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Inert Gas Transport in Blood and Tissues

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Abstract

This article establishes the basic mathematical models and the principles and assumptions used for inert gas transfer within body tissues—first, for a single compartment model and then for a multicompartment model. From these, and other more complex mathematical models, the transport of inert gases between lungs, blood, and other tissues is derived and compared to known experimental studies in both animals and humans. Some aspects of airway and lung transfer are particularly important to the uptake and elimination of inert gases, and these aspects of gas transport in tissues are briefly described. The most frequently used inert gases are those that are administered in anesthesia, and the specific issues relating to the uptake, transport, and elimination of these gases and vapors are dealt with in some detail showing how their transfer depends on various physical and chemical attributes, particularly their solubilities in blood and different tissues. Absorption characteristics of inert gases from within gas cavities or tissue bubbles are described, and the effects other inhaled gas mixtures have on the composition of these gas cavities are discussed. Very brief consideration is given to the effects of hyper‐ and hypobaric conditions on inert gas transport. © 2011 American Physiological Society. Compr Physiol 1:569‐592, 2011.

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Figure 1. Figure 1.

Single element capillary‐tissue model.

Figure 2. Figure 2.

Exponential wash‐in of inert gas in a perfused single tissue element. The tissue (and venous) partial pressure rises from zero asymptotically to arterial partial pressure. The rate constant is reduced by increased tissue volume, increased tissue‐gas partition coefficient, and decreased blood flow.

Figure 3. Figure 3.

Pv(t) calculated using both the PDE model (solid line) and the ODE model (broken line) for the uptake of the anesthetic gas nitrous oxide where Pa(t) has a step change from 0 to 1 at time t = 0. Showing the more rapid response in the PDE model. From Whiteley et al. , with permission

Figure 4. Figure 4.

Schematic representation of body compartments. VRG, vessel‐rich group; MG, muscle group; FG, fat group; and VPG, vessel‐poor group.

Figure 5. Figure 5.

(A) Compartmental venous and tissue partial pressure versus time after imposition of a constant arterial partial pressure of 1.0. At 60 min, the arterial partial pressure is set to zero. Red lines, vessel‐rich group; green lines, muscle group; gray lines, vessel‐poor group; and orange lines, fat group. Solid lines represent the anesthetic vapor desflurane, dotted lines represent ether. (B) The mixed venous partial pressures for the same simulation.

Figure 6. Figure 6.

The simulated arterial Pco2 responses to step changes in ventilatory frequency. The ventilatory frequency was increased or decreased by a factor of 1.5 for each model at t = 0. Gray line, normal lung model; black line, embolism model; and dashed line, emphysema model. The open circles represent end‐tidal points. Main figure −10 to 50 s. Inset figure 0 to 500 s. From Yem et al. , with permission

Figure 7. Figure 7.

Axial distribution of gas transport during inspiration (black columns) and expiration (gray columns) for a tidal breath of cyclopropane (A), ether (B), and acetone (C). Each flux has been normalized by the total inspiratory soluble gas flux. As the blood solubility of gas increases from cyclopropane to acetone, the distribution shifts from a sharp concentrated peak in the alveolar region for cyclopropane to a wider distribution that spreads throughout the airways for acetone. From Anderson et al. , with permission

Figure 8. Figure 8.

The digitized emphysema MIGET distribution (gray, open circles, left ordinate) and the recovered three‐compartment distributions showing for each inert gas, with solubility increasing from left to right (SF6 to acetone) demonstrating an increasing effect of the solubility of the inert gas and that the high areas are affected more than the normal areas for both slow and fast compartments. Open triangles, mid compartment; open squares, fast high compartment; and open circles, slow high compartment. DS, dead space. From Yem et al. , with permission

Figure 9. Figure 9.

(A) Compartmental venous and tissue partial pressure versus time after imposition of a constant inspired partial pressure of 1.0. At 60 min, the inspired partial pressure is set to zero. Red lines, vessel‐rich group; green lines, muscle group; and orange lines, fat group. Solid lines represent the anesthetic vapor desflurane, dotted lines represent ether. (B) The mixed venous partial pressures for the same simulation.

