Biology subjects

Hillen, T.

Publications and source records attributed to Hillen, T..

At least 19 recordsLinked to original sources

bioRxiv2026

A New Paradigm for the Mathematical Modelling of Multiple Sclerosis

Multiple Sclerosis (MS) is an autoimmune disease that affects the central nervous system. It can lead to inflammation, neurodegeneration, and physical or cognitive disability. Currently, no cure for MS exists, but medications are available to slow its progression. To date, mathematical modelling of MS has focussed on a few aspects of the disease, but an overall modelling framework is missing. In this paper, we propose a multiscale paradigm for the mathematical modelling of MS. Based on the underlying biological scale, we propose six consecutive modelling levels and develop the first three model levels in this work using systems of ordinary differential equations. We test if these models can describe known effects related to MS disease risk, with particular focus on estrogen, vitamin D, Epstein-Barr virus (EBV) and HLA-DR mutations. We first show that periodic disease outbreaks are possible in this framework through interactions by antigen-presenting cells, regulatory cells and memory B cells. We show that the presence of Epstein-Barr virus infections can initiate the disease, low and high levels of estrogen and vitamin D deficiency can alleviate it, mutations in the HLA-DR gene can promote MS. We can identify a stable steady state of our model as the widely discussed MS prodrome, and we find that memory B-cells play a dominant role in the disease progression. We hope that this framework may serve as a reference for the development and comparative evaluation of future mathematical and computational models of MS.

immunology↗

bioRxiv2026

Spiral Waves and Turbulence in Mathematical Models of Oncolytic Virotherapy

Oncolytic virotherapy is a promising targeted cancer treatment that employs viruses, which selectively infect tumor cells. Although its clinical efficiency has remained limited and it is often used in conjunction with other therapies, advances in genetic engineering have produced stronger and more selective viral strains, prompting continued interest in their dynamics. In particular, previous studies have noted that viruses with sufficiently high replication rates can induce oscillations reminiscent of predator-prey systems. Here, we extend this analysis to the spatial domain by starting from an established tumor-virus reaction-diffusion model, performing a center-manifold reduction that incorporates nonlinear terms to derive a complex Ginzburg-Landau amplitude equation, and estimating its parameters directly from the original kinetics. This reduced normal form equation explains the emergence of experimentally observed patterns -- such as hollow rings and target waves -- and shows that, at longer timescales, these patterns naturally evolve toward spiral waves and a turbulent regime. Our work provides a mechanistic link between the kinetic Hopf bifurcation and the rich spatiotemporal structures observed in oncolytic virotherapy models, suggesting that these patterns are not numerical artifacts but an intrinsic feature of the system.

cancer biology↗

bioRxiv2025

Qualitative Optimization of Oncolytic Virotherapy and Immune Therapy Combination Treatments

Oncolytic viruses (OVs) are designed to selectively target and destroy cancer cells while sparing normal, healthy tissue. Several viruses for oncolytic virotherapy are currently developed. In this paper, we will use mathematical modeling to consider key strategies that can improve the efficacy of oncolytic virotherapy. These include the integration of immunotherapy approaches with virotherapy to amplify anti-tumor immune responses, as well as optimizing the timing, dosage, and sequencing of viral administrations. Specifically, we consider strategies that increase the burst size of the virus, immunostimulation and immunosuppression, we optimize for different weekly virus injection schedules, and we consider the combination of OV therapy with CAR-T cell therapy. A limiting factor is the availability of data. We parametrize the model from several different data sets. These, however, relate to different cancers and different experimental set up. Hence our model cannot be considered to be validated. Consequently, our results are qualitative. Our results highlight the critical importance of timing for virotherapys efficacy and overall success. They outline strong evidence for promising treatment scenarios that need to be further tested experimentally in the future.

