Geometric Variability of the Abdominal Aorta and Its Major Peripheral ...

Annals of Biomedical Engineering, Vol. 38, No. 3, March 2010 ( 2010) pp. 824–840 DOI: 10.1007/s10439-010-9925-5

Geometric Variability of the Abdominal Aorta and Its Major Peripheral Branches PADRAIG M. O’FLYNN,1,2 GERARD O’SULLIVAN,3 and ABHAY S. PANDIT1,2 1

Department of Mechanical and Biomedical Engineering, National University of Ireland, Galway, University Road, Galway, Ireland; 2National Centre for Biomedical Engineering Science, National University of Ireland, Galway, Galway, Ireland; and 3 Section of Interventional Radiology, University College Hospital, Galway, Galway, Ireland (Received 9 March 2009; accepted 7 January 2010; published online 20 January 2010) Associate Editor Michael B. Lawrence oversaw the review of this article.

Keywords—Peripheral arterial disease, Aortoiliac vessels, Anterior visceral branches, Renal arteries, Bifurcation geometry, Non-planar arterial curvature.

Abstract—Vessel geometry determines blood flow dynamics and plays a crucial role in the pathogenesis of vascular disease. In vivo assessment of three-dimensional (3D) vessel anatomy is vital to improve the realism of arterial flow model geometries and investigate factors associated with the localisation of atherosclerosis. The quantification of vascular geometry is also particularly important for the proper design and preclinical testing of endovascular devices used to treat peripheral arterial disease. The purpose of this study was to quantitatively evaluate the intersubject variability of 3D branching and curvature of the abdominal aorta and its major peripheral arteries. Contrast-enhanced renal MRA scans of healthy abdominal vessels obtained in 12 subjects (8 men, 4 women mean age 49 years, range 27–84 years) were segmented, and smoothed centerlines were determined as descriptors of arterial geometry. Robust techniques were employed to characterise non-planar vessel curvature, arterial taper, and 3D branching parameters. Noticeable 3D curvature and tapering were quantified for the proximal anterior visceral and renal branches. Mean 3D branching angles of 63.5 ± 10.1 and 73.1 ± 6.8 were established for the right and left renal arteries, respectively. Angles describing the ostial position and initial trajectory of the renal arteries confirmed the antero-lateral origin and direction of the right and the more lateral orientation of the left. The anterior visceral branches emerged predominantly from the left side of the anterior aortic wall. Branching parameters determined at the aortic bifurcation demonstrated mild asymmetry and non-planarity at this location. In summary, the results from this study address the scarcity of available in vivo 3D quantitative geometric data relating to the abdominal vasculature and reflect the geometric variability in living subjects.

INTRODUCTION Given the prevalence of atherosclerotic involvement in the abdominal aorta and at the ostia of the renal and anterior visceral branches14,15,22,45,54,68 this region of the vasculature has been the focus of extensive biomedical research. Past investigations have primarily been related to hemodynamic involvement in the pathogenesis and localisation of vascular disease. Hemodynamics in the abdominal aorta and its peripheral branches have been studied, numerically25,33,37,59,60,67,69,70,81 by means of computational fluid dynamics (CFD) and with both qualitative30,35,43,50,58 and quantitative41,42,48,49 experimental flow measurement techniques. More recent patientspecific CFD studies25,67,81 have furthered appreciation for the importance of geometric features, such as anatomically accurate branch trajectory, non-planar arterial curvature, and vessel tapering, on flow patterns. Robust geometric characterisation of abdominal aortic geometry may play an important role in understanding the influence of geometric factors on the origin and progression of vascular disease. Furthermore, examination of variability in geometry among subjects should enable development of more realistic 3D flow models, which are representative of a broader spectrum of the population. Over the last decade catheter-based therapies have emerged as the principal treatment for the vascular pathologies associated with chronic mesenteric ischemia and renovascular hypertension.23 This means that,

Address correspondence to Abhay S. Pandit, Department of Mechanical and Biomedical Engineering, National University of Ireland, Galway, University Road, Galway, Ireland. Electronic mail: [email protected]

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2010 Biomedical Engineering Society

Geometric Variability of the Abdominal Aorta and Its Major Peripheral Branches

aside from relevance to studies of vessel hemodynamics, in vivo aortic and visceral branch geometry has major implications for the design and performance testing of endovascular devices. 3D arterial geometry determines the ease of branch access and catheter placement, which affects technical success during revascularisation procedures. Similarly with placement of an intravascular stent, arterial configuration and vessel movement influence vessel–device interaction and consequently long-term device durability or potential for restenosis. Quantitative knowledge of the asymmetric and non-planar nature of the abdominal aorta and its major peripheral branches may prove useful for endovascular device design and in recreating worst case in vivo anatomic conditions for preclinical fatigue testing and functional device analysis. To date, documentation of the in vivo 3D geometry of the abdominal aorta and visceral arteries has been limited. The anatomical course and branching patterns of the renal and anterior visceral branch arteries are well known1,5,21,38,57,77; however, quantitative studies of in vivo vascular branching of the renal arteries have been confined to 2D analysis of angiograms,17,43 maximum intensity projections (MIPs) from magnetic resonance angiography (MRA),16 and axial transverse views from computed tomography,9,75 while quantitative data regarding the celiac trunk (CT) and superior mesenteric artery (SMA) relate to cadaver studies.52,80 Detailed 3D geometric classification of these sites with objective methods is essential to eliminate the variability introduced by subjective measurements and obviate the errors incurred from planar analysis of arterial anatomy.46 The purpose of this study was to evaluate various geometric parameters relating to the abdominal aorta and its major peripheral branch arteries. Specifically the aims were to investigate intersubject variability in branching angles at visceral and aortic bifurcation sites and quantify 3D curvature, non-planarity and tapering of the abdominal aorta, common iliac arteries, and the proximal anterior visceral and renal branch arteries.

