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1Department of Biomedical Engineering, Boston University, Boston, Massachusetts; 2Bioengineering Institute, The University of Auckland, Auckland, New Zealand; and 3Departments of Anesthesia and Critical Care, Radiology, and Medicine (Pulmonary and Critical Care Unit), Massachusetts General Hospital, Boston, Massachusetts
Submitted 7 April 2005 ; accepted in final form 29 July 2005
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ABSTRACT |
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morphometric lung model; constriction; closure
2 mm (8). Presently, even the most advanced imaging methods cannot routinely resolve human airways <2 mm in diameter with enough spatial resolution (3). Recently, we incorporated airway and tissue structural properties, as well as mechanical function, into an anatomically consistent three-dimensional (3D) airway tree model to predict dynamic lung mechanics after applying heterogeneous constriction to airways in the tree (23). We also suggested the potential for synthesizing this model with positron emission tomographic (PET) images. In this study, we present a new approach, which we call image functional modeling (IFM). The IFM synthesizes imaging and mechanical function data with anatomically explicit computational models to probe detailed structure-function relations at levels not previously possible and on a subject-specific basis. Specifically, we now incorporate the capability to predict the flow distribution to each of the acini in the 3D tree model for any arbitrary heterogeneous constriction pattern. Consequently, we can ensure that 3D model conditions explicitly match the image-determined anatomic locations of ventilation dysfunction. We now combine oscillatory mechanical measures sensitive to heterogeneity of constriction (e.g., dynamic lung RL and EL vs. frequency) and PET ventilation images with the 3D airway tree models to examine the role of large vs. small airways in the simultaneous deterioration of mechanical function and ventilation in asthma.
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METHODS |
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Model structure. We use the 3D asymmetric computational model of the conducting airway tree described by Tawhai et al. (22). The airway tree model is generated in a subject-specific host volume that is derived from computed tomography imaging. A volume-filling branching algorithm generates the airway tree, starting from computed tomography-defined model airways for the same subject. The method is a recursive algorithm that aims to fill the host volume with a bifurcating tree. Diameters of the airway branches are based on mean diameter sizes for each order, as reported in the literature, with an arbitrarily chosen coefficient of variation. The resulting asymmetric conducting airway model (Fig. 1) has 26 generations (generation 1 is the trachea). The distribution of lengths and diameters (Table 1) and the daughter diameter ratios are all consistent with morphometric studies found in the literature (12). The average terminal generation and number of terminal bronchioles also lie within the range of morphometric data. The total number of terminal branches is 28,901.
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Model ventilation distribution.
Ventilation distribution calculations to predict the fraction of input flow (
in) delivered to an acinus have been imposed by us previously for a morphometric Horsfield model (9). This approach was extended for our 3D airway tree. We calculate convective ventilation out to the level of the airways where gas transport is governed by convection (diameters > 0.22 mm). A sinusoidal in of unit amplitude and at a known frequency is presumed to be delivered to the trachea and distributes throughout the airway tree. As a first-order approximation, we assume laminar flow through the conducting airways and calculate the fraction of flow exiting a parent branch and entering its two subtending daughter branches using a current divider relationship and knowing the distribution of downstream airway impedances. The fraction of flow delivered to each acinus was calculated by finding the product of the flow fraction of each branch in the pathway of that acinus to the trachea.
If ventilation were homogeneous, the in delivered to every single acini (acini) would be identical and expressed as:
 | (1) |
acini N) for each terminal branch ending as:
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acini N would be equal to 1. Otherwise, acini N represents the fraction of under (<1) or over (>1) ventilation to that acini relative to a purely homogeneous situation. Because we are calculating ventilation distributions at low frequencies, we assume that the total flow shunting into the nonrigid walls is negligible compared with the flow delivered to the sum of all acini. Experimental Methods
PET ventilation regional data and oscillatory mechanics were acquired from six mild asthmatic subjects (Table 2), while lying supine, at baseline and during methacholine-induced bronchoconstriction. Only subject 5 had a history of smoking that lasted 2 yr, but had quit 2 mo before the experiment. Bronchoconstriction was induced by using a five-breath methacholine challenge, at the previously determined PC20 dose (20% drop in the subject's baseline, upright forced expiratory volume in 1 s). Approximately 5 min after the end of the methacholine challenge, imaging and mechanics data were collected.
