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Technical Advance |
From the Center for Molecular Medicine, Maine Medical Center Research Institute, Scarborough, Maine; and the University of Maine, Orono, Maine
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Abstract |
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Murine models of vascular disease are especially useful in determining the contribution of specific gene products as genetically modified mice are easily generated and readily available. Current models include mice that spontaneously demonstrate chronic obstructive vascular disease2 and induction of obstruction by direct injury of the vasculature.3-7 The complete ligation of the carotid artery is one method of inducing a vascular remodeling response in mice. Originally described by Kumar and Lindner,7 this model has the advantages of being technically simple to perform and yielding a highly reproducible localized vascular remodeling response. This murine model is being increasingly used, and has been instrumental in defining the contributions of plasma protein systems,3,8,9 cytokines,10,11 and physical forces such as pressure12 and shear stress7 in the vascular remodeling response.
Whereas the vascular lesions formed in response to some injuries such as endothelial denudation are relatively consistent over the involved arterial segment, carotid artery ligation induces a response that is generally greatest at the ligature, and gradually diminishes over the involved arterial segment (3 to 5 mm from the site of ligation). This variation with distance from the ligature was noted in the original paper describing murine carotid artery ligation,7 and the need to consider the effect of distance in analysis was recognized by Yogo et al13 and Sindermann et al.14 As the occasional occurrence of thrombus, typically close to the ligature, is another source of variation in this model, most studies have discarded the 1 mm segment closest to the ligature from the analyzed data set. In previous studies using this model, data analysis has occurred in one of two ways: determination of mean response over an entire arterial segment, or limitation of analysis to a specific portion of the segment. Both of these methods of analysis have problems that limit interpretation. In the first method, taking a mean value over a length of vessel that is changing in a predictable manner masks differences in particular regions between groups, and results in an especially large standard deviation. On the other hand, limiting analysis to comparable arterial regions has difficulties as the method uses a smaller data set and inspection of data before analysis violates statistical premises. In this study, we examine the hypothesis that much of the variation in the response to ligation is due to non-genetic factors in addition to genetic factors. Our results build on previous studies that have recognized the importance of considering regional differences, with the demonstration that distance from the ligature contributes to the total variance and is a significant predictor of the remodeling response. Statistical regression is presented as means of simultaneously analyzing the contribution of several variables to the response to ligation. In essence, the method involves fitting a curve to the data set, describing the curve as a function, and then determining the variation of each data point from that function. In addition to being multivariate, this method has the advantage of portioning the total variance to each variable resulting in increased sensitivity. The practical utility of the method is then demonstrated by application to a data set testing the effects of osteopontin (OPN) on the response to carotid artery ligation.15 In addition to providing increased significance, regression analysis revealed significant regional differences due to OPN that cannot be appreciated by conventional analysis methods. As regression analysis is a commonly used statistical method, actual calculations are not presented, and the reader is referred to SAS regression procedures16 for description of the actual calculations performed.
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Materials and Methods |
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The data used in this study were taken from the previously published study,15 and the experimental methods are presented briefly here for clarity. All protocols were approved by the Institutional Animal Care and Use Committee. The OPN-null mutant allele has been described,17 and mice used in this study were 16- to 24-week-old males on a 129 x Black Swiss (Taconic, Germantown, NY) hybrid background. Ligation of the left carotid arteries of mice was performed as previously described7 on a test group of mice (wild-type, n = 8; OPN-null, n = 12) and sham operations were performed on a control group of sham-manipulated mice (wild-type, n = 6; OPN-null, n = 6). Two weeks following ligation, tissues were perfusion fixed with 4% paraformaldehyde (Sigma, St. Louis, MO) in 0.1 mol/L sodium phosphate buffer, pH 7.3. Vessels were harvested and embedded in paraffin such that initial sections from the block came from the internal/external carotid arteries. At least 800 consecutive serial sections were cut from both arteries of each mouse (7 µm thick). Sections including the ligature were easily identified due to the clearly visible suture material. As every section was saved and numbered, the distance from the site of ligation (relative start site in the case of sham manipulation) and between sections was precisely known. Sections of the internal/external carotid arteries were discarded. As analysis of previous work using this strain showed that substantial change in remodeling could be observed in sections 200-µm apart, we considered sections 280-µm apart to be independent observations. Ten sections from each mouse collected every 280-µm apart starting at the site of ligation were analyzed, thus representing a total 3-mm segment. Sections were stained with orcein to accentuate the elastin layers, and morphometric analysis was performed. Digitized images of these vessels were analyzed using image analysis software (NIH Image 1.60). The lumen surface, the perimeter of the neointima, and the perimeter of the tunica media were traced, for circumference and area of the lumen, internal elastic lamina (IEL), and external elastic lamina (EEL), respectively. The medial area was calculated by subtracting the area defined by the IEL from the area defined by the EEL. Intimal area was calculated as the area between the lumen surface and IEL. As the shape of the cross sections is often distorted and the neointima may be unevenly distributed, lumen area could not be measured directly. Assuming the EEL was circular, lumen area was calculated by subtracting medial area and intimal area from the total area calculated from the circumference of the EEL.
