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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Vasc Surg. Author manuscript; available in PMC 2010 April 1.
Published in final edited form as:
PMCID: PMC2695673

Circumferential and Longitudinal Cyclic Strain of The Human Thoracic Aorta: Age-Related Changes



We developed a novel method using the anatomical markers along the thoracic aorta to accurately quantify both longitudinal and circumferential cyclic strain in the thoracic aorta. We have applied this method to quantify circumferential and longitudinal cyclic strain in non-diseased thoracic aortas over the cardiac cycle and to compute age-related changes of the human thoracic aorta.


Changes in thoracic aorta cyclic strains were quantified using the 4D cardiac-gated CT image data of fourteen patients; aged 35-80, with no visible aortic pathology (aneurysms or dissection). We measured the diameter and circumferential cyclic strain in the arch and descending thoracic aorta (DTA), the longitudinal cyclic strain along the DTA, and changes in arch length and motion of the ascending aorta relative to the DTA. Diameters were computed distal to the left coronary artery, proximal and distal to the brachiocephalic trunk, and distal to the left common carotid, left subclavian, and the first and seventh intercostal arteries (ICoA). Cyclic strains were computed using the Green-Lagrange strain tensor. Arch length was defined along the vessel centerline from the left coronary artery to the first ICoA. The length of the DTA was defined along the vessel centerline from the first to seventh ICoA. Longitudinal cyclic strain was quantified as the difference between the systolic and diastolic DTA lengths divided by the diastolic DTA length Comparisons were made between seven young (age 41±7 yrs, 6M, 3F) and seven older (age 68±6 yrs, 6M, 3F) patients.


For the seven locations analyzed, the diameters of the thoracic aorta increased, on average, by 14% with age from the young (mean age 41 years) to the older (mean age 68 years) group. The circumferential cyclic strain of the thoracic aorta decreased, on average, by 55% with age from the young to the older group. The longitudinal cyclic strain decreased with age by 50% from the young to older group (2.0 ± 0.4% versus 1.0 ± 1%, p=0.03). The arch length increased by 14% with age from the young to the older group (134 ± 17mm versus 152 ± 10mm, p=0.03).


The thoracic aorta enlarges circumferentially and axially and deforms significantly less in the circumferential and longitudinal directions with increasing age. This represents the first quantitative description of in vivo longitudinal cyclic strain and length changes for the human thoracic aorta, creating a foundation for standards in reporting data related to in vivo deformation, and may have significant implications in endo-aortic device design, testing and stability.

Keywords: age-related, cyclic deformation, cyclic strain, longitudinal strain, circumferential strain, biomechanics, thoracic aorta, wall motion


Large vessels in the vascular system undergo progressive degeneration as we age. For example, the aorta enlarges and stiffens [1-4] and vascular compliance decreases [5]. These changes increase systolic pressure, decrease diastolic pressure, and greatly affect cardiovascular health and function [6]. Quantifying the cyclic strain of an aging human aorta may yield insight into the changes in the vascular compliance, which is vital in understanding pathogenesis and progression of disease, such as atherosclerosis and aneurysm formation [7], and changes in the in vivo vessel wall properties.

The deformation of large vessels has been described by a variety of terms. Distensibility (cm2/mmHg) has been defined as the fractional change in vessel cross-sectional area divided by the distending pressure, which refers to the capacity of the vessel to stretch [8]. Stiffness (N/cm2) has been related to the compliance (cm3/mmHg) of the vessel wall [9]. Pulsatility (mm) has been defined as the radial displacement of the lumen during a single cardiac cycle [10]. In addition, these methods have been insufficient for quantifying in vivo cyclic strain. Therefore, we developed an effective technique which can be applied to analyze the cyclic strain with cardiac-gated image data. In this study, we applied our technique to examine the longitudinal and circumferential cyclic strain of the thoracic aorta.

Strain is typically defined as the ratio of the change in length to the original length [11]. The true in vivo strain cannot be obtained because the unstressed original configuration cannot be measured noninvasively. However, changes of deformation over the cardiac cycle relative to a reference configuration can be measured using cardiac-gated image data. Therefore, we quantified cyclic strain using a reference length, which we defined as the diastolic length [12]. Moreover, the circumferential cyclic strain was calculated using the actual circumference of the lumen boundary, not the effective diameter or cross-sectional area changes, which have been previously reported [10, 13].

