arXiv subjects

Steffen Lange

Publications and source records attributed to Steffen Lange.

14 recordsLinked to original sources

arXiv2025

Image segmentation of treated and untreated tumor spheroids by Fully Convolutional Networks

Multicellular tumor spheroids (MCTS) are advanced cell culture systems for assessing the impact of combinatorial radio(chemo)therapy. They exhibit therapeutically relevant in-vivo-like characteristics from 3D cell-cell and cell-matrix interactions to radial pathophysiological gradients related to proliferative activity and nutrient/oxygen supply, altering cellular radioresponse. State-of-the-art assays quantify long-term curative endpoints based on collected brightfield image time series from large treated spheroid populations per irradiation dose and treatment arm. Here, spheroid control probabilities are documented analogous to in-vivo tumor control probabilities based on Kaplan-Meier curves. This analyses require laborious spheroid segmentation of up to 100.000 images per treatment arm to extract relevant structural information from the images, e.g., diameter, area, volume and circularity. While several image analysis algorithms are available for spheroid segmentation, they all focus on compact MCTS with clearly distinguishable outer rim throughout growth. However, treated MCTS may partly be detached and destroyed and are usually obscured by dead cell debris. We successfully train two Fully Convolutional Networks, UNet and HRNet, and optimize their hyperparameters to develop an automatic segmentation for both untreated and treated MCTS. We systematically validate the automatic segmentation on larger, independent data sets of spheroids derived from two human head-and-neck cancer cell lines. We find an excellent overlap between manual and automatic segmentation for most images, quantified by Jaccard indices at around 90%. For images with smaller overlap of the segmentations, we demonstrate that this error is comparable to the variations across segmentations from different biological experts, suggesting that these images represent biologically unclear or ambiguous cases.

cs.CV↗

arXiv2025

Generalized, sublethal damage-based mathematical approach for improved modeling of clonogenic survival curve flattening upon hyperthermia, radiotherapy, and beyond

Mathematical modeling can offer valuable insights into the behavior of biological systems upon treatment. Different mathematical models have been designed to predict the efficacy of hyperthermia (HT), radiotherapy (RT), or their combination. However, approaches capable of modeling cell survival from shared general principles for both mono-treatments and their co-application are rare. Moreover, some cell cultures show dose-dependent saturation in response to HT or RT, manifesting in survival curve flattening. An advanced survival model must, therefore, appropriately reflect such behavior. We propose a mathematical approach to model the effect of both treatments based on the general principle of sublethal damage (SLD) accumulation for the induction of cell death and irreversible proliferation arrest. Our approach extends Jung's model on heat-induced cellular inactivation by incorporating dose-dependent recovery rates that delineate changes in SLD restoration. The resulting unified model (Umodel) accurately describes HT and RT survival outcomes, applies to simultaneous thermoradiotherapy modeling, and is particularly suited to reproduce survival curve flattening phenomena. We demonstrate the Umodel's robust performance (R2>0.95) based on numerous clonogenic survival datasets from the literature and experiments. The proposed Umodel allows the use of a single mathematical function based on generalized SLD accumulation principles with implemented radiosensitization, regardless of energy type or mechanism of action. It reproduces various clonogenic survival curve patterns, including flattening, thus encompassing treatment variability and potentially better reflecting tumor responses. Our approach opens options for further model development and therapy outcome predictions of sequential treatments in different orders and recovery intervals.

physics.bio-ph↗

arXiv2024

It depends: Varieties of defining growth dependence

Many socio-economic systems require positive economic growth rates to function properly. Given uncertainty about future growth rates and increasing evidence that economic growth is a driver of social and environmental crises, these growth dependencies pose serious societal challenges. In recent years, more and more researchers have thus tried to identify growth-dependent systems and develop policies to reduce their growth dependence. However, the concept of 'growth dependence' still lacks a consistent definition and operationalization, which impedes more systematic empirical and theoretical research. This article proposes a simple but powerful framework for defining and operationalizing the concept of 'growth dependence' across socio-economic systems. We provide a general definition consisting of four components that can be specified for different empirical cases: (1) the system under investigation, (2) the unit of measurement of growth, (3) the level of growth and (4) the relevant functions or properties of the system under investigation. According to our general definition, a socio-economic system is growth-dependent if it requires a long-term positive growth rate in terms of a unit of economic measurement to maintain all its functions or properties that are relevant within the chosen normative framework. To illustrate the usefulness of our scheme, we apply it to three areas at the heart of the existing literature on growth dependence: employment, social insurance systems and public finance. These case studies demonstrate that whether or not a system is growth-dependent hinges not only on the empirical properties of the system itself but also on the specification of the concept of growth dependence. Our framework enables coherent, robust and effective definitions and research questions, fostering comparability of findings across different cases and disciplines.

