Modelling of oedemous limbs and venous ulcers using partial differential equations

BACKGROUND: Oedema, commonly known as tissue swelling, occurs mainly on the leg and the arm. The condition may be associated with a range of causes such as venous diseases, trauma, infection, joint disease and orthopaedic surgery. Oedema is caused by both lymphatic and chronic venous insufficiency, which leads to pooling of blood and fluid in the extremities. This results in swelling, mild redness and scaling of the skin, all of which can culminate in ulceration. METHODS: We present a method to model a wide variety of geometries of limbs affected by oedema and venous ulcers. The shape modelling is based on the PDE method where a set of boundary curves are extracted from 3D scan data and are utilised as boundary conditions to solve a PDE, which provides the geometry of an affected limb. For this work we utilise a mixture of fourth order and sixth order PDEs, the solutions of which enable us to obtain a good representative shape of the limb and associated ulcers in question. RESULTS: A series of examples are discussed demonstrating the capability of the method to produce good representative shapes of limbs by utilising a series of curves extracted from the scan data. In particular we show how the method could be used to model the shape of an arm and a leg with an associated ulcer. CONCLUSION: We show how PDE based shape modelling techniques can be utilised to generate a variety of limb shapes and associated ulcers by means of a series of curves extracted from scan data. We also discuss how the method could be used to manipulate a generic shape of a limb and an associated wound so that the model could be fine-tuned for a particular patient

Modelling oedemous limbs and venous ulcers using partial differential equations

Background Oedema, commonly known as tissue swelling, occurs mainly on the leg and the arm. The condition may be associated with a range of causes such as venous diseases, trauma, infection, joint disease and orthopaedic surgery. Oedema is caused by both lymphatic and chronic venous insufficiency, which leads to pooling of blood and fluid in the extremities. This results in swelling, mild redness and scaling of the skin, all of which can culminate in ulceration. Methods We present a method to model a wide variety of geometries of limbs affected by oedema and venous ulcers. The shape modelling is based on the PDE method where a set of boundary curves are extracted from 3D scan data and are utilised as boundary conditions to solve a PDE, which provides the geometry of an affected limb. For this work we utilise a mixture of fourth order and sixth order PDEs, the solutions of which enable us to obtain a good representative shape of the limb and associated ulcers in question. Results A series of examples are discussed demonstrating the capability of the method to produce good representative shapes of limbs by utilising a series of curves extracted from the scan data. In particular we show how the method could be used to model the shape of an arm and a leg with an associated ulcer. Conclusion We show how PDE based shape modelling techniques can be utilised to generate a variety of limb shapes and associated ulcers by means of a series of curves extracted from scan data. We also discuss how the method could be used to manipulate a generic shape of a limb and an associated wound so that the model could be fine-tuned for a particular patient

Flow in a double-film-fed fluid bead between contra-rotating rolls, Part 2: bead break and flooding

Two-dimensional flow is considered in a fluid bead located in the gap between a pair of contra-rotating cylinders and bounded by two curved menisci. The stability of such bead flows with two inlet films, and hence no contact line, are analysed as the roll speed ratio S is increased. One of the inlet films can be regarded as an ‘input flux’ whilst the other is a ‘returning film’ whose thickness is specified as a fraction [zeta] of the outlet film on that roll. The flow is modelled via lubrication theory and for Ca [double less-than sign] 1, where Ca represents the capillary number, boundary conditions are formally developed that account for S [not equal] 1 and the non-constant gap. It is shown that there is a qualitative difference in the results between the single and double inlet film models unless small correction terms to the pressure drops at the interfaces are taken into account. Futhermore, it is shown that the inclusion of these small terms produces an O(1) effect on the prediction of the critical value of S at which bead break occurs. When the limits of the returning film fraction are examined it is found that as [zeta] [rightward arrow] 0 results are in good agreement with those for the single inlet film. Further it is shown for a fixed input flux that as [zeta] [rightward arrow] 1 a transition from bead break to upstream flooding of the nip can occur and multiple two-dimensionally stable solutions exist. For a varying input flux and fixed and ‘sufficiently large’ values of [zeta] there is a critical input flux &[lambda]macr;([zeta]) such that as S is increased from zero: (i) bead break occurs for [lambda] < &[lambda]macr;; (ii) upstream flooding occurs for [lambda] > &[lambda]macr;; (iii) when [lambda] = &[lambda]macr; the flow becomes neutrally stable at a specific value of S beyond which there exist two steady solutions (two-dimensionally stable) leading to bead break and upstream flooding, respectively