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20–30 s, providing enough time for the entire perfused alveolar space to fill with the 13NN. At the end of the apneic period, the subject starts to breathe normally and the tracer washes out of the lung by ventilation. In healthy lungs or at baseline in many asthmatic subjects, in <3 min of breathing, the tracer nearly completely washes out of all alveolar regions. In contrast, during bronchoconstriction in asthmatic subjects, there are large alveolar regions that retain a substantial amount of tracer (24). These regions are effectively ventilating slowly. Dynamic RL and EL were measured using the optimal ventilation waveform forced-oscillation technique in the supine position, as previously described in detail (13). Subjects were instructed to relax while a piston pump delivered a waveform that contained the sum of multiple frequencies between 0.15 and 8 Hz, but in a manner such that the waveform still delivered a normal tidal volume. Transpulmonary pressure and flow at the airway opening were measured and subsequently transformed into the frequency domain to estimate RL and EL at each frequency.
Image Functional Modeling
We must first ensure that any candidate constriction pattern matches the spatial information from PET data. This requires mapping slowly ventilating regions imaged by PET into the corresponding locations of the 3D model. Next, we systematically search from a broad spectrum of potential constriction patterns in the airway tree for those patterns, which can produce ventilation defects in precisely the PET-established regions. These constriction patterns are applied first to the highest generations (smallest airways) only, and then increasingly larger airways are included so long as they continue to be consistent with the location of the PET ventilation defects. Each of these patterns is then further distinguished by how well they can or cannot match the measured RL and EL data.
Defining the lung field and mapping the image field into the 3D model. Shown in Fig. 2, left, is an example of a PET transmission mask taken after administration of methacholine. There are 15 contiguous, 6.5-mm-thick slices from the most cranial (top left) to the most caudal (bottom right) portions of the imaged lung. The white regions represent the maximum ventilated imaged lung field as identified from the transmission scan. The postchallenge transmission scan would capture changes in the maximum ventilated lung field that could occur due to lung volume elevations associated with hyperinflation. The terminal airways in the 3D model represent effectively the entrance to lung acini. The spatial locations of each acini in the model are defined by coordinates in 3D space. Using the heart as an anatomic marker and knowing the thickness of each PET image slice (6.5 mm), we approximated the corresponding lung region in the 3D tree model by dividing the model into 15 slices in the craniocaudal direction. We mapped the 3D coordinates of the acini within each slice of the model into 15 individual grid spaces, each composed of 128 x 128 pixels. We then defined a set of boundaries that tightly enclosed each slice in the lung transmission mask (Fig. 2, left). The coordinates of the acini in the 3D model were then further scaled into a new grid space defined by the boundaries that enclosed each imaged lung slice. In Fig. 2, right, we show the equivalent model mask displaying all possible model acini that lie in the corresponding PET image slice.
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 | (3) |
Postconstriction IFM: finding maximum airway sizes responsible for ventilation defects. Synthesis of the PET data with the 3D model allows us to identify the maximum sized airways that might be closed or highly constricted in such a way as to reproduce the locations of nonventilated acini in the PET data. Specifically, Figs. 3 and 4 show the process of first locating model acini marked as nonventilated. Of course, this could occur by simply closing each of these terminal airways. The ventilation defects can also occur by severely constricting or closing proximal airways that lead to these terminal regions, so long as doing so does not also cause a defect elsewhere in acini that the PET data indicated are well ventilated. For every generation, we identified which airways could become severely constricted so as to recreate ventilation defects to the PET-identified terminal units, but without creating ventilation defects elsewhere. Closure of an airway was defined as a 90% reduction of the subject-specific baseline diameters. We chose a limit of 90% rather than full closure reduction, because the imaging data indicate that there is some, albeit much less, ventilation to the defect regions.
