Continuous amperometric monitoring of glucose in a brittle diabetic chimpanzee with a miniature subcutaneous electrode

The performance of an amperometric biosensor, consisting of a subcutaneously implanted miniature (0.29 mm diameter, 5 × 10−4 cm2 mass transporting area), 90 s 10–90% rise/decay time glucose electrode, and an on-the-skin electrocardiogram Ag/AgCl electrode was tested in an unconstrained, naturally diabetic, brittle, type I, insulin-dependent chimpanzee. The chimpanzee was trained to wear on her wrist a small electronic package and to present her heel for capillary blood samples. In five sets of measurements, averaging 5 h each, 82 capillary blood samples were assayed, their concentrations ranging from 35 to 400 mg/dl. The current readings were translated to blood glucose concentration by assaying, at t = 1 h, one blood sample for each implanted sensor. The rms error in the correlation between the sensor-measured glucose concentration and that in capillary blood was 17.2%, 4.9% above the intrinsic 12.3% rms error of the Accu-Chek II reference, through which the illness of the chimpanzee was routinely managed. Linear regression analysis of the data points taken at t>1 h yielded the relationship (Accu-Chek) = 0.98 × (implanted sensor) + 4.2 mg/dl, r2 = 0.94. The capillary blood and the subcutaneous glucose concentrations were statistically indistinguishable when the rate of change was less than 1 mg/(dl⋅min). However, when the rate of decline exceeded 1.8 mg/(dl⋅min) after insulin injection, the subcutaneous glucose concentration was transiently higher.

A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system’s behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken’s cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.

Lack of agreement between tonometric and gastric juice partial carbon dioxide tension

Our goal was to compare measurement of tonometered saline and gastric juice partial carbon dioxide tension (PCO2). In this prospective observational study, 112 pairs of measurements were simultaneously obtained under various hemodynamic conditions, in 15 critical care patients. Linear regression analysis showed a significant correlation between the two methods of measuring PCO2 (r 2 = 0.43; P < 0.0001). However, gastric juice PCO2 was systematically higher (mean difference 51 mmHg). The 95% limits of agreement were 315 mmHg and the dispersion increased as the values of PCO2 increased. Tonometric and gastric juice PCO2 cannot be used interchangeably. Gastric juice PCO2 measurement should be interpreted with caution.

Analysis of linear trade models and relation to scale economies

We discuss linear Ricardo models with a range of parameters. We show that the exact boundary of the region of equilibria of these models is obtained by solving a simple integer programming problem. We show that there is also an exact correspondence between many of the equilibria resulting from families of linear models and the multiple equilibria of economies of scale models.