ORIGINAL PAPER

Left ventricular torsion and longitudinal shortening:two fundamental components of myocardial mechanicsassessed by tagged cine-MRI in normal subjects

Francesc Carreras • Jaume Garcia-Barnes• Debora Gil • Sandra Pujadas•

Chi Hion Li • Ramon Suarez-Arias• Ruben Leta • Xavier Alomar •

Manel Ballester • Guillem Pons-Llado

Received: 11 August 2010 / Accepted: 19 January 2011� Springer Science+Business Media, B.V. 2011

Abstract Cardiac magnetic resonance imaging(Cardiac MRI) has become a gold standard diagnostictechnique for the assessment of cardiac mechanics,allowing the non-invasive calculation of left ventric-ular long axis longitudinal shortening (LVLS) andabsolute myocardial torsion (AMT) between basal andapical left ventricular slices, a movement directlyrelated to the helicoidal anatomic disposition of themyocardial Þbers. The aim of this study is to determineAMT and LVLS behaviour and normal values from agroup of healthy subjects. A group of 21 healthyvolunteers (15 males) (age: 23Ð55 y.o., mean:

30.7 ± 7.5) were prospectively included in an obser-vational study by Cardiac MRI. Left ventricularrotation (degrees) was calculated by custom-madesoftware (Harmonic Phase Flow) in consecutive LVshort axis planes tagged cine-MRI sequences. AMTwas determined from the difference between basal andapical planes LV rotations. LVLS (%) was determinedfrom the LV longitudinal and horizontal axis cine-MRIimages. All the 21 cases studied were interpretable,although in three cases the value of the LV apicalrotation could not be determined. The mean rotationof the basal and apical planes at end-systole were-3.71� ± 0.84� and 6.73� ± 1.69� (n:18) respectively,resulting in a LV mean AMT of 10.48� ± 1.63� (n:18).End-systolic mean LVLS was 19.07± 2.71%. CardiacMRI allows for the calculation of AMT and LVLS,fundamental functional components of the ventriculartwist mechanics conditioned, in turn, by the anatomicalhelical layout of the myocardial Þbers. These valuesprovide complementary information about systolicventricular function in relation to the traditionalparameters used in daily practice.

Keywords Magnetic resonance imaging (MRI)�Tagging MRI � Cardiac mechanics�Ventricular torsion

Introduction

In the 1960s, Torrent-Guasp identiÞed the myocar-dium as a single myocardial band adopting spatially

F. Carreras (&) � S. Pujadas� C. H. Li �R. Leta � G. Pons-LladoCardiac Imaging Unit, Cardiology Department,Hospital de la Santa Creu i Sant Pau,c/Sant Antoni Ma Claret, 167, 08025 Barcelona, Spaine-mail: fcarreras@santpau.cat

J. Garcia-Barnes� D. GilComputer Vision Center, Universitat Auto`noma deBarcelona, Bellaterra, Spain

R. Suarez-AriasCardiology Unit, Hospital Alvarez Buylla,Mieres (Asturias), Spain

X. AlomarRadiology Department, Clõ«nica Creu Blanca, Barcelona,Spain

M. BallesterChair in Cardiology, Universitat de Lleida, Lleida, Spain

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Int J Cardiovasc ImagingDOI 10.1007/s10554-011-9813-6

a double-helical structure [1Ð3]. This prompted acritical review of how the ventricles exert theirfunction. Before any available technique coulddemonstrate the functional implications of thisanatomical structure, he proposed that a cyclicaltorsion/untorsion movement was on the basis of themotion of the ventricles. Nonetheless, it has beennecessary to wait until the development of nonin-vasive techniques such as tagged cine magneticresonance imaging (TMRI) in order to reliably andreproducibly measure theAbsolute Myocardial Tor-

sion (AMT), deÞned as the difference between therotation (measured in angular degrees on the cros-sectional plane) of the basal and the apical planes ofthe left ventricle. In 2000, Lorenz et al. [4]published a seminal article in which TMRI is usedto describe and measure the ventricular torsionmovement in 10 healthy volunteers. Thereafter,TMRI has become the gold standard diagnostictechnique for the assessment of AMT, a movementresultant from the helicoidal anatomical dispositionof the myocardial Þbers.

Myocardial torsion (MT) is a fundamentalcomponent of cardiac function with a directimplication in the functionality of the left ventricle[5]. Due to the particular double-helix structure ofmyocardial Þbers, there exists an opposing systolicrotation between the base and the apex of the leftventricle around its longitudinal axis, which pro-duces MT. This movement causes the ventricularbase to move in an apical direction, this inducinga longitudinal shortening of the left ventricle(LSLV) and, due to the aforementioned double-helix structure, there is a simultaneous reductionof the crossectional area of the ventricular cavity.The resulting action of both movements modiÞesthe volume of the LV and determines the empty-ing (systole), while the untorsion of the myocar-dium would allow the subsequent Þlling (diastole)of the ventricle [6, 7].

