Multi-compartment V/Q lung modeling: Log normal distributions of inspired or expired alveolar gas?

Abstract

Using a 50-compartment Python-coded mathematical lung model, we compared mixed venous blood flow (Q) distributions and arterial oxygen tension/inspired oxygen fraction (PaO₂/FiO₂) relationships in lungs modeled with log normal distributions (LND) of inspired (V_I) versus expired (V_A) alveolar gas volumes. In lungs with normal V/Q heterogeneity, Q versus V_A/Q and Q versus V_I/Q distributions were similar with either approach, and PaO₂/FiO₂ sequences remained indistinguishable. In V/Q heterogeneous lungs at high FiO₂, V_ILND generated low Q versus V_A/Q shoulders and some negative V_A units, while V_ALND preserved Q versus V_A/Q log normality by blood flow diversion from low V_I/Q units. We managed V_ILND-induced negative V_A units either by shunt conversion (V_I decreased to 0) or V_I redistribution simulating collateral ventilation (V_I increased till V_A = 0). Comparing oxygen transfer: V_ALND > V_ILND (redistribution) > V_ILND (shunt). In V/Q heterogeneous lungs V_ALND and V_ILND (redistribution) regained near optimal oxygen transfer on 100% oxygen, while impairment persisted with V_ILND (shunt). Unlike V_ALND, V_ILND (redistribution) produced Q versus V_A/Q distributions in V/Q heterogeneity compatible with multiple inert gas (MIGET) reports. V_ILND (redistribution) is a physiologically-based MIGET-compatible alternative to West's original V_ALND lung modeling approach.

Keywords: MIGET; V/Q model; alveolar gas; expired; inspired; log normal.

FIGURE 1

Effects of West's V _ALND approach on pre‐equilibration Q versus V _I/Q relationships at a low inspired oxygen concentration (FiO₂ = 0.3). Closed circles: Q versus V _A/Q maintained as a log normal distribution. Open circles: Q versus V _I/Q: Remains close to log normal as log SD increases, but with some unilateral rightward shift on the left side of the log normal mean.

FIGURE 2

Effects of the V _ILND approach on post‐equilibration Q versus V _A/Q relationships at FiO₂ = 0.3. Open and closed circles as in Figure 1, but with Q versus V _I/Q (open circles) maintained as log normal. There is an elevated Q versus V _A/Q ‘tail’ on the left of the log normal mean as log SD increases, indicating increased blood flow to low V _A/Q units. At log SD = 1.8 there is also blood flow to 7 negative V _A units.

FIGURE 3

Effects of West's V _ALND approach on Q versus V _I/Q pre‐equilibration relationships at a high inspired oxygen concentration (FiO₂ = 0.9). Open and closed circles as in Figure 1 with Q versus V _A/Q (closed circles) maintained as log normal. As log SD increases there is now significant and progressive unilateral deviation from a log normal Q versus V _I/Q relationship by rightward shifts on the left of the log normal mean.

FIGURE 4

Effects of the V _ILND approach on Q versus V _A/Q post‐equilibration relationships at high FiO₂ (0.9). Open and closed circles as in Figure 1, with Q versus V _I/Q (open circles) maintained as log normal. There is a progressive Q versus V _A/Q “shoulder” on the left of the log normal mean as log SD increases, indicating escalating blood flow to low V _A/Q units. There are now major flows to negative V _A units.

FIGURE 5

Relationships between FiO₂ and PaO₂ for log SD = 0.4, 1.1 and 1.8. Closed circles: West's V _ALND approach. Open triangles: V _ILND approach with conversion of negative V _A units to shunt (V _I/Q = 0) (Option 1). Open circles: V _ILND approach with redistribution of inspired gas to negative V _A units so that V _A/Q = 0 (Option 2). PaO₂ values vs FiO₂ are close to identical at log SD = 0.4 but diverge for all policies at higher log SD values, with West's V _ALND approach achieving the highest oxygen transfer at each FiO₂.

FIGURE 6

Relationships between FiO₂ and venous admixture for log SD = 0.4, 1.1 and 1.8. Closed circles: West's V _ALND policy; Open triangles: V _ILND policy with conversion of negative V _A units to shunt (V _I/Q = 0) (Option 1); Open circles: V _ILND policy with redistribution of inspired gas to negative V _A units so that V _A/Q = 0 (Option 2). Venous admixture values are close to identical for all policies at log SD = 0.4 and log SD = 1.1, and diverging at log SD = 1.8. For log SD = 1.8 and FiO₂ = 1.0, venous admixture persists at approximately 20% for Option 1, but is verging on zero for V _ILND plus Option 2 and for West's V _ALND policy.

FIGURE 7

Illustration of extensive V _I redistribution. Log SD = 1.8. FiO₂ = 0.9. Prior to redistribution 20% of mixed venous flow was to negative V _A units. V _I redistribution to these units was randomized to achieve V _A/Q values between zero and 0.01. The result is 8% mixed venous blood flow to units with V _A/Q < 0.005 (all data points to the left of the Y axis), interpretable by MIGET as shunt flow. The rest (all data points to the right of the Y axis) would potentially be processed by the MIGET smoothing algorithm as a bimodal distribution.