| | The Effect of Aging on Deformations of the Superficial Femoral Artery Resulting from Hip and Knee Flexion: Potential Clinical ImplicationsReceived 14 July 2008; received in revised form 3 July 2009; accepted 26 August 2009. published online 21 December 2009. PurposeVessel deformations have been implicated in endoluminal device fractures, and therefore better understanding of these deformations could be valuable for device regulation, evaluation, and design. The purpose of this study is to describe geometric changes of the superficial femoral artery (SFA) resulting from hip and knee flexion in older subjects. Materials and MethodsThe SFAs of seven healthy subjects aged 50–70 years were imaged with magnetic resonance angiography with the legs straight and with hip and knee flexion. From geometric models constructed from these images, axial, twisting, and bending deformations were quantified. ResultsThere was greater shortening in the bottom third of the SFA than in the top two thirds (top, 5.9% ± 3.0%; middle, 6.7% ± 2.1%; bottom, 8.1% ± 2.0% [mean ± SD]; P < .05), significant twist in all sections (top, 1.3°/cm ± 0.8; middle, 1.8°/cm ± 1.1; bottom, 2.1°/cm ± 1.3), and greater curvature increase in the bottom third than in the top two thirds (top, 0.15 cm−1 ± 0.06; middle, 0.09 cm−1 ± 0.07; bottom, 0.41 cm−1 ± 0.22; P < .001). ConclusionsThe SFA tends to deform more in the bottom third than in the other sections, likely because of less musculoskeletal constraint distal to the adductor canal and vicinity of knee flexion. The SFAs of these older subjects curve off axis with normal joint flexion, probably resulting from known loss of arterial elasticity with age. This slackening of the vessel enables a method for noninvasive quantification of in vivo SFA strain, which may be valuable for treatment planning and device design. In addition, the spatially resolved arterial deformations quantified in this study may be useful for commercial and regulatory device evaluation. AGING and atherosclerosis are accompanied by geometric, material, and consequentially, deformational changes in arteries. For example, age is correlated with a decrease in elastin content in the abdominal aorta concomitant with increased diameter, and increased stiffness as evidenced by decreased diametric pulsatility and increased pulse propagation speed (1, 2, 3, 4, 5, 6, 7, 8). Additionally, these effects may be exacerbated by added tissue stiffening resulting from the process of atherosclerosis (9). Although these effects have been well documented in relation to the radial/circumferential structure of arteries, they are not well understood in relation to the longitudinal direction. Arterial stress and strain may be important characteristics for the understanding of disease processes as well as for diagnosis and therapeutic strategy. For example, it has been shown that circumferential cyclic strain and deformations can cause cellular proliferation and chronic vessel reinjury, as well as modulate gene expression hypothesized to affect the process of atherosclerosis (10, 11). Also, it has been shown that decreases in axial strain and tension in an artery, which can be instigated by vessel lengthening and/or a loss of axial elasticity, can generate a proliferative tissue response (12). Finally, arterial stiffness has been documented to vary with age and the state of vascular disease (13). Therefore, quantification of axial arterial strain may be a useful tool for describing the health and perhaps predicting the progression of disease in blood vessels. In addition, the knowledge of arterial strain may be able to guide therapeutic strategy. Consider the superficial femoral artery (SFA), an artery prone to the development of atherosclerotic disease, for which current surgical and interventional treatments such as endarterectomy and angioplasty plus stent placement are far from optimal (14, 15, 16). The prevalence of atherosclerotic disease and restenosis subsequent to treatment may be caused by proliferative biology influenced by inadequate vessel healing, alteration of hemodynamic conditions, traumatic injury, and cellular mechanobiology (17, 18, 19, 20, 21, 22, 23, 24, 25). These mechanisms can all be related to the biomechanics of the SFA. In addition to the arterial stress and strain factors mentioned earlier, adverse hemodynamic conditions such as slow flow, low wall shear stress, and oscillations in wall shear stress can be affected by tortuous vascular geometry, a corollary of a loss of longitudinal tension (18, 19, 20, 21, 22). In addition, injury caused by stent–vessel interactions, especially in the presence of stent fracture, are hypothesized to cause clinical sequelae and have been hypothesized to be related to the biomechanics of SFA deformations (23, 24, 25, 26). To realize the benefits of describing axial vessel deformations, the methods of quantification must be able to be accomplished in vivo with minimal morbidity. For example, although the method of arterial resection and subsequent length change measurement has been performed experimentally, it is not viable for patient care (27). We present novel methods for quantifying axial deformations of the SFA in vivo with use of magnetic resonance (MR) angiography and simple musculoskeletal manipulation. We describe these three-dimensional deformations of the SFA, along with torsion and bending deformations, in adults aged 50–70 years, resolved along the length of the artery. Materials and Methods  Subjects and Imaging Protocol Seven male adults, aged 