ECG-Correlated Imaging of the Heart with Subsecond Multislice Spiral CT

888 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 9, SEPTEMBER 2000 ECG-Correlated Imaging of the Heart with Subsecond Multislice Spiral CT Marc Kachelrieß*, Stefan Ulzheimer, and Willi A. Kalender Abstract The new spiral multislice computed tomography (CT) scanners and the significant increase in rotation speed offer great potential for cardiac imaging with X-ray CT. We have therefore developed the dedicated cardiac reconstruction algorithms 180 multislice cardio interpolation (MCI) and 180 multislice cardio delta (MCD) and here offer further details and validation. The algorithm 180 MCI is an electrocardiogram (ECG)-correlated filtering (or weighting) algorithm in both the cardiac phase and in the -position. Effective scan times (absolute temporal resolution) of as low as e = 56 ms are possible, assuming = 4 simultaneously measured slices at a rotation time of rot = 0 5 s and 3 for the table feed per rotation, where denotes the collimated slice thickness. The relative temporal resolution (fraction of the heart cycle depicted in the image), which is the more important parameter in cardiac imaging, will then be as low as = 12 5% of the heart cycle. The second approach, 180 MCD, is an ECG-correlated partial scan reconstruction of 180 + data with 8 (fan-angle). Its absolute temporal resolution lies in the order of 250 ms (for the central ray, i.e., for the center of rotation), and the relative temporal resolution increases with increasing heart rate, e.g., from typically = 25%at H = 60min 1 to = 50%at H = 120 min 1, assuming again rot =05s. For validation purposes, we have done simulations of a virtual cardiac motion phantom, measurements of a dedicated cardiac calibration and motion phantom, and we have reconstructed patient data with simultaneously acquired ECG. Both algorithms significantly improve the image quality compared with the standard reconstruction algorithms 180 multislice linear interpolation (MLI) and 180 multislice filtered interpolation (MFI). However, 180 MCI is clearly superior to 180 MCD for all heart rates. This is best illustrated by multiplanar reformations (MPR) or other three-dimensional (3-D) displays of the volume. 180 MCI, due to its higher temporal resolution, is best for spatial and temporal four-dimensional (4-D) tracking of the anatomy. A tunable scanner rotation time to avoid resonance behavior of the heart rate and the scanner s rotation and shorter rotation times would be of further benefit. Index Terms Computed tomography (CT), four-dimensional (4-D) reconstruction, heart, multirow detector systems, multislice spiral CT (MSCT). NOMENCLATURE Indicator function: 1 if odd, otherwise 0. Rectangle function with support and area 1. Manuscript received January 25, 2000; revised May 30, 2000. This work was supported by Bayerische Forschungsstiftung, under Grant AZ262/98. The Associate Editor responsible for coordinating the review of this paper and recommending its publication was G. Wang. Asterisk indicates corresponding author. The authors are with the Institute of Medical Physics, University of Erlangen-Nürnberg, 91054 Erlangen, Germany (e-mail: marc.kachelriess@imp.uni-erlangen.de). Publisher Item Identifier S 0278-0062(00)08084-8. Triangle function of characteristic width ( half width) 1,. Maximum function,. Minimum function,. Projection angle, for a sequence (360 ) scan or -interpolated data, for a spiral scan. Angle associated with reconstruction position. Angle of rotation during one heart cycle. Angles suitable for interpolation at with. Angle within fan,. Cardiac phase (with respect to R R) as a function of the view angle,. Cardiac phase about which to center the reconstruction. Characteristic width of the phase weighting function. Notation used for the window setting, is the window s center in HU, its width in HU. Table feed per 360 rotation. Relative error in calcium scoring,. Fan-angle, in our case,. Abbreviation denoting the fraction of a full rotation needed for reconstruction. Patient s heart rate. Number of heart beats per rotation. Slice index and number of simultaneously measured slices,. Pitch,. Projection data for systems with simultaneously measured slices,. -interpolated spiral raw data at position and for algorithm. Notation for the calcification score. The true value is to be achieved and the measured value has been achieved. Nominal slice thickness. Threshold used for calcium scoring. Absolute temporal resolution effective scan time,. Time for a 360 rotation. Relative temporal resolution relative width (with respect to R R) of the succes- 0278 0062/00$10.00 2000 IEEE

KACHELRIEß et al.: ECG-CORRELATED IMAGING OF THE HEART 889 -axis sive intervals in the cardiac R R cycle. For measured data, is given as the FWTM of the phase sensitivity profile.. Relative temporal resolution assuming that we have to wait -rotations until new data are available. Weighting function of characteristic width for 180 MCI that weights the distance of a measured point to the reconstruction plane,. Weighting function of characteristic width for 180 MCI that weights the cardiac phase deviation of a measured point to the desired reconstruction phase, %. Weight used for -interpolation for the th available projection value at slice. Axis of rotation. Arbitrary selectable reconstruction position,. Characteristic width of the distance weighting function. -position of detector array center,. -position of the center of the th measured slice,. I. INTRODUCTION THE latest great step in computed tomography (CT) development was the introduction of multislice CT scanners in 1998. The number of simultaneously acquired detector slices nowadays is typically. This new technology allows us to increase the -resolution or the volume coverage by about a factor of [1]. In addition, overlapping