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Method for Aortic Wall Strain Measurement With Three-Dimensional Ultrasound Speckle Tracking and Fitted Finite Element Analysis

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Method for Aortic Wall Strain Measurement With Three-Dimensional Ultrasound Speckle Tracking and Fitted Finite Element Analysis
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  Method for Aortic Wall Strain Measurement WithThree-Dimensional Ultrasound Speckle Trackingand Fitted Finite Element Analysis Konstantinos Karatolios, MD, Andreas Wittek, Dipl.-Ing. (FH), Thet Htar Nwe, PhD,Peter Bihari, MD, Amit Shelke, PhD, Dennis Josef, Thomas Schmitz-Rixen, MD, Josef Geks, MD, Bernhard Maisch, MD, Christopher Blase, PhD, Rainer Moosdorf, MD,and Sebastian Vogt, MD Departments of Internal Medicine and Cardiology, Cardiovascular Surgery, and Vascular Surgery, Philipps University, Marburg,Marburg; Institute for Cell Biology and Neuroscience, and Department of Vascular and Endovascular Surgery, Goethe University,Frankfurt, Germany Background.  Aortic wall strains are indicators ofbiomechanical changes of the aorta due to aging or pro-gressing pathologies such as aortic aneurysm. We inves-tigated the potential of time-resolved three-dimensionalultrasonography coupled with speckle-tracking algo-rithms and  fi nite element analysis as a novel methodfor noninvasive in vivo assessment of aortic wall strain.  Methods.  Three-dimensional volume datasets of 6subjects without cardiovascular risk factors and 2abdominal aortic aneurysms were acquired with acommercial real time three-dimensional echocardiogra-phy system. Longitudinal and circumferential strainswere computed of fl ine with high spatial resolutionusing a customized commercial speckle-tracking soft-ware and  fi nite element analysis. Indices for spatialheterogeneity and systolic dyssynchrony were deter-mined for healthy abdominal aortas and abdominalaneurysms. Results.  All examined aortic wall segments exhibitedconsiderable heterogenous in-plane strain distributions.Higher spatial resolution of strain imaging resulted inthe detection of signi fi cantly higher local peak strains(  p  £  0.01). In comparison with healthy abdominal aortas,aneurysms showed reduced mean strains and increasedspatial heterogeneity and more pronounced temporaldyssynchrony as well as delayed systole. Conclusions.  Three-dimensional ultrasound speckletracking enables the analysis of spatially highly resolvedstrain  fi elds of the aortic wall and offers the potential todetect local aortic wall motion deformations and abnor-malities. These data allow the de fi nition of new indicesby which the different biomechanical properties ofhealthy aortas and aortic aneurysms can be characterized.(Ann Thorac Surg 2013;96:1664 – 71)   2013 by The Society of Thoracic Surgeons A rterial stiffening increases with age [1] and is animportant predictor of cardiovascular morbidity andmortality [2]. The stiffness of the aortic wall is dependenton its cellular and acellular components and interactionbetween them [3]. Changes of arterial stiffness may beglobal; ie, affecting the whole arterial system, as in age-related stiffening. On the other hand changes might bemore localized as in the case of arterial pathologies suchas aortic aneurysms. Moreover, in aortic aneurysms aheterogeneous spatial distribution of biomechanicalproperties is observed [4].Several methods and indices have been proposed toassess and quantify arterial stiffness [1]. Determination of pulse-wave velocity has been the gold standard methodfor this measurement; however, it does not take into ac-count the three-dimensional (3D) morphology of theaorta and does not identify local variations [3]. Full 3Dvisualization of the aorta is possible with magnetic reso-nance imaging. However, magnetic