econ.GN↗

arXiv2024

Minimal cellular automaton model with heterogeneous cell sizes predicts epithelial colony growth

Regulation of cell proliferation is a crucial aspect of tissue development and homeostasis and plays a major role in morphogenesis, wound healing, and tumor invasion. A phenomenon of such regulation is contact inhibition, which describes the dramatic slowing of proliferation, cell migration and individual cell growth when multiple cells are in contact with each other. While many physiological, molecular and genetic factors are known, the mechanism of contact inhibition is still not fully understood. In particular, the relevance of cellular signaling due to interfacial contact for contact inhibition is still debated. Cellular automata (CA) have been employed in the past as numerically efficient mathematical models to study the dynamics of cell ensembles, but they are not suitable to explore the origins of contact inhibition as such agent-based models assume fixed cell sizes. We develop a minimal, data-driven model to simulate the dynamics of planar cell cultures by extending a probabilistic CA to incorporate size changes of individual cells during growth and cell division. We successfully apply this model to previous in-vitro experiments on contact inhibition in epithelial tissue: After a systematic calibration of the model parameters to measurements of single-cell dynamics, our CA model quantitatively reproduces independent measurements of emergent, culture-wide features, like colony size, cell density and collective cell migration. In particular, the dynamics of the CA model also exhibit the transition from a low-density confluent regime to a stationary postconfluent regime with a rapid decrease in cell size and motion. This implies that the volume exclusion principle, a mechanical constraint which is the only inter-cellular interaction incorporated in the model, paired with a size-dependent proliferation rate is sufficient to generate the observed contact inhibition.

q-bio.CB↗

arXiv2022

Is cell segregation like oil and water: asymptotic versus transitory regime

Segregation of different cell types is a crucial process for the pattern formation in tissues, in particular during embryogenesis. Since the involved cell interactions are complex and difficult to measure individually in experiments, mathematical modelling plays an increasingly important role to unravel the mechanisms governing segregation. The analysis of these theoretical models focuses mainly on the asymptotic behavior at large times, in a steady regime and for large numbers of cells. Most famously, cell-segregation models based on the minimization of the total surface energy, a mechanism also driving the demixing of immiscible fluids, are known to exhibit asymptotically a particular algebraic scaling behavior. However, it is not clear, whether the asymptotic regime of the numerical models is relevant at the spatio-temporal scales of actual biological processes and in-vitro experiments. By developing a mapping between cell-based models and experimental settings, we are able to directly compare previous experimental data to numerical simulations of cell segregation quantitatively. We demonstrate that the experiments are reproduced by the transitory regime of the models rather than the asymptotic one. Our work puts a new perspective on previous model-driven conclusions on cell segregation mechanisms.

q-bio.CB↗

arXiv2022

Modeling age-specific incidence of colon cancer via niche competition

Cancer development is a multistep process often starting with a single cell in which a number of epigenetic and genetic alterations have accumulated thus transforming it into a tumor cell. The progeny of such a single benign tumor cell expands in the tissue and can at some point progress to malignant tumor cells until a detectable tumor is formed. The dynamics from the early phase of a single cell to a detectable tumor with billions of tumor cells are complex and still not fully resolved, not even for the well-known prototype of multistage carcinogenesis, the adenoma-adenocarcinoma sequence of colorectal cancer. Mathematical models of such carcinogenesis are frequently tested and calibrated based on reported age-specific incidence rates of cancer, but they usually require calibration of four or more parameters due to the wide range of processes these models aim to reflect. We present a cell-based model, which focuses on the competition between wild-type and tumor cells in colonic crypts, with which we are able reproduce epidemiological incidence rates of colon cancer. Additionally, the fraction of cancerous tumors with precancerous lesions predicted by the model agree with clinical estimates. The correspondence between model and reported data suggests that the fate of tumor development is majorly determined by the early phase of tumor growth and progression long before a tumor becomes detectable. Due to the focus on the early phase of tumor development, the model has only a single fit parameter, the time scale set by an effective replacement rate of stem cells in the crypt. We find this effective rate to be considerable smaller than the actual replacement rate, which implies that the time scale is limited by the processes succeeding clonal conversion of crypts.

