# Using integral equations to capture spatiotemporal relations in the brain

> **NIH NIH R16** · IDAHO STATE UNIVERSITY · 2024 · $174,794

## Abstract

Project Summary
Medical recordings contain dynamical information that can provide quantitative
pathological fingerprints that prove crucial to correct diagnostic. Brain recordings are
particularly important for cognitive studies, as the state of the brain at a single instant is
not sufficient to determine cognition, which is a highly complex dynamical process.
Consequently, in order to correctly diagnose the severity of cognitive pathologies, it is
important to analyze brain dynamics through their recordings. Machine Learning (ML)
algorithms based on static approaches tend to miss the dynamical spatiotemporal
relations of the recordings, while ML methods based on local equations do not take into
account the long-distance spatiotemporal relations. Here, we propose to use ML methods
based on nonlocal equations and operators that allow us to extract a dynamical fingerprint
of the brain, and use this to develop diagnostic continuous scores (spectra of severity).
The use of nonlocal equations such as integral equations and integro-differential
equations to model the brain has been pioneered decades ago. However, these studies
have never been extended to ML methods, except in our recent preliminary studies. Our
focus, therefore, is to apply such methodologies to model (predict) brain dynamics, and
employ the learned models to extract the model states (self-attention) that characterize
brain cognition. These states will therefore be used to develop diagnostic scores.

## Key facts

- **NIH application ID:** 10937859
- **Project number:** 1R16GM154734-01
- **Recipient organization:** IDAHO STATE UNIVERSITY
- **Principal Investigator:** Emanuele Zappala
- **Activity code:** R16 (R01, R21, SBIR, etc.)
- **Funding institute:** NIH
- **Fiscal year:** 2024
- **Award amount:** $174,794
- **Award type:** 1
- **Project period:** 2024-08-15 → 2028-07-31

## Primary source

NIH RePORTER: https://reporter.nih.gov/project-details/10937859

## Citation

> US National Institutes of Health, RePORTER application 10937859, Using integral equations to capture spatiotemporal relations in the brain (1R16GM154734-01). Retrieved via AI Analytics 2026-06-12 from https://api.ai-analytics.org/grant/nih/10937859. Licensed CC0.

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