Changes in deformation must be measured in a reference frame. In mechanics, there are two different references frames, the Eulerian (which is fixed in the environment of the object of interest) and the Lagrangian (which is fixed to the object of interest). Previous researchers report circumferential deformation quantified by tracking deformation at a specific location in space rather than at a specific location on the vessel [10, 13, 14]. Mohiaddin et al. [15] was one of the first groups to track age-related changes in the thoracic aorta. They analyzed diameter differences using axial and sagittal planes at end-diastole. Unfortunately, those measurements were not taken orthogonal to the vessel, and thus cannot isolate radial deformation. More recently, Muhs et al. [10] characterized normal aortic motion using cine-CTA at four locations along the descending thoracic aorta (DTA) using an Eulerian reference frame. Similarly, Draney et al. [14] and Wedding et al. [16] used cine-PCMRI to quantify cyclic strain in an Eulerian frame on discrete image slices.

In contrast to these techniques, we have developed a method to effectively “attach” the reference frame to the ostia of the intercostal arteries and the major branch vessels. This enabled us to track the motion of the vessel wall by analyzing the same segment of the vessel at peak-systole and end-diastole, thereby eliminating spurious results due to through-plane motion of the vessel. Tracking the through-plane motion is not possible using an Eulerian reference frame, particularly in the region of the ascending thoracic aorta, where observed motion is large [13]. Additionally, no studies heretofore have implemented a Lagrangian frame, nor have any quantified deformation in the longitudinal direction.

In this retrospective study, we employ simple, yet novel techniques to compute the cyclic deformation of the thoracic aorta using ECG-gated CT image data. Additionally, this technique can be applied to analyze image data of patients with cardiovascular disease (CVD) and is not limited to the thoracic aorta. The purpose of this study is to quantify the age-related changes in the biomechanical cyclic strain and deformations of the human thoracic aorta by computing and comparing the deformation between a group of young and older patients withno visible CVD.


The following analysis involved creating an accurate center-path to represent the vessel geometry at peak-systole, defining a reference frame, extracting the lumen boundary at desired locations along the vessel center-path, and computing and comparing the circumference of the lumen boundary at peak-systole and end-diastole to quantify the biomechanical cyclic strain. Custom software was utilized for image analysis [17].

Patient Population

We selected fourteen ECG-gated CT data sets with no visible evidence of thoracic aortic disease from an existing library of chest and heart scans from the Stanford Medical Center. The scans were performed with a Siemens 64-row CT scanner. The data sets were divided into two groups based on age, which ranged from 35-80 years (young: [35, 36, 37, 37, 45, 49, 51] and older: [64, 64, 66, 66, 68, 70, 80]). The mean age of the younger group was 41 years (range 35-51), and 68 years for the older group (range 64-80). Research conducted by Draney et al. [18] indicated that significant gender differences diminish with age when comparing deformation using MRI between a group of young healthy volunteers (mean age 20 years) and older healthy volunteers (mean age 60 years). Therefore, both patient groups included two females and five males. A volume-rendered image of one patient from each group is displayed in Figure 1.

Figure 1
Above are two volume-rendered thoracic aortas, one from the young (a) and older (b) group. Note the qualitative difference in the curvature of the arch. The older patient has a larger radius of curvature and an increased center line length by approximately ...

Image Processing

The ECG-gated CT data sets consisted of ten 3D volumes of the vasculature, where each volume represented 1/10th of the cardiac cycle. The temporal resolution of the scanning method limited the precise location of specific stages of the cardiac cycle because the cycle was discretized into ten averaged frames. The spatial resolution was 512×512, where the pixel size varied from 0.5×0.5mm to 0.75×0.75mm. Because it has been shown that strain and pressure peak nearly simultaneously in the cardiac cycle [14], we selected the frames in which the aorta had the largest and the smallest cross-sectional area. For our analysis, we referred to those frames as peak-systole and end-diastole, respectively, and all subsequent analysis was completed in those two frames.

Center-path generation

It is crucial in this analysis to accurately represent the vessel geometry with a center-path because the ostia were located along those paths. The center-paths, space-curves that represent the volumetric vessel, were extracted from the CT image data using custom software [17] in the following manner. An initial center-path was generated by an interpolated cubic-hermite-spline curve from hand-picked points selected along the center of the aorta. 2D automatic segmentation techniques were applied along the manual center-path to find the lumen boundary of the vessel at each spline coordinate at 2mm intervals. The centroid of the lumen boundary was calculated by averaging the coordinates of the closed-curve, followed by smoothing to eliminate artificial irregularities of the lumen boundary. Next, a coarse center-path was generated from the calculated set of centroids (approximately 100 points), and 10-mode Fourier smoothing was performed to remove high-frequency fluctuations due to image noise [19]. The finalized smoothed center-path was again interpolated by a cubic-hermite-spline. For each patient, two center-paths were created to represent the vessel at peak-systole and end-diastole. Both paths were subsequently used for the deformation and strain calculations.

