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Importance of initial stress for abdominal aortic aneurysm wall motion: Dynamic MRI validated finite element analysis
ARTICLE IN PRESS Journal of Biomechanics 42 (2009) 2369–2373
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Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Importance of initial stress for abdominal aortic aneurysm wall motion: Dynamic MRI validated finite element analysis M.A.G. Merkx a,b,c,, M. van ’t Veer b, L. Speelman a, M. Breeuwer d, J. Buth e, F.N. van de Vosse c a
Department of Biomedical Engineering, Maastricht University Medical Center, PO Box 5800, 6202 AZ Maastricht, The Netherlands Department of Cardiology, Catharina Hospital, Eindhoven, The Netherlands c Department of Biomedical Engineering, Eindhoven University of Technology, The Netherlands d Philips Healthcare, Healthcare Informatics, Best, The Netherlands e Department of Vascular Surgery, Catharina Hospital, Eindhoven, The Netherlands b
a r t i c l e in fo
abstract
Article history: Accepted 10 June 2009
Currently the transverse diameter is the primary decision criterion to assess rupture risk in patients with an abdominal aortic aneurysm (AAA). To obtain a measure for more patient-specific risk assessment, aneurysm wall stress, calculated using finite element analysis (FEA), has been evaluated in literature. In many cases, initial stress, present in the AAA wall during image acquisition, is not taken into account. In the current study the effect of initial stress incorporation (ISI) is determined by directly comparing wall displacements extracted from FEA and dynamic MRI. Ten patients with an aneurysm diameter 45:5 cm were scanned with cardiac triggered MRI. Semiautomatic segmentation of the AAA was performed on the diastolic phase. The segmented in-slice contours were propagated through the remaining cardiac phases using an active contour model as to track wall displacements on MRI. Consequently, FEA with and without ISI (no-ISI) was performed using the diastolic geometry with simultaneously measured intra-aneurysm pressure values as boundary condition. Contours extracted from FEA were compared with MRI contours at corresponding cardiac phases by distance and relative area differences. The wall displacements from FEA with ISI show significant better correspondence with wall motion from MRI data in comparison with the no-ISI FEA (deviation in wall displacement 1.7% vs. 12.4%; po0:001). Based on these results it can be concluded that incorporation of initial stress significantly improves wall displacement accuracy of FEA and therefore it should be incorporated in future analyses. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Abdominal aortic aneurysm Magnetic resonance imaging Patient specific models Finite element analysis Initial stress Wall displacement analysis
1. Introduction An abdominal aortic aneurysm (AAA) is a permanent dilatation of the abdominal aorta, which is located between renal arteries and the aortic bifurcation. The prevalence of AAA is 4–8% in older men and 0.5–1.5% in older women (Fleming et al., 2005). An AAA is usually asymptomatic until rupture, which leads to death in more than 80% (Basnyat et al., 1999). AAA are often detected during examinations for other symptoms with ultrasound, CT or MRI. Once detected, the AAA anterior–posterior diameter and diameter growth rate are carefully monitored over time. The critical diameter has been determined to be 5.5 cm (Greenhalgh et al., 1998). It is generally accepted that at this value the risk of complications due to rupture exceeds the risk of complications due to intervention. However, AAA ruptures are reported below this criterion, with an annual rupture risk of 0.3%
Corresponding author at: Department of Biomedical Engineering, Maastricht University Medical Center, PO Box 5800, 6202 AZ Maastricht, The Netherlands. E-mail address: [email protected] (M.A.G. Merkx).
0021-9290/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2009.06.053
for AAA below 3.0 cm, up to 1.5% for AAA between 4.0 and 4.9 cm (Brown and Powell, 1999). On the other hand, some AAA above 5.5 cm will not rupture in a patient’s lifetime. The annual rupture risk was estimated to be 9.4% per year for diameters between 5.5 and 5.9 cm and increases to 32.5% for AAA above 7.0 cm (Lederle et al., 2002). To obtain an indication of the patient-specific rupture risk, the value of aneurysm wall stress analysis has been assessed in literature (Raghavan et al., 2000; Fillinger et al., 2002, 2003; Venkatasubramaniam et al., 2004). Wall stress is calculated using finite element analysis (FEA), based on geometry data acquired with CT. To describe the behavior of tissue in the AAA wall, a nonlinear material model (Raghavan and Vorp, 2000) is commonly used for FEA. Despite the fact that initial stress is present inside the aneurysm at the moment of image acquisition, it was not taken into account in the previously mentioned FEA studies. Recently, methods have been developed by Raghavan et al. (2006), Lu et al. (2007) and de Putter et al. (2007) to account for this initial stress. The method of de Putter et al. (2007) calculates initial stress and consequently simulates the in vivo loading path of the AAA. This method is chosen in the current study to
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determine initial stress in the AAA wall, because it showed to produce a stress free solution for the unloaded geometry, which proves the correctness of this method. Unfortunately no method exists for in vivo validation of wall stress. Therefore, the aim of this study is to compare wall displacements derived from dynamic MRI with those derived by strain analyses calculated using FEA as an indirect measure for validation. The effect of initial stress incorporation (ISI) is determined, using the nonlinear material model and parameters of Raghavan et al. (2000).