resonance imagingrequires complex equipment, has low time resolution,and cannot be performed bedside.Ultrasonography coupled with speckle-tracking algo-rithms is a novel technique that has the potential to assessthe deformation and strain of subsurface structures withhigh spatial resolution [5]. So far, ultrasound-based vesselwall motion analysis has been limited to two-dimensional(2D) imaging. Recently, 3D speckle-tracking ultrasoundhas been introduced in clinical practice to evaluate car-diac pathologies [6, 7] , overcoming known limitations of 2D speckle tracking [8]. In recent years computationalmethods such as the  fi nite element method (FEM) havebeen used to overcome the limitations of analytic modelsof vascular mechanics and to generate  “ patient speci fi c ” numeric models, in particular of abdominal aortic Accepted for publication June 6, 2013.*These authors contributed equally to the study.Address correspondence to Prof Dr Vogt, Department of CardiovascularSurgery, Philipps University Marburg, Baldingerstr 35043 Marburg, Ger-many; e-mail: vogts@med.uni-marburg.de.   2013 by The Society of Thoracic Surgeons 0003-4975/$36.00Published by Elsevier Inc http://dx.doi.org/10.1016/j.athoracsur.2013.06.037  A D U L  T  C A R D I   A C  aneurysms (AAA). However, of the mechanical modelparameters in most cases only the reference geometryand the load (transmural pressure) are determined pa-tient speci fi cally [9]. In this study we present a noninva-sive method for full  fi eld displacement and strainmeasurement of the human aorta based on temporallyresolved 3D ultrasound (4D-US) geometry and displace-ment data combined with  fi nite element analysis (FEA).Using 4D-US displacement data as a new type of patient-speci fi c boundary conditions in FEA, aortic wall strainscan be described with high spatial resolution.We hypothesized that the in vivo strain state of thehuman aorta exhibits considerable local variations for agiven transmural pressure in pathologically alteredaortas such as AAA, as well as in healthy subjects. Wefurther hypothesized that the capability to detect localpeak strains depends on the spatial resolution of theapplied imaging method. This capability has the potentialto gain clinical relevance in the monitoring of AAA.Aneurysm rupture is a local event that might be signal-ized by locally con fi ned changes in cyclic strain andstiffness. Material and Methods Study Collective The study was approved by the local Ethics Committee of the University of Marburg. Six adults without cardiovascu-larriskfactorsandwithoutevidenceofaorticdiseaseaswellas2patientswithAAAwereexaminedaftergivinginformedconsent. Clinical variables were obtained from each volun-teer and patient (Table 1). From each healthy subject andpatient, 3D wall motion tracking data (3D-WMT) of theabdominal aorta was recorded. Additionally, the ascendingaorta was imaged in 2 healthy subjects (V1, V2).  4D-US Image Acquisition All measurements were acquired with patients in supineposition after 5 minutes rest. Arterial blood pressureswere measured by sphygmomanometer at the brachialartery. Imaging was done with a commercial real time 3Dechocardiography system (Artida; Toshiba Medical Sys-tems Corporation, Otawara, Japan) with a 3D trans-thoracic probe (PST-25SX, 1 to 4 MHz phased arraymatrix transducer; Toshiba). From each subject and pa-tient a full volume 3D dataset of the epigastric segment of the abdominal aorta was recorded. Three-dimensionalimages of the ascending aorta were obtained from thelong-axis parasternal view. The standard applicationsetting used 6 subvolumes of 90 degrees    15 degrees,which resulted in a 90 degrees  90 degrees triggered fullvolume in 6 heart cycles. Temporal and spatial resolutionof the ultrasound data as well as dimensions of theimaged aortic segments are given in Table 2.  