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At least 1,387 records · Page 77
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Skeletal muscle satellite cells cultured in simulated microgravity

Satellite cells are postnatal myoblasts responsible for providing additional nuclei to growing or regenerating muscle cells. Satellite cells retain the capacity to proliferate and differentiate in vitro and therefore provide a useful model to study postnatal muscle development. Most culture systems used to study postnatal muscle development are limited by the two-dimensional (2-D) confines of the culture dish. Limiting proliferation and differentiation of satellite cells in 2-D could potentially limit cell-cell contacts important for developing the level of organization in skeletal muscle obtained in vivo. Culturing satellite cells on microcarrier beads suspended in the High-Aspect-Ratio-Vessel (HARV) designed by NASA provides a low shear, three-dimensional (3-D) environment to study muscle development. Primary cultures established from anterior tibialis muscles of growing rats (approximately 200 gm) were used for all studies and were composed of greater than 75 % satellite cells. Different inoculation densities did not affect the proliferative potential of satellite cells in the HARV. Plating efficiency, proliferation, and glucose utilization were compared between 2-D flat culture and 3-D HARV culture. Plating efficiency (cells attached - cells plated x 100) was similar between the two culture systems. Proliferation was reduced in HARV cultures and this reduction was apparent for both satellite cells and non-satellite cells. Furthermore, reduction in proliferation within the HARV could not be attributed to reduced substrate availability since glucose levels in media from HARV and 2-D cell culture were similar. Morphologically, microcarrier beads within the HARVS were joined together by cells into three-dimensional aggregates composed of greater than 10 beads/aggregate. Aggregation of beads did not occur in the absence of cells. Myotubes were often seen on individual beads or spanning the surface of two beads. In summary, proliferation and differentiation of satellite cells on microcarrier beads within the HARV bioreactor results in a three dimensional level of organization that could provide a more suitable model to study postnatal muscle development.

Molnar, Greg↗
NASA NTRS1995

The Averaged Face Growth Rates of lysozyme Crystals: The Effect of Temperature

Measurements of the averaged or macroscopic face growth rates of lysozyme crystals are reported here for the (110) face of tetragonal lysozyme, at three sets of pH and salt concentrations, with temperatures over a 4-22 C range for several protein concentrations. The growth rate trends with supersaturation were similar to previous microscopic growth rate measurements. However, it was found that at high super-saturations the growth rates attain a maximum and then start decreasing. No 'dead zone' was observed but the growth rates were found to approach zero asymptotically at very low super-saturations. The growth rate data also displayed a dependence on pH and salt concentration which could not be characterized solely by the super-saturation. A complete mechanism for lysozyme crystal growth, involving the formation of an aggregate growth unit, mass transport of the growth unit to the crystal interface and faceted crystal growth by growth unit addition, is suggested. Such a mechanism may provide a more consistent explanation for the observed growth rate trends than those suggested by other investigators. The nutrient solution interactions leading to the formation of the aggregate growth unit may, thus, be as important as those occurring at the crystal interface and may account for the differences between small molecule and protein crystal growth.

Nadarajah, Arunan↗
NASA NTRS1997

On the Multilevel Solution Algorithm for Markov Chains

We discuss the recently introduced multilevel algorithm for the steady-state solution of Markov chains. The method is based on an aggregation principle which is well established in the literature and features a multiplicative coarse-level correction. Recursive application of the aggregation principle, which uses an operator-dependent coarsening, yields a multi-level method which has been shown experimentally to give results significantly faster than the typical methods currently in use. When cast as a multigrid-like method, the algorithm is seen to be a Galerkin-Full Approximation Scheme with a solution-dependent prolongation operator. Special properties of this prolongation lead to the cancellation of the computationally intensive terms of the coarse-level equations.

