A robust anisotropic hyperelastic formulation for the modelling of soft tissue

The Holzapfel–Gasser–Ogden (HGO) model for anisotropic hyperelastic behaviour of collagen fibre reinforced materials was initially developed to describe the elastic properties of arterial tissue, but is now used extensively for modelling a variety of soft biological tissues. Such materials can be regarded as incompressible, and when the incompressibility condition is adopted the strain energy Ψ of the HGO model is a function of one isotropic and two anisotropic deformation invariants. A compressible form (HGO-C model) is widely used in finite element simulations whereby the isotropic part of Ψ is decoupled into volumetric and isochoric parts and the anisotropic part of Ψ is expressed in terms of isochoric invariants. Here, by using three simple deformations (pure dilatation, pure shear and uniaxial stretch), we demonstrate that the compressible HGO-C formulation does not correctly model compressible anisotropic material behaviour, because the anisotropic component of the model is insensitive to volumetric deformation due to the use of isochoric anisotropic invariants. In order to correctly model compressible anisotropic behaviour we present a modified anisotropic (MA) model, whereby the full anisotropic invariants are used, so that a volumetric anisotropic contribution is represented. The MA model correctly predicts an anisotropic response to hydrostatic tensile loading, whereby a sphere deforms into an ellipsoid. It also computes the correct anisotropic stress state for pure shear and uniaxial deformation. To look at more practical applications, we developed a finite element user-defined material subroutine for the simulation of stent deployment in a slightly compressible artery. Significantly higher stress triaxiality and arterial compliance are computed when the full anisotropic invariants are used (MA model) instead of the isochoric form (HGO-C model)

Focus on the research utility of intravascular ultrasound - comparison with other invasive modalities

Intravascular ultrasound (IVUS) is an invasive modality which provides cross-sectional images of a coronary artery. In these images both the lumen and outer vessel wall can be identified and accurate estimations of their dimensions and of the plaque burden can be obtained. In addition, further processing of the IVUS backscatter signal helps in the characterization of the type of the plaque and thus it has been used to study the natural history of the atherosclerotic evolution. On the other hand its indigenous limitations do not allow IVUS to assess accurately stent struts coverage, existence of thrombus or exact site of plaque rupture and to identify some of the features associated with increased plaque vulnerability. In order this information to be obtained, other modalities such as optical coherence tomography, angioscopy, near infrared spectroscopy and intravascular magnetic resonance imaging have either been utilized or are under evaluation. The aim of this review article is to present the current utilities of IVUS in research and to discuss its advantages and disadvantages over the other imaging techniques

Analysis of Radiofrequency Ultrasound Signals

This thesis consists of two papers which focuses on a particular diffusion type Dirichlet form   where  Here  is the basis in the Cameron-Martin space, H, consisting of the Schauder functions, and ν denotes the Wiener measure. In Paper I, we let  vary over the space of wiener trajectories in a way that the diffusion operator A is almost everywhere an unbounded operator on the Cameron–Martin space. In addition we put a weight function  on theWiener measure  and show that under these changes of the reference measure, the Malliavin derivative and divergence are closable operators with certain closable inverses. It is then shown that under certain conditions on , and these changes of reference measure, the Dirichlet form is quasi-regular. This is done first in the classical Wiener space and then the results are transferred to the Wiener space over a Riemannian manifold. Paper II focuses on the case when  is a sequence of non-decreasing real numbers. The process X associated to  is then an infinite dimensional Ornstein-Uhlenbeck process. In this case we show that the distributions of a sequence of certain finite dimensional Ornstein-Uhlenbeck processes converge weakly to the distribution of the infinite dimensional Ornstein-Uhlenbeck process. We also investigate the quadratic variation for this process, both in the classical sense and in the recent framework of stochastic calculus via regularization. Since the process is Banach space valued, the tensor quadratic variation is an appropriate tool to establish the Itô formula for the infinite dimensional Ornstein-Uhlenbeck process X. Sufficient conditions are presented for the scalar as well as the tensor quadratic variation to exist