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HIGHLIGHTED TOPICS
Lung Growth and Repair
1Medical College of Wisconsin, 2Marquette University and 3Zablocki Veterans Affairs Medical Center, Milwaukee, Wisconsin 53295
Submitted 29 April 2004 ; accepted in final form 25 August 2004
| ABSTRACT |
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micro-computed tomography; distensibility; morphometric; vascular disease; principal pathway
The rat has been used as a model of vascular remodeling because it displays significant pulmonary arterial remodeling when exposed to different challenges, such as chronic hypoxia and monocrotaline exposure. Many histological studies of vascular remodeling have been performed in the rat (7, 30, 32, 37), using chronic hypoxia as an experimental stimulus for studying the mechanisms of pulmonary arterial remodeling (10, 12, 16, 17, 35, 36, 40). The extant luminal morphometry of the pulmonary arterial tree comes almost exclusively from histological measurements performed on plastic corrosion casts (19, 20, 42), which have been important in developing present concepts regarding normal pulmonary structure-function relationships (3, 6, 9). Reid and colleagues (17, 37) characterized the pattern of pulmonary arterial remodeling induced by hypoxia in rats with histological criteria, including extension of smooth muscle into small, previously nonmuscular arteries, medial thickening in normally muscular arteries, and a decrease in the number of arteries that filled with a hot barium-containing casting material injected at high pressure. Although these changes in the composition of the vessel walls are undoubtedly important, it is the arterial tree geometry and the vessel wall mechanical properties that determine the pulmonary arterial function, and there is little information available as to how these are affected by the remodeling process. The need to expand the characterization of pulmonary arterial remodeling is emphasized by the observation that, within the normal pulmonary arterial tree, the vessel wall histology varies substantially with vessel size (17, 38), whereas the passive mechanical properties of the vessel walls appear to be virtually vessel size independent (1, 22). In addition, the pulmonary arterial remodeling that occurs in these rats in response to chronic hypoxia appears to result in vessel wall mechanical properties that tend to retain this size independence.
An immense amount of data analysis and tabulation is required to fully describe the intact arterial tree. Numerous approaches have been examined for summarizing complex branching networks (8, 9, 15, 19, 20). This present work applies a model based on the concept that the pulmonary arterial tree displays a self-consistent structural pattern (13, 14) and exploits its recursive structural properties to reduce the measurements to only the main arterial trunk and the first segment in each daughter branch. Therefore, a self-consistent tree can be defined as one in which all subunits (subtrees) downstream from a segment with a given diameter are similar, at least in a statistical sense. Data reduction methods of this type were shown to be plausible in an earlier study of pulmonary arterial morphometry in the rat by Karau et al. (21). One significant benefit of this approach, however, is that the data set still holds requisite hemodynamic information for analysis of arterial flow.
The primary aim of the present study was to apply methods of imaging morphometry to differentiating the pulmonary arterial trees of control rats from rats with pulmonary vascular remodeling secondary to chronic hypoxic exposure. To accomplish this goal, we further develop and analyze methods for representing the morphology of the pulmonary arterial tree. We use measurements made in micro-computed tomography (CT) scans of Sprague-Dawley (SD) rat pulmonary arterial trees and previously developed (21, 22) models of morphometry 1) to verify that their branching structure conforms to properties of self-consistency, 2) to examine two methods for estimating the distensibility of the pulmonary arterial tree, 3) to use principles of self-consistency to introduce a method for comparing data from the main pulmonary arterial trunk to data from minor subtrunk pathways, and 4) to put forward a morphometric vector summary of the pulmonary arterial tree.
| METHODS |
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Preparation of the lungs.
