Low-level finite state control of knee joint in paraplegic standing

Low-level finite state (locked-unlocked) control is compared with open-loop stimulation of the knee extensor muscles in functional electrical stimulation (FES) induced paraplegic standing. The parameters were: duration of standing, relative torque loss in knee extensor muscles, knee angle stability, average stimulus output and average arm effort during standing. To investigate the impact of external mechanical conditions on controller performance, experiments were performed both under the condition of a freely moving ankle joint and of a mechanically stabilized ankle joint. Finite state control resulted in a 2.5 to 12 times increase of standing duration or in a 1.5 to 5 times decrease of relative torque loss in comparison with open-loop stimulation. Finite state control induced a limit cycle oscillation in the knee joint. Average maximum knee flexion was 6.2° without ankle bracing, and half that value with ankle bracing. Average arm support was 13.9 and 7.5% of the body weight without and with ankle bracing respectively

Convexities related to path properties on graphs; a unified approach

Path properties, such as 'geodesic', 'induced', 'all paths' define a convexity on a connected graph. The general notion of path property, introduced in this paper, gives rise to a comprehensive survey of results obtained by different authors for a variety of path properties, together with a number of new results. We pay special attention to convexities defined by path properties on graph products and the classical convexity invariants, such as the Caratheodory, Helly and Radon numbers in relation with graph invariants, such as clique numbers and other graph properties.

Patient-specific modelling of the cerebral circulation for aneurysm risk assessment

Cerebral aneurysms are localised pathological dilatations of cerebral arteries, most commonly found in the circle of Willis. Although not all aneurysms are unstable, the major clinical concern involved is the risk of rupture. High morbidity and mortality rates are associated with the haemorrhage resulting from rupture. New indicators of aneurysm stability are sought, since current indicators based on morphological factors have been shown to be unreliable. Haemodynamical factors are known to be relevant in vascular wall remodelling, and therefore believed to play an important role in aneurysmdevelopment and stability. Studies suggest that intra-aneurysmal wall shear stress and flow patterns, for example, are candidate parameters in aneurysm stability assessment. These factors can be estimated if the 3D patient-specific intra-aneurysmal velocity is known, which can be obtained via a combination of in vivo measurements and computational fluid dynamics models. The main determinants of the velocity field are the vascular geometry and flow through this geometry. Over the last decade the extraction of the vascular geometry has become well established. More recently, there has been a shift of attention towards extracting boundary conditions for the 3D vascular segment of interest. The aim of this research is to improve the reliability of the model-based representation of the velocity field in the aneurysmal sac. To this end, a protocol is proposed such that patient-specific boundary conditions for the 3D segment of interest can be estimated without the need for added invasive procedures. This is facilitated by a 1D wave propagation model based on patient-specific geometry and boundary conditions measured non-invasively in more accessible regions. Such a protocol offers improved statistical reliability owing to the increased number of patients that can participate in studies aiming to identify parameters of interest in aneurysm stability assessment. In chapter 2 the intra-aneurysmal velocity field in an idealised aneurysm model is validated with particle image velocimetry experiments, after which the flow patterns are evaluated using a vortex identification method. Chapter 3 describes a 1D model wave propagation model of the cerebral circulation with a patient-specific vascular geometry. The resulting flow pulses at the boundaries of the 3D segment of interest are compared to those obtained with a patient-generic geometry. The influence of these different boundary conditions on the 3D intra-aneurysmal velocity field is evaluated in chapter 4 by prescribing the end-diastolic flows extracted from the 1D models. In order to measure blood flow with videodensitometric methods, an injection of contrast agent is required. The effect of this injection on the flow of interest is assessed in chapter 5. In chapter 6, pressure measurements in the internal carotid are used to evaluate the variability of pressure waveform and its effect on the boundary conditions for the 1D model. Finally, a protocol for full patient-specific modelling is discussed in chapter 7

Adsorbent filled membranes for gas separation. Part 1. Improvement of the gas separation properties of polymeric membranes by incorporation of microporous adsorbents

The effect of the introduction of specific adsorbents on the gas separation properties of polymeric membranes has been studied. For this purpose both carbon molecular sieves and zeolites are considered. The results show that zeolites such as silicate-1, 13X and KY improve to a large extent the separation properties of poorly selective rubbery polymers towards a mixture of carbon dioxide/methane. Some of the filled rubbery polymers achieve intrinsic separation properties comparable to cellulose acetate, polysulfone or polyethersulfone. However, zeolite 5A leads to a decrease in permeability and an unchanged selectivity. This is due to the impermeable character of these particles, i.e. carbon dioxide molecules cannot diffuse through the porous structure under the conditions applied. Using silicate-1 also results in an improvement of the oxygen/nitrogen separation properties which is mainly due to a kinetic effect. Carbon molecular sieves do not improve the separation performances or only to a very small extent. This is caused by a mainly dead-end (not interconnected) porous structure which is inherent to their manufacturing process

Spiral order by disorder and lattice nematic order in a frustrated Heisenberg antiferromagnet on the honeycomb lattice

Motivated by recent experiments on Bi$_3$Mn$_4$O$_{12}$(NO$_3$), we study a frustrated $J_1$-$J_2$ Heisenberg model on the two dimensional (2D) honeycomb lattice. The classical $J_1$-$J_2$ Heisenberg model on the two dimensional (2D) honeycomb lattice has N\'eel order for $J_2 J_1/6$, it exhibits a one-parameter family of degenerate incommensurate spin spiral ground states where the spiral wave vector can point in any direction. Spin wave fluctuations at leading order lift this accidental degeneracy in favor of specific wave vectors, leading to spiral order by disorder. For spin $S=1/2$, quantum fluctuations are, however, likely to be strong enough to melt the spiral order parameter over a wide range of $J_2/J_1$. Over a part of this range, we argue that the resulting state is a valence bond solid (VBS) with staggered dimer order - this VBS is a nematic which breaks lattice rotational symmetry. Our arguments are supported by comparing the spin wave energy with the energy of the dimer solid obtained using a bond operator formalism. Turning to the effect of thermal fluctuations on the spiral ordered state, any nonzero temperature destroys the magnetic order, but the discrete rotational symmetry of the lattice remains broken resulting in a thermal analogue of the nematic VBS. We present arguments, supported by classical Monte Carlo simulations, that this nematic transforms into the high temperature symmetric paramagnet via a thermal phase transition which is in the universality class of the classical 3-state Potts (clock) model in 2D. We discuss the possible relevance of our results for honeycomb magnets, such as Bi$_3$M$_4$O$_{12}$(NO$_3$) (with M=Mn,V,Cr), and bilayer triangular lattice magnets.Comment: Slightly revise

Preparation of zeolite filled glassy polymer membranes

The incorporation of zeolite particles in the micrometer range into polymeric matrices was investigated as a way to improve the gas separation properties of the polymer materials used in the form of membranes. The adhesion between the polymer phase and the external surface of the particles appeared to be a major problem in the preparation of such membranes when the polymer is in the glassy state at room temperature. Various methods were investigated to improve the internal membrane structure, that is, surface modification of the zeolite external surface, preparation above the glass-transition temperature, and heat treatment. Improved structures were obtained as observed by scanning electron microscopy, but the influence on the gas separation properties was not in agreement with the observed structural improvements