Nearly half a century after the first report of normal pressure hydrocephalus (NPH), the pathophysiological cause of the disease still remains unclear. Several theories about the cause and development of NPH emphasize disease-related alterations of the mechanical properties of the brain. MR elastography (MRE) uniquely allows the measurement of viscoelastic constants of the living brain without intervention. In this study, 20 patients (mean age, 69.1 years; nine men, 11 women) with idiopathic (n = 15) and secondary (n = 5) NPH were examined by cerebral multifrequency MRE and compared with 25 healthy volunteers (mean age, 62.1 years; 10 men, 15 women). Viscoelastic constants related to the stiffness (µ) and micromechanical connectivity (α) of brain tissue were derived from the dynamics of storage and loss moduli within the experimentally achieved frequency range of 25-62.5 Hz. In patients with NPH, both storage and loss moduli decreased, corresponding to a softening of brain tissue of about 20% compared with healthy volunteers (p < 0.001). This loss of rigidity was accompanied by a decreasing α parameter (9%, p < 0.001), indicating an alteration in the microstructural connectivity of brain tissue during NPH. This disease-related decrease in viscoelastic constants was even more pronounced in the periventricular region of the brain. The results demonstrate distinct tissue degradation associated with NPH. Further studies are required to investigate the source of mechanical tissue damage as a potential cause of NPH-related ventricular expansions and clinical symptoms.

The results indicate the fundamental role of altered viscoelastic properties of brain tissue during disease progression and tissue repair in NPH. Clinical improvement in NPH is associated with an increasing complexity of the mechanical network whose inherent strength, however, remains degraded.

Abstract. In this paper, we consider the inverse problem of determining the permeability of the subsurface from hydraulic head measurements, within the framework of a steady Darcy model of groundwater flow. We study geometrically defined prior permeability fields, which admit layered, fault and channel structures, in order to mimic realistic subsurface features; within each layer we adopt either constant or continuous function representation of the permeability. This prior model leads to a parameter identification problem for a finite number of unknown parameters determining the geometry, together with either a finite number of permeability values (in the constant case) or a finite number of fields (in the continuous function case). We adopt a Bayesian framework showing existence and well-posedness of the posterior distribution. We also introduce novel Markov Chain-Monte Carlo (MCMC) methods, which exploit the different character of the geometric and permeability parameters, and build on recent advances in function space MCMC. These algorithms provide rigorous estimates of the permeability, as well as the uncertainty associated with it, and only require forward model evaluations. No adjoint solvers are required and hence the methodology is applicable to black-box forward models. We then use these methods to explore the posterior and to illustrate the methodology with numerical experiments.

No abstract

This paper considers an inverse problem of shear stiffness imaging in a linear isotropic two-dimensional acoustic media, where the targeted parameter is the shear modulus μ. For given single component displacement data, the mathematical model to recover the shear modulus appears to be a first-order partial differential equation while a much simpler algebraic model, called the direct inversion, can be derived by eliminating the first derivative terms of the shear modulus from the partial differential equation model. The objective of this paper is to establish a theoretical bound on the relative difference between the true value of the modulus and the approximated value reconstructed from the direct inversion. We exhibit a quantitative estimate of the relative error and present reconstruction examples by the direct inversion from simulated data. We demonstrate that the relative error of the numerical solution is well bounded by the theoretical error estimate.