Computational modelling of pathogenic protein behaviour-governing mechanisms in the brain

Most neurodegenerative diseases are caused by pathogenic proteins. Pathogenic protein behaviour is governed by neurobiological mechanisms which cause them to spread and accumulate in the brain, leading to cellular death and eventually atrophy. Patient data suggests atrophy loosely follows a number of spatiotemporal patterns, with different patterns associated with each neurodegenerative disease variant. It is hypothesised that the behaviour of different pathogenic protein variants is governed by different mechanisms, which could explain the pattern variety. Machine learning approaches take advantage of the pattern predictability for differential diagnosis and prognosis, but are unable to reveal new information on the underlying mechanisms, which are still poorly understood. We propose a framework where computational models of these mechanisms were created based on neurobiological literature. Competing hypotheses regarding the mechanisms were modelled and the outcomes evaluated against empirical data of Alzheimer’s disease. With this approach, we are able to characterise the impact of each mechanism on the neurodegenerative process. We also demonstrate how our framework could evaluate candidate therapies

Spectral design of signal-adapted tight frames on graphs

Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph signals based on notions of scale (e.g., coarse to fine). The graph spectrum is more irregular than for conventional domains; i.e., it is influenced by graph topology, and, therefore, assumptions about spectral representations of graph signals are not easy to make. Here, we propose a tight frame design that is adapted to the graph Laplacian spectral content of a given class of graph signals. The design exploits the ensemble energy spectral density, a notion of spectral content of the given signal set that we determine either directly using the graph Fourier transform or indirectly through approximation using a decomposition scheme. The approximation scheme has the benefit that (i) it does not require diagonalization of the Laplacian matrix, and (ii) it leads to a smooth estimate of the spectral content. A prototype system of spectral kernels each capturing an equal amount of energy is defined. The prototype design is then warped using the signal set’s ensemble energy spectral density such that the resulting subbands each capture an equal amount of ensemble energy. This approach accounts at the same time for graph topology and signal features, and it provides a meaningful interpretation of subbands in terms of coarse-to-fine representations