A model for temporal resolution of multidetector computed tomography of coronary arteries in relation to rotation time, heart rate and reconstruction algorithm

A model is presented that describes the image quality of coronary arteries with multidetector computer tomography. The results are discussed in the context of rotation time of the scanner, heart rate, and number of sectors used in the acquisition
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  Eur RadiolDOI 10.1007/s00330-006-0228-z  EXPERIMENTAL M. J. W. GreuterT. FlohrP. M. A. van OoijenM. Oudkerk  Received: 20 July 2005Revised: 25 November 2005 # Springer-Verlag 2006  A model for temporal resolutionof multidetector computed tomography of coronary arteries in relation to rotation time, heart rate and reconstruction algorithm Abstract  A model is presented that describes the image quality of coro-nary arteries with multidetector com- puter tomography. The results arediscussed in the context of rotationtime of the scanner, heart rate, andnumber of sectors used in the acqui-sition process. The blurring of thecoronary arteries was calculated for  heart rates between 50 and 100 bpmfor rotation times of 420, 370, and330 ms, and one-, two-, three-, andfour-sector acquisition modes and ir-regular coronary artery movement isincluded. The model predicts optimaltiming within the RR cycle of 45±3%(RCA), 44±4% and 74±6% (LCX),and 35±4% and 76±5% (LAD). Theoptimal timing shows a negative linear  dependency on heart rate and in-creases with the number of sectorsused. The RCA blurring decreasesfrom 0.98 cm for 420 ms, one-sector  mode to 0.27 cm for 330 ms, four-sector mode. The corresponding val-ues are 0.81 cm and 0.29 cm for LCXand 0.42 cm and 0.17 cm for LAD.The number of sectors used in amultisector reconstruction and thetiming within the cardiac cycle should be adjusted to the specific coronaryartery that has to be imaged. Irregular  coronary artery movement of 1.5 mm       justifies the statement that no morethan two sectors should be used inmultisector acquisition processes inorder to improve temporal resolutionin cardiac MDCT. Keywords  Computed tomographytechnology .Computed tomographyimage quality .Coronary vessels Introduction In recent years multidetector computed tomography(MDCT) has firmly established itself as a noninvasivediagnostic technique for imaging the heart. With anisotropic resolution better than 0.4 mm and a rotationtime of 330 ms [1] the imaging of the heart and especiallythe coronary arteries is on its way to become a standarddiagnostic tool for the diagnosis of coronary artery disease[2, 3] and the followup of invasive procedures like coronary artery bypass graft (CABG) surgery [4  –  6].However, imaging of the heart, and especially of thecoronary arteries by MDCT, is often hampered by motionartifacts [7  –  11]. Because the heart is in constant motionand the temporal resolution of MDCT is limited, thecoronary arteries move during data acquisition, andconsequently a more or less blurred image of the coronaryarteries is obtained. Because the motion-free imaging of          coronary arteries is of the utmost importance in clinicaldiagnostics, manufacturers of MDCT systems haveincreased temporal resolution of their systems dramati-cally over the past few years. The most important contributor to the temporal resolution is the rotation timeof the scanner. Modern MDCT systems nowadays have aminimal rotation time of 330 ms. Because for the fullreconstruction of a tomographic image data from half arotation have to be acquired in a centered region of          interest, the temporal resolution of these systems is165 ms. It has been shown, however, that in order toimage the coronary arteries without motion artifacts, thetemporal resolution of the scanner has to be as low as50 ms [12]. In order to approach this goal as closely as M. J. W. Greuter ( * ) . P. M. A. van Ooijen .M. Oudkerk University of Groningen,Department of Radiology,University Medical Center Groningen,P.O. Box 30.001,9700 RB Groningen, The Netherlandse-mail: m.j.w.greuter@rad.umcg.nlTel.: +31-50-3614712Fax: +31-50-3611798T. Flohr  CT Division,Siemens Medical Solutions,Forchheim, Germany(2007) 17: 784  –  812Accepted: 22 February 2006Published online: 27 April 2006   possible, dedicated cardiac acquisition protocols have been developed [13, 14] that have shown improvements in clinical image quality [15  –  17]. These so-called multi-sector reconstruction algorithms provide an increase in thetemporal resolution depending on the rotation time of thescanner, the heart rate of the patient, and the number of          sectors used in the acquisition process. In principle, thetemporal resolution of the scanner can be calculated fromthese three parameters, and the correlation with imagequality has recently been shown in phantom studies [18,19]. Recently, Begemann et al. reported the influence of          heart rate, pitch, and rotation time on spatial and temporalresolution [27]using one toabout four sectors in the imagereconstruction. The increase in the number of sectors usedin the multisector reconstruction process imposes, how-ever, a decrease in pitch, which in a clinical setting canlead to a considerable increase in patient dose, as has beenshown by Wicky et al. [20]. In addition, a decrease in pitchleads to an increase in scantime, which makes themultisector reconstruction algorithm more sensitive tothe clinical stability of the patient.Maoetal.