2. Methods 2.1. Study population Ten male subjects listed for elective intervention of their AAA were included into the study. Exclusion criteria were contraindications for MRI, cardiac arrhythmia, and obstructed iliac arteries. The study was approved by the institutional review board of the Catharina Hospital Eindhoven, the Netherlands, and written informed consent was obtained from each patient prior to enrolment in the study. 2.2. Magnetic resonance imaging MRI data of the subjects were obtained with a Philips Gyroscan Intera 1.5 Tesla MR Scanner (Rel.10.4) (Philips Healthcare, Best, The Netherlands), using a SENSE cardiac coil. Patients were scanned without contrast enhancement and breath holding. The scanning volume was defined as the region proximal to the renal arteries until distal to the iliac bifurcation. Dynamic threedimensional balanced turbo field echo (3D B-TFE) and 2D B-TFE images were acquired in 15 phases of the cardiac cycle (VCG triggered). The proximal boundary of the AAA model was determined from the 2D quantitative flow (Qflow, Summers et al., 2005) imaging plane, which was placed perpendicular to the vessel wall (directly below the renal arteries). A static recording of the AAA was made with a black blood (BB) protocol. During the MR acquisition, blood pressure was measured using a fluid-filled catheter (van ’t Veer et al., 2008). Assuming abdominal pressure to be negligible compared to AAA pressure this equals transmural pressure. For an overview of the MRI parameters, the reader is referred to Table 1.
correction of the in-slice contours was allowed to correct for segmentation inaccuracies, for example resulting from high AAA tortuosity or presence of the vena cava. For more details on the segmentation procedure see Breeuwer et al. (2008). Thereafter, the patient-specific geometry was exported for FEA as a 3D finite element mesh, assuming a constant wall thickness of 2 mm, consisting of 15-node quadratic Crouzeix–Raviart tetrahedrons. 2.3.2. MRI contour extraction To derive in-slice wall displacements from the MRI data through the complete cardiac cycle, in-slice contours from the 3D segmentation were extracted and propagated to the remaining phases of the cardiac cycle using the contour propagation algorithm of Hautvast et al. (2006). This resulted in 15 series of 2D contours along the AAA, one per cardiac phase. The propagation algorithm uses an active contour model, which balances contour smoothness against image features, in this case correlation of 2D B-TFE image profiles perpendicular to the contour. 2.4. Finite element analysis The 3D mesh was used as geometric input for the patientspecific FEA, which was performed using the finite element package Sepran (Sepra, Den Haag, The Netherlands). An FEA solves the balance equations of mass and momentum, given a material-specific constitutive equation and boundary conditions. These latter were used to fixate the proximal and distal planes. Additionally, the patient-specific blood pressure, measured simultaneously during image acquisition, was applied to the inner wall of the mesh and outside pressure was assumed to be zero. The common nonlinear constitutive model of Raghavan and Vorp (2000) was adapted for FEA:
r ¼ ph I þ 2ða þ 2bðIB 3ÞÞðB IÞ þ 2gðIIIB 1ÞI
with I the identity matrix, B the Finger tensor, and IB and IIIB the first and third invariant of B. For complete derivation see Speelman et al. (2009). The exact material parameters were a ¼ 0:174 MPa, b ¼ 1:881 MPa (Raghavan and Vorp, 2000) and g ¼ 0:5 MPa.
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2.3. Image processing 2.3.1. Segmentation A 3D geometry of the patient’s aneurysm was acquired with prototype segmentation software, developed by Philips Healthcare, The Netherlands, in collaboration with Eindhoven University of Technology, The Netherlands. First, all images were registered to the 3D B-TFE images. The automatic 3D segmentation was performed on the diastolic phase, using image features from the 2D B-TFE, 3D B-TFE and BB acquisitions. Subsequently, manual
Protocol
Slice type
Voxel size (mm)
TR (ms)
TE (ms)
Flip angle (deg)
2D BTFE 3D BTFE 2D Qflow Black blood
Interleaved Continuous Continuous Interleaved
1.34 1.34 3.00 1.34 1.34 6.00 2.34 2.34 6.00 0.78 0.78 6.00
4.5 4.5 9.8 –
2.2 2.3 6.3 18
50 50 15 90
C
80
0 Table 1 Overview of MRI protocols.
ð1Þ
E
B2
A 1
B1
D
1.2
1.4
Fig. 1. Schematic pressure–stretch relations with matching cross-sections. Crosssection B1 represents the geometry as obtained from the MRI data, without initial stress. On the contrary, cross-section B2 is the actual geometry including initial stress. The in vivo (or FEA with ISI) loading path starts from B1 , crosses B2 and ends on systolic pressure at cross-section C ðA2B2 2CÞ. The no-ISI FEA starts at crosssection B1 as well, but neglects initial stress and immediately applies deformations, leading to the path towards systolic cross-section E ðB1 2D2EÞ.
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The initial stress was incorporated using the backward incremental method from de Putter et al. (2007). For both FEA with and without ISI (no-ISI), the diastolic geometry, as obtained by dynamic MRI, was used. In the ISI method, the accompanying measured diastolic pressure was used as reference pressure. Fig. 1 schematically shows the in vivo loading path of an artery. The path starts with an undeformed and unloaded geometry (crosssection A). Upon pressure (or load) application the geometry expands, while stress inside the material increases ðA2B2 2CÞ. Upon imaging, the diastolic geometry B1 is acquired, in which the stresses present in the wall are unknown. The no-ISI FEA starts with the stretched geometry of crosssection B1 and follows the loading path to cross-sections D and E. It can be seen from Fig. 1 that an overestimation of deformations may be expected for patient-specific no-ISI FEA. The FEA with ISI also starts at B1 , but in contrast to the previous method, deformations are discarded during the pressure loading path until diastolic pressure is reached ðB2 Þ. As a result of this method, no equilibrium exists between pressure, stress and displacements in the intermediate iterations. The last pressure step in the FEA is chosen small enough to ensure convergence to a valid diastolic equilibrium state. The loading path is continued according to the in vivo path towards systolic pressure ðCÞ. For the FEA with ISI no overestimation of deformations is expected (Fig. 1).
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Hautvast et al. (2006). In image analysis the Dx is frequently used for assessment of the differences between the contours. This method is not invariant for rotations and rigid body motion, however, therefore the relative area difference DA per slice was determined as well:
DAj ¼
AFj AM j AM j
100 ð%Þ;
j ¼ 1...S
ð3Þ
are the with S the number of slices and where AFj and AM j corresponding areas of the contours of slice j from FEA (F) and MRI (M) respectively (see also Fig. 2). 2.6. Statistical analysis A chi-square goodness-of-fit test was performed to check whether the data can be assumed to be normally distributed. Consequently, a student’s t-test or Wilcoxon rank-sum test was performed when appropriate, to compare the results of MRI with ISI and no-ISI FEA. A significance level of po0:01 was chosen and Bonferroni correction for multiple testing was applied (Rosner, 2005).
