Introduction
Computed tomography (CT) myocardial perfusion (MP) imaging is a technique used to quantitatively measure myocardial blood flow (perfusion) through tracer kinetic modeling of the timeenhancement curves acquired from dynamic contrastenhanced (DCE) CT scanning of the heart. As this technique requires repeated scanning of the heart following a short bolus injection of contrast solution, the associated radiation dose is higher than that required for a standard chest CT scan. A straightforward strategy to minimize radiation exposure is to lower the tube current setting (measured in milliampere or mA) for dynamic scanning, and that to correct for excessive projection noise is to use postprocessing techniques such as highly constrained backprojection local reconstruction (HYPRLR) (1–3), multiband filtering (4), sinogram smoothing (5), or statisticsbased iterative reconstruction (6, 7). However, there are 2 main challenges associated with the ultralowmilliampere approach. First, photon starvation could lead to inaccurate sampling of the arterial and myocardial timeenhancement curves and sequentially the measurement of MP. Second, the CT detector electronic noise becomes dominant at the extremely low milliampere level, which is difficult to model and correct for with Poisson statistics alone.
Sparseview dynamic acquisition, where only a small number of xray projections are acquired in each gantry rotation, is an alternative solution to achieve ultralowdose CT MP imaging. This approach is not restricted by the electronic noise barrier and hence could achieve more dose reduction than the lowmilliampere approach. Furthermore, the feasibility of the sparseview acquisition with a clinical CT scanner capable of rapid xray pulsing has been demonstrated (8). However, sparseview acquisition can induce aliasing streak artifacts in the reconstructed images (9, 10), which could have a significant impact on the measurements of timeenhancement curves and MP.
In this paper, we investigated whether reconstruction of streakfree DCE heart images from undersampled projections by using the standard filtered backprojection (FBP) algorithm is feasible if the missing projections are estimated from neighboring ones. The performance of this view interpolation method was evaluated in CT MP studies of pigs, in which a subset of measured projections was used to generate DCE heart images and MP maps with and without the view interpolation applied, and the image quality and MP measurement against the reference fullview technique were compared.
Methods and Materials
Animal Model
DCECT imaging was performed on 5 farm pigs that weighed 40–50 kg. The animal studies were approved by the institutional animal research ethics review board. Two pigs had acute myocardial infarction induced in the apical wall of the left ventricular myocardium from a transient occlusion of the distal left anterior descending (LAD) artery with a balloon catheter for 1 h followed by reperfusion. The other 3 pigs were normal and without infarction. These pigs collectively provided a wide spectrum of myocardial tissue, from normal to abnormal (ischemic or infarcted), for the validation of the cubicsplineview interpolation method for the sparseview image reconstruction with FBP.
Projection Data Acquisition
In each CT MP study, the pig was intubated and mechanically ventilated, and they were placed in either a supine or lateral position on the CT scanner table. Before each DCECT acquisition, iodinated contrast solution (Iohexol 300 mgI/mL) was injected into a peripheral vein at 3 mL/s and at a dosage of 0.7 mL/kg body weight, followed by saline flush at the same injection rate. The ventilator was turned off to minimize breathing motion during the short acquisition (∼30 s). Using a 64row CT750 HD scanner (GE Healthcare, Waukesha, WI) operating in a prospective electrocardiogramgated acquisition mode, a 4cm section of the heart covering the largest crosssection of the left ventricle in the axial tomographic plane was scanned at 3–4 s after contrast injection over 20–25 heart beats at middiastole. For each full (360°) gantry rotation at 140kV tube voltage, 80mA tube current, 8 × 5mm collimation width, and 0.35s gantry rotation period, the fullview projection set consisted of 984 projections. From each fullview projection set, 1 out of every 4 consecutive projections was selected to generate the sparseview set of 246 projections distributed evenly over 360°.
Image Reconstruction
For each pig, the following 3 sets of DCE heart images were reconstructed from the 3 projection sets with FBP: (a) fullview (984 views), (b) sparseview (246 views), and (c) synthesized fullview (984 views). The synthesized fullview projection set was generated by applying a cubicspline interpolation of the sparseview projection set in (b).
