Lippincott Williams & Wilkins



Supplemental Information

A. Equation details:

Shunt equation: QS/QT = (Cc'O2 - CaO2) / (Cc'O2 - C(O2) (1)

where QS is the amount of blood flow that does not participate in pulmonary gas exchange; QT is total cardiac output (and, thus, QS/QT is the "shunt fraction"); Cc'O2 is the end pulmonary capillary oxygen content; CaO2 is arterial blood oxygen content; and C(O2 is mixed venous oxygen content. The oxygen content of each portion of blood (CxO2) is given by:

CxO2= (Hb)•(1.34)•(SxO2) + (PxO2)•(0.0031) (2)

where Hb is the hemoglobin concentration (g/dL), 1.34 is the volume of oxygen carried by fully saturated hemoglobin, SxO2 is the fraction of hemoglobin saturated with oxygen, and 0.0031 is the Bunsen solubility coefficient for oxygen in plasma. C(O2 was calculated as: CaO2 - AVDO2.

was calculated using

PAO2 = FIO2 • (PB - 47) - PACO2 • {FIO2 + [(1 - FIO2) / RQ]} (3)

Where PB is the ambient barometric pressure, RQ is the respiratory quotient, PACO2 is the partial pressure of CO2 in the alveolus, and FIO2 is the fraction of inspired oxygen.

Thus, the expanded shunt equation is:

QS/QT = {[(Hb•1.34•ScO2) + (PcO2•0.0031)] - [(Hb•1.34•SaO2) + (PaO2•0.0031)]} /

{[(Hb•1.34•ScO2) + (PcO2•0.0031)] -

[(Hb•1.34•S(O2) + (P(O2•0.0031)]} (4)

We assumed that PcO2 equals the alveolar partial pressure of oxygen (PAO2), as equilibration of partial pressures of oxygen in the alveolus and in the end of the pulmonary capillary blood is complete, except in the unusual combination of very low PAO2 with increased cardiac output (low pulmonary capillary transit time) and further with decreased pulmonary capillary blood volume.(1, 2) PAO2 (and, thus, PcO2) was calculated from the alveolar gas equation.(3)

B. Iterative Solutions:

The "goal seek" function in Microsoft Excel proved inadequate because it could not loop to multiple lines of data and the accuracy did not exceed 2 to 3 digits. One of us (JF) developed an iterative loop function using Microsoft Excel that changed PaO2 until the selected desired shunt fraction was achieved using the above equations. From an initial value of PaO2, all the intermediate calculations and shunt value were determined. PaO2 was then adjusted up or down in decreasing increments based on the difference between the calculated and target shunt fractions until QS/QT was solved with an accuracy of not less than ± 10-10; that is, each shunt fraction at the end of the iterative process did not differ by more than 0.0000000001 from the shunt fraction that we had specified. Hemoglobin oxygen saturation for blood in each location was derived from the blood PO2 by use of the equations of Severinghaus(4) and Roughton and Severinghaus.(5) For each curve, we specified increments of 1.0% between values of FIO2 from 0.21 to 1.0; thus, each curve is constructed from 80 calculated points.

C. Venous Values:

Venous values were averaged in Hb ranges 0.5 g/dL above and below the Hb value for which estimated values were desired. Additionally, repeated measures regression analyses (linear and polynomial) of Hb vs. SvO2 or AVDO2 were performed to derive estimates of venous values at each desired Hb concentration because the original data were close to, but not at exactly the desired Hb concentrations. Results are summarized in Table 1S, and were similar for the different calculations. AVDO2 values used in simulations were rounded to the nearest 0.25 mL O2/dL.

Table 1S

|Table 1S. Modeled and calculated AVDO2 and SvO2 from normal healthy humans during acute normovolemic hemodilution (28) |

| |Hb=5 g/dL |Hb=7 g/dL |Hb=10 g/dL |Hb=14 g/dL |

|Linear Model | | | | |

|AVDO2 (mL O2/dL) |2.3 |2.7 |3.3 |4.1 |

|SvO2 (%) |70 |72 |75 |80 |

| | | | | |

|Polynomial Model | | | | |

|AVDO2 (mL O2/dL) |2.4 |2.7 |3.2 |4.4 |

|SvO2 (%) |68 |73 |77 |75 |

| | | | | |

|Hemoglobin “Bins” |Hb 4.5-5.5 g/dL |Hb 6.5-7.5 g/dL |Hb 9.5-10.5 g/dL |Hb 13.5-14.5 g/dL |