3. Results 2.5. Contour comparison Propagated in-slice MRI contours and corresponding calculated FEA contours of the 15 cardiac phases were compared. Two different measures were calculated. The first was the average distance between the contours, the second measure compared differences in cross-sectional area. In Fig. 2 both measures are shown schematically. For distance calculation the contours were segmented into equidistant points ðN ¼ 30Þ. To find the corresponding points between the contours from MRI and FEA a repeated averaging algorithm was applied (Chalana and Kim, 1997). This algorithm iteratively refines the initial single-point correspondence, which is based on the closest point on one contour to a selected point on a second. The average distance per contour was calculated according to the following equation, using the FEA and MRI contours:
Dx ¼
N 1X JxF xM i J N i¼1 i
After careful evaluation of the comparison between FEA and MRI contours for all patients, irregularities were found in the contour registration of two patients, caused by segmentation inaccuracies. These inaccuracies were so large that manual adjustments would mean a totally manual segmentation, therefore further analysis is based on the remaining eight patients. The statistics showed that a normal distribution could not be assumed for the comparison of MRI to ISI FEA ðpo0:001Þ and no-ISI FEA ðpo0:001Þ, therefore the resulting data were analyzed with the
MRI -20 -40
ðmmÞ
ð2Þ
-60
where xFi and xM i are positions of the corresponding points on contours from FEA (F) and MRI (M) respectively (see Fig. 2 for a schematic representation). Detailed information is given in
0.40.81.31.72.12.5
3.87.712 15 19 23
-80
0
20
40
x [mm] MRI -20 -40
M
Aj
M xi
F
-60
xi
0.20.30.50.60.80.9 F
Aj
F Fig. 2. Schematic view of contour comparison measures. Areas AM j (MRI) and Aj (FEA) are used for the relative area difference, points xFi (FEA) and xM (MRI) i schematically show the distance differences for one particular segment on the contour.
1.73.45.16.88.510
-80
0
20
40
x [mm] Fig. 3. Example of the comparison of FEA with MRI for one patient. Distance and area differences are visualized on the FEA contours, using the color map as given below. Note the difference in scale for the FEA with ISI and no-ISI in this color map, used to visualize the range of values inside one FEA method. On the right side an example of the FEA and MRI contours is given for the contour indicated by the arrow.
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Wilcoxon rank-sum test. Statistical data will be expressed as median (IQR), with IQR the interquartile range, in the remaining part of this article. Fig. 3 shows the systolic distance ðDxÞ and area ðDAÞ differences between the FEA and MRI contours on the FEA contour for one patient. Notice the difference in the scale in the comparison. One contour from the total volume is selected (indicated by the arrow) and the resulting contours from the FEA and MRI for this selection are shown on the right side of the figure. For all patients separately and for the complete patient group, the distance ðDxÞ and area ðDAÞ differences were much smaller with ISI than with no-ISI ðpo0:001Þ. Figs. 4 and 5 express the data for the complete group with a box-and-whisker plot for the differences in distance ðDxÞ and area ðDAÞ respectively. Besides the median and interquartile range of the data, also outliers, which are outside 1:5 interquartile range (Rosner, 2005), are shown in these figures. For no-ISI FEA a higher median in the distance differences ðDxÞ was found (no-ISI 1.48 (0.81) mm vs. ISI 0.45 (0.33) mm; po0:001). The no-ISI relative area differences ðDAÞ were also
5 4.5 4
x [mm]
3.5 3 2.5 2 1.5 1 0.5 0
no-ISI
ISI
Fig. 4. Average distance difference between FEA and MRI contours. Values above or below 1:5 interquartile range are considered to be outliers (no-ISI 0.36%; ISI 8.2%).
60 50 40 30 20 10 0 -10
no-ISI
ISI
Fig. 5. Relative area difference between FEA and MRI contours. Values above or below 1:5 interquartile range are considered to be outliers (no-ISI 2.5%; ISI 3.1%).
significantly larger (no-ISI 12.4 (6.0)% vs. ISI 1.7 (3.5)%; po0:001). The median distance and area differences are thus reduced by 70% and 86% for the distance and area differences respectively, when initial stress is accounted for.
