Abstract:

High-resolution X-ray CT (HRCT) provides detailed images of the lungs and bronchial tree. HRCT-based imaging and quantitation of peripheral bronchial airway geometry provides a valuable tool for assessing regional airway physiology. Such measurements have been used to address physiological questions related to the mechanics of airway collapse in sleep apnea, the measurement of airway response to broncho-constriction agents, and to evaluate and track the progression of disease affecting the airways, such as asthma and cystic fibrosis.

Significant attention has been paid to the measurement of extra- and intra-thoracic airways in two-dimensional sections from volumetric X-ray CT. A variety of manual and semi-automatic techniques have been proposed for airway geometry measurement, including the use of standardized display window and level settings for caliper measurements, methods based on manual or semi-automatic border tracing, and more objective, quantitative approaches such as the use of the ``half-max'' criteria. A recently proposed measurement technique uses a model-based deconvolution to estimate the location of the inner and outer airway walls [16, 17]. Validation using a plexiglass phantom indicates that the model-based method is more accurate than the half-max approach for thin-walled structures.

In vivo validation of these airway measurement techniques is difficult because of the problems in identifying a reliable measurement ``gold standard.'' In this paper we report on ex vivo validation of the half-max and model-based methods using an excised pig lung. The lung is sliced into thin sections of tissue and scanned using an electron beam CT scanner. Airways of interest are measured from the CT images, and also measured with using a microscope and micrometer to obtain a measurement gold standard. The results show no significant difference between the model-based measurements and the gold standard (p < 0.01); while the half-max estimates exhibited a measurement bias and were significantly different than the gold standard (p < 0.01).

Keywords: intra-thoracic airways, medical imaging, quantitative image analysis, X-ray computed tomography, high-resolution CT.

INTRODUCTION

High-resolution X-ray CT (HRCT) provides detailed images of the lungs and bronchial tree. HRCT scanning allows researchers to quantitate anatomical features that were previously only indirectly estimated via global measures such as pulmonary function tests. Bronchial airway geometry measurements can be used to help assess regional airway physiology. Measurements of bronchial tree airway geometry have been used to evaluate and track the progression of diseases affecting the airways, such as asthma and cystic fibrosis, to evaluate airway response to external stimuli, and to assess the efficacy of new therapeutic approaches.

There are ongoing research efforts to identify and quantitate the in vivo airway tree in three dimensions [1, 2, 3]. Because no reliable three-dimensional airway segmentation method is available for in vivo human data, significant attention has been paid to the measurement of extra- and intra-thoracic airways on two-dimensional sections from volumetric X-ray CT. To ensure accurate measurements, this analysis must be limited to airways that have the airway long axis perpendicular to the imaging plane (these airways appear approximately circular on the two-dimensional slices). Airway measurement techniques have varied from manual and semi-automatic border tracings performed using a trackball or mouse (including using standard image display window and level settings prior to measurement) [4, 5, 6, 7, 8] to more objective, quantitative approaches such tracking the gradient maxima around the airway border [9, 10, 11], and raycasting approaches using the ``half-max'' [12, 13, 14, 15] or ``model-based'' wall detection criteria [16, 17]. Specialized region-of-interest (ROI) software packages have been designed to facilitate this type of analysis [18, 19, 20]. Such measurements have been used to address physiological questions related to the mechanics of upper airway collapse during sleep apnea and the response of airways to external stimuli such as broncho-constriction agents [5, 6, 7, 13, 14, 21, 22, 8, 15].

To confidently employ any of these measuring techniques in a clinical setting, careful validation of the method is required. The half-max and model-based methods have previously been validated using images obtained from scanning a plexiglass tube phantom [20, 16, 17]. It is desirable to test the measuring techniques using actual, in vivo airways--however it is difficult in this case to obtain a reliable ``gold standard'' measurement for comparison. This paper describes the validation of the half-max and model-based techniques using CT images containing airways within an excised pig lung. The measurements made on the image data are compared against a gold standard obtained from microscope measurements made by a pathologist on the actual lung tissue. The results show that the half-max technique suffers from a considerable measurement bias (underestimating the airway diameter). The model-based technique suffers a much smaller bias, and there is no statistical difference between the measurements obtained from the image data and the gold standard at the p > 0.01 level.

