Dynamic Simulations of Parkinson’s Disease and ALS Propagation in the Brain: A Reaction-Diffusion on Brain Networks Approach

Zaidan Al Arsyad, Faiz Munir, Amanda Allawiyah, Tiara Sania, Irvan Hartawan, Prama Putra

Abstract


Neurodegenerative diseases,  such  as  Parkinson’s Disease  (PD)  and  Amyotrophic Lateral  Sclerosis  (ALS), progressively degrade neural systems, leading to considerable cognitive functional disorders. It is consequential to comprehend how these diseases spread within the brain to develop precise diagnoses and interventions. This study uses a reaction-diffusion model on a human brain network model to explore and replicate the actual dynamic progression of PD and ALS. By incorporating diffusion processes with empirical brain network data, we simulated the disease’s progression through various regions. Our results show unique propagation patterns for PD and ALS and the effect of different network models on disease transmission.  The structure of brain neural networks plays a vital function in neurodegeneration and offers insights that lead to early detection and focused treatments. This study presents a potential viewpoint on handling and interfering in neurodegenerative diseases by perceiving their dependency on brain neural connectivity.

Keywords


Reaction-diffusion; Graph laplacian; Brain connectome; Parkinson’s; Amyotropic lateral sclerosis

Full Text:

PDF

References


C. R. Jack et al., “Prevalence of biologically vs clinically defined alzheimer spectrum entities using the national institute on aging–alzheimers association research framework,” JAMA neurology, vol. 76, no. 10, pp. 1174–1183, 2019. DOI:10.1001/jamaneurol.2019.1971

C. R. Jack et al., “Tracking pathophysiological processes in alzheimer’s disease: an updated hypothetical model of dynamic biomarkers,” The lancet neurology, vol. 12, no. 2, pp. 207–216, 2013. DOI:10.1016/S1474-4422(12)70291-0

J. Sun et al., “Hospital-treated infections in early-and mid-life and risk of alzheimers disease, parkinsons disease, and amyotrophic lateral sclerosis: a nationwide nested case-control study in sweden,” PLoS Medicine, vol. 19, no. 9, p. e1004092, 2022. DOI:10.1371/journal.pmed.1004092

S. Y. Pang et al., “The interplay of aging, genetics and environmental factors in the pathogenesis of parkinsons disease,” Translational Neurodegeneration, vol. 8, no. 1, p. 23, 2019. DOI:10.1186/s40035-019-0165-9

K. A. Johnson et al., “Brain imaging in alzheimer disease,” Cold Spring Harbor perspectives in medicine, vol. 2, no. 4, p. a006213, 2012. DOI:10.1101/cshperspect.a006213

M. Jucker and L. C. Walker, “Propagation and spread of pathogenic protein assemblies in neurodegenerative diseases,” Nature neuroscience, vol. 21, no. 10, pp. 1341–1349, 2018. DOI:10.1038/s41593-018-0238-6

M. Jucker and L. C. Walker, “Self-propagation of pathogenic protein aggregates in neurodegenerative diseases,” Nature, vol. 501, no. 7465, pp. 45–51, 2013. DOI:10.1038/nature12481

A. Liu et al., “Unraveling the intercellular communication disruption and key pathways in alzheimers disease: an integrative study of single-nucleus transcriptomes and genetic association,” Alzheimer’s Research & Therapy, vol. 16, no. 1, p. 3, 2024. DOI:10.1186/s13195-023-01372-w

O. Schmitt et al., “Reaction-diffusion models in weighted and directed connectomes,” PLoS Computational Biology, vol. 18, no. 10, p. e1010507, 2022. DOI:10.1371/journal.pcbi.1010507

H. Braak et al., “Staging of brain pathology related to sporadic parkinsons disease,” Neurobiology of aging, vol. 24, no. 2, pp. 197–211, 2003. DOI:10.1016/s0197-4580(02)00065-9

C. Tian et al., “Erythrocytic α-synuclein as a potential biomarker for parkinsons disease,” Translational neurodegeneration, vol. 8, no. 1, p. 15, 2019. DOI:10.1186/s40035-019-0155-y

J. Brettschneider et al., “Stages of ptdp-43 pathology in amyotrophic lateral sclerosis,” Annals of neurology, vol. 74, no. 1, pp. 20–38, 2013. DOI:10.1002/ana.23937