While LSLV is a parameter that can be easilydetermined from cine-MRI images of the LV on along-axis, non-invasive quantitative analysis of MTof the LV has not become possible until thedevelopment of TMRI sequences [8], allowing thequantitative analysis of LV myocardial torsion [9].The aim of this study is to determine AMT andLSLV normal values determined with cardiac MRIin a group of volunteer healthy subjects.

Materials and methods

The study included 21 healthy volunteers, 15 malesand 6 females, aged between 23 and 55 (30.7± 7.5).

Cardiac MRI

For the cardiac MRI study, a Siemens Avanto 1.5 T(Erlangen, Germany) was used. After obtaining theroutine localization planes, another series of imagesin a single phase was obtained, using theTrue-Fisp

localizing sequence segmented in 2D (voxel size2.4 9 1.69 6 mm, 6 mm slice thickness, TR 337/TE1.16), oriented in a transversal plane from the LVcovering from the base to the apex. This series wasobtained in a single apnea from the patient in order toavoid variations in the position of the slices inrelation to breathing and thus enabling its use as aspatial anatomical reference in subsequent calcula-tions. Afterwards, cine-MRI images were obtainedusing aSteady-State Free-Precision sequence (True-Fisp T-sense: iPAT= 3, voxel size 29 1.3 9

6 mm, 6 mm slice thickness, TR 46/TE 3.8) on sliceswith the same orientation than those of the previoussequence. Finally, TMRI sequences were alsoobtained in the same orientations (voxel size:2 9 1.3 9 6 mm); slice thickness: 6 mm; TR:45/TE: 3.8 ms). In this protocol, acquisition of the slicesis individual, during a period of apnea, aligned three-dimensionally in the post-processing analysis takingas anatomical reference the position of the slices fromthe localizing sequence. The basal slice was chosenas the Þrst one showing a discrete image of the LVmyocardial wall below the LV outßow tract, and theapical slice considered as the last one allowing thevisualization of the LV cavity in diastole.

Calculation of rotation and myocardial torsion

Rotation and torsion were computed using theanalysis software developed by the Computer VisionCenter at the Universitat Autonoma de Barcelona.The computation of rotation and torsion from TMRIsequences requires extracting tissue motion. Tissuedynamics were estimated using a computationalmethod called Harmonic Phase Flow (HPF)[10, 11]. The method allowed for the performanceof calculations precise down to the sub-pixel level,

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which guaranteed the gathering of reliable andreproducible data for clinical analysis [12].

The HPF is a computational algorithm that extractsthe motion of cardiac tissue between consecutiveframes of TMRI sequences. For each sequence frame,it produces a 2D vector Þeld that indicates theposition that each point of the current frame will havein the next one. The vector Þeld matches those pointsin consecutive frames that have a similar appearance(image intensity). In order to cope with tag fadingalong the cardiac cycle [13], HPF works in analternative representation space allowing robusttracking at advanced stages of systole. By thephysical properties of the tagging pattern [13], theorientation of the tagging lines is an attribute thatkeeps constant along the sequence. The taggedpattern is modelled in frequency (Fourier) domainby the maximum response to two Gabor Þlter banks[10, 14] tailored to each tag direction. The use ofGabor Þlters allows capturing tissue local deforma-tions. The response to each Þlter bank produces acomplex image, whose phase is related to the tag lineorientation. Additionally, the amplitude indicateswhich areas of the image present a reliable tag

pattern. The phases of the response to the two GaborÞlter banks are combined into a variational frame-work [15] that takes into account the amplitude ofeach response. The solution to the variational prob-lem deÞnes HPF. At regions where the amplitude islarge, HPF uses the motion information given by thetag lines, while at regions of low amplitude itsmoothly interpolates motion from neighbouringvalid points. In this manner, HPF retrieves a contin-uous motion which does not overestimate motion atinjured motionless areas.

Figure1 sketches the main steps involved in thecomputation of HPF for two consecutive TMRIframes. The response to the Gabor Þlters (shown inthe small images on top) is decomposed into phaseand amplitude. Amplitude images take higher(brighter) values at tagged tissue and, thus, outlinethe myocardium. Phase images present a strippedpattern oriented along the direction of each family oftags. The motion vector provided by HPF is shown inthe bottom images. Close-ups illustrate the capabilityof HPF for restoring motion at tagged tissue whilecancelling it at motionless areas (such as backgroundand bottom non-cardiac tagged tissue).

Fig. 1 Computation ofcardiac motion using theHarmonic Phase Flowmethod

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The rotation of an arbitrary (deforming or not)object is the rigid part of the Þrst order (linear)approximation of its overall motion. The rotation iscentered at the object center of mass, which positionis identiÞed along the object translation.