METHODS Image Acquisition Contrast-enhanced renal MRA scans of healthy abdominal vessels obtained in 12 non-consecutive patients (8 men, 4 women mean age 49 years, range 27–84 years) were chosen from retrospective analysis of a larger population of subjects. This group included patients who had undergone renal MRA for a wide variety of indications. Patients with the following conditions were excluded from the study: presence of

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accessory renal arteries, anatomic anomalies of the celiac trunk, renal or anterior visceral artery stenosis or occlusion, incidence of occlusive or aneurysmal disease in the abdominal aorta, and common iliac arteries. Scans obtained with an insufficient bolus of contrast material and those in which the relevant regions of the vasculature were not entirely contained within the image slab were also omitted. All MRA scans had been performed on patients in the supine position during inspiration breath-hold with a 1.5 Tesla MR system (Symphony, Siemens AG Medical Solutions, Erlangen, Germany), coronal orientation using the same imaging protocol. The imaging parameters for the MR acquisitions were repetition time 3.47 ms, echo time 1.42 ms, flip angle 25, and slice thickness 1.5 mm. The field of view was 292.5 9 360 mm with matrix size 416 9 512 giving an in-plane resolution of 0.703 mm pixel1. Characterisation of Arterial Geometry The abdominal aortic vasculature of each subject was segmented from the MRA scans in commercial image processing and editing software (Mimics, Materialise, Sheffield, UK). The original image data for the specified region of interest were resliced to create a project with cubic voxels of width 0.703 mm, and these images were stacked to form a 3D array of voxels. The contrast-filled vasculature was delineated on the medical images with a combination of 3D dynamic region growing and thresholding operations followed by 3D connected component analysis. This segmentation mask was inspected to ensure its outer edge corresponded with the gradient of image intensity at the vessel boundary, and any irregularities arising from MRA intensity variation along the length of the abdominal aorta and its branches were subject to manual editing. Further post-processing was employed to exclude interfering structures close to the arteries of interest, for instance end organs like the kidneys and adjacent vessels such as closely passing renal veins, which were initially included due to leaking of the segmentation algorithm. Anterior visceral branches were truncated and irrelevant aortic branches such as the vertebral arteries and the inferior mesenteric artery were removed by similar 3D editing of the segmentation mask. A triangulated surface model was then generated by tessellation of the voxels on the external bounds of the segmentation mask. Triangulation smoothing was incorporated to eliminate artifacts typically found in the MR data. Conservation of volume was ensured by supplementing standard Laplacian smoothing with a second step to compensate any shrinkage, an approach similar to that described by Cebral and Lohner11 3D surface models of the

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FIGURE 1. 3D volume models of the healthy abdominal aortic vasculature for the 12 subjects under investigation.

Vessel Curvature and Torsion

FIGURE 2. (a) Transparent 3D volume model demonstrating the medial axes determined by the sequential thinning algorithm. (b) Smoothed B-spline centerline representations of the abdominal aorta, common iliac arteries and the proximal 20 mm portions of the anterior visceral and renal branches.

arterial vessels ranging axially from above the celiac trunk to below the iliac bifurcations were rendered (Fig. 1). Medial axes of the vessels of interest were determined for each subject with a sequential thinning algorithm in Mimics (Fig. 2a). Centerline coordinates at a point spacing of 0.5 mm were generated and served as a basis for further anatomic parameter analysis.

The centerline of the entire abdominal aorta was established from a level 10 mm above the celiac trunk to the apex of the aortic bifurcation. Centerline data points at the levels of the anterior visceral and renal arteries and the terminal aorta were omitted as the branching process was observed to influence the medial axis path determined from the thinning algorithm. The common iliac arteries were analyzed bilaterally from their origin to the iliac bifurcation. An initial 20 mm portion of the unpaired visceral branches and main renal arteries was assessed in each subject. This ostial segment, proximal to any branching, was a focus of interest for geometric characterisation as it represents the section most commonly involved in vascular disease26 and thus the most frequent location for intraluminal stent placement.7 Smoothing of vessel centerline data was undertaken in Matlab to remove any local fluctuations of the medial axes due to segmentation surface irregularities resulting from the image noise associated with MR data. A locally weighted regression function was used to smooth x, y, and z centerline coordinate terms as individually plotted vs. arc length (s) of the medial axis, where arc length was that of an interpolant hermite spline. Similar to the moving average smoothing process, the smoothed term was derived from adjacent data points within the prescribed span. A linear polynomial model and a robust weight function, which made the process resistant to outliers, were used in the regression


as these performed best with the challenges posed by the aortic centerline where sections of data points were absent at the visceral branch levels and terminal aorta. A parametric curve description (r(s) = (x(s),y(s),z(s))) for each arterial centerline was obtained by fitting the smoothed data with quintic B-spline curves (Fig. 2b). An appropriate combination of the prescribed span for smoothing and tolerance values for spline fitting were chosen to ensure all spline points, obtained by resampling the fitted curves at constant 0.2 mm intervals, lay within a voxel width of the original medial axis. In addition to scrutiny of maximum and mean distances between the original data coordinates and the B-spline curve, visual inspection of the calculated curvature profile of the fit ensured that spurious high frequency fluctuations in curvature were purged while the amplitude of the real curvature peaks was preserved. Determination of vessel centerline curvature and torsion required employing principles from differential geometry to analyze the parametric equations describing the smooth vessel centerlines. Curvature and torsion effectively describe 3D bending of the vessel and twisting of the plane of curvature in space along its centerline. In this study curvature (j) and torsion (s) were calculated in Matlab using formulae from the Frenet-Serret theory of differential geometry (Eqs. 1 and 2), j¼

