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On the search of arterial geometry heritability
International Journal of Cardiology 221 (2016) 1013–1021
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International Journal of Cardiology journal homepage: www.elsevier.com/locate/ijcard
On the search of arterial geometry heritability Carlos A. Bulant a,⁎,1, Pablo J. Blanco a,1, Alexandre Pereira b, Thais P. Lima b, Antonildes N. Assunção b, Gabriela Liberato b, Cristiano G. Bezerra b, Jose R. Parga b, Luiz F. Ávila b, Raúl A. Feijóo a,1, Pedro A. Lemos b a b
Laboratório Nacional de Computação Científica, LNCC/MCTI, Av. Getúlio Vargas 333, Quitandinha, 25651-075 Petrópolis, Brazil Heart Institute, University of São Paulo Medical School, INCOR-FM-USP, Av. Dr. Eneas de Carvalho Aguiar, 44, 3rd floor, São Paulo, SP 05403-000, Brazil
a r t i c l e
i n f o
Article history: Received 25 May 2016 Accepted 4 July 2016 Available online 7 July 2016 Keywords: Coronary arteries Geometric descriptors Heritability Geometric risk factors
a b s t r a c t Background: Geometrical risk factors for CAD have been previously proposed before. To date, however, the effect of those factors is not conclusive, and remains as an open research field. Here, we hypothesize that some of these factors have a genetic component explaining inter-individual variability. Objective: To detect heritability indicators of the coronary arterial geometry. Materials and methods: A patient sample of 48 individuals, consisting of 24 siblings, was used. Three dimensional geometry of the LAD, LCx and RCA were reconstructed from standard CCTA. Arterial models were characterized in terms of 20+ geometric descriptors (phenotypes). A comprehensive statistical analysis to detect potential heritability of such phenotypes was employed. Heritability was assessed by means of several statistical indexes. Finally, the association of phenotypes to stenotic lesion is also reported. Results: The RCA scored positive indications for heritability in 15+ phenotypes, while the LAD in 10 and the LCx in only 3 phenotypes. Association between presence of lesion and phenotypes was higher in the LAD, 10 + phenotypes, while for the LCx only 2 phenotypes were significantly associated, and none association was found for the RCA. Conclusion: The RCA showed potential heritability for the largest number of phenotypes, followed by the LAD. The LCx presents the weaker association of morphology among siblings. Regarding lesion-geometry associations, the there are hints of an underlying relation in the LAD, the LCx featured a weaker association and the RCA showed none. This difference could be related to the different hemodynamic environments in these arteries. © 2016 Elsevier Ireland Ltd. All rights reserved.
1. Introduction Coronary artery disease (CAD) continues as the leading cause of death worldwide for several decades now [25]. Ever increasing efforts in the identification of risk factors for CAD have been observed. As a consequence, several risk factors have been recognized, comprising mainly modifiable and non-modifiable systemic factors, such as cigarette smoking, diabetes mellitus, hypertension, hypercholesterolemia, familial history [26–28] and genetic contribution to susceptibility for CAD [9,29–33]. However, whether systemic risk factors can be fully accounted for the burden and presentation of CAD in a given individual remains controversial [34–36], mainly because they do not explain the localization and non-uniformity of atherosclerosis distribution [37,38]. Such medical observations motivated the search for biomechanical and geometrical features involved in the local atherosclerotic process. ⁎ Corresponding author. E-mail addresses: [email protected] (C.A. Bulant), [email protected] (P.J. Blanco), [email protected] (R.A. Feijóo). 1 Tel.: +55-24-2233-6067; fax: +55-24-2233-6071.
http://dx.doi.org/10.1016/j.ijcard.2016.07.064 0167-5273/© 2016 Elsevier Ireland Ltd. All rights reserved.
The effects of biomechanical (e.g. wall shear stress and oscillatory shear index) [39–44], as well as the geometrical factors [1,7,8,11,12, 45,46], have been previously suggested to quantitatively and qualitatively affect atherosclerosis. To date, however, the effects of such factors are not conclusive, and remain as an open research field in the biomechanical community. The idea that specific geometric descriptors might be heritable, like other morphological characteristics are, was hypothesized, but not studied, in the context of geometric risk factors for CAD [11,12]. Although the heritability of stenosis characteristics such as localization, extent and morphology, as well as risk of coronary events in siblings has been studied before [9,10], there is no precedent work in the medical literature addressing the hypothesis of arterial geometry heritability. In a recent study [5], Bulant et al. presented a comprehensive geometric and morphometric analysis of the coronary arteries. Intra and inter coronary associations of the geometric descriptors where studied. Furthermore, they presented evidence of an underlying similarity among siblings in terms of geometric features of the coronary arterial tree. The present work aims to investigate if such similarity can be tracked to individual geometric descriptors of the major coronary
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arteries. That is, the present analysis is focused on the right coronary artery (RCA), the left anterior descending artery (LAD) and the left circumflex artery (LCx). The rest of the document is organized as follows: Section 2 describes the image acquisition processing tools, the patient sample, and summarizes the statistical analysis to be used. In Section 3 results are presented and discussed. Limitations are outlined in Section 4, and conclusions are presented in Section 5.
indentation of at least the width of the artery (in at least one view angle). Any RCA that did not comply with this definition is defined as C-Shape RCA. From the original sample of 48 patients, one RCA model could not be classified because the artery appeared too short in the CCTA image. This patient and the associated sibling were not taken into account in the statistical analysis of the shape phenotype, but where used in the calculations of all other phenotypes. Expert classification resulted in 30 C and 16 Σ shaped RCA. Despite the familial relationship present in the data set, it was shown in [5] that the patient sample is representative in terms of anatomical description of the coronary vasculature, i.e. circulation dominance, radius measurements and arterial occurrence/ distribution.
2. Materials and methods 2.3. Statistical analysis 2.1. Image acquisition and processing Arterial models are obtained from non-invasive Coronary Computed Tomography Angiography (CCTA) medical images, using acquisition protocols and the processing methodology described in [5]. Fig. 1 illustrates coronary arterial trees obtained through the image processing pipeline. Three-dimensional arteries are represented by the so-called centerline structures. Centerlines are widely accepted representations of arterial segments [2,16–19,23,24], because they retain most of the geometric characteristics of arteries in a compact and simple structure. Three-dimensional centerlines are represented by polylines with point-wise information (e.g. lumen radius). Furthermore, centerlines admit classic differential geometry analysis to compute, for example, curvature and torsion. Fig. 2 presents centerlines of the complete coronary tree for two pairs of siblings and emphasizes the similarities in the LAD and RCA arteries. Arterial centerlines can be characterized by several geometric descriptors available in the literature. In this work, for any given artery A, a set of 25 descriptors is used (see Table 1). In addition, the presence of a stenotic lesion (of any grade and tissue type) is used as an additional descriptor. Furthermore, for the RCA, the shape (C or Σ) is also used as a descriptor. In this work, the terms descriptor, feature, variable and phenotype are used as synonyms. It is important to remark that, continuous variables are normalized in order to have a sample-wide zero mean and unit variance. Such normalization is performed for each arterial group separately. 2.2. Patient sample The patient sample used in this work is described in [5]. Such sample consists of 48 patients, formed by 24 pairs of siblings. Making a total of 14 female and 34 male patients with an average age of 53 ± 13 years old. All patients have at least one of the major CAD systemic risks factors (smoker, hypertension, diabetes or dyslipidemia). This work focuses on the analysis of the main coronary arteries, namely: right coronary artery (RCA), left anterior descending coronary artery (LAD) and left circumflex coronary artery (LCx). Existence of arterial lesions in the arteries was specified by physicians, lesions are characterized according to [20] using a tuple of three variables, namely: stenosis grade, tissue type and lesion position. An artery was considered as diseased when a stenotic lesion of any grade, tissue and position was present in the artery. From the 48 patients, 27 LAD, 12 LCx, and 19 RCA arteries were found to be diseased. Furthermore, 28 patients presented at least one diseased artery, the 20 remaining patients featured healthy coronary vasculatures. In turn, the RCA shape was also classified by a specialist directly from the geometrical models. Different classification criteria had been used in the literature, for example, some authors [7,8] defined shape from manual measurements of distance in the angiographic image. In this work, the criterion defined in [1] was used: Σ-Shape arteries have an
Standard statistical indicators, summarized in Table 2, are used to analyze each arterial descriptor for each of the major coronary arteries. Tests for categorical or binary variables are marked with (D) symbol and tests for continuous or ordinal variables are identified with (C) symbol in Table 2. Continuous variables were tested as well as categorical parameters, after being dichotomized, using the mean value of the feature for the patient sample as a cutoff value (i.e. hereafter, saying that a patient tested positive for a given feature, means that the feature value is greater than the mean of the sample); therefore, these types of tests should be interpreted as association of the feature between siblings relative to the sample-mean value of the feature. Association between phenotypes and presence of lesion is assessed by means of standards two-tailed Chi-square, exact Fisher's and Mann-Whitney (U) tests. Statistical significance is assumed at 95% confident interval.
3. Results and discussion 3.1. Left anterior descending coronary artery Table 3 presents the quantitative values for all indicators presented in Table 2, when assessing individual geometric features of the LAD in the patient sample. From these results, it can be inferred that there is a relationship between geometric descriptors of the LAD artery among siblings, particularly, it is noteworthy to remark the following. • The lesion presence in the LAD, which is a binary phenotype (variable), obtained the highest values of PBWR, indicating that the probability of a patient having a lesion in the LAD increases if his sibling has a lesion in the same artery. The SimI test also indicates that the chances of both siblings having the same LAD status (healthy or diseased) is high (70%). It was found that the RR is high (2.22) and statistically significant (CI = [1.16,4.23]). Furthermore, the OR = 5.71 (CI = [1.63, 19.95]) is also significant and credible (COR = 3.62), with a moderate positive association (PHI = 0.36), and a high Pw = 0.82. These results agree with the literature reporting that familial history of CADs is a risk factor [9,10]. • When dichotomizing continuous variables by the mean in the sample, it was found that:
Fig. 1. Illustration of various coronary arterial trees segmentations.