Given the motion estimated by HPF, the globalrotation (quantiÞed in degrees) of transversal sectionsof the myocardium was calculated on TMRI asfollows. The angular difference between the positionof a myocardial material point at time zero and itsposition at a given timet deÞnes the rotation angle forthat point. For each sequence frame and point of themyocardium, its position at the next frame is given byadding the motion vector provided by HPF at thatpoint. The position of myocardial points along thesequence is computed by accumulation of HPFmotion vectors matching consecutive frames. Inorder to account for any translation of the wholeheart, we correct each position by the position of thecenter of mass of the heart at each sequence frame(Fig. 2). That is, the center of mass is the new originof coordinates for both frames so that position vectorsare computed in relation to it. The angleh betweenthe corrected positions is given (in terms of thetrigonometric cosine function) by their normalizedscalar product:

cosðhÞ ¼ P0 � C0;Pt � Cth iP0 � C0k k Pt � Ctk k

for k k denoting the Euclidean norm of a vector,P0, Pt the positions of a point inside the LV at initialtime 0 and a given timet and C0, Ct the centers of

mass of the LV at initial time 0 and a given timet. Notice that by normalizing by the norm of thecorrected position vectors, we account for any scaling(deformation). Figure2 sketches the computation ofh after translation correction by centering at the LVcenter of mass.

The global rotation is given by least squareapproximation to the rotations of all points insidethe myocardium and is computed as the average oftheir rotation angles. Material points are identiÞed bymanual delineation of the LV contours (excludingpapillary muscles).

Looking at the heart from the apex, its counter-clockwise rotation was assigned a positive valuewhile its clockwise rotation was given a negativevalue. AMT was determined as the differencebetween the maximum rotation at the most basalmyocardial section (BMR) and at the apex (AMR),respectively (AMT= AMR - BMR) (Fig. 3). Dueto the fading of myocardial tagging signal intensitythrough the course of time, the analysis of ventricularmyocardial mechanics was circumscribed to thesystolic phase of the cardiac cycle, thus consideringthe end of systole as the image that presented thesmallest area of the LV cavity.

Calculation of LSLV

For the calculation of the maximum LSLV, the LVwas visualized through sequences of cine-MRIoriented in its vertical (2-chamber) and horizontal(4-chamber) planes (Fig.4). Distance (in millimeters)

Fig. 2 Computation ofrotation angle for anarbitrary material point

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was calculated on both planes, between the apex ofthe LV and the center point of the mitral valve ring inthe end-diastolic (d2,0 and d4,0) and end-systolic(d2,1 and d4,1) frames (Fig.4). The longitudinalshortening on the vertical (E2) and horizontal (E4)planes was calculated as the percentage of thereduction in the measured distances.

E2ð%Þ ¼ 100 1� d2;1

d2;0

� �; E4ð%Þ ¼ 100 1� d4;1

d4;0

� �

Finally, the LSLV was deÞned as the simple averageof the aforementioned values.

LSLVð%Þ ¼ E2 þ E4

2

Statistical analysis

Due to the continuous quantitative nature of thestudied variables, they have been described byproviding the arithmetic average as well as itsstandard deviation. The existence of atypical valueswas evaluated using a Box-Plot.

The sample size in terms of number of cases wasnot explicitly calculated due to the preliminary natureof the current study. Important to note, however, thenumber of performed observations allowed for theconsistency of the statistical analyses. For the studybetween the relationship between LSLV and AMT,different curves were adjusted, obtaining the best Þtin a lineal relationship and providing the Pearsonlineal correlation coefÞcient as well as its signiÞ-cance. A normality model was computed by Þtting a

bimodal Gaussian model to AMT and LSLV normalvalues.

All the analyses were bilateral and applied theusual signiÞcance level of 5% (a = 0.05). Thesoftware used was SPSS 15.0 (SPSS Inc., Chicago,Illinois, USA).

Results

All studies were interpretable, although in 3 patients(subjects 15, 17 and 20) the apical rotation valuecould not be determined due to the presence of noisein the TMRI signal data. Thus, values for the BMRand LSLV were determined in all 21 subjects in thestudy group, while the AMR and the AMT valueswere limited to 18 of them. Figure5a shows therotation proÞles at basal level for all 21 volunteersand Fig.5b shows rotation proÞles at apical level for18 subjects. Figure5c shows AMT plots computedfor the later group of 18 subjects. In all three Þgures,plot labeling is given in terms of the subjectidentiÞcation number (ranging from 1 to 21). Finally,Fig. 6 shows the average curves for basal and apicalrotation, as well as normality ranges (average± stan-dard deviation) for AMT. Statistics were computedfor the interpretable studies: 21 subjects for basalrotation and 18 for apical rotation and AMT.