IFM: matching imaging and mechanical data simultaneously. The previous step identifies airway closures that could or could not match ventilation defects from PET. Now, we establish whether and how we must further adjust the remaining airway diameters to simultaneously match the RL and EL data of that subject. Specifically, starting at a generation above the acini, we close the necessary airways at that generation to match the PET image ventilation defects and then imposed constriction distribution patterns of varying mean levels (0–90%) and standard deviations (0–90%) to all of the remaining airways from that generation down to the terminal airways. Also, we include airways both within and outside the field of view of the PET image. So long as they are at the appropriate generation level, this process is repeated for increasingly larger airways (i.e., moving proximal one generation at a time) but applying the constriction distribution to all airways from that generation on down to the terminal airways. We determined the best match of 3D model predictions to the RL and EL data by using Eq. 3 to obtain a set of constriction conditions for each generation that minimized the PI.
The end result of the above process is that, for each generation, we have identified the airway constriction conditions that, when applied to that generation and all higher ones (all airways peripheral to that generation), provide the best possible match to oscillatory mechanics data while being anatomically consistent with simultaneously imaged ventilation defects. Eventually, we find airway generations that provide acceptable matches to the RL and EL data and airway generations that do not. Hence we can establish whether constriction confined to airways too small in size (diameter < 2 mm) can acceptably match both mechanics and PET data in a specific subject and the converse: whether constriction permitted to affect airways that are large can match both data sets.
Of course, the above approach reveals constriction patterns that can match either PET and mechanics data or PET but not mechanics data. We also explored whether there were constriction patterns that can match mechanics but not PET data. Here, we identified heterogeneous constriction patterns that, when applied to a specific airway generation and below, provided a satisfactory match to the mechanical data, but without concern or attempt to incorporate the PET data. Finally, we also performed a sensitivity analysis that constricted only the large airways, to identify whether elevations in measured mechanics postbronchoconstriction could be achieved in the simulated mechanics by constricting the large airways alone.
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RESULTS |
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The first step in IFM was to isolate the largest sized airways in the model that, when closed, could recreate the 3D locations of ventilation defects in the PET image without creating ventilation defects that are inconsistent with the image. While the precise locations of ventilation defects vary from subject to subject, generally we found in our six subjects that the ventilation defects occurred in clusters located in the dependent regions of the lung (Fig. 4). This likely reflects the fact that the subjects were challenged while supine. In these asthmatic subjects, we found that, to maintain consistency in the model and image ventilation defects, the range of allowable closed airways was on the order of 0.22–2.39 mm, with the preponderance of closures needing to occur in airways <0.5 mm in diameter (Table 3).
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In Fig. 5, we show the mean ± SD of RL and EL spectra from all subjects at baseline and postchallenge. We note that, at baseline, there is not much variability in RL and EL from the mean; however, during bronchoconstriction, there is a large variability in the mean level and frequency dependence of RL and EL over the entire subject pool. In Fig. 6, left, we show the dynamic RL and EL for one of our most reactive subjects. Premethacholine, RL decreases from 9 cmH2O·l–1·s at low frequencies to 7 cmH2O·l–1·s at 8 Hz. Such levels are already elevated from what are typical values for a sitting, nonchallenged, mild-moderate asthmatic subject. Also, EL in upright healthy subjects typically crosses zero and goes negative around 4 Hz. However, in this subject, EL at baseline remained positive throughout the entire frequency range. These elevations in RL and EL suggest that, by lying down at baseline, there was some homogenous constriction throughout the entire airway tree, resulting in some mild airway shunting (18). Indeed, for the 3D model to match the baseline mechanics of this subject required a mean constriction of 40% with a small SD of 20%. Postmethacholine, this asthmatic subject displayed considerable evidence of heterogeneous airway constriction, as observed from the increase in frequency dependence of RL and EL from baseline. Two IFM attempts are shown. For case 1, constriction was limited to airways with baseline diameters <2.3 mm, while maintaining anatomic consistency with the PET data. This case provided an excellent replication to the dynamic mechanical data set. Hence, if ventilation were perfectly homogeneous, all acini would receive an equal fraction of the flow and acini N would be equal to 1. This best match occurred with a mean constriction of 60% and SD of 20% to the remaining nonclosed airways. In contrast, for case 2, constriction was confined to airways at diameters even lower in the tree (diameter < 1.3 mm). This case could not produce a competitive match to the mechanical data as that of case 1.
