Left Ventricular Mass and Volume: Fast Calculation with Guide-Point Modeling on MR Images 1

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1 Alistair A. Yong, PhD Brett R. Cowan, BE, MBChB Steven F. Thrpp, MA Warren J. Hedley, ME Lois J. Dell Italia, MD Index terms: Heart, volme, Magnetic resonance (MR), phase imaging, Magnetic resonance (MR), rapid imaging, Magnetic resonance (MR), volme measrement, Radiology 2000; 216: Abbreviations: ED end-diastolic ES end-systolic LV left ventricle 3D three-dimensional 1 From the Departments of Anatomy with Radiology (A.A.Y.), Medicine (B.R.C., S.F.T.), and Engineering Science (W.J.H.), University of Ackland, 85 Park Road, Ackland, New Zealand; and the Department of Medicine, University of Alabama at Birmingham, Ala (L.J.D.). Received Agst 13, 1999; revision reqested October 5; revision received November 12; accepted December 20. Spported in part by the Ackland Medical Research Fondation and the Health Research Concil of New Zealand. Address correspondence to A.A.Y. ( a.yong@ackland.ac.nz). RSNA, 2000 Athor contribtions: Garantor of integrity of entire stdy, A.A.Y.; stdy concepts, A.A.Y., B.R.C.; stdy design, A.A.Y.; definition of intellectal content, A.A.Y., B.R.C.; literatre research, A.A.Y.; clinical stdies, B.R.C., L.J.D.; experimental stdies, A.A.Y., S.F.T., B.R.C., L.J.D.; data acqisition, A.A.Y., S.F.T., B.R.C., L.J.D.; data analysis, A.A.Y., S.F.T., W.J.H.; statistical analysis, A.A.Y.; manscript preparation, A.A.Y.; manscript editing and review, A.A.Y., S.F.T., W.J.H., B.R.C. Left Ventriclar Mass and Volme: Fast Calclation with Gide-Point Modeling on MR Images 1 The athors describe a fast method for calclating left ventricle (LV) mass and volmes from mltiplanar magnetic resonance (MR) images. Mathematic models were fitted to a small nmber of ser-selected gide points in 15 healthy volnteers, 13 patients after myocardial infarction, and a canine model of mitral regrgitation in eight dogs. Errors between model and manal contors were small (LV mass, 1.8 g 4.9 [mean SD]; end-diastolic volme, 2.2 ml 4.6; end-systolic volme, 2.3 ml 3.8). Estimates of global fnction cold be obtained in 6 mintes, a time saving of 5 10 times over estimates with manal contoring. Left ventricle (LV) mass and volmes at end-diastole (ED) and end-systole (ES) are essential clinical parameters for the diagnosis and management of cardiac disease. Magnetic resonance (MR) imaging is able to provide accrate and precise estimations of LV mass and volme since it is a tre three-dimensional (3D) method that is not dependent on geometric assmptions and is not limited in the position or orientation of the image sections (nlike echocardiography or compted tomography [CT]) (1,2). Crrent imaging techniqes allow the acqisition of sections in short- and long-axis orientations, each with frames throgh the cardiac cycle, in clinically acceptable times ( 15 mintes) (3,4). Typically, LV bondaries (contors) are drawn on each section of a series of short-axis images and the otlined areas converted to volmes and smmed to prodce estimates of volme and mass. Previos stdies have shown that this techniqe gives more accrate and reprodcible estimates of volme and mass than do other imaging modalities (2,5 7). A major limitation of the MR imaging section smmation method is the prohibitive time necessary to otline the inner and oter bondaries of the LV in each section at ED and ES. This image contoring bottleneck precldes the se of mltiplanar MR imaging in rotine clinical care and limits its application to small research trials. Many semiatomated image segmentation algorithms have been applied to this problem (8 10), bt these algorithms are not sfficiently robst for rotine clinical se. Image pixel intensities are insfficient to adeqately constrain the segmentation problem, owing to the limited temporal and spatial resoltion, presence of image artifacts, and lack of contrast between blood and mscle. The endocardial trabeclae and papillary mscles also make the inner bondary difficlt to define. At present, the amont of time spent on manal editing and correction renders atomated methods almost as slow as manal contoring in clinical practice. In this stdy, we evalated a fast, accrate method of calclating LV mass and volmes from mltiple MR sections, withot the need for image contoring. The method relies on an accrate mathematic model of the LV that is fitted to a relatively small nmber of data points (gide points) provided by the ser. No image processing is reqired and the method is therefore independent of image qality. Materials and Methods Data Acqisition To determine the accracy and efficiency of this method, we analyzed reslts in 15 healthy volnteers and 13 patients with regional abnormalities in wall motion de to myocardial infarction. In- 597

