We deduce a model for glioma invasion that accounts 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 with respect to all considered 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, according to the local tissue anisotropy. We perform numerical simulations to assess the importance of each tactic term and investigate the influence of two models for tissue dynamics on the tumor shape. We also suggest how the model can be used to perform a numerical necrosis-based tumor grading or support radiotherapy planning by dose painting. Finally, we discuss alternative ways of including cell level environmental influences in such a multiscale modeling approach, ultimately leading in the macroscopic limit to (multiple) taxis.

Starting from a two-scale description involving receptor binding dynamics and a kinetic transport equation for the evolution of the cell density function under velocity reorientations, we deduce macroscopic models for glioma invasion featuring partial differential equations for the mass density and momentum of a population of glioma cells migrating through the anisotropic brain tissue. The proposed first and higher order moment closure methods enable numerical simulations of the kinetic equation. Their performance is then compared to that of the diffusion limit. The approach allows for DTI-based, patient-specific predictions of the tumor extent and its dynamic behavior.

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, 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.

Rigid silos are often under pressure and filled with hazardous materials. Therefore, in very few cases their level can be checked visually. For example, the level of mobile bulk solids silos, which are often used on construction sites, is checked by a worker throwing a stone against the silo and uses the sound to estimate the invisible silo cavity. This method is subjective and shows great errors based on experience. The proposed method should implement this principle robustly by machine application. A sensor unit is to give a mechanical impulse to the outer silo wall with a percussion mechanism and record the resulting sound with a microphone. Just as a human being is able to make an experience-based statement about the filling level of the silo over the growing amount of sounds heard, different machine learning approaches are to be considered in order to imitate this procedure. Machine learning approaches usually aim to find patterns between different sizes. A strongly approximated mathematical model will be used to prove that there is a noisy but demonstrable direct correlation between the level and the acoustic impulse response. This should justify future efforts to find suitable machine learning methods for this application.

No abstract