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Description
The project seeks to retrieve the local mechanical properties of the walls of the blood vessels treated as an anisotropic elastic medium. The applied method relies on solving an inverse problem of blood flow in distensible conduits. The deformation of the arteries and the blood velocity are measured using an ultrasound scanner. Knowing the Young modulus, all other used stiffness measures can be evaluated. A phantom installation will be built where the direct solution of the computational fluid dynamics (CFD) linked with the elastic deformation of the walls within the Fluid-Structure Interaction (FSI) technique will be validated. To test the reliability of the distension and velocity measurements, measurements of these quantities will be conducted using another set of sensors: 3D deformation scanner and high frequency flow meters. The application of the Uncertainty Quantification will produce the error bounds of the results. Sensitivity analysis applied to the model will identify the crucial variables whose values affect mostly the resulting distension fields. At this stage two blood flow models will be used: a full 3D CFD blood flow model with two ways FSI in its strong form and a 1D flow model in an elastic tube. Both models will be compared in the context of using the simpler model in the final formulation. The comparison will encompass the influence of non-circular geometry, material inhomogeneity. The inverse solver will be applied first on artificial data with simulated and controlled pseudo measurement data. This will result in selecting an optimal inverse algorithm. Then the artificial data will be substituted by real data collected on the phantom installation. The results will be compared with the values of the Young modulus of the conduit measured directly in an independent test. The last step or the project will be a sequence of medical experiments executed on the cardiac artery and retrieving the Young modulus using the already tested inverse procedure.
Summary of project results
The project focuses on measurements of the stiffness of the artery wall. The systemic artery system delivers oxygenated blood to the capillaries and thus to all tissues. Although the pressure generated by the heart differs substantially within the cycle, the capillaries receive a nearly constant flow of blood during systole and diastole. The elasticity of the arteries buffers the pulsatility of flow and pressure, protecting the small vascular beds from destruction by rapid pressure changes.
The pressure wave produced by ventricle contraction travels forward and is partially reflected backward. Both forward and backward waves interact. The reflected wave returns to the aorta in late systole and early diastole for healthy young subjects, increasing the coronary flow. Aging and some diseases result in increased stiffness of the vasculature. This leads to a higher velocity of the pressure wave. As a result, the backward pressure wave overlaps with the forward one, causing hypertension.
Assessment of arterial system stiffness is a valuable diagnostic index, used also to predict cardiovascular morbidity and mortality.
Several difficulties were encountered during project execution.
- Measurement of small arterial deformations that rapidly change due to the pulsed nature of blood flow. Three measurement techniques were considered: nuclear magnetic resonance, X-ray computed tomography, and ultrasound. The first modality was excluded from the research plan due to its low temporal and spatial resolution, high cost, and long time for a single measurement. The second method is invasive, requires contrast injection, and irradiates tissues with harmful X radiation. The third method has a high resolution and is noninvasive with a short time of single measurement. However, it can only be used for arteries that run shallowly under the skin surface, such as carotid arteries. The choice was to use ultrasound focused on the carotid artery. However, this required estimating the precision of arterial deformation measurements and developing a method to reproduce the oscillating character of the deformations of the selected carotid artery fragment.
- Finding the relationship between the deformations of the arteries with the flow field and the pressure in the vessel. This required the measurement of the time-dependent pressure and blood flow in the artery. Only this set of data, combined with synchronized (gated) electrocardiogram measurement of variable geometry, could be used to solve the task of blood flow in a deformable artery.
- The solution of blood flow in a deforming vessel is numerically very intensive. The stiffness evaluation is an iterative process in which the stiffness is corrected at each iteration step until the calculated wall deformation corresponds to the measured values. Thus, the acceleration of the solution to the blood flow problem is a crucial question.
The aim of the project was to develop a method of assessment of local stiffness of the carotid artery. This has been done based on noninvasive clinical measurements that involve measurement of arterial deformations and flow by ultrasound apparatus and blood pressure in the vessel using an applanation tonometer. Interpreting clinical trials to determine vessel walls stiffness requires the application of advanced mathematical and computer simulation tools.
- Since in vivo validation of the applied techniques cannot be carried out, the validation of the measurement and the simulation techniques has been conducted using an originally developed phantom. The flow of liquid in the phantom was forced by a pump that generates pressure and changes in flow mimicking the heart cycle.
- The first step of the phantom studies was to estimate the accuracy of the dynamic ultrasound measurements. This was done by comparing the results of the ultrasound apparatus with the measurements produced by high-resolution digital cameras. At the same time, oscillatory pressure changes and cyclic fluid flow were measured. The data obtained were used to verify the precision of the flow model and its impact on the deformation of the vessel wall.
- A method was developed to determine vessel wall stiffness and applied to both phantom experiments, in which stiffness could be measured directly, and clinical trials where the real value of the stiffness is unknown. The latter was the main objective of the project.
- The results of the blood flow simulation in the deformed vessel were critically evaluated, estimating their accuracy. General sensitivity analysis with multi-fidelity Monte Carlo and polynomial chaos expansion was employed in this portion of the research. The calculations used a simplified carotid artery with different complexity of the model (0D, 1D, 3D).
- Variability range of the characteristic size of the carotid artery (lumen, thickness, incremental Young’s modulus, etc.). The population was also estimated based on statistical data, depending on age, sex, weight, and previous diseases.
As a result of the project, a method was created to determine the stiffness of the carotid artery. During the research, a technique was developed to measure the deformation of this artery using a USG apparatus with the appropriate instrumentation and software. The instrumentation allows the subject to be immobilized and the movement of the USG head to be electronically controlled. Based on these measurements, the developed software reconstructs the time-dependent three-dimensional geometry of the examined carotid artery.
An original instrument was also developed to measure pressure inside the carotid artery. Measurement is carried out with an applanation tonometer, with the device fixed in the adjustable arm. As a result, the user has control over the force exerted on the tissue and, above all, makes the measurement independent of involuntary movements of the hand carrying out the measurement. Such movements result, for example, from breathing, heartbeat, swallowing saliva, coughing, etc.
Three types of algorithms were examined to determine arterial stiffness. Techniques based on the solution of the full task of periodic blood flow in deformable arteries could not be applied directly due to the time-consuming nature of such calculations. In this case, a technique based on Gaussian Processes was used to generate simplified solutions (surrogates) based on statistical analysis. Although this technique produces the right results, it requires high computing power and considerable experience.
The second technique is based on a one-dimensional model and does not require large computer resources. Some difficulties associated with this method are the proper selection of the inlet conditions at the outlet and the averaging of the geometry, flow resistance and accumulation ability of the vasculature.
The third most effective method is based on the Kalman filter algorithm. As shown, it can be used to omit the effect of flowing blood, limiting itself only to the dependence of the deformation on the pressure inside the vessel. Very simple analytical models work in this case. During the study, more than 30 healthy volunteers were tested for arterial stiffness.
The results obtained can be used in clinical practice to study the stiffness of the carotid artery. An inevitable increase in arterial stiffness is associated with age. It can also be the result of disease processes. Knowledge of stiffness has a high diagnostic value. The stiffness of the artery walls is also affected by drugs prescribed in the course of various diseases. The method developed allows us to assess this impact.
Summary of bilateral results
The overall evaluation of the bilateral collaboration is positive. The collaboration included project meetings, summer schools, and sharing knowledge. Two Polish PhD students completed research visits in the laboratories of the Norway Partner. They are realizing the double diploma program between SUT and NTNU. As a result of the project realization 6 research papers (including 4 published) were prepared. Moreover, the research results were presented during numerous international conferences.