cancer biology↗

bioRxiv2025

Stacked Waves and Qualitative Analysis of an Oncolytic Virus-Immune Model

Oncolytic virotherapy (OVT) represents an innovative and promising therapeutic method for cancer treatment. This approach involves the introduction of oncolytic viruses into the patient, which are engineered to selectively target and lyse tumor cells. Based on previous mathematical modelling of oncolytic viruses, we consider a mathematical model that describes the intricate interactions between the oncolytic virus, cancer cell populations, and the immune system. Our study includes a detailed qualitative and quantitative analysis of the model to explain why, despite their promise, oncolytic viruses alone rarely lead to complete and lasting regression of established tumors in vivo. We use parameter sensitivity analysis to support our findings. Furthermore, we consider the spatial version of the model in the form of a system of reaction-diffusion equations. A travelling wave analysis shows an unexpected phenomenon. The solution components do not necessarily evolve into a single traveling front; rather, they develop into stacked fronts, where each front propagates at a different speed. We give explicit formulas for these different invasion speeds, confirm those through numerical simulations, and discuss their significance for OVT.

cancer biology↗

bioRxiv2025

Calcium Signalling in Glioblastoma Networks of Different Topologies and Possible Treatments

Glioblastoma cells form connected cell networks, utilizing tumor microtubes to transmit calcium between cells. A new cell type called "periodic cell" is integral in sustaining calcium signalling in a glioblastoma network. Periodic cells are rare, can sustain consistent intracellular calcium transients, are likely to have KCa3.1 pumps, and have on average more tumor microtubes than other glioma cells. Here we adapt an ordinary differential equation model for intracellular as well as intercellular calcium signalling and apply it to a large glioma cell network. Using the model, three main hypotheses for the driving mechanism of periodic cells were tested: 1. a fixed and elevated IP3 concentration, 2. added benefit from influx of calcium due to KCa3.1 pumps, or 3. oscillation in calcium influx into the cell through the plasma membrane. All three hypotheses yield similar calcium oscillation patterns resembling the trends seen in the data of Hausmann et al. 2023. In vivo, glioma networks were shown to have small-world and scale free network properties. We apply our model to small-world, scale-free and random networks. For these networks, we test how communication is inhibited through removal of cells, removal of tumor microtubes, and inhibition of KCa3.1 pumps. All three network types were more vulnerable to random cell damage than to random TM damage. We find that inhibition of KCa3.1 pumps can have a significant impact on the inhibition of network communication, however, to fully degrade the calcium signalling network, all periodic cells must be eradicated, confirming experimental observations.

cancer biology↗

bioRxiv2024

Mathematical Modelling of Microtube-Driven Regrowth ofGlioma After Local Resection

Recently, glioblastoma tumors were shown to form tumor microtubes, which are thin long protrusions that help the tumor grow and spread. Follow-up experiments were conducted on mice in order to test what impact the tumor microtubes have on tumor regrowth after partial removal of a tumor region. The surgery was performed in isolation and along with growth-inhibiting treatments such as a tumor microtube inhibiting treatment and an anti-inflammatory treatment. Here, we propose a partial differential equation model applicable to describe the microtube driven regrowth of the cancer in the lesion. We find that the model is able to replicate the main trends seen in the experiments such as fast regrowth, larger cancer density in the lesion, and further spread into healthy tissue. The model indicates that the dominant mechanisms of re-growth are growth-inducing wound healing mechanisms. The tumor microtubes accelerate this process as the microtubes provide orientational guidance from the untreated tissue into the lesion.

cancer biology↗

bioRxiv2024

Mathematical Modelling of Reoviruses in Cancer Cell Cultures

Oncolytic virotherapy has emerged as a potential cancer therapy, utilizing viruses to selectively target and replicate within cancer cells while preserving normal cells. In this paper, we investigate the oncolytic potential of unmodified reovirus T3wt relative to a mutated variant SV5. In animal cancer cell monolayer experiments it was found that SV5 was more oncolytic relative to T3wt. SV5 forms larger sized plaques on cancer cell monolayers and spreads to farther distances from the initial site of infection as compared to T3wt. Paradoxically, SV5 attaches to cancer cells less efficiently than T3wt, which lead us to hypothesize that there might be an optimal binding affinity with maximal oncolytic activity. To understand the relationship between the binding process and virus spread for T3wt and SV5, we employ mathematical modelling. A reaction-diffusion model is applied, which is fit to the available data and then validated on data that were not used for the fit. Analysis of our model shows that there is an optimal binding rate that leads to maximum viral infection of the cancer monolayer, and we estimate this value for T3wt and SV5. Moreover, we find that the viral burst size is an important parameter for viral spread, and that a combination of efficient binding and large burst sizes is a promising direction to further develop anti-cancer viruses.

