Tumor proliferation and diffusion on percolation clusters

Percolation theory for the recognition of patterns in topographic images of the cortical activity

Electroencephalogram (EEG) is one of the mechanisms used to collect complex data. Its use includes evaluating neurological disorders, investigating brain function and correlations between EEG signals and real or imagined movements. The Topographic Image of Cortical Activity (TICA) records obtained by the EEG make it possible to observe, through color discrimination, the cortical areas that represent greater or lesser activity. Percolation Theory (PT) reveals properties on the aspects of fluid spreading from a central point, these properties being related to the aspects of the medium, topological characteristics and ease of penetration of a fluid in materials. The hypothesis presented so far considers that synaptic activities originate in points and spread from them, causing different areas of the brain to interact in a diffusive associative behavior, generating electric and magnetic fields by the currents that spread through the brain tissue and have an effect on the scalp sensors. Brain areas spatially separated create large-scale dynamic networks that are described by functional and effective connectivity. The proposition is that this phenomenon behaves like a fluidic spreading, so we can use the PT, through the topological analysis we detect specific signatures related to neural phenomena that manifest changes in the behavior of synaptic diffusion. This signature must be characterized by the Fractal Dimension (FD) values of the scattering clusters, these values will be used as properties in the k-Nearest Neighbors (kNN) method, an TICA will be categorized according to the degree of similarity to the preexisting patterns. In this context, our hypothesis will consolidate as a more computational resource in the service of medicine and another way that opens with the possibility of analysis and detailed inferences of the brain through TICA that go beyond a simply visual observation, as it happens in the present day.

In vivo mimicking model for solid tumor towards hydromechanics of tissue deformation and creation of necrosis

The present work addresses transvascular and interstitial fluid transport inside a solid tumor surrounded by normal tissue (close to an in vivo mimicking setup). In general, biological tissues behave like a soft porous material and show mechanical behavior towards the fluid motion through the interstitial space. In general, forces like viscous drag that are associated with the fluid flow may compress the tissue material. On the macroscopic level, we try to model the motion of fluids and macromolecules through the interstitial space of solid tumor and the normal tissue layer. The transvascular fluid transport is assumed to be governed by modified Starling's law. The poroelastohydrodynamics (interstitial hydrodynamics and the deformation of tissue material) inside the tumor and normal tissue regions is modeled using linearized biphasic mixture theory. Correspondingly, the velocity distribution of fluid is coupled to the displacement field of the solid phase (mainly cellular phase and extracellular matrix) in both the normal and tumor tissue regions. The corresponding velocity field is used within the transport reaction equation for fluids and macromolecules through interstitial space to get the overall solute (e.g., nutrients, drug, and other macromolecules) distribution. This study justifies that the presence of the normal tissue layer plays a significant role in delaying/assisting necrosis inside the tumor tissue. It is observed that the exchange process of fluids and macromolecules across the interface of the tumor and normal tissue affects the effectiveness factor corresponding to the tumor tissue.