Horton, Graham↗
NASA NTRS1997

Combustion of PTFE: The Effects of Gravity and Pigmentation on Ultrafine Particle Generation

Ultrafine particles generated during polymer thermodegradation are a major health hazard, owing to their unique pathway of processing in the lung. This hazard in manned spacecraft is poorly understood, because the particulate products of polymer thermodegradation are generated under low gravity conditions. Particulate generated from the degradation of PolyTetraFluoroEthylene (PTFE), insulation coating for 20 AWG copper wire (representative of spacecraft application) under intense ohmic heating were studied in terrestrial gravity and microgravity. Microgravity tests were done in a 1.2-second drop tower at the Colorado School of Mines (CSM). Thermophoretic sampling was used for particulate collection. Transmission Electron Microscopy (TEM) and Scanning Transmission Electron Microscopy (STEM) were used to examine the smoke particulates. Image software was used to calculate particle size distribution. In addition to gravity, the color of PTFE insulation has an overwhelming effect on size, shape and morphology of the particulate. Nanometer-sized primary particles were found in all cases, and aggregation and size distribution was dependent on both color and gravity; higher aggregation occurred in low gravity. Particulates from white, black, red and yellow colored PTFE insulations were studied. Elemental analysis of the particulates shows the presence of inorganic pigments.

McKinnon, J. Thomas↗
NASA NTRS1995

Brief Communication: Buoyancy-Induced Differences in Soot Morphology

Reduction or elimination of buoyancy in flames affects the dominant mechanisms driving heat transfer, burning rates and flame shape. The absence of buoyancy produces longer residence times for soot formation, clustering and oxidation. In addition, soot pathlines are strongly affected in microgravity. We recently conducted the first experiments comparing soot morphology in normal and reduced-gravity laminar gas jet diffusion flames. Thermophoretic sampling is a relatively new but well-established technique for studying the morphology of soot primaries and aggregates. Although there have been some questions about biasing that may be induced due to sampling, recent analysis by Rosner et al. showed that the sample is not biased when the system under study is operating in the continuum limit. Furthermore, even if the sampling is preferentially biased to larger aggregates, the size-invariant premise of fractal analysis should produce a correct fractal dimension.

Ku, Jerry C.↗
NASA NTRS1997

Dynamic Flow Management Problems in Air Transportation

In 1995, over six hundred thousand licensed pilots flew nearly thirty-five million flights into over eighteen thousand U.S. airports, logging more than 519 billion passenger miles. Since demand for air travel has increased by more than 50% in the last decade while capacity has stagnated, congestion is a problem of undeniable practical significance. In this thesis, we will develop optimization techniques that reduce the impact of congestion on the national airspace. We start by determining the optimal release times for flights into the airspace and the optimal speed adjustment while airborne taking into account the capacitated airspace. This is called the Air Traffic Flow Management Problem (TFMP). We address the complexity, showing that it is NP-hard. We build an integer programming formulation that is quite strong as some of the proposed inequalities are facet defining for the convex hull of solutions. For practical problems, the solutions of the LP relaxation of the TFMP are very often integral. In essence, we reduce the problem to efficiently solving large scale linear programming problems. Thus, the computation times are reasonably small for large scale, practical problems involving thousands of flights. Next, we address the problem of determining how to reroute aircraft in the airspace system when faced with dynamically changing weather conditions. This is called the Air Traffic Flow Management Rerouting Problem (TFMRP) We present an integrated mathematical programming approach for the TFMRP, which utilizes several methodologies, in order to minimize delay costs. In order to address the high dimensionality, we present an aggregate model, in which we formulate the TFMRP as a multicommodity, integer, dynamic network flow problem with certain side constraints. Using Lagrangian relaxation, we generate aggregate flows that are decomposed into a collection of flight paths using a randomized rounding heuristic. This collection of paths is used in a packing integer programming formulation, the solution of which generates feasible and near-optimal routes for individual flights. The algorithm, termed the Lagrangian Generation Algorithm, is used to solve practical problems in the southwestern portion of United States in which the solutions are within 1% of the corresponding lower bounds.

Patterson, Sarah Stock↗
NASA NTRS1997

Atmospheric Condensational Properties of Ultrafine Chain and Fractal Aerosol Particles

The purpose for the research sponsored by this grant was to lay the foundations for qualitative understanding and quantitative description of the equilibrium vapor pressure of water vapor over the irregularly shaped, carbonaceous particles that are present in the atmosphere. This work apparently was the first systematic treatment of the subject. Research was conducted in two complementary components: 1. Calculations were performed of the equilibrium vapor pressure of water over particles comprised of aggregates of spheres in the 50-200 nm radius range. The purposes of this work were two-fold. First, since no systematic treatment of this subject had previously been conducted, its availability would be directly useful for quantitative treatment for a limited range of atmospheric aerosols. Second, it would provide qualitative indications of the effects of highly irregular particle shape on equilibrium vapor pressure of aggregates comprised of smaller spheres.

