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The detection of boundary changes as a method for early diagnosis of cardiovascular disease

Final Report Summary - CARDIO-DETECT (The detection of boundary changes as a method for early diagnosis of cardiovascular disease)

The project aimed to establish the necessary scientific basis to pursue new methods to detect cardiovascular disease through the determination of material changes in arteries. The existing diagnostic methods are based mostly on detection of plaque when a disease has been getting progressively worse for decades. The changes in artery walls caused by cardiovascular decease development are very difficult to detect at an early stage. Clinical studies show that these changes usually occur at the inner layer of arteries. Therefore, this effect should be reflected in the long wave region of the dispersion spectrum of wave propagation through the artery walls. To investigate and describe this phenomena a special type of elastically restrained boundary conditions (ERBC) has been introduced and a series of long wave asymptotic models have been developed taking into account such key characteristics of human arteries as anisotropy, pre-stress and multi-layers.

The general approach is to introduce the most general linear combination of classical Neumann (stress free) and Dirichlet (fixed face) boundary conditions to model the influence of boundary changes by examining the behaviour of the fundamental modes and harmonics in the long wave region. Analysis of wave propagation in structures subject to elastically restrained boundary conditions has been performed starting from the simplest model (linear elastic isotropic plate) by increasing the complexity in turn to take into account all the essential characteristics of real human arteries like anisotropy, pre-stress and multi-layers. Generally, the analysis consists of several steps:
derivation of the dispersion relation;
- numerical calculation and analysis of the dispersion relation;
- elucidating of modes transformation mechanism with respect to restraints degree at the boundaries;
- multi-parametric asymptotic analysis of the dispersion relation in the long wave region to obtain the approximate expansions in the vicinity of zero or cut-off frequencies;
- development of asymptotic models describing long wave motion to elucidate the mechanism of influencing of restraint parameters on the structure and type of the governing equations.

This plan has been sequentially applied to a series of problems with elastically restrained boundary conditions. As a result, the following progress has been achieved at the end of the reporting period:
1. Numerical and asymptotic analysis have been performed and long wave asymptotic models been developed for the following problems with ERBC:
- pre-stressed incompressible plate;
- transversely-isotropic plate;
- linear isotropic, single cylindrical layer;
- isotropic, anisotropic or pre-stressed multi-layered plate;
- residually stressed cylindrical layer;
- spirally wounded fibre-reinforced cylindrical layer;
- multi-layered cylinder.
2. The software package DispRel has been developed for numerical solving of the dispersion relations including effects of anisotropy, pre-stress and multi-layers by using various root finding procedures.
3. Special types of asymptotics of the dispersion relation and approximate models uniformed in the area of close cut-off frequencies have been developed.