Geodesic shooting for anatomical curve registration on the plane

The aim of the work presented in this thesis is to develop a method of characterising the shape of curves in the plane that is independent of the parameterisation of the curve. It is important to remove the effect of a specific parameterisation of a curve because it is possible for two curves to have the same shape while having different parameterisations. The characterisation is accomplished by matching curves via deformations, and using the deformations to characterise the difference between them. We specifically aim for a method that is able to characterise the kind of complex curves found in cross sections of the human nasal cavity. In order to match one curve to another, we derive the equations of motion for a geodesic flow, and seeking the flow that deforms an embedded reference curve into the target curve we wish to characterise. The geodesic flow is itself characterised by a conjugate momentum on, and normal to, the reference curve, giving a one dimensional descriptive signal of the deformation. This descriptive signal contains all of the information required to generate the target curve from the reference curve. We therefore say that this descriptive signal characterises the target curve with respect to the reference curve. The descriptive signal is found using a shooting approach, requiring a functional to measure how closely overlaid are two curves. Formulating the problem as an optimisation problem, we first present a parameterisation-independent functional based on geometric currents, but show that we encounter problems in this matching functional due to local minima. We then present a second approach in which we formulate the problem as a landmark matching problem. Since we seek a characterisation that is independent of the choice of landmarks, and the landmark matching functional is parameterisation dependent, we minimise the functional over all reparameterisations of the reference curve. These two approaches solve equivalent problems. We present the results of the reparameterisation-based matching, and show that they overcome the problems observed in the currents-based method. In particular we demonstrate that the method is able to match complex nasal geometries, and show how the descriptive signal can be used to interpolate between two dimensional slices of three dimensional objects to reconstruct three dimensional surfaces representing the objects. Though here we implement the geodesic flow in two dimensions, we note that the flow could be extended to three dimensional space. Since the reparameterisation based matching functional is trivial to implement in three dimensions, this would allow for the characterisation of both curves and surfaces in three dimensional space

THE TOOLS AND MONTE CARLO WORKING GROUP Summary Report from the Les Houches 2009 Workshop on TeV Colliders

This is the summary and introduction to the proceedings contributions for the Les Houches 2009 "Tools and Monte Carlo" working group.Comment: 144 Pages. Workshop site http://wwwlapp.in2p3.fr/conferences/LesHouches/Houches2009/ . Conveners were Butterworth, Maltoni, Moortgat, Richardson, Schumann and Skand

Coarse-grained modelling of blood cell mechanics

This thesis concerns development of mechanically realistic in silico representations of human blood cells using coarse-grained molecular dynamics (CGMD), ultimately building a new model for a lymphocyte-class white blood cell (WBC). This development is approached successively, evaluated through simulation of experimental testing methods common to past in vitro studies on blood cell mechanics. Considering both their biophysical simplicity and the extensive associated literature, the red blood cell (RBC) is first considered. As a foundation, I thus used the CGMD RBC model of Fu et al. [Lennard-Jones type pair-potential method for coarse-grained lipid bilayer membrane simulations in LAMMPS, Fu et al., Comput. Phys. Commun., 210, 193-203 (2017)]. Chapter 3 establishes implementation of this model, and in silico implementations of the three chosen testing methods. In doing so, the first quantitative assessment of the "miniature cell" approach is conducted - being the down-scaling of the physical cell size to make feasible simulation times, as was done in the original article presenting the model. The RBC model is then used as a foundation from which to develop a new whole-cell WBC lymphocyte model. This is approached sequentially. Firstly (Chapter 4), the morphology and mechanics relevant to the existing RBC model are adapted to those of a lymphocyte. As such, a quasi-spherical morphology is induced, and elastic membrane-associated parameters brought in line with the literature on isolated lymphocytes in vitro. A semi-rigid nucleus is then added to the cell interior, again parameterised to produce elastic properties consistent with the literature. These developments produce a cell having macroscopic mechanical properties much more consistent with a WBC, with an "optimal" parameterisation established. After the membrane and nucleus, the entity most influential to the mechanics of nucleated cells (such as WBC) is their complex intracellular actin-based cytoskeleton (CSK). Therefore, Chapter 5 attempts to represent such a system within our new lymphocyte model. This is approached in three successive stages, assessed against recognised CSK mechanical properties, in particular those also common to soft glassy materials. As such, a novel CSK representation is developed, inspired as a discretisation of soft glassy rheology (SGR). It is proposed that the resulting system has characteristics comparable to having undergone a glass-like transition, as relatable to a real CSK. Therefore, the resulting lymphocyte model may lay a foundation for future development towards mechanically accurate representations of other cells - in particular, a circulating tumour cell