Cardiovascular disease, including coronary artery disease and aortic valve stenosis, impacts tens of millions of people annually and carries a massive global economic burden. Advances in medical imaging, hardware and software are leading to an increased interest in the field of cardiovascular computational modelling to help combat the devastating impact of cardiovascular disease. Lumped parameter modelling (a branch of computational modelling) holds the potential of aiding in the early diagnosis of these diseases, assisting clinicians in determining personalized and optimal treatments and offering a unique in-silico setting to study cardiac and circulatory diseases due to its rapid computation time, ease of automation and relative simplicity. In this thesis, cardiovascular lumped parameter modelling is presented in detail and a patient-specific framework capable of simulating blood flow waveforms and hemodynamic data in the heart and coronary arteries was developed. The framework used only non-invasive clinical data and images (Computed Tomography images, echocardiography data and cuff blood pressure) as inputs. The novel model was then applied to 19 patients with aortic stenosis who underwent transcatheter aortic valve replacement. The diastolic coronary flow waveforms in the left anterior descending artery, left circumflex artery and right coronary artery were validated against a previously developed patient-specific 3D fluid-structure interaction model for all 19 subjects (pre and post intervention). There were strong qualitative and quantitative agreements between the two models. After the procedure, aortic valve area and net pressure gradient across the aortic valve improved for almost all the subjects. As for the hemodynamic data, according to the model, there was substantial variability in terms of the increase or decrease post intervention. On average, left ventricle workload and maximum left ventricle pressure decreased by 4.5% and 13.0% while cardiac output, mean arterial pressure and resting heart rate increased by 9.9%, 6.9% and 1.9% respectively. There were also subject specific changes in coronary blood flow (37% had increased flow in all three coronary arteries, 32% had decreased flow in all coronary arteries, and 31% had both increased and decreased flow in different coronary arteries). All in all, a proof-of-concept cardiac and coronary lumped parameter framework was developed, validated, and applied in this thesis. / Thesis / Master of Applied Science (MASc) / The heart is a vital part of the cardiovascular system, which helps deliver and regulate blood flow through the entire human body. The coronary arteries are a crucial part of this system since they deliver blood directly to heart muscles. For numerous reasons, the cardiovascular system can become diseased over time and require clinical treatment. Coronary artery disease and aortic valve stenosis are among the most prevalent cardiovascular diseases globally. While medical imaging on its own is a crucial part of the disease management and treatment process, advanced computational models can further enhance the process and provide clinics with data and predictions they might otherwise miss. In this thesis, a patient specific computational framework capable of simulating blood flow waveforms and cardiovascular data in the heart and coronary arteries using only non-invasive clinical data and images was developed and validated. The novel model was applied to a series of patients with aortic stenosis who underwent heart valve replacement with the aim of studying the impact on coronary blood flow and global cardiovascular metrics.

The work of this thesis is concerned with the aggregation and advancement of modelling practise as used within modern day product development and optimisation environments making use of Model Based Design (¿MBD¿) and similar procedures. A review of model development and use forms the foundation of the work, with the findings being aggregated into two unique approaches for rapid model development and reconfiguration; the Plug-and-Simulate (¿PaS¿) approach and the Paradigm for Large Model Creation (¿PLMC¿); each shown to posses its own advantages. To support the MBD process a model optimisation algorithm that seeks to eliminate parameters that are of little or no significance to a simulation is developed. Eliminations are made on the basis of an energy analysis which determines the activity of a number of energy elements. Low activity elements are said to be of less significance to the global dynamics of a model and thus become targets for elimination. A model configuration tool is presented that brings together the PLMC and parameter elimination algorithm. The tool is shown to be useful for rapid configuration and reconfiguration of models and is capable of automatically running the optimisation algorithms thus producing a simulation model that is parametrically and computationally optimised. The response of the plug-and-simulate drivetrain submodels, assembled to represent a front wheel drive drivetrain, is examined. The resulting model is subjected to a torque step-input and an empirically obtained torque curve that characterises the input to a drivetrain undergoing steady acceleration. The model displays the expected response in both its full parameter and parameter reduced versions with simulation efficiency gains observed in the parameter reduced version. / EPSRC

<p> The dual configuration is innovated as a new approach in sensitivity reduction. Three types of sensitivity due to variations in plant parameters are discussed. It has been shown that cost insensitive and terminal insensitive designs are indeed achievable by applying the dual configuration to implement the optimal control. </p> <p> The theory has been developed for a general class of optimal systems and the linear systems with quadratic cost functionals have been analytically evaluated to illustrate the theory. </p> / Thesis / Master of Engineering (ME)