s¼

jr0 ðsÞ r00 ðsÞj ½r0 ðsÞ3

½r0 ðsÞ; r00 ðsÞ; r000 ðsÞ jr0 ðsÞ r00 ðsÞj2

ð1Þ

ð2Þ

where r¢(s), r¢¢(s), and r¢¢¢(s) are the first, second, and third derivatives of the centerline curve, |r¢(s) 9 r¢¢(s)| is the magnitude of a cross product, and [r¢(s),r¢¢(s),r¢¢¢(s)] denotes a scalar triple product. Fitted curves therefore needed to be three times differentiable to provide the closed form solutions of derivatives along the arterial path essential for curvature and torsion calculations, a requirement which the quintic B-spline curves employed satisfy. Total, average, and maximum values of curvature and torsion were calculated for all vessel segments from longitudinal profiles, and mean values of these parameters were determined for the subject population. Of note, total curvature and total torsion values are dependent on sampling frequency which was maintained constant at 5 points per mm for each smooth spline centerline fit due to the 0.2 mm point spacing. Arterial Dimensions and Tapering The paths of the abdominal aorta, common iliacs, and renal and visceral branches are typically curved

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and oblique to the body axes, confirming the unsuitability of using standard orthogonal planar reformats to derive true cross-sectional lumen dimensions. In order to obtain a more accurate representation of internal arterial dimensions, minimum, maximum, and best-fit diameters for sections perpendicular to vessel medial axes were determined at prescribed intervals along their length in Mimics (Fig. 3). A series of consecutive diameter measurements were obtained at 0.5 mm intervals for the proximal visceral branch segments and for the entire abdominal aorta. Resulting longitudinal profiles of best-fit diameters for each artery were smoothed to remove any artifacts from image resolution or segmentation with the constraint that maximum deviation from the recorded diameters was limited to 1 pixel width. This was done under the assumption of the presence of physiologically smooth vessels, which is reasonable in the absence of any atherosclerosis, aneurysm, or dissection. Smoothing spline fits were resampled at constant intervals of normalised vessel length. Mean graphs were compiled for best-fit diameters of the visceral vessels and the infrarenal abdominal aorta in the subject population to establish the magnitude of tapering. For these measurements, the infrarenal aorta comprised the vessel from a starting point below the lowest renal branch to the level of the aortic throat. The position of the aortic throat was designated as the cross-section with the smallest lumen area near the level of the transition region proximal to the aortic bifurcation. Analysis was performed separately for the various suprarenal aortic segments between the different visceral branches. Average best-fit vessel diameters were determined for the supraceliac, supramesenteric, and suprarenal segments provided that adjacent branch ostia were adequately spaced from each other and medial axes paths in these regions were not affected by the adjacent branching. Lumen cross-sectional eccentricity (e) was calculated and compiled for the available abdominal aortic segments according to Eq. (3), where a and b, normally the semi-major and semi-minor axes of an ellipse, were taken as half the maximum and minimum diameters, respectively. rffiffiffiffiffiffiffiffiffiffiffiffiffi b2 e¼ 1 2 ð3Þ a Longitudinal profiles of minimum and maximum diameters for the abdominal aortic segments were smoothed prior to calculation of eccentricity. Minimum and maximum diameter profiles required increased smoothing compared to best-fit diameters due to their increased sensitivity to any bumps in the segmentation mask. Smoothing was performed with the constraint that mean and maximum deviations from the recorded

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FIGURE 3. Transparent 3D model demonstrating the mean diameter measurements perpendicular to the medial axes of (a) the suprarenal aortic segments, anterior visceral and renal branches and (b) the infrarenal abdominal aorta and common iliac arteries.

Arterial Branching

branch artery origin and the initial direction of the branch relative to the aorta. The position of a side branch along the length of a main vessel was identified on the basis that the perpendicular distance between a point and a line is also the minimum distance between them. The mid-level of the visceral branches was therefore designated as the point on the aortic spline centerline at which the distance to the branch centerline origin was at a minimum. The 3D aortic centerline distance from the apex of the aortic bifurcation to this point was then recorded as the axial branch location. A normalised centerline distance ratio, defined as the ratio of the axial location of a particular branch to that of the celiac trunk, was calculated for the superior mesenteric and renal arteries in each subject. The local direction of the aorta at each branch was taken as the tangent vector to the aortic centerline at the identified mid-level point. Initial directions of each branch were represented as a vector determined from a linear fit of the proximal 4 mm of the vessel’s centerline (Fig. 4a). The 3D branching angle was then defined as the angle between these two directional vectors calculated using (Eq. 4). bd 1 A ¼ Cos ð4Þ jbj jdj

In this study four parameters were determined to characterise the 3D geometry of each anterior visceral and renal artery branch site. These properties primarily describe the circumferential and axial location of the

In this case b and d represented the directional vectors of the aorta and daughter branch, respectively, while (A) was the true angle in radians. The circumferential location of the origin and initial direction of

diameters were less than 1 and 2 pixel widths, respectively. Comparison of the calculated area value of the elliptical cross-section with that of a circular crosssection defined by the best-fit diameter at each sampling point gave an indication of the validity of assuming half the maximum and minimum diameters as semi-major and semi-minor axes. The percentage difference in area between assumed elliptical and circular cross-sections was calculated for this purpose. All values recorded from analysis of abdominal aortic cross-sections were less than 10%, with average values of 1.5 ± 0.9, 2.1 ± 2.1, 1.8 ± 1.5, and 0.79 ± 0.6% obtained for supraceliac, supramesenteric, suprarenal, and infrarenal segments over the entire range of subjects studied. Lumen cross-sectional eccentricity was reported for the aorta alone in this study because accuracy of this parameter could not be guaranteed with the same level of confidence in the medium-sized visceral or iliac vessels. Given the in-plane resolution and slice thickness of the current scans, there was increased potential for partial volume effects or segmentation errors to considerably impact on the lumen surface reconstruction accuracy in smaller vessels.