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Fig. 2. Comparison of two pairs of siblings, the first pair is constituted by pink (P) and red (R) centerlines while the second pair are yellow (Y) and cream (C) centerlines. The first three columns present comparison between the four patients while the fourth column compares the LAD (top) and RCA (bottom) arteries of all patients.
– Several geometric features scored high PBWR; – The RR and OR result in statistically significant association, around 2 and 3.9 respectively, for the mean radius (r), the mean combined curvature (ζ ) and curvature-derived entropy (Hκ) although none of them satisfied the credibility criterion. – In turn, SimI N 0.5 for several features indicates that the probability of both siblings having feature values greater or lower than the mean is high, specially for the tortuosity (χ) and lesion presence. • Test for continuous variables, are also worth of discussion:
LCx shows less heritability than the LAD and RCA (see Section 2.3). Particularly, it is noteworthy to remark the following. • The lesion presence in the LCx does not present statistically significant values of RR nor OR. Furthermore the PBWR and Pw are small. Such results indicate that for any given patient, it would not be appropriate to assume risk of lesion in the LCx, given that his sibling has a lesion in the same artery. • When dichotomizing continuous variables by the mean of the sample yields:
– Pearson's correlation coefficient (ρ), scores significant values (pρ b 0.05) for tortuosity (χ), total curvature (κT) and bending energy (ξκ). – The ICC presented weak (but significant association) for the total curvature and torsion (κT,τT), the bending energy (ξκ) and for the intersection counting temperature and entropy (Tn,Hn).
– Some geometric features score high PBWR; – The RR and OR scored significant values for the mean and total curvature (κ;κ T ) and Tn. Nevertheless, the credibility criterion was only satisfied by the κ and κT, both with good Pw, 82.5% and 78.5%; – In turn, SimI N 0.5 for several features indicates that the probability of both siblings having feature values greater or lower than the mean is high. Particularly for κ and κT.
• Association between LAD phenotypes and presence of lesions showed significant levels for the following set { ‘, κT, ζT, ξκ, ϱ, Υ, β, κ d, Tκ, Tn, Hn). From this set, only the {Tn, Hn, ξκ, κT} scored some kind of heritability (ICC or ρ) different from the SimI.
• Test for continuous phenotypes was not statistically significant for any phenotype. • Association between LCx phenotypes and presence of lesions showed significant levels only for Pn and Λτ, none of which scored some kind of heritability.
3.2. Left circumflex coronary artery 3.3. Right coronary artery Table 4 presents the quantitative values for all indicators presented in Table 2, when assessing individual geometric features of the LCx in the patient sample. In agreement with the results presented in [5], the
Table 5 presents the quantitative values for all indicators presented in Table 2, when assessing individual geometric features of the
Table 1 List of geometrical and morphological descriptors. When appropriate, bibliographic reference that reports previous use in the related literature is given. Spatially-distributed features are condensed in mean and total values, i.e. curvature and torsion. Descriptor list Branch count (Υ) Tortuosity (χ) [19] Curvature [19], mean (κ) and total (κT) Combined curvature [18], mean (ζ ) and total (ζT) Curvature ratio (Λκ) [2] Bending energy (ξκ) [16] Fractal dimension (ϱ) [23] Offspring mean raising angle (β) Intersection-counting entropy (Hn) [3] Intersection counting temperature (Pn) [3] Point-wise curvature temperature (Tκ) [3] Lesion presence
Length (‘Þ Radius,mean (r) Torsion [19], mean (τ) and total (τT) Aspect ratio (Λr) [17] Torsion ratio (Λτ) [2] Twisting energy (ξτ) [16] Rising angle (α) Average distal curvature (κ d ) [4] Intersection-counting temperature (Tn) [3] Point-wise curvature entropy (Hκ) [3] Point-wise curvature pressure (Pκ) [3] RCA shape, C/Σ [8]
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Table 2 Summary of statistical indicators of similarity/association of feature values to the sibling condition. Indicator name
Brief description
ProbandWise ratio, PBWR [D]
Probability that a patient tests positive given that his sibling tested positive. The PBWR is a standard choice for establishing the concordance rate between pairs of patients [15].
Similarity Index, SimI [D]
Probability of both siblings having the same test results.
Pearson correlation coeff., ρ [C]
Measures association of descriptors on a siblings-sibling basis. The p-value is obtained from testing the hypothesis of no correlation against the alternative that there is a nonzero correlation. In this work, if p b 0.05, the correlation ρ is considered to be significantly different from zero.
Interclass corr. coeff., ICC [C]
Describes how strongly siblings resemble each other. The One-way random single measures is used [14]. In addition to estimation of ICC, a hypothesis test is performed with the null hypothesis that ICC = 0. In this work, p-ICC b0.05 indicates statistical significance for the ICC value.
Risk-ratio or relative-risk, RR [D]
In epidemiological terms [21], RR is the risk of testing positive for individuals with a given susceptibility genotype (in this case the sibling tested positive), divided by the risk of disease for those without it. In addition, the confidence interval (RR CI), can be computed to test for statistical significance. If the Confidence interval contains the value 1, then the RR has no statistical significance.
Odds-ratio, OR [D]
The odds ratio (OR) quantifies how strongly the presence or absence of property A is associated with the presence or absence of property B in a given population. If each individual in a population either does or does not have a property “A”, (e.g. “patient has lesion”), and also either does or does not have a property “B” (e.g. “sibling has lesion”) where both properties are appropriately defined, then a ratio can be formed which quantitatively describes the association between the presence/absence of “A” (patient has lesion) and the presence/absence of “B” (sibling has lesion) for individuals in the population. This ratio is the odds ratio (OR) [6]. Furthermore, an associated confidence interval (OR CI) can be computed to test for statistical significance. If the interval contains the value 1, then the OR is not statistically significant.
Association Parameter, PHI [D]
If the OR CI does not encompass the value OR = 1, then the Bayesian Credibility Assessment [22] of the test is computed. If the test is credible, the Association Parameter PHI, can be calculated from the associated chi-square statistic of the contingency table used to compute the OR. PHI N0 implies positive association (risk factor). PHI b0 implies negative association (protective factor). |PHI| ≤ 0.3 is considered a weak association. 0.3 b |PHI| ≤ 0.7 is considered moderate association. |PHI| N0.7 is considered a strong association.
Critical Odds Ratio, COR [D]
In some cases, statistical significance of the OR (although a widespread indicator), is not a good indicator of the credibility of a finding (that is, the extent to which it provides convincing evidence for efficacy), as it fails to take full account of the size of the trial, or of pre-existing insights [13]. The credibility of any given OR with statistical significance can be assessed using a Bayesian method [13]. For a given result to meet this standard the prior evidence for efficacy must exceed a specific level; this level is set by the Critical Odds Ratio (COR). The assessment of a given clinical trial result can then proceed as follows: • If the stated 95% CI excludes an OR of 1.00 (corresponding to no effect), the result can be deemed statistically significant at the 95% level; • If OR is at least as impressive as that indicated by the COR, the result can also be deemed credible at the 95% level.
Power, Pw [D]
It stands for the probability of detecting an effect, given that the effect is really there. Or likewise, the probability of rejecting the null hypothesis when it is in fact false [22]. It is recommended a Pw ≥ 0.8, which means that if a study was performed N times, we would see statistically significance difference 80% of the times.
RCA in the patient sample. A large amount of statistically significant associations of feature among siblings was found. These results agree with those reported in [5], where it was shown that the RCA presents higher similarities among siblings than when compared to non siblings. Particularly, it is noteworthy to remark the following.
phenotypes. Particularly, for the bending energy ξκ reached a SimI = 97%, scoring a perfect Pw. • Test for continuous phenotypes yielded:
• The lesion presence in the RCA, has moderate values of PBWR and SimI, 52% and 62% respectively. Nevertheless the RR and OR are not statistically significant. • Dichotomization of continuous variables by the sample mean shows that:
– Pearson's correlation coefficient (ρ), scored significant values (p b 0.05) for several features, among them: length (‘), tortuosity (χ), mean radius (r), mean/total curvature (κ, κT), total combined curvature (ζT), aspect/curvature ratios (Λr,Λκ), bending/twisting energies (ξκ,ξτ), fractal dimension (ϱ) and temperature/entropy associated to intersection counting (Tn,Hn). – The ICC also scored statistically significant values for these features and for the mean offspring rise angle.
