Mathematical analysis of the time course of alveolar CO2

1960 ◽  
Vol 15 (2) ◽  
pp. 215-219 ◽  
Author(s):  
William S. Yamamoto
Keyword(s):  
Time Series ◽  
Steady State ◽  
Gas Exchange ◽  
Time Course ◽  
Numerical Solutions ◽  
Venous Blood ◽  
Volume Flow ◽  
The Mean ◽  
Instantaneous Concentration ◽  
Steady State Solutions

Continuous respiratory CO2 gas exchange is simulated theoretically by means of a suitably constructed dilution equation of the form (See PDF) where C is instantaneous concentration, Q quantity flow, and V volume flow. When such an equation is constrained in its numerical solutions to yield inflow-outflow equality for CO2 in the steady state, solutions for CO2 as a time series are found to differ according to whether the site of entry of CO2 is entirely by venous blood or is also by inspired CO2. In the case of entry via the venous blood, increasing CO2 is eliminated while keeping mean CO2 constant with increasing fluctuations about this mean. In the case of entry via the lung, increasing CO2 is eliminated by raising the mean and at the same time oscillations diminish. Submitted on August 13, 1959

The Comparative Pharmacodynamics of Remifentanil and Its Metabolite, GR90291, in a Rat Electroencephalographic Model 

1999 ◽  
Vol 90 (2) ◽  
pp. 535-544 ◽  
Author(s):  
Eugene H. Cox ◽  
Mariska W. E. Langemeijer ◽  
Josy M. Gubbens-Stibbe ◽  
Keith T. Muir ◽  
Meindert Danhof
Keyword(s):  
Steady State ◽  
Time Course ◽  
Parent Drug ◽  
Volume Of Distribution ◽  
Pharmacodynamic Model ◽  
Pharmacokinetic Parameters ◽  
Maximal Effect ◽  
Total Blood ◽  
The Mean

Background The purpose of this study was to investigate the in vivo pharmacodynamics and the pharmacodynamic interactions of remifentanil and its major metabolite, GR90291, in a rat electroencephalographic model. Methods Remifentanil and GR90291 were administered according to a stepwise infusion scheme. The time course of the electroencephalographic effect (0.5-4.5 Hz) was determined in conjunction with concentrations of the parent drug and the metabolite in blood. Results Administration of remifentanil resulted in concentrations of remifentanil and GR90291 in the ranges 0-120 ng/ml and 0-850 ng/ml, respectively. When the metabolite was administered, concentrations of the metabolite in the range 0-220 microg/ml and no measurable concentrations of remifentanil were observed. The mean +/- SE values of the pharmacokinetic parameters clearance and volume of distribution at steady state were 920+/-110 ml x min(-1) x kg(-1) and 1.00+/-0.93 l/kg for remifentanil and 15+/-2 ml x min(-1) x kg(-1) and 0.56+/-0.08 l/kg for GR90291. The relative free concentrations in the brain, as determined on the basis of the cerebrospinal fluid/total blood concentration ratio at steady state, were 25+/-5% and 0.30+/-0.11% for remifentanil and GR90291, respectively. Concentration-electroencephalographic effect relations were characterized on the basis of the sigmoidal Emax pharmacodynamic model. The mean +/- SE values for the maximal effect (Emax), the concentration at which 50% of the maximal effect is obtained (EC50), and Hill factor for remifentanil were 109+/-12 microV, 9.4+/-0.9 ng/ml, and 2.2+/-0.3, respectively (n = 8). For GR90291, the mean +/- SE values for EC50 and the Hill factor were 103,000+/-9,000 microg/ml and 2.5+/-0.4, respectively (n = 6). Conclusions Analysis of the data on the basis of a previously postulated, mechanism-based pharmacokinetic-pharmacodynamic model for synthetic opioids revealed that the low in vivo potency of GR90291 can be explained by a low affinity to the mu-opioid receptor in combination with a poor brain penetration.

Gas-blood Pco2 and Po2 equilibration in a steady-state rebreathing dog preparation

1984 ◽  
Vol 56 (5) ◽  
pp. 1229-1236 ◽  
Author(s):  
J. S. Clark ◽  
A. G. Cutillo ◽  
M. J. Criddle ◽  
D. V. Collins ◽  
F. L. Farr ◽  
...  
Keyword(s):  
Mechanical Ventilation ◽  
Steady State ◽  
Spontaneous Breathing ◽  
Time Course ◽  
Venous Blood ◽  
Inert Gas ◽  
Mixed Venous Blood ◽  
Gas Phases ◽  
Pulmonary Capillary ◽  
Pulmonary Capillary Blood