4. Discussion In the pursuit of a more patient-specific rupture risk assessment, many studies have focused on AAA wall stress analyses using FEA (Fillinger et al., 2002; Raghavan et al., 2000; Venkatasubramaniam et al., 2004). A nonlinear material model was defined in the past for the AAA wall (Raghavan et al., 2000), based on tensile tests, to acquire more realistic wall stress calculations. More recently several methods were proposed to correct for the initial stress (Raghavan et al., 2006; Lu et al., 2007; de Putter et al., 2007) present during data acquisition. However, no methods or measurements exist to verify in vivo wall stress computed by these models. In the current study, an indirect method is proposed to evaluate the effect of initial stress incorporation (ISI) in FEA, by comparing wall displacements from dynamic MRI with wall displacements calculated from FEA with and without ISI (no-ISI). Intra-aortic pressure measurements were performed during the image acquisition to facilitate the coupling between the actual aortic blood pressure and the wall excursions due to this blood pressure. Previous research estimated the blood pressure by a non-invasively measured systolic arm cuff pressure (Fillinger et al., 2002; Raghavan et al., 2000; Venkatasubramaniam et al., 2004). It has been shown, however, that values measured with a brachial arm cuff underestimate intra-aneurysm systolic pressure by 5% and overestimate diastolic pressure by 12%, on average (van ’t Veer et al., 2008). If the actual pressure curve is unavailable the corrected systolic and diastolic cuff pressure could be used. In common wall stress analyses a geometry obtained with CT or MRI is presumed to be un-stretched and pressure loading takes place along the nonlinear path B1 D E (Fig. 1). The method of de Putter et al. (2007) takes initial stress in the geometry into account ðB1 2B2 Þ and pressure is consequently built up to C along the in vivo loading path. The effect of this initial stress incorporation was determined. As shown in Fig. 1, an overestimation of the deformations is expected. It could be concluded from this figure that a constant correction factor can be deducted. However, when performing patient-specific FEA, the effect may be different for each patient due to local curvature of the patient’s geometry in combination with nonlinearity of the constitutive equation (Speelman et al., 2009). For the patient group, the contours obtained from MRI were compared with the corresponding contours extracted from the FEA using distance Dx and area DA differences. Fig. 4 shows that the differences in contour distances are lower with ISI. In other words, deformations are better described by FEA with ISI. The DA and Dx both show the superiority of ISI in FEA when compared with MRI contours (Fig. 5). It can be concluded from the data that the method with ISI better agrees with reality than the common no-ISI FEA ðpo0:001Þ. When quantitatively comparing the contours of the FEA with the MRI contours, the median DA approaches zero for the method with ISI, while the median DA in the no-ISI FEA is approximately nine times higher. This emphasizes the need to take initial stress into account. There is still a difference between the measured wall displacements on MRI and the FEA with ISI however. This could be explained by possible inaccuracies in image acquisition, segmentation and because of assumptions made in the current FEA. In the implemented FEA, possible presence of residual stress, thrombus and calcification are ignored and wall thickness is
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assumed to be constant. Furthermore, the spine might restrict backward AAA deformation, but at visual inspection of the data this effect was not confirmed. The influence of these assumptions could be investigated in future research, but their contribution to the deformation is considered to be small, since the calculated contours of FEA with ISI closely approach the MRI contours ðDA 1:7 ð3:5Þ%Þ. In contrast to the previous research of Fillinger et al. (2002), Raghavan et al. (2000) and Venkatasubramaniam et al. (2004), which concentrated on analysis of static CT data, the current study used dynamic MRI data for FEA. A disadvantage of the dynamic MRI used in this study is the long acquisition time. Therefore, concessions were made to the image quality, which may induce inaccuracies in the automatic segmentation and propagation method. However, the segmentation and propagation were verified and manually corrected if necessary, so differences found in the contour comparison measures between ISI and no-ISI FEA cannot be attributed to these inaccuracies. To obtain the AAA wall displacements with improved spatial resolution the current protocol could be extended, or as alternative cardiac gating could be added to the CT acquisition. However, from radiation perspective the former is preferred. The contours of MRI were propagated using the 2D B-TFE images. This explicitly assumes that longitudinal movement of the AAA is small. Currently no methods were available to use the propagation method on the 3D B-TFE images, because AAA wall delineation in the 3D B-TFE is poor compared with the 2D B-TFE images, which justifies this approach.
5. Conclusion The wall displacements from FEA with initial stress incorporation show significant better correspondence with wall motions from MRI data in comparison with FEA in which initial stress is neglected. These values were obtained with the usual parameters for the nonlinear material (Raghavan et al., 2000). Based on these results it can be concluded that incorporation of initial stress significantly improves wall displacement accuracy of FEA and therefore it should be incorporated in future analyses. References Basnyat, P.S., Biffin, A., Moseley, L., Hedgeds, R., Lewis, M.H., 1999. Deaths from ruptured abdominal aortic aneurysm in Wales. Br. J. Surg. Soc. 86 (5), 693. Breeuwer, M., de Putter, S., Kose, U., Speelman, L., Visser, K., Gerritsen, F., Hoogeveen, R., Krams, R., van den Bosch, H., Buth, J., Gunther, T., Wolters, B.,
