Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2006.12322

Modeling glioma invasion with anisotropy- and hypoxia-triggered motility enhancement: from subcellular dynamics to macroscopic PDEs with multiple taxis

G. Corbin·C. Engwer·A. Klar·J. Nieto·J. Soler·C. Surulescu·M. Wenske
View original source ↗Read source document ↗Export metadata ↓

Abstract

We deduce a model for glioma invasion making use of DTI data and accounting for the dynamics of brain tissue being actively degraded by tumor cells via excessive acidity production, but also according to the local orientation of tissue fibers. Our approach has a multiscale character: we start with a microscopic description of single cell dynamics including biochemical and/or biophysical effects of the tumor microenvironment, translated on the one hand into cell stress and corresponding forces and on the other hand into receptor binding dynamics; these lead on the mesoscopic level to kinetic equations involving transport terms w.r.t. all kinetic variables and eventually, by appropriate upscaling, to a macroscopic reaction-diffusion equation for glioma density with multiple taxis, coupled to (integro-)differential equations characterizing the evolution of acidity and macro- and mesoscopic tissue. Our approach also allows for a switch between fast and slower moving regimes, %diffusion- and drift-dominated regimes, according to the local tissue anisotropy. We perform numerical simulations to investigate the behavior of solutions w.r.t. various scenarios of tissue dynamics and the dominance of each of the tactic terms, also suggesting how the model can be used to perform a numerical necrosis-based tumor grading or support radiotherapy planning by dose painting. We also provide a discussion about alternative ways of including cell level environmental influences in such multiscale modeling approach, ultimately leading in the macroscopic limit to (multiple) taxis.

Explore related subjects

q-bio.TOcs.NAmath.NA

Keep this discovery

BibTeXRIS

G. Corbin, C. Engwer, A. Klar, J. Nieto, J. Soler, C. Surulescu, M. Wenske. 2020-06-22. Modeling glioma invasion with anisotropy- and hypoxia-triggered motility enhancement: from subcellular dynamics to macroscopic PDEs with multiple taxis. https://arxiv.org/abs/2006.12322

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Adaptive therapy under parametric, structural, and measurement uncertainty

Adaptive therapy has emerged as a promising treatment strategy that exploits within-tumour competition to delay disease progression. Implementation, however, typically relies on indirect measurements of tumour burden and must account for potentially substantial patient heterogeneity. In this work, we capture patient-to-patient variability, parameter uncertainty, and imperfect biomarker measurements with a mathematical and statistical model that we calibrate to clinical prostate cancer data using a Bayesian inference framework. We use the resulting virtual cohort to demonstrate that, within the simple but now well-established Lotka-Volterra-based model, adaptive therapy robustly improves time-to-progression for the subset of patients that are predicted to eventually progress by the model. To account for other risk factors associated with larger tumour volumes, we introduce a new metric based on the risk of metastasis that demonstrates how adaptive therapy may be disadvantageous when sustained tumour burden is also considered. Given the ubiquity of uncertainty in oncology, we then describe several future modelling directions that also capture uncertainty in the temporal evolution of the underlying tumour or biomarker dynamics. Finally, we demonstrate how model misspecification and non-identifiability can lead to unreliable predictions, especially if uncertainty is inadequately captured.

q-bio.TO↗
arXiv2026

Head Impact Characterization and Cellular Response of a Live-neuron cell-integrated Biomechanical Full-body Surrogate Model

In this study, we develop a novel integrated framework that links the impact response with cellular dynamics using a live-neuron cell-integrated biomechanical full-body surrogate model. The impact event is simulated by allowing the surrogate model to fall from controlled seated release angles of 30-degree, 60-degree, and 90-degree. Three vertically stacked cell-culture Petri dishes, each containing live SH-SY5Y neuroblastoma cells, were placed inside the head of a commercially available surrogate model. The dynamic response of the impact event was evaluated using acceleration measurements from six accelerometers, comprising three sensors mounted on the head surface and three embedded in series with the cell stacks, along with kinematic measurements of the fall and deformation of the head model. In parallel, an OpenSim-based modified musculoskeletal model was used to simulate the fall experiment. We found that variation in contact stiffness produced the largest change in the predicted head acceleration in the simulation. When the cellular response and the measured accelerations are compared, oxidative stress and cell viability showed trends consistent with the regional acceleration and angle of fall. At the 90-degree fall, where median peak linear accelerations ranged from 170-258g, and the maximum headform deformation was approximately 9.4 mm, oxidative stress increased to approximately twice that of the control sample. We also quantified the cellular drift of SH-SY5Y cells, which is focal in nature for the 90-degree impact condition. The corresponding fall scenarios were also simulated in OpenSim and a preliminary calibration relationship was developed to compare the kinematic responses of the physical surrogate and musculoskeletal model. Finally, the framework provides a basis for relating experimental surrogate measurements to human head-neck response during impact.

q-bio.TO↗
arXiv2026

History Matters: Damage-Mediated Amplification of Brain Deformation and Injury Risk under Repeated Head Impacts

Computational head models are typically applied to isolated impacts, leaving repeated head loading largely unexplored. An Ogden-Roxburgh Mullins damage formulation was implemented in a high-fidelity finite element head model to represent loading-history-dependent softening during cyclic brain-tissue deformation. Repeated-loading histories derived from mixed martial arts head-impact data were applied and compared with damage-free hyperelastic (HE) and linear visco-hyperelastic (LVHE) model variants. Under five identical single-axis cycles, Mullins-type softening progressively increased strain and strain rate metrics relative to the HE model. Mullins-based injury probabilities progressively exceeded strain-based HE predictions and diverged from unchanged kinematics-based predictions, indicating that neglecting prior softening may underestimate injury risk. In a randomized twenty-cycle multiaxial sequence, cycles of similar kinematic intensity produced different deformation and injury-risk estimates depending on prior softening. HE and LVHE models predicted higher injury probabilities initially, whereas the Mullins-based model produced the largest later-cycle estimates and highest probability of at least one injury over the sequence. Regional amplification depended on loading direction and prior softening, with no direction-independent trend among brain substructures. Gyral elements exhibited higher cumulative maximum principal strain than sulcal elements, which showed greater amplification relative to initial responses. These findings demonstrate that short-term damage-mediated softening can substantially amplify tissue deformation and injury-risk estimates beyond damage-free head models under the same loading histories. Further experimental characterization of cyclic brain-tissue softening is needed to improve models of repeated head loading and traumatic brain injury.

q-bio.TO↗