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FIGURE 4. (a) 3D directional vectors of the renal and anterior visceral branches with corresponding aortic vectors employed in branching angle calculations (all vectors were positive in the direction of blood flow), (b) Illustration of the nominal branching plane, its normal vector and the 3D directional vectors used for determination of branching parameters at the aortic bifurcation.

FIGURE 5. Schematic representation of angle of trajectory (filled) and angle of origin (arrows) measurements determined in planes perpendicular to the direction of the aorta at renal arteries and visceral branching sites.

each branch relative to the right posterior aspect of the anteroposterior plane were determined in the plane perpendicular to the aortic centerline at the branch mid-level and termed the angle of origin and angle of trajectory, respectively (Fig. 5). The vector describing branch origin was determined from the aortic centerline point and the most proximal point on the branch centerline, while the projection of the branch directional vector d onto this plane used in calculation of the angle of trajectory is given by Eq. (5) db dproj ¼ jdj sin A b ð5Þ j d bj where b which is the tangent to the aortic centerline also serves as the normal vector of the perpendicular plane.

The 3D geometry of the terminal aortic bifurcation was characterised by five angles which aimed to define the branching process into the iliac arteries. The bifurcation angle hb was calculated as the angle between the common iliac artery directional vectors. The 3D branching angles of the right and left common iliac arteries, ur and ul, respectively, were also computed as the acute angles between the 3D vectors of the terminal aorta and iliac branches. 3D angular asymmetry described the absolute difference between branching angles for the right and left common iliac branches in each subject. All directional vectors at the aortic bifurcation were determined from a linear polynomial fit of 6 mm of the respective vessel centerlines adjacent to the branching site (Fig. 4b). The degree of non-planarity at the aortic bifurcation was gauged by the angles (B) that the terminal aortic or common iliac branch vectors (c) made with the reference branching plane (Eq. 6). Mc 1 B ¼ Sin ð6Þ jMj jcj The normal of the reference branching plane (M) was determined from the cross product of two vectors containing the most distal point of the terminal aortic centerline and the most proximal points of the iliac branch centerlines. The term planarity asymmetry was employed to describe the absolute difference of planarity angles for the right and left common iliac branches. For the purpose of accurately analyzing planarity asymmetry, a distinction was made between cases where planarity angles were made with the anterior and posterior aspects of the nominal branching plane.

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analyzed in the celiac trunk and superior mesenteric artery was less than 20 mm due to proximal branching of the vessels, while this was the case in only one subject for each renal artery. Overall on a per subject basis a higher level of average curvature (AC) was observed in the celiac trunk compared to the superior mesenteric artery in ten out of twelve cases. This trend is verified in Table 1 where greater mean average curvature values for the celiac trunk are observed (0.086 ± 0.019 mm1 vs. 0.059 ± 0.014 mm1) along with higher mean total

RESULTS Vessel Curvature and Torsion Values for the summary measures of arterial curvature and torsion determined in the relevant vessel segments are displayed in Table 1. Longitudinal profiles of 3D curvature and torsion (Figs. 6–8) provide an illustration of the non-uniform nature of curvature and non-planarity along the length of the arteries, which is not conveyed by the summary measures alone. In six of the twelve subjects the length of arterial centerline

TABLE 1. Measures of vessel curvature and torsion. L (mm) CT SMA RRA LRA AA RCIA LCIA

16.8 18.3 19.6 19.6 154.2 51.0 50.7

± ± ± ± ± ± ±

4.4 2.2 1.3 1.3 18.9 12.0 19.6

TC (mm1) 7.29 5.44 7.76 6.28 4.77 4.81 3.91

± ± ± ± ± ± ±

2.39 1.30 2.30 1.95 2.05 2.23 3.06

AC (mm1) 0.086 0.059 0.078 0.063 0.006 0.019 0.015

± ± ± ± ± ± ±

0.019 0.014 0.022 0.019 0.002 0.008 0.008

jmax (mm1) 0.129 0.101 0.134 0.098 0.012 0.026 0.022

± ± ± ± ± ± ±

0.034 0.038 0.041 0.033 0.006 0.012 0.014

TT (mm1) 13.80 13.86 17.28 15.33 40.94 8.38 10.74

± ± ± ± ± ± ±

11.89 13.01 10.30 7.50 7.36 6.39 8.82

AT (mm1) 0.146 0.144 0.171 0.154 0.053 0.031 0.038

± ± ± ± ± ± ±

0.121 0.129 0.102 0.073 0.009 0.024 0.025

smax (mm1) 1.446 1.832 1.429 0.970 0.722 0.197 0.164

± ± ± ± ± ± ±

2.401 3.583 1.986 1.089 0.621 0.351 0.198

Mean values ± standard deviations (n = 12).

FIGURE 6. Comparative plots of in vivo centerline curvature and torsion vs. longitudinal position for the analyzed proximal segments of (a) the celiac trunk and (b) the superior mesenteric artery.