Alveolar gas and mixed venous blood PCO2 and PO2 were compared in a steady-state rebreathing dog preparation, during spontaneous breathing and mechanical ventilation, by a new null-balancing method that removes potential biases in the comparison of measurements in the blood and gas phases and includes an inert gas test to verify the equilibration between the rebreathing lung and the bag. No systematic PCO2 and PO2 differences were observed under equilibrium conditions. However, inert gas studies suggested that a high percentage of measurements obtained during spontaneous breathing were unreliable because of inadequate equilibration between blood and rebreathing bag (attributable to reduced ventilation or perfusion) and that all mechanical ventilation measurements were acceptable. The present data support the view that no PCO2 or PO2 gradients exist when the pulmonary capillary blood and alveolar gas are in equilibrium; the data also suggest that the steady-state rebreathing dog preparation may not be completely stable and that the time course of PCO2 and PO2 in the rebreathing bag may not be reliable as a means of assessing the equilibration between blood and bag.

scholarly journals Rotating and propagating LIB stabilized by self-induced magnetic field

1984 ◽  
Vol 2 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Hiroyuki Murakami ◽  
Takayuki Aoki ◽  
Shigeo Kawata ◽  
Keishiro Niu
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Field Intensity ◽  
Magnetic Field Intensity ◽  
Ion Beam ◽  
Axial Direction ◽  
Induced Magnetic Field ◽  
Tearing Instability ◽  
The Mean ◽  
Steady State Solutions

Rotating motion of a propagating LIB is analyzed in order to suppress the mixed mode of the Kelvin-Helmholtz instability, the tearing instability and the sausage instability by the action of a self-induced magnetic field in the axial direction. The beams are assumed to be charge-neutralized but not current-neutralized. The steady-state solutions of a propagating LIB with rotation are first obtained numerically. Through the dispersion relation with respect to the ikonal type of perturbations, which are added to the steady-state solutions, the growth rates of instabilities appearing in an LIB are obtained. It is concluded that if the mean rotating velocity of an LIB is comparable to the propagation velocity, in other words, if the induced magnetic field intensity in the axial direction is comparable to the magnetic field intensity in the azimuthal direction, the instability disappears in the propagating ion beam.

Laminar flow past an abruptly accelerated elliptic cylinder at 45° incidence

1974 ◽  
Vol 65 (4) ◽  
pp. 711-734 ◽  
Author(s):  
H. J. Lugt ◽  
H. J. Haussling
Keyword(s):  
Steady State ◽  
Numerical Solutions ◽  
Fluid Flows ◽  
Elliptic Cylinder ◽  
Finite Difference Schemes ◽  
Quasi Steady State ◽  
Constant Vorticity ◽  
Transient Period ◽  
Incompressible Fluid Flows ◽  
Steady State Solutions

Numerical solutions for laminar incompressible fluid flows past an abruptly started elliptic cylinder at 45° incidence are presented. Various finite-difference schemes for the stream-function/vorticity formulation are used and their merits briefly discussed. Almost steady-state solutions are obtained forRe= 15 and 30, whereas forRe= 200 a Kármán vortex street develops. The transient period from the start to the steady or quasi-steady state is investigated in terms of patterns of streamlines and lines of constant vorticity and drag, lift and moment coefficients.

scholarly journals Gating of maxi K+ channels studied by Ca2+ concentration jumps in excised inside-out multi-channel patches (myocytes from guinea pig urinary bladder).

1992 ◽  
Vol 99 (6) ◽  
pp. 841-862 ◽  
Author(s):  
F Markwardt ◽  
G Isenberg
Keyword(s):  
Steady State ◽  
Time Course ◽  
Boltzmann Distribution ◽  
Hill Coefficient ◽  
K Channel ◽  
Open Probability ◽  
Apparent Dissociation Constant ◽  
K Channels ◽  
The Mean ◽  
Inside Out