[24]reportedthelengthoftheTPintervalin862consecutive asymptomatic patients, where the TP intervalwas defined as the time from the end of the T-wave to the beginning of the P-wave in the electrocardiogram. Theyconcluded that for optimal cardiac imaging, triggeringshould take place in late systole, avoiding the RT-intervalvariability that occurs in diastole.The aim of this study is to provide a simple model for  the temporal resolution of an MDCT scanner and the blurring of the three main coronary arteries in terms of          rotation time of the scanner, the heart rate of the patient,and the number of sectors used in the acquisition process.Withourmodelwecandeterminethe optimaltimingoftheacquisition window within the cardiac cycle as a functionof rotation time, heart rate, and number of sectors. Inaddition,themodeldescribes theoptimal rotation time andnumber of sectors for minimal blurring of the coronaryarteries as a function of heart rate. Finally, the model predicts the influence of an irregular coronary arterymovement on the efficiency of the multisector reconstruc-tion process.In the model description below we first introduce amathematical description of the multisector acquisition process in MDCT. Then, the movement of the coronaryarteries based on patient data and the timing in multisector  acquisition mode is described. Finally, the blurring of thecoronaryarteriesduringtheacquisitionprocessiscalculated. Materials and methods Model descriptionThe acquisition time, Δ T  , of an MDCTsystem is a functionof the heart rate,  HR , of the patient, the rotation time,  RT  , of          the scanner, and the number of sectors,  N  , used in theacquisition process: Δ T   ¼  f HR ;  RT  ;  N  ð Þ :  (1) This function will be evaluated below on the basis of first MDCT principles.The displacement of a scanner during one rotation isgiven by the table feed  d  . If the slice collimation of onedetector is given by  S  , then the helical pitch of the system,  HP  , is given by the ratio of the table feed  d   and the slicecollimation  S  :  HP   ¼  d S   :  (2) The pitch  P   now is given, in accordance with the commonterminology [21], by the ratio of the helical pitch factor    HP  and the number of detectors  D :  P   ¼  HP  D  :  (3)   Now we can define a scan window,  SW  ,which is defined bythe ratio of the rotation time,  RT  , and the pitch factor,  P  : SW   ¼  RT  P   :  (4) The scan window,  SW  , gives a measure for the timewindow in which a certain  z  -position is covered by thedetector, where the  z  -axis coincides with the rotation axisof the scanner by default.If the heart rate of the patient is given by  HR  in beats per  minute (bpm), then the number of heartbeats in scanwindow  BS   is given by the ratio of scan window  SW   and beat time  BT= 60  /HR :  BS   ¼  SW  BT   ¼  D    RT  HP  HR 60  :  (5)   Now consider the case where a multisector acquisitionmode is performed on a patient with a beat time given by  BT  seconds on a scanner with a rotation time of            RT  seconds. 785  The angle  ϕ 1  the detector will rotate during one heartbeat of the patient is given by: ϕ 1  ¼  360 o  BT  RT   :  (6) Because in a multisector reconstruction method the secondheartbeat is also used for the acquisition of the same slice,the angle that the detector will rotate until the secondheartbeat   ϕ 2  is given by: ϕ 2  ¼  2 ϕ 1 :  (7) In general for an  N   sector mode, the angle  ϕ i  that thedetector will rotate until the  N  th heartbeat is given by: ϕ i  ¼  2 ϕ i  1  2    i    N  :  (8)   Now the angles  ϕ i  can be reduced to 180° angles  ϕ 0 i  by: ϕ 0 i  ¼  ϕ i  mod180  1    i    N :  (9) For image reconstruction, 180° plus fan angle (50 to 60°depending on system geometry) is needed in any point of          the scan field of view of usually 50 cm diameter. Typically,modern CT scanners perform a fan beam to parallel beamrebinning. In parallel geometry, 180° of scan data isneeded, but 180° plus fan angle of fan beam data is neededto generate 180° of parallel data for any image point in thescan field of view [15]. In the center of rotation, however,only 180° of fan beam data is needed to generate 180° of           parallel data. Since the heart is usually sufficientlycentered, it is