In this paper we describe how an ordinary differential equation model of corticothalamic interactions may be obtained from a more general system of delay differential equations. We demonstrate that transitions to epileptic dynamics via changes in system parameters are qualitatively the same as in the original model with delay, as well as demonstrating that the onset of epileptic activity may arise due to regions of bistability. Hence, the model presents in one unique framework, two competing theories for the genesis of epileptiform activity. Similarities between model transitions and clinical data are presented and we argue that statistics obtained from, and a parameter estimation of this model may be a potential means of classifying and predicting the onset and offset of seizure activity.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.79.021911 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Radiogenomic explainable AI with neural ordinary differential equation for identifying post-SRS brain metastasis radionecrosis.
Med Phys
January 2025
Deparment of Radiation Oncology, Duke University, Durham, North Carolina, USA.
Background: Stereotactic radiosurgery (SRS) is widely used for managing brain metastases (BMs), but an adverse effect, radionecrosis, complicates post-SRS management. Differentiating radionecrosis from tumor recurrence non-invasively remains a major clinical challenge, as conventional imaging techniques often necessitate surgical biopsy for accurate diagnosis. Machine learning and deep learning models have shown potential in distinguishing radionecrosis from tumor recurrence.
View Article and Find Full Text PDFMathematical model and stability of SWCNT- and MWCNT-based nanofluid flow with thermal and chemically reactive effects inside a porous vertical cone.
Front Chem
January 2025
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan.
This study investigates the significance of single-walled (SWCNTs) and multi-walled (MWCNTs) carbon nanotubes with a convectional fluid (water) over a vertical cone under the influences of chemical reaction, magnetic field, thermal radiation and saturated porous media. The impact of heat sources is also examined. Based on the flow assumptions, the fundamental flow equations are modeled as partial differential equations (PDEs).
View Article and Find Full Text PDFPredicting biomass conversion and COD removal in wastewater treatment by phototrophic bacteria with interpretable machine learning.
J Environ Manage
January 2025
School of Energy & Environmental Engineering, Hebei University of Technology, Tianjin, 300401, China. Electronic address:
Photosynthetic bacteria (PSB) excel in wastewater treatment by removing pollutants and generating biomass but are challenging to optimize due to complex operational and environmental interactions. Neural Ordinary Differential Equations, Elastic Net, Stacking, and Categorical Boosting were applied as artificial intelligence methods to predict chemical oxygen demand (COD) removal efficiency, biomass productivity, biomass yield, and energy yield. Among these, the Stacking model demonstrated superior predictive performance across all targets.
View Article and Find Full Text PDFRacial and Geographic Disparities in Colorectal Cancer Incidence and Associated County-Level Risk Factors in Mississippi, 2003-2020: An Ecological Study.
Cancers (Basel)
January 2025
Program in Public Health, Stony Brook Medicine, Stony Brook, NY 11794, USA.
Introduction: Colorectal cancer (CRC) is the third most commonly diagnosed cancer in the United States (U.S.).
View Article and Find Full Text PDFEfficient stochastic simulation of piecewise-deterministic Markov processes and its application to the Morris-Lecar model of neural dynamics.
Biol Cybern
January 2025
Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24-25, 14476, Potsdam, Germany.
Piecewise-deterministic Markov processes combine continuous in time dynamics with jump events, the rates of which generally depend on the continuous variables and thus are not constants. This leads to a problem in a Monte-Carlo simulation of such a system, where, at each step, one must find the time instant of the next event. The latter is determined by an integral equation and usually is rather slow in numerical implementation.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!