<p> Small scale tests were utilized in order to obtain characteristic fracture mechanics parameters such as the crack opening displacement (C.O.D.) and the J-integral. Two main types of steels were used (H.S.L.A. and AISI 4340) in obtaining data over a wide range of yield strengths and ductilities. Tests were done to see the effect of both notch geometry and sample geometry·in one of the H.S.L.A. steels, and it is verified that the minimum value of C.O.D., at crack initiation in plane strain, is independent of the geometry and plastic zone size. Further the development of a simple single specimen J-integral test method is done during this work. In terms of the data obtained both the minimum C.O.D.i values and the Jlc values increase with increasing ductility of the materials tested. In the attempt to relate the magnitude of the fracture toughness with microstructural parameters and the limiting processes occuring at the crack tip prior to fracture, the concept of the process zone is discussed. For this study a simple plain carbon steel spheroidized with different carbon contents was examined in addition to the H.S.L.A. and 4340 steels. From the data obtained the minimum C.O.D.i at crack initiation was found to be approximately equal to the product of the materials plain strain ductility and a characteristic distance scaling with the spacing between large non metallic inclusions or the spacing between the bands of the sulphides. </p> / Thesis / Master of Engineering (MEngr)

A mathematical model of blood flow in infants with hypoplastic left heart syndrome (HLHS) was improved by adding cerebral autoregulation. This is the process by which blood vessels constrict or dilate to keep blood flow steady in certain organs during pressure changes. The original lumped parameter model transformed the fluid flow into an electrical circuit. Its behavior is described using a system of thirty-three coupled differential equations that are solved numerically using a fourth-order Runge-Kutta method implemented in MATLAB. A literature review that includes a discussion of autoregulation mechanisms and approaches to modeling them is followed by a description of the model created for this paper. The model is based on the baroreceptor or neurogenic theory of autoregulation. According to this theory, nerves in certain places within the cardiovascular system detect changes in blood pressure. The brain then compensates by sending a signal to blood vessels to constrict or dilate. The model of the control system responded fairly well to a pressure drop with a steady state error of about two percent. Running the model with or without the control system activated had little effect on other parameters, notably cardiac output. A more complete model of blood flow control would include autonomic regulation. This would vary more parameters than local autoregulation, including heart rate and contractility. This is suggested as a topic of further research.

This thesis focuses on an adaptive quadratic spiking model of a motoneuron that is both versatile in its ability to represent a range of experimentally observed neuronal firing patterns as well as computationally efficient for large network simulation. The objective of research is to fit membrane voltage data to the model using a parameter estimation approach involving simulated annealing. By manipulating the system dynamics of the model, a realizable model with linear parameterization (LP) can be obtained to simplify the estimation process. With a persistently excited current input applied to the model, simulated annealing is used to efficiently determine the best model parameters that minimize the square error function between the membrane voltage reference data and data generated by the LP model. Results obtained through simulation of this approach show feasibility to predict a range of different neuron firing patterns.

The Kitaev model has become a source of much excitement in the field of condensed matter. It is a two dimensional model of spins ½ on a honeycomb lattice with bond-dependent interactions. Its interesting properties include a quantum spin liquid ground state and anyonic excitations. These properties could lead to exciting applications in quantum computing if materials were found to behave similarly to the Kitaev model. Such materials have been found, however the Kitaev model is too simple to describe these materials and additional interactions must be considered. The Heisenberg interaction is one such additional interaction. As such, we can define the Kitaev-Heisenberg model by combining the Kitaev and Heisenberg interactions. We can now ask ourselves if the quantum spin liquid ground state and anyonic excitations still exist in the Kitaev-Heisenberg model. To answer this question, a non-local string order parameter has been defined which is non-zero inside the quantum spin liquid phase and zero outside of it. This string order parameter was shown to exist and survive the Heisenberg interaction on the 2-leg ladder. In this thesis, we look to expand this result to multileg ladders such as the 3-leg, 4-leg, and 5-leg ladders to see if the string order parameter survives in the Kitaev-Heisenberg model in 2 dimensions. Our results show that the string order parameter does exist in multileg ladders, however the phase space window in which it survives the Heisenberg interaction is narrower than in the 2-leg ladder. / Thesis / Master of Science (MSc)

There have been several studies that aim to determine the most superior Weibull parameter recovery approach of specifying a given forest stand’s Weibull diameter distribution, but no consensus has been made. The lack of agreement could be attributed to studies using different moments/percentile prediction models as well as using different plot size data. This study investigates how plot size and prediction model form affects the performance for moments, hybrid, and percentile Weibull parameter recovery approaches. Five plot sizes and three moments/percentile prediction models were used to determine their effects. Weibull parameters were calculated using each recovery method for each plot size and moments/percentile prediction model combination. Each combination’s diameter distribution was recovered and assessed using absolute error index. Results showed that plot size affected rank of precision for parameter recovery methods. Findings suggest that order statistics may be important in recovering Weibull distribution parameters from stand diameter summary statistics.

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