Alzheimer's disease (AD) is characterized by progressive cognitive deterioration together with declining activities of daily living and neuropsychiatric symptoms. It is the most common cause of dementia. It is recognized that the production and maintenance of myelin is essential for normal brain function. Aging-related breakdown of myelin negatively impacts the cognitive performances with the neurofibrilary tangles and amyloid plaques being the hallmarks of the disease. Nowadays, the only definite way to diagnose AD is to find out whether there are plaques and tangles in brain tissue. This requires histopathological examination of brain tissue. Previous researches on AD using MRI mainly focus on direct plaque imaging. This study aims to validate the hypothesis that AD alters the mechanical properties of the axons in the region between hippocampus and cortex, i.e. within the corpus callosum (CC) which is an area strongly affected by demyelination. As a unique tool to study non-invasively those properties, we use 3D MR-elastography operating at 1000 Hz mechanical excitation frequency. Post-processing of the complex-valued displacement field provides the local fiber direction (determined by two Euler angles) and two complex shear moduli: one perpendicular to the local fiber direction and one parallel to it. Each modulus is a complex number giving access to both the anisotropic elasticity mu and viscosity eta. The displacement fields are measured at an isotropic resolution of 300 mum. Four transgenic female mice expressing mutant human APP/PS1 genes and three wild-type (WT) control mice were studied over several weeks. We observe locally enhanced elasticity and viscosity in the corpus callosum compared to the rest of the brain. As expected from normal anatomy, this region also shows a significantly higher anisotropy (mupar- muperp) characterizing the transversal isotropic mechanical properties of this white matter region. The AD group shows a decr-
ease in both mupar and muperp. It also seems to have a decreased value of perpendicular viscosity suggesting easier wave propagation in the transverse direction due to demyelination. Those preliminary results indicate that AD alters the mechanical properties of the white matter. Those differences were not detectable when utilizing an isotropic model for the reconstruction of the viscoelastic properties.
"In recent years, brain elasticity has also been imaged in vivo by magnetic resonance elastography (MRE) both on humans – and on small animals –. MRE  is a noninvasive elasticity imaging technique based on a phase-sensitive MR sequence that detects the propagation of shear waves generated by an external vibrator. However, the spatial resolution of this technique remains limited because it is intrinsically linked to acquisition time. "
[Show abstract][Hide abstract] ABSTRACT: A combination of radiation force and ultrafast ultrasound imaging is used to both generate and track the propagation of a shear wave in the brain whose local speed is directly related to stiffness, characterized by the dynamic shear modulus G*. When performed on trepanated rats, this approach called shear wave imaging (SWI) provides 3-D brain elasticity maps reaching a spatial resolution of 0.7 mm×1 mm×0.4 mm with a good reproducibility (<13%). The dynamic shear modulus of brain tissues exhibits values in the 2-25 kPa range with a mean value of 12 kPa and is quantified for different anatomical regions. The anisotropy of the shear wave propagation is studied and the first in vivo anisotropy map of brain elasticity is provided. The propagation is found to be isotropic in three gray matter regions but highly anisotropic in two white matter regions. The good temporal resolution (~10 ms per acquisition) of SWI also allows a dynamic estimation of brain elasticity to within a single cardiac cycle, showing that brain pulsatility does not transiently modify local elasticity. SWI proves its potential for the study of pathological modifications of brain elasticity both in small animal models and in clinical intra-operative imaging.
[Show abstract][Hide abstract] ABSTRACT: L'échographie constitue aujourd'hui un des piliers de l'imagerie médicale. Appliquée en clinique depuis plus de quarante ans, elle repose sur les ultrasons, ondes mécaniques de compression à hautes fréquences, pour réaliser des images principalement morphologiques des organes. Développée plus récemment, l'élastographie permet de sonder directement les propriétés viscoélastiques des tissus et pourrait ainsi renseigner sur l'état pathologique des tissus comme le fait la palpation du médecin. L'élastographie transitoire, basée sur l'étude de la propagation des ondes de cisaillement naturelles ou artifi- cielles, permet une mesure quantitative de ces propriétés viscoélastiques. Combinant la pression de radiation ultrasonore, véritable palpation à distance, et l'échographie ultrarapide, le Supersonic Shear Imaging peut gé- nérer et suivre des ondes de cisaillement in vivo en quelques millisecondes. On peut alors, par inversion de l'équation d'onde, former des cartes d'élasticité du milieu. Nous proposons ici une nouvelle méthode de reconstruction des cartes d'élasticité, plus robuste, qui est ensuite appliquée, in vivo et en clinique, à l'imagerie des lésions du sein, à l'étude de la fibrose du foie ainsi qu'à celle des maladies neuromusculaires. Une méthode de mesure de la dispersion de l'onde de cisaillement générée est aussi proposée et testée in vivo. Elle permet de retrouver, en une seule acquisition, les propriétés viscoélastiques complètes des tissus et a été appliquée au foie et au muscle de plusieurs volontaires sains. Finalement, nous nous intéressons à l'échographie ultrarapide de la contraction du muscle, déclenchée par électrostimulation. Cette méthode, locale et transitoire, permet de retrouver les paramètres clés de la réponse musculaire et offre ainsi, couplée avec l'électromyographie, des perspectives cliniques très intéressantes pour l'étude de la physiologie du muscle ou les maladies neuromusculaires.
[Show abstract][Hide abstract] ABSTRACT: The imaging problem of elastography is an inverse problem. The nature of an inverse problem is that it is ill-conditioned. We consider properties of the mathematical map which describes how the elastic properties of the tissue being reconstructed vary with the field measured by magnetic resonance imaging (MRI). This map is a nonlinear mapping, and our interest is in proving certain conditioning and regularity results for this operator which occurs implicitly in this problem of imaging in elastography. In this treatment we consider the tissue to be linearly elastic, isotropic, and spatially heterogeneous. We determine the conditioning of this problem of function reconstruction, in particular for the stiffness function. We further examine the conditioning when determining both stiffness and density. We examine the Fréchet derivative of the nonlinear mapping, which enables us to describe the properties of how the field affects the individual maps to the stiffness and density functions. We illustrate how use of the implicit function theorem can considerably simplify the analysis of Fréchet differentiability and regularity properties of this underlying operator. We present new results which show that the stiffness map is mildly ill-posed, whereas the density map suffers from medium ill-conditioning. Computational work has been done previously to study the sensitivity of these maps, but our work here is analytical. The validity of the Newton—Kantorovich and optimization methods for the computational solution of this inverse problem is directly linked to the Fréchet differentiability of the appropriate nonlinear operator, which we justify.
Riddhi U Bodani, Urmi Sengupta, Diana L Castillo-Carranza, Marcos J Guerrero-Muñoz, Julia E Gerson, Jai Rudra, Rakez Kayed
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