Examination of myocardial electrophysiology using novel panoramic optical mapping techniques

Optical mapping of voltage signals has revolutionised the field and study of cardiac electrophysiology by providing the means to visualise changes in electrical activity at a high temporal and spatial resolution from the cellular to the whole heart level under both normal and disease conditions. The aim of this thesis was to develop a novel method of panoramic optical mapping using a single camera and to study myocardial electrophysiology in isolated Langendorff-perfused rabbit hearts. First, proper procedures for selection, filtering and analysis of the optical data recorded from the panoramic optical mapping system were established. This work was followed by extensive characterisation of the electrical activity across the epicardial surface of the preparation investigating time and heart dependent effects. In an initial study, features of epicardial electrophysiology were examined as the temperature of the heart was reduced below physiological values. This manoeuvre was chosen to mimic the temperatures experienced during various levels of hypothermia in vivo, a condition known to promote arrhythmias. The facility for panoramic optical mapping allowed the extent of changes in conduction timing and pattern of ventricular activation and repolarisation to be assessed. In the main experimental section, changes in epicardial electrical activity were assessed under various pacing conditions in both normal hearts and in a rabbit model of chronic MI. In these experiments, there was significant changes in the pattern of electrical activation corresponding with the changes in pacing regime. These experiments demonstrated a negative correlation between activation time and APD, which was not maintained during ventricular pacing. This suggests that activation pattern is not the sole determinant of action potential duration in intact hearts. Lastly, a realistic 3D computational model of the rabbit left ventricle was developed to simulate the passive and active mechanical properties of the heart. The aim of this model was to infer further information from the experimental optical mapping studies. In future, it would be feasible to gain insight into the electrical and mechanical performance of the heart by simulating experimental pacing conditions in the model.

Trajectory prediction uncertainty modelling for Air Traffic Management

The anticipated growth of air traffic worldwide requires enhanced Air Traffic Management (ATM) technologies and procedures to increase the system capacity, efficiency, and resilience, while reducing environmental impact and maintaining operational safety. To deal with these challenges, new automation and information exchange capabilities are being developed through different modernisation initiatives toward a new global operational concept called Trajectory Based Operations (TBO), in which aircraft trajectory information becomes the cornerstone of advanced ATM applications. This transformation will lead to higher levels of system complexity requiring enhanced Decision Support Tools (DST) to aid humans in the decision making processes. These will rely on accurate predicted aircraft trajectories, provided by advanced Trajectory Predictors (TP). The trajectory prediction process is subject to stochastic effects that introduce uncertainty into the predictions. Regardless of the assumptions that define the aircraft motion model underpinning the TP, deviations between predicted and actual trajectories are unavoidable. This thesis proposes an innovative method to characterise the uncertainty associated with a trajectory prediction based on the mathematical theory of Polynomial Chaos Expansions (PCE). Assuming univariate PCEs of the trajectory prediction inputs, the method describes how to generate multivariate PCEs of the prediction outputs that quantify their associated uncertainty. Arbitrary PCE (aPCE) was chosen because it allows a higher degree of flexibility to model input uncertainty. The obtained polynomial description can be used in subsequent prediction sensitivity analyses thanks to the relationship between polynomial coefficients and Sobol indices. The Sobol indices enable ranking the input parameters according to their influence on trajectory prediction uncertainty. The applicability of the aPCE-based uncertainty quantification detailed herein is analysed through a study case. This study case represents a typical aircraft trajectory prediction problem in ATM, in which uncertain parameters regarding aircraft performance, aircraft intent description, weather forecast, and initial conditions are considered simultaneously. Numerical results are compared to those obtained from a Monte Carlo simulation, demonstrating the advantages of the proposed method. The thesis includes two examples of DSTs (Demand and Capacity Balancing tool, and Arrival Manager) to illustrate the potential benefits of exploiting the proposed uncertainty quantification method.

A deformation model of flexible, high area-to-mass ratio debris under perturbations and validation method