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DISCUSSION |
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Airway Closures: Sizes and Locations
The first level of IFM used only the PET data with the 3D model to identify the airway sizes and locations, which could be closed while still only matching the spatial size and location of the imaged ventilation defects. Over our six asthmatic subjects, closures had to occur in diameters <2.39 mm and mostly <0.44 mm. To do otherwise would create ventilation defects that were inconsistent with the imaging information. Thus the first novel conclusion derived from our IFM method is that airway closures (or near closures) leading to severe ventilation defects occurs during airway provocation in mild-to-moderate asthmatic subjects, and these closures are confined to airways in the lung periphery. Our methods are semi-subject specific. The tight consistency of results related to maximum closed airways across our six subjects (Table 3) suggests that this conclusion would remain unchanged by adding more subjects and is likely endemic to mild-to-moderate asthmatic subjects. Interestingly, the remaining airway constrictions outside the closures necessary for ventilation defects differed more from subject to subject (Table 5). Indeed, the data of Fig. 5 motivate the personalized nature of the IFM approach when exploring the nonclosed airways. Specifically, during airway provocation in asthma, while Table 3 indicates that airway closure sizes are similar and confined to very small airways, the remaining heterogeneity of constriction is more variable among asthmatic subjects. This leads to variability in measured postchallenge mechanics. With only six subjects, it is difficult to make grand conclusions, if such variability were to exist across a wider swath of asthmatic subjects, but the finding is interesting and worthy of future analysis. We acknowledge that, in more severe asthmatic subjects, airway closures may occur in airways >2 mm due to remodeling and/or inflammation. Of course, if closures occurred in the larger airways, it is likely the size of the gas trapping clusters in the PET images would increase. We could then apply our IFM approach to establish whether, indeed, closure airways of diameter >2 mm were necessary and/or allowable.
One possible limitation of our approach is that, in 3D space, there is not a precise one-to-one mapping between acini in the model and in the image, which can lead to an underestimation of the maximum size of the closed airways allowable for matching a ventilation defect image. We probed the potential impact of model/image misregistration as follows. First we identified the required closed terminal airways to match acinar ventilation defects in PET (as described in METHODS). We then calculated the area of ventilation defects in each slice of the PET image as mapped into the model. We also found the maximum sized airway above the closure such that the match to the PET data is retained in each slice without creating any new nonventilated acini in the model (again, as described previously in the METHODS). Next, we closed the airways one generation less (proximal) to these and quantified the increase in the number of ventilation defects in the model relative to the data. The goal is to see at which point closure of larger airways creates a gross mismatch between the images and the model, which could not be explained on the basis of minor misregistration alone. Shown in Fig. 10 is the maximum percent increase in the volume of ventilation defects in the model as we moved up generation by generation and continue to close these larger airways. Moving up just two generations caused a 50% increase in model ventilation defect area from the case that best matched the PET. The increase grows to 100% by the third generation. In summary, misregistration may underestimate some of the closures, but overall matching to PET data still requires confining closures to small airways.
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After isolating the airways necessary to reproduce the ventilation defects, we applied varying constriction conditions to the rest of the airway tree. Our results illustrated that matching mechanics simultaneously with ventilation defects is best done by constricting airways greater than generation 14. Surprisingly, we could get similar quality matches to the measured mechanics by also affecting much larger airways in tandem with small airways. As a result, we found that, so long as small airways are constricted, there was a large family of constriction patterns that produced the lung mechanics that were not very distinct from one another. In contrast (Fig. 9), constricting the large airways alone, even while maintaining the small airway closures necessary to recreate ventilation defects, would not be sufficient to match the mean level and frequency dependence of RL and EL associated with bronchoconstricted asthmatic subjects.
Finally, we demonstrated (Fig. 7) that we can create a variety of heterogeneous constriction conditions that produce RL and EL very similar to each other. However, only by employing the IFM approach were we able to isolate conditions that would result in ventilation images on a slice-by-slice basis that were consistent with those occurring in the specific patient's lung. Hence, airway closures are not occurring totally randomly and need to be assigned to specific regions in the lung.