q-bio.TO↗

arXiv2021

Surfing along concentration filaments: sperm chemotaxis in physiological shear flows

Many motile biological cells navigate along concentration gradients of signaling molecules: This chemotaxis guides for instance sperm cells from marine invertebrates, which have to find egg cells in the ocean. While chemotaxis has been intensively studied for idealized conditions of rotationally symmetric gradients in still water, natural gradients are usually distorted, e.g., by turbulent flows in the ocean. Recent experiments and direct numerical simulations with sperm cells and bacteria surprisingly suggest the existence of an optimal flow strength at which chemotaxis is more effective than for still water. We use sperm chemotaxis in simple shear flow as a prototypical example to understand the origin of such an optimal flow strength theoretically: We quantify how flow accelerates spreading of signaling molecules released by the egg, but distorts the resulting concentration field into long and thin filaments. The competition between these two effects sets an optimal flow strength that maximizes sperm-egg encounter. We characterize how sperm cells `surf' along concentration filaments, typical for scalar turbulence, revealing a general navigation paradigm in the presence of flow. We compare both simulation and theory with previous experimental results and find good agreement.

physics.bio-ph↗

arXiv2018

3D billiards: visualization of regular structures and trapping of chaotic trajectories

The dynamics in three-dimensional billiards leads, using a Poincaré section, to a four-dimensional map which is challenging to visualize. By means of the recently introduced 3D phase-space slices an intuitive representation of the organization of the mixed phase space with regular and chaotic dynamics is obtained. Of particular interest for applications are constraints to classical transport between different regions of phase space which manifest in the statistics of Poincaré recurrence times. For a 3D paraboloid billiard we observe a slow power-law decay caused by long-trapped trajectories which we analyze in phase space and in frequency space. Consistent with previous results for 4D maps we find that: (i) Trapping takes place close to regular structures outside the Arnold web. (ii) Trapping is not due to a generalized island-around-island hierarchy. (iii) The dynamics of sticky orbits is governed by resonance channels which extend far into the chaotic sea. We find clear signatures of partial transport barriers. Moreover, we visualize the geometry of stochastic layers in resonance channels explored by sticky orbits.

nlin.CD↗

arXiv2017

Optimal decision making for sperm chemotaxis in the presence of noise

For navigation, microscopic agents such as biological cells rely on noisy sensory input. In cells performing chemotaxis, such noise arises from the stochastic binding of signaling molecules at low concentrations. Using chemotaxis of sperm cells as application example, we address the classic problem of chemotaxis towards a single target. We reveal a fundamental relationship between the speed of chemotactic steering and the strength of directional fluctuations that result from the amplification of noise in the chemical input signal. This relation implies a trade-off between slow, but reliable, and fast, but less reliable, steering. By formulating the problem of optimal navigation in the presence of noise as a Markov decision process, we show that dynamic switching between reliable and fast steering substantially increases the probability to find a target, such as the egg. Intriguingly, this decision making would provide no benefit in the absence of noise. Instead, decision making is most beneficial, if chemical signals are above detection threshold, yet signal-to-noise ratios of gradient measurements are low. This situation generically arises at intermediate distances from a target, where signaling molecules emitted by the target are diluted, thus defining a `noise zone' that cells have to cross. Our work addresses the intermediate case between well-studied perfect chemotaxis at high signal-to-noise ratios close to a target, and random search strategies in the absence of navigation cues, e.g. far away from a target. Our specific results provide a rational for the surprising observation of decision making in recent experiments on sea urchin sperm chemotaxis. The general theory demonstrates how decision making enables chemotactic agents to cope with high levels of noise in gradient measurements by dynamically adjusting the persistence length of a biased persistent random walk.

physics.bio-ph↗

arXiv2016

What is the mechanism of power-law distributed Poincaré recurrences in higher-dimensional systems?

