A multidimensional ODE-based model of Alzheimer’s disease progression

Abstract

Data-driven Alzheimer’s disease (AD) progression models are useful for clinical prediction, disease mechanism understanding, and clinical trial design. Most dynamic models were inspired by the amyloid cascade hypothesis and described AD progression as a linear chain of pathological events. However, the heterogeneity observed in healthy and sporadic AD populations challenged the amyloid hypothesis, and there is a need for more flexible dynamical models that accompany this conceptual shift. We present a statistical model of the temporal evolution of biomarkers and cognitive tests that allows diverse biomarker paths throughout the disease. The model consists of two elements: a multivariate dynamic model of the joint evolution of biomarkers and cognitive tests; and a clinical prediction model. The dynamic model uses a system of ordinary differential equations to jointly model the rate of change of an individual’s biomarkers and cognitive tests. The clinical prediction model is an ordinal logistic model of the diagnostic label. Prognosis and time-to-onset predictions are obtained by computing the clinical label probabilities throughout the forecasted biomarker trajectories. The proposed dynamical model is interpretable, free of one-dimensional progression hypotheses or disease staging paradigms, and can account for the heterogeneous dynamics observed in sporadic AD. We developed the model using longitudinal data from the Alzheimer’s Disease Neuroimaging Initiative. We illustrate the patterns of biomarker rates of change and the model performance to predict the time to conversion from MCI to dementia.

Generative AI unlocks PET insights: brain amyloid dynamics and quantification

“…Another promising extension is the joint modeling of PET amyloid with other dynamical variables, including imaging, biofluid biomarkers, or cognitive assessments. Aβ and tau levels in the blood or cerebrospinal fluid (CSF), neurodegeneration measured as brain atrophy in structural MRI, and metabolism (e.g., FDG PET) could inform more precisely the expected change in brain amyloid levels, and, in turn, amyloid PET could predict the expected progression on these biomarkers (Bossa et al, 2022 ; Bossa and Sahli, 2023 ).…”

“…Given the expected effect of a treatment on slowing amyloid accumulation, the model could be used to simulate PET images from the untreated group from specific populations and predict the effect size. Then, clinical trial costs could be optimized by tuning parameters such as follow-up duration (Bossa and Sahli, 2023 ). Some authors proposed using ODE-based progression models to simulate the effect of amyloid treatments on the disease course (Abi Nader et al, 2021 ).…”

Investigating the Potential Impact of Air Pollution on Alzheimer’s Disease and the Utility of Multidimensional Imaging for Early Detection

“…The part that tracks changes uses equations to follow how an individual's biomarkers and cognitive tests change. 56 When selecting a method for picking out important features, it is essential to choose the one that suits the classification task best. For instance, when comparing Alzheimer's disease to healthy controls, SMML is a better choice than HGM-FS for achieving higher accuracy.…”

“…Researchers have given us insights into a statistical model (two components: one that looks at how biomarkers and cognitive tests change together and another that predicts clinical outcomes) that tracks how biomarkers and cognitive tests change over time in Alzheimer’s disease. The part that tracks changes uses equations to follow how an individual’s biomarkers and cognitive tests change . When selecting a method for picking out important features, it is essential to choose the one that suits the classification task best.…”

Mathematical models of cystic fibrosis as a systemic disease

“…This alignment of change and contributing factors is exactly what ODEs represent. Indeed, ODEs have been used to develop models of diseases many times; examples include models of diabetes (Rathee & Nilam, 2017; Shiang & Kandeel, 2010), liver disease (Remien et al, 2012; Ricken et al, 2015), Parkinson's disease (Bakshi et al, 2019; Qi et al, 2012), Alzheimer's disease (Bossa et al, 2022; Bossa & Sahli, 2023), depression (Dalvi‐Garcia et al, 2021; Demic & Cheng, 2014), schizophrenia (Qi et al, 2011; Rosjat et al, 2014), and cancer (Koziol et al, 2020; Sachs et al, 2001), to name but a few. While very widely used, ODEs are no panacea, and there are various alternatives.…”