data acquisition, which means spiral pitch, with being the collimated slice thickness, allows us to drastically increase the temporal resolution without decreasing the spatial resolution by using data from successive rotations for reconstruction. Of course, the motion must be periodic in some sense as it is the case with cardiac motion. Potential distortions from this periodicity, as they might result from patient breathing or from contrast injection, are of low speed compared with the cardiac motion and do not take a significant influence. Moreover, because the transit time of the detector array and a given reconstruction position has increased, multislice technology allows us to become phase-selective: for a retrospectively selected cardiac phase and reconstruction position, simply the detector row(s) closest to both (in spatial domain) and to (in temporal domain) has to be chosen for reconstruction. Although similar ideas have been proposed for single slice CT, a few years ago [2], [3], their generalization to multislice CT turned out to be very effective and to overcome the known problems of cardiac imaging from single slice CT [4], [5]. Unlike other manual approaches that retrospectively select the best images for diagnosis [6], [7] or retrospectively determine the optimal timing shift about which to center a partial scan reconstruction [8], the algorithms developed by our group are dedicated cardiac reconstruction algorithms that automatically allow us to reconstruct complete volumes at any cardiac phase. They require the simultaneously recorded electrocardiogram (ECG) of the patient for synchronization purposes. Synchronization is done with respect to the R-peaks, the most pronounced peaks of the ECG signal. Cardiac cycles are defined as the R R intervals of the ECG, and the cardiac phase runs from 0% to 100% within each cardiac cycle. This paper will briefly state the definitions of the two algorithms 180 multislice cardio interpolation (MCI) and 180 multislice cardio delta (MCD) and then evaluate their performance in comparison to the standard -interpolaton algorithms 180 multislice linear interpolation (MLI) and 180 multislice filtered interpolation (MFI). Simulated raw data of a virtual cardiac motion phantom, measurements of a dedicated physical cardiac calibration and motion phantom, as well as measured patient data are used to evaluate our approaches. Theoretical evaluations of both algorithms, 180 MCI and 180 MCD, including image noise, -resolution, and temporal resolution, are given elsewhere [5]. II. MATERIALS AND METHODS For our patient examinations, we have used the four-slice scanner SOMATOM Volume Zoom (Siemens Medical Systems, Erlangen, Germany) with a rotation time s. The fan-angle is. Per rotation, 1160 projections, each with 4 672 channels, are collected. The scan parameters were chosen as 4 1 mm collimation and mm table feed per rotation. This ensures the complete coverage of the heart during a single breath-hold and achieves high -resolution. The patient s ECG signal was recorded simultaneously during the scan to correlate the cardiac phase to the projection angle. It is well known that quantitative cardiac imaging, such as coronory calcification measurements, suffer from intrascanner and interscanner variability [9]. To reduce these variations and to improve calcium scoring, a semiantropomorphic cardiac phantom (QRM GmbH, Möhrendorf, Germany) has been designed that not only allows for stationary calibration inserts, but is also able to move arbitrary objects along arbitrary, freely progammable three-dimensional (3-D) paths [Fig. 1(a)], as described in [10] and [11]. We used this phantom equipped with the motion insert this insert consists of an open water tank that contains the object to be moved by an external robot to evaluate the cardiac reconstruction algorithms. Measurement of the dedicated cardiac motion and calibration phantom was performed using the same scan parameters as for our patient measurements. The motion phantom generates a realistic ECG signal, which is processed by the same ECG monitor as has been used for the patient scans. Thus, phantom scans and patient scans are directly comparable. In addition, we have simulated raw data for the virtual cardiac phantom [4], [5], [10] to be reconstructed with the various approaches. The phantom consists of a lattice of calcifications; some of them are subjected to motion, and some of them are stationary, to be used as a reference standard. Fig. 1(b) shows the three rows of calcifications of varying diameter: 3 mm, 2 mm, and 1 mm. The five columns consist of stationary cylinders

890 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 9, SEPTEMBER 2000 (a) (b) Fig. 1. Two phantoms are used to evaluate our algorithms. Both (a) the physical heart phantom and (b) the virtual heart phantom are semiantropomorphic phantoms to mimic the patient anatomy, including cardiac motion. The motion insert (here, a water equivalent rod with a calcium cylinder) of the physical phantom can move arbitrary objects along one arbitrary, freely programmable 3-D path at a time. The virtual phantom can move arbitrary objects along many arbitrary, freely programmable 3-D paths at a time. Here, it moves six objects horizontally and three objects along z; thus, two paths at a time are simulated. (left), horizontally moving cylinders (second left), stationary spheres (middle), horizontally moving spheres (second right), and spheres moving along (right), respectively. The simulated motion consists of a sinusoidal covering 80% of the cardiac cycle and a stationary part of 20% of R R. Depicting the phantom artifact-free indicates that the respective algorithm allows us to freeze cardiac motion within % of one heart beat. The motion amplitude was simulated as 5 mm because the typical linear dimension of cardiac motion lies