Marlow, William H.↗
NASA NTRS1998

Precipitation Structure in the Sierra Nevada of California During Winter

The influences of upper air characteristics along the coast of California upon the winter time precipitation in the Sierra Nevada region were investigated. Most precipitation episodes in the Sierra are associated with moist southwesterly winds and also tend to occur when the 700-mb temperature is close to -2 C. This favored wind direction and temperature signifies the equal importance of moisture transport and orographic lifting for maximum precipitation frequency. Making use of this observation, simple linear models were formulated to quantify the precipitation totals observed at different sites as a function of moisture transport. The skill of the model is least for daily precipitation and increases with time scale of aggregation. In terms of incremental gain, the skill of the model is optimal for an aggregation period of 5-7 days, which is also the duration of the most frequent precipitation events in the Sierra. This indicates that upper air moisture transport at can be used to make reasonable estimates of the precipitation totals for most frequent events in the Sierra region.

Pandey, Ganesh R.↗
NASA NTRS1998

Three Dimensional Primary Hepatocyte Culture

Our results demonstrated for the first time the feasibility of culturing PHH in microgravity bioreactors that exceeded the longest period obtained using other methods. Within the first week of culture, isolated hepatocytes started to form aggregates, which continuously increased in size (up to 1 cm) and macroscopically appeared as a multidimensional tissue-like assembly. To improve oxygenation and nutrition within the spheroids we performed experiments with the biodegradable nonwoven fiber-based polymers made from PolyGlycolic Acid (PGA). It has been shown that PGA scaffolds stimulate isolated cells to regenerate tissue with defined sizes and shapes and are currently being studied for various tissue-engineering applications. Our data demonstrated that culturing hepatocytes in the presence of PGA scaffolds resulted in more efficient cell assembly and formations of larger cell spheroids (up to 3 cm in length, see figure). The histology of cell aggregates cultured with PGA showed polymer fibers with attached hepatocytes. We initiated experiments to co-culture primary human hepatocytes with human microvascular endothelial cells in the bioreactor. The presence of endothelial cells in co-cultures were established by immunohistochemistry using anti-CD34 monoclonal Ab. Our preliminary data demonstrated that cultures of purified hepatocytes with human microvascular endothelial cells exhibited better growth and expressed higher levels of albumin MRNA for a longer period of time than cultures of ppfified, primary human hepatocytes cultured alone. We also evaluated microsomal deethylation activity of hepatocytes cultured in the presence of endothelial cells.In summary, we have established liver cell culture, which mimicked the structure and function of the parent tissue.

Yoffe, Boris↗
NASA NTRS1999

Effects of Microgravity on the Formation of Aerogels

This paper describes research to investigate fundamental aspects of the effects of microgravity on the formation of the microstructure of metal oxide alcogels and aerogels. We are studying the role of gravity on pore structure and gel uniformity in collaboration with Marshall Space Flight Center (MSFC) on gelling systems under microgravity conditions. While this project was just initiated in May 1998, related research performed earlier is described along with the plans and rationale for the current microgravity investigation to provide background and describe newly developing techniques that should be useful for the current gellation studies. The role of gravity in materials processing must be investigated through the study of well-mastered systems. Sol-gel processed materials are near-perfect candidates to determine the effect of gravity on the formation and growth of random clusters from hierarchies of aggregated units. The processes of hydrolysis, condensation, aggregation and gellation in the formation of alcogels are affected by gravity and therefore provide a rich system to study under microgravity conditions. Supercritical drying of the otherwise unstable wet alcogel preserves the alcogel structure produced during sol-gel processing as aerogel. Supercritically dried aerogel provides for the study of material microstructures without interference from the effects of surface tension, evaporation, and solvent flow. Aerogels are microstructured, low density open-pore solids. They have many unusual properties including: transparency, excellent thermal resistance, high surface area, very low refractive index, a dielectric constant approaching that of air, and extremely low sound velocity. Aerogels are synthesized using sol-gel processing followed by supercritical solvent extraction that leaves the original gel structure virtually intact. These studies will elucidate the effects of microgravity on the homogeneity of the microstructure and porosity of aerogel. The presence of poorly controlled microporosity in aerogel leads to material non-uniformity that gives rise to increased light scattering. Investigation of the effect of gravity driven solute flows within microclusters and their effect on condensation and agglomeration reactions will enable us to improve the preparation and properties of aerogel. Increased clarity of images viewed through aerogel and decreased scattering from the pores of aerogel will significantly improve the prospects for large-scale adoption of aerogel in such applications as transparent insulating windows, high performance thermal insulation, and Cherenkov detectors.