2 Figre 1. ED (left) and ES (right) gradient-echo short-axis images with manal contors shown as lines. Top: Volnteer images (8/5 with 10 flip angle). Bottom: Patient images (30/14 with 40 flip angle). Note the wall motion abnormality (lack of motion and wall thickening) in the basal lateral wall on the patient image (arrow). Figre 2. Same images as in Figre 1 with model contors shown as light lines to indicate reslts of gide-point (F) fit. formed consent was obtained for all hman stdies, which were performed with the approval of the instittional ethical committees. Volnteers. A grop of 15 healthy sbjects (10 men and five women; mean age, 23 years; age range, years) nderwent MR imaging with a 1.5-T imager (Vision; Siemens, Erlangen, Germany). Prospectively gated cardiac cine images were acqired in eight to nine short-axis sections and three long-axis sections with se of a segmented k-space plse seqence (repetition time msec/echo time msec of 8/5, flip angle of 10, field of view of mm) with view sharing (11 19 frames per section) (3,4). Each section was acqired dring a breath hold of cardiac cycles. The shortaxis sections spanned the heart from apex to base with a section thickness of 8.0 mm and section gap of mm. Phase-contrast velocity images (11) were acqired in a section positioned perpendiclar to the ascending aorta approximately 20 mm above the aortic valve. Since the entire imaging protocol performed with the volnteers consisted of several hors of imaging (inclding tagging and many flow-qantification seqences), all sbjects had a break of 1 2 hors between cine anatomic imaging (inclding the short-axis cine sections sed in the volme calclations) and the phase-contrast flow imaging. At the latter, prospectively gated cine gradientecho imaging was performed (24/6, flip angle of 30, field of view of 250 mm, section thickness of 8.0 mm, velocity encoding of 150 or 250 cm/sec, and frames throgh the cardiac cycle). Velocity sensitization was encoded in the throgh-plane (section-select) direction. Patients. MR imaging data from 13 patients, who nderwent MR imaging as part of a previos stdy (12) at 2 weeks (n 6) and 3 months (n 7) after their first acte Q wave myocardial infarction, were selected for analysis of global fnction. The 13 stdies were selected consectively in alphabetical order from a database of 70 stdies, details of which are given by Johnson et al (12). All MR stdies were performed with a 1.5-T imager (Gyroscan; Philips, Shelton, Conn). Respiration-compensated gradient-echo cine images (30/14, flip angle of 40, field of view of mm) were acqired in nine to 10 short-axis sections, each 8.0-mm thick with a 1.0-mm section gap. Animal stdies. MR data from eight dogs imaged 5 6 months after indction of mitral regrgitation, as part of a previos stdy (13) approved by the instittional animal care committee, were analyzed by means of gide-point modeling. Mitral regrgitation was indced by means of perctaneos chordal rptre of the mitral valvlar apparats, as described in reference 13. MR imaging was performed with a 1.5-T imager (Gyroscan) with the same gradient-echo cine imaging seqences as were sed with the patients (six to eight short-axis sections, 8-mm-thick sections, section gap, field of view of 350 mm). After imaging, the hearts were arrested with KCl and removed from the chest. After the atria and right ventriclar free wall were removed from the interventriclar septm and LV, the portions were weighed. Image Analysis Manal contoring and section smmation. The inner and oter bondaries of the LV were defined on each image as follows. First, a semiatomatic regiongrowing method was sed to locate preliminary bondaries (10). These bondaries were then manally corrected for each image. To the best ability of the observer (S.F.T.), papillary mscles were exclded from the myocardim and inclded in the blood pool. Great care was taken to identify the exact bondary of the myocardim. The contors were then reviewed by another observer (B.R.C.), and a consenss was achieved in all cases 598 Radiology Agst 2000 Yong et al