in the order of 10 mm [12], [13]. As a standard algorithm for comparison, we use 180 MLI [1], which is a linear -interpolation between the two nearest data points on each side of the reconstruction plane at. 180 MLI was modified to take a slice number as an additional parameter to use only this slice for reconstruction. In this sense, it is equivalent to the single slice algorithm 180 LI. This modification will have no significant impact on the achievable -resolution because all scans are performed overlapping, at pitch values, and thus, no data gaps will be introduced by using one of the -measured slices only. Moreover, the effective scan time will remain the same as well: of data contribute to each image. The second standard algorithm investigated is 180 MFI [1], which is a standard -filtering approach that is typically used in commercial multislice scanners. For overlapping data acquisition, as is the case in this paper, more than one gantry rotation will contribute to the image. To be more precise, roughly rotations this is the number of rotations necessary to advance the table by -collimated slice thicknesses will play a role for each interpolation. Although the exact value depends on the width of the -filter, it can be expected that the temporal resolution of 180 MFI is much worse compared with 180 MLI, which only uses one gantry rotation [the exact value is -rotations] for reconstruction. Thus,

KACHELRIEß et al.: ECG-CORRELATED IMAGING OF THE HEART 891 some of the cardiac motion artifacts will be averaged away by 180 MFI because the contributing data might cover one complete or more than one heart cycle. However, this averaging will evidently result in a significant loss of in-plane and -resolutions. All reconstruction algorithms were implemented on a standard PC with the dedicated image evaluation and reconstruction software package ImpactIR (VAMP GmbH, Möhrendorf, Germany). Reconstruction time lies below 2 s per 512 512 image on a 700-MHz dual Pentium processor with 512 MB of memory. the fact that the corresponding slices used for interpolation change too abruptly and too often during the interpolation of one planar data set. Therefore, a filtering (or weighting) approach appears to be the most promising choice. These filtering algorithms are already known from standard multislice spiral CT [1]. For the spatial direction ( -direction), 180 MCI simply uses this wellknown -filtering approach. In the temporal direction (cardiac phase ), a -filtering approach is used III. RECONSTRUCTION We will denote the measured attenuation values (projections) by, where stands for the angle within the fan, describes the gantry s rotation angle, and is the slice number. Because for a spiral scan there is a one-to-one correspondence between the projection angle and the -position of the focus, the -position is not stated explicitly but can be derived from The -position of slice simply is The reconstruction position will be denoted by, and because we are dealing with a phase-selective reconstruction, we need to define the cardiac phase at which the reconstruction is performed:. The ECG information will be denoted as, i.e., as the cardiac phase as a function of the rotation angle. We have. Arithmetics using the cardiac phase are meant to be modulo 1. For the interpolated data at position and, assuming -interpolation algorithm, the general interpolation equation can be stated as where the weights are real-valued and where defines the rebinning to access data points from opposite views (180 algorithms). The denominator of the -interpolation equation properly normalizes the procedure. A. -Interpolation 180 MCI The algorithm 180 MCI uses data from successive heart beats and successive gantry rotations to collect a complete data set and to yield the optimal temporal resolution for a given heart rate and rotation time. Due to the complex -sampling pattern of multislice spiral CT and due to the potentially arhythmic heart motion, a true linear interpolation algorithm yields streaking artifacts in the resulting images that arise from with the weight (1a) (1b) chosen as the product of the distance and the phase weight. The parameter denotes the retrospectively selectable reconstruction position, and, the reconstruction phase, can be selected retrospectively as well. The weight functions were chosen to be triangular where denotes the width of the filter in -direction and % denotes the filter width for the cardiac phase. is a triangle function of base width 2 and area 1. The base width of the cardiac weight function is, and we find that the fraction of the cardiac cycle depicted in the image is. The relative temporal resolution as given in the results section will be slightly lower than because it is calculated as the full-width at tenth maximum (FWTM) of the phase sensitivity profile because this represents the contributions of the cardiac phases to the final image more adequately. Fig. 2 shows a schematic plot of 180 MCI. The plot is drawn for a four-slice scanner at and a heart rate of min, assuming s. The four temporal axes correspond to the four measured slices reaching the reconstruction position. Thus, they are shifted with respect to each other by, which is the time needed to increment the table by a distance of. Only those data points falling below both the -filter and the -filter will contribute to the image. Although 180 MCI allows for arbitrary pitch values, it should be taken care that i.e., This restriction follows from the demand that the detector array should not advance by more than slice thicknesses during the length of one heart beat. Otherwise, the request for interpolation at arbitrary and arbitrary would deteriorate the slice sensitivity profile (SSP) or the phase sensitivity profile (PSP) and, thus, reduce the algorithm s -resolution or its temporal resolution significantly.