Figure 10. Figure 10.

Washout of desflurane (green), N2O (blue), and isoflurane (purple) and a 30:70 MAC ratio mixture of isoflurane and N2O (pink dashed) from the VRG after 60 and 120 min of exposure at 1.0 MAC inspired throughout. Partial pressures are normalized, that is, expressed as a fraction of the value at t = 0.

Figure 11. Figure 11.

Sample data from two experimental runs in one volunteer showing the decline in end‐tidal sevoflurane and halothane concentrations during rebreathing from a 1‐liter bag. Filled symbols, sevoflurane; open symbols, halothane. Solid lines show monoexponential model fits (y = a et/τ) for each set of data points. Concentrations are expressed relative to the first end‐tidal value recorded during rebreathing.

Figure 12. Figure 12.

When ventilation to an area of lung ceases, lung collapses at a rate dependent on the inspired gas composition. Shown is the time to collapse found when breathing various mixtures of O2 and N2O was modeled. Results are given for when hypoxic pulmonary vasoconstriction (HPV) was, and was not, incorporated into the model. As Fio2 decreases from 1.0, time for collapse decreases to a minimum at Fio2 = 0.5. Further decreases in Fio2 result in increase in time to collapse. When HPV was incorporated into the model, time to collapse was approximately the same with Fio2 = 1.0 as with Fio2 = 0.3. When HPV was not incorporated, collapse took about the same time with Fio2 = 1.0 as with Fio2 = 0.25. Inclusion of HPV in the model resulted in prolongation of time to collapse with increasing effect as Fio2 decreased. Maximal prolongation was at Fio2 = 0.2 (lowest Fio2 considered) when time to collapse was 50% longer with than without HPV incorporation. From Joyce et al. , with permission

Figure 13. Figure 13.

The Kety‐Schmidt method of prolonged N2O wash‐in to the brain via inhalation. Closed circles show arterial sampling; open circles show cerebral venous sampling.

Figure 14. Figure 14.

Venous concentration‐time profile following rapid intra‐arterial injection of a bolus of tracer.

Figure 15. Figure 15.

Transit time probability function, h(t) (upper trace), cumulative probability, H(t) (middle trace), and 1 – cumulative probability, 1 – H(t) (lower trace).

Figure 16. Figure 16.

Diffusion paths from the capillary to tissue for rapid, complete diffusive equilibration (bold arrows, large compartment) and slower, incomplete diffusive equilibrium (faint arrows, dashed compartment).

Figure 17. Figure 17.

The tissue response (dashed line) to a sinusoidally varying arterial inert gas partial pressure (solid line).



Figure 1.

Single element capillary‐tissue model.



Figure 2.

Exponential wash‐in of inert gas in a perfused single tissue element. The tissue (and venous) partial pressure rises from zero asymptotically to arterial partial pressure. The rate constant is reduced by increased tissue volume, increased tissue‐gas partition coefficient, and decreased blood flow.



Figure 3.

Pv(t) calculated using both the PDE model (solid line) and the ODE model (broken line) for the uptake of the anesthetic gas nitrous oxide where Pa(t) has a step change from 0 to 1 at time t = 0. Showing the more rapid response in the PDE model. From Whiteley et al. , with permission



Figure 4.

Schematic representation of body compartments. VRG, vessel‐rich group; MG, muscle group; FG, fat group; and VPG, vessel‐poor group.



Figure 5.

(A) Compartmental venous and tissue partial pressure versus time after imposition of a constant arterial partial pressure of 1.0. At 60 min, the arterial partial pressure is set to zero. Red lines, vessel‐rich group; green lines, muscle group; gray lines, vessel‐poor group; and orange lines, fat group. Solid lines represent the anesthetic vapor desflurane, dotted lines represent ether. (B) The mixed venous partial pressures for the same simulation.



Figure 6.

The simulated arterial Pco2 responses to step changes in ventilatory frequency. The ventilatory frequency was increased or decreased by a factor of 1.5 for each model at t = 0. Gray line, normal lung model; black line, embolism model; and dashed line, emphysema model. The open circles represent end‐tidal points. Main figure −10 to 50 s. Inset figure 0 to 500 s. From Yem et al. , with permission



Figure 7.