3D-Wall Motion Tracking  Aortic wall motion analysis was performed off-line on thestored 3D raw data using the speckle tracking algorithmimplemented in the Advanced Cardiac Package (ACP) of the UltraExtend Workstation (Toshiba Medical SystemsCorporation) [10]. The datasets were rotated to give a5-plane view as shown in Figure 1. The luminal border of the aortic wall was identi fi ed manually in the 2 longitu-dinal views (Fig 1: plane A, plane B) of the end-diastolic Table 1. Clinical Characteristics of Study Population Study Population Age (Years) Sex BMI (kg/m 2 )Heartrate (bpm)SystolicBP (mm Hg)DiastolicBP (mm Hg)Healthy Volunteers V1 19 Male 22 67 110 75 V2 20 Male 26 60 120 70 V3 22 Male 24 68 130 80 V4 44 Male 26 71 120 80 V5 24 Male 24 53 125 70 V6 49 Male 25 49 130 75Mean    SD 29.7    13.2 24.5    1.5 61.3    8.9 122.5    7.6 75    4.5PatientsAAA1 84 Female 31 58 100 60AAA2 70 Male 25 63 120 70 AAA  ¼  abdominal aortic aneurysm; BMI  ¼  body mass index; bpm  ¼  beats per minute; BP  ¼  blood pressure. Abbreviations and Acronyms 3D = three-dimensional3D-WMT = three-dimensional wall motiontracking4D = four-dimensionalAAA = abdominal aortic aneurysmACP = advanced cardiac packageCS = circumferential strainCV = coef  fi cient of variationFE =  fi nite elementFEA =  fi nite element analysisFEM =  fi nite element methodLV = left ventricleSD = standard deviationSDI = systolic dyssynchrony indexUS = ultrasound 1665 Ann Thorac Surg KARATOLIOS ET AL2013;96:1664 – 71 AORTIC WALL 3D SPECKLE TRACKING ANALYSIS      A     D     U     L     T     C     A     R     D     I     A     C  reference volume. Because the tracking software has beendesigned for the left ventricle, we had to create a “ pseudo-apex ”  within the aortic lumen (Fig 2A). Subse-quently, 3D-WMT was performed automatically.Seo and colleagues [7] and Bihari and colleagues [11] performed validation experiments in vivo and in vitro,respectively. Good correlation between 3D-WMT andsonomicrometry was found in vivo and the error of the3D-WMT has been determined in vitro to be less than 2%. Determination of Systolic In-Plane Strains Strainisarelativedeformationmeasure,relatingthelengthchange  D l i  to the chosen reference length l i,0 :  ε i  ¼  D l i /l i,0 .Given a 3D deformation, the strain value depends on thespatialdirectionthatisindicatedbytheindexi.Longitudinal(i  ¼  1) and circumferential (i  ¼  2) strain were chosen asphysiologically meaningful in plane strains of the aorticwall. The systolic time frame was identi fi ed as the oneexhibiting the maximum mean circumferential strain (CS). Strain Measurement With Standard Version of ACP  In the standard version of the ACP the tracked segment of the aorta was automatically divided into 16 3D sub-segments (including the pseudo-apex) and wall strainswere calculated for these. For strain analysis the 4 seg-ments of the pseudo-apex were excluded. This method isreferred to as  “ standard postprocessing ”  in this article. Strain Measurement With Customized Displacement Data Interface Combined With Finite Element Analysis Toshiba Medical Systems Europe provided a customizedversion of the ACP with a data interface that allowed theexport of position vector  fi elds of 36    36 measuringpoints on the inner border of the arterial wall for eachtemporal frame throughout an entire cardiac cycle.The arti fi cial measuring points of the pseudo-apexwere separated from the displacement  fi eld depictingthe aortic wall, so that  fi elds of 36    24 position vectorswere used for further analysis (Fig 2A, 2B), except in thecase of patient AAA2, where only 36  12 position vectorscould be used. A 3D  fi nite element (FE) model of theaortic section was generated using custom written soft-ware. The measuring points of the end-diastolic volume(t  ¼  0s) were taken as nodes of the FE discretization.These were