50–70 years, were imaged with a General Electric 1.5-T Signa MR scanner (GE Medical Systems, Milwaukee, Wisconsin). Six of the seven volunteers had age-expected hypertension and hypercholesterolemia, but all were physically active and controlled their risk factors with medication. One subject had undergone coronary stent implantation after infarction, and another had smoked for 30 years; however, neither exhibited symptoms of cardiovascular disease. The subjects were imaged in the supine position (Fig 1a) and then in left decubitus position with hip and knee flexion angles to be at least equal to the maximum flexion angles during a normal gait cycle (Fig 1b) (28). Gadolinium-enhanced MR angiography was performed for each subject with a transmit/receive torso coil for both body positions. The study protocol was approved by the institutional review board and written consent was obtained from each volunteer. Oblique MR angiography volumes were prescribed by localizers to encompass the superficial femoral arteries of both legs. It was confirmed by noncontrast MR angiography before contrast agent injection that the femoropopliteal arteries were included at least from the profunda femoris artery to the most superior genicular artery (sometimes including the most superior portion of the popliteal arteries as well). For each subject, a time-resolved MR angiography pulse sequence was employed to capture multiple temporal phases, with a temporal resolution of 16–22 seconds, lasting a total of 3–5 minutes. The scan parameters were as follows: 8 msec repetition time, 1.6 msec echo time, 45° flip angle, 42–48 cm square field of view, 512 × 224 acquisition matrix, 48–54 slices, and 2.6 mm slice thickness with 1.3 mm overlap. For each of the two body positions, 20 mL of MultiHance gadolinium (Bracco, Milan, Italy) was injected via intravenous catheter into the antecubital vein of the right arm at a rate of 3 mL/sec followed by 20 mL of saline solution flush at 3 mL/sec. Image Processing and Vessel Path Identification Each MR angiography volume data set was corrected for slice direction gradient warping (29), and the temporal phase with the optimal arterial visualization was selected for image processing and geometric quantification. Hip flexion was measured as the angle between the superior–inferior axis of the torso and the femur, and knee flexion was defined as the angle between the femur and the tibia. For both limbs, approximate centerline spline paths were constructed by hand-picked points, with the use of custom modeling software (30), for the iliofemoral path and all of its identifiable branches, including the profunda femoris artery, descending genicular artery, superior medial and lateral genicular arteries, and unnamed muscle branches (Fig 2a). Perpendicular two-dimensional lumen boundaries were then determined on these approximate centerlines with use of a level set method (31), image intensity thresholding, or manual segmentation (Fig 2b), from which lumen centroids were found and refined centerlines were constructed with cubic splines (Fig 2c). These centerline splines are analytic representations of the path, which were used to perform mathematical quantification of path characteristics, such as arc length, twist, and curvature. For curvature calculations, a 30-mode Fourier smoothing step was performed on these spline curves to eliminate artificial jaggedness caused by interpolation. Arterial Deformation Quantification Before deformations could be quantified, the ostia of branch arteries were identified as fiducial markers. From views perpendicular to the branches at the ostia, center points of the ostial lumens were selected manually. This process was performed by one operator in dual image volumes simultaneously to minimize errors associated with manual operation (Fig 3a). Branch bifurcation points were defined as the projection points of the branch vessel paths onto the SFA centerline (Fig 3b). The projected bifurcation points were used as fiducial markers to determine the corresponding SFA segments between branch vessels for the straight and flexed leg positions to compute axial length change, axial twist, and curvature values. Axial length was defined from the supine to flexed leg position as the change in arc length between two adjacent branch points normalized to the supine position arc length (Fig 4a). Axial twist was defined as the absolute change (in degrees), caused by leg flexion, in angle of separation between two adjacent arterial branch takeoff vectors. In the simplest case, the vessel is straight in both configurations, and the twisting angle is the difference of the angles of separation (Fig 4b). However, actual vessel deformations are a superposition of length change, planar bending, out-of-plane torsion, and axial twisting effects. As such, the off-axis components were separated from the total deformation to obtain pure twisting (32). Change in curvature was computed as the average change in curvature for a particular arc length window size (Fig 4c). The window size was selected by maximizing an off-axis deflection metric cost function as described in the Appendix. We observed dramatic variations in lower-extremity vascular anatomy in terms of number of muscle branches, location of branches, and distance between branches. To enable statistical analysis of the quantitative data, we computed the deformations of each SFA for equal thirds—the top, middle, and bottom—along the vessel path by linear weighted averages (Fig 5). These thirds were established with