Lagrangian reference frame

As noted, one novel feature of our method lies in the definition of the reference frame. We utilized anatomical markers along the thoracic aorta to examine the lumen boundary just distal to the ostia of intersecting vessels. To demonstrate the technique, we describe the method applied at the distal location of the left coronary artery (LCoA). First we traversed the center-path from peak-systole until the segmentation plane (which is perpendicular to the lumen) was just distal to the LCoA (see Figure 2a) and outlined the lumen boundary using automatic segmentation. We then used the center-path and image data from end-diastole and outlined the lumen boundary, again, just distal to the LCoA (see Figure 2b). These steps yielded two closed-curves that represented the same lumen boundary at peak-systole and end-diastole, enabling us to compare the lumen boundary of the vessel at the same anatomic location as it deformed over the cardiac cycle. This approach is analogous to fixing the reference frame to the vessel, known in mechanics as a Lagrangian reference frame. This approach contrasts the former methods of tracking deformation of the vessel at a fixed location in space [10, 13] using an Eulerian reference frame. To demonstrate the potential errors introduced using an Eulerian frame, we took the lumen boundary in peak-systole, as described above, and then in end-diastole fixed the location of the segmentation plane as shown in Figure 2c. If we applied the automatic segmentation at that location of the segmentation plane, we would have outlined a larger, incorrect lumen boundary, resulting from the through-plane motion of the ascending aorta.

Figure 2
A partial 3D volume-rendering of the ascending aorta is shown at (a) peak-systole, (b) end-diastole in the Lagrangian frame, and (c) end-diastole in the Eulerian frame. The white line is the segmentation plane aligned at the distal location of the LCA ...

Deformation Metrics of the Thoracic Aorta

We quantified the diameters and circumferential cyclic strain along the arch and DTA, the longitudinal cyclic strain of the DTA, and the length of the arch for the present study. These metrics are depicted in the schematic shown in Figure 3a and 3b. The diameter and circumferential cyclic strain was calculated at seven locations along the aorta: (1) distal to the left-coronary artery (LCoA), (2) proximal and (3) distal to the brachiocephalic trunk (BRC), (4) distal to the left-common carotid (LCC), (5) distal to the left subclavian (LSC), and distal to the (6) first and (7) seventh ICoA. The arch length was measured along the center-path from the LCoA to the first ICoA and the DTA length was measured along the vessel center-path from the first to seventh ICoA. Additionally, we quantified the relative motion between the ascending and descending aorta.

Figure 3
Displayed is a schematic of the thoracic aorta, where the branch vessels are drawn in-plane, which is not typical for patients. (a) The labels for the left coronary artery (LCA), the left subclavian artery (LSC), the first, third and seventh intercostal ...

Using the Lagrangian frame, we extracted seven lumen boundaries (Figure 3b) along the center-path of the aorta at peak-systole and end-diastole. A representative lumen boundary from peak-systole and end-diastole are shown in Figure 4a. Because each extracted lumen boundary was a 2D-closed curve represented by a series of points, the circumference of the lumen boundary was calculated by summing the distance between each of the points on the closed curve. The circumference was used in the calculation of the cyclic strain, not diameters or cross-sectional areas, as previously done by other researchers.

Figure 4
(a) An axial slice of the DTA was captured just distal to an intercostal artery. The white curve, from peak-systole, is super-imposed with the grey curve from end-diastole. Both curves are from the same material location. Notice the circumferential deformation ...

We used the Green-Lagrange strain tensor [20] to compute the circumferential cyclic strain. We assumed the deformation through the thickness of the vessel and in the axial direction was small compared to the circumferential deformation. As a result of those assumptions, the following expression was used to calculate the circumferential cyclic strain,


where CS was the systolic circumference and CD was the diastolic circumference. Additionally, we quantified the diameters at peak-systole using the simple circumference relationship, D=C/π.

We used the small strain approximation to calculate the longitudinal cyclic strain, which is simply the difference between the systolic and diastolic DTA lengths divided by the diastolic DTA length. Figure 4b illustrates the longitudinal cyclic motion of the DTA. The DTA length was quantified as the arc length along the center-path between the first and seventh ICoA. Likewise, the length of the arch was computed as the arc length along the center-path between the LCoA and the first ICoA.

