Solar particle event storm shelter requirements for missions beyond low Earth orbit.

Protecting spacecraft crews from energetic space radiations that pose both chronic and acute health risks is a critical issue for future missions beyond low Earth orbit (LEO). Chronic health risks are possible from both galactic cosmic ray and solar energetic particle event (SPE) exposures. However, SPE exposures also can pose significant short term risks including, if dose levels are high enough, acute radiation syndrome effects that can be mission- or life-threatening. In order to address the reduction of short term risks to spaceflight crews from SPEs, we have developed recommendations to NASA for a design-standard SPE to be used as the basis for evaluating the adequacy of proposed radiation shelters for cislunar missions beyond LEO. Four SPE protection requirements for habitats are proposed: (1) a blood-forming-organ limit of 250 mGy-equivalent for the design SPE; (2) a design reference SPE environment equivalent to the sum of the proton spectra during the October 1989 event series; (3) any necessary assembly of the protection system must be completed within 30 min of event onset; and (4) space protection systems must be designed to ensure that astronaut radiation exposures follow the ALARA (As Low As Reasonably Achievable) principle.

Functional recovery of untreated human immunodeficiency virus-associated Guillain-Barré syndrome: a case report.

HIV-associated Guillain-Barré syndrome is a well-documented phenomenon, typically occurring at seroconversion. GBS may result in functional impairment treated with a combination of medications, plasmapheresis, and rehabilitation. The quantified functional recovery of HIV-associated GBS with or without HIV treatment is not well described. Utilizing serial FIM scoring, we describe a patient's recovery from HIV-associated GBS after treatment with IVIg and acute inpatient rehabilitation without HIV treatment.

Singular perturbation analysis of the steady-state Poisson-Nernst-Planck system: Applications to ion channels.

Ion channels are proteins with a narrow hole down their middle that control a wide range of biological function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biological time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst-Planck) equations called PNP in biophysics. We use singular perturbation techniques to analyse the steady-state PNP system for a channel with a general geometry and a piecewise constant permanent charge profile. We construct an outer solution for the case of a constant permanent charge density in three dimensions that is also a valid solution of the one-dimensional system. The asymptotical current-voltage (I-V ) characteristic curve of the device (obtained by the singular perturbation analysis) is shown to be a very good approximation of the numerical I-V curve (obtained by solving the system numerically). The physical constraint of non-negative concentrations implies a unique solution, i.e., for each given applied potential there corresponds a unique electric current (relaxing this constraint yields non-physical multiple solutions for sufficiently large voltages).

Turing pattern outside of the Turing domain.

There are two simple solutions to reaction-diffusion systems with limit-cycle reaction kinetics, producing oscillatory behaviour. The reaction parameter mu gives rise to a 'space-invariant' solution, and mu versus the ratio of the diffusion coefficients gives rise to a 'time-invariant' solution. We consider the case where both solution types may be possible. This leads to a refinement of the Turing model of pattern formation. We add convection to the system and investigate its effect. More complex solutions arise that appear to combine the two simple solutions. The convective system sheds light on the underlying behaviour of the diffusive system.

Limit cycles in the presence of convection: a traveling wave analysis.

We consider a diffusion model with limit cycle reaction functions. In an unbounded domain, diffusion spreads the pattern outwards from the source. Convection adds instability to the reaction-diffusion system. The result of this instability is a readiness to create a pattern. We choose the Lambda-Omega reaction functions for their simple limit cycle. We carry out a transformation of the dependent variables into polar form. From this we consider the initiation of the pattern to approximate a traveling wave. We carry out numerical experiments to test our analysis. These confirm the premise of the analysis, that the initiation can be modeled by a traveling wave. Furthermore, the analysis produces a good estimate of the numerical results. Most significantly, we confirm that the pattern consists of two different types.

A space radiation transport method development.

Improved spacecraft shield design requires early entry of radiation constraints into the design process to maximize performance and minimize costs. As a result, we have been investigating high-speed computational procedures to allow shield analysis from the preliminary design concepts to the final design. In particular, we will discuss the progress towards a full three-dimensional and computationally efficient deterministic code for which the current HZETRN evaluates the lowest-order asymptotic term. HZETRN is the first deterministic solution to the Boltzmann equation allowing field mapping within the International Space Station (ISS) in tens of minutes using standard finite element method (FEM) geometry common to engineering design practice enabling development of integrated multidisciplinary design optimization methods. A single ray trace in ISS FEM geometry requires 14 ms and severely limits application of Monte Carlo methods to such engineering models. A potential means of improving the Monte Carlo efficiency in coupling to spacecraft geometry is given in terms of re-configurable computing and could be utilized in the final design as verification of the deterministic method optimized design.

Nystrom plus correction method for solving bound-state equations in momentum space.

