Feedback control of unsupported standing in paraplegia. Part I: optimal control approach

This is the first of a pair of papers which describe an investigation into the feasibility of providing artificial balance to paraplegics using electrical stimulation of the paralyzed muscles. By bracing the body above the shanks, only stimulation of the plantarflexors is necessary. This arrangement prevents any influence from the intact neuromuscular system above the spinal cord lesion. Here, the authors extend the design of the controllers to a nested-loop LQG (linear quadratic Gaussian) stimulation controller which has ankle moment feedback (inner loops) and inverted pendulum angle feedback (outer loop). Each control loop is tuned by two parameters, the control weighting and an observer rise-time, which together determine the behavior. The nested structure was chosen because it is robust, despite changes in the muscle properties (fatigue) and interference from spasticity

Feedback control of unsupported standing

This paper presents the results of continuing work on feedback control of unsupported standing in paraplegia. Our experimental setup considers a situation in which all joints above the ankle are braced, and stabilising torque at the ankle is generated by stimulation of the plantarflexors. A previous study showed that short periods of unsupported standing with paraplegic subjects could be achieved. In order to improve consistency and reliability of unsupported standing we are currently investigating several modifications to the control strategy. The paper reports progress towards this goal

Feedback control of unsupported standing in paraplegia. Part II: experimental results

For pt. I see ibid., vol. 5, no. 4, p. 331-40 (1997). This is the second of a pair of papers which describe an investigation into the feasibility of providing artificial balance to paraplegics using electrical stimulation of the paralyzed muscles. By bracing the body above the shanks, only stimulation of the plantar flexors is necessary. This arrangement prevents any influence from the intact neuromuscular system above the spinal cord lesion. Here, the authors present experimental results from intact and paraplegic subjects

Optimal control of ankle joint moment: Toward unsupported standing in paraplegia

This paper considers part of the problem of how to provide unsupported standing for paraplegics by feedback control. In this work our overall objective is to stabilize the subject by stimulation only of his ankle joints while the other joints are braced, Here, we investigate the problem of ankle joint moment control. The ankle plantarflexion muscles are first identified with pseudorandom binary sequence (PRBS) signals, periodic sinusoidal signals, and twitches. The muscle is modeled in Hammerstein form as a static recruitment nonlinearity followed by a linear transfer function. A linear-quadratic-Gaussian (LQG)-optimal controller design procedure for ankle joint moment was proposed based on the polynomial equation formulation, The approach was verified by experiments in the special Wobbler apparatus with a neurologically intact subject, and these experimental results are reported. The controller structure is formulated in such a way that there are only two scalar design parameters, each of which has a clear physical interpretation. This facilitates fast controller synthesis and tuning in the laboratory environment. Experimental results show the effects of the controller tuning parameters: the control weighting and the observer response time, which determine closed-loop properties. Using these two parameters the tradeoff between disturbance rejection and measurement noise sensitivity can be straightforwardly balanced while maintaining a desired speed of tracking. The experimentally measured reference tracking, disturbance rejection, and noise sensitivity are good and agree with theoretical expectations

Killing the goose

The regulatory framework for implanted medical devices is preventing severely impaired people from benefitting from rehabilitation research. Consequently, research effort is wasted and we are unable to use implants to reduce the costs of healthcare. The framework should be altered so that it is economically possible to get new devices for small patient groups into widespread use

Supermembrane limit of Yang-Mills theory

We consider Yang-Mills theory with $N{=}1$ super translation group in eleven auxiliary dimensions as the structure group. The gauge theory is defined on a direct product manifold $\Sigma_3\times S^1$, where $\Sigma_3$ is a three-dimensional Lorentzian manifold and $S^1$ is a circle. We show that in the infrared limit, when the metric on $S^1$ is scaled down, the Yang-Mills action supplemented by a Wess-Zumino-type term reduces to the action of an M2-brane.Comment: 1+6 page

Amenity Effect or Supply Effect? Metropolitan Amenities and their Interaction with Housing Supply

