Overshooting tipping point thresholds in a changing climate.

Palaeorecords suggest that the climate system has tipping points, where small changes in forcing cause substantial and irreversible alteration to Earth system components called tipping elements. As atmospheric greenhouse gas concentrations continue to rise as a result of fossil fuel burning, human activity could also trigger tipping, and the impacts would be difficult to adapt to. Previous studies report low global warming thresholds above pre-industrial conditions for key tipping elements such as ice-sheet melt. If so, high contemporary rates of warming imply that exceeding these thresholds is almost inevitable, which is widely assumed to mean that we are now committed to suffering these tipping events. Here we show that this assumption may be flawed, especially for slow-onset tipping elements (such as the collapse of the Atlantic Meridional Overturning Circulation) in our rapidly changing climate. Recently developed theory indicates that a threshold may be temporarily exceeded without prompting a change of system state, if the overshoot time is short compared to the effective timescale of the tipping element. To demonstrate this, we consider transparently simple models of tipping elements with prescribed thresholds, driven by global warming trajectories that peak before returning to stabilize at a global warming level of 1.5 degrees Celsius above the pre-industrial level. These results highlight the importance of accounting for timescales when assessing risks associated with overshooting tipping point thresholds.

Abrupt changes in Great Britain vegetation carbon projected under climate change.

Past abrupt 'regime shifts' have been observed in a range of ecosystems due to various forcing factors. Large-scale abrupt shifts are projected for some terrestrial ecosystems under climate change, particularly in tropical and high-latitude regions. However, there is very little high-resolution modelling of smaller-scale future projected abrupt shifts in ecosystems, and relatively less focus on the potential for abrupt shifts in temperate terrestrial ecosystems. Here, we show that numerous climate-driven abrupt shifts in vegetation carbon are projected in a high-resolution model of Great Britain's land surface driven by two different climate change scenarios. In each scenario, the effects of climate and CO2 combined are isolated from the effects of climate change alone. We use a new algorithm to detect and classify abrupt shifts in model time series, assessing the sign and strength of the non-linear responses. The abrupt ecosystem changes projected are non-linear responses to climate change, not simply driven by abrupt shifts in climate. Depending on the scenario, 374-1,144 grid cells of 1.5 km × 1.5 km each, comprising 0.5%-1.5% of Great Britain's land area show abrupt shifts in vegetation carbon. We find that abrupt ecosystem shifts associated with increases (rather than decreases) in vegetation carbon, show the greatest potential for early warning signals (rising autocorrelation and variance beforehand). In one scenario, 89% of abrupt increases in vegetation carbon show increasing autocorrelation and variance beforehand. Across the scenarios, 81% of abrupt increases in vegetation carbon have increasing autocorrelation and 74% increasing variance beforehand, whereas for decreases in vegetation carbon these figures are 56% and 47% respectively. Our results should not be taken as specific spatial or temporal predictions of abrupt ecosystem change. However, they serve to illustrate that numerous abrupt shifts in temperate terrestrial ecosystems could occur in a changing climate, with some early warning signals detectable beforehand.

Early-warning indicators for rate-induced tipping.

A dynamical system is said to undergo rate-induced tipping when it fails to track its quasi-equilibrium state due to an above-critical-rate change of system parameters. We study a prototypical model for rate-induced tipping, the saddle-node normal form subject to time-varying equilibrium drift and noise. We find that both most commonly used early-warning indicators, increase in variance and increase in autocorrelation, occur not when the equilibrium drift is fastest but with a delay. We explain this delay by demonstrating that the most likely trajectory for tipping also crosses the tipping threshold with a delay, and therefore, the tipping itself is delayed. We find solutions of the variational problem determining the most likely tipping path using numerical continuation techniques. The result is a systematic study of the most likely tipping time in the plane of two parameters, distance from tipping threshold and noise intensity.

Early mobilization on continuous renal replacement therapy is safe and may improve filter life.

INTRODUCTION: Despite studies demonstrating benefit, patients with femoral vascular catheters placed for continuous renal replacement therapy are frequently restricted from mobilization. No researchers have reported filter pressures during mobilization, and it is unknown whether mobilization is safe or affects filter lifespan. Our objective in this study was to test the safety and feasibility of mobilization in this population. METHODS: A total of 33 patients undergoing continuous renal replacement therapy via femoral, subclavian or internal jugular vascular access catheters at two general medical-surgical intensive care units in Australia were enrolled. Patients underwent one of three levels of mobilization intervention as appropriate: (1) passive bed exercises, (2) sitting on the bed edge or (3) standing and/or marching. Catheter dislodgement, haematoma and bleeding during and following interventions were evaluated. Filter pressure parameters and lifespan (hours), nursing workload and concern were also measured. RESULTS: No episodes of filter occlusion or failure occurred during any of the interventions. No adverse events were detected. The intervention filters lasted longer than the nonintervention filters (regression coefficient = 13.8 (robust 95% confidence interval (CI) = 5.0 to 22.6), P = 0.003). In sensitivity analyses, we found that filter life was longer in patients who had more position changes (regression coefficient = 2.0 (robust 95% CI = 0.6 to 3.5), P = 0.007). The nursing workloads between the intervention shift and the following shift were similar. CONCLUSIONS: Mobilization during renal replacement therapy via a vascular catheter in patients who are critically ill is safe and may increase filter life. These findings have significant implications for the current mobility restrictions imposed on patients with femoral vascular catheters for renal replacement therapy. TRIAL REGISTRATION: Australian and New Zealand Clinical Trials Registry ACTRN12611000733976 (registered 13 July 2011).