J. Weickenmeier et al., “A physics-based model explains the prion-like features of neurodegeneration in alzheimers disease, parkinsons disease, and amyotrophic lateral sclerosis,” Journal of the Mechanics and Physics of Solids, vol. 124, pp. 264–281, 2019. DOI:10.1016/j.jmps.2018.10.013

J. Weickenmeier, E. Kuhl, and A. Goriely, “Multiphysics of prionlike diseases: Progression and atrophy,” Physical review letters, vol. 121, no. 15, p. 158101, 2018. DOI:10.1103/PhysRevLett.121.158101

P. Putra et al., “Front propagation and arrival times in networks with application to neurodegenerative diseases,” SIAM Journal on Applied Mathematics, vol. 83, no. 1, pp. 194–224, 2023. DOI:10.1137/21M1467547

P. Putra et al., “Braiding braak and braak: Staging patterns and model selection in network neurodegeneration,” Network Neuroscience, vol. 5, no. 4, pp. 929–956, 2021. DOI:10.1162/netn_a_00208

G. S. Brennan and A. Goriely, “A network aggregation model for amyloid-β dynamics and treatment of alzheimers diseases at the brain scale,” Journal of Mathematical Biology, vol. 90, no. 2, p. 22, 2025. DOI:10.1007/s00285-024-02179-5

G. S. Brennan et al., “The role of clearance in neurodegenerative diseases,” SIAM Journal on Applied Mathematics, vol. 84, no. 3, pp. S172–S198, 2023. DOI:10.1137/22M1487801

M. Goedert, M. Masuda-Suzukake, and B. Falcon, “Like prions: the propagation of aggregated tau and α-synuclein in neurodegeneration,” Brain, vol. 140, no. 2, pp. 266–278, 2017. DOI:10.1093/brain/aww230

A. Raj et al., “Combined model of aggregation and network diffusion recapitulates alzheimer’s regional tau-positron emission tomography,” Brain connectivity, vol. 11, no. 8, pp. 624–638, 2021. DOI:10.1089/brain.2020.0841

A. Raj et al., “Network diffusion model of progression predicts longitudinal patterns of atrophy and metabolism in alzheimers disease,” Cell reports, vol. 10, no. 3, pp. 359–369, 2015. DOI:10.1016/j.celrep.2014.12.034

A. Raj, A. Kuceyeski, and M. Weiner, “A network diffusion model of disease progression in dementia,” Neuron, vol. 73, no. 6, pp. 1204–1215, 2012. DOI:10.1016/j.neuron.2011.12.040

T. B. Thompson et al., “Protein-protein interactions in neurodegenerative diseases: A conspiracy theory,” PLoS computational biology, vol. 16, no. 10, p. e1008267, 2020. DOI:10.1371/journal.pcbi.1008267

L. M. Smith et al., “α-synuclein and anti-α-synuclein antibodies in parkinsons disease, atypical parkinson syndromes, rem sleep behavior disorder, and healthy controls,” PLoS One, vol. 7, no. 12, p. e52285, 2012. DOI:10.1371/journal.pone.0052285

B. Szalkai et al., “Parameterizable consensus connectomes from the human connectome project: the budapest reference connectome server v3. 0,” Cognitive neurodynamics, vol. 11, no. 1, pp. 113–116, 2017. DOI:10.1007/s11571-016-9407-z

B. Szalkai et al., “The budapest reference connectome server v2. 0,” Neuroscience Letters, vol. 595, pp. 60–62, 2015. DOI:10.1016/j.neulet.2015.03.071

M. Xia, J. Wang, and Y. He, “Brainnet viewer: a network visualization tool for human brain connectomics,” PloS one, vol. 8, no. 7, p. e68910, 2013. DOI:10.1371/journal.pone.0068910




DOI: https://doi.org/10.37905/jjbm.v6i4.30557

Copyright (c) 2025 Zaidan Al Arsyad, Faiz Munir, Amanda Allawiyah, Tiara Sania, Irvan Hartawan, Prama Putra

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Jambura Journal of Biomathematics (JJBM) has been indexed by:

EDITORIAL OFFICE OF JAMBURA JOURNAL OF BIOMATHEMATICS

 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango 96554, Gorontalo, Indonesia
 Email: [email protected]
 Jambura Journal of Biomathematics (JJBM) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Powered by Public Knowledge Project OJS.