INTRODUCTION

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X-RAY MICROCOMPUTED TOMOGRAPHY (CT) promises to be a valuable source of vascular structure-function information and vascular phenotypes of small laboratory animals (7, 13, 25, 36). The rat has been widely used to study pulmonary vascular remodeling (12, 17, 29, 32, 38) and is being used increasingly for physiological genomics in general (14, 15, 23, 41, 46) and for physiological genomics of the pulmonary vasculature in particular (21, 26, 29, 42, 47). Thus the objective of this study was to develop an approach for X-ray micro-CT measurement of pulmonary arterial diameters and their three-dimensional locations within the intact rat lung. The method was applied to the measurement of rat pulmonary arterial distensibility, which is a potentially useful pulmonary vascular phenotype for identifying quantitative trait loci (15, 41) as well as an input to rat lung physiome models (4, 16, 18, 40) used to understand pulmonary vascular function.

	METHODS

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Animal Preparation

Imaging

View larger version (116K): [in this window] [in a new window]   Fig. 1.   Schematic of the imaging system. Projection of the pyramidal object representing the lung within its X-ray transparent cylinder is magnified on the image-intensifier face. Stage permits measured movements of the object perpendicular (in x and z directions) and parallel to the X-ray beam axis (y), and it can be rotated ().

Image Preprocessing

Dewarping. The spatial distortion correction algorithm consisted of two steps. First, the uncorrected individual bb center of mass coordinates (x',y') were determined from the BB phantom image. These coordinates for each set of four neighboring BBs were represented by a set of eight equations (Eq. 1 and 2 for each BB, where i is bb number, 1, 2, 3 or 4). These equations were solved simultaneously for the coefficients a-h which map x',y' via bilinear interpolation onto the known x,y coordinates of the grid vertices.

(1)

(2)

The process, illustrated in Figs. 2 and 3, shows the result of this dewarping on the bb phantom image. The comparison between Fig. 3, A and B, can be made by observing that the top row of BBs follows a curved line before, and a straight line after, dewarping. Because the image intensifier and X-ray source were fixed in space, the dewarping coefficients were independent of projection angle. The coefficients were applied to interpolate the correct location of each pixel of the 360 projection images in every lung or phantom data set.

View larger version (14K): [in this window] [in a new window]   Fig. 2.   Schematic representation of the transformation involved in the dewarping process described by Eqs. 1 and 2.

View larger version (174K): [in this window] [in a new window]   Fig. 3.   Image preprocessing steps demonstrated on the BB phantom. a, Raw image of BB phantom; b, BB phantom after applying dewarping algorithm; c, dewarped flood-field image, d, dewarped and flood-field normalized BB phantom (b divided by c).

Central axis location. The rotation axis was determined as the midpoint between the left- and right-most excursions of a high-contrast feature in a two-dimensional radon transform or sinogram using the same row of pixels extracted from each of the 360 projection images. Once this location was established, each planar image was cropped so that the axis of rotation occupied the central column of pixels. This resulted in a final preprocessed image size of 497 × 497 pixels.

Spatial normalization. The flood-field image acquired with the same X-ray voltage, current, and geometry as the lung projection images provided the unattenuated incident illumination intensity for each pixel. Thirty frames were averaged to suppress temporal noise (primarily quantum mottle). The spatially corrected, cropped projections were then divided by the flood-field image to provide pixel values proportional to X-ray absorption. The uniform background on the BB phantom image in Fig. 3d illustrates the result of the latter step.

Temporal normalization. Finally, three 20 × 20 pixel regions of interest (ROI) unobscured by the object in any projection were located within the volume. The mean intensity for the three ROI divided by the respective mean flood-field intensity was used as a scaling factor for each image. This scaling factor corrected for any temporal drift in the overall illumination intensity during planar image acquisition (24). This scaling step turned out to be unnecessary because there was no systematic temporal drift in the mean ROI intensities between projection images and the coefficient of variation (CV) in the mean ROI intensity for the 360 projection images comprising an image volume was only about 0.1% for these data sets.