Axial distribution of gas transport during inspiration (black columns) and expiration (gray columns) for a tidal breath of cyclopropane (A), ether (B), and acetone (C). Each flux has been normalized by the total inspiratory soluble gas flux. As the blood solubility of gas increases from cyclopropane to acetone, the distribution shifts from a sharp concentrated peak in the alveolar region for cyclopropane to a wider distribution that spreads throughout the airways for acetone. From Anderson et al. , with permission



Figure 8.

The digitized emphysema MIGET distribution (gray, open circles, left ordinate) and the recovered three‐compartment distributions showing for each inert gas, with solubility increasing from left to right (SF6 to acetone) demonstrating an increasing effect of the solubility of the inert gas and that the high areas are affected more than the normal areas for both slow and fast compartments. Open triangles, mid compartment; open squares, fast high compartment; and open circles, slow high compartment. DS, dead space. From Yem et al. , with permission



Figure 9.

(A) Compartmental venous and tissue partial pressure versus time after imposition of a constant inspired partial pressure of 1.0. At 60 min, the inspired partial pressure is set to zero. Red lines, vessel‐rich group; green lines, muscle group; and orange lines, fat group. Solid lines represent the anesthetic vapor desflurane, dotted lines represent ether. (B) The mixed venous partial pressures for the same simulation.



Figure 10.

Washout of desflurane (green), N2O (blue), and isoflurane (purple) and a 30:70 MAC ratio mixture of isoflurane and N2O (pink dashed) from the VRG after 60 and 120 min of exposure at 1.0 MAC inspired throughout. Partial pressures are normalized, that is, expressed as a fraction of the value at t = 0.



Figure 11.

Sample data from two experimental runs in one volunteer showing the decline in end‐tidal sevoflurane and halothane concentrations during rebreathing from a 1‐liter bag. Filled symbols, sevoflurane; open symbols, halothane. Solid lines show monoexponential model fits (y = a et/τ) for each set of data points. Concentrations are expressed relative to the first end‐tidal value recorded during rebreathing.



Figure 12.

When ventilation to an area of lung ceases, lung collapses at a rate dependent on the inspired gas composition. Shown is the time to collapse found when breathing various mixtures of O2 and N2O was modeled. Results are given for when hypoxic pulmonary vasoconstriction (HPV) was, and was not, incorporated into the model. As Fio2 decreases from 1.0, time for collapse decreases to a minimum at Fio2 = 0.5. Further decreases in Fio2 result in increase in time to collapse. When HPV was incorporated into the model, time to collapse was approximately the same with Fio2 = 1.0 as with Fio2 = 0.3. When HPV was not incorporated, collapse took about the same time with Fio2 = 1.0 as with Fio2 = 0.25. Inclusion of HPV in the model resulted in prolongation of time to collapse with increasing effect as Fio2 decreased. Maximal prolongation was at Fio2 = 0.2 (lowest Fio2 considered) when time to collapse was 50% longer with than without HPV incorporation. From Joyce et al. , with permission



Figure 13.

The Kety‐Schmidt method of prolonged N2O wash‐in to the brain via inhalation. Closed circles show arterial sampling; open circles show cerebral venous sampling.



Figure 14.

Venous concentration‐time profile following rapid intra‐arterial injection of a bolus of tracer.



Figure 15.

Transit time probability function, h(t) (upper trace), cumulative probability, H(t) (middle trace), and 1 – cumulative probability, 1 – H(t) (lower trace).



Figure 16.

Diffusion paths from the capillary to tissue for rapid, complete diffusive equilibration (bold arrows, large compartment) and slower, incomplete diffusive equilibrium (faint arrows, dashed compartment).



Figure 17.

The tissue response (dashed line) to a sinusoidally varying arterial inert gas partial pressure (solid line).

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A. Barry Baker, Andrew D. Farmery. Inert Gas Transport in Blood and Tissues. Compr Physiol 2011, 1: 569-592. doi: 10.1002/cphy.c100011