use of the supine data set, with the profunda femoris artery and the most superior geniculate branch as the superior and inferior boundaries, respectively. These same two branch vessels were then used to set the boundaries of the vessel in the flexed position. Axial length changes and axial twist rates were averaged for each third, whereas curvature changes were presented as maximums for each third to indicate maximum off-axis vessel buckling. Statistical Analysis Deformation quantities were compared among different sections of the SFA with paired, two-tailed t tests with post-hoc Holm-Bonferroni correction for multiple comparisons, with a P value corresponding to a probability of type I error less than 5% (33). F-tests were performed to query differences in variance between populations of data. Based on a previous study, the left and right SFA deformations were grouped together for all statistical calculations for a total of 14 unique data sets (25). All calculations were performed using the statistical package in Excel (Microsoft, Redmond, Washington). Results Mean age among the seven male subjects was 56 years ± 5 (SD; range, 51–65 y); height was 178 cm ± 9 (range, 168–193 cm), and weight was 87 kg ± 9 (range, 73–98 kg). Their hip and knee flexion angles were 39° ± 6° (range, 32°–50°) and 86° ± 6° (range, 75°–93°), respectively. Quantitative deformation metrics of arc length change, axial twist rate, and maximum curvature change from supine to flexed positions for the subject population are shown in the Table, as are maximum curvatures for the supine and flexed positions. Data are shown for each of the top, middle, and bottom thirds, as well as for the top and middle thirds combined, middle and bottom thirds combined, and the entire SFA combined. The average changes in arc length of the SFA were −5.9 ± 3.0 %, −6.7 ± 2.1 %, and −8.1 ± 2.0 % for the top, middle, and bottom thirds, respectively, and all represented significant shortening (P < .001). The shortening observed in the bottom third was significantly greater than that of the top third (P < .005) as well as the top two thirds combined (P < .005). In addition, the variability in percent shortening of the top third was greater than that of the bottom two thirds (P < .05). The axial twist rates were 1.3°/cm ± 0.8, 1.8°/cm ± 1.1, and 2.1°/cm ± 1.3 for the top, middle, and bottom thirds of the SFA, respectively. The amount of axial twist resulting from hip and knee flexion was found to be significant for all sections of the SFA (P < .01). Although there were no significant differences in twist among the three sections of the SFA, there was a trend toward greater twisting moving inferiorly along the SFA. In the supine position, the maximum curvatures were 0.11 cm−1 ± 0.05, 0.08 cm−1 ± 0.01, and 0.11 cm−1 ± 0.06 for the top, middle, and bottom thirds of the SFA, respectively. Although there were no significant differences in maximum curvature among the thirds, the middle third had less variability than the top and bottom thirds (P < .001). In the flexed position, the maximum curvatures were 0.21 cm−1 ± 0.07, 0.14 cm−1 ± 0.06, and 0.47 cm−1 ± 0.24 for the top, middle, and bottom thirds of the SFA, respectively. The bottom third exhibited the greatest maximum curvature, followed by the top third and then the middle third (bottom vs top vs middle, P < .01). The bottom third also exhibited greater population variability in maximum curvature compared with the top and middle thirds (P < .001). The maximum changes in curvature when bending from supine to flexed leg position were 0.15 cm−1 ± 0.06, 0.09 cm−1 ± 0.07, and 0.41 cm−1 ± 0.22 for the top, middle, and bottom thirds of the SFA, respectively (P < .005). The SFA showed the greatest curvature change in the bottom third, next in the top third, and least in the middle third (bottom vs top vs middle, P < .005). In addition, the variability in maximum curvature change was significantly greater in the bottom third compared with the top and middle thirds (P < .001). Discussion For the population in this study, the observation that shortening of the SFA resulting from leg flexion was greater in the bottom third than in the top two thirds (P < .005) is likely because knee flexion was significantly greater than hip flexion (P < .001). In addition, the greater variability of arc length shortening in the top third of the SFA is likely because of the lesser musculoskeletal constraints around the hip versus the knee. The nonsignificant trend toward greater twisting in the inferior sections of the SFA could be a result of greater flexion in the knee as already mentioned, as well as the more complex musculoskeletal influences on the geniculate branches as described by Cheng et al (25). The spatially resolved curvature metrics for the SFA reveal markedly nonuniform deformations. In the straight leg position, the SFA appears to be relatively straight for the entire length; however, with hip and knee flexion, the curvature values become disparate (ie, bottom greater than the top, with the middle least curved), and the variability of the bottom third's curvature is greater than those of the top and middle thirds. This can be explained by the fact that the adductor canal provides more muscular and membranous constraint proximal to the adductor hiatus (22). In addition, the vastoadductor membrane creates an increasingly constrained space progressing distally along the adductor canal (34). Therefore, the increase in vessel curvature is greatest in the bottom third, adjacent to the greatest joint