Reply: On the Use of <sup>3</sup>He Diffusion Magnetic Resonance as Evidence of Neo-Alveolarization during Childhood and Adolescence
Authors: Manjith Narayanan, John Owers-Bradley, Caroline S. Beardsmore, Claudia E. Kuehni, Michael Silverman
Journal: American Journal of Respiratory and Critical Care Medicine (2014)

From the Authors:

We thank the editor of the Journal for giving us the opportunity to respond to the letter by Parra-Robles and Wild.

Using helium-3 (3He) magnetic resonance (MR), we investigated whether lung growth during childhood was achieved by expansion of pre-existing alveoli or by new alveolarization (1). We measured how the parameters obtained from 3HeMR change during enlargement of the lung by controlled inhalation, and compared them with those occurring during lung growth in a cross-section of over 100 children. The parameters changed very little with growth compared with the predicted changes, suggesting that the peripheral lung structures altered little in size during a period when lung volume increased up to 3.6-fold. The implication is that alveolarization occurred throughout childhood. Our study is just one of several in recent literature supporting alveolarization beyond early childhood in mammals (2–6). Following the publication of our paper, there has been more evidence supporting post-mature alveolarization in humans (7).


Three major issues were identified in the letter from Parra-Robles and Wild and are dealt with here: (1) length scale used in our measurements, (2) use of the “expansion model” (based on inhalation) to test the hypothesis of no alveolarization, and (3) the mathematical model on which they base their criticisms. These issues are discussed in more detail and their other concerns are explored in the online supplement to this letter.


1.

In free space, helium atoms undergo diffusion. The root-mean-square displacement s due to diffusion is related to the measurement interval (“diffusion time”) t as

s=2Dt,

(Eq.1)



where D is unrestricted diffusion coefficient.


In a restricted space, diffusion is limited by the barriers. Therefore, the measured value is an “apparent diffusion coefficient” (ADC). Using ADC as a measure of dimension of the barriers is practical only if the dimensions are of the same order as s (8) (and therefore, the diffusion time t should be appropriately chosen). The diameter of alveoli based on previous histological studies is of the order of 0.25 to 0.3 mm (9–11). For a diffusion time of 2 ms, suggested by Parra-Robles and Wild (12, 13), the value for s in Equation 1 is 0.57 mm, assuming D = 0.8 cm2/s for helium in air. For longer diffusion times, this changes by a factor of (t) (s is only 1.58 times larger for t = 5 ms). Therefore, we hold that our measurements are still sensitive to alveolar dimensions.


The alveolar duct and the sacs do not have an independent wall (open geometry). The “boundaries” of the ducts and sacs are in fact the openings of alveoli (14), and so diffusing atoms are in fact restricted by alveolar walls. Our measurements are sensitive to alveolar dimensions as long as the alveolar ducts and sacs do not change in dimension without a corresponding change in alveolar dimension (see online supplement to this letter). There is evidence that the relative size of alveoli and alveolar ducts remains constant between 7 and 14 years (15).


We believe that our technique has the sensitivity to distinguish between two alternative hypotheses: enlargement of acinar structures during lung growth happens as a result of either an increase in volume of pre-existing structures (the pre-existing hypothesis), or by formation of new alveoli during lung development as we propose. Our expansion model (below) provides evidence that our technique is sensitive to an appropriate range of changes of dimensions of peripheral lung structures.




2.

We used the change in ADC during controlled inhalation to predict its change when lung enlarges without alveolarization (the green line in Figure 2 of our article [1]). This is valid if the inhalation enlarges peripheral lung structures in the same way as growth without alveolarization. We believe that this is the case for gentle inhalation from functional residual capacity, taking care not to overdistend the lung (i.e., not to inflate near the limits of total lung capacity). Other possible models for lung expansion including recruitment of new alveoli (16) will actually cause our predicted line of lung growth without alveolarization (1) to be steeper than depicted, strengthening rather than weakening our argument of neo-alveolarization (see online supplement to this letter). Further, the expansion model was tested on children with a range of functional residual capacity from 0.98 to 2.63 L.


3.

Parra-Robles and Wild base their critique heavily on their simulations based on their model alveolar duct (12, 13). We have some concerns about the assumptions underlying the simulation. While the length scales in the model are realistic, the model is mathematically simplified. We enlarge upon the following additional concerns in the online supplement:


a.

Assumptions about the branching structure are not realistic.


b.

The branching is assumed to be infinite, but the blind ending alveolar sacs are greater in number than the alveolar ducts.


c.

The expansion of alveoli is modeled as expansion of one dimension alone (13) (increasing axial dimension of the alveoli without increase in depth or cross-sectional diameter). This is implausible, and the paper from which they draw this assumption (7) never attempted to model alveolar expansion due to inhalation. In fact, it concludes that their findings were due to neo-alveolarization.


d.

In contrast to the model proposed by Parra-Robles and Wild (12, 13), ADC correlates to histological measures of alveolar dimensions in animal and human lungs (17–20).






We feel that the results based on this model are open to question. We suggest that their model could be run with lung expansion modeled in a realistic manner.

In conclusion, our results were not based on any geometric lung model. Our only assumption is that the expansion of the lung during moderate degrees of inhalation is an acceptable model of lung expansion during development in the absence of new alveolarization. Given that assumption, all subsequent analysis was based on statistical approaches. In contrast, other techniques proposed by Parra-Robles and Wild in their letter, such as computed tomography and DlCO, are either unethical in healthy children or do not give information about alveolar dimensions.

We would welcome further research into lung development in children using shorter diffusion times, and we would also welcome further refinement of computer models to assist the interpretation of physiological measurements.