Currents through maxi K+ channels were recorded in inside-out macro-patches. Using a liquid filament switch (Franke, C., H. Hatt, and J. Dudel. 1987. Neurosci, Lett. 77:199-204) the Ca2+ concentration at the tip of the patch electrode ([Ca2+]i) was changed in less than 1 ms. Elevation of [Ca2+]i from less than 10 nM to 3, 6, 20, 50, 320, or 1,000 microM activated several maxi K+ channels in the patch, whereas return to less than 10 nM deactivated them. The time course of Ca(2+)-dependent activation and deactivation was evaluated from the mean of 10-50 sweeps. The mean currents started a approximately 10-ms delay that was attributed to diffusion of Ca2+ from the tip to the K+ channel protein. The activation and deactivation time courses were fitted with the third power of exponential terms. The rate of activation increased with higher [Ca2+]i and with more positive potentials. The rate of deactivation was independent of preceding [Ca2+]i and was reduced at more positive potentials. The rate of deactivation was measured at five temperatures between 16 and 37 degrees C; fitting the results with the Arrhenius equation yielded an energy barrier of 16 kcal/mol for the Ca2+ dissociation at 0 mV. After 200 ms, the time-dependent processes were in a steady state, i.e., there was no sign of inactivation. In the steady state (200 ms), the dependence of channel openness, N.P(o), on [Ca2+]i yielded a Hill coefficient of approximately 3. The apparent dissociation constant, KD, decreased from 13 microM at -50 mV to 0.5 microM at +70 mV. The dependence of N.P(o) on voltage followed a Boltzmann distribution with a maximal P(o) of 0.8 and a slope factor of approximately 39 mV. The results were summarized by a model describing Ca2+- and voltage-dependent activation and deactivation, as well as steady-state open probability by the binding of Ca2+ to three equal and independent sites within the electrical field of the membrane at an electrical distance of 0.31 from the cytoplasmic side.

scholarly journals A level-set method for modeling the evolution of glacier geometry

2004 ◽  
Vol 50 (171) ◽  
pp. 485-491 ◽  
Author(s):  
Antoine Pralong ◽  
Martin Funk
Keyword(s):  
Steady State ◽  
Mass Balance ◽  
Level Set Method ◽  
Level Set ◽  
Numerical Solutions ◽  
Glacier Surface ◽  
Surface Evolution ◽  
Proposed Model ◽  
Steady State Solutions ◽  
Over Time

AbstractA level-set method is proposed for modeling the evolution of a glacier surface subject to a prescribed mass balance. This leads to a simple and versatile approach for computing the evolution of glaciers: the description of vertical fronts and overriding phenomena presents no difficulties, topological changes are handled naturally and steady-state solutions can be calculated without integration over time. A numerical algorithm is put forth as a means of solving the proposed model of glacier surface evolution. It is evaluated by comparing different numerical solutions of the model with analytical and published numerical solutions. The level-set method appears to be a reliable approach for dealing with different glaciological problems.

Pharmacokinetics and Arteriovenous Differences in Clevidipine Concentration following a Short- and a Long-term Intravenous Infusion in Healthy Volunteers

2000 ◽  
Vol 92 (4) ◽  
pp. 993-1001 ◽  
Author(s):  
Hans Ericsson ◽  
Ulf Bredberg ◽  
Ulf Eriksson ◽  
Åse Jolin-Mellgård ◽  
Margareta Nordlander ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Steady State ◽  
Healthy Volunteers ◽  
Venous Blood ◽  
Volume Of Distribution ◽  
Pharmacokinetic Parameters ◽  
Blood Levels ◽  
Blood Concentrations ◽  
Arterial Blood ◽  
The Mean

Background Clevidipine is an ultra-short-acting calcium antagonist developed for reduction and control of blood pressure during cardiac surgery. The objectives of the current study were to determine the pharmacokinetics of clevidipine after 20-min and 24-h intravenous infusions, and to determine the relation between the arterial and venous concentrations and the hemodynamic responses to clevidipine in healthy volunteers. Methods Four volunteers received clevidipine for 20 min, and eight subjects were administered clevidipine intravenously for 24 h at two different dose rates. Arterial and venous blood samples were drawn for pharmacokinetic evaluation, and blood pressure and heart rate were recorded. Results A triexponential disposition model described the pharmacokinetics of clevidipine. The mean arterial blood clearance of clevidipine was 0.069l/kg-1/min-1 and the mean volume of distribution at steady state was 0.19 l/kg. The duration of the infusion had negligible effect on the pharmacokinetic parameters, and the context-sensitive half-time for clevidipine, simulated from the mean pharmacokinetic parameters derived after 24 h infusion at the highest dose, was less than 1 min. The arterial blood levels reached steady state within 2 min of the start of infusion and were about twice as high as those in the venous blood at steady state. The peak response preceded the peak venous concentration and was slightly delayed from the peak arterial blood concentration. Conclusion Clevidipine is a high clearance drug with a small volume of distribution, resulting in extremely short half-lives in healthy subjects. The initial rapid increase in the arterial blood concentrations and the short equilibrium time between the blood and the biophase suggest that clevidipine can be rapidly titrated to the desired effect.