Fig. 3 The absolute myocardial torsion (AMT) of the LV isdetermined through the difference between the most basalmyocardial section (BMR) and the apex (AMR), respectively(AMT = AMR - BMR)

Fig. 4 Calculation of the longitudinal shortening of the LVfrom the cine-MRI sequences oriented in the vertical andhorizontal longitudinal axes

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Fig. 5 a Individual valuesfor the rotation in basalsegments of the LVthroughout the systoliccycle. b Individual valuesfor the rotation in the apicalsegment of the LVthroughout the systoliccycle. c Individual valuesfor the absolute myocardialtorsion between the LVbase and apex throughoutthe systolic cycle

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Table1 shows the numerical range of AMR, BMRand AMT for predetermined phases of the systoliccycle. The rotation ranges were determined using theaverage± the standard deviation, the latter acting asan indicator of the stability of the rotation angle.Considering the average values for the entire group,the basal rotation was observed to achieve itsmaximum positive value at 33% of the systolic phase

(1.05� ± 0.67�) and then changing its direction ofrotation, achieving the maximum negative value atthe end (100%) of systole (-3.71� ± 0.84�). Simul-taneously, the apical rotation increases withoutchanging its direction, also achieving its maximumvalue at the end of systole (6.73� ± 1.69�). Themaximum difference between BMR and AMR thustakes place at the end of systole, resulting in a medianAMT value for all studied patients of 10.48� ± 1.63�(Fig. 6). On the other hand, the median LSLV in end-systole for the entire group of studied patients was19.07± 2.71% (Fig.7).

The scattered plot in Fig.8 shows the relationshipbetween LSLV and AMT values at end-systole forthe 18 subjects (blue dots). Additional values from 3patients presenting different levels of depressed leftventricular function have been included (red num-bered crosses) for purposes of comparison. Healthysubjects are grouped in a quadrant determined by theminimum values of 15% for LSLV and 7� for AMTand present with a weak linear correlation betweenthese parameters (r = 0.598, p = 0.024). Values inpatients with depressed ventricular function are

Fig. 6 Graphicalrepresentation of theaverage rotation andtorsion. Thehorizontal axisshows the percentage run ofthe systolic cycle and thevertical shows the rotationsand torsions in degrees. Theapical rotation curve isrepresented in a dotted line,the basal rotation in abroken line and torsion inbold. The variability rangefor torsion is represented ingrey lines and its value iscalculated from the standarddeviation of the 21 subjectcurves studied

Table 1 Left ventricular basal and apical myocardial rotation ranges (BMR and AMR) and absolute myocardial torsion (AMT) fordifferent phases (%) of the systolic cycle

10% 25% 50% 75% 100% (End-systole)

AMR 0.88 ± 0.62 2.46± 0.97 4.15± 1.49 5.02± 1.61 6.73± 1.69

BMR 0.38± 0.31 0.94± 0.52 0.39± 0.89 -1.86± 0.99 -3.71 ± 0.84

AMT 0.47 ± 0.58 1.52± 0.93 3.81± 1.41 6.97± 1.35 10.48± 1.63

Fig. 7 Percentage of the longitudinal systolic shortening ofthe LV for each case. Thehorizontal line shows the averagevalue for the entire group of patients studied (19.07± 2.71%)

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clearly different from the healthy group. The Maha-lanobis distance [16] in observations on patients wasused as score of their deviation from normal cases.The values obtained for the Mahalanobis distance(7.1567, 17.1241, and 36.9817) discriminate patho-logical values from normal ones when using bothLSLV and AMT.

Discussion

The values of left ventricular torsion obtained in thepresent study do not differ from those initiallydescribed by Lorenz [4], resulting in a median LVAMT of 10.48� ± 1.63� in a healthy heart. On theother hand, the torsion movement is associated with adescent of the ventricular base, resulting in an LSLVexceeding 15% in all cases.

The functional information thus obtained by TMRIon the torsion movement mechanism and the longi-tudinal shortening experienced by the LV myocar-dium during systole Þts with the known anatomicalfact of the helical structure of the myocardial ÞbersThis information is essential for understanding the

mechanical derangement in cases of myocardialdysfunction [17], and may potentially facilitate theappropriate design of therapeutic strategies [18]. Therelationship between LSLV and function of the LVhas been known for years, as it is a parameter that canbe easily determined by echocardiography [19]. It hasbeen observed that a reduction of LSLV can be anearly sign of left ventricular dysfunction usuallypreceding the alteration of other parameters of LVfunction [20] including ventricular torsion [21].

