A Mathematical Model for Lymphangiogenesis in Normal and Diabetic Wounds

Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis) very few have been proposed for the regeneration of the lymphatic network. Moreover, lymphangiogenesis is markedly distinct from angiogenesis, occurring at different times and in a different manner. Here a model of five ordinary differential equations is presented to describe the formation of lymphatic capillaries following a skin wound. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from experimental and clinical data. The system is then solved numerically and the results are compared with the available biological literature. Finally, a parameter sensitivity analysis of the model is taken as a starting point for suggesting new therapeutic approaches targeting the enhancement of lymphangiogenesis in diabetic wounds. The work provides a deeper understanding of the phenomenon in question, clarifying the main factors involved. In particular, the balance between TGF-$\beta$ and VEGF levels, rather than their absolute values, is identified as crucial to effective lymphangiogenesis. In addition, the results indicate lowering the macrophage-mediated activation of TGF-$\beta$ and increasing the basal lymphatic endothelial cell growth rate, \emph{inter alia}, as potential treatments. It is hoped the findings of this paper may be considered in the development of future experiments investigating novel lymphangiogenic therapies

Rocket nozzle thermal shock tests in an arc heater facility

A rocket motor nozzle thermal structural test technique that utilizes arc heated nitrogen to simulate a motor burn was developed. The technique was used to test four heavily instrumented full-scale Star 48 rocket motor 2D carbon/carbon segments at conditions simulating the predicted thermal-structural environment. All four nozzles survived the tests without catastrophic or other structural failures. The test technique demonstrated promise as a low cost, controllable alternative to rocket motor firing. The technique includes the capability of rapid termination in the event of failure, allowing post-test analysis

A study to determine the applicability of noise abatement approach procedures to McDonnell Douglas Aircraft

Analyses of McDonnell Douglas DC-8, DC-9, and DC-10 jet transports were conducted to investigate the applicability of two segment approach noise abatement procedures to these airplanes. All models had the required glide slope capability at the certified landing flap settings. The DC-8 models would probably be limited to an upper segment glide slope of 5.5 degrees and would probably not be suitable for the two segment procedure in icing conditions. The DC-8 would not be compatible with this procedure at a reduced landing flap setting. The feasibility of installing a two segment approach system in the Douglas-built fleet of commercial jet transports from a hardware viewpoint is discussed. The candidate system consists of a two segment computer plus the necessary peripheral equipment interfaced with the existing autopilot and associated avionics. The required modifications and additions to existing equipment are described and the attendant costs estimated. Potential problems which may be encountered are also discussed

Measurement of spontaneous emission from a two-dimensional photonic band gap defined microcavity at near-infrared wavelengths

An active, photonic band gap-based microcavity emitter in the near infrared is demonstrated. We present direct measurement of the spontaneous emission power and spectrum from a microcavity formed using a two-dimensional photonic band gap structure in a half wavelength thick slab waveguide. The appearance of cavity resonance peaks in the spectrum correspond to the photonic band gap energy. For detuned band gaps, no resonances are observed. For devices with correctly tuned band gaps, a two-time enhancement of the extraction efficiency was demonstrated compared to detuned band gaps and unpatterned material

Photonic Crystal Nanocavities and Waveguides

Fabrication of optical structures has evolved to a precision which allows us to control light within etched nanostructures. Nano-optic cavities can be used for efficient and flexible concentration of light in small volumes, and control over both emission wavelength and frequency. Conversely, if a periodic pattern is defined in the top semitransparent metal layer by lithography, it is possible to efficiently couple out the light out of a semiconductor and to simultaneously enhance the spontaneous emission rate. Here we demonstrate the use of photonic crystals for efficient light localization and light extraction

Photonic bandgap disk laser

A two-dimensional photonic crystal defined hexagonal disk laser which relies on Bragg reflection rather than the total internal reflection as in traditional microdisk lasers is described. The devices are fabricated using a selective etch to form free standing membranes suspended in air. Room temperature lasing at 1650nm for a 150nm thick, ~15μm wide cavity fabricated in InP/GaAsP is demonstrated with pulsed optical pumping

Photonic Crystals and their Applications to Efficient Light Emitters

When combined with high index contrast slabs in which light can be efficiently guided, microfabricated two-dimensional photonic bandgap mirrors provide us with the geometries needed to confine and concentrate light into extremely small volumes and to obtain very high field intensities. Fabrication of optical structures has now evolved to a precision which allows us to control light within such etched nanostructures. Sub-wavelength nano-optic cavities can be used for efficient and flexible control over both emission wavelength and frequency, and nanofabricated optical waveguides can be used for efficient coupling of light between devices. The reduction of the size of optical components leads to their integration in large numbers and the possibility to combine different functionalities on a single chip. We show uses of such crystals in functional nonlinear optical devices, such as lasers, modulators, add/drop filters, polarizers and detectors

Lasers incorporating 2D photonic bandgap mirrors

Semiconductor lasers incorporating a 2D photonic lattice as a one end mirror in a Fabry-Perot cavity are demonstrated. The photonic lattice is a 2D hexagonal close-packed array with a lattice constant of 220 nm. Pulsed threshold currents of 110 mA were observed from a 180 μm laser

Two-dimensional photonic band-gap mirrors at 850 and 980 nm

Summary form only given. Photonic band-gap (PBG) crystals can be fabricated in semiconductor devices through the etching of patterns of holes in the device, resulting in a periodic dielectric structure. One of the more practical uses of photonic crystals in optoelectronic devices is for thin, high-reflectivity mirrors. The use of hexagonal arrays of etched circular holes results in a 2-D photonic band-gap mirror that can be tuned to a specific wavelength by varying the hole radius and the lattice spacing. 2-D mirror characterization is performed by evaluating the light emission from an active waveguide