Image Reconstruction

The postreconstruction voxel gray scale values (I) were equalized so that the range from air to PFOB was the same for all reconstructed volumes. First, a region of the volume known to contain only air was selected and its I values were averaged. _i represents the average I value for air in a particular image volume. The maximum I in the volume, _i, was then determined. Each voxel's intensity was then adjusted according to Eq. 3

(3)

to arrive at I', the equalized voxel intensity expressed as the gray scale number (GSN). The terms W and M were chosen before performing the equalization to describe the mean air GSN and the maximum GSN, respectively, for all of the postequalization image volumes. Any remaining negative values were set to zero. The resulting I' GSN values ranged from 0 to 255.

To test the linearity of the resulting GSN with respect to object density following this equalization procedure, nine serial dilutions of iodinated contrast medium (0 to 0.282 g/ml of iodine in the form of diatrizoate meglumine) were loaded into lengths of 1.67-mm ID polyethylene tubing and imaged within a single volume. After reconstruction and equalization, the GSN value over the center of each cross section was determined. The coefficient of determination between GSN and iodine concentration was 0.996, indicating that the GSN was linearly proportional to X-ray absorbance.

The left side of Fig. 4 is a three-dimensional rendering of the reconstructed image volume to provide a sense of the data set obtained as a result of these procedures. It was obtained after thresholding the CT volume to allow appreciation of the gross structure. In what follows, the full, unthresholded data set, exemplified by the two transaxial slices depicted in Fig. 4, was used to make quantitative measurements.

View larger version (100K): [in this window] [in a new window]   Fig. 4.   A three-dimensional rendering of the image volume with the threshold set to accent the contrast enhanced pulmonary arterial tree. Right, two transaxial slices (a and b) through the unthresholded image volume.

	MEASUREMENTS

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Mapping

View larger version (82K): [in this window] [in a new window]   Fig. 5.   Identifying vessel segments in the image volume. Left, rendering of portion of rat pulmonary artery. Right, sequence of transaxial slices on which the bifurcations demarking a vessel segment can be seen. Arrows connect bifurcation crotch points on rendered image with corresponding points on transaxial slices. The red line (left) and red dots (right) designate the central axis of the contiguous vessels.

View larger version (55K): [in this window] [in a new window]   Fig. 6.   Schematic of vessel segment central axis and orthogonal plane through segment midpoint. (x1, y1, z1) and (x2, y2, z2) are endpoints of the central axis (C) through the vessel segment. A and B: vectors passing midway between (x1, y1, z1) and (x2, y2, z2), perpendicular to each other and to C, establishing the orientation of the orthogonal plane.

Locating Orthogonal Slices

View larger version (82K): [in this window] [in a new window]   Fig. 7.   Top: three-dimensional rendering of portion of a rat pulmonary artery. Bottom, left: transaxial slice with its elliptical cross section of the vessel due to the oblique angle between the vessel segment central axis and the imaging system axis of rotation. Bottom, right: orthogonal slice through the vessel showing the nearly circular cross section.

Measuring Diameters

In a theoretical imaging system whose PSF is a delta function and the CT slice has no thickness, the intensity of the line of pixels (a line scan) across the minimum diameter of the elliptical cross section of an obliquely cut vessel would appear as a rectangular function. In reality, blurring is introduced in the image acquisition and reconstruction and by finite pixel size and slice thickness. The latter is eliminated by the use of only orthogonal slices, as indicated above. The actual blurred image of the vessel is then essentially the PSF, or blurring function, convolved with the theoretical vessel cross section. The FWHM approach applied to the line scans recovers the vessel diameter as long as the diameter is large enough compared with the FWPSF, but it over estimates the diameter when the diameter approaches the FWPSF. This can be appreciated by assuming a Gaussian distribution for the PSF as in Eq. 4

(4)

where x is the axis increment on which the PSF is defined and  is the standard deviation. Half the maximum height of the PSF occurs at x = ±1.175 . Thus the FWPSF is ~2.35 . As the actual vessel diameter decreases below FWPSF, the FWHM of the blurred line scan approaches FWPSF. The smallest imaginable diameter may be thought of as almost a delta function that when convolved with the PSF would return the PSF, in which case the FWHM method would return the FWPSF rather than the diameter.