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van Dam, F., van de Vosse, F., 2008. Towards patient-specific risk assessment of abdominal aortic aneurysm. Med. Biol. Eng. Comput. 46 (11), 1085–1095. Brown, L.C., Powell, J.T., 1999. Risk factors for aneurysm rupture in patients kept under ultrasound surveillance. Ann. Surg. 230 (3), 289–296. Chalana, V., Kim, Y., 1997. A methodology for evaluation of boundary detection algorithms on medical images. IEEE Trans. Med. Imaging 16 (5), 642–652. de Putter, S., Wolters, B.J.B.M., Rutten, M.C.M., Breeuwer, M., Gerritsen, F.A., van de Vosse, F.N., 2007. Patient-specific initial wall stress in abdominal aortic aneurysms with a backward incremental method. J. Biomech. 40 (5), 1081–1090. Fillinger, M.F., Marra, S.P., Raghavan, M.L., Kennedy, F.E., 2003. Prediction of rupture risk in abdominal aortic aneurysm during observation: wall stress versus diameter. J. Vasc. Surg. 37 (4), 724–732. Fillinger, M.F., Raghavan, M.L., Marra, S.P., Cronenwett, J.L., Kennedy, F.E., 2002. In vivo analysis of mechanical wall stress and abdominal aortic aneurysm rupture risk. J. Vasc. Surg. 36 (3), 589–597. Fleming, C., Whitlock, E.P., Beil, T.L., Lederle, F.A., 2005. Screening for abdominal aortic aneurysm: a best-evidence systematic review for the U.S. preventive services task force. Ann. Int. Med. 142 (3), 203–211. Greenhalgh, R.M., Forbes, J.F., Fowkes, F.G., Powel, J.T., Ruckley, C.V., Brady, A.R., Brown, L.C., Thompson, S.G., 1998. Early elective open surgical repair of small abdominal aortic aneurysms is not recommended: results of the UK small aneurysm trial. Eur. J. Vasc. Endovasc. Surg. 16 (6), 462–464. Hautvast, G., Lobregt, S., Breeuwer, M., Gerritsen, F., 2006. Automatic contour propagation in cine cardiac magnetic resonance images. IEEE Trans. Med. Imaging 25 (11), 1472–1482. Lederle, F.A., Johnson, G.R., Wilson, S.E., Ballard, D.J., Jordan, W.D.J., Blebea, J., Littooy, F.N., Freischlag, J.A., Bandyk, D., Rapp, J.H., Salam, A.A., 2002. Rupture rate of large abdominal aortic aneurysms in patients refusing or unfit for elective repair. JAMA 287 (22), 2968–2972. Lu, J., Zhou, X., Raghavan, M.L., 2007. Inverse elastostatic stress analysis in predeformed biological structures: demonstration using abdominal aortic aneurysms. J. Biomech. 40 (3), 693–696. Raghavan, M.L., Ma, B., Fillinger, M.F., 2006. Non-invasive determination of zeropressure geometry of arterial aneurysms. Ann. Biomed. Eng. 34 (9), 1414–1419. Raghavan, M.L., Vorp, D.A., 2000. Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability. J. Biomech. 33 (4), 475–482. Raghavan, M.L., Vorp, D.A., Federle, M.P., Makaroun, M.S., Webster, M.W., 2000. Wall stress distribution on three-dimensionally reconstructed models of human abdominal aortic aneurysm. J. Vasc. Surg. 31 (4), 760–769. Rosner, B., 2005. Fundamentals of Biostatistics, sixth ed. Cengage Learning. Speelman, L., Bosboom, M., Schurink, G., Buth, J., Breeuwer, M., Jacobs, M., van de Vosse, F. 2009. Initial stress and nonlinear material behavior in patient-specific AAA wall stress analysis. J. Biomech., in press, doi:10.1016/j.jbiomech.2009.04. 020. Summers, P.E., Holdsworth, D.W., Nikolov, H.N., Rutt, B.K., Drangova, M., 2005. Multisite trial of MR flow measurement: phantom and protocol design. J. Magn. Reson. Imaging 21 (5), 620–631. van ’t Veer, M., Buth, J., Merkx, M.A.G., Tonino, P., van den Bosch, H., Pijls, N., van de Vosse, F., 2008. Biomechanical properties of abdominal aortic aneurysms assessed by simultaneously measured pressure and volume changes in humans. J. Vasc. Surg. 48 (6), 1401–1407. Venkatasubramaniam, A.K., Fagan, M.J., Mehta, T., Mylankal, K.J., Ray, B., Kuhan, G., Chetter, I.C., McCollum, P.T., 2004. A comparative study of aortic wall stress using finite element analysis for ruptured and non-ruptured abdominal aortic aneurysms. Eur. J. Vasc. Endovasc. Surg. 28 (2), 168–176.
Contents lists available at ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Importance of initial stress for abdominal aortic aneurysm wall motion: Dynamic MRI validated finite element analysis M.A.G. Merkx a,b,c,, M. van ’t Veer b, L. Speelman a, M. Breeuwer d, J. Buth e, F.N. van de Vosse c a
Department of Biomedical Engineering, Maastricht University Medical Center, PO Box 5800, 6202 AZ Maastricht, The Netherlands Department of Cardiology, Catharina Hospital, Eindhoven, The Netherlands c Department of Biomedical Engineering, Eindhoven University of Technology, The Netherlands d Philips Healthcare, Healthcare Informatics, Best, The Netherlands e Department of Vascular Surgery, Catharina Hospital, Eindhoven, The Netherlands b
a r t i c l e in fo
abstract
Article history: Accepted 10 June 2009
Currently the transverse diameter is the primary decision criterion to assess rupture risk in patients with an abdominal aortic aneurysm (AAA). To obtain a measure for more patient-specific risk assessment, aneurysm wall stress, calculated using finite element analysis (FEA), has been evaluated in literature. In many cases, initial stress, present in the AAA wall during image acquisition, is not taken into account. In the current study the effect of initial stress incorporation (ISI) is determined by directly comparing wall displacements extracted from FEA and dynamic MRI. Ten patients with an aneurysm diameter 45:5 cm were scanned with cardiac triggered MRI. Semiautomatic segmentation of the AAA was performed on the diastolic phase. The segmented in-slice contours were propagated through the remaining cardiac phases using an active contour model as to track wall displacements on MRI. Consequently, FEA with and without ISI (no-ISI) was performed using the diastolic geometry with simultaneously measured intra-aneurysm pressure values as boundary condition. Contours extracted from FEA were compared with MRI contours at corresponding cardiac phases by distance and relative area differences. The wall displacements from FEA with ISI show significant better correspondence with wall motion from MRI data in comparison with the no-ISI FEA (deviation in wall displacement 1.7% vs. 12.4%; po0:001). Based on these results it can be concluded that incorporation of initial stress significantly improves wall displacement accuracy of FEA and therefore it should be incorporated in future analyses. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Abdominal aortic aneurysm Magnetic resonance imaging Patient specific models Finite element analysis Initial stress Wall displacement analysis
1. Introduction An abdominal aortic aneurysm (AAA) is a permanent dilatation of the abdominal aorta, which is located between renal arteries and the aortic bifurcation. The prevalence of AAA is 4–8% in older men and 0.5–1.5% in older women (Fleming et al., 2005). An AAA is usually asymptomatic until rupture, which leads to death in more than 80% (Basnyat et al., 1999). AAA are often detected during examinations for other symptoms with ultrasound, CT or MRI. Once detected, the AAA anterior–posterior diameter and diameter growth rate are carefully monitored over time. The critical diameter has been determined to be 5.5 cm (Greenhalgh et al., 1998). It is generally accepted that at this value the risk of complications due to rupture exceeds the risk of complications due to intervention. However, AAA ruptures are reported below this criterion, with an annual rupture risk of 0.3%
Corresponding author at: Department of Biomedical Engineering, Maastricht University Medical Center, PO Box 5800, 6202 AZ Maastricht, The Netherlands. E-mail address: [email protected] (M.A.G. Merkx).