A new type of space debris was recently discovered by Schildknecht in near -geosynchronous orbit (GEO). These objects were later identified as exhibiting properties associated with High Area-to-Mass ratio (HAMR) objects. According to their brightness magnitudes (light curve), high rotation rates and composition properties (albedo, amount of specular and diffuse reflection, colour, etc), it is thought that these objects are multilayer insulation (MLI). Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that their shapes are easily deformed leading to changes in the Area-to-Mass ratio (AMR) over time. This thesis proposes a simple effective flexible model of the thin, deformable membrane with two different methods. Firstly, this debris is modelled with Finite Element Analysis (FEA) by using Bernoulli-Euler theory called “Bernoulli model”. The Bernoulli model is constructed with beam elements consisting 2 nodes and each node has six degrees of freedom (DoF). The mass of membrane is distributed in beam elements. Secondly, the debris based on multibody dynamics theory call “Multibody model” is modelled as a series of lump masses, connected through flexible joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account with lump masses in the joints. The dynamic equations for the masses, including the constraints defined by the connecting rigid rod, are derived using fundamental Newtonian mechanics. The physical properties of both flexible models required by the models (membrane density, reflectivity, composition, etc.), are assumed to be those of multilayer insulation. Both flexible membrane models are then propagated together with classical orbital and attitude equations of motion near GEO region to predict the orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field, luni-solar gravitational fields and self-shadowing effect. These results are then compared to two rigid body models (cannonball and flat rigid plate). In this investigation, when comparing with a rigid model, the evolutions of orbital elements of the flexible models indicate the difference of inclination and secular eccentricity evolutions, rapid irregular attitude motion and unstable cross-section area due to a deformation over time. Then, the Monte Carlo simulations by varying initial attitude dynamics and deformed angle are investigated and compared with rigid models over 100 days. As the results of the simulations, the different initial conditions provide unique orbital motions, which is significantly different in term of orbital motions of both rigid models. Furthermore, this thesis presents a methodology to determine the material dynamic properties of thin membranes and validates the deformation of the multibody model with real MLI materials. Experiments are performed in a high vacuum chamber (10-4 mbar) replicating space environment. A thin membrane is hinged at one end but free at the other. The free motion experiment, the first experiment, is a free vibration test to determine the damping coefficient and natural frequency of the thin membrane. In this test, the membrane is allowed to fall freely in the chamber with the motion tracked and captured through high velocity video frames. A Kalman filter technique is implemented in the tracking algorithm to reduce noise and increase the tracking accuracy of the oscillating motion. The forced motion experiment, the last test, is performed to determine the deformation characteristics of the object. A high power spotlight (500-2000W) is used to illuminate the MLI and the displacements are measured by means of a high resolution laser sensor. Finite Element Analysis (FEA) and multibody dynamics of the experimental setups are used for the validation of the flexible model by comparing with the experimental results of displacements and natural frequencies.

Eulerian-Lagrangian definition of coarse bed-load transport: Theory and verification with low-cost inertial measurement units

Fluvial sediment transport is controlled by hydraulics, sediment properties and arrangement, and flow history across a range of time scales. This physical complexity has led to ambiguous definition of the reference frame (Lagrangian or Eulerian) in which sediment transport is analysed. A general Eulerian-Lagrangian approach accounts for inertial characteristics of particles in a Lagrangian (particle fixed) frame, and for the hydrodynamics in an independent Eulerian frame. The necessary Eulerian-Lagrangian transformations are simplified under the assumption of an ideal Inertial Measurement Unit (IMU), rigidly attached at the centre of the mass of a sediment particle. Real, commercially available IMU sensors can provide high frequency data on accelerations and angular velocities (hence forces and energy) experienced by grains during entrainment and motion, if adequately customized. IMUs are subjected to significant error accu- mulation but they can be used for statistical parametrisation of an Eulerian-Lagrangian model, for coarse sediment particles and over the temporal scale of individual entrainment events. In this thesis an Eulerian-Lagrangian model is introduced and evaluated experimentally. Absolute inertial accelerations were recorded at a 4 Hz frequency from a spherical instrumented particle (111 mm diameter and 2383 kg/m3 density) in a series of entrainment threshold experiments on a fixed idealised bed. The grain-top inertial acceleration entrainment threshold was approximated at 44 and 51 mg for slopes 0.026 and 0.037 respectively. The saddle inertial acceleration entrainment threshold was at 32 and 25 mg for slopes 0.044 and 0.057 respectively. For the evaluation of the complete Eulerian-Lagrangian model two prototype sensors are presented: an idealised (spherical) with a diameter of 90 mm and an ellipsoidal with axes 100, 70 and 30 mm. Both are instrumented with a complete IMU, capable of sampling 3D inertial accelerations and 3D angular velocities at 50 Hz. After signal analysis, the results can be used to parametrize sediment movement but they do not contain positional information. The two sensors (spherical and ellipsoidal) were tested in a series of entrainment experiments, similar to the evaluation of the 111 mm prototype, for a slope of 0.02. The spherical sensor entrained at discharges of 24.8 ± 1.8 l/s while the same threshold for the ellipsoidal sensor was 45.2 ± 2.2 l/s. Kinetic energy calculations were used to quantify the particle-bed energy exchange under fluvial (discharge at 30 l/s) and non-fluvial conditions. All the experiments suggest that the effect of the inertial characteristics of coarse sediments on their motion is comparable to the effect hydrodynamic forces. The coupling of IMU sensors with advanced telemetric systems can lead to the tracking of Lagrangian particle trajectories, at a frequency and accuracy that will permit the testing of diffusion/dispersion models across the range of particle diameters.