Diffusion resistances of serial alveolar barrier layers

Diffusion resistances of serial alveolar barrier layers describe how successive tissue layers share the total gas partial pressure drop while carrying the same steady molar flux. The alveolar-capillary barrier contains alveolar epithelium, intervening basement membrane material and capillary endothelium. The distinction between a layer's thickness and its resistance matters because gas solubility and diffusion coefficient also enter.

For a planar layer $j$, let dissolved concentration be $c_j=S_{j}p$, thickness ${\delta }_j$ and diffusion coefficient $D_j$. With equilibrium partitioning at interfaces and no chemical consumption within a layer, Fick's first law givesThus $\Delta p=J{\sum }_j{r}_j$ and total molar transfer through common area $A$ is $\dot{n}=A\Delta p/{\sum }_j{r}_j$. These are area-specific resistances; the resistance for total transfer is $R_j=r_j/A$. Mixing those two conventions loses a factor of area.

An original normalized calculation sets $r_1=1$, $r_2=2$, $r_3=1$ and end-to-end partial pressure difference 40 in compatible units. The flux is 10, and layer drops are 10, 20 and 10. Doubling only the middle layer's thickness raises total resistance from 4 to 6 and lowers flux to $40/6\approx 6.667$. The middle layer now carries two thirds of the total drop. One total transfer measurement cannot separately identify all three layer resistances.

Spatial heterogeneity introduces a different averaging rule. Suppose two equal-area patches have total area-specific resistances 1 and 4 under the same imposed partial pressure difference. Parallel patch fluxes add, giving conductance per total area $(1/1+1/4)/2=0.625$ and effective resistance 1.6. Taking the arithmetic average resistance 2.5 would predict the wrong transfer. This is parallel-path averaging of alveolar diffusion resistance.

The tissue layers themselves have an observational basis: H. E. Karrer's electron-microscope study described variation in the apparent width of the intervening basement membrane, including possible sectioning effects.^[ref] A measured image thickness does not independently establish every $D_j{S}_j$, patch area or blood-side reaction rate. The derivation is a steady transport model, not a complete clinical gas-transfer test.