892 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 9, SEPTEMBER 2000 Fig. 2. Schematic plot of 180 MCI for the central ray for arbitrary z and c. The solid lines depict the measured spirals, whereas the dashed lines depict the rebinned data obtained from opposite views. The numbers m at the top count the simultaneously measured slices m = 1; 111;M. The figure is drawn for M =4;p =3=7 0:43, and f t =3=4. Tick marks at the z-axis are spaced by the table feed d, and tick marks at the four temporal axes are separated by t. The heart symbols map the reconstruction phase c onto the temporal axes. These axes are shifted by a temporal offset corresponding to the time needed to advance the table by the distance S with respect to each other. The width w in R R was chosen as w =25% for this plot. The roman numbers i, ii, iii, and iv correspond to the number of rotations involved in the graph. Concentrating, for example, on the temporal axis ticks labeled with the roman number ii shows the z-positions of the respective slices at time t, i.e., just when the second rotation contributing to this figure has started. Moreover, at the figure s top, the z-positions of all four measured slices are denoted by the arabic numbers 1, 2, 3, and 4 for times t ;t ;t, and t. For all 180 MCI reconstructions shown in this paper, we have used and have chosen the minimal possible width to yield complete, i.e., at least contiguous, -interpolated data. It can be shown that this minimal required width and, thus, the maximal relative temporal resolution strongly depend on the number of heart beats during one gantry rotation [3], [5]. We will give here an alternative derivation of the respective results. A complete data set consists of -adjacent data on either side of the reconstruction plane, with giving the fraction of a full rotation. During one heart cycle, the gantry rotates by the angle. We will now assume, which is valid for all patients and for rotation times below or in the order of 0.75 s. This assumption ensures that the heart will not beat twice during one rotation. It can be the case, however, that the gantry rotates twice or even more often until one cardiac cycle has been finished. To be able to collect new data after one, two, or even more rotations, we must demand, where denotes the length of the newly acquired data inverval and gives the number of rotations to wait until new data are available. The gantry rotates by an angle of while covering a given -position, i.e., while advancing by a distance of. This corresponds to heart beats and to a contiguous data range of length, assuming that during each heart beat, a fraction of data is collected. The product of the number of heart beats and the acquired interval size per beat must at least make a complete data set of size. follows and, consequently,. The optimum situation is given whenever equality occurs. Using, we find that the optimal relative temporal resolution can only be achieved if with (2) From (2), it becomes clear that a tunable rotation time is required to achieve the optimal relative temporal resolution for any constant heart rate. This is graphically depicted in Fig. 3: for all typical heart rates, the required settings for are given. For

KACHELRIEß et al.: ECG-CORRELATED IMAGING OF THE HEART 893 (a) (b) ) and for are given in (b) and (c) for completeness. However, for the scanners available today, the rotation time cannot be chosen freely. Only a few discrete values are available, and thus, the optimal can only be achieved for a few heart rates. Assuming 0.5-s rotation time, and, these optimal heart rates would be 35 min, 45 min, 52.5 min, 67.5 min, 105 min, and 135 min, as can be seen from Fig. 3(a). For all other heart rates, 180 MCI yields a lower relative temporal resolution. Nevertheless, it has been shown that typically lies in the range from 15% to 35%, depending on the patient s heart rate [5]. Thus, 180 MCI will still have significant advantages over standard reconstruction algorithms. It must be mentioned that regardless of the heart rate, 180 MCI always is a phase-selective reconstruction algorithm and all images will correspond to the same cardiac phase throughout the complete volume. B. -Interpolation 180 MCD The algorithm 180 MCD is a partial scan approach to reduce the effective scan time. Contiguous spiral data corresponding to a half scan are taken and used for reconstruction. Assuming that the table feed is low enough to have a given reconstruction position covered by the detector array (length ) longer than the duration of one heart beat, i.e., demanding again (c) Fig. 3. Optimal t for 180 MCI as a function of the heart rate f for three different pitch values. This plot assumes 8 = 0(central ray) and, thus, f = 1=2. The curves yield (a) w = pf = 12:5%, (b) w = pf = 18:75%, and (c) w = pf = 25%. The numbers matching the expression n to the right of the solid curves correspond to the n and to the 6 of (2). The dashed curves correspond to the rotation time needed