Past Studies Probing Small Airways
Speculation on the relative importance of small vs. larger airways to lung disease, and asthma in particular, date back to the 1960s, when it was assumed that, because of the parallel nature of the airway tree, the peripheral airways contributed very little to total resistance and were subsequently termed the "silent zone" (19). Histological and morphometric analyses certainly suggest that important structural changes occur in the airway walls and airway smooth muscle of the peripheral and central airways (7, 16). Functionally, more sensitive measures of peripheral airway function (e.g., imaging and frequency dependence of dynamic RL and EL) have become more readily applicable to human subjects (1, 13–15). These techniques provide indirect and direct evidence about the role of large and small airways during constriction. Brown and Mitzner (4), using high-resolution computed tomography (HRCT), showed that, in canines, both large and small airways constrict after methacholine challenge. Moreover, airway closure could occur in both sized airways. In human asthmatic subjects, Brown et al. (6) used HRCT and measured a decreased diameter of larger airways following methacholine. The occurrence of such is consistent with our IFM results that larger airways can constrict in creating the mechanical response in asthmatic subjects to a provocation. Generally, however, reliable information related to the smaller peripheral airways (diameter <2 mm) in humans is not forthcoming from HRCT or any imaging modality (3). Kaminsky et al. (14) used a bronchoscope to measure increases in the mean level and frequency dependence of resistance in the periphery of the lung in human asthmatic subjects after installation of methacholine. Their data showed that the small airways were also hyperreactive in asthmatic subjects and that this constriction occurs heterogeneously. Experimental studies that assess airway closure using the single-breath washout technique have shown that airways at the level of the acini are likely to close and contribute to the overall airway response (10). Clearly, there is ample evidence in the literature that confirms large and small airway involvement, but none is able to confirm their relative importance in changes in lung function.
Advances in computational modeling studies have shown that inflammation and airway wall thickening work together with the peripheral airway constriction to influence the mechanical response and amplify the heterogeneous constriction (8, 14). Indeed, peripheral heterogeneities influence RL and EL at the breathing frequency far more than increases in airway resistance alone (at 8 Hz). Our approach, of combining experimental data and computational models, is a step forward because it requires matching heterogeneity of two functional measures simultaneously: ventilation and mechanics. Our premise was that each data form is likely quite sensitive to the lung periphery. Synthesizing our models with both data forms allowed us to distill the forms of small vs. larger airways allowable in a specific postconstricted asthmatic subject.
In summary, we have synthesized a 3D structurally consistent computational lung model with anatomically explicit information extracted from PET imaging simultaneously with dynamic mechanical function data most sensitive to the impact of heterogeneous airway constriction. We call this IFM. In principle, as other new imaging methods (e.g., hyperpolarized He3 MRI) become more quantitative, the IFM concept may be extended to them as well (1, 21).
The goal of this study was to explore the relative importance of large and small airways during asthmatic bronchoconstriction. Because the 3D model has many degrees of freedom, the IFM is not projected as a pathway by which one can precisely establish the constriction pattern for all airways in a given patient. Nevertheless, the IFM approach is able to provide unique and more specific insights on airway constriction in asthma. Because of the spatial and functional specificity embedded in the IFM technique, we can definitively rule out which airway sizes could not be involved during bronchoconstriction because they do not match either the mechanics or the PET ventilation defects, or perhaps they can match one measurement form but not the other. The first important new finding from this IFM application is that ventilation defects in asthmatic subjects require heterogeneous closures confined to very small airways (<2 mm) in mild asthmatic subjects. The second important finding is that severe constriction of such airways alone is insufficient to drive the simultaneous degradation in mechanical function. The latter requires constricting the remaining small airways as well, perhaps in concert with larger airways, but not larger airways alone. The implication is that asthma therapy must prevent small airway closures and may also need to ensure sufficient reduction in airway conditions promoting hyperreactivity in both small and larger airways.
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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R. S. Harris and D. P. Schuster Visualizing lu |