After 21 days, each rat was anesthetized with pentobarbital sodium (40 mg/kg ip), and a midline sternotomy was performed. The rat was heparinized (200 IU/kg) by right ventricular injection, and a blood sample was removed for hematocrit determination. The trachea and pulmonary artery were cannulated, and the heart was excised for right ventricular free wall and left ventricle plus septum weight determination. The lung was ventilated with a 15% O2, 6% CO2, balance nitrogen mixture, 3 mmHg end-expiratory pressure, and 8 mmHg end-inspiratory pressure. The lung was subjected to two or three brief peak inspiratory episodes of 1215 mmHg to eliminate any atelectasis that might have occurred during the excision (5, 22, 43). The lung was rinsed free of blood and perfused with a 37°C physiological salt solution containing 5% bovine serum albumin, then a recirculation circuit was created and 6 mg of papaverine in solution were added to the perfusate circulated at 10 ml/min for
2 min. The arterial pressure-vs.-flow relationship was measured over a range from 0 to 40 ml/min, and airway pressure was held constant at 6 mmHg. The lung was immediately placed in the imaging chamber and ventilated with the same gas mixture. Using a 10-ml syringe body with the plunger removed as a reservoir for perfluorooctyl bromide (PFOB), we connected one end of the syringe to the pulmonary artery cannula via a clamped 1/8 ID Tygon tubing and left the large end of the syringe open to the atmosphere. The physiological salt solution in the lung was then replaced by PFOB in the reservoir by unclamping the Tygon tubing. PFOB does not pass through the capillary bed and therefore only fills the pulmonary arterial tree. Accounting for the density of the PFOB, intravascular pressure was determined by measuring the difference between the height of the surface of PFOB in the reservoir and the center of the lung. The arteries were conditioned by cycling the intravascular pressure from 0 to 30 mmHg several times. As the intravascular pressure is reduced, excess PFOB returns to the reservoir. Ventilation was halted during imaging, and airway pressure was again maintained constant at 6 mmHg. The arterial pressure was set to 30 mmHg, and the lungs were rotated in the X-ray beam at 1° increments to obtain 360 planar images. The pressure was lowered successively to 21, 12, and 5 mmHg, with complete CT scans obtained at each pressure (see Fig. 1). Each scan took
3 min. After imaging, the lungs were drained of PFOB, dried in an oven for at least 2 wk, and then weighed.
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70 to 2,800 µm. Multiple pathway analysis, which was performed on one lung from each group, required mapping and measuring of anatomical points, at locations similar to those shown for the main trunk in Fig. 3, for 10 pathways in the arterial tree of both rats. Although Fig. 3 schematically represents conventional dichotomous branching, the mapping technique accounts for branches coming off the main pulmonary trunk at all angles. Therefore supernumerary vessels branching at approximately right angles from main trunk are included in the morphometric data. Orientation of the plane used for measurement was initially approximated by calculating the plane normal to and midway between the consecutive postbifurcation coordinates. After calculating the estimate, a program written in MATLAB (MathWorks, Natick, MA) enabled the user to visualize and finely manipulate the measurement plane with respect to the artery. The plane was positioned such that, first, it was perpendicular to the central axis of the vessel, and second, the 2-D cross section of the lumen revealed the circular structure characteristic of the pulmonary arteries.
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Data reduction techniques. Performing measurements on data confined to the principal pathway, presented above, provides a scheme by which to reduce, to a reasonable extent, the number of measurements required to provide satisfactory results. The notion of a self-consistent tree holds important implications about how much of the vascular tree must be measured to adequately characterize the structure and function of the vascular network. A tree that satisfies the conditions of self-consistency will display the property that the structure of all branches off the main trunk is statistically indistinguishable from their respective subregions of the main trunk. A respective subregion is defined as the portion of the main trunk distal to a point at which the main trunk diameter equals the inlet diameter of the branch being compared. If this condition is met, the momentous feat of measuring all the vessels in the pulmonary tree is reduced to measuring only the main pulmonary trunk and the inlet diameter of the daughter branches along the main trunk. Therefore, measurement of only the main trunk and the inlets to its daughter branches (the "principal pathway") is justified provided that the assumption based on the self-consistency property holds true for the pulmonary arterial branching structure. In this context, self-consistency provides a means for summarizing the global morphometric and mechanical properties of the vascular tree from a reduced set of measurements. Self-consistency allows an entire tree structure to be characterized and "rebuilt" from principal pathway data. Evidence of self-consistency in the structure of the pulmonary arterial tree was shown in previous work carried out in Fawn-Hooded (FH) rats, a strain that has a known susceptibility to PH (22). In this study we investigated the SD rat, a common laboratory strain. The data presented below shows that these structural characteristics also hold true for normoxic (control) and hypoxia-adapted SD rat lungs.
