Fractal Analysis of Right Ventricular Trabeculae in Pulmonary Hypertension

T form a complex mesh of myocardial strands that protrude into the lumen of both ventricular chambers. In the mammalian heart, trabeculae are highly conserved structures believed to be associated with embryonic development of the coronary vasculature and conduction system (1). Their physiologic role in adults is uncertain, but numerical simulations suggest they influence vortex formation and promote mechanical efficiency (2,3). Trabecular morphology in the left ventricle (LV) is associated with environmental and hemodynamic factors, indicating that it might be a modifiable phenotype that adapts to altered loading conditions (4). A similar response is observed in the right ventricle (RV), where elevated afterload in patients with pulmonary hypertension (PH) leads to hypertrophy of both the compact myocardium and the trabeculae (5). Survival of patients with PH is closely related to RV function; however, there is substantial variability between patients (6), and quantifying trabecular adaptation could offer a sensitive marker of adverse changes in wall stress and remodeling (7). Complex biologic structures, such as trabeculae, have self-similar properties that enable them to be quantified by their fractal dimension (FD). This semiautomated index of trabecular complexity is highly reproducible in the LV in both healthy subjects and patients with disease (4,8). To our knowledge, fractal analysis of the RV has not been previously reported, beyond assessment of tissue morphology in animal models of PH (9); therefore, its value as a marker of RV remodeling is unknown. In our study, we developed software to measure FD in both ventricles in healthy subjects and patients with PH; we assessed its relationship with hemodynamic, functional, and biochemical parameters; and we tested the hypothesis that the addition of FD to conventional risk factors would improve the accuracy of survival prediction. Fractal Analysis of Right Ventricular Trabeculae in Pulmonary Hypertension

T rabeculae form a complex mesh of myocardial strands that protrude into the lumen of both ventricular chambers. In the mammalian heart, trabeculae are highly conserved structures believed to be associated with embryonic development of the coronary vasculature and conduction system (1). Their physiologic role in adults is uncertain, but numerical simulations suggest they influence vortex formation and promote mechanical efficiency (2,3). Trabecular morphology in the left ventricle (LV) is associated with environmental and hemodynamic factors, indicating that it might be a modifiable phenotype that adapts to altered loading conditions (4). A similar response is observed in the right ventricle (RV), where elevated afterload in patients with pulmonary hypertension (PH) leads to hypertrophy of both the compact myocardium and the trabeculae (5). Survival of patients with PH is closely related to RV function; however, there is substantial variability between patients (6), and quantifying trabecular adaptation could offer a sensitive marker of adverse changes in wall stress and remodeling (7).
Complex biologic structures, such as trabeculae, have self-similar properties that enable them to be quantified by their fractal dimension (FD). This semiautomated index of trabecular complexity is highly reproducible in the LV in both healthy subjects and patients with disease (4,8). To our knowledge, fractal analysis of the RV has not been previously reported, beyond assessment of tissue morphology in animal models of PH (9); therefore, its value as a marker of RV remodeling is unknown. In our study, we developed software to measure FD in both ventricles in healthy subjects and patients with PH; we assessed its relationship with hemodynamic, functional, and biochemical parameters; and we tested the hypothesis that the addition of FD to conventional risk factors would improve the accuracy of survival prediction.

Subjects
Our retrospective study was approved by the Health Research Authority. All participants gave written informed consent. Outcome data for all of the patient groups in this study previously have been reported (10). The prior article reported on machine learning algorithms for outcome prediction using motion-based cardiac models, whereas in this article we report on the development of fractal analysis of trabecular complexity. In our single-center observational study, patients referred to The National Pulmonary Hypertension Service at Imperial College Healthcare NHS Trust for routine diagnostic assessment and cardiac imaging between May 2004 and October 2013 were included for analysis. Survival status of subjects was monitored until September 2014 or until the date of surgery in subjects who were undergoing pulmonary endarterectomy or transplantation. A diagnosis of PH was made if the resting mean pulmonary artery pressure was 25 mmHg or higher at right-sided heart catheterization (11). Congenital causes of PH were excluded. Clinical classification was performed in accordance with European guidelines (11). Clinical severity was categorized in accordance with World Health Organization guidelines (12). All patients underwent standard therapy in accordance with current guidelines and NHS England treatment policy (13). In total, 256 matched healthy control subjects were drawn from 1265 participants in the United Kingdom Digital Heart Project who were investigated between February 2011 and July 2016 at the Medical Research Council London Institute of Medical Sciences (14,15).

