Multiphysics of Prionlike Diseases: Progression and Atrophy

Abstract

Many neurodegenerative diseases are related to the propagation and accumulation of toxic proteins throughout the brain. The lesions created by aggregates of these toxic proteins further lead to cell death and accelerated tissue atrophy. A striking feature of some of these diseases is their characteristic pattern and evolution, leading to well-codified disease stages visible to neuropathology and associated with various cognitive deficits and pathologies. Here, we simulate the anisotropic propagation and accumulation of toxic proteins in full brain geometry. We show that the same model with different initial seeding zones reproduces the characteristic evolution of different prionlike diseases. We also recover the expected evolution of the total toxic protein load. Finally, we couple our transport model to a mechanical atrophy model to obtain the typical degeneration patterns found in neurodegenerative diseases.

Prion-like spreading of Alzheimer’s disease within the brain’s connectome

“…1, middle. The quantitative comparison of both curves confirms that our network model excellently captures the global characteristics of continuum models for Alzheimer's disesase [13]. The solid lines in Fig.…”

“…Throughout the past decade, three conceptually different models have emerged to simulate the physics of protein misfolding and transport: (i) kinetic growth and fragmentation models to study the interaction of aggregates of different sizes using a set of ordinary differential equations [14]; (ii) network diffusion models to study the prion-like spreading of misfolded proteins [12], continuum model (middle) [13], and network model (bottom). using graph theories [4]; and (iii) reaction-diffusion continuum models to study the spatio-temporal evolution of pathogenic proteins using partial differential equations [15].…”

“…using graph theories [4]; and (iii) reaction-diffusion continuum models to study the spatio-temporal evolution of pathogenic proteins using partial differential equations [15]. Figure 1, middle, shows that continuum models with nonlinear reaction and anisotropic diffusion accurately predict the typical pattern of tau protein misfolding in Alzheimer's disease [13]. This simulation used a Fisher-Kolmogorov type equation [16,17], discretized with 400,000 tetrahedral finite elements and 80,000 degrees of freedom.…”

Local vulnerability and global connectivity jointly shape neurodegenerative disease propagation

“…408 We took advantage of several useful features of agent-based models to provide an 409 understanding of factors involved in disease propagation. Others have applied more 410 traditional diffusion models to Alzheimer's Disease [9,10] and to neurodegeneration 411 more generally [46]; however the agent-based model used here affords us the possibility 412 of testing different mechanisms of disease, likelihood of outbreak, effect of emergent 413 properties (such as the effect of regional neuronal death on subsequent disease The small-world properties of brain networks that favour information flow may also 423 potentiate disease spread [47]. These properties include short path lengths [48] and 424 community structure [49,50], the second of which may potentiate global disease spread 425 by enhancing local, intra-community infection [51].…”

Spatially-extended nucleation-aggregation-fragmentation models for the dynamics of prion-like neurodegenerative protein-spreading in the brain and its connectome

“…The kinetic of aggregation and fragmentation of misfolded proteins and their spatiotemporal evolution can be modeled by either following the total concentration of toxic proteins [16,17], the concentration of healthy and toxic proteins using a heterodimer model [18], or a Smoluchowski-type model where the concentrations of polymers of different sizes are followed independently [19].…”