SUMMARY Patterns of dementia are known to fall into dissociated but dispersed brain networks, suggesting that the disease is transmitted along neuronal pathways rather than by proximity. This view is supported by neuropathological evidence for “prion-like” transsynaptic transmission of disease agents like misfolded tau and beta amyloid. We mathematically model this transmission by a diffusive mechanism mediated by the brain’s connectivity network obtained from tractography of 14 healthy-brain MRIs. Subsequent graph theoretic analysis provides a fully quantitative, testable, predictive model of dementia. Specifically, we predict spatially distinct “persistent modes,” which, we found, recapitulate known patterns of dementia and match recent reports of selectively vulnerable dissociated brain networks. Model predictions also closely match T1-weighted MRI volumetrics of 18 Alzheimer’s and 18 frontotemporal dementia subjects. Prevalence rates predicted by the model strongly agree with published data. This work has many important implications, including dimensionality reduction, differential diagnosis, and especially prediction of future atrophy using baseline MRI morphometrics.

The relationship between anatomic connectivity of large-scale brain networks and their functional connectivity is of immense importance and an area of active research. Previous attempts have required complex simulations which model the dynamics of each cortical region, and explore the coupling between regions as derived by anatomic connections. While much insight is gained from these non-linear simulations, they can be computationally taxing tools for predicting functional from anatomic connectivities. Little attention has been paid to linear models. Here we show that a properly designed linear model appears to be superior to previous non-linear approaches in capturing the brain’s long-range second order correlation structure that governs the relationship between anatomic and functional connectivities. We derive a linear network of brain dynamics based on graph diffusion, whereby the diffusing quantity undergoes a random walk on a graph. We test our model using subjects who underwent diffusion MRI and resting state fMRI. The network diffusion model applied to the structural networks largely predicts the correlation structures derived from their fMRI data, to a greater extent than other approaches. The utility of the proposed approach is that it can routinely be used to infer functional correlation from anatomic connectivity. And since it is linear, anatomic connectivity can also be inferred from functional data. The success of our model confirms the linearity of ensemble average signals in the brain, and implies that their long-range correlation structure may percolate within the brain via purely mechanistic processes enacted on its structural connectivity pathways.

Summary Alzheimer’s Disease pathology (AD) originates in the hippocampus and subsequently spreads to temporal, parietal and prefrontal association cortices in a relatively stereotyped progression. Current evidence attributes this orderly progression to trans-neuronal transmission of misfolded proteins along the projection pathways of affected neurons. A network diffusion model was recently proposed to mathematically predict disease topography resulting from trans-neuronal transmission on the brain’s connectivity network. Here we use this model to predict future patterns of regional atrophy and metabolism from baseline regional patterns of 418 patients. The model accurately predicts end of study regional atrophy and metabolism starting from baseline data, with significantly higher correlation strength than given by the baseline statistics directly. The model’s rate parameter encapsulates overall atrophy progression rate; group analysis revealed this rate to depend on diagnosis as well as baseline CSF biomarker levels. This work helps validate the model as a prognostic tool for Alzheimer’s disease assessment.

How structural connectivity (SC) gives rise to functional connectivity (FC) is not fully understood. Here we mathematically derive a simple relationship between SC measured from diffusion tensor imaging, and FC from resting state fMRI. We establish that SC and FC are related via (structural) Laplacian spectra, whereby FC and SC share eigenvectors and their eigenvalues are exponentially related. This gives, for the first time, a simple and analytical relationship between the graph spectra of structural and functional networks. Laplacian eigenvectors are shown to be good predictors of functional eigenvectors and networks based on independent component analysis of functional time series. A small number of Laplacian eigenmodes are shown to be sufficient to reconstruct FC matrices, serving as basis functions. This approach is fast, and requires no time-consuming simulations. It was tested on two empirical SC/FC datasets, and was found to significantly outperform generative model simulations of coupled neural masses.

Accurate prediction of brain dysfunction caused by disease or injury requires the quantification of resultant neural connectivity changes compared with the normal state. There are many methods with which to assess anatomical changes in structural or diffusion magnetic resonance imaging, but most overlook the topology of white matter (WM) connections that make up the healthy brain network. Here, a new neuroimaging software pipeline called the Network Modification (NeMo) Tool is presented that associates alterations in WM integrity with expected changes in neural connectivity between gray matter regions. The NeMo Tool uses a large reference set of healthy tractograms to assess implied network changes arising from a particular pattern of WM alteration on a region-and network-wise level. In this way, WM integrity changes can be extrapolated to the cortices and deep brain nuclei, enabling assessment of functional and cognitive alterations. Unlike current techniques that assess network dysfunction, the NeMo tool does not require tractography in pathological brains for which the algorithms may be unreliable or diffusion data are unavailable. The versatility of the NeMo Tool is demonstrated by applying it to data from patients with Alzheimer's disease, fronto-temporal dementia, normal pressure hydrocephalus, and mild traumatic brain injury. This tool fills a gap in the quantitative neuroimaging field by enabling an investigation of morphological and functional implications of changes in structural WM integrity.