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FIGURE 7. Comparative plots of in vivo centerline curvature and torsion vs. longitudinal position for the analyzed proximal segments of (a) the right renal artery and (b) the left renal artery.

curvature (TC) values despite a shorter mean vessel length. Generally both the celiac trunk and superior mesenteric artery exhibited elevated curvature in the proximal 10 mm portion which then decreased distally (Fig. 6). This corresponds to the noticeable bending of these branch arteries to a caudal direction from their initial more perpendicular trajectory. Proximal maxima of curvature tended to be lower for the superior mesenteric with jmax less than 0.103 mm1 in all but three cases; in contrast to this, jmax for the celiac trunk was greater than 0.110 mm1 in all but three cases. Greatest jmax values recorded for the celiac trunk and superior mesenteric artery were 0.179 and 0.169 mm1 which equate to minimum radii of curvature of 5.6 and 5.9 mm for the respective centerlines. Levels of torsion were similar for the CT and SMA as demonstrated by mean total torsion (TT) and average torsion (AT) values reported in Table 1. In proximal portions of the CT and SMA centerlines torsion values were generally of a magnitude less than ±0.5 mm1 with change in sign rarely observed. Distally oscillations between positive (clockwise) and negative (anti-clockwise) torsion were more frequently observed along with sharp

changes in the plane of curvature, represented by peaks in torsion, in some cases. The distal increase in torsion may be explained by the evident change in plane of curvature turning the direction of the CT and SMA vessels medially or slightly to the right in many cases from their initial left antero-lateral direction. Curvature values for the renal artery segments analyzed were in the same range as those recorded for the proximal anterior visceral branches. Mean average curvature values of 0.078 and 0.063 mm1 were documented for the right and left renal artery, respectively, corresponding to mean average radii of curvature of 12.8 and 15.9 mm over the proximal 20 mm of the arteries. Despite the natural variability of branch origins, trajectory and kidney position at inspiration breath-hold between subjects, a repeatable pattern of proximal renal vessel path was identifiable in a number of cases. Mean curvature profiles (Figs. 7a and 7b) demonstrated a trend for higher initial levels of curvature in the right renal artery (RRA) for the overall subject population. The primary component of this elevated initial curvature in the RRA corresponded to the artery turning from its antero-lateral origin and

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FIGURE 8. Comparative plots of in vivo centerline curvature and torsion vs. longitudinal position for the analyzed proximal segments of (a) the abdominal aorta, (b) the right common iliac, and (c) the left common iliac artery.

initial trajectory to an eventual postero-lateral direction. For the left renal artery (LRA), which emerged laterally or postero-laterally from the aorta, maximal levels of curvature generally occurred beyond the first 5 mm and principally represented the vessel turning laterally or even cranially in some cases from the initial inferior branch angulation. Curvature for both right an left renal arteries exhibited a distinct non-planarity

represented by non-trivial values of torsion (Fig. 7 and Table 1).This was manifested physically by the renal arterial paths bending posteriorly while also returning to a more lateral path from their original caudal direction. The mean length of the abdominal aorta (AA), from 10 mm above the celiac trunk to the apex of the aortic bifurcation was 154.2 ± 18.9 mm. Mean length of the


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right and left common iliacs were similar (51.0 ± 12.0 mm vs. 50.7 ± 19.6 mm) with greater variability in length of the left. Mean average curvature of the abdominal aorta, left common iliac artery (LCIA) and right common iliac artery (RCIA) were significantly lower than those observed for the renal and anterior visceral arteries. These values presented in Table 1 convert to mean average radii of curvature of 166, 53, and 66 mm for the AA, RCIA, and LCIA, respectively. Although some lateral curvature was observed proximally, the majority of abdominal aortic curvature constituted a mild anterior bowing of the vessel following the lumbar curvature in the antero-posterior plane. The common iliac arteries generally diverged laterally from the descending path of the abdominal aorta while continuing to curve posteriorly on entering the pelvis. Individual maximum curvature values observed for these arteries, which were incidentally all recorded in the same subject (Fig. 8, Subject 11), were 0.022, 0.053, and 0.052 mm1, respectively. Levels of torsion were also relatively low for the AA, RCIA, and LCIA when compared with the visceral branches as demonstrated by mean average measures and the longitudinal torsion profiles in Fig. 8. Arterial Dimensions and Tapering Average best-fit vessel diameter measurements for supraceliac, supramesenteric, and suprarenal segments were 20.9 ± 2.9, 20.4 ± 2.9, and 17.6 ± 2.6 mm, indicating a step-wise decrease in lumen dimensions from one segment to the next. Abdominal aortic bestfit diameters decreased by 4.4 ± 1.2 mm over the visceral aortic segment from a supraceliac level to a level just below the lowest renal artery. Mean profiles of infrarenal aortic, visceral branch, and common iliac artery best-fit diameter are shown in Fig. 9a. On average a moderate taper of the infrarenal AA was evident by the transition in diameter from 16.5 ± 2.7 mm proximally to 15.2 ± 2.4 mm distally (mean length of the infrarenal AA segment analyzed was 83.0 mm). The maximum taper recorded for an infrarenal AA corresponded to a decrease in Dfit of 3.2 mm over the length of 84.5 mm, while in contrast no tapering or a mild increase in diameter distally was observed in three cases. Mean diameter profiles of the unpaired anterior visceral branches and the renal arteries followed similar patterns, with the majority of diameter reduction occurring within the first 5 mm. The celiac trunk and superior mesenteric artery diameter tapered on average approximately 4.5 mm (CT: 11.4 ± 1.8 to 6.9 ± 1.1; SMA: 11.8 ± 1.7 to 7.0 ± 1.7) over the normalised length of the analyzed proximal segment. Mean best-fit diameters for the right and left renal arteries were

