Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

Determination of the minimum alveolar concentration of isoflurane in Shetland ponies using constant current or constant voltage electrical stimulation

OBJECTIVE: To determine the minimum alveolar concentration (MAC) of isoflurane in Shetland ponies using a sequence of three different supramaximal noxious stimulations at each tested concentration of isoflurane rather than a single stimulation. STUDY DESIGN: Prospective, experimental trial. ANIMALS: Seven 4-year-old, gelding Shetland ponies. METHODS: The MAC of isoflurane was determined for each pony. Three different modes of electrical stimulation were applied consecutively (2 minute intervals): two using constant voltage (90 V) on the gingiva via needle- (CVneedle) or surface-electrodes (CVsurface) and one using constant current (CC; 40 mA) via surface electrodes applied to the skin over the digital nerve. The ability to clearly interpret the responses as positive, the latency of the evoked responses and the inter-electrode resistance were recorded for each stimulus. RESULTS: Individual isoflurane MAC (%) values ranged from 0.60 to 1.17 with a mean (+/-SD) of 0.97 (+/-0.17). The responses were more clearly interpreted with CC, but did not reach statistical significance. The CVsurface mode produced responses with a longer delay. The CVneedle mode was accompanied by variable inter-electrode resistances resulting in uncontrolled stimulus intensity. At 0.9 MAC, the third stimulation induced more positive responses than the first stimulation, independent of the mode of stimulation used. CONCLUSIONS: The MAC of isoflurane in the Shetland ponies was lower than expected with considerable variability among individuals. Constant current surface electrode stimulations were the most repeatable. A summation over the sequence of three supramaximal stimulations was observed around 0.9 MAC. CLINICAL RELEVANCE: The possibility that Shetland ponies require less isoflurane than horses needs further investigation. Constant current surface-electrode stimulations were the most repeatable. Repetitive supramaximal stimuli may have evoked movements at isoflurane concentrations that provide immobility when single supramaximal stimulation was applied.

The pharmacokinetics of dexmedetomidine administered as a constant rate infusion in horses.

Dexmedetomidine, the most selective α2 -adrenoceptor agonist in clinical use, is increasingly being used in both conscious and anaesthetized horses; however, the pharmacokinetics and sedative effects of this drug administered alone as an infusion are not previously described in horses. Seven horses received an infusion of 8 μg dexmedetomidine/kg/h for 150 min, venous blood samples were collected, and dexmedetomidine concentrations were assayed using liquid chromatography-mass spectrometry (LC/MS) and analyzed using noncompartmental pharmacokinetic analysis. Sedation was scored as the distance from the lower lip of the horse to the ground measured in centimetre. The harmonic mean (SD) plasma elimination half-life (Lambda z half-life) for dexmedetomidine was 20.9 (5.1) min, clearance (Cl) was 0.3 (0.20) L/min/kg, and volume of distribution at steady-state (Vdss ) was 13.7 (7.9) L/kg. There was a considerable individual variation in the concentration of dexmedetomidine vs. time profile. The level of sedation covaried with the plasma concentration of dexmedetomidine. This implies that for clinical use of dexmedetomidine constant rate infusion in conscious horses, infusion rates can be easily adjusted to effect, and this is preferable to an infusion at a predetermined value.