About

Andreas Buttenschoen is an assistant professor in the Department of Mathematics and Statistics at the University of Massachusetts Amherst. He is an applied mathematician focused on building bridges between the mathematical, computational, and biological sciences. His work involves identifying key biological problems, contributing to theoretical mathematical foundations, and developing advanced computational tools. Buttenschoen's research interests include mathematical biology, non-local partial differential equations, numerical and analytical bifurcation theory, reaction-diffusion equations, and computational biology. He is particularly interested in collective cell behaviors, which he views as swarms with a twist, considering cells as entities with spatial extent and complex interactions that go beyond simple attraction-repulsion. His studies encompass biological processes such as wound healing, embryogenesis, immune response, and cancer metastasis. Buttenschoen employs mathematical modeling and computational biology to uncover universal principles that shape biological tissues, analyzing interactions across multiple temporal and spatial scales using various mathematical frameworks. These include differential equations for large populations and cell-based models for tracking individual cell behavior and forces. He holds a Ph.D. from the University of Alberta, obtained in 2017, and his research encompasses mathematical biology, non-local PDEs, bifurcation theory, reaction-diffusion equations, and computational biology.

Research topics

• Biology
• Anatomy
• Classical mechanics
• Medicine
• Cell biology
• Physics
• Chemistry
• Biochemistry
• Biophysics
• Pathology

Selected publications

• The interplay between biomechanics and cell kinetics explains the spatial pattern in liver fibrosis

  bioRxiv (Cold Spring Harbor Laboratory) · 2025-08-02 · 1 citations

  preprintOpen access

  Abstract The formation of liver fibrosis patterns, characterized by excess extracellular matrix (ECM), is a complex process that is difficult to investigate experimentally. To complement experimental approaches, we developed a digital twin (DT) model to simulate the pattern formation of septal and biliary fibrosis, the two common forms of liver fibrosis. This model is based on iterative calibration with experiments from animal models treated with the hepatotoxic substance CCl 4 (septal form) and Abcb4-knockout mice (biliary form). Septal fibrosis is characterized by ECM accumulation along the connective line between the central veins of neighboring liver lobules, while biliary fibrosis is marked by a scattered ECM pattern within the portal fields. This mechanistic DT model includes the components of hepatocytes (Heps ♠ ), hepatic stellate cells (HSCs), macrophages (Mphs), bile duct (BD) cells, collagen fibers secreted by activated HSCs, blood vessels, and cell-cell communication. It allows for the integration and simultaneous modulation of multiple hypothesized mechanisms underlying fibrotic wall formation. The model simulates the formation of liver fibrosis pattern and demonstrates that ECM distribution results from the pattern of cell death zones and biomechanical compression due to cell proliferation. "Healthy" Heps proliferate to compensate for cell loss. In septal fibrosis, where the cell death zones are several cells thick, the proliferating Heps surrounding a zone mechanically compress the deposited collagen network. After a transient phase of collagen scattered between/around Heps, the ECM eventually adopts a sharp, "wall"-like structure. Whereas, in biliary fibrosis, the pattern of cell death is more scattered, leading to a corresponding scattered ECM pattern. In this case, a pattern of scattered distributed collagen forms without transitioning to a sharp wall. Notably, the failure of fibrotic wall formation in endothelial cell-specific GATA4 LSEC-KO mice, due to the disrupted pattern of CYP2E1-expressing Heps, validates our DT model. In conclusion, the DT model provided a deeper understanding of liver fibrosis pattern formation. It enabled comparison between simulated outcomes of hypothesized mechanisms and experimental data. Additionally, it guided the design of validation experiments and enabled the identification of optimal strategies for drug testing and extrapolation to humans.

  PublisherOA PDFDOI

• A digital liver twin demonstrating the interplay between biomechanics and cell kinetics can explain fibrotic scar formation

  Research Square (Research Square) · 2024

  • Cell biology
  • Chemistry
  • Medicine
  PublisherOA PDFDOI

• Spatio-temporal mathematical model describing the interplay between biomechanics and cell kinetics during fibrotic scar formation

  Zeitschrift für Gastroenterologie · 2023

  • Pathology
  • Biophysics
  • Cell biology

  Liver fibrosis is characterized by the accumulation of overexpressed extracellular matrix (ECM) proteins as a result of exposure of tissue to repeated damage. There are distinct patterns of fibrosis such as collagen septa (from tissue sections called “fibrotic walls”) connecting two central veins due to toxic injury. In the past decade, some computational models using either rule-based models 2D or partial differential equations of liver fibrosis to study the cellular and molecular mechanisms. Within a 3D single-cell-based model resolving tissue microarchitecture, we now incorporate the collagen fiber mechanics to address fibrosis formation. The same model approach already simulated regeneration after acute liver damage hence fibrosis formation is a further step towards a digital liver twin. The pattern-characterizing parameters in this study were obtained through image analysis of images from animal experiments that were compared to human histopathology. We explored alternative model mechanisms and parameters for a detailed in silico study of possible mechanism on the formation of characteristic fibrotic walls in liver fibrosis.