The statistics of Poincaré recurrence times in Hamiltonian systems typically shows a power-law decay with chaotic trajectories sticking to some phase-space regions for long times. For higher-dimensional systems the mechanism of this power-law trapping is still unknown. We investigate trapped orbits of a generic 4D symplectic map in phase space and frequency space and find that, in contrast to 2D maps, the trapping is (i) not due to a hierarchy in phase space. Instead, it occurs at the surface of the regular region, (ii) outside of the Arnold web. The chaotic dynamics in this sticky region is (iii) dominated by resonance channels which reach far into the chaotic region: We observe (iii.a) clear signatures of some kind of partial transport barriers and conjecture (iii.b) a stochastic process with an effective drift along resonance channels. These two processes lay the basis for a future understanding of the mechanism of power-law trapping in higher-dimensional systems.

nlin.CD↗

arXiv2016

Bifurcations of families of 1D-tori in 4D symplectic maps

The regular structures of a generic 4D symplectic map with a mixed phase space are organized by one-parameter families of elliptic 1D-tori. Such families show prominent bends, gaps, and new branches. We explain these features in terms of bifurcations of the families when crossing a resonance. For these bifurcations no external parameter has to be varied. Instead, the longitudinal frequency, which varies along the family, plays the role of the bifurcation parameter. As an example we study two coupled standard maps by visualizing the elliptic and hyperbolic 1D-tori in a 3D phase-space slice, local 2D projections, and frequency space. The observed bifurcations are consistent with analytical predictions previously obtained for quasi-periodically forced oscillators. Moreover, the new families emerging from such a bifurcation form the skeleton of the corresponding resonance channel.

nlin.CD↗

arXiv2016

Do Mature Economies Grow Exponentially?

Most models that try to explain economic growth indicate exponential growth paths. In recent years, however, a lively discussion has emerged considering the validity of this notion. In the empirical literature dealing with drivers of economic growth, the majority of articles is based upon an implicit assumption of exponential growth. Few scholarly articles have addressed this issue so far. In order to shed light on this issue, we estimate autoregressive integrated moving average time series models based on Gross Domestic Product Per Capita data for 18 mature economies from 1960 to 2013. We compare the adequacy of linear and exponential growth models and conduct several robustness checks. Our fndings cast doubts on the widespread belief of exponential growth and suggest a deeper discussion on alternative economic grow theories.

econ.GN↗

arXiv2014

Global structure of regular tori in a generic 4D symplectic map

For the case of generic 4D symplectic maps with a mixed phase space we investigate the global organization of regular tori. For this we compute elliptic 1-tori of two coupled standard maps and display them in a 3D phase-space slice. This visualizes how all regular 2-tori are organized around a skeleton of elliptic 1-tori in the 4D phase space. The 1-tori occur in two types of one-parameter families: (a) Lyapunov families emanating from elliptic-elliptic periodic orbits, which are observed to exist even far away from them and beyond major resonance gaps, and (b) families originating from rank-1 resonances. At resonance gaps of both types of families either (i) periodic orbits exist, similar to the Poincare-Birkhoff theorem for 2D maps, or (ii) the family may form large bends. In combination these results allow for describing the hierarchical structure of regular tori in the 4D phase space analogously to the islands-around-islands hierarchy in 2D maps.

nlin.CD↗

arXiv2014

Visualization and comparison of classical structures and quantum states of 4D maps

For generic 4D symplectic maps we propose the use of 3D phase-space slices which allow for the global visualization of the geometrical organization and coexistence of regular and chaotic motion. As an example we consider two coupled standard maps. The advantages of the 3D phase-space slices are presented in comparison to standard methods like 3D projections of orbits, the frequency analysis, and a chaos indicator. Quantum mechanically, the 3D phase-space slices allow for the first comparison of Husimi functions of eigenstates of 4D maps with classical phase space structures. This confirms the semi-classical eigenfunction hypothesis for 4D maps.

nlin.CD↗