Standard models in urban economics assume that the boundary of an urban area will expand as long as the present value of land for urban uses is greater than the present value of land for rural uses. Under this assumption, the boundary of the urban area is endogenously determined by the rent paid to rural landowners. But this assumption is not realistic. The physical expansion of many major urban areas in the United States is impeded by an exogenous boundary. For example, geographic growth of the three most populated metropolitan areas in the country is limited by an ocean or a Great Lake. In this thesis, we argue that such exogenous boundaries affect land prices throughout the urban area because inter-city migration is costly and these boundaries effectively constrain the supply of land. Specifically, we develop a theoretical model in support of this conclusion and show that prices are highest in cities with the most restrictive exogenous boundaries, ceteris paribus. This argument implies that researchers who do not control for exogenous boundaries could be introducing a systematic bias in their findings if they use land prices or rents to measure the value of public amenities in urban areas or the relative desirability of different cities

Global W2,pW^{2,p} estimates for solutions to the linearized Monge--Amp\`ere equations

In this paper, we establish global $W^{2,p}$ estimates for solutions to the linearized Monge-Amp\`ere equations under natural assumptions on the domain, Monge-Amp\`ere measures and boundary data. Our estimates are affine invariant analogues of the global $W^{2,p}$ estimates of Winter for fully nonlinear, uniformly elliptic equations, and also linearized counterparts of Savin's global $W^{2,p}$ estimates for the Monge-Amp\`ere equations.Comment: v2: presentation improve

Corrosion of silicon integrated circuits and lifetime predictions in implantable electronic devices

Corrosion is a prime concern for active implantable devices. In this paper we review the principles underlying the concepts of hermetic packages and encapsulation, used to protect implanted electronics, some of which remain widely overlooked. We discuss how technological advances have created a need to update the way we evaluate the suitability of both protection methods. We demonstrate how lifetime predictability is lost for very small hermetic packages and introduce a single parameter to compare different packages, with an equation to calculate the minimum sensitivity required from a test method to guarantee a given lifetime. In the second part of this paper, we review the literature on the corrosion of encapsulated integrated circuits (ICs) and, following a new analysis of published data, we propose an equation for the pre-corrosion lifetime of implanted ICs, and discuss the influence of the temperature, relative humidity, encapsulation and field-strength. As any new protection will be tested under accelerated conditions, we demonstrate the sensitivity of acceleration factors to some inaccurately known parameters. These results are relevant for any application of electronics working in a moist environment. Our comparison of encapsulation and hermetic packages suggests that both concepts may be suitable for future implants

Flexible active electrode arrays with ASICs that fit inside the rat's spinal canal

Epidural spinal cord electrical stimulation (ESCS) has been used as a means to facilitate locomotor recovery in spinal cord injured humans. Electrode arrays, instead of conventional pairs of electrodes, are necessary to investigate the effect of ESCS at different sites. These usually require a large number of implanted wires, which could lead to infections. This paper presents the design, fabrication and evaluation of a novel flexible active array for ESCS in rats. Three small (1.7 mm2) and thin (100 μm) application specific integrated circuits (ASICs) are embedded in the polydimethylsiloxane-based implant. This arrangement limits the number of communication tracks to three, while ensuring maximum testing versatility by providing independent access to all 12 electrodes in any configuration. Laser-patterned platinum-iridium foil forms the implant’s conductive tracks and electrodes. Double rivet bonds were employed for the dice microassembly. The active electrode array can deliver current pulses (up to 1 mA, 100 pulses per second) and supports interleaved stimulation with independent control of the stimulus parameters for each pulse. The stimulation timing and pulse duration are very versatile. The array was electrically characterized through impedance spectroscopy and voltage transient recordings. A prototype was tested for long term mechanical reliability when subjected to continuous bending. The results revealed no track or bond failure. To the best of the authors’ knowledge, this is the first time that flexible active electrode arrays with embedded electronics suitable for implantation inside the rat’s spinal canal have been proposed, developed and tested in vitro