A method is presented for solving the momentum-space Schrödinger equation with a linear potential. The Lande-subtracted momentum-space integral equation can be transformed into a matrix equation by the Nystrom method. The method produces only approximate eigenvalues in the cases of singular potentials such as the linear potential. The eigenvalues generated by the Nystrom method can be improved by calculating the numerical errors and adding the appropriate corrections. The end results are more accurate eigenvalues than those generated by the basis function method. The method is also shown to work for a relativistic equation such as the Thompson equation.

Creation and utilization of a World Wide Web based space radiation effects code: SIREST.

In order for humans and electronics to fully and safely operate in the space environment, codes like HZETRN (High Charge and Energy Transport) must be included in any designer's toolbox for design evaluation with respect to radiation damage. Currently, spacecraft designers do not have easy access to accurate radiation codes like HZETRN to evaluate their design for radiation effects on humans and electronics. Today, the World Wide Web is sophisticated enough to support the entire HZETRN code and all of the associated pre and post processing tools. This package is called SIREST (Space Ionizing Radiation Effects and Shielding Tools). There are many advantages to SIREST. The most important advantage is the instant update capability of the web. Another major advantage is the modularity that the web imposes on the code. Right now, the major disadvantage of SIREST will be its modularity inside the designer's system. This mostly comes from the fact that a consistent interface between the designer and the computer system to evaluate the design is incomplete. This, however, is to be solved in the Intelligent Synthesis Environment (ISE) program currently being funded by NASA.

Lotka-Volterra equations with chemotaxis: walls, barriers and travelling waves.

In this paper we consider a simple two species model for the growth of new blood vessels. The model is based upon the Lotka-Volterra system of predator and prey interaction, where we identify newly developed capillary tips as the predator species and a chemoattractant which directs their motion as the prey. We extend the Lotka-Volterra system to include a one-dimensional spatial dependence, by allowing the predators to migrate in a manner modelled on the phenomenon of chemotaxis. A feature of this model is its potential to support travelling wave solutions. We emphasize that in order to determine the existence of such travelling waves it is essential that the global relationships of a number of phase plane features other than the equilibria be investigated.

Optical model methods of predicting nuclide production cross sections from heavy ion fragmentation.

Quantum mechanical optical potential methods for calculating inclusive isotope and element production cross sections from the fragmenting of heavy nuclei by intermediate- and high-energy protons and heavy ions are presented based upon a modified abrasion-ablation-FSI (frictional spectator interaction) collision model. The abrasion stage is treated as a quantum mechanical knockout process that leaves the residual prefragment in an excited state. Prefragment excitation energies are estimated using a combined liquid drop and FSI method. In ablation the prefragment deexcites by particle and photon emission to produce the final fragment. Contributions from electromagnetic dissociation to single nucleon removal cross sections are incorporated using a Weiszacker-Williams theory that includes electric dipole and electric quadrupole interactions. Estimates of elemental and isotopic production cross sections are in good agreement with published cross section measurements for a variety of projectile-target-beam energy combinations.

A model of wound-healing angiogenesis in soft tissue.

Angiogenesis, or blood vessel growth, is a critical step in the wound-healing process, involving the chemotactic response of blood vessel endothelial cells to macrophage-derived factors produced in the wound space. In this article, we formulate a system of partial differential equations that model the evolution of the capillary-tip endothelial cells, macrophage-derived chemoattractants, and the new blood vessels during the tissue repair process. Chemotaxis is incorporated as a dominant feature of the model, driving the wave-like ingrowth of the wound-healing unit. The resulting model admits traveling wave solutions that exhibit many of the features characteristic of wound healing in soft tissue. The steady propagation of the healing unit through the wound space, the development of a dense band of fine, tipped capillaries near the leading edge of the wound-healing unit (the brush-border effect), and an elevated vessel density associated with newly healed wounds, prior to vascular remodeling, are all discernible from numerical simulations of the full model. Numerical simulations mimic not only the normal progression of wound healing but also the potential for some wounds to fail to heal. Through the development and analysis of a simplified model, insight is gained into how the balance between chemotaxis, tip proliferation, and tip death affects the structure and speed of propagation of the healing unit. Further, expressions defining the healed vessel density and the wavespeed in terms of known parameters lead naturally to the identification of a maximum wavespeed for the wound-healing process and to bounds on the healed vessel density. The implications of these results for wound-healing management are also discussed.

Biological inferences from a mathematical model for malignant invasion.

Invasive cells show changes in adhesion, motility and the protease-antiprotease balance. In this paper the authors derive a model based on a continuum approach that describes the behaviour of the invasive cells. The invasive cells are studied in the context of their interaction with normal cells, noninvasive tumour cells, ECM proteins and the proteases. The authors briefly describe the methods of mathematical analysis used and then go on to highlight the biological inferences drawn from the mathematical analysis. Based on the results from the modelling the authors suggest that the movement of cells under the simultaneous effects of a haptotactic gradient and a concomitantly created chemotactic gradient is oscillatory both with respect to the speed of invasion and the wave profile of the invasive cells. They further demonstrate that the average speed of invasion can be computed as a measure of the phenotypic properties of the cell and the matrix. They use the model to suggest an intuitive explanation for the occurrence of noninvasion with high protease expression on the basis of chemotactic gradients that prevent invasion. The authors have studied the effect of the diffusivity of the protease on an invading cell and shown that increase in diffusivity initially results in enhanced invasion, but extreme increases in protease diffusivity can result in noninvasion.