  PublisherDOI

• A digital liver twin demonstrating the interplay between biomechanics and cell kinetics can explain fibrotic scar formation

  HAL (Le Centre pour la Communication Scientifique Directe) · 2022

  • Biology
  • Physics
  • Anatomy
  PublisherOA PDF

• Cops-on-the-dots: The linear stability of crime hotspots for a 1-D reaction-diffusion model of urban crime

  European Journal of Applied Mathematics · 2019-11-11 · 14 citations

  article1st authorCorresponding

  In a singularly perturbed limit, we analyse the existence and linear stability of steady-state hotspot solutions for an extension of the 1-D three-component reaction-diffusion (RD) system formulated and studied numerically in Jones et. al. [Math. Models. Meth. Appl. Sci., 20 , Suppl., (2010)], which models urban crime with police intervention. In our extended RD model, the field variables are the attractiveness field for burglary, the criminal population density and the police population density. Our model includes a scalar parameter that determines the strength of the police drift towards maxima of the attractiveness field. For a special choice of this parameter, we recover the ‘cops-on-the-dots’ policing strategy of Jones et. al., where the police mimic the drift of the criminals towards maxima of the attractiveness field. For our extended model, the method of matched asymptotic expansions is used to construct 1-D steady-state hotspot patterns as well as to derive nonlocal eigenvalue problems (NLEPs) that characterise the linear stability of these hotspot steady states to ${\cal O}$ (1) timescale instabilities. For a cops-on-the-dots policing strategy, we prove that a multi-hotspot steady state is linearly stable to synchronous perturbations of the hotspot amplitudes. Alternatively, for asynchronous perturbations of the hotspot amplitudes, a hybrid analytical–numerical method is used to construct linear stability phase diagrams in the police vs. criminal diffusivity parameter space. In one particular region of these phase diagrams, the hotspot steady states are shown to be unstable to asynchronous oscillatory instabilities in the hotspot amplitudes that arise from a Hopf bifurcation. Within the context of our model, this provides a parameter range where the effect of a cops-on-the-dots policing strategy is to only displace crime temporally between neighbouring spatial regions. Our hybrid approach to study the NLEPs combines rigorous spectral results with a numerical parameterisation of any Hopf bifurcation threshold. For the cops-on-the-dots policing strategy, our linear stability predictions for steady-state hotspot patterns are confirmed from full numerical PDE simulations of the three-component RD system.

  PublisherDOI

• Non-Local Cell Adhesion Models: Derivation, Bifurcations, and Boundary Conditions

  cIRcle (University of British Columbia) · 2019-01-01

  articleOpen access1st authorCorresponding

  In both normal tissue and disease states, cells interact with one another, and other tissue components using cellular adhesion proteins. These interactions are fundamental in determining tissue fates, and the outcomes of normal development, wound healing and cancer metastasis. Traditionally continuum models (PDEs) of tissues are based on purely local interactions. However, these models ignore important nonlocal effects in tissues, such as long-ranged adhesion forces between cells. For this reason, a mathematical description of cell adhesion had remained a challenge until 2006, when Armstrong et. al. proposed the use of an integro-partial differential equation (iPDE) model. The initial success of the model was the replication of the cell-sorting experiments of Steinberg (1963). Since then this approach has proven popular in applications to embryogenesis (Armstrong et. al. 2009), zebrafish development (Painter et. al. 2015), and cancer modelling (e.g. Painter et. al. 2010, Domschke et. al. 2014, Bitsouni et. al. 2018). While popular, the mathematical properties of this non-local term are not yet well understood. I will begin this talk by outlining, the first systematic derivation of non-local (iPDE) models for adhesive cell motion. The derivation relies on a framework that allows the inclusion of cell motility and the cell polarization vector in s stochastic space-jump process. The derivation's significance is that, it allows the inclusion of cell-level properties such as cell-size, cell protrusion length or adhesion molecule densities into account. In the second part, I will present the results of our study of the steady-states of a non-local adhesion model on an interval with periodic boundary conditions. The significance of the steady-states is that these are observed in experiments (e.g. cell-sorting). Combining global bifurcation results pioneered by Rabinowitz, equivariant bifurcation theory, and the mathematical properties of the non-local term, we obtain a global bifurcation result for the branches of non-trivial solutions. Using the equationâ s symmetries the solutions of a branch are classified by the derivativeâ s number of zeros. We further show that the non-local operatorâ s properties determine whether a sub or super-critical pitchfork bifurcation occurs. Finally, I want to demonstrate how the equation's derivation from a stochastic random walk can be extended to derive different non-local adhesion operators describing cell-boundary adhesion interactions. The significance is that in the past, boundary conditions for non-local equations were avoided, because their construction is subtle. I will describe the three challenges we encountered, and their solutions.

  PublisherOA PDFDOI

Frequent coauthors

• Yueni Li

  University Hospital Heidelberg

  6 shared

• Jan G. Hengstler

  Leibniz Research Centre for Working Environment and Human Factors

  6 shared

• Pia Erdoesi

  Heidelberg University

  6 shared

• Niels Grabe

  Heidelberg University

  5 shared

• Steven Dooley

  Heidelberg University

  4 shared

• Matthias P. Ebert

  University Medical Centre Mannheim

  4 shared

• Philipp‐Sebastian Koch

  University Medical Centre Mannheim

  4 shared

• Sina W. Kürschner

  University Hospital Heidelberg

  4 shared

Education

• Phd Applied Mathematics, Mathematical and Statistical Sciences

  University of Alberta

  2017