AIRWAY MEASUREMENT TECHNIQUES

Airway geometry can be evaluated on two-dimensional slices of a CT data set. To ensure accurate measurements, this analysis must be limited to airways whose long axis is perpendicular to the imaging plane (these airways appear approximately circular on the two-dimensional slices). Specialized region-of-interest (ROI) software packages have been designed to facilitate this type of analysis [18, 19, 20]. A popular technique for airway geometry measurement uses a ``ray casting'' technique, in which a set of rays are cast outward from the approximate airway centroid. The gray level profile along each ray is examined to determine the radial location at which the ray crosses the airway wall. Each ray gives an independent estimate of the inner (and/or outer) wall location(s), and these estimates can be averaged to yield a mean diameter estimate for the airway. If both inner and outer airway walls are detected, airway wall thickness can also be determined. D'Souza et al. [20] describe a system that uses ray casting for interactive airway geometry analysis.

This section describes two methods for estimating wall location along the gray level profile: (1) the half-max criteria; and (2) the model-based approach. Sections 3 and 4 describe how these methods are validated using real lung tissue.

Half-Max Criteria

The half-max approach estimates the airway wall location based on the extrema of the gray level intensity profile observed along a ray crossing the airway wall. The profile along a ray is examined and the minimum and maximum gray levels are determined. As shown in Figure 1, the inner wall and outer wall locations are estimated to lie at a radial location corresponding to a gray level halfway between the measured minimum and maximum gray levels along the ray. However, because the scanning process introduces blurring and partial volume effects, the half-max approach may not be uniformly accurate across airways of different sizes [23, 17, 16]. It has been shown [17, 16] that that the half-max technique exhibits a size-dependent bias: airway diameters are underestimated for small, thin-walled structures. To confidently employ CT-based imaging to discriminate subtle changes in lung physiology, such as small differences in central vs. peripheral airway responses, it is critical to develop a technique that provides accurate measurements across all lumen diameters and wall thicknesses.

  
Figure 1: Illustration of using the half-max criteria to estimate inner and outer airway wall locations. The minima and maximum along the ray is computed and the walls are estimated to lie at the radial location with a gray level halfway between the minimum and maximum.

Model-Based Wall Location Estimates

In this section we describe a model-based approach for airway measurement. We model the scanning process of an ideal airway and use the model to predict the shape of the gray level profiles of rays crossing the airway wall. Using an optimization technique, the model parameters are adjusted to minimize the difference between the modeled profile and the actual profiles observed in the data. The set of parameters that minimizes the difference between the model and the data yields an estimate of the airway geometry. Since we explicitly model the scanning process, this approach can be accurately applied to airways of different sizes.

To address the size-dependent biases present when applying the half-max method to measure airway geometry, a ``model-based'' parameter estimation technique for estimating airway wall locations has been proposed [17, 16]. The model-based method assumes a circular airway cross-section on a two-dimensional slice and incorporates knowledge about the scanning process to estimate airway wall locations. In contrast to the two or three extrema used by the half-max approach to estimate wall locations, the model-based technique considers all the intensity values along the ray profile.

Figure 2 shows the two-dimensional model of a single slice of an ideal airway cut perpendicular to the long axis. The airway centroid is at the origin, and the airway has inner radius l_i and outer radius (). The density of the airway wall is unity and the density of the lumen (air) is zero. The airway is surrounded by tissue of constant density (typically, ), which models the lung parenchyma.

  
Figure 2: Ideal two-dimensional airway model with inner radius and outer radius . Density of airway wall (dark gray) is unity; density of airway lumen (white) is zero; parenchymal tissue external to airway (light gray) has mean density ( ).

