors, fibroblasts, and macrophages. Two of these equations include non-local (integral) terms that characterize adhesive cell-cell and cell-matrix interactions. Here, we follow up on an earlier numerical study of a similar model that showed the solutions of this class of models approaching either spatially-homogeneous steady states or spatially-heterogenous states with overgrown cell densities. The goal of this current study is to investigate (from the perspective of normal/abnormal wound healing) the linear stability of the steady states, and further prove the local in-time existence and uniqueness of solutions for this class of non-local models using the framework of the analytic semigroups of operators. We also discuss the impact of different types of kernels (smooth and non-smooth) for non-local cell-cell and cell-matrix interactions, on these analytical results. Overall, the complexity of this 2D non-local model, which incorporates various discontinuous functions, leads to new approaches for some of these analytical results.

SignificanceGlioblastoma is a deadly brain tumour with a low survival time. The INDYGO clinical trial aims to increase survival by maximizing tumour resection via PDT. A simulation of the trial protocol is independently produced with the aim of increasing understanding of the treatment parameters and their effect on treatment outcome.ApproachMonte Carlo Radiative Transport (MCRT) is used to simulate light travel and PDT within an in-silico brain model containing a glioblastoma. Treatment parameters were changed, and the effect determined based on the percentage of tumour killed.ResultsSimulating the standard trial setup with a 5 μM photosensitizer concentration resulted in 42 % cell kill by the end of treatment. Increasing treatment time and light power resulted in increased cell kill, however an increase in photosentisiser concentration had the biggest effect.ConclusionsThese results provide detailed information that can be used when planning intraoperative PDT treatments for glioblastoma.

Cell segregation caused by collective cell migration (CCM) is crucial for morphogenesis, functional development of tissue parts, and is an important aspect in other diseases such as cancer and its metastasis process. Efficiency of the cell segregation depends on the interplay between: (1) biochemical processes such as cell signaling and gene expression and (2) physical interactions between cells. Despite extensive research devoted to study the segregation of various co-cultured systems, we still do not understand the role of physical interactions in cell segregation. Cumulative effects of these physical interactions appear in the form of physical parameters such as: (1) tissue surface tension, (2) viscoelasticity caused by CCM, and (3) solid stress accumulated in multicellular systems. These parameters primarily depend on the interplay between the state of cell-cell adhesion contacts and cell contractility. The role of these physical parameters on the segregation efficiency is discussed on model systems such as co-cultured breast cell spheroids consisting of two subpopulations that are in contact. This review study aims to: (1) summarize biological aspects related to cell segregation, mechanical properties of cell collectives, effects along the biointerface between cell subpopulations and (2) describe from a biophysical/mathematical perspective the same biological aspects summarized before. So that overall it can illustrate the complexity of the biological systems that translate into very complex biophysical/mathematical equations. Moreover, by presenting in parallel these two seemingly different parts (biology vs. equations), this review aims to emphasize the need for experiments to estimate the variety of parameters entering the resulting complex biophysical/mathematical models.