Pre-operative optimisation employing dopexamine or adrenaline for patients undergoing major elective surgery: a cost-effectiveness analysis

&lt;b&gt;Objective&lt;/b&gt;: To compare the cost and cost-effectiveness of a policy of pre-operative optimisation of oxygen delivery (using either adrenaline or dopexamine) to reduce the risk associated with major elective surgery, in high-risk patients. &lt;b&gt;Methods&lt;/b&gt;: A cost-effectiveness analysis using data from a randomised controlled trial (RCT). In the RCT 138 patients undergoing major elective surgery were allocated to receive pre-operative optimisation employing either adrenaline or dopexamine (assigned randomly), or to receive routine peri-operative care. Differential health service costs were based on trial data on the number and cause of hospital in-patient days and the utilisation of health care resources. These were costed using unit costs from a UK hospital. The cost-effectiveness analysis related differential costs to differential life-years during a 2 year trial follow-up. &lt;b&gt;Results&lt;/b&gt;: The mean number of in-patient days was 16 in the pre-optimised groups (19 adrenaline; 13 dopexamine) and 22 in the standard care group. The number (%) of deaths, over a 2 year follow-up, was 24 (26%) in the pre-optimised groups and 15 (33%) in the standard care group. The mean total costs were EUR 11,310 in the pre-optimised groups and EUR 16,965 in the standard care group. Life-years were 1.68 in the pre-optimised groups and 1.46 in the standard care group. The probability that pre-operative optimisation is less costly than standard care is 98%. The probability that it dominates standard care is 93%. Conclusions: Based on resource use and effectiveness data collected in the trial, pre-operative optimisation of high-risk surgical patients undergoing major elective surgery is cost-effective compared with standard treatment

Optimisation of the spark gap parameters for high powered ultrasound applications

There is considerable interest in the industrial and commercial applications of high power ultrasound (HPU) generated using pulsed power techniques. These applications include metal peening, the treatment of ores and minerals before extraction, drilling technologies and the comminution and recovery of waste materials. In all of these applications, it is important to optimise the parameters of the discharge causing the shock wave in the working medium to maximise the efficiency of the treatment. In a research project at the University of Strathclyde, some applications of HPU to the treatment of waste to assist in recycling have been investigated. Two systems have been considered, slag from the manufacture of stainless steel and bottle glass. With the slag material, it is intended to separate stainless steel from the silicate matrix to permit its recovery. With the bottle glass, the intention is comminution of the material to allow it to be recycled in a more valuable form. Measurements of the efficiency of these processes have been made in terms of the mass of material processed versus the energy input as the parameters of the discharge gap have been varied. In parallel with this work, measurements have been made using pinducer sensors to determine the energy in HPU pulses generated by discharges under identical conditions. Correlations are made between the efficiency of material treatment and the intensity of the HPU pulse measured in the far field. It is hoped that this approach will allow the optimal gap parameters to be determined using pinducer measurements rather than time consuming trials based around materials processing

An Investigation of Void Fraction in the Stratified/Annular Flow Regions in Smooth, Horizontal Tubes

