Bohr equation

Abstract: An analytical solution of the collective Bohr equation with a Coulomb-like and a Kratzer-like $\gamma-$unstable potential in quadrupole deformation space is presented. Eigenvalues and eigenfunctions are given in closed form and transition rates are calculated for the two cases. The corresponding SO(2,1)$\times$SO(5) algebraic structure is discussed.

Abstract: A comparison was made of methods used to calculate cardiac output by the indirect (CO2) Fick procedure (equilibrium method). Alternative methods for calculation of arterial PCO2, mixed venous PCO2, and conversion of gas tension to content were tested. Cardiac output values determined with a "corrected" equilibrium PCO2, to approximate mixed venous PCO2, were observed to be closest to cardiac output values determined on similar populations by the dye dilution method. Arterial PCO2 was best estimated from the Bohr equation using a dead space in exercise from prediction equations in the literature applicable to the populations under study. CO2 dissociation curves used to derive the veno-arterial CO2 content difference, were shown to differ considerably. For the present, the curve by McHardy [25], as modified by Jones (personal communication), and similar to the standard Comroe curve [5], was chosen.

Abstract: Anatomical dead space was measured in 72 normal children aged from 5 to 16 years, using the single breath method. There was a linear increase in this measurement with height, weight, and end-inspiratory lung volume. Physiological dead space was measured in 52 normal children using the Bohr equation and substituting a rebreathing PCO2 for alveolar PCO2. There was a parallel increase in this measurement with height, weight, and end-inspiratory lung volume. The difference between the two dead space measurements constitutes the alveolar dead space and was constant over the whole age range at 45 +/- 22 ml. The ratio of physiological dead space to tidal volume was 33-6 +/-4-6% and was unaltered by age or change in lung volume. The effect of airways obstruction on the dead space volumes was studied in 36 children with asthma and 28 with cystic fibrosis. Physiological dead space increased with increasing airways obstruction. Anatomical dead space remained constant in spite of marked increases in lung volume associated with the airways obstruction.

Abstract: Physiologic dead space is defined as the volume of the lung where gas exchange does not occur. Apparatus dead space increases dead space volume, causing either increased PaCO2 or the need to increase minute ventilation to maintain normocapnia. Children are especially vulnerable because small increases in apparatus dead space can significantly increase dead space to tidal volume ratio (Vd/Vt). The effect of changes in dead space on arterial CO2 (PaCO2) and required minute ventilation were calculated for patients weighing 2 to 17 kg that corresponds to 0 to 36 months of age. Apparatus volumes for typical devices were obtained from the manufacturer or measured by the volume of water required to fill the device. The relationship between the fraction of alveolar CO2 (FaCO2) and dead space volume (Vd) was derived from the Bohr equation, FaCO2 = VCO2/(RR*(Vt - Vd)), where VCO2 is CO2 production, RR is respiratory rate, and Vt is tidal volume. VCO2 was estimated by using Brody's equation for humans aged up to 36 months, (VCO2 = 5.56*(wt)), where weight is in kilogram. Initial conditions were Vt = 8 mL/kg, Vd/Vt = 0.3, and a RR of 20 breaths per minute. The relationship between PaCO2 and dead space was determined for increasing Vd. Rearranging the Bohr equation, the RR required to maintain PaCO2 of 40 mm·Hg was determined as dead space increased. The apparatus Vd of typical device arrangements ranged from 8 to 55 mL, and these values were used for the dead space values in the model. PaCO2 increased exponentially with increasing apparatus dead space. For smaller patients, the PaCO2 increased more rapidly for small changes in Vd than that in larger patients. Similarly, RR required to maintain PaCO2 of 40 mm·Hg increased exponentially with increasing dead space. Increasing apparatus Vd can lead to exponential increases in PaCO2 and/or RR required to maintain normal PaCO2. The effect on PaCO2 is less as patient weight increases, but these data suggest it can be significant for typical circuit components up to at least 17 kg or aged 36 months.