PH Investigations
Right-sided heart catheterization was performed with a balloon-tipped flow-directed Swan-Ganz catheter (Baxter Healthcare, Irvine, Calif ) to derive cardiac output, mean pulmonary artery pressure, mean pulmonary capillary wedge pressure, and mean pulmonary vascular resistance. We considered pulmo-Abbreviations BSA = body surface area, CI = confidence interval, EF = ejection fraction, FD = fractal dimension, HR = hazard ratio, IQR = interquartile range, LV = left ventricle, PH = pulmonary hypertension, RV = right ventricle Summary Fractal analysis of the right ventricle is practical and reproducible in both healthy subjects and patients with disease, offering insights into cardiac efficiency, hemodynamic adaptation, and tissue characterization in right-sided heart failure; however, it does not provide incremental benefit in predicting survival.

Implications for Patient Care
n Fractal analysis of the right ventricle offers a highly reproducible semiautomated technique to measure trabeculation.
n Fractal analysis may be of value in assessing right ventricular functional adaptation to pulmonary hypertension, which is a key determinant of survival.
n Fractal dimension is more strongly correlated with pulmonary vascular resistance than compacted ventricular mass, suggesting that trabeculae have a greater sensitivity to hemodynamic load than does the myocardial wall.
nary vascular resistance as an estimate of RV afterload. B-type natriuretic peptide and 6-minute walk distance were measured; the latter was measured according to the American Thoracic Society guidelines (16).

Imaging Investigations
Cardiac MRI was performed at one site with a 1.5-T Achieva unit (Philips, Best, the Netherlands), and a standard clinical protocol was followed according to published international guidelines (17). Software updates were applied during the course of the study. Ventricular function was assessed using balanced steady-state free precession cine images acquired in conventional cardiac short-and long-axis planes. Typical parameters were as follows: repetition time msec/echo time msec, 3.2/1.6; voxel size, 1.5 3 1.5 3 8.0 mm; flip angle, 60°; and temporal resolution, 29 msec; however, parameters were adjusted from patient to patient, which was in line with routine practice, and not all parameters were constant. Images were stored on an open-source database (MRIdb; Imperial College London, England) (18).

Quantification of Ventricular Function
Indexed biventricular end-diastolic and end-systolic volumes were calculated by analyzing cine images with ViewForum software (Philips), and indexed stroke volume and ejection fraction derived from both ventricles. Heart rate was measured at rest, and cardiac index was calculated as the product of heart rate and stroke volume index. Endocardial borders were defined at end-diastole and end-systole using a standard published protocol (19). Indexed RV mass excluded the interventricular septum and was the sum of the compacted freewall and noncompacted (papillary muscles and trabeculae) mass. All mass and volume measurements were indexed to body surface area (BSA), as estimated with the Mosteller formula.