Nevertheless, considered as a 3D phenomenon, thedeformation of the heart across the cardiac cycle is acomplex movement. The overall motion (includingdeformation) of an arbitrary object can be split intolinear and non-linear terms. The linear term is a Þrstorder approximation that decomposes into rigid(global translation and rotation) and non-rigid (globalscaling) global motions [22]. Meanwhile, higherorder terms account for non-local deformations.Given that the global rotation is the average of therotation angles for all points inside the LV, itsummarizes the overall twisting of each short axiscut. As reported by Liu et al. [23], it might have asigniÞcant diagnostic value, since it is signiÞcantlyreduced in the presence of LV dysfunction. This isalso the case for overall LV shortening (which is theglobal scaling in the longitudinal direction).

Although, in an ideal setting, AMT and LSLVshould be computed in 3D, in TMRI 2D acquisitionsthey can be accurately assessed in complementaryplanes: short axis for rotation and long axis forlongitudinal shortening. Given that they are the resultof the same 3D motion, such 2D computations arecoupled phenomena physically related. Therefore, itis appropriate to consider their coupled values forcomparison without any adjustment.

Thus, systolic ventricular contraction results fromthe combined action of myocardial torsion andshortening of the longitudinal ventricular axis, aclear example of the anatomy-function interaction[24]. Figure8 shows how the end-systolic values ofLSLV and AMT are grouped in a quadrant deter-mined by the minimum values of 15% for LSLV and7� for AMT. Since we know that both values are notsimultaneously affected by the appearance of ven-tricular dysfunction [25], the graphical representationof both values can be useful for the identiÞcation ofpathological patterns for LV dysfunction. A recentpublication described the usefulness of considering

Fig. 8 Relation between individual LSLV values and AMT inend-systole in the study group of normal subjects (blue dots).In addition, values obtained in a separate small group of 3patients with increasingly depressed left ventricular ejectionfraction (number 1: 40%; 2: 35%; and 3: 20%) have beenincluded for comparison (red crosses)

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both parameters in order to understand the mecha-nisms that contribute to the preservation of theejection fraction in those patients with diastolic heartfailure [20]. Moreover, our data obtained from3 patients presenting LV dysfunction seem to suggesta diagnostic value of these two parameters consideredsimultaneously.

Myocardial torsion is explained by the particularangles of ventricular myocardial Þbers due to theiranatomic layout which forms a double-helix [26, 27].In a classic study from Rademakers [28], averageÞber angles with respect to the short-axis plane deÞnedby pathological analysis were-68.6 ± 12.7�, 10.5±

3.6� and 74.5± 4.2� for epicardium, midwall andendocardium respectively. These angles have beenconÞrmed, to a greater or lesser extent, usingdiffusion tensor MRI techniques [29], coincident alsowith the histological measurements originally per-formed by Streeter, [30] who studied the orientationof myocardial Þbers in canine samples of the leftventricle and, more recently, by Harrington [31], whoused samples of the anterolateral ventricular myo-cardium of sheepÕs hearts.

Torrent-GuaspÕs anatomical dissections, whichshowed how the myocardial Þbers of the LV are laidout helicoidally in opposite directions, also coincidewith the data obtained from both histological studiesas well as sophisticated imaging techniques, thuspermitting the outline of the structural layout of themyocardial Þbers of the left ventricle [32]. Thisexplains the essential movements of cardiac mechan-ics such as the opposing rotation of the ventricularbase and apex, which allows for myocardial torsionand the systolic descent of the ventricular base,resulting in a signiÞcant shortening of the longitudi-nal axis of the LV. Even though some authors havedoubted the existence of a continuous helical struc-ture in myocardial Þbers and its functional implica-tions [33], it has been recently demonstrated theexistence of a functional helical myocardial bandthrough the study of the 3D deformation of myocar-dial Þbers during the cardiac cycle as measured bycine-MRI diffusion tensor imaging, showing how thedirection of the deformation can be overimposed tothe anatomical layout of myocardial Þbers accordingto Torrent-GuaspÕs model of the myocardial band[34]. It must also be noted that the helical structure ofmyocardial Þbers is fundamental for achieving themost efÞcient reduction in volume for the LV cavity.

Due to the fact that the shortening of the sarcomeredoes not usually exceed 15% of its length, thereduction of the cavity would not exceed 30% ifmyocardial Þbers were structured in a strict circum-ferential direction, while this reduction is increased to60% because of the helical layout of these Þbers [35].In addition to this, the anatomical structure of theopposing myocardial bundles permits an efÞcienttorsion and straightening movement, which facilitatesventricular Þlling and emptying [36, 37] according tothe most basic laws of mechanics. In a recentpublication Bertini et al. [38] review the role of leftventricular twist mechanics in the assessment ofcardiac disynchrony in heart failure, emphasizing theimportant aspect of the spiral architecture of themyocardial Þbers.