Refrigerants R134a and R410A have been used for void fraction measurements in smooth horizontal tubes with diameters between 4mm and 7mm. Quality and mass flux were varied from 5% to 90% and 75 kglm2-s to 700 kglm2-s, respectively. Two test loops, one for condensing flows at 35C and the other for evaporating flows at 5C, were used in the investigation. Results show that near the transition from annular to stratified flow void fraction changed from viscousinertial dependence to gravitational-inertial dominated dependence. An important feature observed is the annular flow region's relative insensitivity to mass flux while the border region between annular and stratified flows is characterized by strong mass flux dependence.Air Conditioning and Refrigeration Project 7

Radio Source Heating in the ICM: The Example of Cygnus A

One of the most promising solutions for the cooling flow problem involves energy injection from the central AGN. However it is still not clear how collimated jets can heat the ICM at large scale, and very little is known concerning the effect of radio lobe expansion as they enter into pressure equilibrium with the surrounding cluster gas. Cygnus A is one of the best examples of a nearby powerful radio galaxy for which the synchrotron emitting plasma and thermal emitting intra-cluster medium can be mapped in fine detail, and previous observations have inferred possible shock structure at the location of the cocoon. We use new XMM-Newton observations of Cygnus A, in combination with deep Chandra observations, to measure the temperature of the intra-cluster medium around the expanding radio cavities. We investigate how inflation of the cavities may relate to shock heating of the intra-cluster gas, and whether such a mechanism is sufficient to provide enough energy to offset cooling to the extent observed.Comment: To appear in the Proceedings of "Heating vs. Cooling in Galaxies and Clusters of Galaxies", August 2006, Garching (Germany), Eds. H. Boehringer, G.W. Pratt, A. Finoguenov, P. Schuecker, Springer-Verlag series "ESO Astrophysics Symposia", p.101, in press. 8 pages, 3 multiple figure

A methodology for determining the dynamic exchange of resources in nuclear fuel cycle simulation

Simulation of the nuclear fuel cycle can be performed using a wide range of techniques and methodologies. Past efforts have focused on specific fuel cycles or reactor technologies. The CYCLUS fuel cycle simulator seeks to separate the design of the simulation from the fuel cycle or technologies of interest. In order to support this separation, a robust supply–demand communication and solution framework is required. Accordingly an agent-based supply-chain framework, the Dynamic Resource Exchange (DRE), has been designed implemented in CYCLUS. It supports the communication of complex resources, namely isotopic compositions of nuclear fuel, between fuel cycle facilities and their managers (e.g., institutions and regions). Instances of supply and demand are defined as an optimization problem and solved for each timestep. Importantly, the DRE allows each agent in the simulation to independently indicate preference for specific trading options in order to meet both physics requirements and satisfy constraints imposed by potential socio-political models. To display the variety of possible simulations that the DRE enables, example scenarios are formulated and described. Important features include key fuel-cycle facility outages, introduction of external recycled fuel sources (similar to the current mixed oxide (MOX) fuel fabrication facility in the United States), and nontrivial interactions between fuel cycles existing in different regions

Surface flashover of oil-immersed dielectric materials in uniform and non-uniform fields

The applied electrical fields required to initiate surface flashover of different types of dielectric material immersed in insulating oil have been investigated, by applying impulses of increasing peak voltage until surface flashover occurred. The behavior of the materials in repeatedly over-volted gaps was also analyzed in terms of breakdown mode (some bulk sample breakdown behaviour was witnessed in this regime), time to breakdown, and breakdown voltage. Cylindrical samples of polypropylene, low-density polyethylene, ultra-high molecular weight polyethylene, and Rexolite, were held between two electrodes immersed in insulating oil, and subjected to average applied electrical fields up to 870 kV/cm. Tests were performed in both uniform- and non-uniform-fields, and with different sample topologies. In applied field measurements, polypropylene required the highest levels of average applied field to initiate flashover in all electrode configurations tested, settling at similar to 600 kV/cm in uniform fields, and similar to 325 kV/cm in non-uniform fields. In over-volted point-plane gaps, ultra-high molecular weight polyethylene exhibited the longest pre-breakdown delay times. The results will provide comparative data for system designers for the appropriate choice of dielectric materials to act as insulators for high-voltage, pulsed-power machines