Mechanistic multiscale modelling of energy metabolism in human astrocytes reveals the impact of morphology changes in Alzheimer's Disease.

Astrocytes with their specialised morphology are essential for brain homeostasis as metabolic mediators between blood vessels and neurons. In neurodegenerative diseases such as Alzheimer's disease (AD), astrocytes adopt reactive profiles with molecular and morphological changes that could lead to the impairment of their metabolic support and impact disease progression. However, the underlying mechanisms of how the metabolic function of human astrocytes is impaired by their morphological changes in AD are still elusive. To address this challenge, we developed and applied a metabolic multiscale modelling approach integrating the dynamics of metabolic energy pathways and physiological astrocyte morphologies acquired in human AD and age-matched control brain samples. The results demonstrate that the complex cell shape and intracellular organisation of energetic pathways determine the metabolic profile and support capacity of astrocytes in health and AD conditions. Thus, our mechanistic approach indicates the importance of spatial orchestration in metabolism and allows for the identification of protective mechanisms against disease-associated metabolic impairments.

Model-based simulations of pulsed laser ablation using an embedded finite element method.

A model of thermal ablation with application to multi-pulsed laser lithotripsy is presented. The approach is based on a one-sided Stefan-Signorini model for thermal ablation, and relies on a level-set function to represent the moving interface between the solid phase and a fictitious gas phase (representing the ablated material). The model is discretized with an embedded finite element method, wherein the interface geometry can be arbitrarily located relative to the background mesh. Nitsche's method is adopted to impose the Signorini condition on the moving interface. A bound constraint is also imposed to deal with thermal shocks that can arise during representative simulations of pulsed ablation with high-power lasers. We report simulation results based on experiments for pulsed laser ablation of wet BegoStone samples treated in air, where Begostone has been used as a phantom material for kidney stone. The model is calibrated against experimental measurements by adjusting the percentage of incoming laser energy absorbed at the surface of the stone sample. Simulation results are then validated against experimental observations for the crater area, volume, and geometry as a function of laser pulse energy and duration. Our studies illustrate how the spreading of the laser beam from the laser fiber tip with concomitantly reduced incident laser irradiance on the damaged crater surface explains trends in both the experimental observations and the model-based simulation results.

Adaptivity in Bayesian Inverse Finite Element Problems: Learning and Simultaneous Control of Discretisation and Sampling Errors.

The local size of computational grids used in partial differential equation (PDE)-based probabilistic inverse problems can have a tremendous impact on the numerical results. As a consequence, numerical model identification procedures used in structural or material engineering may yield erroneous, mesh-dependent result. In this work, we attempt to connect the field of adaptive methods for deterministic and forward probabilistic finite-element (FE) simulations and the field of FE-based Bayesian inference. In particular, our target setting is that of exact inference, whereby complex posterior distributions are to be sampled using advanced Markov Chain Monte Carlo (MCMC) algorithms. Our proposal is for the mesh refinement to be performed in a goal-oriented manner. We assume that we are interested in a finite subset of quantities of interest (QoI) such as a combination of latent uncertain parameters and/or quantities to be drawn from the posterior predictive distribution. Next, we evaluate the quality of an approximate inversion with respect to these quantities. This is done by running two chains in parallel: (i) the approximate chain and (ii) an enhanced chain whereby the approximate likelihood function is corrected using an efficient deterministic error estimate of the error introduced by the spatial discretisation of the PDE of interest. One particularly interesting feature of the proposed approach is that no user-defined tolerance is required for the quality of the QoIs, as opposed to the deterministic error estimation setting. This is because our trust in the model, and therefore a good measure for our requirement in terms of accuracy, is fully encoded in the prior. We merely need to ensure that the finite element approximation does not impact the posterior distributions of QoIs by a prohibitively large amount. We will also propose a technique to control the error introduced by the MCMC sampler, and demonstrate the validity of the combined mesh and algorithmic quality control strategy.