flexion (at the knee) and where there is the least constraint, and least in the middle third, not close to any joint flexion and where the adductor canal is highly constrained. Whereas the superficial femoral arteries remain visually smooth and relatively straight in younger subjects with hip and knee flexion, older subjects exhibit substantial curvature and buckling with flexion (Fig 6). This may indicate that younger subjects retain tension in the SFA with hip and knee flexion whereas older subjects do not. This is consistent with documented variation in arterial tension with age. Although body growth persistently stretches arteries through adolescence, when maximum body height is reached, the chronic tension that arteries experience should decrease in the absence of further stretching, and with the degradation of elastin in arteries with age (7, 8), older adults have longer and less elastic arteries than young adults. Comparing the SFA deformations presented in this study with those of a younger population (age 27 y ± 5 years) described by Cheng et al (25), some notable differences in biomechanical behavior were found. Note that there was significantly less flexion in the older population compared with the younger population at the hip (older, 39° ± 6°; younger, 120° ± 9°; P < .001) and knee (older, 86° ± 6°; younger, 134° ± 3°; P < .001), and that the data for the younger subjects were averaged along the entire length of the SFA rather than divided into thirds. The variation in length change in the young population (−13% ± 11 %) was greater than that of all three sections of the older subjects' SFAs (P < .001). Also, there was greater variability in SFA twist in the young subjects compared with the older adults (young, 2.8°/cm ± 1.7; older, 0.7°/cm ± 0.5; P < .001). In addition, the older subjects exhibited greater maximum change in curvature than the young subjects in the bottom third (young, 0.04 cm−1 ± 0.16; older, 0.41 cm−1 ± 0.22; P < .001). Along with the visual angiographic evidence in Figure 6, these comparisons support the postulate that aging decreases stretch and elasticity in the SFA. For example, the far lower variability in arterial shortening caused by leg flexion for the older adults compared with the young adults indicates that the percentage shortening of the older SFAs is more narrowly distributed in the population. This narrow distribution may indicate that the population of older subjects all shortened their SFAs to their minimum slack length, corresponding to zero tension and strain. This hypothesis is strengthened by the fact that the older subjects had significantly lower hip and knee flexion angles than the young subjects, and the minimum SFA slack lengths were reached nonetheless. Similarly, the variability in overall SFA degrees of twist per centimeter was significantly greater in the younger population than in the older population. A more narrow distribution of arterial twisting angles in the older population also supports less compliant arteries. However, the most definitive evidence is that the bottom thirds of the older SFAs increase their maximum curvature more dramatically than the bottom thirds of the younger SFAs, which indicates that the older SFAs shortened past their point of slack and then buckled off axis, whereas the younger SFAs did not. As mentioned earlier, it may be beneficial to characterize the axial strain of a target vessel. Whereas younger SFAs do not experience significant increases in curvature when flexing from supine to fetal position (25), the older SFAs curved significantly in the top, middle, and bottom thirds. Assuming that large increases in curvature indicated off-axis buckling in the older subjects (Fig 6), it can be deduced that the arteries were straight and in tension while in the supine position and past the point of slack when the legs were flexed. Therefore, the percent shortening of the SFA from supine to flexed position is the approximate axial tensile strain that the SFA experiences in a straight leg. Analogously, in the younger subjects, because the arteries remain straight even with full fetal position flexion and the point of slack is never exceeded, we can logically deduce that the chronic axial tensile strain of the SFA in a straight leg is greater than or equal to the percent shortening quantified. The evidence presented here shows that with hip and knee flexions approximately commensurate with walking, the distal and proximal portions of the SFA are subject to greater longitudinal and bending deformations than the middle of the SFA, with the distal SFA deforming the most. In addition, we hypothesize that there is decrease in baseline strain in femoral arteries with aging. Combined with the natural decrease in compliance of vessels with age, the relative fixed musculoskeletal geometry of the adult anatomy, and the shortening of the SFA path length with leg flexion, it follows that repetitive arterial deformations may vary qualitatively and quantitatively with age. Namely, with decreased vessel stretch and increased vessel stiffness, the SFAs of older people tend to shorten less as a result of reaching the point of slack and buckle off axis, whereas younger SFAs remain straight. With the presence of atherosclerotic disease, arteries tend to be even stiffer, have longer equilibrium lengths, and lower longitudinal strain, probably resulting in more exacerbated off-axis buckling with repetitive lower extremity movements. There were limitations to this study that warrant mention as well as future