assuming a partial scan (half-scan) reconstruction (such as 180 MCD, as given in the next section) that also shall yield the same relative temporal resolution of w =12:5%; 18:75%, or 25%, respectively. Obviously, for a given heart rate, 180 MCI always performs better (solid curves are above the dashed line) than does the partial scan approach. The horizontal grid lines are placed at rotation time values of typical scanners (the 0.3-s line corresponds to a hypothetical scanner in the future), and the vertical grid lines depict the intersection of our 0.5-s mode with 180 MCI., the parameter of (2) ranges from 1 to 3. For each value of, there are two curves corresponding to the plus or the minus sign of the equation above. Each heart rate, thus, requires one of six possible rotation times to achieve the optimal [Fig. 3(a)]. Moreover, the optimal settings for as used for our patient scans (i.e., mm, mm, and allows us to center the partial scan data range of around any cardiac reconstruction phase by selecting the appropriate detector lines for reconstruction. In other words, because the temporal coverage of the active detector area and agiven -position exceeds the length of one heart cycle, the temporal reconstruction center can always be chosen to coincide with any desired cardiac phase, whereas the spatial reconstruction center can be freely selected as. Thus, the interpolated raw data and the corresponding image will be centered about and and 180 MCD is phase-selective. The interpolation equation is with (3a) (3b) The parameter is the view angle about which the reconstruction is centered. It must fulfill. The function denotes a rectangle function of width 1, and from Fig. (3b), it can be seen directly that the data are centered about and : The first rectangle function takes care that the necessary 180 data range, which is required for data completeness, will be available and the second rectangle function collects those contributions in that are separated by not more than a distance of from the

894 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 9, SEPTEMBER 2000 Fig. 4. Schematic plot of 180 MCD for the central ray. The axes and the labeling are equivalent to Fig. 2. However, because 180 MCD has no explicit phase weights, the weight function is illustrated as gray rectangles. The dark rectangles represent the heart beat around which the reconstruction is centered; i.e., all contributions to the final image are taken from this heart beat. The interpolated data at z are made of exactly 180 of data (central ray), which stems from the measured slices 3 and 4 (shaded area in the upper part of the graph). desired reconstruction position. An illustration of 180 MCD is given in Fig. 4. Because 180 MCD only uses a half scan of data, its absolute temporal resolution will be, which gives regarding the central ray only. The relative temporal resolution of 180 MCD can, thus, be easily calculated and yields which is much more simple than for 180 MCI. The main drawback, as can be concluded from this equation, is that the relative temporal resolution is getting worse with increasing heart rate. This prediction will be confirmed by the phantom and patient images in the results section. IV. RESULTS A. Patient Studies A very good impression of the behavior of the two standard algorithms 180 MLI and 180 MFI and the two dedicated cardiac algorithms 180 MCD and 180 MCI is given in Fig. 5, which shows various reconstructions of a patient with the low heart rate min. The axial views show optimal image quality for both cardiac algorithms and a surprisingly good image quality for 180 MLI, which only suffers from some motion artifacts around the high-contrast calcifications. The low artifact content for the axial 180 MLI image is due to the short rotation time of 0.5 s, which for this patient corresponds to 46% of the cardiac cycle. Of course, the relative and the absolute temporal resolutions for the cardiac algorithms are much better and no artifacts appear in the axial images. Regarding the corresponding 180 MFI image, we find severely overlapping structures at the edge of the ventricles. The image seems to be blurred compared with the other three images, and some of the calcifications, although depicted without apparent motion artifacts, have lost contrast. As mentioned above, this behavior results from the very low temporal resolution of 180 MFI. The image depicts the average of significantly more than one cardiac cycle, and the averaging results in image blurring and overlapping structures. The MPRs, in contrast, are much more conclusive. Here, 180 MFI seems to perform better than does 180 MLI. Evidently, neither 180 MLI nor 180 MFI are phase-selective and