Parameterization of spectral distributions for pion and kaon production in proton-proton collisions.

Accurate semi-empirical parameterizations of the energy-differential cross sections for charged pion and kaon production from proton-proton collisions are presented at energies relevant to cosmic rays. The parameterizations depend on the outgoing meson momentum and also the proton energy, and are able to be reduced to very simple analytical formulas suitable for cosmic-ray transport.

Cross section parameterizations for cosmic-ray nuclei. II. Double nucleon removal.

Parameterizations of double nucleon removal from the electromagnetic and strong interactions of cosmic rays with nuclei are presented. These parameterizations are an extension of previous single nucleon removal parameterizations and combined they represent the dominant part of the electromagnetic dissociation encountered by a cosmic ray on its traversal through matter. Such parameterizations should be very useful in studying cosmic-ray transport through the interstellar medium, the Earth's atmosphere, spacecraft walls, and extraterrestrial matter.

Cross section parameterizations for cosmic-ray nuclei. I. Single nucleon removal.

Parameterizations of single nucleon removal from the electromagnetic and strong interactions of cosmic rays with nuclei are presented. These parameterizations are based upon the theoretical models developed by Baur, Bertulani, Benesh, Cook, Vary, Norbury, and Townsend. They should be very suitable for use in cosmic-ray propagation through interstellar space, Earth's atmosphere, lunar samples, meteorites, spacecraft walls, and lunar and martian habitats.

Calculations of hadronic dissociation of 28Si projectiles at 14.6A GeV by nucleon emission.

An optical potential abrasion-ablation collision model is used to calculate hadronic dissociation cross sections for one, two, and three nucleon removal for the first time for a 14.6A GeV 28Si beam fragmenting in aluminum, tin, and lead targets. These estimates are compared with recent semi-inclusive measurements. Significant differences between some calculated and measured semi-inclusive cross sections exist which cannot be resolved without measurements of the exclusive channel hadronic cross sections. Calculations for each exclusive reaction channel contributing to the semi-inclusive cross sections are presented and discussed.

Optical model description of momentum transfer in relativistic heavy ion collisions.

An optical model description of momentum transfer in relativistic heavy ion collisions, based upon composite particle multiple-scattering theory, is presented. The imaginary component of the complex momentum transfer, which comes from the absorptive part of the optical potential, is shown to be the main contributor to the momentum loss of the projectile. Within the context of the Goldhaber formalism, predictions of fragment momentum distribution observables are made and compared with experimental data. Use of the model as a tool for estimating collision impact parameters is also discussed.

Higgs-boson production in nucleus-nucleus collisions.

Cross-section calculations are presented for the production of intermediate-mass Higgs bosons produced in ultrarelativistic nucleus-nucleus collisions via two-photon fusion. The calculations are performed in position space using Baur's method for folding together the Weizsacker-Williams virtual-photon spectra of the two colliding nuclei. It is found that two-photon fusion in nucleus-nucleus collisions is a plausible way of finding intermediate-mass Higgs bosons at the Superconducting Super Collider or the CERN Large Hadron Collider.

Charge dependence and electric quadrupole effects on single-nucleon removal in relativistic and intermediate energy nuclear collisions.

Single-nucleon removal in relativistic and intermediate energy nucleus-nucleus collisions is studied using a generalization of Weizsäcker-Williams theory that treats each electromagnetic multipole separately. Calculations are presented for electric dipole and quadrupole excitations and incorporate a realistic minimum impact parameter, Coulomb recoil corrections, and the uncertainties in the input photonuclear data. Discrepancies are discussed. The maximum quadrupole effect to be observed in future experiments is estimated and also an analysis of the charge dependence of the electromagnetic cross sections down to energies as low as 100 MeV/nucleon is made.

Single nucleon emission in relativistic nucleus-nucleus reactions.

Significant discrepancies between theory and experiment have previously been noted for nucleon emission via electromagnetic processes in relativistic nucleus-nucleus collisions. The present work investigates the hypothesis that these discrepancies have arisen due to uncertainties about how to deduce the experimental electromagnetic cross section from the total measured cross section. An optical-model calculation of single neutron removal is added to electromagnetic cross sections and compared to the total experimental cross sections. Good agreement is found thereby resolving some of the earlier noted discrepancies. A detailed comparison to the recent work of Benesh, Cook, and Vary is made for both the impact parameter and the nuclear cross section. Good agreement is obtained giving an independent confirmation of the parametrized formulas developed by those authors.