The behavior of a line scan across a vessel image is further demonstrated in Fig. 8, top, illustrating three sets of rectangular functions representing line scans of slices through the ideal (unblurred) image volumes containing cylinders of one X-ray-absorbing medium embedded in three different absorbing media (simulating different tissue densities). These functions were convolved with the PSF of Eq. 4 to simulate line scans of the reconstructed images (Fig. 8, bottom). The graph in Fig. 9A is the FWHM for the simulated line scans in Fig. 8, bottom. The FWHM versus the diameter relationship is independent of the GSN of the imbedding medium, and linearly proportional to diameter when the diameter is larger than FWPSF, but it approaches the constant FWPSF when the diameter is small. The GSN height (G_max) of the simulated line scans above that of the imbedding medium (GSN_m) is constant for large cylinders and then becomes proportional to the diameter as the diameter decreases (Fig. 9B). Taken together, the quantity FWHM × (G_max  GSN_m), which approximates the area between the line scan and GSN_m is linearly proportional to the diameter over the entire diameter range (Fig. 9C) as is the actual area under the line scan (Fig. 9D). However, the slope of the area versus diameter line depends on GSN_m as summarized by Eq. 5

(5)

where A is the measured area, D is the measured diameter, s₀ is the slope of the area-diameter line when GSN_m = 0, and GSN_max is the maximum GSN for the entire image volume. To take advantage of the area for measuring diameter, s₀, can be determined by including, in the imaged volume, an object with known diameter and with similar X-ray absorbance as the vessel contrast medium. We obtain the area as follows.

View larger version (38K): [in this window] [in a new window]   Fig. 8.   Top: three sets of superimposed theoretical line scans [in arbitrary gray scale number (GSN) vs. diameter units] through the axis of orthogonal cross sections of images of six simulated cylinders, each with a different diameter and with PSF = (x). Each set of cylinders is surrounded by a different medium having X-ray absorbance equivalent to either 0%, 25%, or 50% of that of the cylinders themselves. Bottom: simulated line scans from the top convolved with PSF = ex2/22 (see Eq. 4), where  = 0.12 times the diameter of the largest cylinder.

View larger version (28K): [in this window] [in a new window]   Fig. 9.   A: FWHM of line scans from bottom panel of Fig. 8 versus actual diameter for the three different surrounding media indicated by open triangle, open circle, and closed circle, for media with X-ray absorbance of 50%, 25%, and 0%, respectively, of that of the cylinders themselves. B: gray scale height above the medium (Gmax  GSNm) vs. actual diameter. C: FWHM × height vs. actual diameter. D: area under line scans in Fig. 8, bottom, vs. actual diameter. Diameter and FWHM are in units of 2.35 × .

Assuming a Gaussian PSF, the functional form of a line scan through the axis of a vessel can be approximated by Eq. 6, referred to subsequently as the modified Gaussian function (MGF) and illustrated in Fig. 10.

View larger version (30K): [in this window] [in a new window]   Fig. 10.   Top: diagrammatic representation of Eq. 6 showing the modified Gaussian function (MGF) for the GSN of a line scan across a vessel cross section. Bottom: modified Gaussian surface (MGS).

When the MGF is fit to the line scan, the integral of MGF  GSN_m produces an area proportional to diameter. Thus a method for measuring vessel diameters is achieved. However

(6)

there are additional practical problems involved in selecting a line scan that passes through the central voxel of the vessel cross section and in minimizing the effect of random variations in the estimated diameter resulting from using a single line scan. The solution for both was to obtain the orthogonal slices as indicated above and, then, to fit the MGF to the entire cylindrical cross section viewed as a surface of revolution using a least-square fit of Eq. 6. The result is an axially symmetric surface [the modified Gaussian surface (MGS)] such as illustrated in Fig. 10, which represents an average of all radial line scans through the center of the cylindrical vessel cross section. Thus the integral of Eq. 6 provides the value of A in Eq. 5.