FIGURE 9. Tapering of the analyzed vessel segments presented as profiles of average best-fit diameters vs. normalised arterial length [(n 5 12); AA, infrarenal abdominal aorta].

generally smaller with fractionally less significant taper (RRA: 10.0 ± 0.7 to 6.1 ± 0.8; LRA: 10.5 ± 1.4 to 6.1 ± 1.2). The common iliac arteries demonstrated a slight initial taper followed by a correspondingly moderate diameter expansion in the distal half of the artery on the approach to the iliac bifurcation. Best-fit diameters at the origins and end points of these vessels showed little difference (RCIA 10.4 ± 1.7 to 11.0 ± 1.8; LCIA 10.5 ± 2.1 to 10.5 ± 2.0). A marked eccentricity was observed in the lumen cross-section of all aortic segments. Cross-sectional eccentricity values for supraceliac, supramesenteric, and suprarenal aortic segments were 0.48 ± 0.08, 0.54 ± 0.08, and 0.48 ± 0.10, respectively. Mean infrarenal aortic eccentricity and its variation along the length of the vessel segment are demonstrated in Fig. 9b. This portrays a general trend of relatively constant eccentricity with a slight increase distally prior to the aortic bifurcation site. Eccentricity values were predominantly between 0.4 and 0.6 for the subjects analyzed as indicated by the errorbars; however, in one case a considerably more circular aortic crosssection was encountered (e 0.2).

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O’FLYNN et al. TABLE 2. Branching parameters of the renal and anterior visceral arteries. Axial branch location (mm)

CT SMA RRA LRA

137.4 120.8 105.6 105.0

± ± ± ±

Normalised CL distance ratio

18.1 15.8 14.7 15.0

1 0.880 ± 0.027 0.769 ± 0.058 0.764 ± 0.035

3D branching angle () 64.0 66.9 63.5 73.1

± ± ± ±

13.1 10.3 10.1 6.8

Angle of trajectory () 202.1 199.4 121.1 282.3

± ± ± ±

14.3 14.2 18.8 21.9

Angle of origin () 206.2 194.5 124.1 278.0

± ± ± ±

10.5 9.8 21.2 17.9

Mean values ± standard deviations (n = 12).

Arterial Branching A summary of parameters describing the visceral bifurcation sites is given in Table 2. The celiac trunk, the most superior of the visceral branches, was located on average 137.4 ± 18.1 mm from the apex of the aortic bifurcation. The mean distance between the level of the CT and SMA branches was 16.6 ± 4.9 mm. On average, the RRA and LRA arose at levels approximately 15 mm below the SMA (RRA: 15.2 ± 8.9 mm and LRA: 15.8 ± 5.9 mm). The RRA originated higher than the LRA in 50% of cases, and the overall mean separating distance of the renal branching levels was 4.9 ± 1.8 mm. Branching angles of 63.5 ± 10.1 and 73.1 ± 6.8 were obtained for the RRA and LRA, respectively. The LRA branching angle was greater than that of the RRA in 9 of 12 subjects, for which cases the mean difference was 14.2 ± 1.8. Mean branching angles for the CT and SMA were similar to that of the RRA; however, a larger range of values were observed for each of these branches (CT: 37.8– 83.4; SMA: 47.4–81.3). Minimum recorded branching angles for the right and left renal artery (50.3 and 63.2, respectively) were less acute than those for the anterior visceral branches. The unpaired visceral branches originated slightly to the left rather than perfectly from the mid-anterior wall of the aorta. The CT had a greater angle of origin than the SMA in 11/12 cases studied, with a mean difference of 14.1 ± 7.8 in ostial location between the branches for these subjects. Both branches followed a somewhat similar left antero-lateral initial direction as described by mean angle of trajectory values. The conventional finding that the RRA origin has an antero-lateral location and the LRA origin has a lateral location was confirmed by the mean angle of origin values obtained in this study. Truly opposite renal arteries were rare (180 ± 5 in 1 case) with the angles between the renal origins ranging from 100.5 to 188.4 (mean ± SD: 154.7 ± 7.5). Initial trajectory of the right and left renal arteries were also substantially different from each other with the right consistently originating with an antero-lateral direction while the left was more dorsally oriented. Overall renal origins and trajectories showed noticeably greater variability over the subject population than the anterior visceral branches. Angles

of origin and trajectory were rarely the same for an individual branch, and mean differences between these parameters for CT, SMA, RRA, and LRA branches were 9.1 (range: 0.1–27.2), 10.2 (range: 1.3–24.0), 13.4 (range: 0.7–42.0), and 5.8 (range: 0.1–14.5), respectively. Geometric parameters for the aortic bifurcation analyzed included a 3D bifurcation angle (hb) of 34.2 ± 12.7, and right and left common iliac branching angles, ur and ul, of 20.3 ± 7.7 and 15.8 ± 9.1, respectively. Aortic bifurcations varied in their asymmetry. The difference between common iliac branching angles averaged 8.2 ± 7.9 but was as large as 22.3 in one case. Mean planarity angles recorded for the terminal aorta, right common iliac, and left common iliac were 4.4 ± 4.1, 5.4 ± 3.5, and 4.5 ± 3.2, respectively. The mean asymmetry in common iliac planarity values was 6.2 ± 4.8 with a maximum recorded value of 14.9. Maximum asymmetry in common iliac planarity tended to occur when the iliacs made angles with opposite sides of the reference branching plane, which was the case with six subjects.