investigation. Because of variations in vascular anatomy, the arterial branches were not consistent among subjects, necessitating that deformation data be averaged into top, middle, and bottom thirds of the SFA. In addition, the subjects included in this study did not have lower-extremity vascular disease. In the presence of disease, which could cause nonhomogeneous vessel properties along the length of the SFA, the motions and deformations could be qualitatively and quantitatively different from those of these healthy subjects. Ultimately, deformation analysis should be performed before and after treatment to better evaluate how different treatments and implants may change the properties of the vessel, as well as provide insight into how to treat the artery back to a healthy biomechanical state. The results and concepts of this study can be used to improve current device testing and development of future devices, as well as guide therapeutic strategies. The longitudinal, twisting, and bending deformations of the SFA can be used to refine computational and benchtop durability tests for industry and Food and Drug Administration evaluation. Although flexibility is not the only factor in efficacy, benchtop and clinical experience with SFA stents have shown that greater flexibility, and greater uniformity of flexibility, are correlated to fracture resistance. For example, along the spectrum of open-cell versus closed-cell designs, the more open the design, the greater the axial twisting and bending flexibility, resulting in lower fracture rate (24, 35, 36). In addition, evidence shows that longer stent-implanted regions correlate with higher stent fracture rates, especially in the presence of stiffness nonuniformities caused by stent overlap (36, 37). We can postulate that the low fracture rate of stent-grafts may result from their flexibility as well as the stiffness-homogenizing effect of the graft material on the device. Not only can the results from this study extend the understanding of fracture mechanisms of SFA stents, they can also motivate the invention of next-generation devices and therapies that better consider the biomechanical environment of the SFA. Perhaps most importantly, the measurement of in vivo longitudinal strain provides mechanical tissue data that can be used to help evaluate the biomechanical health of a vessel, potentially enhancing the diagnostic process (8), as well as providing information to enable subject-specific devices and therapies. For example, implants and treatments can be designed to be more harmonious with the biomechanical environment by matching the strain state of an implant with that of the target vessel (eg, implanting a stretched stent in the stretched vessel of a straight leg, or implanting a neutral stent in the nonstrained vessel of a flexed leg). In addition, with vessel strains derived from these techniques and vessel stiffness derived from pulse propagation studies, vessel stresses and forces can be computed, creating more opportunities for anatomically focused design. Acknowledgment The authors thank Nathan M. Wilson, PhD, for assistance with the imaging processing software. Appendix: Optimal Window Size for Averaging Curvature To compute an average curvature value, an arc length over which to average needs to be determined first. An off-axis deflection metric was devised to estimate vessel curvature and served as a cost function to find the optimal window size of arc length. The metric was defined as the maximum ratio of off-axis distance  of the vessel centerline path from the straight line  over the arc length of the vessel centerline path (Fig 7). The window size was determined by a recursive algorithm such that the off-axis deflection metric was maximized along the centerline path of interest. In a formulated form, if we let f be the off-axis deflection metric cost function, we need to find the optimal moving window size α that maximizes f(s, s+α), where s represents any point along the path. The Matlab optimization toolbox (MathWorks, Natick, Massachusetts) was used to solve this formulation. This calculation provides the optimal arc length window to effectively include regions vessel bending and buckling. After finding the optimal arc length window α, average curvature was calculated along the entire path as follows: 
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a Department of Surgery, Stanford University, Clark Center, Room E350, Stanford, CA 94305-5431 b Department of Mechanical Engineering, Stanford University, Clark Center, Room E350, Stanford, CA 94305-5431 c Department of Radiology, Stanford University, Clark Center, Room E350, Stanford, CA 94305-5431 d Department of Bioengineering, Stanford University, Clark Center, Room E350, Stanford, CA 94305-5431  Address correspondence to C.P.C.
This work was supported by members of the RESIStent SRI/Stanford Consortium on Stent Fracture in the Superficial Femoral Artery (phase II): Cordis/Nitinol Devices & Components, Boston Scientific, W.L. Gore & Associates, Medtronic Vascular, Abbott Vascular, and Bard/Angiomed. This work was also supported by National Institutes of Health grant P41RR09784, the Lucas Center for Magnetic Resonance Imaging at Stanford University, and General Electric Medical Systems. None of the authors have identified a conflict of interest. From the SIR 2009 Annual Meeting. PII: S1051-0443(09)01001-X doi:10.1016/j.jvir.2009.08.027 © 2010 SIR. Published by Elsevier Inc. All rights reserved. | |
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