Motion along the ascending aorta was more difficult to quantify because there are limited anatomical markers to track. Therefore, we calculated the relative motion between the ascending and descending aorta. Our technique involved constructing a straight line from the centroid of the lumen boundary at the distal location of the LCoA to the centroid of the lumen boundary at the third ICoA, shown by the dashed line in Figure 3a. The relative motion was calculated as the difference between the systolic and diastolic lengths divided by the diastolic length.

Statistical Analysis

We extracted the lumen boundary distal to each vessel ostium to avoid manual segmentation and intra-user variability. This enabled us to compute the circumferences of the lumen boundary for each patient without bias. The results for each group were organized by increasing age, and the comparisons were made using the paired t-test. P-values greater than 0.05 were considered not significant (NS), otherwise the p-value was reported for each metric.


The diameters of the thoracic aorta increased, on average, by 14% with age from the young (mean age 41 years) to the older (mean age 68 years) group. The circumferential cyclic strain of the thoracic aorta decreased, on average, by 55% with age from the young to the older group. The systolic diameters and circumferential cyclic strains for each of the seven locations for both groups are listed in Table 1. The systolic diameters for each aortic location are displayed in the top graph of Figure 4 and the circumferential cyclic strains are displayed in the bottom graph of Figure 4. The longitudinal cyclic strain decreased with age by 50% from the young to older group (2.0 ± 0.5% versus 1.0 ± 0.6%, p=0.004). The arch length increased by 14% with age from the young to the older group (134 ± 17mm versus 152 ± 10mm, p=0.03). Finally, the relative displacement between the ascending and descending aorta decreased with age by 65% from young to older group (6.7 ± 2% versus 2.3 ± 1%, p=0.01).

Table 1
The diameters (upper half) and circumferential cyclic strains (lower half) for the ascending aorta, the arch and the descending aorta are reported for the young and older groups, where each number 1-7 corresponds to the aortic location shown in the figure. ...

The diameters of the ascending aorta at the location of the LCoA and proximal to the BRC were not statistically different between the young and older group, approximately 32mm. However, the circumferential strain decreased at both locations by approximately 70% from the young to the old group (10 ± 3% versus 3 ± 1%, p<0.01 at LCoA and 11 ± 6% versus 3 ± 2%, p<0.01 proximal to the BRC). The diameters in the arch of the aorta increased with age by 20% at the distal BRC (27.1±2mm versus 32.4±4mm, p=0.02), by 15% at the distal LCC (25.2±1mm versus 29.1±3mm, p=0.006), and by 11% at the distal LSC (23.5±1mm versus 26.1±3mm, p=0.04). The latter location correlated to a similar increase in the proximal DTA, (22.8±1mm versus 26.6±3mm, p=0.02) and the distal DTA (21.1±1mm versus 24.5±3mm, p=0.02).

The diameters of the thoracic aorta also decreased with aortic location for both patient populations. This trend is evident in the top graph of Figure 4, where location 6 was statistically smaller than location 2 (p < 0.001), and location 7 was statistically smaller than location 6 (p < 0.001) for both groups. On the other hand, the circumferential cyclic strain did not decrease significantly with aortic location. In fact, the circumferential cyclic strain was not statistically different between locations 6 and 7 for the young group but was for the older group (p<0.03).

In summary, the diameters increased with age and decreased with aortic location, and the cyclic strain significantly decreased with age.


Deformation of the vessel lumen has been described by pulsatility, compliance, stiffness, radial displacement, and distensibility. In this work, we measured lumen deformation to quantify cyclic strain in the thoracic aorta, and then compared the measurements between a group of young (mean age 41-yrs) and older (mean age 68-yrs) patients. Specifically, we quantified the cyclic strain in the circumferential (around the lumen orthogonal to the length) and the longitudinal (along the length of the vessel) directions using the circumference lumen boundary. We report, for the first time, longitudinal cyclic strain, approximately 2% for the young group, which was about one-quarter that of the circumferential cyclic strain. We also report that the circumferential and longitudinal cyclic strain in the DTA decreased by at least 50% with age.

In addition, we observed that the aorta not only enlarges in the circumferential direction (≈10-15%) with age, but the aortic arch lengthens by a similar amount. We also discovered that the circumferential cyclic strain is nearly constant down the length of the aorta. The implication of constant cyclic strain is larger volumetric compliance in the proximal aorta compared with the distal aorta because the diameters are statistically larger in the proximal aorta (p<0.01).