	RESULTS

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The MGS fit method was tested on a phantom consisting of calibrated titanium alloy (90% titanium, 6% aluminum, and 4% vanadium) wire segments of 50, 100, 200, 460, 500, and 1,000 µm diameters. Two different surrounding absorbing media were obtained by immersing a portion of the wire lengths in a silicone gel medium, whereas the rest of the wire lengths were surrounded by only air. Figure 11 shows the image data in the same format as the simulations in Fig. 9.

View larger version (30K): [in this window] [in a new window]   Fig. 11.   Data from wire phantom represented in same format as Fig. 9. Squares and circles, different imbedding media as indicated in text.

To evaluate the effects of both the orientation and position of objects within the cone beam field of view, another phantom was constructed with 50 µm and 500 µm wires scattered in a medium of silicone gel so that they were oriented from 0 to 45° relative to the axis of rotation and 0 to 90% of the cone beam angle from the center to the edge of the field of view. The CV in the estimated diameter was 14.5% for the 50-µm wire and 9.4% for the 500-µm wire. Less than 4.1% of the variation in estimated diameter could be attributed to the angle relative to the axis of rotation and <7.4% to vertical distance above or below the central plane perpendicular to the axis of rotation. Although the wire phantom may not exactly reproduce the conditions of an actual vessel lumen imbedded in its unique tissue medium, the similarities of the average and CV of the standard deviations () of the PSF obtained with wire phantoms [2.42 ± 0.41 pixels (CV = 17%)], and the 783 vessel diameters measured for the distensibility study indicated below [2.03 ± 0.36 pixels (CV = 18%)] is one measure of consistency between the two.

Fig. 12 shows the results of the method applied to a large (1,150 µm) and a small (43 µm) artery in an image volume of a rat lung.

View larger version (36K): [in this window] [in a new window]   Fig. 12.   Examples of the MGS fit to cross sections of vessels 43 and 1,150 µm in diameter. A difference between Fig. 10 and this figure is the pixellation of the real image as shown. Note that the height of the MGF (right) is considerably shorter for the small vessel than for the large vessel.

To investigate the distensibility of rat pulmonary arteries, 162 arterial vessel segments ranging from ~106 to 1,681 µm at the lowest pressure and from about 151 to 2,743 µm at the highest pressure were measured at the five intravascular pressure settings. Over this range of pressures and vessel sizes, the diameter versus pressure relationship was nearly linear, as exemplified in Fig. 13 by a representative group of vessel segments covering the range of diameters studied. Therefore, the diameter versus pressure data were parameterized by a slope () and intercept [D(0)] using Eq. 7 after Yen et al. (49) and others (2)

(7)

where P is the intravascular pressure (in mmHg), D is the vessel diameter (in µm) and D(0) is the diameter extrapolated to P = 0. 

View larger version (17K): [in this window] [in a new window]   Fig. 13.   Diameter vs. intravascular pressure for 4 individual vessel segments with Eq. 7 fit to the data. The points at ~30 mmHg are double, one being obtained at the beginning and the other being obtained at the end of the data collection sequence.