Using these reduction techniques, we have developed models of morphometry that quantify the rat pulmonary arterial tree using its principal pathway data. Drawing from self-consistency, these models imply that if the diameter-vs.-distance relationship for the main trunk is described by Eq. 1 (below), then the distance-vs.-diameter graph of any branch of the tree is described by Eq. 2 (below).
Studies in left lobes. After hemodynamic analysis in four of the control lungs, the right lobar artery was ligated and the lobes distal to it were removed. Only the left lung lobe was imaged in these four lungs. Because of the smaller specimen volume, the left lobe could be moved closer to the X-ray source, which provided a gain in the geometric magnification and the resolution of slightly smaller vessels. The left lobes were mapped and measured similarly to full lungs; however, to directly compare morphometrics of left lobes to full lungs, a protocol (presented below) was designed, using properties of self-consistency, to compensate for differences at the primary lobar artery bifurcation. For this reason the left lobe data could be used to calculate the distensibility of the arteries through the individual segment method (also presented below) but not from the surface fit method.
Statistics analysis.
Data are expressed as means ± SE. The level of statistical significance was defined as P
0.001 for each group of data unless otherwise specified. Student's t-test and one- and two-way analyses of variance for multiple responses were performed.
Animal care. All protocols were performed according to Institutional Animal Care and Use Committee and conformed to the "Guide for the Care and Use of Laboratory Animals" of the National Institutes of Health.
| RESULTS |
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0.01) increase in dry lung weight in the hypoxic compared with the control group, 0.322 ± 0.010 g vs. 0.257 ± 0.018 g, respectively, both before and after normalizing by body weight. Quantitative morphometric differences between the two groups were also found by analyzing the CT data.
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![]() | (1) |
![]() | (2) |
![]() | (3) |
![]() | (4) |
In addition to Eqs. 1 and 3, which are used to represent the main pulmonary trunk, we model the daughter branches by introducing the equation
![]() | (5) |
is a variable diameter increment representing the size heterogeneity of the branch diameters. In this case the parameter cBr, unlike c, is no longer a description of contour of the taper of the main trunk, but rather it is an attribute of the general trend of the distribution of daughter branch diameters as a function of distance along the main trunk. An appropriate way to model the parameter
is to let it equal the coefficient of variation (CVBr) obtained from the variance in the measurement of the branch diameters around the fitted Eqs. 1 and 5, using the five free parameters D(0), DBr(0), Ltot, c, and cBr, with
= 0.
![]() | (6) |
Therefore, a reduced set, graphical characterization of any given lung can be represented by a graph analogous to those shown in Fig. 6, where the main trunk and the daughter branches have been fit by the appropriate functional model equations, and D(0), Ltot, and c are free parameters, although Ltot was limited to a value greater than or equal to the length of the measured pathway. It is important to note that although Eq. 5 is a continuous function, the physical relevance only is applicable at the Ntot discrete locations along the main trunk where the daughter branches actually exist.
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![]() | (7) |
is a distensibility coefficient relating a fractional change in diameter per unit change in pressure with respect to the unstressed vessel diameter, D(x, P = 0). This pressure dependence can be consolidated into Eqs. 1 and 5 in the following forms
![]() | (8) |
![]() | (9) |
for a lung, both the main trunk and daughter branches are initially fit for the free parameters of D(0), Ltot, c, and
values, and then Eqs. 8 and 9 are simultaneously fit only for the free parameter
. Figure 8 shows the
values estimated for the individual components of the principal pathway compared with the value generated from a global fit for the entire principal pathway. The difference in
was significant for each group of measurements.
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. Alternatively, one could use the linear pressure vs. diameter relationship proposed by Yen et al. (41), which is essentially true over the range of pressures investigated in this study, that is
![]() | (10) |
is a related distensibility coefficient for the individual vessel segments. We can then calculate
from the normalized relationship
![]() | (11) |
value are estimated.