During our analysis, we observed nonuniform circumferential deformation in the DTA where the deformation was the largest in the direction away from the paired-ICoA, a location of minimal displacement near the spine, as displayed in Figure 4a. These results are also similar to those measured by Draney et al. [21] in the thoracic aorta and by Goergen et al. [22] in the abdominal aorta, where the deformation was quantified as largest in the anterior direction. Although we cannot decompose the observed deformation into “nonuniform deformation” or “rigid-body motion with uniform deformation” components, it is likely that the observed deformation is nonuniform because we directly compare the same material locations. Heretofore, no stent-graft compensates for the nonuniform deformation or circumferential variations in cyclic strain of the thoracic aortic. This information may prove useful for design and bench-top testing of stent-grafts.

The cyclic strain information currently available is limited and conflicting. For example, Muhs et al. reported the diameter changes in the DTA in ten patients with AAA (no age or gender information was reported) at locations similar to 4, 5, 6, and 7 in Figure 3b. To compare our results with theirs, we assumed the patients were at least 55-years old because they had AAA. Their analysis yielded an average of 10% change in diameter in the DTA, which correlated with those measured in our young patient group. However, these values were at least 50% larger than the values measured in our older patient group. Additionally, van Prehn et al. reported diameter changes in the ascending aorta, at locations 1 and 2 in Figure 3b, of fifteen patients with AAA (mean age 72-years old). Their results were substantially larger than the cyclic strains we quantified for the older group (mean age 68). Both groups used cine-CTA in an Eulerian reference frame, which may account for some of the discrepancies because that approach does not account for though-plane motion. Moreover, we report the changes in the actual circumference of the lumen, not the changes in effective diameters, which were computed by assuming a circular lumen for the cross-sectional areas. For comparison, we computed the effective diameter from our cross-sectional area measurements and found the cyclic strains were approximately 30% larger. We believe this may result from the nonuniform circumferential deformation of the lumen, which cannot be captured by computing an effective diameter. These discrepancies demonstrate the need for consistent terminology and standards for reporting deformation in the human body. We should also mention that typical strain calculations assume a uniform radial expansion. By comparing the length changes in the circumference of the aorta, we eliminate that assumption, and we significantly decrease the error in the measurement. The lumen expands about 3-5 pixels in the largest radial direction and barely 1 pixel in the smallest direction. However, by comparing the circumference, we are comparing length changes on the order of 6-10mm (or 10-20 pixels), thereby minimizing the measurement error substantially.

Regarding the age-related changes in the thoracic aorta, qualitative inspection of the aortas suggested that in the older group the arch was more curved, with a visibly larger radius of curvature, and the great vessels branched off the arch at varying degrees and locations. For example, in Figure 1a, it appears as if the branch vessels are connected to the arch at about 90°, for the younger patient, whereas in Figure 1b, an older patient, the angle is less than 90°, and slightly more proximal to the ascending aorta. We are currently quantifying the curvature in the arch and DTA. The arch length and the angle at which the great vessels branch off of the arch can greatly affect device implantation, particularly for stent-grafts with side-branches. It would be advantageous to understand curvature changes of the arch for endovascular procedures. Further attention should also be given to the ascending aorta, where we observed large axial deformations and rigid-body motion. In addition, further analysis should be completed on patients with aneurysms and dissections, as well as patients (who may be young) that undergo traumatic injuries that result in cardiovascular pathology. Our methods are directly applicable to the study of diseased aortas.

Finally, because this was a retrospective examination of pre-existing CT image data, and demographics other than age and gender were unknown, the results of this study warrant a prospective study in the future.

In conclusion, we have reported the longitudinal and circumferential biomechanical cyclic strain in young and older patients with no visible signs of aortic pathology, along with length and diameter changes in the arch, and diameter changes along the thoracic aorta. The aorta enlarges circumferentially and axially and deforms significantly less in the circumferential and longitudinal directions. This analysis was a first step in understanding and quantifying the cyclic strains of the thoracic aorta, and creating a foundation for standards in reporting data related to in vivo deformation.

Figure 5
The top graph displays the diameters along the thoracic aorta at seven locations. The light and dark shaded bars correspond to the young and older patient populations, respectively. The diameters in the older group are statistically larger that the young ...


Funding Sources: Stanford School of Medicine, National Institutes of Health, and Medtronic Vascular, Inc.

Tina Morrison was supported by the Dean's Post Doctoral Fellowship at the Stanford School of Medicine. This work was also supported by the National Institutes of Health, through the NIH Roadmap for Medical Research Grant U54 GM072970 and by R01 HL064327. Funding was also provided by a research grant from Medtronic Vascular, Inc.


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