Hunt, A. J.↗
NASA NTRS1998

Relationship Between Ecosystem Productivity and Photosynthetically Active Radiation for Northern Peatlands

We analyzed the relationship between net ecosystem exchange of carbon dioxide (NEE) and irradiance (as photosynthetic photon flux density or PPFD), using published and unpublished data that have been collected during midgrowing season for carbon balance studies at seven peatlands in North America and Europe, NEE measurements included both eddy-correlation tower and clear, static chamber methods, which gave very similar results. Data were analyzed by site, as aggregated data sets by peatland type (bog, poor fen, rich fen, and all fens) and as a single aggregated data set for all peatlands. In all cases, a fit with a rectangular hyperbola (NEE = alpha PPFD P(sub max)/(alpha PPFD + P(sub max) + R) better described the NEE-PPFD relationship than did a linear fit (NEE = beta PPFD + R). Poor and rich fens generally had similar NEE-PPFD relationships, while bogs had lower respiration rates (R = -2.0 micro mol m(exp -2) s(exp -1) for bogs and -2.7 micro mol m(exp -2) s(exp -1)) for fens) and lower NEE at moderate and high light levels (P(sub max)= 5.2 micro mol m(exp -2) s(exp -1) for bogs and 10.8 micro mol m(exp -2) s(exp -1) for fens). As a single class, northern peatlands had much smaller ecosystem respiration (R = -2.4 micro mol m(exp -2) s(exp -1)) and NEE rates (alpha = 0.020 and P(sub max)= 9.2 micro mol m(exp -2) s(exp -1)) than the upland ecosystems (closed canopy forest, grassland, and cropland). Despite this low productivity, northern peatland soil carbon pools are generally 5-50 times larger than upland ecosystems because of slow rates of decomposition caused by litter quality and anaerobic, cold soils.

Frolking, S. E.↗
NASA NTRS1995

Intent Specifications

We have been investigating the implications of using abstractions based on intent rather than the aggregation and information-hiding abstractions commonly used in software en- gineering: Cognitive psychologists have shown that intent abstraction is consistent with human problem-solving processes. We believe that new types of specifications and designs based on this concept can assist in understanding and specifying requirements, capturing the most important design rationale information in an efficient and economical way, and supporting the process of identifying and analyzing required changes to minimize the introduction of errors. The goal of hierarchical abstraction is to allow both top-down and bottom-up reasoning about a complex system. In computer science, we have made much use of (1) part-whole abstractions where each level of a hierarchy represents an aggregation of the components at a lower level and of (2) information-hiding abstractions where each level contains the same conceptual information but hides some details about the concepts, that is, each level is a refinement of the information at a higher level.

Leveson, Nancy G.↗
NASA NTRS1997

Surface Plasmon Resonance Evaluation of Colloidal Metal Aerogel Filters

We have fabricated aerogels containing gold, silver, and platinum nanoparticles for gas catalysis applications. By applying the concept of an average or effective dielectric constant to the heterogeneous interlayer surrounding each particle, we extend the technique of immersion spectroscopy to porous or heterogeneous media. Specifically, we apply the predominant effective medium theories for the determination of the average fractional composition of each component in this inhomogeneous layer. Hence, the surface area of metal available for catalytic gas reaction is determined. The technique is satisfactory for statistically random metal particle distributions but needs further modification for aggregated or surfactant modified systems. Additionally, the kinetics suggest that collective particle interactions in coagulated clusters are perturbed during silica gelation resulting in a change in the aggregate geometry.