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for all the vessel segments reveals that the data are well represented by a line, which has an intercept that is not significantly different from zero, as seen in Fig. 10. To confirm there was no significant difference between the standard regression line and the regression line forced to have a zero intercept, an F-test was performed on all of the data sets, according to methods proposed by Motulsky and Ransnas (34). Because the regression line effectively passes through zero, we conclude that the distensibilities of the vessels throughout the tree are diameter independent and, thus, it conditionally allows us to use the estimated slope of this line as a global representation of the tree's distensibility
. The mean estimated values (±SE) of
in both groups for both the surface fit method (full lung data used) and the individual distensibility method for determining
, as described above, are given in Table 1.
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, CVBr to describe the morphometry of each tree. ET is the sum of the squared errors between the main trunk data and the model. Table 2 presents values (means ± SE) calculated for the two experimental groups, for full lung data and for the left lobe and equivalent lobe data. The overall morphology of control and hypoxic lungs is similar. However, in addition to the significant difference in the
parameter, the trend that there is a better fit of the main trunk data to the model for the full hypoxic lungs compared with the full control lungs becomes significant (P < 0.005) for the equivalent lobes.
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| DISCUSSION |
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There are fundamental differences between the models presented in this paper and those that represent the pulmonary arterial tree structure as fractal. The criteria used to demonstrate that a structure is self-consistent are less strict than those in fractal models used to verify that a structure is self-similar. Rather than prove that the branching characteristics of the pulmonary arterial tree display similar characteristics at different scales of measurement and consequently have mathematically definable fractal dimensions, we show that the morphology of daughter branches is analogous to a respective portion of the main trunk. Because a self-consistent tree does not strictly follow fractal scaling rules, the deviations from fractal dimension seen in the first several generations in many biological trees do not necessarily apply as criteria for characterizing differences between trees.
Morphometric models. The models proposed in this paper are useful and descriptive. Although concise morphology can be determined from the arterial tree by using the present method of analysis, there are several characteristics of arterial morphology that are not adequately represented. For example, in Figs. 57, there are interesting stair-step patterns located in approximately the middle third of the main trunk diameter-vs.-distance relationship. The steps, most evident at the higher intravascular pressures, are almost ubiquitous and characteristically different between the two experimental groups. In the control group, the steps are concave downward, whereas the steps tend to be flat or have a slight upward curvature in the hypoxic rats. Compared with data from hypoxic rats, control data have a larger divergence from the main trunk model, as seen in the parameter "trunk fit SSE" in Table 2. This difference is significant in the equivalent lobe data. The stair-steps reflect underlying structure associated with a range of relatively large branches off the main trunk that may coincide with the thick walled oblique muscle segment identified by Meyrick et al. (29) in the range of the 9th and the 20th generation.
In addition, inspection of the planar images reveals subtle differences between the control and hypoxic arterial trees. One important difference is the decrease in "background haze" observed by others (12, 17) and also seen in our arteriograms, Fig. 1, of rats exposed to chronic hypoxia. The haze represents small, probably subresolvable vessels that have a large impact on recruitment and consequently hemodynamics. The principal pathway is a set of contiguous segments that reflect the single longest path from the inlet (main pulmonary artery) to the terminal vessel (the smallest measurable artery in our analysis) and defines the minimal data required to represent the tree. The principal pathway analysis does not comprehensively address what may be occurring in many of the parallel distal vessels. Our models did show a significant difference in the morphometric parameters Ntot and Ltot in the chronic hypoxic group; however, when normalized by body weight, the differences were no longer significant. A more comprehensive measurement and parameterization of the distal tree would provide better insight into the changes in the small arterial network.
Another parameter of interest is the branch size heterogeneity. Changes in this parameter may reflect developmental or remodeled structure resulting in differences in flow distribution throughout the main trunk. We have suggested a way to model the parameter
in Eq. 5 is to estimate a coefficient of variation (CVBr), described in Eq. 6, to quantitate the branch size heterogeneity. In this calculation we consider the idea that there is variability in the main trunk data, which could be due to actual distortions dependent on proximity of the measurement plane to a bifurcation or could be due to errors in the diameter measurement. Similarly, this variability exists in the daughter branch measurements. Subtracting the variance about the fit to Eq. 1 from that about Eq. 5 provides some approximation to the variance in branch diameters due to the heterogeneity in the branch-to-trunk ratio. The normality of diameter measurements for each of the first 20 generations of main trunk and daughter branches for hypoxic and control rats was tested individually with a Kolmogorov-Smirnov test with P
0.05 and passed. Therefore, estimating the CVBr parameter according to Eq. 6 should be a fair measure of a branch heterogeneity index.
