Multiple Sclerosis (MS) is an autoimmune condition leading to the degeneration of brain tissue, occurring when the immune system attacks the myelin sheath surrounding axons of white brain matter thereby disrupting brain signals. This study aimed to evaluate how MS lesions alter stress distribution through grey and white brain matter with lesions (active, chronic, and inactive). A linear viscoelastic model represents the tissue-scale dynamic deformation and time dependency of brain tissue. A Prony series expansion was used to model viscous effects including stress relaxation. An elastic modulus, within the viscoelastic model, was either reduced by 11 % for active lesions, or increased by 35 % increase for inactive lesions. These material properties were then implemented to model healthy tissue, active, chronically inflamed, and inactive lesions. Finite element analysis enabled stress evaluation in response to a peak cyclic displacement of 0.5 mm (1 % strain) with the healthy model acting as a control model. Chronic lesions had the largest effect on stress induced, in terms of high (171 Pa) and low stress (108 Pa). Inactive lesions induced an increase in stress of 11 Pa with areas of low stress (105 Pa). Active lesions caused the least deviation in peak induced stress (7 Pa). In conclusion, a hierarchy in stress induced across the lesion types has been found, from highest to lowest: chronic, inactive and active, with potential implications for lesion progression. In conclusion, MS lesions within brain tissue should model lesions, avoid assuming homogeneity during degeneration, and should distinguish between active and passive lesions.
Alzheimer’s disease is the most common dementia worldwide. Its pathological development is well known to be connected with the accumulation of two toxic proteins: tau protein and amyloid-. Mathematical models and numerical simulations can predict the spreading patterns of misfolded proteins in this context. However, the calibration of the model parameters plays a crucial role in the final solution. In this work, we perform a sensitivity analysis of heterodimer and Fisher–Kolmogorov models to evaluate the impact of the equilibrium values of protein concentration on the solution patterns. We adopt advanced numerical methods such as the IMEX-DG method to accurately describe the propagating fronts in the propagation phenomena in a polygonal mesh of sagittal patient-specific brain geometry derived from magnetic resonance images. We calibrate the model parameters using biological measurements in the brain cortex for the tau protein and the amyloid- in Alzheimer’s patients and controls. Finally, using the sensitivity analysis results, we discuss the applicability of both models in the correct simulation of the spreading of the two proteins.
Statement of significance: Alzheimer’s disease is related to the accumulation of tau protein and amyloid-. Mathematical models to predict the spreading patterns require accurate parameter calibration. In this work, we perform a sensitivity analysis of heterodimer and Fisher–Kolmogorov models to evaluate the impact of the equilibrium values of protein concentration on the solution patterns obtained with advanced numerical simulations on patient-specific brain geometry derived from magnetic resonance images. By using biological measurements in the brain cortex for the proteins in Alzheimer’s patients and controls, we use sensitivity analysis to discuss the applicability of models in simulating protein spreading.