Recently, the study of ventricular torsion has beenfavored by the incorporation of a new echocardio-graphic technique based on the identiÞcation andtracking of the movement of myocardial Þbers by theacoustic signals generated by the interaction ofultrasounds with structures of a size smaller thantheir wavelengths (speckle tracking) [39]. This tech-nique is gaining popularity in publications [40, 41]and retains a good correlation with MRI studies [39].Of particular interest is a publication by Hui et al.

[42] which studied the contribution to ventricularrotation of the two bundles of myocardial Þbers thatform the interventricular septum. Because of its wideavailabity in comparison with TMRI, speckle track-ing echocardiography may become the technique ofchoice for the determination of AMT at patientÕsbedside.

Limitations

Because of the limited availability of TMRI studies,the small number of studied subjects did not allow thesubdivision in age groups. However, since most ofthe studied subjects were in their 20 s or 30 s, theresults obtained can be considered representative ofthis age group. As already mentioned, speckletracking echocardiography allows the study of agreater number of patients, and even though AMTstudies subdivided by age group done through thistechnique had already been published [43], morecomparative studies with TMRI are necessary toproperly assess the deÞnitive reliability of the afore-mentioned technique. Also the scores of AMT and

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LSLV considered in this study are representative ofthe whole LV mechanics. In order to properlyidentify regional impairment, segmental values (notconsidered in this article) should be taken intoaccount. Statistical analysis of regional rotationrequires extensive gathering of data (given that thedimensionality of the space increases up to thenumber of regions considered) and it is currentlyunder development in our laboratory. Finally, a largerstudy considering a wide set of patients with myo-cardial dysfunction is also under development.

The visual selection of the basal and apicalsections could lead to a certain degree of variabilityin its exact position for each patient, a fact that couldhave inßuenced the value of AMT. This fact makes itnecessary to be extremely cautious in the method forselecting the layering sections, which is difÞcult dueto the absence of precise anatomical references. Inorder to select the corresponding section for theventricular base, one that would include the totality ofthe myocardial circumference while excluding anypartial volume of the left ventricular outßow tractwas considered. For the apex, the most distal sectionin which the ventricular cavity could still be observedat end-systole was selected.

In our series, we can observe how the range ofvariability in the Þrst half of the systolic cycle issmall (less than 2�). In the second half of the cycle,we can see a slight increase in variability, up to 3�,which remains constant through 75% of the cycle.The almost non-existent variability in the Þrst half ofthe systolic cycle indicates an identical behaviour inhealthy subjects. The constant variance that we Þndin the second part of the cycle indicates that thecalculation algorithm used is reliable, as the variabil-ity would otherwise increase throughout the cycle dueto error accumulation (Table1). Thus, the variabilityobserved among the individuals in our series can beattributed to both an individual variation in the natureof each subject and to the slight variation in positionand orientation of the axial slices in each patient inspite of anatomical references. Even though the besteffort was made to ensure the acquisition of imagesfrom the same basal and apical regions for eachpatient, they do not necessarily have to be the samesince there exists a certain variation in the height andorientation from the longitudinal axis. One way oranother, the fact that the maximum deviationobserved was inferior to 3� makes AMT a

reproducible pattern that represents ventricular func-tion in healthy subjects.

Conclusions

Cardiac MRI allows for the calculation of AMT andLVLS. Both parameters are fundamental functionalcomponents of the ventricular twist mechanics con-ditioned, in turn, by the anatomical helical layout ofthe myocardial Þbers. These values provide comple-mentary information about systolic ventricular func-tion in relation to the traditional parameters used indaily practice, as LV ejection fraction, and shouldbecome useful tools for the study of complexventricular electromechanical dysfunction, as cardiacdisynchrony.

Acknowledgments We would like to thank Elena Ferre«, AnaBele«n Cabanillas and David Bordalas, radiology technicians atClınica Creu Blanca, for their assistance in performing cardiacMRI studies. We also thank Dr Ignasi Gich for his contributionto the statistical data analysis. This study was funded by theInstituto de Salud Carlos III, with the research projects of theFondo de Investigacion Sanitaria (FIS) numbers 04/2663,07/0454, 07/1188 and by the Spanish government projectsTIN2009-13618, CONSOLIDERINGENIO 2010 (CSD2007-00018). The third author has been supported byThe Ramon yCajal Program.

Conßict of interest None declared.