The branch diameter heterogeneity is also a reflection of the developmental 3-D, volume-filling nature of the pulmonary vasculature. Consequently there is likely a predictable dependence on branch rotation angle, as evident by observing the top view in Fig. 2. The models presented here do not include parameterization of the branch rotation angle. Future models that include rotation angle and its dependence on the daughter branching pattern will be important and are very compelling.
We found that a decrease in the pulmonary arterial distensibility measured in rats subject to hypoxic exposure is significant and related to the vascular remodeling that occurs in this group. We calculated a similar value for the pulmonary arterial tree distensibility using both methods presented. Estimating distensibility and other model-fitting procedures in this study require only modest computation time; however, the process of measuring the individual principal pathway segment diameters at each pressure is very time consuming. We are investigating new methods to autonomously detect, measure, and represent the tree more comprehensively and at the same time save resources and increase repeatability.
In addition to identifying differences seen in models of hypoxia, reduced-set morphometric measurements in the intact pulmonary arterial tree can be used to build predictive, analytical models of the pulmonary circulation (8, 23, 24). These models can provide information regarding flow partitioning, blood volume distribution, and insights into the hemodynamic consequences of remodeling. Our results suggest that a key hemodynamic feature in the PH rat model may be the decreasing distensibility in the pulmonary arteries. Some preliminary work by our group using mathematical hemodynamic models suggests that a change in arterial distensibility alone does not account for the pulmonary pressure elevations seen in chronically hypoxic rats (G. S. Krenz, unpublished observations), and further study is required to understand the roles of the individual remodeling components.
Hemodynamics, weights, and hematocrit. Changes in the measured hemodynamic and physiological parameters, such as increased pulmonary vascular resistance, right ventricular hypertrophy, increased hematocrit, and a reduction in vessel filling in rats chronically exposed to hypoxic are consistent with the changes reported by other groups (31, 37). Although we did not measure pulmonary arterial pressure (PAP) in vivo, we can safely assume that, in addition to the high perfusion pressure noted in Fig. 4, the elevated hematocrit in the hypoxic group would have greatly accentuated the in vivo PAP. Large increases in PAP have been implicated as a "second hit," promoting further vascular remodeling and the development of neointimal lesions (4). Histological examination was not performed on the lung tissue in this study, although the significant increase in the dry lung weight in the hypoxic group suggests that remodeling was present. The remodeling was likely a combination of an increase in arterial wall thickness, extension and hypertrophy of smooth muscle cells, as well as an increase in the extracellular matrix well describe in hypoxic SD rats (17).
Isolated lung preparations. The ventilation and perfusion parameters for the isolated lung preparations were chosen to match those used in previous studies (5, 21, 37, 43). They maintain the perfusate pH close to 7.4 through the bicarbonate buffer system and provide adequate inflation and lung clearance. Papaverine was added to the perfusate to eliminate the effect of active muscle tone. A measure of the parenchymal mechanical status, the lung compliance, has been shown not to change after chronic hypoxic exposure (2) and was not measured in this study. Variations in airway pressure will affect the pulmonary vascular resistance. For example, increasing airway pressure increases the PAP measured in perfusion studies. In our experiments, constant airway pressure of 6 mmHg provided a transpulmonary differential within the physiological range and consistency between hemodynamic and imaging studies.
Vessel measuring methodologies. Vascular casting with either barium gel or plastic resins has unquestionably contributed to our understanding of normal pulmonary structure-function relationships (3, 7, 9, 29). Besides the process being arduous, technical difficulties, such as filling the entire arterial network homogeneously, validation of downstream pressures, and measuring the mechanical response to a range of intravascular pressures have dissuaded its use as a tool for characterizing vascular remodeling; consequently, the data obtained to date are from a relatively small number of lungs. In addition, histological observations, which have been the primary tool for evaluating pulmonary vascular remodeling, do not provide information on intact 3-D vascular tree structure or the mechanical properties of the vessels. As an alternative, we have developed a volumetric X-ray micro-CT imaging technique that increases the throughput enough to make such studies more practical. In our preparations, the arterial tree is filled with perfluorooctyl bromide, a very-low-viscosity contrast agent that does not pass through the capillary bed. CT has the key advantages that the resulting 3-D data set is rapidly available in digitized form and comprised of all the vessels with their correct spatial orientation and connectivity; in addition, the data can be collected on the same lung under different experimental conditions, allowing for evaluation of vessel mechanics as well as structure (22, 27).