– Several geometric features score high PBWR, above 70%; – The number of features with significant values of RR and OR is higher than in the LAD and LCx cases, several of which also satisfied the credibility criterion and featured high Pw values. – Furthermore, it was obtained SimI N 0.5 for several features, resulting in higher values than in the LAD and LCx arteries for the same
• The RCA has an extra phenotype, the Σ-shaped (binary variable). It is noteworthy that a high degree of heritability of the arterial shape is indicated by all tests. It was found that, the PBWR is 62%; the SimI indicates high probability (73% chance) that both siblings have the same shape (C or Σ); The RR = 3.13 (CI = [1.39,7.03]) and OR = 6.67
Table 3 Statistical indicators for individual geometric descriptor similarity for the LAD artery. Association to lesion presence
PBWR
SimI⁎
ρ#
ICC#
RR [CI]$
OR [CI]$
PHI⁎⁎
COR@
Pw~
p- Chi^2#
p- Fisher's#
p-U-Test#
Length Tortuosity Mean radius Mean curvature Total curvature Mean torsion Total torsion Mean Comb. Curv. Total Comb. Curv. Aspect ratio Curvature ratio Torsion ratio Bending energy Twisting energy Fractal dimension Branch count Rising angle Mean offspring rise angle Average distal curvature Temperature (curvature) Preassure (curvature) Entropy (curvature) Temperature (cut points) Preassure (cut points) Entropy (cut points) Lesion Presence
0.552 0.400 0.636 0.375 0.316 0.571 0.571 0.636 0.480 0.571 0.429 0.222 0.333 0.476 0.522 0.609 0.500 0.545 0.316 0.417 0.667 0.692 0.571 0.615 0.609 0.741
0.458 0.750 0.667 0.583 0.458 0.625 0.625 0.667 0.458 0.500 0.667 0.417 0.667 0.542 0.542 0.625 0.500 0.583 0.458 0.417 0.625 0.667 0.625 0.583 0.625 0.708
0.127 0.438 0.300 0.335 0.474 0.180 0.355 0.179 0.087 0.078 0.317 0.178 0.725 0.174 0.188 0.177 (0.006) 0.032 0.057 (0.234) 0.067 0.196 0.396 0.180 0.404 -
0.147 0.108 0.312 0.305 0.371 0.187 0.358 0.186 0.102 0.098 0.303 0.193 0.338 0.194 0.183 0.182 0.013 0.052 0.048 (0.227) 0.077 0.167 0.344 0.121 0.363 -
0.806 [0.515, 1.262] 2.533 [0.881, 7.284] 2.068 [1.072, 3.991] 1.200 [0.531, 2.711] 0.704 [0.324, 1.530] 1.714 [0.895, 3.282] 1.714 [0.895, 3.282] 2.068 [1.072, 3.991] 0.849 [0.493, 1.462] 0.952 [0.589, 1.540] 1.821 [0.774, 4.288] 0.476 [0.185, 1.225] 1.500 [0.548, 4.105] 1.169 [0.617, 2.214] 1.186 [0.657, 2.140] 1.691 [0.912, 3.133] 1.000 [0.568, 1.761] 1.418 [0.764, 2.631] 0.704 [0.324, 1.530] 0.714 [0.399, 1.278] 1.556 [0.887, 2.727] 1.904 [1.035, 3.501] 1.714 [0.895, 3.282] 1.354 [0.782, 2.345] 1.691 [0.912, 3.133] 2.222 [1.166, 4.234]
0.568 [0.169, 1.911] 3.556 [0.765, 16.528] 3.938 [1.182, 13.117] 1.320 [0.375, 4.645] 0.568 [0.169, 1.911] 2.667 [0.821, 8.659] 2.667 [0.821, 8.659] 3.938 [1.182, 13.117] 0.710 [0.228, 2.216] 0.889 [0.277, 2.854] 2.438 [0.650, 9.145] 0.327 [0.087, 1.226] 1.750 [0.417, 7.346] 1.322 [0.419, 4.176] 1.388 [0.445, 4.329] 2.765 [0.859, 8.907] 1.000 [0.323, 3.101] 1.920 [0.606, 6.080] 0.568 [0.169, 1.911] 0.510 [0.162, 1.608] 2.667 [0.821, 8.659] 3.938 [1.182, 13.117] 2.667 [0.821, 8.659] 1.920 [0.606, 6.080] 2.765 [0.859, 8.907] 5.714 [1.636, 19.957]
0.287 0.287 0.287 0.365
9.096 9.096 9.096 3.626
0.143 0.403 0.631 0.066 0.143 0.375 0.375 0.631 0.085 0.039 0.276 0.387 0.130 0.069 0.081 0.403 0.025 0.196 0.143 0.207 0.375 0.631 0.375 0.196 0.403 0.825
0.026 0.067 0.633 0.081 0.028 0.289 0.289 0.533 0.081 0.190 0.212 0.299 0.017 0.088 0.021 0.018 0.884 0.028 0.003 0.004 0.493 0.755 0.034 0.271 0.051 -
0.237 0.297 0.561 0.237 0.039 0.771 0.771 0.776 0.259 0.382 0.750 0.765 0.095 0.382 0.145 0.040 0.561 0.019 0.008 0.080 0.565 0.776 0.144 0.244 0.383 -
0.005 0.062 0.448 0.088 0.014 0.448 0.357 0.498 0.037 0.194 0.159 0.448 0.008 0.074 0.020 0.036 0.892 0.060 0.002 0.006 0.607 0.665 0.030 0.291 0.048 -
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Heritability estimates Feature
⁎ Highlighted when larger than 0.5 # Highlighted when significant (95% confidence) $ Highlighted when CI (at 95% level) does not include the value 1 ⁎⁎ Highlighted when larger than 0.3 @ Highlighted when the OR is significant and at least as impressive as the COR (credible at the 95% level.) ~ Highlighted when larger than 0.8
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Table 4 Statistical indicators for individual geometric descriptor similarity for the LCx artery.
Feature
PBWR
Length Tortuosity Mean radius Mean curvature Total curvature Mean torsion Total torsion Mean Comb. Curv. Total Comb. Curv. Aspect ratio Curvature ratio Torsion ratio Bending energy Twisting energy Fractal dimension Branch count Rising angle Mean offspring rise angle Average distal curvature Temperature (curvature) Preassure (curvature) Entropy (curvature) Temperature (cut points) Preassure (cut points) Entropy (cut points) Lesion Presence
0.545 0.476 0.526 0.667 0.632 0.462 0.480 0.545 0.545 0.400 0.250 0.444 0.286 0.375 0.476 0.500 0.522 0.500 0.375 0.333 0.667 0.667 0.545 0.462 0.545 0.167
0.583 0.542 0.625 0.708 0.708 0.417 0.458 0.583 0.583 0.375 0.500 0.583 0.583 0.583 0.542 0.583 0.542 0.583 0.583 0.333 0.583 0.583 0.583 0.417 0.583 0.583
#
#
$
ρ
ICC
RR [CI]
0.055 (0.066) (0.069) 0.292 0.126 (0.174) (0.066) 0.401 0.133 (0.098) (0.095) 0.057 0.007 (0.109) 0.004 0.320 0.223 0.070 0.219 (0.256) 0.089 (0.053) 0.034 (0.076) 0.037 -
0.068 (0.047) (0.058) 0.307 0.130 (0.154) (0.046) 0.404 0.100 (0.072) (0.067) 0.071 0.005 (0.081) 0.024 0.262 0.218 0.077 0.235 (0.237) 0.106 (0.034) 0.055 (0.059) 0.057 -
1.418 [0.764, 2.631] 1.169 [0.617, 2.214] 1.696 [0.850, 3.382] 2.571 [1.270, 5.208] 2.617 [1.260, 5.435] 0.725 [0.430, 1.222] 0.849 [0.493, 1.462] 1.418 [0.764, 2.631] 1.418 [0.764, 2.631] 0.613 [0.348, 1.079] 0.667 [0.255, 1.740] 1.333 [0.647, 2.748] 0.971 [0.365, 2.584] 1.200 [0.531, 2.711] 1.169 [0.617, 2.214] 1.400 [0.722, 2.716] 1.186 [0.657, 2.140] 1.400 [0.722, 2.716] 1.200 [0.531, 2.711] 0.500 [0.266, 0.941] 1.200 [0.739, 1.948] 1.200 [0.739, 1.948] 1.418 [0.764, 2.631] 0.725 [0.430, 1.222] 1.418 [0.764, 2.631] 0.600 [0.152, 2.362]
⁎ Highlighted when larger than 0.5 # Highlighted when significant (95% confidence) $ Highlighted when CI (at 95% level) does not include the value 1 ⁎⁎ Highlighted when larger than 0.3 @ Highlighted when the OR is significant and at least as impressive as the COR (credible at the 95% level.) ~ Highlighted when larger than 0.8
Association to lesion presence OR [CI]
PHI⁎⁎
COR
1.920 [0.606, 6.080] 1.322 [0.419, 4.176] 2.469 [0.747, 8.163] 5.714 [1.636, 19.957] 5.388 [1.525, 19.029] 0.490 [0.153, 1.565] 0.710 [0.228, 2.216] 1.920 [0.606, 6.080] 1.920 [0.606, 6.080] 0.356 [0.110, 1.149] 0.556 [0.146, 2.119] 1.600 [0.482, 5.313] 0.960 [0.243, 3.794] 1.320 [0.375, 4.645] 1.322 [0.419, 4.176] 1.800 [0.559, 5.792] 1.388 [0.445, 4.329] 1.800 [0.559, 5.792] 1.320 [0.375, 4.645] 0.250 [0.075, 0.830] 1.600 [0.482, 5.313] 1.600 [0.482, 5.313] 1.920 [0.606, 6.080] 0.490 [0.153, 1.565] 1.920 [0.606, 6.080] 0.520 [0.097, 2.802]
0.365 0.347 0.375 -
3.626 4.169 0.125 -
$
@
~
Pw
p- Chi^2#
p- Fisher's#
p-U-Test#
0.196 0.069 0.320 0.825 0.785 0.223 0.085 0.196 0.196 0.413 0.126 0.119 0.028 0.066 0.069 0.165 0.081 0.165 0.066 0.645 0.119 0.119 0.196 0.223 0.196 0.095
0.094 0.240 0.394 0.614 0.865 0.738 0.868 0.316 0.094 0.868 0.480 0.016 0.714 0.480 0.065 1.000 0.617 0.499 0.480 0.505 0.731 0.731 0.094 0.019 0.094 -
0.111 0.319 0.501 0.741 1.000 1.000 1.000 0.341 0.111 1.000 0.500 0.036 0.726 0.500 0.095 1.000 0.743 0.737 0.500 0.740 0.743 0.743 0.111 0.042 0.111 -
0.229 0.080 0.439 0.748 0.186 0.642 0.660 0.300 0.131 0.877 0.398 0.020 0.186 0.098 0.098 0.769 0.915 0.202 0.660 0.766 0.385 0.279 0.194 0.019 0.179 -
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Heritability estimates SimI⁎