Smith, David D.↗
NASA NTRS1998

Determining the Molecular Growth Mechanisms of Protein Crystal faces by Atomic Force Microscopy

A high resolution atomic force microscopy (AFM) study had shown that the molecular packing on the tetragonal lysozyme (110) face corresponded to only one of two possible packing arrangements, suggesting that growth layers on this face were of bimolecular height (Li et al., 1998). Theoretical analyses of the packing had also indicated that growth of this face should proceed by the addition of growth units of at least tetramer size corresponding to the 43 helices in the crystal. In this study an AFM linescan technique was devised to measure the dimensions of individual growth units on protein crystal faces. The growth process of tetragonal lysozyme crystals was slowed down by employing very low supersaturations. As a result images of individual growth events on the (110) face were observed, shown by jump discontinuities in the growth step in the linescan images. The growth unit dimension in the scanned direction was obtained by suitably averaging these images. A large number of scans in two directions on the (110) face were performed and the distribution of lysozyme aggregate sizes were obtained. A variety of growth units, all of which were 43 helical lysozyme aggregates, were shown to participate in the growth process with a 43 tetramer being the minimum observed size. This technique represents a new application for AFM allowing time resolved studies of molecular process to be carried out.

Li, Huayu↗
NASA NTRS1998

Noble Metal Immersion Spectroscopy of Silica Alcogels and Aerogels

We have fabricated aerogels containing gold and silver nanoparticles for gas catalysis applications. By applying the concept of an average or effective dielectric constant to the heterogeneous interlayer surrounding each particle, we extend the technique of immersion spectroscopy to porous or heterogeneous media. Specifically, we apply the predominant effective medium theories for the determination of the average fractional composition of each component in this inhomogeneous layer. Hence, the surface area of metal available for catalytic gas reaction is determined. The technique is satisfactory for statistically random metal particle distributions but needs further modification for aggregated or surfactant modified systems. Additionally, the kinetics suggest that collective particle interactions in coagulated clusters are perturbed during silica gelation resulting in a change in the aggregate geometry.

Smith, David D.↗
NASA NTRS1992

Black Carbon (Soot) Aerosol in the Lower Stratosphere and Upper Troposphere

We have used two approaches to measure BCA in the stratosphere. The first method consists of collecting aerosols by impaction on quartz rods, upon which are mounted strips of polystyrene filter material. Each 25 mm by 0.5 mm filter strip is alternately masked and exposed in 5 mm long sections. After sampling, the optical density of the exposed sections is measured and compared with the optical density of the masked (unexposed) sections. The filter strip is a Lambertian collector, the scattering property of which is not affected by the deposition of liquid sulfuric acid droplets which dominate the stratospheric aerosol. Hence, all attenuation greater in the exposed than in the non-exposed sections is due to absorption by BCA or rare opaque materials such as meteoritic iron. In a second approach we expose carbon-coated gold or palladium wires to air outside the aircraft boundary layer [Farlow et al., 1979; Pueschel et al., 1989]. With a field emission scanning electron microscope we are able to characterize BCA particles in addition to the dominant sulfuric acid droplets. Typically, soot is comprised of 20 nm diameter spheres linked together as branching chains or loosely packed aggregates (Figure 1a). The microscope has a lateral image resolution of 1.5 nm and can clearly resolve individual spheres making up BCA aggregates. Their morphology is uniquely different from that of the liquid sulfuric acid-water aerosol (Figure 1b). We approximate the size of each BCA particle by that of a sphere of equivalent volume and fit a lognormal size distribution to both the BCA and H2SO4/H2O aerosols. Both sampler types have been mounted on NASA's ER-2 high-altitude research aircraft (altitude ceiling of 70,000 feet), and on NASA's DC-8 (40,000 feet ceiling) aircraft to sample aerosols from a significant portion of the atmosphere.