fair to say that for cardiac CT 180° of datais sufficient.This means that the temporal resolution  Δ T  1  in a one-sector mode is given by the effective acquisition time of theone sector    T  1 : Δ T  1  ¼  T  1  ¼  180 0 360 0  RT   ¼  12  RT  :  (10) In a two-sector mode, the angle of acquisition depends onthe relative angular position of the two sectors  ϕ 0 1 respectively  ϕ 0 2  . If we define the angles the detectorshave to acquire for these two sectors by  Δ ϕ 1  and  Δ ϕ 2 ,respectively, we have: Δϕ 1  ¼  ϕ 0 2   ϕ 0 1  (11) and Δϕ 2  ¼  180 0  Δϕ 1 :  (12)   Now the temporal resolution of the two-sector mode Δ T  2  isgiven by the maximum of the acquisition times of bothsectors: Δ T  2  ¼  max  T  1 ; T  2 ð Þ ¼  max  Δϕ 1 ; Δϕ 2 ð Þ 360 0  RT   (13) We can extend our model to a general  N  -sector mode. Inthis case, the angular position of the detector for the first sector is still given by Eq. (6) and the reduced 180° degreesangular position by Eq. (9). The angular positions of thedetector for the remaining  N  -1 sectors are given by Eq. (8)and the reduced 180° degrees angular positions again byEq. (9). The acquisition angles of the  N   sectors are given byan extension of Eqs. (11) and (12): Δϕ i  ¼  ϕ 0 i þ 1   ϕ 0 i  1    i    N     1 Δϕ  N   ¼  180 0  X  N   1 i ¼ 1 Δϕ i (14)   Now the temporal resolution for the  N  -sector mode Δ T   N   isgiven by a generalization of Eq. (13) for the  N   acquisitionangles given in Eq. (14): Δ T   N   ¼  max  T  1 ; ::::; T   N  ð Þ¼  max  Δϕ 1 ; ::::; Δϕ  N  ð Þ 360 0  RT  (15) Equation (15) is the generalized equation for the temporalresolution of an MDCT system as a function of heart rate,rotation time, and number of sectors used in the acquisition process.The velocity of the three main coronary arteries, the left anterior descending (LAD), the right coronary artery(RCA), and the left circumflex (LCX), varies considerablyduring the cardiac cycle, as has been shown in severalstudies [12, 22, 23]. In our model, the velocities of the coronary arteries are calculated using the data of          Achenbach et al. [22] from 25 patients with a heart rateranging from 51 to 86 bpm and a mean heart rate of 71 bpm(Fig. 1), where we assume that the velocity distribution inthe RR cycle is linear dependent on heart rate in the rangewe consider from 50 to 100 bpm. Achenbach has shownthat the mean velocity of the RCA, 70±23 mm/s, issignificantly faster than that of the LAD, 22±4 mm/s, andthe LCX, 48±15 mm/s. The variation in the coronaryvelocity among the different patients, however, is relativelarge. The maximum and average deviation in the RCAvelocity are, respectively, 87% and 52%. The correspond-ing values for the LCX are, respectively, 86% and 61%,and for the LAD 67% and 49%.In the model we use a so-called  N  -segment fixed start reconstruction technique [15] with retrospective gating. 786  The starting position of the reconstruction windows in eachcardiac cycle is set at the same relative delay in percentageof the RR interval, while the ending position is floating inorder to dynamically adapt to changing heart rates. Nowconsider the case where we use a one-sector mode for  imaging of a coronary artery. The acquisition will start at  t  11 , a user-defined delay time  T  d   after    t  = t  0 . The acquisitionwill end at time  t  12  ¼  t  11  þ  T  1  . The timing of this one-sector acquisition mode is shown in Fig. 2 (top).  Now consider a two-sector acquisition mode. Again thefirst sector will be scanned from  t  11  to  t  12  ¼  t  11  þ  T  1 . Inorder to have a perfect match of the next sector to the previous one, the second sector has to acquire data from t  21  ¼  BT   þ  T  d   to  t  22  ¼  t  21  þ  T  2  . The temporal resolutionof the two-sector mode  Δ T  2  is given by Eq. (13) and isequal to  Δ T  2 =max( T  1 , T  2 ). The timing of the two-sector  mode is shown in Fig. 2 (middle). This argumentation caneasily be extended to an  N  -sector mode. The three-sector  mode timing is shown as an illustration in Fig. 2 (bottom).During a one-sector mode a coronary artery willexperience a displacement   Δ  x 1  in the acquisition interval T  1  from  t  11  to  t  12  given by: Δ  x 1   Z  t  12 t  11 v t  ð Þ dt    X t  12 t  11 v t  i ð Þ Δ t  i ;  (16) where the velocities  v  ( t  i ) at discrete time intervals  t  i  aregiven by the data from Achenbach in Fig. 1 [22] and the difference between the time intervals is given by  Δ t  i .Equation (16) is a measure for the blurring of the coronaryartery in the reconstructed image due to the displacement of          the artery during data acquisition.If we use an  N  -sector mode, the blurring of the coronaryartery in the reconstructed image will be given by a sum of          the  N   acquisition intervals and the velocity distribution of          the coronary artery in these  