Table 5 Statistical indicators for individual geometric descriptor similarity for the RCA artery. Association to lesion presence
PBWR
SimI⁎
ρ#
ICC#
RR [CI]$
OR [CI]$
PHI⁎⁎
COR@
Pw~
p- Chi^2#
p- Fisher's#
p-U-Test#
Length Tortuosity Mean radius Mean curvature Total curvature Mean torsion Total torsion Mean Comb. Curv. Total Comb. Curv. Aspect ratio Curvature ratio Torsion ratio Bending energy Twisting energy Fractal dimension Branch count Rising angle Mean offspring rise angle Average distal curvature Temperature (curvature) Preassure (curvature) Entropy (curvature) Temperature (cut points) Preassure (cut points) Entropy (cut points) Lesion Presence Σ-Shaped
0.696 0.636 0.636 0.667 0.714 0.370 0.429 0.522 0.727 0.571 0.750 0.435 0.800 0.556 0.588 0.667 0.421 0.476 0.526 0.519 0.538 0.593 0.700 0.273 0.625 0.526 0.625
0.708 0.667 0.667 0.792 0.833 0.292 0.333 0.542 0.750 0.625 0.833 0.458 0.917 0.667 0.708 0.708 0.542 0.542 0.625 0.458 0.500 0.542 0.750 0.333 0.750 0.625 0.739
0.555 0.480 0.622 0.607 0.823 (0.189) (0.161) (0.025) 0.629 0.579 0.446 0.063 0.836 0.523 0.483 0.316 0.065 0.374 0.472 0.117 0.259 0.301 0.519 (0.054) 0.732 -
0.539 0.489 0.586 0.617 0.800 (0.161) (0.130) (0.018) 0.626 0.563 0.417 0.064 0.769 0.508 0.493 0.284 0.066 0.391 0.472 0.133 0.264 0.301 0.458 (0.117) 0.602 -
2.484 [1.253, 4.925] 2.068 [1.072, 3.991] 2.068 [1.072, 3.991] 4.400 [1.819, 10.641] 6.071 [2.282, 16.150] 0.458 [0.268, 0.780] 0.536 [0.331, 0.866] 1.186 [0.657, 2.140] 3.152 [1.493, 6.652] 1.714 [0.895, 3.282] 6.000 [2.299, 15.660] 0.836 [0.459, 1.522] 15.20 [3.808, 60.665] 2.083 [1.011, 4.293] 2.605 [1.214, 5.590] 2.571 [1.270, 5.208] 1.110 [0.549, 2.243] 1.169 [0.617, 2.214] 1.696 [0.850, 3.382] 0.838 [0.511, 1.374] 0.987 [0.586, 1.663] 1.131 [0.677, 1.891] 3.267 [1.520, 7.021] 0.443 [0.210, 0.935] 3.333 [1.475, 7.531] 1.696 [0.850, 3.382] 3.125 [1.390, 7.025]
5.878 [1.692, 20.421] 3.938 [1.182, 13.117] 3.938 [1.182, 13.117] 11.20 [2.668, 47.015] 18.75 [3.941, 89.209] 0.138 [0.036, 0.529] 0.188 [0.050, 0.707] 1.388 [0.445, 4.329] 8.889 [2.402, 32.900] 2.667 [0.821, 8.659] 21.00 [4.493, 98.161] 0.710 [0.228, 2.216] 72.00 [8.778, 590.536] 3.438 [1.002, 11.790] 4.898 [1.360, 17.639] 5.714 [1.636, 19.957] 1.190 [0.366, 3.872] 1.322 [0.419, 4.176] 2.469 [0.747, 8.163] 0.663 [0.208, 2.114] 0.972 [0.311, 3.039] 1.322 [0.419, 4.176] 8.556 [2.297, 31.871] 0.234 [0.069, 0.799] 7.222 [1.879, 27.755] 2.469 [0.747, 8.163] 6.667 [1.727, 25.737]
0.374 0.287 0.287 0.467 0.546 0.481 0.414 0.455 0.578 0.684 0.244 0.317 0.365 0.443 0.385 0.391 0.377
3.427 9.096 9.096 2.883 2.665 0.291 0.178 2.662 2.474 3.285 NN3.43 5.741 3.626 2.772 0.143 3.496 3.935
0.844 0.631 0.631 0.955 0.991 0.892 0.753 0.081 0.955 0.375 0.997 0.085 1.000 0.517 0.714 0.825 0.048 0.069 0.320 0.101 0.028 0.069 0.943 0.671 0.866 0.320 0.832
0.951 0.444 0.675 0.551 0.317 0.315 0.212 0.514 0.863 0.315 0.835 0.597 0.155 0.939 0.433 0.853 0.372 0.683 0.135 0.110 0.675 0.853 0.960 0.675 0.404 0.702
1.000 0.557 0.771 0.751 0.354 0.380 0.245 0.566 1.000 0.380 1.000 0.769 0.276 1.000 0.541 1.000 0.547 0.770 0.227 0.143 0.771 1.000 1.000 0.771 0.535 0.762
0.899 0.950 0.541 0.555 0.704 0.487 0.423 0.658 0.643 1.000 0.720 0.264 0.628 0.613 0.643 0.983 0.158 0.088 0.461 0.332 0.850 0.784 0.966 0.365 0.950 0.715
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Heritability estimates Feature
⁎ Highlighted when larger than 0.5 # Highlighted when significant (95% confidence) $ Highlighted when CI (at 95% level) does not include the value 1 ⁎⁎ Highlighted when larger than 0.3 @ Highlighted when the OR is significant and at least as impressive as the COR (credible at the 95% level) ~ Highlighted when larger than 0.8
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(CI = [1.73,25.74]) are statistically significant and the OR satisfied the credibility criterion (COR = 3.94); showing a moderate positive association (PHI = 0.38), and a high Pw = 0.83. These results strongly indicate that the RCA shape may have a genetic contribution. • None of the RCA phenotypes presented significant association to presence of lesions. 4. Study limitations This study presents some limitations associated to the patient sample. Since all patients were referred to a CCTA study due to high risk of coronary artery disease, the sample may be biased towards diseased. Nevertheless, in obtaining a sample with asymptomatic patients, would require volunteers. This preliminary, prospective analysis may serve as a proof of concept towards conducting such study. The possible bias of the patient sample should be considered when interpreting lesion heritability in the LAD, since prior chances of concordance are already latent. Nevertheless, the RCA and LCx arteries presented no heritability of lesion presence. Nonetheless, it is noteworthy that this study presents the first attempt to explore heritability of geometric characteristic of coronary arteries. 5. Final comments This work explored, for the first time, association of coronary artery morphology among sibling patients. More than 20 geometric descriptors were used to characterize the RCA, LAD and LCx arteries of 48 patients (24 siblings). It was found that the RCA scored positive for the largest number of phenotypes, followed by the LAD. The LCx presents the weaker association of morphology among siblings. The LAD was the only artery showing positive association of stenotic lesion among siblings, furthermore, few descriptors indicated some kind of correlation among siblings. Although the lesion presence in the RCA showed no association, the shape (C/Σ) as well as more than 15 geometric descriptors scored positive association among sibling. The LAD artery presented association between phenotypes and presence of lesion in more than 10 phenotypes, while the LCx presented such association only for 2, and the RCA featured no association. Such differences could be related to the intrinsic differences in the hemodynamics loads in the arteries. These results are encouraging, and strongly suggest that morphology of the coronary arterial tree may have genetic mediators. This pilot, prospective study opens the door for a new kind of analysis of coronary artery disease. Conflict of interest The authors report no relationships that could be construed as a conflict of interest References [1] Y. Arbel, D. Dvir, M.S. Feinberg, R. Beigel, M. Shechter, The association between right coronary artery morphology and endothelial function, Int. J. Cardiol. 115 (1) (Jan. 2007) 19–23. [2] H. Bogunovic, J.M. Pozo, R. Cárdenes, M.C. Villa-Uriol, R. Blanc, M. Piotin, A.F. Frangi, Automated landmarking and geometric characterization of the carotid siphon, Med. Image Anal. 16 (4) (May 2012) 889–903. [3] C.A. Bulant, P.J. Blanco, A. Clausse, C. Bezerra, T.P. Lima, L.F.R. Ávila, P.A. Lemos, R.A. Feijóo, Thermodynamic Analogies for the Characterization of 3D Human Coronary Arteries, Pattern Recogn. Lett. (2016) (Submitted for publication). [4] C.A. Bulant, P.J. Blanco, A. Clausse, A.N. Assunção, T.P. Lima, L.F.R. Ávila, R.A. Feijóo, L. P.A., Association between three-Dimensional Vessel Geometry and the Presence of Atherosclerotic Plaque in the Left Anterior Descending Coronary Artery of HighRisk Patients, Biomed. Signal Process. Control (2016) (Submitted for publication). [5] C.A. Bulant, P.J. Blanco, T.P. Lima, A.N. Assunção, G. Liberato, J.R. Parga, L.F.R. Ávila, A.C. Pereira, R.A. Feijóo, P.A. Lemos, A Computational Framework to Characterize and Compare the Geometry of Coronary Networks, International Journal for Numerical Methods in Biomedical Engineering, 2016. [6] J. Cornfield. A method of estimating comparative rates from clinical data; applications to cancer of the lung, breast, and cervix. J. Natl Cancer Inst., 11(6):1269–1275.