0021-9290/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2009.06.053
for AAA below 3.0 cm, up to 1.5% for AAA between 4.0 and 4.9 cm (Brown and Powell, 1999). On the other hand, some AAA above 5.5 cm will not rupture in a patient’s lifetime. The annual rupture risk was estimated to be 9.4% per year for diameters between 5.5 and 5.9 cm and increases to 32.5% for AAA above 7.0 cm (Lederle et al., 2002). To obtain an indication of the patient-specific rupture risk, the value of aneurysm wall stress analysis has been assessed in literature (Raghavan et al., 2000; Fillinger et al., 2002, 2003; Venkatasubramaniam et al., 2004). Wall stress is calculated using finite element analysis (FEA), based on geometry data acquired with CT. To describe the behavior of tissue in the AAA wall, a nonlinear material model (Raghavan and Vorp, 2000) is commonly used for FEA. Despite the fact that initial stress is present inside the aneurysm at the moment of image acquisition, it was not taken into account in the previously mentioned FEA studies. Recently, methods have been developed by Raghavan et al. (2006), Lu et al. (2007) and de Putter et al. (2007) to account for this initial stress. The method of de Putter et al. (2007) calculates initial stress and consequently simulates the in vivo loading path of the AAA. This method is chosen in the current study to
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determine initial stress in the AAA wall, because it showed to produce a stress free solution for the unloaded geometry, which proves the correctness of this method. Unfortunately no method exists for in vivo validation of wall stress. Therefore, the aim of this study is to compare wall displacements derived from dynamic MRI with those derived by strain analyses calculated using FEA as an indirect measure for validation. The effect of initial stress incorporation (ISI) is determined, using the nonlinear material model and parameters of Raghavan et al. (2000).
2. Methods 2.1. Study population Ten male subjects listed for elective intervention of their AAA were included into the study. Exclusion criteria were contraindications for MRI, cardiac arrhythmia, and obstructed iliac arteries. The study was approved by the institutional review board of the Catharina Hospital Eindhoven, the Netherlands, and written informed consent was obtained from each patient prior to enrolment in the study. 2.2. Magnetic resonance imaging MRI data of the subjects were obtained with a Philips Gyroscan Intera 1.5 Tesla MR Scanner (Rel.10.4) (Philips Healthcare, Best, The Netherlands), using a SENSE cardiac coil. Patients were scanned without contrast enhancement and breath holding. The scanning volume was defined as the region proximal to the renal arteries until distal to the iliac bifurcation. Dynamic threedimensional balanced turbo field echo (3D B-TFE) and 2D B-TFE images were acquired in 15 phases of the cardiac cycle (VCG triggered). The proximal boundary of the AAA model was determined from the 2D quantitative flow (Qflow, Summers et al., 2005) imaging plane, which was placed perpendicular to the vessel wall (directly below the renal arteries). A static recording of the AAA was made with a black blood (BB) protocol. During the MR acquisition, blood pressure was measured using a fluid-filled catheter (van ’t Veer et al., 2008). Assuming abdominal pressure to be negligible compared to AAA pressure this equals transmural pressure. For an overview of the MRI parameters, the reader is referred to Table 1.
correction of the in-slice contours was allowed to correct for segmentation inaccuracies, for example resulting from high AAA tortuosity or presence of the vena cava. For more details on the segmentation procedure see Breeuwer et al. (2008). Thereafter, the patient-specific geometry was exported for FEA as a 3D finite element mesh, assuming a constant wall thickness of 2 mm, consisting of 15-node quadratic Crouzeix–Raviart tetrahedrons. 2.3.2. MRI contour extraction To derive in-slice wall displacements from the MRI data through the complete cardiac cycle, in-slice contours from the 3D segmentation were extracted and propagated to the remaining phases of the cardiac cycle using the contour propagation algorithm of Hautvast et al. (2006). This resulted in 15 series of 2D contours along the AAA, one per cardiac phase. The propagation algorithm uses an active contour model, which balances contour smoothness against image features, in this case correlation of 2D B-TFE image profiles perpendicular to the contour. 2.4. Finite element analysis The 3D mesh was used as geometric input for the patientspecific FEA, which was performed using the finite element package Sepran (Sepra, Den Haag, The Netherlands). An FEA solves the balance equations of mass and momentum, given a material-specific constitutive equation and boundary conditions. These latter were used to fixate the proximal and distal planes. Additionally, the patient-specific blood pressure, measured simultaneously during image acquisition, was applied to the inner wall of the mesh and outside pressure was assumed to be zero. The common nonlinear constitutive model of Raghavan and Vorp (2000) was adapted for FEA:
r ¼ ph I þ 2ða þ 2bðIB 3ÞÞðB IÞ þ 2gðIIIB 1ÞI
with I the identity matrix, B the Finger tensor, and IB and IIIB the first and third invariant of B. For complete derivation see Speelman et al. (2009). The exact material parameters were a ¼ 0:174 MPa, b ¼ 1:881 MPa (Raghavan and Vorp, 2000) and g ¼ 0:5 MPa.
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2.3. Image processing 2.3.1. Segmentation A 3D geometry of the patient’s aneurysm was acquired with prototype segmentation software, developed by Philips Healthcare, The Netherlands, in collaboration with Eindhoven University of Technology, The Netherlands. First, all images were registered to the 3D B-TFE images. The automatic 3D segmentation was performed on the diastolic phase, using image features from the 2D B-TFE, 3D B-TFE and BB acquisitions. Subsequently, manual
Protocol
Slice type
Voxel size (mm)
TR (ms)
TE (ms)
Flip angle (deg)
2D BTFE 3D BTFE 2D Qflow Black blood
Interleaved Continuous Continuous Interleaved
1.34 1.34 3.00 1.34 1.34 6.00 2.34 2.34 6.00 0.78 0.78 6.00
4.5 4.5 9.8 –
2.2 2.3 6.3 18
50 50 15 90
C
80
0 Table 1 Overview of MRI protocols.
ð1Þ
E
B2
A 1
B1
D
1.2
1.4
Fig. 1. Schematic pressure–stretch relations with matching cross-sections. Crosssection B1 represents the geometry as obtained from the MRI data, without initial stress. On the contrary, cross-section B2 is the actual geometry including initial stress. The in vivo (or FEA with ISI) loading path starts from B1 , crosses B2 and ends on systolic pressure at cross-section C ðA2B2 2CÞ. The no-ISI FEA starts at crosssection B1 as well, but neglects initial stress and immediately applies deformations, leading to the path towards systolic cross-section E ðB1 2D2EÞ.