The values of  for all the measured vessel segments are plotted versus D(0) in Fig. 14. Because the fractional differences in diameters over the pressure range studied are small, and because  and D(0) are highly correlated in the regression analysis for Eq. 7, errors in the diameter measurements can have a proportionately larger impact on the estimates of  and D(0) than on the estimates of the individual vessel diameters. This is reflected in the fact that the CV in the paired measurements obtained at the high pressure was only 4.1%, whereas the average of the coefficients of variations in  and D(0) (standard error of the estimate divided by the estimated value) calculated for the individual vessels were 29 and 28%, respectively. Also the distributions of the coefficients of variation were highly skewed as reflected by the fact that respective medians were only 20 and 12%. To graphically represent the distribution of the standard errors of the estimates in Fig. 14, the gray level of the symbol representing [D(0),] for each vessel is inversely proportional to the standard error. The key observation from this weighting of the data symbols is that the outlying points tend to have large standard errors. Thus the variability in the relationship between  and D(0) includes a component that is due to the amplification of errors in the diameter measurements resulting from the transformation resulting from fitting Eq. 7 to the data. To evaluate the relationship between  and D(0) for the data in Fig. 14, linear regression was carried out assuming proportionate errors in both y and x values, i.e., by minimizing the sum of the squared distances orthogonal to the regression line (10). The values were either weighted equally or they were weighted according to the standard error of the estimate as indicated by the symbol gray levels in Fig. 14. Also, the intercept was either a free parameter or fixed at zero. The F-test was used to determine whether the weighting significantly altered the fit and whether a nonzero intercept was supported by the data. The results were essentially the same whether the data were weighted or not, and there was no significant improvement in the fits when the intercept was free. The latter implies that the average vessel distensibility, , defined as /D(0) for an individual vessel, was independent of vessel size with the average value approximated by the slope of the Fig. 14 graph. The slope was 2.85 ± 0.19 for the weighted and 2.82 ± 0.19%/mmHg (SE) for the unweighted fit. The average of the values of  calculated for each individual vessel was 3.23 ± 3.56%/mmHg (SD) (CV = 110%), but the distribution is quite skewed as expected for this transformation of the diameter data (34). This is reflected by the fact that the median of the individual values was 2.73%/mmHg, and thus closer to the regressed values from Fig. 14.

View larger version (21K): [in this window] [in a new window]   Fig. 14.   vs. D(0) for all the measured vessels. The gray scale of the symbols is weighted inversely by the standard error from the fit to Eq. 7. The line is the unweighted linear regression line through (0,0) (see text).

Discussion

The vessel distensibility results indicate that over the vessel diameter range studied the distensibility of the rat pulmonary arteries (2.8%/mmHg) is within the range of values for pulmonary arteries of larger species studied previously. In summarizing the data available at the time, Al-Tinawi et al. (2) found that an average value of about 2%/mmHg was consistent with measurements on dog, cat, and human pulmonary arteries over the full range of arterial diameters. However, the variability from study to study tends to confound the issue of possible species differences. The distensibility of rat pulmonary arteries has been studied previously either by mounting isolated vessel segments on wires so that the force and distance between the wires could be measured (12, 28) or by cannulating isolated vessel segments such that the transmural pressure could be manipulated while the diameters were monitored via video microscopy (32). The distensibility calculated for the cannulated arteries in the 500- to 700-µm diameter range was also about 2.8%/mmHg (32). For the wire-mounted vessels segments in the 120-µm to 1-mm range studied, the average was about 3.7%/mmHg (12, 28). The somewhat larger latter values might have something to do with the different vessel preparation. The distensibility in the present study is defined by the intravascular pressure rather than transmural pressure. Transmural pressure is also affected by transpulmonary pressure and lung volume (1, 27, 45). Thus the distensibility values obtained in this study have to be considered to be specific for the transpulmonary pressure used. It is also possible that transmural pressure is a variable contributing to the range of previously reported values in other species. Such questions can be addressed in future studies using the methods described herein.

Although it has been suggested by some studies that pulmonary arterial distensibility may be vessel size dependent (33), the summary provided by Al-Tinawi et al. (2) suggested that the distensibility of the pulmonary arteries of the various species studied is nearly the same for vessels of any size, or that any systematic dependence on vessel size is small compared with the variability among vessels of a given diameter. In this regard, the present rat lung data are consistent with the results from the larger species. This diameter independence may be somewhat surprising given how vessel wall composition varies over this diameter range (17). However, there may be an adaptive advantage to the constancy of this mechanical property.

