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Dynamic Spatial Treatment Effects in Neurotransmitter Diffusion: Applications to Movement Disorders

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  • Kikuchi, Tatsuru

Abstract

Traditional spatial treatment effect methods impose arbitrary boundaries between treated and control regions, obscuring how treatments spread through neural tissue. We develop a continuous functional framework deriving explicit treatment boundaries from diffusion physics, eliminating discretization artifacts while providing testable predictions. Our approach applies partial differential equations to neurotransmitter diffusion, unifying spatial scales from synaptic spillover (micrometers) to volume transmission (centimeters). We validate using synthetic data calibrated to established neuroscience parameters across five conditions: healthy controls, dystonia, Parkinson's disease, Alzheimer's disease, and acute ischemia. Results demonstrate systematic disease-induced boundary alterations. Dystonia reduces treatment reach by 16.3\% (p $

Suggested Citation

  • Kikuchi, Tatsuru, 2025. "Dynamic Spatial Treatment Effects in Neurotransmitter Diffusion: Applications to Movement Disorders," MPRA Paper 126720, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:126720
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    File URL: https://mpra.ub.uni-muenchen.de/126720/1/MPRA_paper_126720.pdf
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • I10 - Health, Education, and Welfare - - Health - - - General
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health

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