Correction to 'A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation'.

[This corrects the article DOI: 10.1098/rspa.2018.0231.][This corrects the article DOI: 10.1098/rspa.2018.0231.].

Mechanics of human brain organoids.

Organoids are prototypes of human organs derived from cultured human stem cells. They provide a reliable and accurate experimental model to study the physical mechanisms underlying the early developmental stages of human organs and, in particular, the early morphogenesis of the cortex. Here we propose a mathematical model to elucidate the role played by two mechanisms which have been experimentally proven to be crucial in shaping human brain organoids: the contraction of the inner core of the organoid and the microstructural remodeling of its outer cortex. Our results show that both mechanisms are crucial for the final shape of the organoid and that perturbing those mechanisms can lead to pathological morphologies which are reminiscent of those associated with lissencephaly (smooth brain).

Poynting effect of brain matter in torsion.

We investigate experimentally and model theoretically the mechanical behaviour of brain matter in torsion. Using a strain-controlled rheometer, we perform torsion tests on fresh porcine brain samples. We quantify the torque and the normal force required to twist a cylindrical sample at constant twist rate. Data fitting gives a mean value for the shear modulus of µ = 900 ± 312 Pa and for the second Mooney-Rivlin parameter of c2 = 297 ± 189 Pa, indicative of extreme softness. Our results show that brain always displays a positive Poynting effect; in other words, it expands in the direction perpendicular to the plane of twisting. We validate the experiments with finite element simulations and show that when a human head experiences a twisting motion in the horizontal plane, the brain can experience large forces in the axial direction.

A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation.

The theory of quasi-linear viscoelasticity (QLV) is modified and developed for transversely isotropic (TI) materials under finite deformation. For the first time, distinct relaxation responses are incorporated into an integral formulation of nonlinear viscoelasticity, according to the physical mode of deformation. The theory is consistent with linear viscoelasticity in the small strain limit and makes use of relaxation functions that can be determined from small-strain experiments, given the time/deformation separability assumption. After considering the general constitutive form applicable to compressible materials, attention is restricted to incompressible media. This enables a compact form for the constitutive relation to be derived, which is used to illustrate the behaviour of the model under three key deformations: uniaxial extension, transverse shear and longitudinal shear. Finally, it is demonstrated that the Poynting effect is present in TI, neo-Hookean, modified QLV materials under transverse shear, in contrast to neo-Hookean elastic materials subjected to the same deformation. Its presence is explained by the anisotropic relaxation response of the medium.

Evidence for sub-haplogroup h5 of mitochondrial DNA as a risk factor for late onset Alzheimer's disease.

BACKGROUND: Alzheimer's Disease (AD) is the most common neurodegenerative disease and the leading cause of dementia among senile subjects. It has been proposed that AD can be caused by defects in mitochondrial oxidative phosphorylation. Given the fundamental contribution of the mitochondrial genome (mtDNA) for the respiratory chain, there have been a number of studies investigating the association between mtDNA inherited variants and multifactorial diseases, however no general consensus has been reached yet on the correlation between mtDNA haplogroups and AD. METHODOLOGY/PRINCIPAL FINDINGS: We applied for the first time a high resolution analysis (sequencing of displacement loop and restriction analysis of specific markers in the coding region of mtDNA) to investigate the possible association between mtDNA-inherited sequence variation and AD in 936 AD patients and 776 cognitively assessed normal controls from central and northern Italy. Among over 40 mtDNA sub-haplogroups analysed, we found that sub-haplogroup H5 is a risk factor for AD (OR=1.85, 95% CI:1.04-3.23) in particular for females (OR=2.19, 95% CI:1.06-4.51) and independently from the APOE genotype. Multivariate logistic regression revealed an interaction between H5 and age. When the whole sample is considered, the H5a subgroup of molecules, harboring the 4336 transition in the tRNAGln gene, already associated to AD in early studies, was about threefold more represented in AD patients than in controls (2.0% vs 0.8%; p=0.031), and it might account for the increased frequency of H5 in AD patients (4.2% vs 2.3%). The complete re-sequencing of the 56 mtDNAs belonging to H5 revealed that AD patients showed a trend towards a higher number (p=0.052) of sporadic mutations in tRNA and rRNA genes when compared with controls. CONCLUSIONS: Our results indicate that high resolution analysis of inherited mtDNA sequence variation can help in identifying both ancient polymorphisms defining sub-haplogroups and the accumulation of sporadic mutations associated with complex traits such as AD.