Figures 13 and 14 reflect two key relationships, namely, the nearly linear diameter versus pressure relationship for the individual vessels over the pressure range studied and the diameter independence of the vessel distensibility over the diameter range studied. One functional consequence of such relationships is that they tend to minimize the sensitivity of the distribution of flow among the branches of a heterogeneous, asymmetric, vascular tree to changes in total flow rate. If the distensibility were diameter dependent, for example decreasing or increasing in proportion to vessel diameter, increasing cardiac output would tend toward a redistribution of flow to, or away from, respectively, the smaller branch at an asymmetric bifurcation. Likewise, because of the arterial-to-venous pressure drop through the vascular network, a nonlinear diameter versus pressure relationship might have a similar effect when the pressure drop is affected by a change in total pulmonary flow. This can be appreciated by noting that the inflow pressure (P_in) versus flow () relationship for a distensible vessel segment having a cylindrical configuration at D(0), length L, outflow pressure P_out, viscosity µ, distensibility , defined by D(P) = D(0)(1 + P), and Poiseuille flow (19, 30, 50) is

(8)

Figure 15 shows the effect of changing flow into a simulated vascular tree made up of the asymmetrical branches depicted in Fig. 16 when  is constant for all vessel segments, regardless of D(0) and with  as a function of D(0). With  constant, the relative distribution of flow among the branches and out the outlets is independent of the total flow entering the tree. However, with  either directly or inversely proportional to D(0) the flow distribution is dependent on the total flow, as exemplified by the outlet flow distributions in Fig. 15.

View larger version (31K): [in this window] [in a new window]   Fig. 15.   The effect of changing inlet flow on the distribution of the six outlet flows in the simulation network depicted in Fig. 16. Flow ratio, fraction of the total flow leaving a particular outlet, with one unit of total inlet flow, to the fraction of the flow leaving the same outlet with four units of inlet flow. Abscissa, outlet D(0) as a fraction of the inlet D(0). Pressure at each outlet was fixed at zero. A:  = 0.2 Di(0) per unit pressure. B:  = 0.2 per unit pressure. C:  = [0.2 Di(0) + 0.21] per unit pressure, where Di(0) for each outlet is a fraction of the inlet D1(0).

View larger version (23K): [in this window] [in a new window]   Fig. 16.   A diagrammatic representation of the simulated tree from which the data in Fig. 15 were obtained. The numbers are Di(0) for each vessel segment as a fraction of the inlet D1(0).

Changes in total pulmonary blood flow have been accompanied by changes in the spatial distribution of pulmonary blood flow to lesser and greater extents in different experimental settings (6, 8, 11, 35, 44), and various factors may be involved. However, it might be assumed that the observed distensibility pattern helps to maintain the robustness of the flow distributing network in the face of changing flow, thereby helping to keep the pulmonary flow distribution within bounds appropriate for efficient gas exchange, regardless of the cardiac output.

One of the anticipated uses of this pulmonary vascular imaging approach is for the collection of more extensive pulmonary vascular morphometric data. In the past, pulmonary vascular morphometry has been carried out mainly on a small number of plastic casts of ostensibly normal lungs (20). Imaging methods such as these should be useful for expanding the morphometric database available for evaluating structure/function relationships in abnormal and remodeled pulmonary arteries as well. The concept behind microfocal X-ray imaging is that the small focal spot minimizes the penumbral contribution to the PSF, allowing for high resolution even when the object is close to the source. As magnification is inversely proportional to the distance between the X-ray source and object, a smaller object may be placed closer to the source and still be completely contained within the cone of the beam delimited by the source-to-detector distance and detector diameter. For example, the maximum resolution is greater for a mouse lung, for which the described procedures are also applicable, than for a rat lung. The rat was the subject of this study because of its history of use in studies of pulmonary vascular remodeling and because of its increasing importance in physiological genomics.