Tau Story, Part One: inferring a connectome from a tau-spreading model of Alzheimer’s disease
Poster No:
198
Submission Type:
Abstract Submission
Authors:
Andre Altmann1, Elinor Thompson2, Neil Oxtoby3
Institutions:
1UCL, London, Other, 2UCL, London, United Kingdom, 3University College London,, London, United Kingdom
First Author:
Co-Author(s):
Introduction:
Understanding structural connectivity of the brain is important for neuroscience in both health and disease. The limitations of tractography (e.g., many false positive connections) represent a particular challenge to this field [1,2], especially in spreading models of Alzheimer's disease pathology. Such models typically use a DWI-based connectome and a differential equation describing pathology spread along this connectome, estimating model parameters by fitting to observed data such as standardised uptake value ratio (SUVR) from PET imaging [3,4]. Here we invert the problem and estimate a connectome based on observed patterns of pathology spread: the "spreadome".
Methods:
We used a neural ordinary differential equation (NODE) model [5] to estimate the Laplacian (L) of the spreadome from cross-sectional observations. The NODE implemented the standard network diffusion formula, dx/dt=-L x, as the forward function. The loss function of the model has three components (i) prediction loss: difference between predictions and observed SUVRs (ii) orthogonality loss: enforcing orthogonality of L's eigenvectors; and (iii) sparsity loss. For optimization we used Adam [6]; with batch size 300, learning rate 0.01 for 2000 epochs.
We performed experiments on both simulated and real data. For simulations we used the left hemisphere of the structural connectome obtained from DWI [7] and retained the top 10% of connections (86 of 861 connections). Next, we fixed the entorhinal cortex as seed region and sampled 1000 time points in [0.0, 15.0]. The spread from the seed region was simulated using the network diffusion formula: x(t)= e(-t L)x(0), where x(0) is the initial condition, L the Laplacian, and t is time. We tested five different initializations: ground truth, randomly changing 5%, 10%, or 15% of edges of the ground truth, and random. Performance was measured using the area under the ROC curve (AUC) between edges in the ground truth and the estimated network. Experiments were repeated 5 times.
For real data we used regional tau PET SUVR values from ADNI. First, using 1151 scans on 399 participants (2.9 ± 1.3 visits each), we computed a pseudo disease time "tau time" using a DE model [8] of SUVR in the middletemporal gyrus. Next, we trained our NODE with tau time and SUVR in 84 brain regions (DK atlas) of participants' most recent PET scans. Optimization was initialized with DWI tractography and run for 2500 epochs with batch size 50. We benchmarked the spreadome against the DWI-connectome in predicting tau accumulation amyloid and tau positive participants in ADNI as previously described [4]. Performance is measured using Spearman's rank correlation.
We performed experiments on both simulated and real data. For simulations we used the left hemisphere of the structural connectome obtained from DWI [7] and retained the top 10% of connections (86 of 861 connections). Next, we fixed the entorhinal cortex as seed region and sampled 1000 time points in [0.0, 15.0]. The spread from the seed region was simulated using the network diffusion formula: x(t)= e(-t L)x(0), where x(0) is the initial condition, L the Laplacian, and t is time. We tested five different initializations: ground truth, randomly changing 5%, 10%, or 15% of edges of the ground truth, and random. Performance was measured using the area under the ROC curve (AUC) between edges in the ground truth and the estimated network. Experiments were repeated 5 times.
For real data we used regional tau PET SUVR values from ADNI. First, using 1151 scans on 399 participants (2.9 ± 1.3 visits each), we computed a pseudo disease time "tau time" using a DE model [8] of SUVR in the middletemporal gyrus. Next, we trained our NODE with tau time and SUVR in 84 brain regions (DK atlas) of participants' most recent PET scans. Optimization was initialized with DWI tractography and run for 2500 epochs with batch size 50. We benchmarked the spreadome against the DWI-connectome in predicting tau accumulation amyloid and tau positive participants in ADNI as previously described [4]. Performance is measured using Spearman's rank correlation.
Results:
Figure 1 shows our DEM-estimated 30 years of "tau time" used to train our NODE model. The zero point is anchored at SUVR=1.25. On simulated data, models initialized based on ground truth matrices reached median AUC>0.75 (Figure 2A). Figure 2B shows the inferred tau spreadome on PET SUVR data from 399 subjects. The spreadome (Spearman's ρ=0.745) outperforms the DWI-connectome (ρ=0.599) in predicting group-averaged tau spread in amyloid and tau positive participants.
·Figure 1
·Figure 2
Conclusions:
Inferring the most likely tau-spreading pathway from cross-sectional observations is a challenging inverse problem. Simulations confirmed that a NODE-based approach can recover the ground truth network structure when the initialization is reasonably close to the truth (AUC 0.8 with up to 15% flipped edges). Experiments on real data demonstrated that the connectivity modelled using the spreadome provides superior performance for estimating the spread of tau through the brain compared to structural connectivity based on DWI. Future work requires validation of the approach in other datasets. Our model provides a novel means to investigate brain connectivity via disease progression modelling.
Disorders of the Nervous System:
Neurodegenerative/ Late Life (eg. Parkinson’s, Alzheimer’s) 1
Modeling and Analysis Methods:
Connectivity (eg. functional, effective, structural) 2
Keywords:
Data analysis
Degenerative Disease
Machine Learning
1|2Indicates the priority used for review
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[2] Schroder, Anna, et al. "False-positive potential of tractography-derived connections improves network reconstruction for disease spreading models." ISMRM (2021).
[3] Raj, Ashish, Amy Kuceyeski, and Michael Weiner. "A network diffusion model of disease progression in dementia." Neuron 73.6 (2012): 1204-1215.
[4] Thompson, Elinor, et al. "Combining multimodal connectivity information improves modelling of pathology spread in Alzheimer’s disease." Imaging Neuroscience 2 (2024): 1-19.
[5] Chen, Ricky TQ, et al. "Neural ordinary differential equations." Advances in neural information processing systems 31 (2018).
[6] Kingma, Diederik P. "Adam: A method for stochastic optimization." arXiv preprint arXiv:1412.6980 (2014).
[7] Royer, Jessica, et al. "An open MRI dataset for multiscale neuroscience." Scientific data 9.1 (2022): 569.
[8] Oxtoby, Neil P., et al. "Data-driven models of dominantly-inherited Alzheimer’s disease progression." Brain 141.5 (2018): 1529-1544.