3 model in the longitdinal ( ) direction was set to correspond to the most basal extent of the LV in the long-axis images at each time point. Gide-Point Modeling Figre 3. Three-dimensional displays of the model fits in Figre 2. endocardial gide points. Endocardial srface is shaded, and element bondaries are drawn as lines. Interventriclar septm is to the left. Note the distorted LV shape at ES on the patient image owing to the basal lateral infarct (arrow). where there was a difference in opinion. Figre 1 shows short-axis sections at ED and ES together with the final bondaries (called manal contors in this article since extensive manal correction of the segmentation reslt was reqired). The areas otlined in each image were then mltiplied by the section thickness pls the section gap and the resltant volmes smmed to prodce estimates of ED and ES volmes. LV mass was calclated from the mean of the ED and ES myocardial volmes (as the difference between the volmes enclosed by the epicardial and endocardial contors) mltiplied by 1.05 g/ml. Flow qantification. The phase-contrast velocity images were segmented manally (B.R.C.) into vessel lmen and backgrond. The throgh-plane velocity component was integrated across the vessel lmen and across all frames in the cycle to prodce aortic flow. Note that the flow measrement is insensitive to small inclinations in the angle between the aorta and the section plane (11). Model Definition A finite element model was sed to represent the geometry of the LV. This model was similar to those sed previosly to describe LV deformation (14,15). The model consisted of 16 elements, each with cbic interpolation in the circmferential and longitdinal directions. Linear interpolation was sed to cople the inner and oter srfaces into a coherent 3D model. The model was defined in a polar coordinate system (Appendix). This simplified the soltion process, allowing the radial coordinate ( ) ofthe model to be fitted as a fnction of the two anglar coordinates ( and in the circmferential and longitdinal directions, respectively). Use of a polar coordinate system imposes two constraints on the shape of the model. First, there mst be a straight central axis passing within the LV cavity from apex to base. Second, the location of the LV inner and oter srfaces mst be niqely specified on the basis of a radial distance from the central axis at all points. These constraints are not as severe as those typically applied in the case of echocardiography (16), and the piecewise cbic interpolation allows a variety of normal and deformed LV shapes to be accrately modeled, inclding LV anerysms and severe hypertrophy (as in reference 14). Initially, the model was scaled to each heart according to the distance between the base and the apex of the LV. The initial shape of the LV model was a reglar ellipsoid, which was obtained by setting the inner and oter srfaces to a constant radial vale. The extent of the Gide points were interactively placed on the images by the ser and the twodimensional image coordinates converted to 3D coordinates with the section position information encoded in the image header. The model shape was fitted to the 3D gide-point positions by minimizing an error fnction consisting of the sm of a smoothing term and a term penalizing the distance between each gide point and the corresponding model position (Appendix). The smoothing term penalized changes in slope and crvatre arond the LV, allowing the model to realistically interpolate the very sparse gide-point data. The error fnction was qadratic in the model parameters, reslting in a simple linear least sqares soltion process. As the ser placed or modified gide points, the model fit was pdated in real time. The intersections of the model with the image planes were recalclated after each fit by means of a sbdivision algorithm (17) and redisplayed on each image. The ser contined to interactively add or modify gide points ntil the model-image intersections provided a good representation of the bondaries of the LV. Figre 2 shows the intersections of the model with the images shown in Figre 1. To provide an estimate of interobserver error, gide-point models were created by two operators (A.A.Y., S.F.T.) for each of the volnteers and patients. As previosly, papillary mscles were exclded from the myocardim and inclded in the blood pool. Model Mass and Volme