KACHELRIEß et al.: ECG-CORRELATED IMAGING OF THE HEART 895 Fig. 5. Comparison of the standard algorithms and the dedicated cardiac algorithms for a patient with the relatively low heart rate f = 55 min. The cardiac reconstructions were centered about c =75%. In-plane image quality of 180 MLI is superior to 180 MFI, which shows double contours and significant image blurring. However, 180 MLIs sagittal and coronal MPRs clearly show that the standard algorithms are not phase correlated: the anatomy is depicted discontinuously, and the calcifications appear to be torn apart. This is not the case for 180 MFI because it averages over more than one complete cardiac cycle. Its z-resolution is greatly reduced due to the cardiac motion, and the blurring disturbs the overall image impression. The cardiac algorithms show no motion artifacts but high in-plane and z-resolutions, and their image quality is better compared with the standard z-interpolation approaches in all respects (0/500). cannot depict the heart in the same phase of motion throughout the complete volume. 180 MLI s MPRs, thus, show severe discontinuities. These are not shown by 180 MFI because its blurring does not only affect the in-plane resolution, but also the -resolution, and the respective discontinuities are simply averaged or smeared away. The cardiac algorithms 180 MCD and 180 MCI depict the complete volume nearly artifact-free with high resolution for both the axial images and the multiplanar reformations. In contrast to 180 MCD, which shows a few negligible streak artifacts in the MPRs, the cardio interpolation algorithm 180 MCI depicts the volume without apparent artifacts. Higher heart rates, however, can only be coped with by 180 MCI. This is clearly demonstrated in Fig. 6, which does the same comparison as Fig. 5, but for a patient with a heart rate of 90 min. 180 MLI shows unacceptable discontinuities in the MPRs and motion artifacts in the transversal image, 180 MFI suffers extremely from image blurring, and 180 MCD shows stepping artifacts in the MPRs. The image quality of 180 MCI, in contrast, is very good for this relatively

896 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 9, SEPTEMBER 2000 Fig. 6. Same comparison as in Fig. 5, but for a patient with a higher heart rate of f = 90 min. The main difference here is that 180 MCD shows severe artifacts in the MPR. Obviously, the partial scan approach cannot handle heart rates as high as 90 min as well as in the MPR (100/800). well. Only 180 MCI yields good image quality in-plane high heart rate. Artifacts appear neither in the axial image nor in the MPR displays. B. Physical Cardiac Motion Phantom To confirm our findings in a well-defined environment, we have measured the dedicated cardiac calibration and motion phantom using the same scan parameters as for our patient measurements. Some results can be seen in Fig. 7. Performing a realistic three-dimensional (3-D) left anterior descending coronary artery (LAD) motion yields unacceptable image quality for 180 MLI [Fig. 7(a)]. The object s contrast is not recovered correctly, and the MPR pretends the object (a small cylinder) is disrupted. The algorithms 180 MCD and 180 MCI depict the object much better than does the standard approach. In addition, the respective images suggest advantages of 180 MCI over 180 MCD already at this low heart rate. The results of comparing two different heart rates (low 60 min and high 105 min ) given in Fig. 7(b) confirm what has been observed in patient measurements: 180 MCI achieves good image quality for all heart rates, and 180 MCD only for low heart rates. C. Virtual Cardiac Motion Phantom The virtual cardiac phantom was used to study motion and motion artifacts for in-plane as well as axial motion at various heart rates. Images (axial and MPR) are given in Fig. 8.

KACHELRIEß et al.: ECG-CORRELATED IMAGING OF THE HEART 897 shown in Fig. 8 was performed. The underlying heart was taken into account by thresholding the object function using the threshold, subtracting and integrating. The score, thus, is given by (a) For, we have chosen 130 HU because this is used for the wellknown Agatston score [14]. The true score is defined here by placing the VOI around one of the steady objects (cylinders or spheres), whereas the measured score is obtained by integrating around the corresponding moving object (cylinder moving along or sphere moving along or ). The relative error introduced by the reconstruction algorithm, then, is (b) Fig. 7. The measurements of the physical cardiac phantom using a motion robot equipped with a 5-mm (diameter and height) HA400 (hydroxy apatite, 400 mg/cm ) cylinder that is oriented parallel to the z-axis prove again that the dedicated cardiac algorithms are to be preferred over the standard 180 MLI approach in the case of cardiac motion. (a) The motion performed was a realistic 3-D LAD motion corresponding to a heart rate of 55 min. The cardiac algorithms yield significantly better images in-plane (upper row) and in the MPRs (lower row) compared with 180 MLI. (b) The phantom performs the sinusoidal motion equivalent to the virtual cardiac phantom in x-direction at 60 min (upper row) and 105 min (lower row). Although better than the standard approach, 180 MCD is not able to depict the cylinder correctly for the high heart rate. Only 180 MCI displays the calcification correctly for all cases (0/800). 