References

1. Torrent Guasp F (1966) Sobre morfologõ«a y funcionalismocardiacos (partes I, II y III). Rev Esp Cardiol 19: 48Ð55,56Ð71, 72Ð82

2. Torrent Guasp F (1980) La estructuracio«n macrosco«picadel miocardio ventricular. Rev Esp Cardiol 33:265Ð287

3. Internet web page:http://www.torrent-guasp.com/PAGES/Publications.htm

4. Lorenz C, Pastorek J, Bundy J (2000) Delineation of nor-mal human left ventricular twist troughout systole by tag-ged cine magnetic resonance imaging. J Cardiovasc MagnReson 2:97Ð108

5. Sengupta PP, Krishnamoorthy VK, Korinek J, Narula J,Vannan MA, Lester SJ et al (2007) Left ventricular formand function revisited: applied translational science tocardiovascular ultrasound imaging. J Am Soc Echocardi-ogr 20:539Ð551

6. Moon MR, Ingels NB Jr, Daughters GT, Stinson EB,Hansen DE, Miller DC (1994) Alterations in left ventric-ular twist mechanics with inotropic stimulation and volumeloading in human subjects. Circulation 89:142Ð150

Int J Cardiovasc Imaging

123

7. Torrent-Guasp F, Ballester M, Buckberg GD, Carreras F,Flotats A, Carrio« I et al (2001) Spatial orientation of theventricular muscle band: physiologic contribution and sur-gical implications. J Thorac Cardiovasc Surg 122:389Ð392

8. Masood S, Yang GZ, Pennell DJ, Firmin DN (2000)Investigating intrinsic myocardial mechanics: the role ofMR tagging, velocity phase mapping, and diffusionimaging. J Magn Reson Imaging 12:873Ð883

9. Buchalter MB, Weiss JL, Rogers WJ, Zerhouni EA,Weisfeldt ML, Beyar R et al (1990) Noninvasive quanti-Þcation of left ventricular rotational deformation in normalhumans using magnetic resonance imaging myocardialtagging. Circulation 81:1236Ð1244

10. Garcia-Barnes J, Gil D, Barajas J, Carreras F, Pujadas S,Radeva P (2006) Characterization of ventricular torsion inhealthy subjects using gabor Þlters and a variationalframework. Comput Cardiol 33:887Ð890

11. Garcia-Barnes J, Gil D, Pujadas S, Carreras F (2008) Avariational framework for assessment of the left ventriclemotion. Math Model Nat Phenom 3:76Ð100

12. Castillo E, Osman NF, Rosen BD, El-Shehaby I, Pan L,Jerosch-Herold M et al (2005) Quantitative assessment ofregional myocardial function with MR-tagging in a multi-center study: interobserver and intraobserver agreement offast strain analysis with Harmonic Phase (HARP) MRI.J Cardiovasc Magn Reson 7:783Ð791

13. Osman NF, McVeigh ER, Prince JL (2000) Imaging heartmotion using harmonic phase MRI. IEEE Trans MedImaging 19:186Ð202

14. Montillo A, Metaxas D, Axel L (2004) Extracting tissuedeformation using Gabor Þlter banks. Proc SPIE 5369:1Ð9

15. Evans LC (1993) Partial differential equations. BerkeleyMath Lect Notes

16. Duda RO, Hart PE, Stork DG (2001) Pattern classiÞcation.Wiley, New York

17. Sengupta PP, Tajik JA, Chandrasekaran K, Khanderia BK(2008) Twist mechanics of the left ventricle: principles andapplication. J Am Coll Cardiol Img 1:366Ð376

18. Vannan MA, Pedrizzetti G, Li P, Gurudevan S, Houle H,Main J et al (2005) Effect of cardiac resinchronizationthereapy on longitudinal and circumferential left ventricularmechanics by velocity vector imaging: description and ini-tial clinical application of a novel method using high-framerate B-mode echocardiographic images. Echocardiography22:826Ð830

19. Jones CJ, Raposo L, Gibson DG (1990) Functionalimportance of the long axis dynamics of the human leftventricle. Br Heart J 63:215Ð220

20. Ha JW, Lee HC, Kang ES, Ahn CM, Kim JM, Ahn JA et al(2007) Abnormal left ventricular longitudinal functionalreserve in patients with diabetes mellitus: implication fordetecting subclinical myocardial dysfunction using exer-cise tissue Doppler echocardiography. Heart 93:1571Ð1576

21. Wang J, Khouri DS, Yue Y, Torre-Amione G, Nagueh SF(2008) Preserved left ventricular twist and circumferentialdeformation, but depressed longitudinal and radial deforma-tion in patients with diastolic heart failure. Eur Heart J29:1283Ð1289

22. Waks E, Prince J, Andrew S (1996) Cardiac motion sim-ulator for tagged MRI. In Proceedings of mathematicalmethods in biomedical image analysis IEEE, pp 182Ð191

23. Liu Y et al (2009) Reconstruction of myocardial tissue motionand strainÞelds fromdisplacementencoded MRimaging.AmJ Physiol Heart Circ Physiol 297(3):H1151ÐH1162