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Contents lists available at ScienceDirect
International Journal of Cardiology journal homepage: www.elsevier.com/locate/ijcard
On the search of arterial geometry heritability Carlos A. Bulant a,⁎,1, Pablo J. Blanco a,1, Alexandre Pereira b, Thais P. Lima b, Antonildes N. Assunção b, Gabriela Liberato b, Cristiano G. Bezerra b, Jose R. Parga b, Luiz F. Ávila b, Raúl A. Feijóo a,1, Pedro A. Lemos b a b
Laboratório Nacional de Computação Científica, LNCC/MCTI, Av. Getúlio Vargas 333, Quitandinha, 25651-075 Petrópolis, Brazil Heart Institute, University of São Paulo Medical School, INCOR-FM-USP, Av. Dr. Eneas de Carvalho Aguiar, 44, 3rd floor, São Paulo, SP 05403-000, Brazil
a r t i c l e
i n f o
Article history: Received 25 May 2016 Accepted 4 July 2016 Available online 7 July 2016 Keywords: Coronary arteries Geometric descriptors Heritability Geometric risk factors
a b s t r a c t Background: Geometrical risk factors for CAD have been previously proposed before. To date, however, the effect of those factors is not conclusive, and remains as an open research field. Here, we hypothesize that some of these factors have a genetic component explaining inter-individual variability. Objective: To detect heritability indicators of the coronary arterial geometry. Materials and methods: A patient sample of 48 individuals, consisting of 24 siblings, was used. Three dimensional geometry of the LAD, LCx and RCA were reconstructed from standard CCTA. Arterial models were characterized in terms of 20+ geometric descriptors (phenotypes). A comprehensive statistical analysis to detect potential heritability of such phenotypes was employed. Heritability was assessed by means of several statistical indexes. Finally, the association of phenotypes to stenotic lesion is also reported. Results: The RCA scored positive indications for heritability in 15+ phenotypes, while the LAD in 10 and the LCx in only 3 phenotypes. Association between presence of lesion and phenotypes was higher in the LAD, 10 + phenotypes, while for the LCx only 2 phenotypes were significantly associated, and none association was found for the RCA. Conclusion: The RCA showed potential heritability for the largest number of phenotypes, followed by the LAD. The LCx presents the weaker association of morphology among siblings. Regarding lesion-geometry associations, the there are hints of an underlying relation in the LAD, the LCx featured a weaker association and the RCA showed none. This difference could be related to the different hemodynamic environments in these arteries. © 2016 Elsevier Ireland Ltd. All rights reserved.
1. Introduction Coronary artery disease (CAD) continues as the leading cause of death worldwide for several decades now [25]. Ever increasing efforts in the identification of risk factors for CAD have been observed. As a consequence, several risk factors have been recognized, comprising mainly modifiable and non-modifiable systemic factors, such as cigarette smoking, diabetes mellitus, hypertension, hypercholesterolemia, familial history [26–28] and genetic contribution to susceptibility for CAD [9,29–33]. However, whether systemic risk factors can be fully accounted for the burden and presentation of CAD in a given individual remains controversial [34–36], mainly because they do not explain the localization and non-uniformity of atherosclerosis distribution [37,38]. Such medical observations motivated the search for biomechanical and geometrical features involved in the local atherosclerotic process. ⁎ Corresponding author. E-mail addresses: [email protected] (C.A. Bulant), [email protected] (P.J. Blanco), [email protected] (R.A. Feijóo). 1 Tel.: +55-24-2233-6067; fax: +55-24-2233-6071.
http://dx.doi.org/10.1016/j.ijcard.2016.07.064 0167-5273/© 2016 Elsevier Ireland Ltd. All rights reserved.
The effects of biomechanical (e.g. wall shear stress and oscillatory shear index) [39–44], as well as the geometrical factors [1,7,8,11,12, 45,46], have been previously suggested to quantitatively and qualitatively affect atherosclerosis. To date, however, the effects of such factors are not conclusive, and remain as an open research field in the biomechanical community. The idea that specific geometric descriptors might be heritable, like other morphological characteristics are, was hypothesized, but not studied, in the context of geometric risk factors for CAD [11,12]. Although the heritability of stenosis characteristics such as localization, extent and morphology, as well as risk of coronary events in siblings has been studied before [9,10], there is no precedent work in the medical literature addressing the hypothesis of arterial geometry heritability. In a recent study [5], Bulant et al. presented a comprehensive geometric and morphometric analysis of the coronary arteries. Intra and inter coronary associations of the geometric descriptors where studied. Furthermore, they presented evidence of an underlying similarity among siblings in terms of geometric features of the coronary arterial tree. The present work aims to investigate if such similarity can be tracked to individual geometric descriptors of the major coronary
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arteries. That is, the present analysis is focused on the right coronary artery (RCA), the left anterior descending artery (LAD) and the left circumflex artery (LCx). The rest of the document is organized as follows: Section 2 describes the image acquisition processing tools, the patient sample, and summarizes the statistical analysis to be used. In Section 3 results are presented and discussed. Limitations are outlined in Section 4, and conclusions are presented in Section 5.
indentation of at least the width of the artery (in at least one view angle). Any RCA that did not comply with this definition is defined as C-Shape RCA. From the original sample of 48 patients, one RCA model could not be classified because the artery appeared too short in the CCTA image. This patient and the associated sibling were not taken into account in the statistical analysis of the shape phenotype, but where used in the calculations of all other phenotypes. Expert classification resulted in 30 C and 16 Σ shaped RCA. Despite the familial relationship present in the data set, it was shown in [5] that the patient sample is representative in terms of anatomical description of the coronary vasculature, i.e. circulation dominance, radius measurements and arterial occurrence/ distribution.
2. Materials and methods 2.3. Statistical analysis 2.1. Image acquisition and processing Arterial models are obtained from non-invasive Coronary Computed Tomography Angiography (CCTA) medical images, using acquisition protocols and the processing methodology described in [5]. Fig. 1 illustrates coronary arterial trees obtained through the image processing pipeline. Three-dimensional arteries are represented by the so-called centerline structures. Centerlines are widely accepted representations of arterial segments [2,16–19,23,24], because they retain most of the geometric characteristics of arteries in a compact and simple structure. Three-dimensional centerlines are represented by polylines with point-wise information (e.g. lumen radius). Furthermore, centerlines admit classic differential geometry analysis to compute, for example, curvature and torsion. Fig. 2 presents centerlines of the complete coronary tree for two pairs of siblings and emphasizes the similarities in the LAD and RCA arteries. Arterial centerlines can be characterized by several geometric descriptors available in the literature. In this work, for any given artery A, a set of 25 descriptors is used (see Table 1). In addition, the presence of a stenotic lesion (of any grade and tissue type) is used as an additional descriptor. Furthermore, for the RCA, the shape (C or Σ) is also used as a descriptor. In this work, the terms descriptor, feature, variable and phenotype are used as synonyms. It is important to remark that, continuous variables are normalized in order to have a sample-wide zero mean and unit variance. Such normalization is performed for each arterial group separately. 2.2. Patient sample The patient sample used in this work is described in [5]. Such sample consists of 48 patients, formed by 24 pairs of siblings. Making a total of 14 female and 34 male patients with an average age of 53 ± 13 years old. All patients have at least one of the major CAD systemic risks factors (smoker, hypertension, diabetes or dyslipidemia). This work focuses on the analysis of the main coronary arteries, namely: right coronary artery (RCA), left anterior descending coronary artery (LAD) and left circumflex coronary artery (LCx). Existence of arterial lesions in the arteries was specified by physicians, lesions are characterized according to [20] using a tuple of three variables, namely: stenosis grade, tissue type and lesion position. An artery was considered as diseased when a stenotic lesion of any grade, tissue and position was present in the artery. From the 48 patients, 27 LAD, 12 LCx, and 19 RCA arteries were found to be diseased. Furthermore, 28 patients presented at least one diseased artery, the 20 remaining patients featured healthy coronary vasculatures. In turn, the RCA shape was also classified by a specialist directly from the geometrical models. Different classification criteria had been used in the literature, for example, some authors [7,8] defined shape from manual measurements of distance in the angiographic image. In this work, the criterion defined in [1] was used: Σ-Shape arteries have an
Standard statistical indicators, summarized in Table 2, are used to analyze each arterial descriptor for each of the major coronary arteries. Tests for categorical or binary variables are marked with (D) symbol and tests for continuous or ordinal variables are identified with (C) symbol in Table 2. Continuous variables were tested as well as categorical parameters, after being dichotomized, using the mean value of the feature for the patient sample as a cutoff value (i.e. hereafter, saying that a patient tested positive for a given feature, means that the feature value is greater than the mean of the sample); therefore, these types of tests should be interpreted as association of the feature between siblings relative to the sample-mean value of the feature. Association between phenotypes and presence of lesion is assessed by means of standards two-tailed Chi-square, exact Fisher's and Mann-Whitney (U) tests. Statistical significance is assumed at 95% confident interval.
3. Results and discussion 3.1. Left anterior descending coronary artery Table 3 presents the quantitative values for all indicators presented in Table 2, when assessing individual geometric features of the LAD in the patient sample. From these results, it can be inferred that there is a relationship between geometric descriptors of the LAD artery among siblings, particularly, it is noteworthy to remark the following. • The lesion presence in the LAD, which is a binary phenotype (variable), obtained the highest values of PBWR, indicating that the probability of a patient having a lesion in the LAD increases if his sibling has a lesion in the same artery. The SimI test also indicates that the chances of both siblings having the same LAD status (healthy or diseased) is high (70%). It was found that the RR is high (2.22) and statistically significant (CI = [1.16,4.23]). Furthermore, the OR = 5.71 (CI = [1.63, 19.95]) is also significant and credible (COR = 3.62), with a moderate positive association (PHI = 0.36), and a high Pw = 0.82. These results agree with the literature reporting that familial history of CADs is a risk factor [9,10]. • When dichotomizing continuous variables by the mean in the sample, it was found that:
Fig. 1. Illustration of various coronary arterial trees segmentations.