DISCUSSION It is widely recognised that the 3D nature of the vasculature induces non-uniform flow associated with skewing of velocity profiles and the development of secondary flow patterns and swirling streamlines.10,28,73,79 Certain variations in vessel configuration however are prone to the formation of complex flow features, such as recirculation and axial flow separation adjacent to the vessel wall, which adversely affect shear stress distribution, fluid phase transport, and the potential for disease.19,53,61,82 Accurate methods for quantitative characterisation of internal arterial morphology are therefore critical to further examine the hemodynamic significance of salient geometric features. The ability to identify geometric parameters that adversely influence hemodynamic behavior may eventually lead to a more thorough understanding of geometric risk factors in the localisation of atherosclerotic disease. Secondary to this, the complexity of arterial geometry affects the


ability to deploy endovascular devices with adequate positioning control and has a bearing on the loading of implants in vivo. Hence, systematic classification of arterial geometry may also lead to improvements in endovascular device design. Overall, given the prevalence of atherosclerotic involvement in the aorta and its major peripheral branches, a detailed examination of in vivo 3D vessel geometry was warranted. Despite recent advances in image-based 3D modeling techniques,2,8,11,31 full automation of vital medical analysis tasks has yet to be achieved. In this study, user-dependent tasks were confined to the processes of segmentation, identification of vessel centerline extents, and medial axis smoothing. The current methods for geometric characterisation employed contained various improvements from our previously published work.46 These modifications included the introduction of an automated centerline extraction algorithm, refinement of the vessel centerline smoothing and curve-fitting schemes, and further automation of geometric parameter calculations. The changes made the methods more reliable for curvature and torsion determination and more suitable to studies involving greater numbers of cases or larger scale and more tortuous vessels. Overall, the judicious combination of automated analysis and computer-based user interaction employed in this study limited the error associated with each stage of the process and enabled robust arterial geometric characterisation. When applied to in vivo datasets, the methods developed demonstrated the innate intersubject variability of the aortic vasculature. Although some comparable work exists regarding certain isolated aspects of the vascular geometry evaluated, the majority of previous studies have involved subjective measurements from planar imaging or cadavers. In this study, documentation of the curvature, branching, and dimensions of the healthy abdominal aorta and its peripheral branches was undertaken to provide more detailed and more accurate geometric data. Previous data related to the 3D curvature in the abdominal vasculature are scarce. Although average curvatures for the infrarenal abdominal aorta and iliac branches have been reported in an earlier methods article for three patients46 and in recent work by Choi et al.12,13 related to physiological vessel movement, to our knowledge no comprehensive analysis of proximal renal artery or anterior visceral branch curvature exists. The curvature and torsion profiles presented for the various vessels in this study give a novel insight into the regional variation of the parameters over the actual artery length in different subjects. In the case of the renal and visceral branches local levels of curvature and torsion may prove important for defining the flexural and torsional requirements of stent designs to

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ensure adequate conformability to the native vessel contour. Renal artery curvature is also likely to be a major factor governing the mechanical challenges facing renal stents in vivo and the potential for fatigue fracture.55 Respiratory induced renal artery bending however is expected to be even more critical and 3D geometric analysis of in vivo dynamics pre- and poststenting will therefore be required in the future to fully define the biomechanical environment affecting renal artery stent fatigue. The aortoiliac diameters and the magnitude of tapering of the infrarenal abdominal aorta determined in this study are comparable with published values.18,24,27,51 The incidence of mild negative proximalto-distal taper of the infrarenal aorta as observed in two cases in this study has also previously been reported.18,51 Previous studies have further demonstrated that the normal diameters of the abdominal aorta in healthy adults are greater in men than in women and that enlargement occurs with age and body size.18,32,51,62 The variation in aortic dimensions between the subjects in the current analysis therefore may well be attributable to differences in such influential factors. This study gives new information on the profile of vessel eccentricity along the abdominal aorta. Despite widespread acknowledgment of the noncircular nature of arterial cross-sections, only a couple of studies have previously reported elliptical aortic lumen dimensions39,44 with these involving MRI and cadaver measurements at a small number of locations in the thoracic aorta and aortic bifurcation. Data determined by various measurement methods exist regarding the in vivo caliber of renal4,27,66,71 and anterior visceral36 branches. The studies in question, however, have generally reported a single representative diameter sampled at a uniform segment of the vessel. In the case of the renal and visceral arteries the significant proximal taper of these branches is seldom if ever quantified. Results from this study, which do just that, may have implications for stent design and performance. Decrease in vessel diameter over the length of a stent due to tapering may result in the stent imposing excessive stresses on the vessel wall at its distal end.74 This distension of the vessel beyond its normal physiological limits owing to diameter mismatch may provoke a cellular response resulting in complications such as restenosis or neointimal hyperplasia.40 Although there are tapered stents available for the carotid market due to the frequent need to deploy a stent from the parent common carotid into the narrowing internal carotid, the application of tapered stent technology has not been extended to other regions of the vasculature. The concept of developing flared stents that are anatomically shaped to conform to the ostial bifurcation geometry is