|AVDO2 (mL O2/dL) |2.4 ± 0.6 |2.7 ± 0.5 |3.3 ± 0.6 |4.3 ± 0.9 |

|SvO2 (%) |66.5 ± 8.5 |72.7 ± 6.5 |75.8 ± 4.8 |77.3 ± 4.0 |

| | | | | |

|Values used for models | | | | |

|AVDO2 (mL O2/dL) |2.5 |2.75 |3.5 |4.25 |

| | | | | |

|Data are predicted values at specified hemoglobin (Hb) concentration, or mean ± SD for “bins”. AVDO2, arterial to venous oxygen content difference; SvO2, mixed venous oxygen |

|saturation. |

Figure 1S

[pic]

P/F Ratio (PaO2/FIO2) as a function of shunt fractions (QS/QT) from normal (0.01), to extremely high (0.6) for different FIO2 levels. Simulations were calculated for a hemoglobin concentration (Hb) of 10 g/dL and arterial-venous oxygen content difference (AVDO2) of 3.5 mL O2/dL.

Figure 2S

[pic]

P/F Ratio (PaO2/FIO2) as a function of FIO2 for shunt fractions (QS/QT) from normal (0.01), to extremely high (0.5). Each panel shows a different hemoglobin concentration (Hb): (A, 5 g/dL; B, 7 g/dL; C, 10 g/dL; D, 14 g/dL), with a constant arterial to venous oxygen content difference (AVDO2) value of 3.5 mL O2/dL, representing no cardiovascular compensation.

Figure 3S

[pic]

P/F Ratio (PaO2/FIO2) as a function of FIO2 at different values of shunt fraction (QS/QT) from normal (0.01), to extremely high (0.5). Each panel shows a different hemoglobin concentration (Hb), (A, 5 g/dL; B, 7 g/dL; C, 10 g/dL; D, 14 g/dL), using arterial to venous oxygen content differences (AVDO2) values for appropriate physiological cardiovascular compensation. A: Hb 5 g/dL, AVDO2 2.5 mL O2/dL; B: Hb 7 g/dL, AVDO2 2.75 mL O2/dL; C: Hb 10 g/dL, AVDO2 3.5 mL O2/dL; D: Hb 14 g/dL, AVDO2 4.25 mL O2/dL.

Figure 4S

[pic]

P/F Ratio (PaO2/FIO2) as a function of shunt fraction (QS/QT) at hemoglobin concentrations (Hb) from 5 g/dL to 14 g/dL, using arterial to venous oxygen content differences (AVDO2) values for appropriate physiological cardiovascular compensation. Each panel shows a different FIO2: A, 0.21; B, 0.4; C, 0.5; D, 0.6; E, 0.8; F, 1,0.

Figure 5S

[pic]

P/F Ratio (PaO2/FIO2) as a function of FIO2 at values of shunt fraction (QS/QT) from normal (0.1), to extremely high (0.5). Each panel shows a different value of arterial to venous oxygen content differences (AVDO2) at a hemoglobin concentration of 10 g/dL. Panel A: AVDO2 1.5 mL O2/dL; AVDO2 2.5 mL O2/dL; AVDO2 3.5 mL O2/dL; AVDO2 6.0 mL O2/dL.

References:

1. Weiskopf RB, Severinghaus JW. Diffusing capacity of the lung for CO in man during acute acclimation to 14,246 ft. J Appl Physiol 1972;32(3):285-289.

2. Staub NC. Alveolar-arterial oxygen tension gradient due to diffusion. J Appl Physiol 1963;18:673-680.

3. Fenn WO, Rahn H, Otis AB. A theoretical study of the composition of the alveolar air at altitude. The American journal of physiology 1946;146:637-653.

4. Severinghaus J. Simple, accurate equations for human blood O2 dissociation computations. J App Physiol 1979;46:599-602.

5. Roughton F, Severinghaus J. Accurate determination of O2 dissociation curve of human blood above 98.7% saturation with data on O2 solubility in unmodified human blood from 0°C to 37°C. J App Physiol 1973;35:861-869.

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