Response to the Letter to the Editor “Airflow Simulation in Pulmonary Conducting Airways” by M. Monjezi and H. Jamaati

To the Editor,

We thank Drs. Monjezi and Jamaati for their careful review1 of our paper titled “Airflow Simulations in Infant, Child, and Adult Pulmonary Conducting Airways.”2 First, we acknowledge a typo in the equation for $R^n_{i,j}$ in first paragraph of page 501.2 The second term on the right hand side of that equation should have been divided by $C_{i,j}$. The correct form is

$$\begin{aligned} R^n_{i,j} = \frac{dt}{dV_{\Gamma _{i,j}}} \Big [ \Delta P_{\Gamma _{i,j}} - \frac{V_{\Gamma _{i,j}}}{C_{i,j}} \Big ] \end{aligned}$$

(1)

We note that Eq. (1) is derived directly from Eq. (5) in our paper,2 which is presented correctly. We also note that we employed the correct Eq. (1), and not the one with the typo, for our simulation results.

Secondly, Drs. Monjezi and Jamaati highlight1 our finding that approximately 10% of the total pressure drop ($\Delta P$) of the lung occurs within our simulated conducting airways $\Delta P_{3D}$, which they argue is in disagreement with the pressure relationship given by Pedley et al.4 However, the expression presented by Pedley et al. only models the pressure gradient that results from viscous airflow and not across the entire lung. In contrast, the $\Delta P$ that we calculate2 includes the combined pressure drop due to total viscous ($R_{\text{global}}$) and compliance ($C_{\text{global}}$) effects. Moreover, in agreement with Otis et al.,3 we posit that the majority of energy loss is due to movement of the parenchyma and not due to viscous forces. Namely, by performing an order-of-magnitude analysis for the adult, where the pressure drop across the resistor is $\Delta P_R \approx R_{\text{global}} Q_{\text{mean}} \approx 1.75$ cmH₂O and the pressure drop across the capacitor is $\Delta P_C \approx \frac{TV}{C_{\text{global}}} \approx 8.47$ cmH₂O, we find that the pressure drop due solely to viscous losses ($\Delta P_R$) is roughly 17% of the total pressure drop $\left(100 \Big [ \frac{\Delta P_R}{ \Delta P_R + \Delta P_C} \Big ]\right)$. Thus, we believe that our finding of $\Delta P_{3D}$$\sim$10% of $\Delta P$ is reasonable.

Finally, we note that the 3D model had on average 6–7 airway generations. The adult model spanned up to 11 generations along paths where we were able to resolve more generations based on image quality.2