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The initial stress was incorporated using the backward incremental method from de Putter et al. (2007). For both FEA with and without ISI (no-ISI), the diastolic geometry, as obtained by dynamic MRI, was used. In the ISI method, the accompanying measured diastolic pressure was used as reference pressure. Fig. 1 schematically shows the in vivo loading path of an artery. The path starts with an undeformed and unloaded geometry (crosssection A). Upon pressure (or load) application the geometry expands, while stress inside the material increases ðA2B2 2CÞ. Upon imaging, the diastolic geometry B1 is acquired, in which the stresses present in the wall are unknown. The no-ISI FEA starts with the stretched geometry of crosssection B1 and follows the loading path to cross-sections D and E. It can be seen from Fig. 1 that an overestimation of deformations may be expected for patient-specific no-ISI FEA. The FEA with ISI also starts at B1 , but in contrast to the previous method, deformations are discarded during the pressure loading path until diastolic pressure is reached ðB2 Þ. As a result of this method, no equilibrium exists between pressure, stress and displacements in the intermediate iterations. The last pressure step in the FEA is chosen small enough to ensure convergence to a valid diastolic equilibrium state. The loading path is continued according to the in vivo path towards systolic pressure ðCÞ. For the FEA with ISI no overestimation of deformations is expected (Fig. 1).
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Hautvast et al. (2006). In image analysis the Dx is frequently used for assessment of the differences between the contours. This method is not invariant for rotations and rigid body motion, however, therefore the relative area difference DA per slice was determined as well:
DAj ¼
AFj AM j AM j
100 ð%Þ;
j ¼ 1...S
ð3Þ
are the with S the number of slices and where AFj and AM j corresponding areas of the contours of slice j from FEA (F) and MRI (M) respectively (see also Fig. 2). 2.6. Statistical analysis A chi-square goodness-of-fit test was performed to check whether the data can be assumed to be normally distributed. Consequently, a student’s t-test or Wilcoxon rank-sum test was performed when appropriate, to compare the results of MRI with ISI and no-ISI FEA. A significance level of po0:01 was chosen and Bonferroni correction for multiple testing was applied (Rosner, 2005).
3. Results 2.5. Contour comparison Propagated in-slice MRI contours and corresponding calculated FEA contours of the 15 cardiac phases were compared. Two different measures were calculated. The first was the average distance between the contours, the second measure compared differences in cross-sectional area. In Fig. 2 both measures are shown schematically. For distance calculation the contours were segmented into equidistant points ðN ¼ 30Þ. To find the corresponding points between the contours from MRI and FEA a repeated averaging algorithm was applied (Chalana and Kim, 1997). This algorithm iteratively refines the initial single-point correspondence, which is based on the closest point on one contour to a selected point on a second. The average distance per contour was calculated according to the following equation, using the FEA and MRI contours:
Dx ¼
N 1X JxF xM i J N i¼1 i
After careful evaluation of the comparison between FEA and MRI contours for all patients, irregularities were found in the contour registration of two patients, caused by segmentation inaccuracies. These inaccuracies were so large that manual adjustments would mean a totally manual segmentation, therefore further analysis is based on the remaining eight patients. The statistics showed that a normal distribution could not be assumed for the comparison of MRI to ISI FEA ðpo0:001Þ and no-ISI FEA ðpo0:001Þ, therefore the resulting data were analyzed with the
MRI -20 -40
ðmmÞ
ð2Þ
-60
where xFi and xM i are positions of the corresponding points on contours from FEA (F) and MRI (M) respectively (see Fig. 2 for a schematic representation). Detailed information is given in
0.40.81.31.72.12.5
3.87.712 15 19 23
-80
0
20
40
x [mm] MRI -20 -40
M
Aj
M xi
F
-60
xi
0.20.30.50.60.80.9 F
Aj
F Fig. 2. Schematic view of contour comparison measures. Areas AM j (MRI) and Aj (FEA) are used for the relative area difference, points xFi (FEA) and xM (MRI) i schematically show the distance differences for one particular segment on the contour.
1.73.45.16.88.510
-80
0
20
40
x [mm] Fig. 3. Example of the comparison of FEA with MRI for one patient. Distance and area differences are visualized on the FEA contours, using the color map as given below. Note the difference in scale for the FEA with ISI and no-ISI in this color map, used to visualize the range of values inside one FEA method. On the right side an example of the FEA and MRI contours is given for the contour indicated by the arrow.
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Wilcoxon rank-sum test. Statistical data will be expressed as median (IQR), with IQR the interquartile range, in the remaining part of this article. Fig. 3 shows the systolic distance ðDxÞ and area ðDAÞ differences between the FEA and MRI contours on the FEA contour for one patient. Notice the difference in the scale in the comparison. One contour from the total volume is selected (indicated by the arrow) and the resulting contours from the FEA and MRI for this selection are shown on the right side of the figure. For all patients separately and for the complete patient group, the distance ðDxÞ and area ðDAÞ differences were much smaller with ISI than with no-ISI ðpo0:001Þ. Figs. 4 and 5 express the data for the complete group with a box-and-whisker plot for the differences in distance ðDxÞ and area ðDAÞ respectively. Besides the median and interquartile range of the data, also outliers, which are outside 1:5 interquartile range (Rosner, 2005), are shown in these figures. For no-ISI FEA a higher median in the distance differences ðDxÞ was found (no-ISI 1.48 (0.81) mm vs. ISI 0.45 (0.33) mm; po0:001). The no-ISI relative area differences ðDAÞ were also
5 4.5 4
x [mm]
3.5 3 2.5 2 1.5 1 0.5 0
no-ISI
ISI
Fig. 4. Average distance difference between FEA and MRI contours. Values above or below 1:5 interquartile range are considered to be outliers (no-ISI 0.36%; ISI 8.2%).