24. Buckberg G, Hoffman JIE, Mahajan A, Saleh S, Coghlan C(2008) Cardiac mechanics revisited. Circulation118:2571Ð2587

25. Wang J, Khoury DS, Yue Y, Torre-Amione G, Nagueh SF(2008) Preserved left ventricular twist and circumferentialdeformation, but depressed longitudinal and radial defor-mation in patients with diastolic heart failure. Eur Heart J29:1283Ð1289

26. Torrent-Guasp F (1998) Estructura y funcio«n del corazo«n.Rev Esp Cardiol 51:91Ð102

27. Ballester M, Ferreira A, Carreras F (2008) The myocardialband. Heart Fail Clin 4:261Ð272

28. Rademakers FE, Rogers WJ, Guier WH, Hutchins GM, SiuCO, Weisfeldt MD et al (1994) Relation of regional cross-Þber shortening to wall thickening in the intact heart.Three-dimensional strain analysis by NMR tagging.Circulation 89:1174Ð1182

29. Helm PA, Tseng HJ, Younes L, McVeigh ER, Winslow RL(2005) Ex Vivo 3D diffusion tensor imaging and quanti-Þcation of cardiac laminar structure. Magn Res Med54:850Ð859

30. Streeter DDJ, Spotnitz HM, Patel DP, Ross JJ, SonnenblickEH (1969) Fiber orientation in the canine left ventricleduring diastole and systole. Circ Res 24:339Ð347

31. Harrington KB, Rodriguez F, Cheng A, Langer F, Ashik-aga H, Daughters GT et al (2005) Direct measurement oftransmural laminar architecture in the anterolateral wall ofthe ovine left ventricle: new implications for the wallthickening mechanics. Am J Physiol Heart Circ Physiol288:H1324ÐH1330

32. Carreras F, Ballester M, Pujadas S, Leta R, Pons-Llado G(2006) Morphological and functional evidences of thehelical heart from non-invasive cardiac imaging. Eur JCardiothorac Surg 29:50Ð55

33. Anderson RH, Smerup M, Sanchez-Quintana D, Loukas M,Lunkenheimer PP (2009) The three-dimensional arrange-ment of the myocites in the ventricular walls. Clin Anat22:64Ð76

34. Nasiraei-Moghaddam A, Gharib M (2009) Evidence forthe existence of a functional helical myocardial band. Am JPhysiol Heart Circ Physiol 296:H127ÐH131

35. Buckberg GD, Coghlan HC, Hoffman JI, Torrent-Guasp F(2001) The structure and function of the helical heart and itsbuttresswrapping. VII.Critical importanceof septumfor rightventricular function. Semin Thorac Cardiovasc Surg13:402Ð416

36. Torrent-Guasp F, Kocica MJ, Corno A, Komeda M, Cox J,Flotats A et al (2004) Systolic ventricular Þlling. Eur JCardiothorac Surg 25:376Ð386

37. Sengupta PP, Khanderia BK, Narula J (2008) Twist anduntwist mechanics of the left ventricle. Heart Failure Clin4:315Ð324

38. Bertini M, Sengupta PP, Nucifora G, Delgado V, Ng ACT,Marsan NA, Shanks M et al (2009) Role of left ventriculartwist mechanics in the assessment of cardiac dyssynchronyin heart failure. J Am Coll Cardiol Img 2:1425Ð1435

39. Helle-Valle T, Crosby J, Edvardsen T, Lyseggen E,Amundsen BH, Smith HJ et al (2005) New noninvasive

Int J Cardiovasc Imaging

123

method for assessment of left ventricular rotation: speckletracking echocardiography. Circulation 112:3149Ð3156

40. Delgado V, Ypenburg C, van Bommel RJ, Tops LF,Mollema SA, Marsan NA et al (2008) Strain in cardiacresynchronization therapy imaging: comparison betweenlongitudinal, circumferential, and radial assessment of leftventricular dyssynchrony by speckle tracking strain. J AmColl Cardiol 51:1944Ð1952

41. Zo«calo Y, Guevara E, Bla D, Giacche E, Pessana F, PeidroR, Armentano RL (2008) A reduction in the magnitude andvelocity of left ventricular torsion may be associated with

increased left ventricular efÞciency: evaluation by speckle-tracking echocardiography. Rev Esp Cardiol 61:705Ð713

42. Hui L, Pemberton J, Hickey E, Kui Li X, Lysyansky P,Ashraf M et al (2007) The contribution of left ventricularmuscle bands to left ventricular rotation: assessment by a2-dimensional speckle tracking method. J Am Soc Echo-cardiogr 20:486Ð491

43. Takeuchi M, Nakai H, Kokumai M, Nishikage T, Otani S,Lang RM (2006) Age-related changes in left ventriculartwist assessed by two-dimensional speckle-tracking imag-ing. J Am Soc Echocardiogr 19:1077Ð1084

Int J Cardiovasc Imaging

123