Comparisons LV mass and volme cold be estimated from the model in a nmber of ways. To assess the accracy of the techniqe, we needed a consistent method of volme calclation that cold be sed for both manal and gide-point modeling methods; therefore, we sed the intersections of the model with each image section plane as model contors at ED and ES (Fig 2). The model contors were then inpt to the same cstom-written software sed to calclate the volmes from the manal contors. In this way, the ability of the modeling process to reprodce the manal contors for the prposes of volme calclation cold be directly assessed. Volme 216 Nmber 2 Left Ventriclar Mass and Volme: Fast Calclation 599

4 TABLE 1 Time Reqired (Mintes) for Each Stdy for Estimation of Global Fnction Sbject Statistical Tests Volmes and mass were compared between the two methods by means of paired t tests. Differences with a P vale of.05 were considered statistically significant. Reslts Manal Contoring Gide-Point Modeling Patients Volnteers Note. Data are the means SDs. Figre 2 shows the reslt of the fitting process on typical short-axis images obtained in a volnteer and a patient at 3 months after myocardial infarction. Figre 3 shows the corresponding 3D LV models and illstrates the ability of the model to describe distorted LV shapes. This patient s infarct was located in the basal lateral LV wall, leading to a wall motion abnormality in this region, which is clearly seen in Figre 3. For the 15 volnteers, a mean 66 gide points (range, 49 81) were needed for each stdy to fit the original images (approximately six per section). For the 13 patients, a mean 32 gide points (range, 22 51) were needed for each stdy (approximately three per section). Approximately 6 mintes were reqired by each operator to generate the gide-point models at ED and ES and estimate LV mass and volmes, ejection fraction, and stroke volme for each stdy. This represents an improvement of five to 10 times over the times reqired for manal contoring (Table 1). Table 2 shows the mean vales obtained in the volnteers for ED volme and ES volme, LV mass, stroke volme, and ejection fraction. Reslts are given for both manal and model contors (two operators), together with the mean paired difference and SD of the differences between the two methods and the two operators. Similarly, Table 3 shows the reslts for the patient grop. Figre 4 shows Bland-Altman plots of the differences between the two measres verss their mean. Taken over both grops (volnteers and patients) and both observers, errors in mass and global fnction indexes were small in all cases (left ventriclar mass, 1.8 g 4.9 [mean SD]; stroke volme, 0.2 ml 4.8; ejection TABLE 2 Data in Healthy Volnteers (n 15) Contor Method ED Volme ES Volme LV Mass (g) fraction, 1.1% 2.5%; ED volme, 2.2 ml 4.6; and ES volme, 2.3 ml 3.8). Althogh statistically significant differences exist in some of the fnctional indexes between model and manal methods and between observers for the modeling method, the magnitde of these differences is small in all cases and nlikely to be clinically important. These differences were likely de to biases in the placement of contors by different observers and to differences in the software sed to create the manal contors and the gide-point model contors. The phase-contrast velocity images of the ascending aorta were obtained at the end of a long imaging protocol, as long as 2 hors after acqisition of the cine short-axis sections sed for the manal and modeling calclations. In many sbjects, heart rate changed sbstantially between the two measrements (range for the 15 sbjects, 12 to 13 beats per minte). The difference in stroke volme between the flow and section-smmation methods was fond to be strongly correlated to the change in heart rate between the two images (P.001, r 0.83). This correlation was linear and was likely de to -adrenergic effects becase of the long imaging time. On the basis of analysis of covariance, or AN- COVA, to correct for heart rate as a covariate, there was no difference between the aortic flow and either the gide-point modeling or manal contoring estimates of stroke volme (manal vs phase contrast, 0.6 ml 5.4; operator 1 model vs phase contrast, 0.2 ml 9.0; operator 2 model vs phase contrast, 0.9 ml 7.7). Figre 5 part A shows Bland-Altman plots for these comparisons. Postmortem mass measrements also agreed well with model estimates of LV mass in the