Let g(x,y) be the two-dimensional density profile of ideal airway model shown in Figure 2. The response of an ideal scanner is modeled as the two-dimensional convolution of the density function g(x,y) and the scanner point spread function h(x, y):

where K is a constant scale factor and A is a constant representing the background gray level output of the scanner. Assume h(x, y) can be modeled as a symmetric two-dimensional Gaussian with standard deviation : [24]. Without loss of generality, consider the single ray running from x=0 along the x axis in the positive x direction. For this single ray, (1) can be written as:

Simplifying, we obtain

where is the modified Bessel function of order zero [25]. Equation (3) allows us to predict the scanner response at any radial location along the ray for a given airway geometry.

To use (3) to estimate airway wall locations for a real airway, assume that a number of rays have been cast outward from the approximate airway centroid through the airway wall and into the parenchyma.. Let P(r) represent the gray levels along a single ray, where r is the radial distance from the centroid. A non-linear optimization technique is used to match the observed ray profile, P(r), with the ideal ray profile model given in (3). If the observed ray P(r) is sampled at M discrete points in the image, we can compute the model-matching error for the ray, E:

where is the sample along the ray, . The summation in (4) is taken over all M points lying along the observed ray profile. The response function f(.,0) in (3) can be easily differentiated with respect to the parameters l_i , , K, and , so we employ an efficient technique to minimize E based on the Levenberg-Marquardt algorithm [26]. After the minimization, the model parameters l_i and yield estimates of the airway inner and outer radius.

Initial estimates of the model parameters are required to start the optimization process. The half-max method is used to obtain initial estimates of the inner and outer radii l_i and . The parameter K may be estimated from the gray level at the centroid of the airway lumen, P(0), using the approximation that . However, if (i.e., if ), this method yields a very poor estimate of K. Since K is not expected to vary much across images, rather than using P(0) to estimate K we instead use an initial value for K determined experimentally. The initial value for is determined from the gray level measured in the parenchyma, P(R), using .

Mean Diameter Estimates

Both the half-max and model-based techniques can provide estimates of inner and outer wall locations along a single ray profile. Because each ray is assessed independently, there can be considerable ray-to-ray variation in the estimated wall locations. The contour obtained by connecting the estimated wall locations can be smoothed to reduce local variations and yield a better contour for visualization. For quantitative comparisons, mean inner and outer diameters can be obtained by averaging measurements over a number of rays.

By casting a number of different rays at different angles of orientation, a set of independent estimates can be used to reduce the effects of noise and irregularities in the airway morphology. Recall the airway centroid is at the origin and is assumed to lie within the airway lumen. If N rays of length R ( ) are cast from the centroid outward toward the airway wall, the ray, , is oriented at an angle with respect to the x axis and connects the points (0, 0) and in the image. If the estimated centroid is accurate and the airway is approximately circular, aggregate measurements of the inner and outer radii can be formed by computing the arithmetic average of the measurements made on the individual rays. More sophisticated methods of combining the individual wall location estimates, such as cost-based methods (e.g., graph searching [27]) that take into account airway circularity and local homogeneity, can be employed. As an additional consideration, it is desirable to exclude from any average those rays that are likely to have passed through external structures such as blood vessels (these structures would affect the gray level profile and introduce measurement error). A set of three heuristic ray rejection criteria that can be used to discard rays from the averaging process is given by D'Souza et al. [20].

EXPERIMENTAL PROTOCOL

To assess measurement accuracy, the half-max and model-based approaches were used to make airway geometry measurements on two-dimensional slices of images obtained by scanning actual lung tissue. A pair of fixed, excised pig lungs (35 kg white pig) were obtained.

The lungs had been fixed in a solution of 90% buffered formalin by injecting formalin through the bronchus and immersing the lungs in a formalin bath. Care was taken to ensure that the lungs remained expanded and the lung shape remained undistorted during fixation. After several weeks of fixation, the lungs were removed from the formalin bath, thoroughly rinsed, and air dried for 5 days. During the air drying, the lungs were held partially inflated by an external air source.