FD Analysis
FD, a scale-invariant measurement of trabecular complexity, was derived from LV short-axis cine images (Fig 1) by a reader with 5 years of experience (T.J.W.D.) who did not participate in the software development. Analysis was performed with Matlab software (Mathworks, Natick, Mass) by using a custom-written code (FracAnalyse) that has been made freely available online (20). Images were preprocessed with bicubic interpolation to 0.25 3 0.25 mm pixels to enable consistent analysis between subjects acquired at different native resolutions. For each section, a polygonal boundary for each ventricle was manually defined within the midwall myocardium on the first image of the retrospectively gated cine sequence. Subsequent image processing consisted of bias-field correction using histogram stretching, application of a region-based level-set algorithm, and binarization of the blood pool and myocardium (21). The endocardial and trabecular borders were then detected by using a Sobel filter. Trabecular mass and FD were derived from the same contours. FD was calculated by using a standard fully automated box-counting method, in which the target image was overlain by a grid of known box size, and the number of boxes containing nonzero radiology.rsna.org n Radiology: Volume 288: Number 2-August 2018 image pixels was recorded (the box count). This process was repeated with box sizes between two pixels and 45% of the image size (8). Fractal dimension was defined as the negative gradient of an ordinary least-squares fit line to the logarithm of box size and box count. This approach to fractal analysis is similar in principle to previously published algorithms for the LV (22); however, for the RV, a convex hull was applied after image thresholding to ensure the contours were confined to the inner surface of the RV. The following summary measures were derived for both ventricles: for global FD, the mean value from all measured sections was calculated; for maximum apical FD and maximum basal FD, the maximum FD from the apical or basal halves of the ventricle was calculated, in keeping with other studies in the LV (4,23). As the number of short-axis sections varied per subject, FD values were interpolated to a 10-section model. To test interobserver reproducibility, images from 30 patients with PH were analyzed independently by two readers (T.J.W.D., M.Q.; each with 5 years of experience).   ) and healthy con-Mortality prediction was assessed by using univariable Cox regression analysis. Statistically significant univariable parameters were grouped into four categories: noninvasive (demographics and functional status), cardiac MRI (volumetric analysis), invasive (rightsided heart catheterization and B-type natriuretic peptide), and FD. A multivariable nested model was built by the sequential addition of categories of predictors. The purpose of this was to demonstrate the incremental benefit of each parameter group in survival prediction accuracy (pec function, pec R package). We used x 2 analysis to test the significance of adding a parameter group. A baseline reference model was fitted by using a constant rate of death.

Statistical Analyses
To demonstrate out-of-sample accuracy, models were fitted in 80% of the patients with PH (randomly selected), and accuracy was tested in the remaining 20%. This process was repeated 50 times to avoid selection bias. To test the value of trabecular complexity in risk stratification, patients with PH were split into quartiles based on global FD, maximum apical FD, and maximum basal FD, and adjusted Cox regression analysis models were constructed with all significant univariable predictors as covariates (ggcoxadjustedcurves function, survminer R package). The proportional hazards assumption was checked by visualizing the Schoenfeld residuals (ggcoxzph function, survminer R package) and hazard ratio (HR) for survival calculated for each quartile.

