Augmenting forearm crutches with wireless sensors for lower limb rehabilitation

Forearm crutches are frequently used in the rehabilitation of an injury to the lower limb. The recovery rate is improved if the patient correctly applies a certain fraction of their body weight (specified by a clinician) through the axis of the crutch, referred to as partial weight bearing (PWB). Incorrect weight bearing has been shown to result in an extended recovery period or even cause further damage to the limb. There is currently no minimally invasive tool for long-term monitoring of a patient's PWB in a home environment. This paper describes the research and development of an instrumented forearm crutch that has been developed to wirelessly and autonomously monitor a patient's weight bearing over the full period of their recovery, including its potential use in a home environment. A pair of standard forearm crutches are augmented with low-cost off-the-shelf wireless sensor nodes and electronic components to provide indicative measurements of the applied weight, crutch tilt and hand position on the grip. Data are wirelessly transmitted between crutches and to a remote computer (where they are processed and visualized in LabVIEW), and the patient receives biofeedback by means of an audible signal when they put too much or too little weight through the crutch. The initial results obtained highlight the capability of the instrumented crutch to support physiotherapists and patients in monitoring usage

Mapping the Stellar Dynamics of M31

Using the Planetary Nebula Spectrograph, we have observed and measured the velocities for some 2764 PNe in the disk and halo of the Andromeda galaxy. Preliminary analysis using a basic ring model shows a rotation curve in good agreement with that obtained from HI data out to ~20kpc. Some substructure has also been detected within the velocity field, which can be modeled as the continuation of the tidal-remnant known as the Southern Stream, as it passes through Andromeda's disk.Comment: 5 pages, 3 figures, to appear in the proceedings of the ESO-Workshop "Planetary Nebulae beyond the Milky Way", May 19 - 21 (2004), ed. J. R. Walsh, L. Stanghellini, Springer-Verla

Tracing the star stream through M31 using planetary nebula kinematics

We present a possible orbit for the Southern Stream of stars in M31, which connects it to the Northern Spur. Support for this model comes from the dynamics of planetary nebulae (PNe) in the disc of M31: analysis of a new sample of 2611 PNe obtained using the Planetary Nebula Spectrograph reveals ∼20 objects with kinematics inconsistent with the normal components of the galaxy, but which lie at the right positions and velocities to connect the two photometric features via this orbit. The satellite galaxy M32 is coincident with the stream both in position and velocity, adding weight to the hypothesis that the stream comprises its tidal debri

A deep kinematic survey of planetary nebulae in the Andromeda galaxy using the Planetary Nebula Spectrograph

We present a catalogue of positions, magnitudes and velocities for 3300 emission-line objects found by the Planetary Nebula Spectrograph in a survey of the Andromeda galaxy, M31. Of these objects, 2615 are found likely to be planetary nebulae (PNe) associated with M31. The survey area covers the whole of M31's disc out to a radius of . Beyond this radius, observations have been made along the major and minor axes, and the Northern Spur and Southern Stream regions. The calibrated data have been checked for internal consistency and compared with other catalogues. With the exception of the very central, high surface brightness region of M31, this survey is complete to a magnitude limit of m5007∼ 23.75, 3.5 mag into the PN luminosity function. We have identified emission-line objects associated with M31's satellites and other background galaxies. We have examined the data from the region tentatively identified as a new satellite galaxy, Andromeda VIII, comparing it to data in the other quadrants of the galaxy. We find that the PNe in this region have velocities that appear to be consistent with membership of M31 itself. The luminosity function of the surveyed PNe is well matched to the usual smooth monotonic function. The only significant spatial variation in the luminosity function occurs in the vicinity of M31's molecular ring, where the luminosities of PNe on the near side of the galaxy are systematically ∼0.2 mag fainter than those on the far side. This difference can be explained naturally by a modest amount of obscuration by the ring. The absence of any difference in luminosity function between bulge and disc suggests that the sample of PNe is not strongly populated by objects whose progenitors are more massive stars. This conclusion is reinforced by the excellent agreement between the number counts of PNe and the R-band light. The number counts of kinematically selected PNe also allow us to probe the stellar distribution in M31 down to very faint limits. There is no indication of a cut-off in M31's disc out to beyond four scalelengths, and no signs of a spheroidal halo population in excess of the bulge out to 10 effective bulge radii. We have also carried out a preliminary analysis of the kinematics of the surveyed PNe. The mean streaming velocity of the M31 disc PNe is found to show a significant asymmetric drift out to large radii. Their velocity dispersion, although initially declining with radius, flattens out to a constant value in the outer parts of the galaxy. There are no indications that the disc velocity dispersion varies with PN luminosity, once again implying that the progenitors of PNe of all magnitudes form a relatively homogeneous old population. The dispersion profile and asymmetric drift results are shown to be mutually consistent, but require that the disc flares with radius if the shape of its velocity ellipsoid remains invarian