A single lung was used for this study. The lung was cross-sectioned by an experienced pathologist (S.A.R.) into approximately 1 cm thick slices. The slices were spaced at 0.5 cm to 2 cm intervals. A total of seven slices of lung tissue were obtained. The lung slices were mounted between two pieces of plexiglass and scanned in an EBCT scanner. The lung slices were oriented so the scan plan was approximately parallel to the surface of the tissue cut during the lung sectioning. The lung tissue was scanned using 1.5 mm thin contiguous CT slices using a 600 msec scan aperture. The images were reconstructed using the HRCT reconstruction kernel with a 15 cm field-of-view. The resulting pixels in the image plane were 0.29 mm/side.

The image-based measurements were made using the ASAP system [20]. ASAP is a system for interactive measurement of airways on two-dimensional slices of a CT data set. As described by D'Souza et al. [20], ASAP can be configured to use the half-max criteria to estimate inner and outer wall location. For this analysis, ASAP was modified to support both the half-max and model-based techniques for airway measurement.

Fifteen airways ranging in size from about 2.5-9 mm inner diameter were selected for analysis. Each airway was measured on two different slices of the CT data set. To measure airways using ASAP, the user must manually select the approximate airway centroid using the mouse. ASAP then casts of a set of rays outward from the centroid (in this case we used N=20 rays) through the airway wall. Manual adjustments of ray length were made if required. A set heuristic ray rejection criteria [20] were used to reject rays that passed through external structures such as pulmonary blood vessels. After the rays were cast, the mean inner diameter and lumen cross-sectional area was computed from the estimated wall locations [20]. This procedure was performed once for each airway using the half-max technique, and then repeated using the model-based method.

The pathologist examined the lung slices and performed the ``gold standard'' measurements. These measurements were made using a Reichart StereoStar ZOOM dissecting scope (0.7 to 4.2 x 570) (Reichart Scientific Instruments, Buffalo, NY). The lung slices were removed from the plexiglass mounting device, placed on the microscope stage, and brought into focus using low power. The airways of interest had been previously marked on a copy of the CT film. These airways were identified and brought into higher power. Using the micrometer attached to the focus handle, the inside diameter of each airway was measured. Each micrometer measurement was checked against the measurement taken by a Fischer calibrated scientific ruler, which was placed on the microscope stage adjacent to the airway of interest. For each airway, two perpendicular diameters were measured to approximate minor and major axes of an elliptical airway. The airway wall was not included in the measurements. The minor and major axes were used to compute mean inner radius and luminal cross-sectional area estimates.

RESULTS

Figures 3 and 4 compare the image-based measurements made using the half-max and model-based techniques to the pathology lab gold standard. A total of fifteen individual airways, ranging in size from about 2 mm to 8 mm inner diameter, were examined. The image-based measurements were made on two slices of the CT data set (slices 3 and 6). The mean errors for the measurements made on the individual slices are reported in addition to the total error averaged over all airways on both slices.

For slices 3 and 6 combined, the results show that the mean inner radius measurement error for the half-max technique is approximately 0.68 0.04 mm (mean std. error), corresponding to about a 2.25 pixels bias (underestimating the true inner radius). For the model-based technique, the mean error averaged across slices 3 and 6 is approximately 0.16 0.03 mm, corresponding to about a 0.5 pixel bias (again, underestimating the true value). For the comparison of lumen cross-sectional areas, the half-max technique underestimates the area by approximately 9.58 0.53 mm ² , while the model-based approach underestimates the area by about 3.14 0.46 mm ² . It is interesting to note that the model-based technique has a slightly reduced mean errors on slice 3, and a slightly increased mean errors on slice 6. For the half-max method there is little difference between measurement errors on slices 3 and 6.

For the inner radius estimates, Figures 5 and 6 plot the model-based measurements versus the pathology lab measurements and half-max measurements versus the pathology lab measurements. The regression lines for both techniques is close to unity (1.03 mm/mm for the model-based and 0.95 mm/mm for the half-max). The regression line intercept for the model-based technique is 0.09 mm, indicating little systematic bias. For the half-max the regression line intercept is 0.76 mm, indicating a estimation bias. The correlation coefficients for the regression analysis are 0.84 for the model-based method and 0.67 for the half-max technique.