Study Population Characteristics
In total, 405 consecutive patients referred for investigation were evaluated for eligibility, and 256 subjects with confirmed PH were enrolled (Fig 2). Of these, 33% (93 of 256) died and 46 underwent either pulmonary endarterectomy or lung transplantation during follow-up. Median length of follow-up was 4.0 years (IQR, 2.0-5.7 years). In this cohort, 6% (16 of 256) of patients were unable to do the 6-minute walk test, and in 25% (66 of 256) BNP levels were unavailable. Anthropometric, hemodynamic, cardiac MRI, and subgroup data are given in Table 1 and Tables E1-E4 (online).
From a cohort of 1265 healthy control subjects, 256 matched participants were selected. Their anthropometric data are also shown in Table 1   In patients with PH, RV global FD was weakly associated with (a) higher indexed RV end-diastolic volume, indexed RV end-systolic volume, heart rate, and cardiac index and (b) lower indexed RV stroke volume and RV EF ( Table 2). In patients with PH, RV global FD was weakly associated with pulmonary vascular resistance (r = 0.30, P , .001) and compacted indexed RV mass (r = 0.19, P = .003) and was moderately associated with noncompacted indexed RV mass (r = 0.59, P , .001). trol (median, 1.309; [IQR, 1.285-1.332]) groups (P , .001). In healthy control subjects, RV global FD was higher in male subjects (P = .003) and showed a weak positive association with BSA (r = 0.30, P , .001) (Fig E2 [online]); however, there was no association with sex (P = .47) or BSA (r = 0.10, P = .12) in patients with PH. Differences in FD were largest near the apex (section seven of ten), where median RV global FD was 1.368 (IQR, 1.326-1.405) in patients with PH and 1.295 (IQR, 1.263-1.334; P , .001) in healthy control subjects.  . (a, b) Left ventricular short-axis images at the base (left), midventricle (center), and apex (right). A polygonal region of interest is manually defined in the myocardium (top row). The enclosed region (red shading) is then used for automated analysis with FracAnalyse, which normalizes contrast, identifies an internal perimeter (middle row), and extracts a binary perimeter (bottom row) for fractal dimension analysis via box counting. (c) Tukey box-and-whisker plots show the relationship between quartiles of RV maximum apical FD and RV ejection fraction (left) and RV end-diastolic volume index (EDVI) (right). The jittered points show data for each subject (n = 256), including data for the patients in a (blue •) and b (red •).  Note.-CI = cardiac index, EDP = end-diastolic pressure, EDVI = end-diastolic volume index, EF = ejection fraction, ESVI = end-systolic volume index, FD = fractal dimension, HR = heart rate, MI = mass index, mPAP = mean pulmonary artery pressure, PVR = pulmonary vascular resistance, RV = right ventricle, SVI = stroke volume index.
In adjusted Cox regression analysis, categorization by RV maximum apical FD yielded greater discrimination in 5-year survival between the first and the fourth quartiles (mean, 19.6 years; 95% CI: 19.6, 19.7) compared with RV global FD (mean, 8.9 years; 95% CI: 8.9, 9.0) or maximum basal FD (mean, 7.3 years; 95% CI: 7.3, 7.4). Out-of-sample validation suggested that gains in the accuracy of survival prediction with the addition of RV maximum apical FD were small (0.2%) compared with adding noninvasive and cardiac MRI parameters and were less than the gain in accuracy from adding invasive parameters (1.7%).

Discussion
The main findings of our study are (a) fractal analysis of RV trabecular complexity is practical in both healthy participants and patients with PH, with excellent interobserver reproducibility; (b) RV FD is higher in patients with PH than in healthy control subjects and weakly correlates with invasive measures of afterload (pulmonary vascular resistance); and (c) FD enables prediction of survival but yields no incremental prognostic benefit over conventional parameters of RV remodeling.
Myocyte lineage tracing suggests that trabeculae have a molecular and developmental identity which is distinct from the compact layer of the RV free wall (24). Blood flow-related transmural stresses during cardiac development may influence trabecular patterning, which typically shows a base-to-apex and lateral-to-septal gradient of complexity (25). The physiologic role of trabeculae in the adult heart is uncertain, but residual whether higher trabecular complexity in patients with PH is simply a passive consequence of remodeling or an adaptive response to maintain contractile efficiency.
Our study had limitations. We assumed that none of the healthy control subjects had an abnormal degree of RV trabeculations, because in studies of the LV there was no evidence that this was a risk factor in asymptomatic adults (33). Despite nearest-neighbor matching, healthy control subjects were younger than patients with PH. Patients commonly have several diagnoses that contribute to PH, although in accordance with international guidelines, classification was made on the predominant cause. We included all subtypes of PH except congenital disease, and although RV failure is a final common pathway, there are differences in physiologic response that depend on the cause of the disease (34). A proportion of patients were selected for surgical intervention; thus, data collection was censored at the time of surgery. This may have led to underestimation of the prognostic strength of FD and related parameters. Fractal dimension is correlated with other hemodynamic and volumetric parameters, indicating its association with loading conditions and remodeling, but it did not enable prediction of survival independently of conventional risk factors. Patients underwent treatment in accordance with current guidelines, though we acknowledge that treatment may influence RV remodeling (35). Imaging protocols were as consistent as possible throughout the study, and we applied spatial interpolation and intensity correction to reduce bias in FD calculation due to variation in acquisition parameters. Future work will assess how well this technique can be generalized to other centers and patient groups.
In conclusion, FD is a reproducible measure of RV trabecular complexity on cardiac MR images, a marker of elevated afterload in patients with PH, and enables prediction of all-cause mortality, though the gains over traditional volumetric markers are not significant.