C.A. Bulant et al. / International Journal of Cardiology 221 (2016) 1013–1021
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Fig. 2. Comparison of two pairs of siblings, the first pair is constituted by pink (P) and red (R) centerlines while the second pair are yellow (Y) and cream (C) centerlines. The first three columns present comparison between the four patients while the fourth column compares the LAD (top) and RCA (bottom) arteries of all patients.
– Several geometric features scored high PBWR; – The RR and OR result in statistically significant association, around 2 and 3.9 respectively, for the mean radius (r), the mean combined curvature (ζ ) and curvature-derived entropy (Hκ) although none of them satisfied the credibility criterion. – In turn, SimI N 0.5 for several features indicates that the probability of both siblings having feature values greater or lower than the mean is high, specially for the tortuosity (χ) and lesion presence. • Test for continuous variables, are also worth of discussion:
LCx shows less heritability than the LAD and RCA (see Section 2.3). Particularly, it is noteworthy to remark the following. • The lesion presence in the LCx does not present statistically significant values of RR nor OR. Furthermore the PBWR and Pw are small. Such results indicate that for any given patient, it would not be appropriate to assume risk of lesion in the LCx, given that his sibling has a lesion in the same artery. • When dichotomizing continuous variables by the mean of the sample yields:
– Pearson's correlation coefficient (ρ), scores significant values (pρ b 0.05) for tortuosity (χ), total curvature (κT) and bending energy (ξκ). – The ICC presented weak (but significant association) for the total curvature and torsion (κT,τT), the bending energy (ξκ) and for the intersection counting temperature and entropy (Tn,Hn).
– Some geometric features score high PBWR; – The RR and OR scored significant values for the mean and total curvature (κ;κ T ) and Tn. Nevertheless, the credibility criterion was only satisfied by the κ and κT, both with good Pw, 82.5% and 78.5%; – In turn, SimI N 0.5 for several features indicates that the probability of both siblings having feature values greater or lower than the mean is high. Particularly for κ and κT.
• Association between LAD phenotypes and presence of lesions showed significant levels for the following set { ‘, κT, ζT, ξκ, ϱ, Υ, β, κ d, Tκ, Tn, Hn). From this set, only the {Tn, Hn, ξκ, κT} scored some kind of heritability (ICC or ρ) different from the SimI.
• Test for continuous phenotypes was not statistically significant for any phenotype. • Association between LCx phenotypes and presence of lesions showed significant levels only for Pn and Λτ, none of which scored some kind of heritability.
3.2. Left circumflex coronary artery 3.3. Right coronary artery Table 4 presents the quantitative values for all indicators presented in Table 2, when assessing individual geometric features of the LCx in the patient sample. In agreement with the results presented in [5], the
Table 5 presents the quantitative values for all indicators presented in Table 2, when assessing individual geometric features of the
Table 1 List of geometrical and morphological descriptors. When appropriate, bibliographic reference that reports previous use in the related literature is given. Spatially-distributed features are condensed in mean and total values, i.e. curvature and torsion. Descriptor list Branch count (Υ) Tortuosity (χ) [19] Curvature [19], mean (κ) and total (κT) Combined curvature [18], mean (ζ ) and total (ζT) Curvature ratio (Λκ) [2] Bending energy (ξκ) [16] Fractal dimension (ϱ) [23] Offspring mean raising angle (β) Intersection-counting entropy (Hn) [3] Intersection counting temperature (Pn) [3] Point-wise curvature temperature (Tκ) [3] Lesion presence
Length (‘Þ Radius,mean (r) Torsion [19], mean (τ) and total (τT) Aspect ratio (Λr) [17] Torsion ratio (Λτ) [2] Twisting energy (ξτ) [16] Rising angle (α) Average distal curvature (κ d ) [4] Intersection-counting temperature (Tn) [3] Point-wise curvature entropy (Hκ) [3] Point-wise curvature pressure (Pκ) [3] RCA shape, C/Σ [8]
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Table 2 Summary of statistical indicators of similarity/association of feature values to the sibling condition. Indicator name
Brief description
ProbandWise ratio, PBWR [D]
Probability that a patient tests positive given that his sibling tested positive. The PBWR is a standard choice for establishing the concordance rate between pairs of patients [15].
Similarity Index, SimI [D]
Probability of both siblings having the same test results.
Pearson correlation coeff., ρ [C]
Measures association of descriptors on a siblings-sibling basis. The p-value is obtained from testing the hypothesis of no correlation against the alternative that there is a nonzero correlation. In this work, if p b 0.05, the correlation ρ is considered to be significantly different from zero.
Interclass corr. coeff., ICC [C]
Describes how strongly siblings resemble each other. The One-way random single measures is used [14]. In addition to estimation of ICC, a hypothesis test is performed with the null hypothesis that ICC = 0. In this work, p-ICC b0.05 indicates statistical significance for the ICC value.
Risk-ratio or relative-risk, RR [D]
In epidemiological terms [21], RR is the risk of testing positive for individuals with a given susceptibility genotype (in this case the sibling tested positive), divided by the risk of disease for those without it. In addition, the confidence interval (RR CI), can be computed to test for statistical significance. If the Confidence interval contains the value 1, then the RR has no statistical significance.
Odds-ratio, OR [D]
The odds ratio (OR) quantifies how strongly the presence or absence of property A is associated with the presence or absence of property B in a given population. If each individual in a population either does or does not have a property “A”, (e.g. “patient has lesion”), and also either does or does not have a property “B” (e.g. “sibling has lesion”) where both properties are appropriately defined, then a ratio can be formed which quantitatively describes the association between the presence/absence of “A” (patient has lesion) and the presence/absence of “B” (sibling has lesion) for individuals in the population. This ratio is the odds ratio (OR) [6]. Furthermore, an associated confidence interval (OR CI) can be computed to test for statistical significance. If the interval contains the value 1, then the OR is not statistically significant.
Association Parameter, PHI [D]
If the OR CI does not encompass the value OR = 1, then the Bayesian Credibility Assessment [22] of the test is computed. If the test is credible, the Association Parameter PHI, can be calculated from the associated chi-square statistic of the contingency table used to compute the OR. PHI N0 implies positive association (risk factor). PHI b0 implies negative association (protective factor). |PHI| ≤ 0.3 is considered a weak association. 0.3 b |PHI| ≤ 0.7 is considered moderate association. |PHI| N0.7 is considered a strong association.
Critical Odds Ratio, COR [D]
In some cases, statistical significance of the OR (although a widespread indicator), is not a good indicator of the credibility of a finding (that is, the extent to which it provides convincing evidence for efficacy), as it fails to take full account of the size of the trial, or of pre-existing insights [13]. The credibility of any given OR with statistical significance can be assessed using a Bayesian method [13]. For a given result to meet this standard the prior evidence for efficacy must exceed a specific level; this level is set by the Critical Odds Ratio (COR). The assessment of a given clinical trial result can then proceed as follows: • If the stated 95% CI excludes an OR of 1.00 (corresponding to no effect), the result can be deemed statistically significant at the 95% level; • If OR is at least as impressive as that indicated by the COR, the result can also be deemed credible at the 95% level.
Power, Pw [D]
It stands for the probability of detecting an effect, given that the effect is really there. Or likewise, the probability of rejecting the null hypothesis when it is in fact false [22]. It is recommended a Pw ≥ 0.8, which means that if a study was performed N times, we would see statistically significance difference 80% of the times.
RCA in the patient sample. A large amount of statistically significant associations of feature among siblings was found. These results agree with those reported in [5], where it was shown that the RCA presents higher similarities among siblings than when compared to non siblings. Particularly, it is noteworthy to remark the following.
phenotypes. Particularly, for the bending energy ξκ reached a SimI = 97%, scoring a perfect Pw. • Test for continuous phenotypes yielded:
• The lesion presence in the RCA, has moderate values of PBWR and SimI, 52% and 62% respectively. Nevertheless the RR and OR are not statistically significant. • Dichotomization of continuous variables by the sample mean shows that:
– Pearson's correlation coefficient (ρ), scored significant values (p b 0.05) for several features, among them: length (‘), tortuosity (χ), mean radius (r), mean/total curvature (κ, κT), total combined curvature (ζT), aspect/curvature ratios (Λr,Λκ), bending/twisting energies (ξκ,ξτ), fractal dimension (ϱ) and temperature/entropy associated to intersection counting (Tn,Hn). – The ICC also scored statistically significant values for these features and for the mean offspring rise angle.