N   intervals: Δ  x    max  Δ  x 1 ; :::; Δ  x  N  ð Þ þ  N     1 ð Þ  x 0 ;  (17) where x 0  is an average random displacement of thecoronary artery between the acquisition intervals due toirregular movements of the heart. Because in an  N  -sector  mode the reconstruction of the acquired data set issubdivided into smaller parts in concurrent heart cycles,the coronary artery has to move along exactly the sametrajectory in each cardiac cycle in order to avoid additionalmotion artifacts. If the average random displacement of thecoronary artery between concurrent cardiac cycles is  x 0 , theadditional displacement of the coronary artery is given bythe last term in Eq. (17).For a multisegment reconstruction (  N  >1) Flohr et al. [14]have shown that the pitch  p  is limited by the patient  ’ s heart cycle time  BT  :  p   ð  D    1  N   þ  2  N  Þ  RT  BT   :  (18) This relation states that the number of sectors  N   ismaximized by the number of heartbeats in scan window  BS   as given by Eq. (5) and the number of detectors  D :  N     BS D  þ  1 ð Þ :  (19) For a detailed discussion we refer the reader to [14].MethodsTo determine the optimal timing within the cardiac cyclefor the RCA, LCX, and LAD as a function of rotation time,heart rate, and number of sectors, we set the rotation time at 330, 370, and 420 ms. The heart rate was varied between50 and 100 bpm with an increment of 10 bpm, the number  of sectors in the reconstruction process was varied between1 and 4, and the timing of the acquisition window withinthe cardiac cycle was varied between 0 and 100% with anincrement of 5%. The blurring of the RCA, LCX, and LADwas calculated from Eq. (17). The optimal timing withinthe cardiac cycle, which is the minimum in the blurringcurves, was determined by using a second-order poly-nomial fit.The blurring of the RCA, LCX, and LAD as a functionof rotation time, heart rate, and number of sectors wascalculated by using the above-determined optimal timingfor each coronary artery. Again the rotation time was set at 330, 370, and 420 ms, the heart rate was varied between 50and 100 bpm with an increment of 5 bpm, and the number  of sectors used in the reconstruction process was varied Fig. 1  Velocity of in-plane motion in millimeters per second (mm/s)during cardiac cycle for right coronary artery (RCA) ( red  ), left anterior descending artery (LAD) ( blue ), and left circumflex artery(LCX) (  green ), after Achenbach et al. [22]787   between one and four. The blurring of the RCA, LCX, andLAD was calculated from Eq. (17).Finally, the influence on image quality of an irregular  artery movement of 1.5 mm between each concurrent sector was simulated by calculation of the blurring of theRCA, LCX, and LAD as a function of rotation time, heart rate, and number of sectors. Results Consider the situation where the heart rate is given by  HR =80 bpm and the rotation time of the scanner is given by  RT  =400 ms. Then the angular position of detectors 1 and 2can be calculated from Eqs. (6) and (7), respectively, which yields  ϕ 0 1  ¼  675  and  ϕ 0 2  ¼  1350  . The 180°-reduced Fig. 2  Timing of multisector acquisition mode during one-sector  ( top ), two-sector ( middle ), and three-sector acquisition ( bottom ).Patient ECG and beat time are shown with time  BT   during RR interval. A user-defined delay time  T  d   is shown before acquisitionwill start. Length of acquisition interval is given by start and endtimes of acquisition intervals  t  11  and  t  12,  respectively, with duration T  1 . Data are acquired during  gray area  where indices in  gray areas indicate (from  top  to  bottom ) first sector (1), second sector (2), andthird sector (3) of one-, two-, and three-sector modes, respectively.In two-sector acquisition mode ( middle ), the first sector is acquiredafter time delay  T  d  , starts at   t  11 , and ends at   t  12  with duration  T  1 .During next RR interval the second sector is scanned after timedelay  T  d  , starts at   t  21 , and ends at   t  22  with duration  T  2 . In three-sector  acquisition mode ( bottom ), first sector is acquired after time delay T  d  , starts at   t  11 , and ends at   t  12  with duration  T  1 . During next RR interval second sector is scanned after time delay  T  d  , starts at   t  21 , andends at   t  22  with duration  T  2 . Finally, third sector is scanned duringnext RR interval after time delay  T  d  , starts at   t  31 , and ends at   t  32  withduration  T  3 Fig. 3  Multisector acquisitionmode in parallel geometry using  N   equal to two, three, or four  sectors ( left   to  right  ).  Red  : first sector;  green : second sector; blue : third sector;  yellow : fourthsector. Acquisition angles of          sectors are as indicated for heart rate  HR =80 bpm and rotationtime  RT  =400 ms788
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