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Peer-reviewedCC BYJournal of The Royal Society Interface

Optimal control for anti-abeta treatment in Alzheimer’s disease using a reaction–diffusion model

  • Sun Lee1
  • Chiu‐Yen Kao2
  • Zhiyuan Li3
  • Tingting Dan4
  • Guorong Wu A5
  • Wenrui Hao1
5 affiliations
  1. 1Department of Mathematics, The Pennsylvania State University 1 , State College, PA, USA
  2. 2Department of Mathematical Sciences, Claremont McKenna College 2 , Claremont, CA, USA
  3. 3Department of Mathematics, The Ohio State University 3 , Columbus, OH, USA
  4. 4Department of Psychiatry, The University of North Carolina at Chapel Hill 4 , Chapel Hill, NC, USA
  5. 5Departments of Psychiatry, Computer Science, Statistics and Operations Research, The University of North Carolina at Chapel Hill 5 , Chapel Hill, NC, USA
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Abstract

Alzheimer's disease (AD) is a progressive neurodegenerative disorder that severely impairs survival and quality of life. While anti-amyloid beta (Aβ) therapies can slow disease progression, their efficacy depends on personalized dosing that maximizes benefits and minimizes risks, such as amyloid-related imaging abnormalities (ARIA). Mathematical modelling offers a powerful tool for understanding AD dynamics and optimizing treatment, yet most models focus solely on temporal behaviour, overlooking spatial heterogeneity within the brain. In this study, we propose a spatially explicit reaction-diffusion model to describe Aβ plaque dynamics. We formulate an optimal control problem to minimize plaque concentration while balancing therapeutic efficacy and treatment risk. Under reasonable assumptions, we establish well-posedness and uniqueness of the optimal solution. A finite element method (FEM)-based numerical framework is developed to compute personalized treatment strategies. Our model is calibrated using longitudinal Aβ positron emission tomography (PET) data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), enabling estimation of patient-specific parameters, such as growth rate and effective diffusivity. Results show that optimized treatment strategies consistently outperform constant dosing regimens across patient groups, achieving substantial reductions in cumulative amyloid burden while minimizing side effects. This integrated, data-driven framework advances personalized, spatially informed therapeutic optimization for AD.

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Cite

BibTeXRIS
BibTeX
@article{lee2026optimal,
  title = {{Optimal control for anti-abeta treatment in Alzheimer’s disease using a reaction–diffusion model}},
  author = {Sun Lee and Chiu‐Yen Kao and Zhiyuan Li and Tingting Dan and Guorong Wu A and Wenrui Hao},
  journal = {Journal of The Royal Society Interface},
  year = {2026},
  month = jul,
  doi = {10.1098/rsif.2025.1158},
  url = {https://doi.org/10.1098/rsif.2025.1158},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Optimal control for anti-abeta treatment in Alzheimer’s disease using a reaction–diffusion model
AU  - Sun Lee
AU  - Chiu‐Yen Kao
AU  - Zhiyuan Li
AU  - Tingting Dan
AU  - Guorong Wu A
AU  - Wenrui Hao
PY  - 2026
DA  - 2026/07/08
JO  - Journal of The Royal Society Interface
DO  - 10.1098/rsif.2025.1158
UR  - https://doi.org/10.1098/rsif.2025.1158
AB  - Alzheimer's disease (AD) is a progressive neurodegenerative disorder that severely impairs survival and quality of life. While anti-amyloid beta (Aβ) therapies can slow disease progression, their efficacy depends on personalized dosing that maximizes benefits and minimizes risks, such as amyloid-related imaging abnormalities (ARIA). Mathematical modelling offers a powerful tool for understanding AD dynamics and optimizing treatment, yet most models focus solely on temporal behaviour, overlooking spatial heterogeneity within the brain. In this study, we propose a spatially explicit reaction-diffusion model to describe Aβ plaque dynamics. We formulate an optimal control problem to minimize plaque concentration while balancing therapeutic efficacy and treatment risk. Under reasonable assumptions, we establish well-posedness and uniqueness of the optimal solution. A finite element method (FEM)-based numerical framework is developed to compute personalized treatment strategies. Our model is calibrated using longitudinal Aβ positron emission tomography (PET) data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), enabling estimation of patient-specific parameters, such as growth rate and effective diffusivity. Results show that optimized treatment strategies consistently outperform constant dosing regimens across patient groups, achieving substantial reductions in cumulative amyloid burden while minimizing side effects. This integrated, data-driven framework advances personalized, spatially informed therapeutic optimization for AD.
SN  - 1742-5662
SN  - 1742-5689
ER  -