Data Analysis
Data were analyzed using SAS Version 8.0. See the Table legends for descriptions of methods used for each analysis.
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Results |
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To test the hypothesis that distance from the ligature significantly modifies the remodeling response, we re-analyzed the data from our previously published study,15
using the alternate method of analysis described below. Interpretation of the data were initiated with scatter plots of the different vessel areas versus distance for each mouse, and mean values for each distance were calculated. Consistent with the description of Kumar and Lindner,7
while sham-manipulated vessels showed no changes in vessel areas over the length of the arterial segment, quantitative analysis of ligated arteries demonstrated changes in total, medial, intimal, and lumen area depending on the region (Figure 1C)
. For example, intimal area was greatest in the 1 mm closest to the ligature, and gradually decreased in the direction of the aortic arch. Conversely, lumen area was small in the 1 mm closest to the ligature, and increased with distance from the ligature. As the scatter plots for both the individual mice and groups appeared well behaved (continuous and differentiable), we considered the data suitable for regression analysis. The data, including distance from the site of ligation for each analyzed section, were coded into SAS Version 8.0. The contribution of variability with distance to the total variability was determined using Proc GLM. As changes in medial area, intimal area, lumen area, and total area all contribute to the remodeling response, separate models were calculated for each using the following command: Proc GLM; Model Total, Media, Intima, Lumen = ligature distance ligature*distance/solution;
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. The output also provided parameter estimates for the linear regression model. With the exception of total area, these data indicated distance or the interaction of ligation with distance to significantly contribute to total variance.
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We then sought to improve the models through fitting a curve to the mean response. Various functions were tested against the data for best fit. The scatter plots suggested y = arctan(x), y = e-x, and y = e-(x2) as possibilities for lumen and intimal areas. Models were determined for total, medial, intimal, and lumen area using Proc Reg (Table 2)
with the following command: Proc Reg; Model total media intima lumen = ligation distance ligation*distance;
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Regression Analysis Provides a Better Description of the Role of Specific Genes in the Response to Carotid Artery Ligation
An advantage of regression analysis is that multiple factors can be considered simultaneously. We suspected this property would be especially useful in the comparison of the response to ligation of genetic mutant to wild-type mice. To validate the utility of the method, the regression model was easily expanded with the addition of variables to consider the effect of a null mutation of the spp1 gene (encodes OPN) on the vascular response to ligation. We applied regression analysis to a data set in which we have previously used traditional methods to show OPN affects both neointima formation and constrictive remodeling.15
As was detected previously using Student’s t-test, the regression method identified OPN as significantly affecting the lumen area and total area before ligation (the variable OPN is a significant predictor of lumen and total area), and intimal area and total area following ligation (the variable OPN*Ligation is a significant predictor of lumen and total area). However, due to the ability of regression to assign portions of total variance to each variable, regression analysis was more sensitive than Student’s t-test as evidenced by increased statistical significance. Our previous results using Student’s t-test to compare OPN-null to wild-type at 14 days following ligation were: total area, P = 0.024; intimal area, P = 0.003; lumen area, P = 0.420; medial area, P = 0.040 (compare to Table 3
). More importantly, the regression method also identified an interaction between OPN, ligation, and distance in lumen area that was not previously detected (the variables Ligation*Distance and OPN*Ligation*Distance are significant predictors of lumen area). This difference is due to the fact that analysis by Student’s t-test simply cannot consider multiple variables (compare Figure 1, C and D
, Table 3
). These interactions mathematically describe the dramatic change in lumen area with increasing distance from the ligature evident in wild-type mice in Figure 1C
. This change in area with increasing distance from the ligature does not occur in the lumen area of OPN-null mice following ligation. In essence, the regression analysis identified, quantified, and determined the statistical significance of a marked difference in the response to carotid artery ligation that was not detected by traditional analysis.