then meshed by 4-node membrane elementsand local nodal and element coordinate systems weregenerated (Fig 2C, 2D). Displacement vector  fi elds werecalculated as differences of the position vector  fi elds fromsubsequent volumes and applied as boundary conditionsfor the FEA, so that every degree of freedom of the modelwas constrained by measured displacement data. Thesolution of the boundary value problem with the FEsolver Abaqus 6.10 (Simulia, Providence, RI) accountedfor geometric nonlinearities due to  fi nite deformations.Separate local strain values for each element (864 or 432for AAA2) of the modeled aortic wall segments werecalculated. This method of determining highly spatiallyresolved strain  fi elds is referred to as  “ customized post-processing ”  in the following. 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Strain Indices: Spatial Heterogeneity and TemporalDyssynchrony Mean and coef  fi cient of variation (CV) were calculated forlongitudinal and CS distributions. The CV is de fi ned asthe ratio of standard deviation (SD) and mean. It can beunderstood as an index of the spatial heterogeneity of systolic strain distributions; increased CV indicatesgreater heterogeneity of systolic strains.To quantify the differences in temporal CS distributionsbetween healthy abdominal aortas and AAAs we calcu-lated indices that characterize dyssynchrony of aortic wallmotion [6]. The time between the end-diastolic frame andthe frame, for which a subsegment of the aortic wallexhibitedmaximal CS,was expressedinpercent ofthe fullcardiac cycle. Mean and SD of these timings were calcu-lated for the whole aortic segment. The SD was used assystolic dyssynchrony index (SDI). Higher SDI indicatesincreased dyssynchrony of aortic wall motion. Comparative Analysis of the Dependence of Peak Strainon Spatial Resolution In addition to the highly spatially resolved CS values thatwere obtained by customized postprocessing, systolic CSof the abdominal aortas of the 6 volunteers was computedusing 2 other methods. Average CS was calculated as theratio of systolic diameter change  D d (Table 2) and end- diastolic diameter d 0 :  D d/d 0  (referred to as  “ diameterratio ” ) and the standard postprocessing of the ACP wasused to compute systolic CS.  Fig 2. Processing of three-dimensional (3D)wall motion tracking data. (A) The exported measurement points (36    36 points) are processed and represented as a 3D point cloud including the arti  fi cial pseudo-apex.(B) Point   fi eld of the luminal surface of theaortic wall without pseudo-apex. (C) Finiteelement discretization with  fi rst order 4 nodemembrane elements. (D) Longitudinaland circumferential directions of localelement coordinate systems. Mesh and coordinate systems were generated by a custom written Finite Element- preprocessor. Fig 1. Representative example of a three-dimensional speckle tracking image of theabdominal aorta obtained in a healthyvolunteer. The 5-plane view consists of alongitudinal view in plane A, a longitudinalview orthogonal to plane A (plane B) and 3short axis views (planes C3, C5, and C7). 1667 Ann Thorac Surg KARATOLIOS ET AL2013;96:1664 – 71 AORTIC WALL 3D SPECKLE TRACKING ANALYSIS      A     D     U     L     T     C     A     R     D     I     A     C  Statistics Temporal or spatial mean strain values were comparedby paired 2-sample  t   tests for means with dependent spotchecks. Statistical analysis was performed using Mathe-matica 9 (Wolfram Research, Champaign, IL) andMicrosoft Excel 2010 (Microsoft, Redmond, WA). Results Dependence of Peak Strains on Spatial Resolution The average end-diastolic wall section area sizes obtainedby standard and customized postprocessing for allimaged aortic segments are shown in Table 2. In healthysubjects the average size of the sections for which sepa-rate strain values were computed