cancer biology↗

bioRxiv2024

How the Tulip Breaking Virus Creates Striped Tulips

The beauty of tulips has enchanted mankind for centuries. The striped variety has attracted particular attention for its intricate and unpredictable patterns. A good understanding of the mechanism that drives the striped pattern formation of the broken tulips has been missing since the 17th century. It is known since 1928 that these patterned tulips suffer from a viral infection by the tulip breaking virus. Here, we present a mathematical model to understand how a virus infection of the petals can lead to stripes, thereby solving a 350 year old mystery. The model, which describes the viral inhibition of pigment expression (anthocyanins) and their interaction with viral reproduction, incorporates a pattern formation mechanism identified as an activator-substrate mechanism, similar to the well-known Turing instability, working together with a Wolperts positional information mechanism. The model is solved on a growing tulip petal shaped domain, whereby we introduce a new method to describe the tulip petal growth explicitly. This work contributes to the theory of pattern formation of reaction-diffusion systems on growing domains applied to the fields of virology and botany.

plant biology↗

bioRxiv2023

Oscillations in a Spatial Oncolytic Virus Model

Virotherapy treatment is a new and promising target therapy that selectively attacks cancer cells without harming normal cells. Mathematical models of oncolytic viruses have shown predator-prey like oscillatory patterns as result of an underlying Hopf bifurcation. In a spatial context, these oscillations can lead to different spatio-temporal phenomena such as hollow-ring patterns, target patterns, and dispersed patterns. In this paper we continue the systematic analysis of these spatial oscillations and discuss their relevance in the clinical context. We consider a bifurcation analysis of a spatially explicit reaction-diffusion model to find the above mentioned spatio-temporal virus infection patterns. The desired pattern for tumor eradication is the hollow ring pattern and we find exact conditions for its occurrence. Moreover, we derive the minimal speed of travelling invasion waves for the cancer and for the oncolytic virus. Our numerical simulations in 2-D reveal complex spatial interactions of the virus infection and a new phenomenon of a periodic peak splitting. An effect that we cannot explain with our current methods.

cancer biology↗

bioRxiv2023

Modelling Microtube Driven Invasion of Glioma

Malignant gliomas are notoriously invasive, a major impediment against their successful treatment. This invasive growth has motivated the use of predictive partial differential equation models, formulated at varying levels of detail, and including (i) "proliferation-infiltration" models, (ii) "go-or-grow" models, and (iii) anisotropic diffusion models. Often, these models use macroscopic observations of a diffuse tumour interface to motivate a phenomenological description of invasion, rather than performing a detailed and mechanistic modelling of glioma cell invasion processes. Here we close this gap. Based on experiments that support an important role played by long cellular protrusions, termed tumour microtubes, we formulate a new model for microtube-driven glioma invasion. In particular, we model a population of tumour cells that extend tissue-infiltrating microtubes. Mitosis leads to new nuclei that migrate along the microtubes and settle elsewhere. A combination of steady state analysis and numerical simulation is employed to show that the model can predict an expanding tumour, with travelling wave solutions led by microtube dynamics. A sequence of scaling arguments allows us reduce the detailed model into simpler formulations, including models falling into each of the general classes (i), (ii), and (iii) above. This analysis allows us to clearly identify the assumptions under which these various models can be a posteriori justified in the context of microtube-driven glioma invasion. Numerical simulations are used to compare the various model classes and we discuss their advantages and disadvantages.

cancer biology↗

bioRxiv2021

Personalized Virus Load Curves of SARS-CoV-2 Infection

This manuscript has been withdrawn due to submission errors. Therefore, the authors do not wish this work to be cited as a reference. Please see and cite for reference the manuscript posted on medRxiv https://doi.org/10.1101/2021.01.21.21250268 If you have any questions, please contact the corresponding author.

physiology↗

bioRxiv2021

Homogenization of a Reaction Diffusion Equation can Explain Influenza A Virus Load Data