eight dogs stdied ( 0.3 g 5.8 [Fig 5 part B]). Discssion Stroke Volme Ejection Fraction (%) Gide-point model Operator Operator Manal Operator 1 vs manal * * * Operator 2 vs manal Operator 1 vs operator * * Note. Data are the mean paired differences SDs. * P.05 for difference between estimates. TABLE 3 Data in MI Patients (n 13) Contor Method ED Volme ES Volme LV Mass (g) Stroke Volme Ejection Fraction (%) Gide-point model Operator Operator Manal Operator 1 vs manal * Operator 2 vs manal * Operator 1 vs operator Note. Data are the mean paired differences SDs. * P.05 for difference between estimates. The gide-point modeling method can be sed with any mathematic model and 3D image data set (eg, 3D ltrasonography or CT). Use of smoothing constraints in conjnction with gide points provided an intitive and efficient ser interface with which to maniplate the model. Since the position of the gide points inflenced the model shape in a consistent 3D manner, relatively few gide points were reqired for adeqate fits to the images (three to six 600 Radiology Agst 2000 Yong et al

5 Figre 4. Bland-Altman plots show differences in global fnction parameters (model mins manal) verss the mean of the two methods. A, ED volme (EDV); B, ES volme (ESV); C, stroke volme (SV); D, ejection fraction (EF); and E, LV mass. } and { volnteers, and patients; } and observer 1, { and observer 2. Figre 5. A, Bland-Altman plot shows differences in stroke volme (SV) between phase-contrast flow measrements (corrected for heart rate) and manal method (}) and modeling method ( observer 1, E observer 2) in volnteers. B, Bland-Altman plot shows differences in mass between postmortem measrements and modeling method (single observer) in eight dogs. points per section), which redced the amont of ser interaction reqired. In or experiments, more gide points were needed for the volnteers than for the patients with wall motion abnormalities. The breath-hold volnteer images were of mch higher qality than were the non breathhold patient images, with minimal motion artifact, better signal-to-noise ratio and greater contrast between blood and mscle, particlarly abot the papillary mscles and endocardial trabeclae. This higher qality may have contribted to the increased nmber of gide points reqired for good correspondence between the model and the image in these cases. The gide-point modeling method relies on the ser to sccessively refine placement of the model on the images. No image processing is reqired. Crrent methods that rely on image processing lack the robstness and accracy necessary for sccessfl clinical application; however, local image information can be inclded in the model optimization (18). LV absolte volmes tended to be overestimated with the model contors of operator 1 relative to operator 2 and the manal contors in the healthy grop. These differences were spread evenly over all sections and cold be eqated with a small bias in the perceived position of the bondary. It is vital in any instittion that a consenss be achieved among all operators in the placement of ventriclar bondaries on the images. Small biases in contor placement can easily lead to large errors in volmes and mass. In this stdy, the SDs of the differences between manal and modeling methods were small, and the bias is nlikely to be clinically important. Reslts of analysis of covariance comparing phase-contrast aortic flow measrements with manal and model estimates of stroke volme showed that there was no effect (other than heart rate) de to the measrement method. The comparison of LV mass with postmortem measrements showed an apparent overestimation of mass with the gide-point method, since papillary mscles were inclded in the postmortem weighing bt were exclded from the gide-point model. The eight dogs were stdied after 5 6 months of mitral regrgitation cased by rptre of the chordae and ths exhibited severe LV remodeling de to chronic volme overload (13). The contribtion of the papillary mscles to LV mass was therefore likely to be smaller than sal, and some papillary mscle may have been inclded in the gide-point model owing to failre to distingish it from LV wall. Also, errors de to trabeclation of the inner srface of the LV, possible inclsion of epicardial fat (together with the specific gravity factor of 1.05 g/ml sed for comparison), and the slight overestimation of model mass relative to manal contors (Tables 2, 3) may