Inverse-square law between time and amplitude for crossing tipping thresholds.

A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the threshold. We derive a simple criterion that relates how far the parameter exceeds the tipping threshold maximally and how long the parameter stays above the threshold to avoid tipping in an inverse-square law to observable properties of the dynamical system near the fold. For the case when the dynamical system is subject to stochastic forcing we give an approximation to the probability of tipping if a parameter changing in time reverses near the tipping point. The derived approximations are valid if the parameter change in time is sufficiently slow. We demonstrate for a higher-dimensional system, a model for the Indian summer monsoon, how numerically observed escape from the equilibrium converge to our asymptotic expressions. The inverse-square law between peak of the parameter forcing and the time the parameter spends above a given threshold is also visible in the level curves of equal probability when the system is subject to random disturbances.

Probability of noise- and rate-induced tipping.

We propose an approximation for the probability of tipping when the speed of parameter change and additive white noise interact to cause tipping. Our approximation is valid for small to moderate drift speeds and helps to estimate the probability of false positives and false negatives in early-warning indicators in the case of rate- and noise-induced tipping. We illustrate our approximation on a prototypical model for rate-induced tipping with additive noise using Monte Carlo simulations. The formula can be extended to close encounters of rate-induced tipping and is otherwise applicable to other forms of tipping. We also provide an asymptotic formula for the critical ramp speed of the parameter in the absence of noise for a general class of systems undergoing rate-induced tipping.

Surgical management of cartilage defects in athletes.

The synovial joints provide a unique environment in which to carry out their critical mechanical function. The complex architecture of the articular cartilage normally provides painless motion throughout a variety of activities. Fluids secreted by cells in the superficial layers of the articular cartilage as well as in the synovium provide an almost frictionless articulation. The synovium also helps to maintain the aseptic environment found within the joint. The cartilage and fluid provide critical protection to the underlying bone. If any of these structures are damaged, or lose their efficiency, the ensuing cascade of damage inflicted on the joint can lead to catastrophic failure.

Dislocation of rotating hinge total knee prostheses. A biomechanical analysis.

BACKGROUND: Symptomatic instability and implant dislocation are occasionally encountered in patients with a rotating hinge total knee prosthesis. A biomechanical study of rotating hinge total knee implants was performed to determine the association between the design (length and taper) of the central rotational stem and the stability of the implant. METHODS: The stem lengths and tapers of knee implants made by seven manufacturers were measured. The tilting laxity of each design was tested by measuring the degree of tilting of the central rotational stem within the tibial housing that occurred with increasing amounts of distraction. The maximum amount of distraction that was possible before the stem dislocated was determined for each design. RESULTS: Implant designs with a short and/or markedly tapered central rotational stem had the greatest tilting, laxity, and instability of that stem. The Howmedica, Techmedica, Intermedics/Sulzer Medica, and Wright Medical Technology/ Dow Corning Wright designs required > or = 39 mm of distraction before they dislocated. The Biomet knee implant required 33 or 44 mm of distraction to dislocate, depending on the thickness of the polyethylene tray that was utilized. The S-ROM knee required only 26 mm of distraction before dislocation occurred. CONCLUSIONS: The measurements confirmed that the shorter the stem and the greater its taper, the greater the instability and laxity at any given amount of joint distraction.

Shoulder instability: return to play.

Shoulder instability in the competitive athlete is a relatively common problem. The etiology of glenohumeral instability that can affect the athlete runs a wide spectrum, from an isolated traumatic dislocation to repeated microtrauma or congenital laxity. Although many athletes are able to adapt to a mild laxity that might only occasionally affect them, it can be much more difficult to adapt or return to play after a dislocation or repeated subluxation episodes. This article focuses on the return to play for competitive individuals after a glenohumeral dislocation or reconstructive surgery for shoulder instability.

Triceps reconstruction using hamstring graft for triceps insufficiency or recurrent rupture.

Triceps ruptures are relatively rare injuries. When they occur, primary surgical repair of the tendon to the proximal ulna is recommended. However, some patients require reconstruction using tendon grafting due to shortening or insufficiency of the native triceps tendon. Triceps ruptures associated with biological abnormalities (such as renal insufficiency or metabolic disease) or recurrence of rupture represent situations where a stout augmented repair is desirable. Multiple allograft and autologous tendons have been described for augmentation, but the use of gracilis and semitendinosus tendons provides superior length and size for use in triceps reconstruction. Using an illustrative case example, the evaluation of triceps insufficiency and the need for additional graft is shown. The technique of autologous hamstring augmentation for triceps insufficiency is described in detail. The importance of graded rehabilitation is emphasized with a complete program of triceps strengthening over time.