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Related Concept Videos

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Alzheimer's Disease (AD) is a continually advancing neurodegenerative disorder, distinguished by escalating memory loss, cognitive dysfunction, and dementia. The disease unfolds in three stages: preclinical, mild cognitive impairment (MCI), and dementia. Its onset is insidious, and the progression gradual, with the cause not well explained by other disorders.
The clinical diagnosis of AD hinges on the presence of memory and other cognitive impairments. Biomarkers, such as changes in Aβ and tau...
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Related Experiment Video

Updated: May 25, 2026

DeepOmicsAE: Representing Signaling Modules in Alzheimer's Disease with Deep Learning Analysis of Proteomics, Metabolomics, and Clinical Data
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Model Validation Pipeline Against Longitudinal Alzheimer's Biomarker Data.

Rabha W Ibrahim1,2, Mona Hmoud AlSheikh3

  • 1Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences (SIMATS), Chennai, Tamil Nadu, 602105, India. rabhaibrahim@yahoo.com.

Neuroinformatics
|May 23, 2026
PubMed
Summary
This summary is machine-generated.

This study models Alzheimer's disease using a novel fractional-order approach. The model accurately simulates disease progression and demonstrates how treatments can reduce tau buildup and protect neurons.

Keywords:
[Formula: see text]-Gamma functionAlzheimer’s diseaseAtangana–Baleanu operatorFractional calculusMemory effectNeuron regenerationStability analysis

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Area of Science:

  • Mathematical Biology
  • Computational Neuroscience
  • Biophysics

Background:

  • Alzheimer's disease is characterized by the accumulation of amyloid-beta and tau proteins.
  • Understanding the spatiotemporal dynamics of these proteins is crucial for developing effective treatments.
  • Fractional calculus offers a powerful framework for modeling complex biological processes with memory effects.

Purpose of the Study:

  • To develop a novel fractional-order model for Alzheimer's disease (AD) progression.
  • To investigate the spatiotemporal dynamics of amyloid-beta and tau proteins using a generalized Atangana-Baleanu-Caputo (ABC) operator.
  • To simulate the impact of therapeutic interventions on AD pathology and neuron survival.

Main Methods:

  • Development of a fractional-order mathematical model incorporating a [Formula: see text]-generalized Atangana-Baleanu-Caputo (ABC) operator.
  • Analysis of fractional parameters (α, [Formula: see text], τ) influencing memory depth, kernel deformation, and temporal scaling.
  • Numerical simulations to explore disease spread, nonlocal interactions, and the effects of a treatment term with drug diffusion and decay.

Main Results:

  • Intermediate fractional orders ([Formula: see text]) yield biologically realistic propagation delays in disease spread.
  • Lower [Formula: see text] values accelerate tau diffusion across the brain connectome due to enhanced nonlocal interactions.
  • Increasing the scaling parameter τ slows tau accumulation, simulating effective clearance or treatment efficacy.
  • Sustained low drug decay rates ([Formula: see text]) significantly reduce tau concentrations and preserve neuron populations.

Conclusions:

  • The developed [Formula: see text]-ABC fractional-order model effectively captures the hereditary and memory-dependent aspects of Alzheimer's disease progression.
  • The model provides a flexible computational platform for simulating various therapeutic strategies and predicting disease trajectories.
  • Findings highlight the potential of fractional calculus in understanding complex neurodegenerative diseases and evaluating treatment outcomes.