Pueschel, R. F.↗
NASA NTRS1999

The MECA Payload as a Dust Analysis Laboratory on the MSP 2001 Lander

In a companion abstract, the "Mars Environmental Compatibility Assessment" (MECA) payload for Mars Surveyor Program 2001 (MSP 2001) is described in terms of its capabilities for addressing exobiology on Mars. Here we describe how the same payload elements perform in terms of gathering data about surface dust on the planet. An understanding of the origin and properties of dust is important to both human exploration and planetary geology. The MECA instrument is specifically designed for soil/dust investigations: it is a multifunctional laboratory equipped to assess particulate properties with wet chemistry, camera imagery, optical microscopy (potentially with LTV fluorescence capability), atomic force microscopy (AFM; potentially with mineral-discrimination capabilities), electrometry, active & passive external materials-test panels, mineral hardness testing, and electrostatic & magnetic materials testing. Additionally, evaluation of soil chemical and physical properties as a function of depth down to about 50 cm will be facilitated by the Lander/MECA robot arm on which the camera (RAC) and electrometer are mounted. Types of data being sought for the dust include: (1) general textural and grain-size characterization of the soil as a whole --for example, is the soil essentially dust with other components or is it a clast-supported material in which dust resides only in the clast interstices, (2) size frequency distribution for dust particles in the range 0.01 to 10.00 microns, (3) particle-shape distribution of the soil components and of the fine dust fraction in particular, (4) soil fabric such as grain clustering into clods, aggregates, and cemented/indurated grain amalgamations, as well as related porosity, cohesiveness, and other mechanical soil properties, (5) cohesive relationship that dust has to certain types of rocks and minerals as a clue to which soil materials may be prime hosts for dust "piggybacking", (6) particle, aggregate, and bulk soil electrostatic properties, (7) particle hardness, (8) particle magnetic properties, (9) bulk dust geochemistry (solubility, reactivity, ionic and mineral species). All of these quantities are needed in order for the human exploration program to make assessments of hazards on Mars, and to better enable the production on earth, of soil/dust simulants that can act as realistic test materials in terms of those properties that render dust a contaminant.Such properties include the small grain size that enables penetration of space-suit joints, mechanical interfaces and bearings, seals, etc., and presents difficulty for filtration systems. Size also plays a critical role in the potential for lung disease in long-term habitats. The properties of grain shape and hardness are important parameters in determining the abrasiveness of dust as it enters mechanical systems, or bombards helmet visors and habitat windows in dust-laden winds. Adhesive electrostatic and magnetic properties of dust will be prime causes of contamination of space suits and equipment. Contamination causes mechanical malfunction, tracking of dirt into habitats, "piggybacking" of toxins on dust into habitats, changes in albedo and efficiency of solar arrays and heat exchangers, and changes in electrical conductivity of suit surfaces and other materials that may have specific safety requirements regarding electrical conductivity. Other potentially hazardous properties of dust include the possibility of high solubility of some component grains (rendering them reactive), and toxicity of some materials --grains of superoxidants and heavy metals (there is always the slim, but not inconceivable possibility of biogenic components such as spores). Because Mars has no active surface aqueous regime, volcanic emissions, meteoritic debris, weathering products, and photochemical products of Mars have nowhere to go except reside in the surface; there are few mechanical or chemical (buffering) processes to remove the accumulation of eons. From a planetology perspective, there are many enigmatic issues relating to dust and the aeolian regime in general. MECA will be able to address many questions in this area. For example, if MECA determines a particular particle size distribution (size and sorting values), it will be possible to make inferences about the origin of the dust - - is it all aeolian, or a more primitive residue of weathering, volcanic emissions, and meteoritic gardening? Trenching with the Lander/MECA robot arm will enable local stratigraphy to be determined in terms of depositional rates, amounts and cyclicity in dust storms and/or local aeolian transport. Grain shape will betray the origin of the dust fragments as being the product of recent or ancient weathering, or the comminution products of aeolian transport --the dust-silt ratio might be a measure of aeolian comminution energy. Additional information is contained in the original.

Marshall, J.↗
NASA NTRS1999

"EGM" (Electrostatics of Granular Matter): A Space Station Experiment to Examine Natural Particulate Systems

A granular-materials experiment is being developed for a 2002 launch for Space Station deployment. The experiment is funded by NASA HQ and managed through NASA Lewis Research Center. The experiment will examine electrostatic aggregation of coarse granular materials with the goals of (a) obtaining proof for an electrostatic dipole model of grain interactions, and (b) obtaining knowledge about the way aggregation affects the behavior of natural particulate masses: (1) in unconfined dispersions (clouds such as nebulae, aeolian dust palls, volcanic plumes), (2) in semi-confined, self-loaded masses as in fluidized flows (pyroclastic surges, avalanches) and compacted regolith, or (3) in semi-confined non-loaded masses as in dust layers adhering to solar cells or space suits on Mars. The experiment addresses both planetary/astrophysical issues as well as practical concerns for human exploration of Mars or other solar system bodies. Additional information is contained in the original.

Marshall, J.↗