60 50 40 30 20 10 0 -10
no-ISI
ISI
Fig. 5. Relative area difference between FEA and MRI contours. Values above or below 1:5 interquartile range are considered to be outliers (no-ISI 2.5%; ISI 3.1%).
significantly larger (no-ISI 12.4 (6.0)% vs. ISI 1.7 (3.5)%; po0:001). The median distance and area differences are thus reduced by 70% and 86% for the distance and area differences respectively, when initial stress is accounted for.
4. Discussion In the pursuit of a more patient-specific rupture risk assessment, many studies have focused on AAA wall stress analyses using FEA (Fillinger et al., 2002; Raghavan et al., 2000; Venkatasubramaniam et al., 2004). A nonlinear material model was defined in the past for the AAA wall (Raghavan et al., 2000), based on tensile tests, to acquire more realistic wall stress calculations. More recently several methods were proposed to correct for the initial stress (Raghavan et al., 2006; Lu et al., 2007; de Putter et al., 2007) present during data acquisition. However, no methods or measurements exist to verify in vivo wall stress computed by these models. In the current study, an indirect method is proposed to evaluate the effect of initial stress incorporation (ISI) in FEA, by comparing wall displacements from dynamic MRI with wall displacements calculated from FEA with and without ISI (no-ISI). Intra-aortic pressure measurements were performed during the image acquisition to facilitate the coupling between the actual aortic blood pressure and the wall excursions due to this blood pressure. Previous research estimated the blood pressure by a non-invasively measured systolic arm cuff pressure (Fillinger et al., 2002; Raghavan et al., 2000; Venkatasubramaniam et al., 2004). It has been shown, however, that values measured with a brachial arm cuff underestimate intra-aneurysm systolic pressure by 5% and overestimate diastolic pressure by 12%, on average (van ’t Veer et al., 2008). If the actual pressure curve is unavailable the corrected systolic and diastolic cuff pressure could be used. In common wall stress analyses a geometry obtained with CT or MRI is presumed to be un-stretched and pressure loading takes place along the nonlinear path B1 D E (Fig. 1). The method of de Putter et al. (2007) takes initial stress in the geometry into account ðB1 2B2 Þ and pressure is consequently built up to C along the in vivo loading path. The effect of this initial stress incorporation was determined. As shown in Fig. 1, an overestimation of the deformations is expected. It could be concluded from this figure that a constant correction factor can be deducted. However, when performing patient-specific FEA, the effect may be different for each patient due to local curvature of the patient’s geometry in combination with nonlinearity of the constitutive equation (Speelman et al., 2009). For the patient group, the contours obtained from MRI were compared with the corresponding contours extracted from the FEA using distance Dx and area DA differences. Fig. 4 shows that the differences in contour distances are lower with ISI. In other words, deformations are better described by FEA with ISI. The DA and Dx both show the superiority of ISI in FEA when compared with MRI contours (Fig. 5). It can be concluded from the data that the method with ISI better agrees with reality than the common no-ISI FEA ðpo0:001Þ. When quantitatively comparing the contours of the FEA with the MRI contours, the median DA approaches zero for the method with ISI, while the median DA in the no-ISI FEA is approximately nine times higher. This emphasizes the need to take initial stress into account. There is still a difference between the measured wall displacements on MRI and the FEA with ISI however. This could be explained by possible inaccuracies in image acquisition, segmentation and because of assumptions made in the current FEA. In the implemented FEA, possible presence of residual stress, thrombus and calcification are ignored and wall thickness is
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assumed to be constant. Furthermore, the spine might restrict backward AAA deformation, but at visual inspection of the data this effect was not confirmed. The influence of these assumptions could be investigated in future research, but their contribution to the deformation is considered to be small, since the calculated contours of FEA with ISI closely approach the MRI contours ðDA 1:7 ð3:5Þ%Þ. In contrast to the previous research of Fillinger et al. (2002), Raghavan et al. (2000) and Venkatasubramaniam et al. (2004), which concentrated on analysis of static CT data, the current study used dynamic MRI data for FEA. A disadvantage of the dynamic MRI used in this study is the long acquisition time. Therefore, concessions were made to the image quality, which may induce inaccuracies in the automatic segmentation and propagation method. However, the segmentation and propagation were verified and manually corrected if necessary, so differences found in the contour comparison measures between ISI and no-ISI FEA cannot be attributed to these inaccuracies. To obtain the AAA wall displacements with improved spatial resolution the current protocol could be extended, or as alternative cardiac gating could be added to the CT acquisition. However, from radiation perspective the former is preferred. The contours of MRI were propagated using the 2D B-TFE images. This explicitly assumes that longitudinal movement of the AAA is small. Currently no methods were available to use the propagation method on the 3D B-TFE images, because AAA wall delineation in the 3D B-TFE is poor compared with the 2D B-TFE images, which justifies this approach.
5. Conclusion The wall displacements from FEA with initial stress incorporation show significant better correspondence with wall motions from MRI data in comparison with FEA in which initial stress is neglected. These values were obtained with the usual parameters for the nonlinear material (Raghavan et al., 2000). Based on these results it can be concluded that incorporation of initial stress significantly improves wall displacement accuracy of FEA and therefore it should be incorporated in future analyses. References Basnyat, P.S., Biffin, A., Moseley, L., Hedgeds, R., Lewis, M.H., 1999. Deaths from ruptured abdominal aortic aneurysm in Wales. Br. J. Surg. Soc. 86 (5), 693. Breeuwer, M., de Putter, S., Kose, U., Speelman, L., Visser, K., Gerritsen, F., Hoogeveen, R., Krams, R., van den Bosch, H., Buth, J., Gunther, T., Wolters, B.,
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