Final Report Summary - CARDIO-DETECT (The detection of boundary changes as a method for early diagnosis of cardiovascular disease)
The project aimed to finalise the research carried out during the incoming phase in Keele University, UK (FP7-PEOPLE-IIF-2008/236045) and establish the necessary theoretical and experimental basis to pursue new methods to detect cardiovascular disease through the determination of material changes in arteries. At early stages of cardiovascular decease, the changes in arteries should be reflected in the long wave region of the dispersion spectrum of wave propagation through the artery walls. Within the approach, the hardening of the intima (inner layer of the arteries) is modelled by a special type of elastically restrained boundary conditions (ERBC) where the influence of thin and relatively stiff inner layer is taken into account by a proper choice of the restraint parameters at the boundary. A series of mathematical models should be developed and analysed to elucidate the correspondence between restraint parameters, characterising the changes at the boundary, and dispersion spectrum distortion at the long wave region. To establish the necessary experimental basis for mathematical modelling the real geometrical, morphological and mechanical properties of the artery examined should be measured using the resources of Biomechanics Laboratory of Saratov State University.
The general approach to the model development includes the following stages:
- 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.
Analysis of wave propagation in structures subject to elastically restrained boundary conditions has been performed taking into account all the essential characteristics of real human arteries like anisotropy, pre-stress and multi-layers.
A series of experiments has been carried out at the Biomechanics Laboratory of Saratov State University (Equipment: Instron 5940 single column testing system) to obtain the real geometrical, morphological and mechanical properties of coronary artery walls. The parameters of healthy, pathologically altered and surgically treated (patched) coronary artery have been used in mathematical modelling of wave propagation in cylinders with ERBC.
The following progress has been achieved at the end of the reporting period:
1. Numerical and asymptotic analysis have been performed for the following problems with ERBC:
- two-layered residually stressed cylinder subjected to ERBC,
- two-layered spirally wounded fibre-reinforced cylinder subjected to ERBC.
2. Dependence of the fundamental mode behaviour on different layer properties, thickness, anisotropy and pre-stress parameters has been established for cylindrical geometry.
3. Experimental measurement of geometrical, morphological and mechanical properties of healthy pathologically altered and surgically treated coronary artery walls in vitro.
4. Mathematical and computer modelling of the most complicated models with ERBC using the experimentally obtained properties of artery walls.
A description of the main results achieved so far
1. The mechanism of frequency gap formation has been elucidated for different types of ERBC for multi-layered pre-stressed and anisotropic cylinders.
2. Experimental data have been analysed to obtain a natural range of the restraint parameters within the ERBC models to describe the changes in mechanical properties of the deceased arterial walls.
3. Dependence between coronary artery inner layer stiffness and atherosclerosis stage has been established for different age groups justifying the applicability of the ERBC approach for wave propagation modelling to identify the changes in arterial walls by frequency spectrum analysis.
A novel technique has been developed which allows detection of the inner arterial wall mechanical changes through analysis of the fundamental mode. As a main result of the project, the interaction between fundamental mode behaviour and boundary condition changes has been established, which provides the scientific basis for much easier and more reliable methods for detection of cardiovascular disease at a much earlier stage. The potential applicability of the approach has been analysed for stented arteries where a stent is modelled by the proper choice of the ERBC parameters. This will help to elucidate the mechanism of re-stenosis commonly encountered in stented arteries.
Upon elaborating a reliable non-invasive method of transmitted waves logging in arteries, the models developed during the project can be used for the interpretation of the dispersion spectrum of the waves to identify changes at the inner boundary of the artery examined. This will give valuable information as a basis for new methods to detect cardiovascular disease in a novel and highly innovative way. The potential long-term socio-economic impact of new methods for early detection of cardiovascular disease is difficult to overestimate.
The general approach to the model development includes the following stages:
- 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.
Analysis of wave propagation in structures subject to elastically restrained boundary conditions has been performed taking into account all the essential characteristics of real human arteries like anisotropy, pre-stress and multi-layers.
A series of experiments has been carried out at the Biomechanics Laboratory of Saratov State University (Equipment: Instron 5940 single column testing system) to obtain the real geometrical, morphological and mechanical properties of coronary artery walls. The parameters of healthy, pathologically altered and surgically treated (patched) coronary artery have been used in mathematical modelling of wave propagation in cylinders with ERBC.
The following progress has been achieved at the end of the reporting period:
1. Numerical and asymptotic analysis have been performed for the following problems with ERBC:
- two-layered residually stressed cylinder subjected to ERBC,
- two-layered spirally wounded fibre-reinforced cylinder subjected to ERBC.
2. Dependence of the fundamental mode behaviour on different layer properties, thickness, anisotropy and pre-stress parameters has been established for cylindrical geometry.
3. Experimental measurement of geometrical, morphological and mechanical properties of healthy pathologically altered and surgically treated coronary artery walls in vitro.
4. Mathematical and computer modelling of the most complicated models with ERBC using the experimentally obtained properties of artery walls.
A description of the main results achieved so far
1. The mechanism of frequency gap formation has been elucidated for different types of ERBC for multi-layered pre-stressed and anisotropic cylinders.
2. Experimental data have been analysed to obtain a natural range of the restraint parameters within the ERBC models to describe the changes in mechanical properties of the deceased arterial walls.
3. Dependence between coronary artery inner layer stiffness and atherosclerosis stage has been established for different age groups justifying the applicability of the ERBC approach for wave propagation modelling to identify the changes in arterial walls by frequency spectrum analysis.
A novel technique has been developed which allows detection of the inner arterial wall mechanical changes through analysis of the fundamental mode. As a main result of the project, the interaction between fundamental mode behaviour and boundary condition changes has been established, which provides the scientific basis for much easier and more reliable methods for detection of cardiovascular disease at a much earlier stage. The potential applicability of the approach has been analysed for stented arteries where a stent is modelled by the proper choice of the ERBC parameters. This will help to elucidate the mechanism of re-stenosis commonly encountered in stented arteries.
Upon elaborating a reliable non-invasive method of transmitted waves logging in arteries, the models developed during the project can be used for the interpretation of the dispersion spectrum of the waves to identify changes at the inner boundary of the artery examined. This will give valuable information as a basis for new methods to detect cardiovascular disease in a novel and highly innovative way. The potential long-term socio-economic impact of new methods for early detection of cardiovascular disease is difficult to overestimate.