= Diffusion resistances of serial alveolar barrier layers
\b[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 $c_j=S_jp$, thickness $\delta_j$ and <diffusion coefficient> $D_j$. With equilibrium partitioning at interfaces and no chemical consumption within a layer, <Fick's first law> gives
$$
J=\frac{D_jS_j}{\delta_j}(p_{j-1}-p_j),\qquad
r_j=\frac{\delta_j}{D_jS_j}.
$$
Thus $\Delta p=J\sum_jr_j$ and total molar transfer through common <area> $A$ is $\dot n=A\Delta p/\sum_jr_j$. 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 $40/6\approx6.667$. 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.<The Ultrastructure of Mouse Lung: Some Remarks Regarding the Fine Structure of the Alveolar Basement Membrane by H. E. Karrer>[Abstract: three electron micrographs and variable apparent width]{ref} A measured image thickness does not independently establish every $D_jS_j$, patch <area> or blood-side reaction rate. The derivation is a steady transport model, not a complete clinical gas-transfer test.
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