180 MCDs results are satisfactory only for min (assuming s), and 180 MCI depicts the phantom correctly for a wide range of heart rates. Obviously, there is no significant difference whether the object moves in-plane or along. The images for the standard algorithms were omitted because, as has become clear above, they severely suffer from motion artifacts for all heart rates. Because the moving objects are at rest over 20% of R R, Fig. 8 confirms that 180 MCI is able to do with less than 20%; i.e., %. Obviously, the statement % is valid for all motion phases, although 180 MCI would tend to show slight motion artifacts for phases with motion within the depicted 20%. Moreover, we have performed coronary calcium measurements using our virtual phantom to determine the accuracy of the various algorithms. The coronary calcification score to be used here is a simple volume score. Integration of a volume of interest (VOI) placed around one of the phantom s calcifications the reconstructed volume under consideration is the volume which is graphically depicted in Fig. 9 for the 3-mm sphere moving along and the three algorithms 180 MLI, 180 MCD, and 180 MCI. Again, 180 MCI performs superior to the other algorithms. This applies also to the resonance cases min and min, where 180 MCI and 180 MCD yield the same temporal resolution (see below and Fig. 10). Apparently, the - and -filtering approaches yield less image errors than does the partial scan reconstruction. The scoring errors of 180 MCD and 180 MLI increase with increasing heart rate. This is not the case for 180 MCI. However, only the general bias to the calcium quantification error of the respective algorithms (180 MCI is clearly the best performing algorithm) should be derived from this experiment. The exact error values are likely to depend on the respective motion function and on the scoring algorithm (e.g., an error of precisely 0%, as it is the case for 180 MCI at 105 min, is unlikely to occur for other motion functions). D. Other Results Our cardiac algorithm implementations internally perform a spinoff calculation of the so-called PSP. This profile contains the weighted contributions of the cardiac phase to the reconstructed image (similar to the slice sensitivity profile that contains the weighted contributions of the -positions to the reconstructed image). Although its exact shape is not of importance, its FWTM serves as a conservative measure of the achieved relative temporal resolution. The results for some typical heart rates are given in Fig. 10. The relative temporal resolution of 180 MLI, which is not a cardiac algorithm and, thus, has no knowledge about, can be calculated because its PSP is of triangular shape. It is included in the figure as well. It can be seen that the cardiac algorithm 180 MCI always has a better temporal resolution than do the other algorithms. The only cases in which 180 MCI and 180 MCD are equally good regarding temporal resolution are those cases in which the heart rate and the scanner s rotation time are in resonance, e.g., the 2 : 3 resonance at 80 min. Then, 180 MCI cannot gain new information from one of the succeeding heart cycles. These situations can principally be avoided by selecting a different rotation time if available [3], [5].

898 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 9, SEPTEMBER 2000 Fig. 8. Views of the virtual heart phantom at the heart rates 70 min, 90 min, and 135 min for the two cardiac algorithms 180 MCD and 180 MCI. The simulated motion function is sinusoidal with an amplitude of 65 mm over 80% of R R and constant over 20% of R R. The reconstructions have been centered about the slow motion phase (i.e., about the constant part of the motion function). The coronal view shows the 2-mm calcifications of the virtual heart (see navigation lines). Obviously, 180 MCI s image quality is always superior to the algorithm 180 MCD, and its image noise is apparently lower than for the partial scan approach (0/250). Image noise properties as well as the -resolution using SSPs of the two new cardiac algorithms 180 MCI and 180 MCD have already been investigated in [5]. We will simply state the results for completeness. Analyzing the SSPs of 180 MCI has shown no significant loss in -resolution compared with standard algorithms. The full-width at half maximum (FWHM) of the SSPs lies in the order of to, independent of the pitch value and the patient s heart rate. The typical theoretical value that can be achieved by standard -filtering algorithms over a wide range of pitch values is given by the FWHM of a threefold convolution of a rectangle function of width and thus yields. Comparing this value to 180 MCI shows that the cardio interpolation algorithms does not significantly change the -resolution. Similar results are obtained for 180 MCD, although, in general, its FWHM is with roughly slightly smaller than for 180 MCI.