– Several geometric features score high PBWR, above 70%; – The number of features with significant values of RR and OR is higher than in the LAD and LCx cases, several of which also satisfied the credibility criterion and featured high Pw values. – Furthermore, it was obtained SimI N 0.5 for several features, resulting in higher values than in the LAD and LCx arteries for the same
• The RCA has an extra phenotype, the Σ-shaped (binary variable). It is noteworthy that a high degree of heritability of the arterial shape is indicated by all tests. It was found that, the PBWR is 62%; the SimI indicates high probability (73% chance) that both siblings have the same shape (C or Σ); The RR = 3.13 (CI = [1.39,7.03]) and OR = 6.67
Table 3 Statistical indicators for individual geometric descriptor similarity for the LAD artery. Association to lesion presence
PBWR
SimI⁎
ρ#
ICC#
RR [CI]$
OR [CI]$
PHI⁎⁎
COR@
Pw~
p- Chi^2#
p- Fisher's#
p-U-Test#
Length Tortuosity Mean radius Mean curvature Total curvature Mean torsion Total torsion Mean Comb. Curv. Total Comb. Curv. Aspect ratio Curvature ratio Torsion ratio Bending energy Twisting energy Fractal dimension Branch count Rising angle Mean offspring rise angle Average distal curvature Temperature (curvature) Preassure (curvature) Entropy (curvature) Temperature (cut points) Preassure (cut points) Entropy (cut points) Lesion Presence
0.552 0.400 0.636 0.375 0.316 0.571 0.571 0.636 0.480 0.571 0.429 0.222 0.333 0.476 0.522 0.609 0.500 0.545 0.316 0.417 0.667 0.692 0.571 0.615 0.609 0.741
0.458 0.750 0.667 0.583 0.458 0.625 0.625 0.667 0.458 0.500 0.667 0.417 0.667 0.542 0.542 0.625 0.500 0.583 0.458 0.417 0.625 0.667 0.625 0.583 0.625 0.708
0.127 0.438 0.300 0.335 0.474 0.180 0.355 0.179 0.087 0.078 0.317 0.178 0.725 0.174 0.188 0.177 (0.006) 0.032 0.057 (0.234) 0.067 0.196 0.396 0.180 0.404 -
0.147 0.108 0.312 0.305 0.371 0.187 0.358 0.186 0.102 0.098 0.303 0.193 0.338 0.194 0.183 0.182 0.013 0.052 0.048 (0.227) 0.077 0.167 0.344 0.121 0.363 -
0.806 [0.515, 1.262] 2.533 [0.881, 7.284] 2.068 [1.072, 3.991] 1.200 [0.531, 2.711] 0.704 [0.324, 1.530] 1.714 [0.895, 3.282] 1.714 [0.895, 3.282] 2.068 [1.072, 3.991] 0.849 [0.493, 1.462] 0.952 [0.589, 1.540] 1.821 [0.774, 4.288] 0.476 [0.185, 1.225] 1.500 [0.548, 4.105] 1.169 [0.617, 2.214] 1.186 [0.657, 2.140] 1.691 [0.912, 3.133] 1.000 [0.568, 1.761] 1.418 [0.764, 2.631] 0.704 [0.324, 1.530] 0.714 [0.399, 1.278] 1.556 [0.887, 2.727] 1.904 [1.035, 3.501] 1.714 [0.895, 3.282] 1.354 [0.782, 2.345] 1.691 [0.912, 3.133] 2.222 [1.166, 4.234]
0.568 [0.169, 1.911] 3.556 [0.765, 16.528] 3.938 [1.182, 13.117] 1.320 [0.375, 4.645] 0.568 [0.169, 1.911] 2.667 [0.821, 8.659] 2.667 [0.821, 8.659] 3.938 [1.182, 13.117] 0.710 [0.228, 2.216] 0.889 [0.277, 2.854] 2.438 [0.650, 9.145] 0.327 [0.087, 1.226] 1.750 [0.417, 7.346] 1.322 [0.419, 4.176] 1.388 [0.445, 4.329] 2.765 [0.859, 8.907] 1.000 [0.323, 3.101] 1.920 [0.606, 6.080] 0.568 [0.169, 1.911] 0.510 [0.162, 1.608] 2.667 [0.821, 8.659] 3.938 [1.182, 13.117] 2.667 [0.821, 8.659] 1.920 [0.606, 6.080] 2.765 [0.859, 8.907] 5.714 [1.636, 19.957]
0.287 0.287 0.287 0.365
9.096 9.096 9.096 3.626
0.143 0.403 0.631 0.066 0.143 0.375 0.375 0.631 0.085 0.039 0.276 0.387 0.130 0.069 0.081 0.403 0.025 0.196 0.143 0.207 0.375 0.631 0.375 0.196 0.403 0.825
0.026 0.067 0.633 0.081 0.028 0.289 0.289 0.533 0.081 0.190 0.212 0.299 0.017 0.088 0.021 0.018 0.884 0.028 0.003 0.004 0.493 0.755 0.034 0.271 0.051 -
0.237 0.297 0.561 0.237 0.039 0.771 0.771 0.776 0.259 0.382 0.750 0.765 0.095 0.382 0.145 0.040 0.561 0.019 0.008 0.080 0.565 0.776 0.144 0.244 0.383 -
0.005 0.062 0.448 0.088 0.014 0.448 0.357 0.498 0.037 0.194 0.159 0.448 0.008 0.074 0.020 0.036 0.892 0.060 0.002 0.006 0.607 0.665 0.030 0.291 0.048 -
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Heritability estimates Feature
⁎ Highlighted when larger than 0.5 # Highlighted when significant (95% confidence) $ Highlighted when CI (at 95% level) does not include the value 1 ⁎⁎ Highlighted when larger than 0.3 @ Highlighted when the OR is significant and at least as impressive as the COR (credible at the 95% level.) ~ Highlighted when larger than 0.8
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Table 4 Statistical indicators for individual geometric descriptor similarity for the LCx artery.
Feature
PBWR
Length Tortuosity Mean radius Mean curvature Total curvature Mean torsion Total torsion Mean Comb. Curv. Total Comb. Curv. Aspect ratio Curvature ratio Torsion ratio Bending energy Twisting energy Fractal dimension Branch count Rising angle Mean offspring rise angle Average distal curvature Temperature (curvature) Preassure (curvature) Entropy (curvature) Temperature (cut points) Preassure (cut points) Entropy (cut points) Lesion Presence
0.545 0.476 0.526 0.667 0.632 0.462 0.480 0.545 0.545 0.400 0.250 0.444 0.286 0.375 0.476 0.500 0.522 0.500 0.375 0.333 0.667 0.667 0.545 0.462 0.545 0.167
0.583 0.542 0.625 0.708 0.708 0.417 0.458 0.583 0.583 0.375 0.500 0.583 0.583 0.583 0.542 0.583 0.542 0.583 0.583 0.333 0.583 0.583 0.583 0.417 0.583 0.583
#
#
$
ρ
ICC
RR [CI]
0.055 (0.066) (0.069) 0.292 0.126 (0.174) (0.066) 0.401 0.133 (0.098) (0.095) 0.057 0.007 (0.109) 0.004 0.320 0.223 0.070 0.219 (0.256) 0.089 (0.053) 0.034 (0.076) 0.037 -
0.068 (0.047) (0.058) 0.307 0.130 (0.154) (0.046) 0.404 0.100 (0.072) (0.067) 0.071 0.005 (0.081) 0.024 0.262 0.218 0.077 0.235 (0.237) 0.106 (0.034) 0.055 (0.059) 0.057 -
1.418 [0.764, 2.631] 1.169 [0.617, 2.214] 1.696 [0.850, 3.382] 2.571 [1.270, 5.208] 2.617 [1.260, 5.435] 0.725 [0.430, 1.222] 0.849 [0.493, 1.462] 1.418 [0.764, 2.631] 1.418 [0.764, 2.631] 0.613 [0.348, 1.079] 0.667 [0.255, 1.740] 1.333 [0.647, 2.748] 0.971 [0.365, 2.584] 1.200 [0.531, 2.711] 1.169 [0.617, 2.214] 1.400 [0.722, 2.716] 1.186 [0.657, 2.140] 1.400 [0.722, 2.716] 1.200 [0.531, 2.711] 0.500 [0.266, 0.941] 1.200 [0.739, 1.948] 1.200 [0.739, 1.948] 1.418 [0.764, 2.631] 0.725 [0.430, 1.222] 1.418 [0.764, 2.631] 0.600 [0.152, 2.362]
⁎ Highlighted when larger than 0.5 # Highlighted when significant (95% confidence) $ Highlighted when CI (at 95% level) does not include the value 1 ⁎⁎ Highlighted when larger than 0.3 @ Highlighted when the OR is significant and at least as impressive as the COR (credible at the 95% level.) ~ Highlighted when larger than 0.8
Association to lesion presence OR [CI]
PHI⁎⁎
COR
1.920 [0.606, 6.080] 1.322 [0.419, 4.176] 2.469 [0.747, 8.163] 5.714 [1.636, 19.957] 5.388 [1.525, 19.029] 0.490 [0.153, 1.565] 0.710 [0.228, 2.216] 1.920 [0.606, 6.080] 1.920 [0.606, 6.080] 0.356 [0.110, 1.149] 0.556 [0.146, 2.119] 1.600 [0.482, 5.313] 0.960 [0.243, 3.794] 1.320 [0.375, 4.645] 1.322 [0.419, 4.176] 1.800 [0.559, 5.792] 1.388 [0.445, 4.329] 1.800 [0.559, 5.792] 1.320 [0.375, 4.645] 0.250 [0.075, 0.830] 1.600 [0.482, 5.313] 1.600 [0.482, 5.313] 1.920 [0.606, 6.080] 0.490 [0.153, 1.565] 1.920 [0.606, 6.080] 0.520 [0.097, 2.802]
0.365 0.347 0.375 -
3.626 4.169 0.125 -
$
@
~
Pw
p- Chi^2#
p- Fisher's#
p-U-Test#
0.196 0.069 0.320 0.825 0.785 0.223 0.085 0.196 0.196 0.413 0.126 0.119 0.028 0.066 0.069 0.165 0.081 0.165 0.066 0.645 0.119 0.119 0.196 0.223 0.196 0.095
0.094 0.240 0.394 0.614 0.865 0.738 0.868 0.316 0.094 0.868 0.480 0.016 0.714 0.480 0.065 1.000 0.617 0.499 0.480 0.505 0.731 0.731 0.094 0.019 0.094 -
0.111 0.319 0.501 0.741 1.000 1.000 1.000 0.341 0.111 1.000 0.500 0.036 0.726 0.500 0.095 1.000 0.743 0.737 0.500 0.740 0.743 0.743 0.111 0.042 0.111 -
0.229 0.080 0.439 0.748 0.186 0.642 0.660 0.300 0.131 0.877 0.398 0.020 0.186 0.098 0.098 0.769 0.915 0.202 0.660 0.766 0.385 0.279 0.194 0.019 0.179 -
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Heritability estimates SimI⁎
Table 5 Statistical indicators for individual geometric descriptor similarity for the RCA artery. Association to lesion presence