We study the influence of spatial heterogeneity on the antiviral activity of mouse embryonic fibroblasts (MEF) infected with influenza A. MEF of type Ube1L-/- are composed of two distinct sub-populations, the strong type that sustains a strong viral infection and the weak type, sustaining a weak viral load. We present new data on the virus load infection of Ube1L-/-, which have been micro-printed in a checker board pattern of different sizes of the inner squares. Surprisingly, the total viral load at one day after inoculation significantly depends on the sizes of the inner squares. We explain this observation by using a reaction diffusion model and we show that mathematical homogenization can explain the observed inhomogeneities. If the individual patches are large, then the growth rate and the carrying capacity will be the arithmetic means of the patches. For finer and finer patches the average growth rate is still the arithmetic mean, however, the carrying capacity uses the harmonic mean. While fitting the PDE to the experimental data, we also predict that a discrepancy in virus load would be unobservable after only half a day. Furthermore, we predict the viral load in different inner squares that had not been measured in our experiment and the travelling distance the virions can reach after one day.

microbiology↗

bioRxiv2019

Implications of Immune-Mediated Metastatic Growth on Metastatic Dormancy, Blow-Up, Early Detection, and Treatment

Metastatic seeding of distant organs can occur in the very early stages of primary tumor development. Once seeded, these micrometastases may enter a dormant phase that can last decades. Curiously, the surgical removal of the primary tumor can stimulate the accelerated growth of distant metastases, a phenomenon known as metastatic blow-up. Although several theories have been proposed to explain metastatic dormancy and blow-up, most mathematical investigations have ignored the important pro-tumor effects of the immune system. In this work, we address that shortcoming by developing an ordinary differential equation model of the immune-mediated theory of metastasis. We include both anti- and pro-tumor immune effects, in addition to the experimentally observed phenomenon of tumor-induced immune cell phenotypic plasticity. Using geometric singular perturbation analysis, we derive a rather simple model that captures the main processes and, at the same time, can be fully analyzed. Literature-derived parameter estimates are obtained, and model robustness is demonstrated through a sensitivity analysis. We determine conditions under which the parameterized model can successfully explain both metastatic dormancy and blow-up. Numerical simulations suggest a novel measure to predict the occurrence of future metastatic blow-up, in addition to new potential avenues for treatment of clinically undetectable micrometastases.

cancer biology↗

bioRxiv2019

A Mathematical Model for the Immune-Mediated Theory of Metastasis

Accumulating experimental and clinical evidence suggest that the immune response to cancer is not exclusively anti-tumor. Indeed, the pro-tumor roles of the immune system -- as suppliers of growth and pro-angiogenic factors or defenses against cytotoxic immune attacks, for example -- have been long appreciated, but relatively few theoretical works have considered their effects. Inspired by the recently proposed "immune-mediated" theory of metastasis, we develop a mathematical model for tumor-immune interactions at two anatomically distant sites, which includes both anti-and pro-tumor immune effects, and the experimentally observed tumor-induced phenotypic plasticity of immune cells (tumor "education" of the immune cells). Upon confrontation of our model to experimental data, we use it to evaluate the implications of the immune-mediated theory of metastasis. We find that tumor education of immune cells may explain the relatively poor performance of immunotherapies, and that many metastatic phenomena, including metastatic blow-up, dormancy, and metastasis to sites of injury, can be explained by the immune-mediated theory of metastasis. Our results suggest that further work is warranted to fully elucidate the protumor effects of the immune system in metastatic cancer.

cancer biology↗

bioRxiv2018

A Stochastic Model for Cancer Metastasis: Branching Stochastic Process with Settlement

We introduce a new stochastic model for metastatic growth, which takes the form of a branching stochastic process with settlement. The moving particles are interpreted as clusters of cancer cells while stationary particles correspond to micro-tumors and metastases. The analysis of expected particle location, their locational variance, the furthest particle distribution, and the extinction probability leads to a common type of differential equation, namely, a non-local integro-differential equation with distributed delay. We prove global existence and uniqueness results for this type of equation. The solutions asymptotic behavior for long time is characterized by an explicit index, a metastatic reproduction number R0: metastases spread for R0 > 1 and become extinct for R0 < 1. Using metastatic data from mouse experiments, we show the suitability of our framework to model metastatic cancer.