Influence of G-suit abdominal bladder inflation on gas exchange during +GZ stress

1985 ◽  
Vol 58 (2) ◽  
pp. 506-513
Author(s):  
H. I. Modell ◽  
P. Beeman ◽  
J. Mendenhall
Keyword(s):  
Gas Exchange ◽  
Time Course ◽  
Venous Blood ◽  
Blood Gas Analysis ◽  
Gas Analysis ◽  
Mixed Venous Blood ◽  
Blood Gas ◽  
Series Of Experiments ◽  
Spontaneously Breathing ◽  
Arterial Po2

Available data relating duration of +GZ stress to blood gas exchange status is limited. Furthermore, studies focusing on pulmonary gas exchange during +GZ stress when abdominal restriction is imposed have yielded conflicting results. To examine the time course of blood gas changes occurring during exposure to +GZ stress in dogs and the influence of G-suit abdominal bladder inflation on this time course, seven spontaneously breathing pentobarbital-anesthetized adult mongrel dogs were exposed to 60 s of up to +5 GZ stress with and without G-suit abdominal bladder inflation. Arterial and mixed venous blood were sampled for blood gas analysis during the first and last 20 s of the exposure and at 3 min postexposure. Little change in blood gas status was seen at +3 GZ regardless of G-suit status. However, with G-suit inflation, arterial PO2 fell by a mean of 14.7 Torr during the first 20 s at +4 Gz (P less than 0.01, t test) and 20.6 Torr at +5 GZ (P less than 0.01). It continued to fall an additional 10 Torr during the next 40 s at both +4 and +5 GZ. Arterial PO2 was still 5–10 Torr below control values (P less than 0.05) 3 min postexposure. A second series of experiments paralleling the first focused on blood gas status during repeated exposure to acceleration. Blood gas status was assessed in five dogs during the late 20 s of two 60-s exposures separated by 3 min at 0 GZ. No significant differences between the initial and repeated exposures were detected. The data indicate that G-suit abdominal bladder inflation promotes increased venous admixture.

Optimality in landscape channelization and analogy with turbulence

2020 ◽  
Author(s):  
Milad Hooshyar ◽  
Sara Bonetti ◽  
Arvind Singh ◽  
Efi Foufoula-Georgiou ◽  
Amilcare Porporato
Keyword(s):  
Steady State ◽  
Governing Equations ◽  
Power Law Decay ◽  
Logarithmic Scaling ◽  
The Mean ◽  
Optimality Principles ◽  
Steady State Solutions ◽  
Average Domain ◽  
Logarithmic Velocity Profile ◽  
Wall Bounded Turbulence

<p>The channelization cascade observed in terrestrial landscapes describes the progressive formation of large channels from smaller ones starting from diffusion-dominated hillslopes. This behavior is reminiscent of other non-equilibrium complex systems, particularly fluids turbulence, where larger vortices break down into smaller ones until viscous dissipation dominates. Based on this analogy, we show that topographic surfaces emerging between parallel zero-elevation boundaries present a logarithmic scaling in the mean-elevation profile, which resembles the well-known logarithmic velocity profile in wall-bounded turbulence. Within this region of elevation fluctuation, the power spectrum exhibits a power-law decay resembling the Kolmogorov -5/3 scaling of turbulence. We also demonstrate that similar scaling behaviors emerge in surfaces from a laboratory experiment, natural basins, and constructed following optimality principles. In general, we show that the steady-state solutions of the governing equations of landscape evolution are the stationary surfaces of a functional defined as the average domain elevation. Depending on the exponent of the specific drainage area in the erosion term (m), the steady-state surfaces are local minimum (m<1) or maximum (m>1) of the average domain elevation.</p>

Upwelling of a stratified fluid in a rotating annulus: steady state. Part 2. Numerical solutions

1973 ◽  
Vol 59 (2) ◽  
pp. 337-368 ◽  
Author(s):  
J. S. Allen
Keyword(s):  
Steady State ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Rotational Frequency ◽  
Navier Stokes ◽  
Rossby Number ◽  
Navier Stokes Equations ◽  
Finite Difference Approximations ◽  
Side Walls ◽  
Steady State Solutions

Numerical solutions of finite-difference approximations to the Navier–Stokes equations have been obtained for the axisymmetric motion of a Boussinesq liquid in a rigidly bounded rotating annulus. For most of the cases studied, a temperature difference is maintained between the top and bottom surfaces such that essentially a basic stable density stratification is imposed on the fluid. The side walls are thermally insulated and the motion is driven by a differential rotation of the top surface. Approximate steady-state solutions are obtained for various values of the Rossby number ε and the stratification parameter S = N2/Ω2, where N is the Brunt–Väisälä frequency and Ω is the rotational frequency. The changes in the flow field with the variation of these parameters is studied. Particular attention is given to an investigation of the meridional, or up welling, circulation and its dependence on the stratification parameter. The effects on the flow of different boundary conditions, such as an applied stress driving, specified temperature at the side walls and an applied heat flux at the top and bottom surfaces, are also investigated.

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