was reduced to 2.0  0.4mm 2 (customized) compared with 139.4    26.7 mm 2 (standard).Table 3 gives a comparison among the results of 3different methods to compute the systolic CS (diameterratio, standard and customized postprocessing) of theabdominal aortas of 6 volunteers. The mean CS calculatedby customized postprocessing do not differ signi fi cantlyfrom the results of standard postprocessing for any of thedatasets (  p  0.05). The averaged values obtained for eachdataset by both methods are in good agreement with thediameter ratios. Neither mean standard nor meancustomized strains differ signi fi cantly from mean diam-eter ratio  D d/d 0  (  p    0.05), nor do customized from stan-dard means. In case of the maximum values as well as theratios of maximum and mean values the differences be-tween the results obtained by customized and by standardpostprocessing are highly signi fi cant (  p  0.01). Systolic Longitudinal and Circumferential Strain Table 4 gives an overview of the means    CV of the spatial distributions of systolic longitudinal andcircumferential strains with regard to the end-diastolicgeometry. The strain values obtained for the 2 includedascending aortas are quite similar. Both samples show CSof about 10% and considerable systolic lengthening of more than 15%. In contrast, the mean longitudinal strainof the abdominal aortas was close to zero. All straincomponents exhibited remarkable inter-individual vari-ation in the abdominal aortas of the 6 healthy subjects;the mean CV was 2.4 for longitudinal strain and 0.5 forCS. The high spatial heterogeneity was supported by thelocal peak CS detected by the customized postprocessingprocedure (Table 3).The values obtained for the 2 AAAs differed decisively;systolic CS was less than 1% in both cases. However, localpeak CS (AAA1, 17.6%; AAA2, 12.3%) were comparablewith strains observed in healthy aortas. The CV of CSdistributions was 4.1 (AAA1) and 14.3 (AAA2). Thisindicated a remarkably increased spatial heterogeneity of strain distribution compared with healthy abdominalaortas (Fig 3). Table 3. Comparison of Systolic Circumferential Strain (CS) of the Abdominal Aortas of 6 Volunteers Without Cardiovascular Risk Factors Obtained by Diameter Ratio, Standard and Customized Postprocessing  Patient ID  D d/d 0 Circumferential Strain [%]Standard Postprocessing Customized PostprocessingMean    SD MaxRatioMax/Mean Mean    SD MaxRatioMax/Mean V1 20.8 19.2    7.9 33.5 1.75 23.7    10.5 57.3 2.42 V2 19.3 17.8    4.5 26.8 1.51 18.2    7.9 39.5 2.17 V3 10.3 11.0    3.9 18.8 1.71 10.2    5.2 25.3 2.48 V4 12.4 12.4    2.4 16.3 1.32 12.5    4.0 28.0 2.24 V5 7.5 6.7    1.7 10.5 1.57 6.7    3.5 23.9 3.57 V6 9.0 9.3    2.9 13.9 1.49 8.0    4.0 19.1 2.39Mean    SD 13.2    5.6 12.7    4.9 20.0    8.6 1.56    0.16 13.2    6.5 32.2    14.1 a 2.54    0.5 a a In the case of the maximum values as well as the ratios of maximum and mean values the differences between the results obtained by customized and bystandard postprocessing are highly signi fi cant for  p    0.01. Table 4. Systolic Longitudinal and Circumferential StrainsWith Regard to the End Diastolic Reference Con  fi  guration;Values Are Given as Means    Coef   fi cient of Variation (CV) Systolic Strain, Mean    CV [%]Patient ID Longitudinal CircumferentialAscending aorta V1 15.2    2.0 9.2    1.5 V2 17.1    1.6 10.0    1.6Abdominal aorta V1 -7.4    0.9 23.7    0.4 V2 0.3    23.7 18.2    0.4 V3 -2.2    2.4 10.2    0.5 V4 1.2    4.3 12.5    0.3 V5 -1.1    6.5 6.7    0.5 V6 1.2    5.6 8.0    0.5Mean    SD -1.3    2.4 13.2    0.5AAAAAA1 0.1    59.0 0.7    4.1AAA2 -0.5    11.0 0.3    14.3 AAA  ¼  abdominal aortic aneurysm. 1668  KARATOLIOS ET AL Ann Thorac SurgAORTIC WALL 3D SPECKLE TRACKING ANALYSIS 2013;96:1664 – 71  A D U L  T  C A R D I   A C
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