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particularly relevant for renal artery stenosis as they may facilitate more accurate positioning64 and the reduction of current restenosis rates.56 Further analysis of the renal branch ostium’s non-circular cross-sectional shape and of the influence of stenosis on lumen morphology in diseased vessels may be required for such purposes. Overall, the diameters recorded in this article were taken from smooth geometries reconstructed from routine MRA scans and can be generally assumed to reflect in vivo arterial geometry under mean arterial pressure. As such, the current measurements do not address diameter change over the cardiac cycle due to arterial pulsation. Furthermore when analyzing arterial diameters no allowances were made to compensate for the potential effects of differences in blood pressure levels between individuals. The in vivo variability in vessel diameters presented could therefore be partially due to intersubject variability in blood pressure levels and vessel compliance rather than differences in the zero-pressure geometry of the vessels. Anterior visceral or renal branch levels, whether presented as a centerline distance from the aortic bifurcation or as a function of the longitudinal position relative to that of the celiac trunk, compare favorably with those previously determined from autopsy studies52,80 or quantitative vascular CTA.18 While the individual visceral branches emerged from the aorta at different locations in our different study participants; branch separation distances showed less variation. As observed by others, the relative spacing of the renal arteries was generally small9,18,52 and neither renal branch emerged consistently superior to the other.3,9,29,47 Although some studies have previously quantified the renal branching anatomy, the in vivo 3D geometric configuration of the anterior visceral branches has not been properly documented. In past studies branches from the visceral aortic segment have generally been described by a single measure of branch direction. The angles of origin and trajectory derived in this study enabled any misalignment between the circumferential position origin and the initial trajectory of the branch to be quantified. Although not obvious from comparison of mean values over the subject population, a difference in these angles was found in most cases for all four branches. The difference was most pronounced for the right renal artery and least evident for the left renal artery. Angle of origin measurements determined in this study confirm earlier qualitative observations from cadaveric studies that the anterior visceral branch origins lie to the left of the midline, with the SMA origin located inferior and to the right of the celiac trunk ostium.47,52 The CT and SMA branching angles recorded however were significantly greater than the only previous comparable measurements obtained

from cadaveric specimens which suggested average values in the region of 30 for both branches.52 This discrepancy may stem from vessel deformation introduced in this previous study during post-mortem preparations or from measurement of vessel geometry in a zero-pressure state. Parameters determined describing the orientation of renal artery origin and initial trajectory corroborate the large amount of vascular anatomic variation previously observed among individuals.9,16,20,52,75,78 In this respect the renal branches showed noticeably greater variability over the subject population than the anterior visceral branches. With regards to renal branching there were also definite asymmetries between the left and right sides of the same individual. Apart from obvious differences in origin and trajectory, the branching angle of the right renal artery was also generally more acute than that of the left renal artery; a feature that may be explained by the lower position of the right kidney in the abdomen due to the anatomical position of the liver. The branching parameters reported in this study for the aortic bifurcation are within the ranges previously reported from analysis of angiograms,34 cadavers6 and 3D MRI data.63 The determination of bifurcation planarity through the identification of the nominal branching plane enabled the effect of out-of-plane dorsal–ventral curvature, in the immediate vicinity of the bifurcation to be quantified in a novel and meaningful way. This highlighted the existence of asymmetry in common iliac planarity, accompanying the frequently observed asymmetry in common iliac branching angle. In summary, a marked variability in vessel curvature and individual branching parameters was observed in this study. The current results indicate that certain aspects of renal and visceral branch geometry may be less variable than previously anticipated by other investigators. The reduction in variability observed in this study was most obvious for the 3D branching angles and this may be explained by the additional variability that was introduced in earlier studies by subjective measurements and projection errors associated with planar analysis. Although wider variations in arterial geometry have been found with older subjects in the past,18,72 no comparison of geometric parameters for different age groups was attempted in the current series given the small sample size. Finally, it should be noted that the present methodology lacks the sensitivity required to detect pulsatile arterial deformation, when using routine tomographic imaging data. There is however potential for applying the methods to datasets from dynamic MRA or electrocardiographically gated CT in the future to overcome this limitation. This would enable


changes in longitudinal and circumferential vessel dimensions as well as deformation in vessel configuration over the cardiac cycle to be quantified. Furthermore, quantification of the effects of musculoskeletal or respiratory motion on vascular dynamics would be possible through analysis of datasets from subjects imaged in different body positions or different breath-hold states. These types of studies are essential for defining the in vivo conditions affecting endovascular device durability. From a hemodynamics viewpoint, methods of quantitative vascular characterisation could prove useful in clarifying the exact relevance of geometric variability to the considerable variability in disease risk between individuals. A combination of geometric analysis and patient-specific numerical simulations incorporating vessel compliance65 and accurate inlet velocity profiles67,76 should give a greater insight into disease risk for in vivo anatomical vessel configurations.

CONCLUSION This study demonstrates the suitability of the current medical image analysis framework to accurately and objectively quantitate in vivo arterial geometry in a reproducible manner. Vessel centerline control points as determined by the automatic centerline function served as a basis for analysis of arterial branching, 3D vessel length, non-planar curvature, and lumen cross-sectional morphology. The geometric data presented have possible applications in aiding endovascular device development and in the realistic modeling of this region of the vasculature for hemodynamic studies and device design verification testing. Furthermore, the approach used to characterise vessel geometry provides capabilities for future quantification of the extent of vessel motion and vessel–device interaction in dynamic environments or the effects of vascular aging. Similarly with further automation, this scheme for vascular quantification may prove useful for pre-operative patient evaluation and computeraided planning of complex endovascular procedures. Alternatively the methods may be incorporated in a framework for understanding the effect of geometric parameters on vessel hemodynamics and disease risk. In conclusion, robust means for characterisation of in vivo arterial geometry were applied to systematically classify the morphology of the abdominal aorta and its major visceral branches. The results from this study address the scarcity of available in vivo 3D quantitative geometric data relating to these vessels and accurately reflect the geometric variability in living subjects.

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ACKNOWLEDGMENTS The authors would like to acknowledge Ms. Geraldine Dowd, Clinical Specialist Radiographer, University College Hospital, Galway for her help, and James Coburn for his technical expertise. This study was supported with funds from Irish Research Council for Science, Engineering, and Technology (IRCSET): funded by the National Development Plan.

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