Tracing the star stream through M31 using planetary nebula kinematics

We present a possible orbit for the Southern Stream of stars in M31, which connects it to the Northern Spur. Support for this model comes from the dynamics of planetary nebulae (PNe) in the disk of M31: analysis of a new sample of 2611 PNe obtained using the Planetary Nebula Spectrograph reveals ~20 objects whose kinematics are inconsistent with the normal components of the galaxy, but which lie at the right positions and velocities to connect the two photometric features via this orbit. The satellite galaxy M32 is coincident with the stream both in position and velocity, adding weight to the hypothesis that the stream comprises its tidal debris.Comment: 6 pages, 2 figures, MNRAS Letters, accepted; for hi-res version see http://as1.chem.nottingham.ac.uk/~Aaron/m31stream.pdf (pdf) or http://as1.chem.nottingham.ac.uk/~Aaron/m31stream.ps.gz (ps

Planetary Nebula Velocities in the Disk and Bulge of M31

We present radial velocities for a sample of 723 planetary nebulae (PNe) in the disk and bulge of M31, measured using the WYFFOS fibre spectrograph on the William Herschel telescope. Velocities are determined using the [OIII] 5007 Angstrom emission line. Rotation and velocity dispersion are measured to a radius of 50 arcminutes (11.5 kpc), the first stellar rotation curve and velocity dispersion profile for M31 to such a radius. Our kinematics are consistent with rotational support at radii well beyond the bulge effective radius of 1.4kpc, although our data beyond a radius of 5kpc are limited. We present tentative evidence for kinematic substructure in the bulge of M31 to be studied fully in a later work. This paper is part of an ongoing project to constrain the total mass, mass distribution and velocity anisotropy of the disk, bulge and halo of M31.Comment: 27 pages, accepted for publication in MNRA

Gravitational stability and dynamical overheating of stellar disks of galaxies

We use the marginal stability condition for galactic disks and the stellar velocity dispersion data published by different authors to place upper limits on the disk local surface density at two radial scalelengths $R=2h$. Extrapolating these estimates, we constrain the total mass of the disks and compare these estimates to those based on the photometry and color of stellar populations. The comparison reveals that the stellar disks of most of spiral galaxies in our sample cannot be substantially overheated and are therefore unlikely to have experienced a significant merging event in their history. The same conclusion applies to some, but not all of the S0 galaxies we consider. However, a substantial part of the early type galaxies do show the stellar velocity dispersion well in excess of the gravitational stability threshold suggesting a major merger event in the past. We find dynamically overheated disks among both seemingly isolated galaxies and those forming pairs. The ratio of the marginal stability disk mass estimate to the total galaxy mass within four radial scalelengths remains within a range of 0.4---0.8. We see no evidence for a noticeable running of this ratio with either the morphological type or color index.Comment: 25 pages, 5 figures, accepted to Astronomy Letter

A deep kinematic survey of planetary nebulae in the Andromeda Galaxy using the Planetary Nebula Spectrograph

We present a catalogue of positions, magnitudes and velocities for 3300 emission-line objects found by the Planetary Nebula Spectrograph in a survey of the Andromeda Galaxy, M31. Of these objects, 2615 are found likely to be planetary nebulae (PNe) associated with M31. Initial results from this survey include: the likely non-existence of Andromeda VIII; a universal PN luminosity function, with the exception of a small amount of obscuration, and a small offset in normalization between bulge and disk components; very faint kinematically-selected photometry implying no cut-off in the disk to beyond 4 scalelengths and no halo population in excess of the bulge out to 10 effective bulge radii; disk kinematics that show significant dispersion and asymmetric drift out to large radii, consistent with a warm flaring disk; and no sign of any variation in kinematics with PN luminosity, suggesting that PNe arise from a fairly uniform population of old stars.Comment: Accepted by MNRAS. 23 pages, 37 figures. A full resolution version is available at http://www.astro.rug.nl/~pns/pns_pub.htm

A fast and accurate energy source emulator for wireless sensor networks

The capability to either minimize energy consumption in battery-operated devices, or to adequately exploit energy harvesting from various ambient sources, is central to the development and engineering of energy-neutral wireless sensor networks. However, the design of effective networked embedded systems targeting unlimited lifetime poses several challenges at different architectural levels. In particular, the heterogeneity, the variability, and the unpredictability of many energy sources, combined to changes in energy required by powered devices, make it difficult to obtain reproducible testing conditions, thus prompting the need of novel solutions addressing these issues. This paper introduces a novel embedded hardware-software solution aimed at emulating a wide spectrum of energy sources usually exploited to power sensor networks motes. The proposed system consists of a modular architecture featuring small factor form, low power requirements, and limited cost. An extensive experimental characterization confirms the validity of the embedded emulator in terms of flexibility, accuracy, and latency while a case study about the emulation of a lithium battery shows that the hardware-software platform does not introduce any measurable reduction of the accuracy of the model. The presented solution represents therefore a convenient solution for testing large-scale testbeds under realistic energy supply scenarios for wireless sensor networks