A paired t-test was used to compare the two image-based techniques to the pathology lab measurements. For the half-max technique, the measurements were significantly different than the gold standard on slices 3, 6, and slices 3 and 6 combined (N=15 for the slices individually, N=30 for the slices 3 and 6 combined, p < 0.01). For the model-based method, there was no significant difference between the image-based measurements and the pathology lab measurements on slices 3, 6, and slices 3 and 6 combined (N=15 for the slices individually, N=30 for the slices 3 and 6 combined, p < 0.01).

  
Figure 3: Comparison of half-max and model-based methods to measurements made by pathology lab using a dissecting microscope. For each method, the figure shows mean inner radius measurement error averaged over 15 airways of interest. The image-based techniques exhibit a bias that causes them to underestimate the true airway inner radius.

  
Figure 4: Comparison of half-max and model-based methods to measurements made by pathology lab using a dissecting microscope. For each method, the figure shows mean cross-sectional airway lumen area measurement error averaged over 15 airways of interest. The image-based techniques exhibit a bias that causes them to underestimate the true airway lumen cross-sectional area.

  
Figure 5: Comparison of model-based measurements versus pathology lab measurements for mean inner airway radius on slices 3 and 6. Slope of regression line is 1.03 mm/mm, intercept 0.09 mm, with correlation coefficient 0.84.

  
Figure 6: Comparison of model-based measurements versus pathology lab measurements for mean inner airway radius on slices 3 and 6. Slope of regression line is 0.95 mm/mm, intercept 0.76 mm, with correlation coefficient 0.67. The intercept of the regression line indicates that the half-max method exhibits a systematic measurement bias.

DISCUSSION

The results show that the model-based technique exhibits considerably less measurement bias than the half-max method, as predicted by other theoretical analyses [17, 16]. Averaged across all fifteen airways and both slices 3 and 6, the model-based technique has a mean inner radius measurement error of approximately 0.5 pixels, compared to about 2.25 pixels for the half-max method. Further, there is no statistical difference between the model-based measurements and the pathology lab measurements at the p < 0.01 level, while there is a significant difference between the half-max measurements and the pathology lab measurements at the p < 0.01 level.

From a practical perspective, the CT images used in the study exhibited very poor contrast between the airway wall and surrounding parenchyma. We hypothesize this may be due to the process of fixing the lungs in formalin, and then air drying before scanning. This poor contrast may have been the cause of the large measurement error variance for both of the image-based approaches. Both of the ray-casting techniques were prone to significant ray-to-ray variations in the estimated wall locations. These variations were smoothed by averaging over many rays to form a mean inner radius estimate, and by the ray rejection criteria employed by ASAP.

It is important to note that the gold standard measurements were made on a single surface of the slice of lung tissue, while the CT-based measurements were made on CT image slices passing through the interior of the tissue. Thus, pathology lab measurements could have been displaced from the CT image slices by several millimeters (each CT slice is 1.5 mm thick). Airway taper and change in orientation during the several millimeters of travel could introduce measurement error.

SUMMARY

We have considered two approaches for estimating airway wall locations from gray level profiles: (1) the half-max technique and (2) the model-based approach. It has been previously shown that the half-max technique is prone to size-dependent biases. The model-based approach was introduced to reduce the size of these measurement biases. Both techniques have been previously validated on phantom data. This work validates the two techniques using CT scans of real lung tissue, with the measurement gold standard obtained from measurements made using a dissecting microscope and micrometer.

The results show that the model-based technique exhibits considerably less measurement bias than the half-max method. Averaged across all fifteen airways and two CT image slices, the model-based technique has a mean inner radius measurement error of approximately 0.5 pixels, compared to about 2.25 pixels for the half-max method. Further, there is no statistical difference between the model-based measurements and the pathology lab measurements at the p < 0.01 level, while there is a significant difference between the half-max measurements and the pathology lab measurements at the p < 0.01 level.

ACKNOWLEDGEMENTS

This project was supported in part by the National Library of Medicine (contract N01-LM-4-3511).

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