Articles, chapters & preprints

We extend the framework of measure PDEs on proper spaces introduced in the 2021 monograph to Polish metric spaces. Formulating models on such generic metric spaces facilitates the study on infinite dimensional state spaces or graphs with a combination of discrete and continuous structures.

We combine mathematical modelling and new experimental data on Hydra Notch-signalling in order to better understand, amongst others, how different pathways (particularly Wnt- and Notch-signalling) interplay during Hydra bud formation and constriction.

Based on an intense interplay of previous experimental data, mathematical models, simulations, analytical insights and new experimental data we demonstrate that head and boxy axis formation are driven by two separate pattern formation systems acting on different spatial scales in Hydra.

In this paper we obtain an existence result for a measure differential equation with an additional nonlinear growth/decay term that may change the sign. This generalizes the model setting proposed by Piccoli and Rossi from pedestrian flows to applications in life sciences describing for example birth/death processes of individuals.

In this review we showcase and overview of existing mechanistic models for adult neurogenesis, and the sometimes counter-intuitive insights that they provided. We further outline existing approaches aiming at modelling the single-cell sequencing data. Finally, we discuss what is still missing for understanding dynamics and underlying mechanisms from single-cell data and ponder on how we can link data and processes.

We derive a macroscopic limit for a sharp interface version of a model to investigate pattern formation due to competition of chemical and mechanical forces in biomembranes. We identify sub- and supercrital parameter regimes and show with the autocorrelation function that limit energy leads to the isoperimetric problem in the subcritical regime, which is interpreted to not form fine scale patterns.

Based on energy minimisation methods, our simulations of dynamic membrane behaviour help to understand how cnidocytes are formed in the freshwater polyp Hydra.

In this paper, we further explore the complex interplay between wounding and pattern formation in the context of head and foot regeneration in Hydra.

The Nile perch fishery of Lake Victoria is regulated by restrictions of legal catch and gear sizes. This study provides an assessment of the effectiveness of the the slot size regulation by simulating the Nile perch fishery with a size structured population model. We find that the annual yield could be increased by 17.7% through sparing fish below 50cm.

Kidney development is a complex process. In this work we investigate aspects of this process by simulating them with discrete (individual-based) methods and comparing them with experiments.

A Markov process model of stem cell dynamics during postembryonic organ growth identifies that only few functionally heterogeneous stem cells are actively involved in growing and maintaining fish gills. The functional heterogeneity refers to their division behaviour, such that a cell which has already been activated and divided has a much higher probability to divide again, in contrast to cells that have never divided.

This recent monograph provides the functional analytic background for structured population models in spaces of Radon measures on proper metric spaces.

Using mathematical models of stem cell self-renewal and differentiation, we show that competition in the stem cell niche is a key determinant of acute myeloid leukemia progression. Model-based estimated parameters allow to refine the risk-stratification and are independent predictors of overall and disease-free survival.

It is a collaborative paper with the experimental lab of J.U. Lohmann. We develop a novel spatio-temporal model (partial differential equation with a moving boundary) of a stem-cell based organ growth regulated by diffusive signals and apply it to describe stem cell fate transition in the Arabidopsis meristem development.

It is a collaborative paper with the experimental lab of A. Martin-Villalba. Using mathematical models, we show that age-related changes of neural stem cell numbers can be explained by an age-dependent downregulation of the activation rate from quiescence. The model-based novel hypothesis is then tested experimentally.

We develop and simulate a new mathematical model of spatio-temporal dynamics of biological tissue accounting for mechano-chemical feedbacks, showing its ability for symmetry breaking and pattern formation that goes beyond the classical Turing theory of pattern formation.

We show that diffusion-driven instability may lead to singularities in reaction-diffusion-ODE models.. For a shadow-limit reduction, we prove emergence of spike solutions (a concentration phenomenon).

We establish mathematical models of adult neurogenesis in mouse hippocampus. Integrating mathematical modelling with data analysis, we show for the first time that the activation from quiescence is dynamically regulated during the aging process.

This paper is an example of how rigorous mathematical analysis may help understanding complex dynamics of mathematical models. Deciphering the mechanism of clonal selection in the model of acute leukaemia, the model provides explanation of the clonal selection observed in the course of disease.

We develop a mathematical model of acute leukaemia and apply it to patient data. This allows inferring curves of cancer stem cell parameters of individual patients and link them to disease dynamics and patient prognosis.

This publication is an example of rigorous multiscale analysis to justify and derive complex models.

We introduce a general mathematical model framework for continuous and discrete cell differentiation in measure spaces and show its well-posedness.

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