have combined to prodce the apparent overestimation. The gide-point modeling method was fond to redce the time reqired to estimate LV mass, ED volme, ES volme, stroke volme, and ejection fraction by a factor of 5 10 withot loss of accracy. In conjnction with recent advances in fast cardiac imaging (3,4), a comprehensive cardiac examination inclding imaging (scot images pls eight to 12 cine sections in short- and long-axis orientations) and analysis (global and possibly regional fnction) wold typically reqire less than half an hor to complete. This time saving enables high-spatial-resoltion mltiplanar MR stdies of cardiac fnction to be efficiently sed in rotine clinical practice. Volme 216 Nmber 2 Left Ventriclar Mass and Volme: Fast Calclation 601

6 Appendix A finite element model was constrcted as described previosly (14,15,19). Within each element, the geometry of the LV was given by a weighted mean of vales at the nodes: 1, 2, 3 n n 1, 2, 3 n, (A1) where n are the nodal vales, n are basis fnctions that give the relative weighting of each nodal vale, and ( 1, 2, 3 ) are the element coordinates. The geometric field was defined to be the radial coordinate in a prolate spheroidal coordinate system: x f cosh cos y f sinh sin cos z f sinh sin sin (A2) where (,, ) are the radial, longitdinal, and circmferential coordinates of the polar system and (x, y, z) are the corresponding rectanglar cartesian coordinates. The focal length f of the prolate system was chosen so that the 1 srface gave a good initial approximation of the LV epicardial srface. This provided an overall scale factor for each case. In each element, element coordinates 1, 2, and 3 were in the circmferential, longitdinal, and transmral directions, respectively. The basis fnctions were chosen to be bicbic Hermite in 1 and 2 and linear in 3 (19). Nodal vales were shared between neighboring elements to give continity in both slope and position throghot the LV. The model consisted of 16 3D elements: for elements in the longitdinal direction by for elements in the circmferential direction (Fig 3). The model was fitted to gide-point data by minimizing the following error fnction: E S g g g 2, (A3) where g are the positions of the gidepoint data and ( g ) are the model positions at element coordinates g corresponding to g. The element coordinates were fond by projecting the gide data onto the model along lines of constant and. S( ) denotes a smoothing term that was inclded in the error fnction to constrain the model to smoothly interpolate between the sparse gide points. As done previosly (20), we sed a weighted Sobolev norm that penalized displacement of the model from a prior shape: S d, (A4) where *, where * is the prior shape (in this article, * 1 [ie, a reglar ellipsoid] is sed for the prior shape). The weights 1 and 2 penalized the slope of the displacement field in the circmferential and longitdinal directions, respectively, whereas the weights 1 and 2 penalized crvatre, and the weights 1, 2, and 3 copled slopes between directions. The smoothing weights sed in this article are 1 2 0, , The isse of which weights are optimal for gide-point fitting remains an active area of research. However, the optimality criterion is difficlt to qantify since the ser always places the gide points in sch a way as to adeqately model the ventricle. A wide range of weights were tried in or experiments, and these vales provided good reslts in all cases. The error fnction (Eq [A3]) was qadratic in the nknown nodal parameters ( n ), allowing direct soltion by means of the standard least sqares methods. Acknowledgments: We thank Dr Tom Gentles, MBChB, (Department of Paediatrics) and Dr Chris Occleshaw, MBChB, (Department of Radiology) of Green Lane Hospital, Ackland, New Zealand, for their assistance with the recritment and imaging of the volnteers. We also thank Andrew Cantell, BE, for his technical expertise. References 1. Reichek N. Magnetic resonance imaging for assessment of myocardial fnction. Magn Reson Q 1991; 7: Pattynama PMT, De Roos A, Van der Wall EE, Van Voorthisen AE. Evalation of cardiac fnction with magnetic resonance imaging. Am Heart J 1994; 128: Atkinson DJ, Edelman RR. Cineangiography of the heart in a single breath hold with a segmented trboflash seqence. Radiology 1991; 178: Foo TKF, Bernstein MA, Aisen AM, Hernandez RJ, Collick BD, Bernstein T. 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