Imaging limitations.
The resolution limit of the scanner theoretically approaches the system's focal spot size of 3 µm but is also impacted by the imaging chain and the reconstruction algorithm. Although the closer the object can be placed to the X-ray source, the higher the resolution possible, the smallest vessel measured,
70 µm, was effectively limited by the size of the object (the lung) scanned and the requirement that the object remain in the detector (the image intensifier) field for every projection view used to reconstruct the tomographic data. The detector aperture can be set as large as 22 cm to image larger objects; however, magnification is lost because large objects require the source-to-object and source-to-detector distance to increase, limiting the size of the smallest contrasted vessel that can be resolved and consequently measured. A significant amount of remodeling is known to occur in the partially muscular and nonmuscular arteries with diameters <100 µm (37). Our measurements only sample the upper range of small vessels and do not extend to the capillary level. In addition to not having data for this important portion of the arterial tree, methods for branch ordering, such as Horsfield and Strahler systems (18, 19), which require knowledge of the end branches, are not directly applicable.
Genetic and clinical relevance. Idiopathic forms of PH have been linked to a mutation in bone morphogenetic protein receptor (BMPR2) (25, 28). We also now know the number of genes coding for pulmonary structure is much fewer in number than components that make up the lung, i.e., there is not an individual gene for every capillary, alveolus, and peripheral branch. Earlier we showed (22) that the FH lung displays self-consistency. Here we have shown arterial trees in SD rats are also self-consistent and therefore can assume that, in addition to the vascular structure, the distribution of blood flow in any subtree of the arterial network is also statistically indistinguishable from its respective main trunk subregion. It is then logical that a self-consistent or recursive rule exists at some level that guides arterial development and plays some role in guiding the remodeling process, because, before and after significant remodeling, vessel distensibility remains virtually independent of diameter. The FH rat is known and studied for its susceptibility to pulmonary hypertension. We are presently performing studies to compare the morphometry of the pulmonary arterial tree in different rat strains. The FH rat has an increased baseline pulmonary vascular resistance, is more sensitive to hypoxic exposure, and develops PH spontaneously. However, estimates of arterial distensibility under control and hypoxia are equivalent in SD and FH strains (R. C. Molthen, unpublished observations). We still suspect that phenotypic structural differences exist between strains that determine underlying factors that cause susceptibility or resistance to PH.
Although the initiation and progression of arterial remodeling is still unclear, we know that a positive feedback control loop is at work in the remodeling process. Genetic predisposition seemingly sets the stage for an increased sensitivity to this counterproductive response. The FH rat and humans genetically predisposed to PH may be more sensitive to remodeling stimuli, effectively short-circuiting loops of the feedback algorithm.
3-D volumetric CT is becoming a standard-of-care in the clinical environment and is often ordered for lung and thoracic scans. Methods presented here for estimating pulmonary arterial distensibility are not directly applicable to clinical studies; however, one could envision imaging technology improving to the point that accurate temporal scanning of the pulmonary vasculature could be recorded at different points in the cardiac cycle, i.e., at systole and diastole, such that estimates of pulmonary arterial distensibility could be used to diagnose occult remodeling accompanying PH. A parametric vector-based approach, such as the one presented in this study, would identify quantitative differences between groups; it may also help to diagnose what stage of the process an individual is at and the most effective strategy for treatment at particular stage.
In conclusion, we believe that strong arguments exist for applying CT imaging and 3-D isotropic reconstruction to the problem of measuring arterial morphology and biomechanical measurements. These measurements provide important information about the current state of the pulmonary vessels and how the vessels respond to external stimuli and could supply clues regarding the genetic influences driving the development of pulmonary hypertension and its pathophysiology.
| GRANTS |
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| ACKNOWLEDGMENTS |
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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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