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Discussion |
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Distance from the ligature, a significant predictor of the response to carotid artery ligation, is a variable common to all carotid artery ligation experiments. Inclusion of distance as a variable led to a 1.07- to 2.9-fold model improvement. Furthermore, the addition of a distance variable reveals aspects of the response that univariate methods simply cannot consider. Such information improves the description of the response as compared to previously used methods. Interestingly, it was the relatively small 1.07-fold improvement with the inclusion of distance in the model of lumen area that revealed the regional aspect of the vascular response of wild-type mice not present in OPN-null mice. Thus, even small model improvement can provide important insights into the remodeling response.
Further analysis of the data and regression models reveals that one mouse had a response to ligation that was much greater than that of the other ligated mice. Examination of the injury response in this mouse showed a large clot in the lumen in the region less than 1 mm from the ligature. This clot is probably the result of altered coagulation or a procedural problem and demonstrates the many influences involved in the vascular response. Interestingly, the outlying data came not just from sections containing the clot, but also from sections observed to be free of clot. We interpret this as showing that the presence of the deposit alters not just the response of sections containing the clot, but the response along the entire vessel. Thus, the routine exclusion of the data from the 1 mm arterial segment closest to the ligature removes the ability to detect an important source of response variation. To determine the effect of these outlying data on the analysis we repeated the analysis with the outlying data included. Though slight decreases in r-square values occurred for the linear models of the different vessel areas, inclusion of the outlier data did not alter the predictor significance of each variable. However, our attempt to improve the model with curve fitting was not as successful. The curvilinear model offered little improvement over the linear model using the data set containing outlying data. Thus, the exclusion of data from mice that demonstrate an obviously atypical response to the ligation procedure is important to the development of good models of the vascular response.
The vascular response induced by carotid artery ligation is typically localized in the region from 3 mm to 5 mm region closest to the ligature. In this study the response was observed to involve approximately 3 mm. Several other models of obstructive vascular pathology involve a similarly localized response. These pathology models might also benefit from regression analysis as the responses are multifactoral and may vary with distance along an arterial segment.
As often occurs in the regression analysis of data from experiments, there are some theoretical problems in applying regression analysis to the data from carotid artery ligation experiments. Regression analysis requires observations to be independent. This condition is not met in these experiments as the response at one point in the artery is physically linked to the response at every other point. We addressed this problem with the selection of a distance between arterial points (280 µm) over which previous work has shown substantial change can occur. Regression analysis also requires equal variance at each independent variable point. This condition was not met, as the standard deviation of each point measured was different. Although this problem can be addressed with the use of weighted regression, we found that this approach gave minimal improvement in the models. Thus, the method is not presented. Lastly, our models do not present a hierarchy of effects. We found the inclusion of non-significant variables to greatly complicate the models without providing any additional insight. Thus, the variables are not included. We consider these theoretical problems to be minimal as compared to those of typically used methods (appropriateness of mean to describe changing data, and inspection of data before analysis).
In summary, distance from the site of ligation is a significant predictor of the vascular remodeling response in carotid artery ligation experiments. By allowing simultaneous consideration of many factors, regression analysis provides both improved description of the response to carotid artery ligation as well as increased comparative power through the portioning of the total variance to its different sources.
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Acknowledgements |
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Footnotes |
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Supported by a grant from the American Heart Association to L.L. (025250N).
Accepted for publication September 10, 2003.
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References |
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