PBWR
SimI⁎
ρ#
ICC#
RR [CI]$
OR [CI]$
PHI⁎⁎
COR@
Pw~
p- Chi^2#
p- Fisher's#
p-U-Test#
Length Tortuosity Mean radius Mean curvature Total curvature Mean torsion Total torsion Mean Comb. Curv. Total Comb. Curv. Aspect ratio Curvature ratio Torsion ratio Bending energy Twisting energy Fractal dimension Branch count Rising angle Mean offspring rise angle Average distal curvature Temperature (curvature) Preassure (curvature) Entropy (curvature) Temperature (cut points) Preassure (cut points) Entropy (cut points) Lesion Presence Σ-Shaped
0.696 0.636 0.636 0.667 0.714 0.370 0.429 0.522 0.727 0.571 0.750 0.435 0.800 0.556 0.588 0.667 0.421 0.476 0.526 0.519 0.538 0.593 0.700 0.273 0.625 0.526 0.625
0.708 0.667 0.667 0.792 0.833 0.292 0.333 0.542 0.750 0.625 0.833 0.458 0.917 0.667 0.708 0.708 0.542 0.542 0.625 0.458 0.500 0.542 0.750 0.333 0.750 0.625 0.739
0.555 0.480 0.622 0.607 0.823 (0.189) (0.161) (0.025) 0.629 0.579 0.446 0.063 0.836 0.523 0.483 0.316 0.065 0.374 0.472 0.117 0.259 0.301 0.519 (0.054) 0.732 -
0.539 0.489 0.586 0.617 0.800 (0.161) (0.130) (0.018) 0.626 0.563 0.417 0.064 0.769 0.508 0.493 0.284 0.066 0.391 0.472 0.133 0.264 0.301 0.458 (0.117) 0.602 -
2.484 [1.253, 4.925] 2.068 [1.072, 3.991] 2.068 [1.072, 3.991] 4.400 [1.819, 10.641] 6.071 [2.282, 16.150] 0.458 [0.268, 0.780] 0.536 [0.331, 0.866] 1.186 [0.657, 2.140] 3.152 [1.493, 6.652] 1.714 [0.895, 3.282] 6.000 [2.299, 15.660] 0.836 [0.459, 1.522] 15.20 [3.808, 60.665] 2.083 [1.011, 4.293] 2.605 [1.214, 5.590] 2.571 [1.270, 5.208] 1.110 [0.549, 2.243] 1.169 [0.617, 2.214] 1.696 [0.850, 3.382] 0.838 [0.511, 1.374] 0.987 [0.586, 1.663] 1.131 [0.677, 1.891] 3.267 [1.520, 7.021] 0.443 [0.210, 0.935] 3.333 [1.475, 7.531] 1.696 [0.850, 3.382] 3.125 [1.390, 7.025]
5.878 [1.692, 20.421] 3.938 [1.182, 13.117] 3.938 [1.182, 13.117] 11.20 [2.668, 47.015] 18.75 [3.941, 89.209] 0.138 [0.036, 0.529] 0.188 [0.050, 0.707] 1.388 [0.445, 4.329] 8.889 [2.402, 32.900] 2.667 [0.821, 8.659] 21.00 [4.493, 98.161] 0.710 [0.228, 2.216] 72.00 [8.778, 590.536] 3.438 [1.002, 11.790] 4.898 [1.360, 17.639] 5.714 [1.636, 19.957] 1.190 [0.366, 3.872] 1.322 [0.419, 4.176] 2.469 [0.747, 8.163] 0.663 [0.208, 2.114] 0.972 [0.311, 3.039] 1.322 [0.419, 4.176] 8.556 [2.297, 31.871] 0.234 [0.069, 0.799] 7.222 [1.879, 27.755] 2.469 [0.747, 8.163] 6.667 [1.727, 25.737]
0.374 0.287 0.287 0.467 0.546 0.481 0.414 0.455 0.578 0.684 0.244 0.317 0.365 0.443 0.385 0.391 0.377
3.427 9.096 9.096 2.883 2.665 0.291 0.178 2.662 2.474 3.285 NN3.43 5.741 3.626 2.772 0.143 3.496 3.935
0.844 0.631 0.631 0.955 0.991 0.892 0.753 0.081 0.955 0.375 0.997 0.085 1.000 0.517 0.714 0.825 0.048 0.069 0.320 0.101 0.028 0.069 0.943 0.671 0.866 0.320 0.832
0.951 0.444 0.675 0.551 0.317 0.315 0.212 0.514 0.863 0.315 0.835 0.597 0.155 0.939 0.433 0.853 0.372 0.683 0.135 0.110 0.675 0.853 0.960 0.675 0.404 0.702
1.000 0.557 0.771 0.751 0.354 0.380 0.245 0.566 1.000 0.380 1.000 0.769 0.276 1.000 0.541 1.000 0.547 0.770 0.227 0.143 0.771 1.000 1.000 0.771 0.535 0.762
0.899 0.950 0.541 0.555 0.704 0.487 0.423 0.658 0.643 1.000 0.720 0.264 0.628 0.613 0.643 0.983 0.158 0.088 0.461 0.332 0.850 0.784 0.966 0.365 0.950 0.715
C.A. Bulant et al. / International Journal of Cardiology 221 (2016) 1013–1021
Heritability estimates Feature
⁎ Highlighted when larger than 0.5 # Highlighted when significant (95% confidence) $ Highlighted when CI (at 95% level) does not include the value 1 ⁎⁎ Highlighted when larger than 0.3 @ Highlighted when the OR is significant and at least as impressive as the COR (credible at the 95% level) ~ Highlighted when larger than 0.8
1019
1020
C.A. Bulant et al. / International Journal of Cardiology 221 (2016) 1013–1021
(CI = [1.73,25.74]) are statistically significant and the OR satisfied the credibility criterion (COR = 3.94); showing a moderate positive association (PHI = 0.38), and a high Pw = 0.83. These results strongly indicate that the RCA shape may have a genetic contribution. • None of the RCA phenotypes presented significant association to presence of lesions. 4. Study limitations This study presents some limitations associated to the patient sample. Since all patients were referred to a CCTA study due to high risk of coronary artery disease, the sample may be biased towards diseased. Nevertheless, in obtaining a sample with asymptomatic patients, would require volunteers. This preliminary, prospective analysis may serve as a proof of concept towards conducting such study. The possible bias of the patient sample should be considered when interpreting lesion heritability in the LAD, since prior chances of concordance are already latent. Nevertheless, the RCA and LCx arteries presented no heritability of lesion presence. Nonetheless, it is noteworthy that this study presents the first attempt to explore heritability of geometric characteristic of coronary arteries. 5. Final comments This work explored, for the first time, association of coronary artery morphology among sibling patients. More than 20 geometric descriptors were used to characterize the RCA, LAD and LCx arteries of 48 patients (24 siblings). It was found that the RCA scored positive for the largest number of phenotypes, followed by the LAD. The LCx presents the weaker association of morphology among siblings. The LAD was the only artery showing positive association of stenotic lesion among siblings, furthermore, few descriptors indicated some kind of correlation among siblings. Although the lesion presence in the RCA showed no association, the shape (C/Σ) as well as more than 15 geometric descriptors scored positive association among sibling. The LAD artery presented association between phenotypes and presence of lesion in more than 10 phenotypes, while the LCx presented such association only for 2, and the RCA featured no association. Such differences could be related to the intrinsic differences in the hemodynamics loads in the arteries. These results are encouraging, and strongly suggest that morphology of the coronary arterial tree may have genetic mediators. This pilot, prospective study opens the door for a new kind of analysis of coronary artery disease. Conflict of interest The authors report no relationships that could be construed as a conflict of interest References [1] Y. Arbel, D. Dvir, M.S. Feinberg, R. Beigel, M. Shechter, The association between right coronary artery morphology and endothelial function, Int. J. Cardiol. 115 (1) (Jan. 2007) 19–23. [2] H. Bogunovic, J.M. Pozo, R. Cárdenes, M.C. Villa-Uriol, R. Blanc, M. Piotin, A.F. Frangi, Automated landmarking and geometric characterization of the carotid siphon, Med. Image Anal. 16 (4) (May 2012) 889–903. [3] C.A. Bulant, P.J. Blanco, A. Clausse, C. Bezerra, T.P. Lima, L.F.R. Ávila, P.A. Lemos, R.A. Feijóo, Thermodynamic Analogies for the Characterization of 3D Human Coronary Arteries, Pattern Recogn. Lett. (2016) (Submitted for publication). [4] C.A. Bulant, P.J. Blanco, A. Clausse, A.N. Assunção, T.P. Lima, L.F.R. Ávila, R.A. Feijóo, L. P.A., Association between three-Dimensional Vessel Geometry and the Presence of Atherosclerotic Plaque in the Left Anterior Descending Coronary Artery of HighRisk Patients, Biomed. Signal Process. Control (2016) (Submitted for publication). [5] C.A. Bulant, P.J. Blanco, T.P. Lima, A.N. Assunção, G. Liberato, J.R. Parga, L.F.R. Ávila, A.C. Pereira, R.A. Feijóo, P.A. Lemos, A Computational Framework to Characterize and Compare the Geometry of Coronary Networks, International Journal for Numerical Methods in Biomedical Engineering, 2016. [6] J. Cornfield. A method of estimating comparative rates from clinical data; applications to cancer of the lung, breast, and cervix. J. Natl Cancer Inst., 11(6):1269–1275.
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