cancer biology↗

bioRxiv2017

Effects of G2 checkpoint dynamics on the low-dose hyper-radiosensitivity

We develop and analyze a system of differential equations to investigate the effects of G2 checkpoint dynamics on the low-dose hyper-radiosensitivity. In experimental studies, it has been found that certain cell lines are more sensitive to low-dose radiation than would be expected from the classical Linear Quadratic model (LQ model). In fact, it is frequently observed that cells incur more damage at a low dose (say 0.3 Gy) than at higher dose (say 1 Gy). This effect has been termed hyper-radiosensitivity (HRS). The HRS is followed by a period of relative radioresistance (per unit dose) of cell kill over the dose range of ~ 0.5 - 1 Gy. This latter phenomenon is termed increased radioresistance (IRR). These effects depend on the type of cells and on their phase in the cell cycle. Here we focus on the HRS phenomenon by fitting a model for the cell cycle that includes G2-checkpoint dynamics and radiation treatment to surviving fraction data for different cell lines including glioma cells, prostate cancer cells, as well as to cell populations that are enriched in certain phases of the cell cycle. The HRS effect is measured in the literature through [Formula], the ratio of slope s, of the surviving fraction curve at zero dose to slope of the corresponding LQ model. We derive an explicit formula for this ratio and we show that it corresponds very closely to experimental observations. Finally, we can identify the dependence of this ratio on the surviving fraction at 2 Gy. It was speculated in the literature that such a relation exists. Our theoretical analysis will help to more systematically identify the HRS in cell lines and opens doors to analyze its use in cancer treatment.\n\nPACS and mathematical subject classification numbers as needed.

cancer biology↗

bioRxiv2016

Aggregation of biological particles under radial directional guidance.

Many biological environments display an almost radially-symmetric structure, allowing proteins, cells or animals to move in an oriented fashion. Motivated by specific examples of cell movement in tissues, pigment protein movement in pigment cells and animal movement near watering holes, we consider a class of radially-symmetric anisotropic diffusion problems, which we call the star problem. The corresponding diffusion tensor D(x) is radially symmetric with isotropic diffusion at the origin. We show that the anisotropic geometry of the environment can lead to strong aggregations and blow-up at the origin. We classify the nature of aggregation and blow-up solutions and provide corresponding numerical simulations. A surprising element of this strong aggregation mechanism is that it is entirely based on geometry and does not derive from chemotaxis, adhesion or other well known aggregating mechanisms. We use these aggregate solutions to discuss the process of pigmentation changes in animals, cancer invasion in an oriented fibrous habitat (such as collagen fibres), and sheep distributions around watering holes.\n\nJTB classification21.050, 21.160, 52.250, 71.060

systems biology↗

bioRxiv2016

A Reaction-Diffusion Model for Radiation-InducedBystander Effects

We develop and analyze a reaction-diffusion model to investigate the dynamics of the lifespan of a bystander signal emitted when cells are exposed to radiation. Experimental studies by Mothersill and Seymour 1997, using malignant epithelial cell lines, found that an emitted bystander signal can still cause bystander effects in cells even 60h after its emission. Several other experiments have also shown that the signal can persist for months and even years. Also, bystander effects have been hypothesized as one of the factors responsible for the phenomenon of low-dose hyper-radiosensitivity and increased radioresistance (HRS/IRR). Here, we confirm this hypothesis with a mathematical model, which we fit to Joiners data on HRS/IRR in a T98G glioma cell line. Furthermore, we use phase plane analysis to understand the full dynamics of the signals lifespan. We find that both single and multiple radiation exposure can lead to bystander signals that either persist temporarily or permanently. We also found that, in an heterogeneous environment, the size of the domain exposed to radiation and the number of radiation exposures can determine whether a signal will persist temporarily or permanently. Finally, we use sensitivity analysis to identify those cell parameters that affect the signals lifespan and the signal-induced cell death the most.

cancer biology↗