Abstract
Models of misfolded proteins (MP) aim at discovering the bio-mechanical propagation properties of neurological diseases (ND) by identifying plausible associated dynamical systems. Solving these systems along the full disease trajectory is usually challenging, due to the lack of a well defined time axis for the pathology. This issue is addressed by disease progression models (DPM) where long-term progression trajectories are estimated via time reparametrization of individual observations. However, due to their loose assumptions on the dynamics, DPM do not provide insights on the bio-mechanical properties of MP propagation. Here we propose a unified model of spatio-temporal protein dynamics based on the joint estimation of long-term MP dynamics and time reparameterization of individuals observations. The model is expressed within a Gaussian Process (GP) regression setting, where constraints on the MP dynamics are imposed through non-linear dynamical systems. We use stochastic variational inference on both GP and dynamical system parameters for scalable inference and uncertainty quantification of the trajectories. Experiments on simulated data show that our model accurately recovers prescribed rates along graph dynamics and precisely reconstructs the underlying progression. When applied to brain imaging data our model allows the bio-mechanical interpretation of amyloid deposition in Alzheimer’s disease, leading to plausible simulations of MP propagation, and achieving accurate predictions of individual MP deposition in unseen data.
Data used in preparation of this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Soto, C., Pritzkow, S.: Protein misfolding, aggregation, and conformational strains in neurodegenerative diseases. Nat. Neurosci. 21(10), 1332–1340 (2018)
Jucker, M., Walker, L.C.: Self-propagation of pathogenic protein aggregates in neurodegenerative diseases. Nature 501(7465), 45 (2013)
Carbonell, F., Iturria-Medina, Y., Evans, A.C.: Mathematical modeling of protein misfolding mechanisms in neurological diseases: a historical overview. Front. Neurol. 9, 37 (2018)
Raj, A., Kuceyeski, A., Weiner, M.: A network diffusion model of disease progression in dementia. Neuron 73(6), 1204–1215 (2012)
Oxtoby, N.P., et al.: Data-driven sequence of changes to anatomical brain connectivity in sporadic Alzheimer’s disease. Front. Neurol. 8, 580 (2017)
Zhou, J., Gennatas, E.D., Kramer, J.H., Miller, B.L., Seeley, W.W.: Predicting regional neurodegeneration from the healthy brain functional connectome. Neuron 73(6), 1216–1227 (2012)
Iturria-Medina, Y., Carbonell, F.M., Sotero, R.C., Chouinard-Decorte, F., Evans, A.C.: Multifactorial causal model of brain (dis)organization and therapeutic intervention: application to Alzheimer’s disease. Neuroimage 152, 60–77 (2017)
Cauda, F., et al.: Brain structural alterations are distributed following functional, anatomic and genetic connectivity. Brain 141(11), 3211–3232 (2018)
Young, A.L., et al.: A data-driven model of biomarker changes in sporadic Alzheimer’s disease. Brain 137(9), 2564–2577 (2014)
Lorenzi, M., Filippone, M., Frisoni, G.B., Alexander, D.C., Ourselin, S., Alzheimer’s Disease Neuroimaging Initiative: Probabilistic disease progression modeling to characterize diagnostic uncertainty: application to staging and prediction in Alzheimer’s disease. Neuroimage 190, 56–68 (2019)
Schiratti, J.B., Allassonniàre, S., Colliot, O., Durrleman, S.: A Bayesian mixed-effects model to learn trajectories of changes from repeated manifold-valued observations. J. Mach. Learn. Res. 18(1), 4840–4872 (2017)
Donohue, M.C., et al.: Estimating long-term multivariate progression from short-term data. Alzheimer’s Dementia 10(5), S400–S410 (2014)
Lorenzi, M., Filippone, M.: Constraining the dynamics of deep probabilistic models. In: Proceedings of the 35th International Conference on Machine Learning, vol. 80, pp. 3233–3242 (2018)
Cutajar, K., Bonilla, E. V., Michiardi, P., Filippone, M.: Random feature expansions for deep Gaussian processes. In: Proceedings of the 34th International Conference on Machine Learning, vol. 70, pp. 884–893 (2017)
Thal, D.R., Rub, U., Orantes, M., Braak, H.: Phases of A\({\upbeta }\)-deposition in the human brain and its relevance for the development of AD. Neurology 58(12), 1791–1800 (2002)
Irvine, G.B., El-Agnaf, O.M., Shankar, G.M., Walsh, D.M.: Protein aggregation in the brain: the molecular basis for Alzheimer’s and Parkinson’s diseases. Mol. Med. 14(7–8), 451–464 (2008)
Author information
Authors and Affiliations
Consortia
Corresponding author
Editor information
Editors and Affiliations
1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Garbarino, S., Lorenzi, M., for the Alzheimer’s Disease Neuroimaging Initiative. (2019). Modeling and Inference of Spatio-Temporal Protein Dynamics Across Brain Networks. In: Chung, A., Gee, J., Yushkevich, P., Bao, S. (eds) Information Processing in Medical Imaging. IPMI 2019. Lecture Notes in Computer Science(), vol 11492. Springer, Cham. https://doi.org/10.1007/978-3-030-20351-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-20351-1_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-20350-4
Online ISBN: 978-3-030-20351-1
eBook Packages: Computer ScienceComputer Science (R0)