KACHELRIEß et al.: ECG-CORRELATED IMAGING OF THE HEART 899 V. DISCUSSION Fig. 9. Relative error 1 in calcium scoring achieved by the three algorithms 180 MLI, 180 MCD, and 180 MCI as a function of typical heart rates. Obviously, 180 MCI performs best for all heart rates regarding the errors in calcium scoring. Fig. 10. Relative temporal resolution w achieved by the three algorithms 180 MLI, 180 MCD, and 180 MCI as a function of typical heart rates. Obviously, 180 MCI performs best for all heart rates, regarding the temporal resolution. This plot assumes d = S; M =4, and t =0:5s. Image noise of 180 MCD is increased by approximately 22% compared with 180 MLI because only half a rotation (partial scan) contributes to each image. The noise properties of 180 MCI are more complex. If a resonance case occurs, i.e., if the heart rate and the scanner s rotation time are in resonance, 180 MCI cannot gain new information from successive heart beats and gantry rotations, as has been mentioned above. Thus, 180 MCI uses the redundant data for averaging because it is a filtering approach. Image noise will be very low in those cases. Especially for, which is for example min at s, noise reductions of down to 42% of the original 180 MLI image noise values have been observed. However, these resonance cases are not what 180 MCI has been designed for. It is rather desirable to have a high temporal resolution and to avoid resonances by properly selecting the rotation time (cf. Fig. 3). For those optimal situations, image noise is very close to 180 MLI. Typical values are 90% of the original 180 MLI image noise; i.e., noise is reduced by 10% for those cases. The limitations of cardiac imaging using standard CT scanners have been greatly overcome by introducing the dedicated reconstruction algorithms 180 MCI and 180 MCD. We have shown that these new algorithms are clearly superior to the standard -interpolation algorithms. Effective scan time can be significantly reduced, and the motion artifacts are almost completely eliminated using the phase-correlated reconstruction algorithms. Phase selectivity and high temporal resolution have been demonstrated clearly. However, 180 MCD is useful only for relatively low heart rates, and even there, 180 MCI produces better images than does 180 MCD. For higher heart rates, 180 MCI is clearly superior. This is due to 180 MCI s high temporal resolution. Relative temporal resolution of down to 12.5%, corresponding to an absolute effective scan time of 56 ms, can be achieved, assuming, and s. It has been shown that the scan parameters must be restricted to to allow us to reconstruct at any retrospectively selectable reconstruction position and heart phase. The advantage of the retrospective gating methods is that they can cope with patient cases, such as severe arhythmic heart motion and extremely varying heart rate, during one scan. An impressive example is shown in Fig. 11. The patient s heart rate varies between 42 min and 97 min during the 30-s scan. Nevertheless the images show that 180 MCI is able to resolve the aortic valve throughout the complete cardiac cycle with acceptable image quality [Fig. 11(c)]. It must be noted that these images of the aortic valve are taken from the oblique slice depicted in Fig. 11(b), and consequently, almost the complete volume and the complete range of heart rates from 42 min to 97 min contribute to each oblique MPR! Considering these facts clearly shows the great flexibility and potential of 180 MCI for cardiac imaging. True 3-D displays such as the shaded surface display (SSD) of the heart given in Fig. 12 demonstrate again the image quality of 180 MCI. Although the segmentation of complete volumes at different heart phases still requires high effort, it results in very descriptive images. Of course, animations of such 4-D data sets can be performed as well; examples are provided at http://www.imp.uni-erlangen.de/e/research/cardio/. The advantages of our cardio interpolation approaches 180 CI for single-slice and 180 MCI for multislice spiral CT over the partial scan approaches 180 CD and 180 MCD are also reflected by current investigations of other groups and manufacturers: This year they started to switch from half scan or partial scan to multisector or pulse-rate adaptive reconstruction algorithms [15] [16]. These algorithms, similar to 180 MCI, use data of adjacent heart cycles to improve the temporal resolution. However, due to the absence of a true phase weighting approach, they seem to be less elegant and tend to show new artifacts [17]. The advantages of the new cardiac imaging algorithms can further be improved by a rawdata-based motion detection (kymogram) to allow for a phase-selective reconstruction of the heart without acquiring the ECG [18]. It has been proven that the dedicated cardiac algorithms are clearly superior to the standard -interpolation approaches.

900 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 9, SEPTEMBER 2000 (a) (b) (c) Fig. 11. Patient with strongly varying heart rate. For each image reconstructed (z = 1 mm, 2 mm, 111; 99 mm), the local mean heart rate, i.e., the mean heart rate contributing to each reconstructed image, is given in (a). The patient s global mean heart rate during the data acquisition was 79 min. The 180 MCI reconstructions (b) and (c) show that the cardiointerpolation algorithm can handle this situation well. For example, the aortic valve can be depicted in its different functional states with sufficient temporal and spatial resolution (100/700). Fig. 12. SSD of the complete heart at three different reconstruction phases c. The fast-moving right coronary artery is only depicted well in the second image, which has been centered at diastole. An animated video of the same patient is available at http://www.imp.uni-erlangen.de/e/research/cardio/. Phase selectivity and a high temporal resolution have become available. Especially, 180 MCI improves cardiac imaging by subsecond multislice CT drastically. The potential for accurate calcium scoring has been demonstrated. Cardiac CT imaging could be improved further by freely selectable and by higher rotation speeds.

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