Numerical Modelling of Blood Flow for Coarctation of the Aorta: Pre- and Post-treatment Simulations

Coarctation of the Aorta (CoA) is a disease that is present in newborns and is commonly described as a short section of narrowing in the aorta. This thesis uses mathematical and numerical modelling to investigate both pre- and post-treatment issues experienced by CoA patients, by examining the effect of the coarctation, some associated cardiovascular abnormalities, as well as treatments for CoA, on blood flow properties. CoA is a serious congenital heart disease, and the mean age of mortality has been estimated to be 34 years. Treatments generally focus on resolving the physical restriction in the aorta, which is the coarctation, although CoA is associated with many cardiovascular abnormalities. Despite the availability of several treatments, treated CoA patients experience late hypertension and have a decreased life expectancy compared to normal people. Two examples of treatments are resection and end-to-end anastomosis (REA) and stents. REA is a surgical treatment that involves excising the coarctation and suturing the remaining aorta together. Stents are a catheter-based intervention where a catheter is inserted into the artery and used to expand a metal stent into the coarctation. It is unclear whether a particular treatment is superior, as there is insufficient long-term data for some treatments. Several reviews of treatments for CoA have concluded that additional data are required to understand whether these recently utilised treatments result in superior long-term outcomes. Numerical simulation of mathematical models of blood flow in arteries can be used to investigate and compare treatments where clinical data are lacking, and difficult or expensive to obtain. This thesis uses existing one-dimensional mathematical models of blood flow in arteries, which have been shown to reproduce the main features of hemodynamics. Equations are developed to implement altered arterial properties, such as artery wall stiffness and cross-sectional luminal area, in the models. These are used in simulations to investigate the effect of various conditions that are observed in CoA patients, pre- and post-treatment, on blood flow properties that are related to negative outcomes. Treatments for coarctation necessarily affect the compliance and wall properties of the aorta, in the region where they are implemented. REA involves excising the coarctation and suturing the remaining aorta together, and is studied as a short section of increased stiffness in the aorta wall in this thesis. Stents are studied as a longer region of increased stiffness. First a single tube model of the aorta is used to investigate the local effects of the REA and stent treatments. It is found that the increased stiffness in the aorta wall from REA and stent treatments, compared to normal people, results in increased blood pressure and increased radial expansion of the artery walls, which may contribute to the incidence of hypertension and aneurysms in treated CoA patients. This increased blood pressure and radial expansion is found in both untapered and tapered aortas. Flow in a tapered stent, which narrows with the aorta in a tapered aorta model, is also simulated and compared to flow in a straight stent in a tapered aorta. Unexpectedly, the straight stent produces some superior (closer to normal) blood flow properties, compared to the tapered stent. To identify possible causes of isolated systolic hypertension, which is common in CoA patients, parameters in the model are modified and simulations are performed to identify the effect of altered parameters on blood flow properties. Of the parameters tested, artery wall stiffness is identified as a suitable parameter for further investigation, based on the results of this thesis, as well as other studies that have shown increased stiffness in the upper body arteries of CoA patients. Next a network model of the major arteries is adapted to incorporate a range of coarctation severities, various increases to the stiffness in the arteries in the upper body, the REA and stent treatments used in the previous aorta model, and eccentric left ventricular hypertrophy, which are all present in some CoA patients pre- or post-treatment. CoA is known to be difficult to diagnose and is underdiagnosed in early life, and simulation results suggest CoA with mild or moderate severity coarctations may not produce the symptoms that are typically associated with CoA. The artery stiffness associated with CoA is known to increase with age in untreated patients, and simulations show that increased stiffness may increase the severity of CoA symptoms, which may explain why some CoA patients are not diagnosed until later in life. This increased stiffness is known to persist post-treatment, and it results in increased systolic blood pressure when simulated, which may explain why hypertension persists in treated patients. Two blood velocity indices, Gosling’s pulsatility index and Pourcelot’s resistivity index, are calculated from results in the models, in an attempt to find measurements that could be tested in patients to aid in diagnosis. Gosling’s pulsatility index, which is a calculation involving systolic, diastolic and average blood velocity, is found to differentiate between mild, moderate and severe coarctations, which may improve diagnosis rates in infants. The stent and REA treatments are also compared in the network artery model. REA is found to produce the most normal blood flow properties, which suggests that the REA treatment is likely to produce better long-term outcomes for patients than the stent treatment. Eccentric left ventricular hypertrophy is an increase in the mass of the left ventricle of the heart, without a relative increase in wall thickness, and is detected in a significant number of CoA patients, including post-treatment. In all presented simulations, the inflow from the heart into the aorta is specified as a flow waveform, and eccentric left ventricular hypertrophy is modelled as a scaling of the waveform. The results in this thesis suggest that this type of hypertrophy could be associated with the hypertension and aneurysms observed in CoA patients. Other results that are found suggest that the diagnosis and treatment of CoA patients may be affected by eccentric left ventricular hypertrophy. Although CoA increasingly appears to have life-long negative outcomes despite treatment, it is hoped that the findings in this thesis may help to explain and improve these outcomes for patients.