Different algorithms are available to generate missing projections from a discrete set of sampled projections. Generally speaking, with n measured data points, a single (n − 1)^{th} order polynomial can be used for the interpolation. Although polynomial interpolation is a common choice of interpolants, the associated error of interpolation can be large when a highorder polynomial function is used for data fitting. Such an interpolation error can be minimized by using spline interpolation which applies loworder polynomials to subsets of data points (11). Let us denote f(x) as a function between the sampled data points, x_{i − 1} and x_{i,} with i = [1, …, n]. A spline S(x) is a piecewise (composite) function formed by n loworder polynomials P(x) each fitting f(x).
Compared with a single highorder polynomial function, spline interpolation should provide a more accurate approximation of f(x), particularly if there exists local abrupt changes (such as the edges between high and lowcontrast regions). A cubic spline is a spline constructed of piecewise thirdorder polynomials (12, 13). Let us consider 3 consecutive data points, namely, x_{i−1}, x_{i}, x_{i+1}. Mathematically, a thirdorder polynomial P(x) on the interval between data points x_{i − 1} and x_{i} can be expressed as follows:
where
a_{i},
b_{i},
c_{i}, and
d_{i} are coefficients, and 1 ≤
i <
n. Similarly, the thirdorder polynomial between data points
x_{i} and
x_{i+1} has the following form:
The polynomials in
equations (2) and
(3) at their connecting data point (
x_{i}) should be identical so that
S(
x) is continuous:
In addition, the derivatives of the polynomials should be identical at
x_{i} for
S(x) to be smooth. For instance:
Solving the above equations yield
n − 1 equations with
n + 1 unknowns. The assumption of boundary conditions can be made to obtain 2 additional equations that are required to solve for all the unknowns. Conventionally, we can assume the first and second derivatives at the end points
x_{0} and
x_{n}, respectively, are zero:
The cubicspline interpolation is based on the least squares method with the cubic convolution interpolation function (
12,
13). Taking
equations (1) to
equations (6) into account, the cubicspline interpolation function
I(x) can be expressed as follows (
14):
where
x_{i} are the interpolation nodes,
S is the spline interpolation kernel as defined above,
h is the sampling interval, and
c_{i} is selected so that the interpolation function is continuous. Cubicspline interpolation of the measured projections was implemented using Matlab.
Image Analysis
Comparison of MP measurement.
The 3 sets of DCE heart images of each pig were analyzed with the CT Perfusion software (GE Healthcare, Waukesha, Wisconsin) to generate MP maps with a modelbased deconvolution algorithm (15). The mean MP value in the lateral, apical, and septal walls of the left ventricular myocardium in the axial view over 8 consecutive 5mm slices were compared between the 3 image reconstruction schemes. In total, 120 ischemic and nonischemic myocardial segments from 5 pigs were available for comparison. Bland–Altman graphical analysis was used to determine the mean bias of the sparseview and synthesized fullview MP measurements with respect to that of the reference fullview MP measurements. The limits of agreement were presented as 95% confidence intervals.
Comparison of Image Difference.
We used an image difference metric described by Busono and Hussein (16) to determine which between the sparseview and the synthesized fullview FBP reconstruction produced DCE heart images best matched with images from the fullview FBP reconstruction. The image difference at time point t, δ_{Dif}^{t}, is defined as follows:
where
I_{Rec}^{t} is the image at time
t reconstructed with FBP from either the 246view or synthesized 984view projection set;
I_{FV}^{t} is the reference fullview FBP image at time
t; and ‖⋅‖ denotes the Euclidean norm.
Results
Figure 1A shows the sinogram of a fullview projection set acquired at one slice location. This fullview sinogram was then subsampled to generate a sparseview set of 246 projections evenly distributed over 360° as shown in Figure 1B. The dark vertical lines in Figure 1B are projections in the fullview set that were left out in the sparseview set. The sinogram of the corresponding synthesized fullview projection set is shown in Figure 1C for comparison. The 2 sinograms in Figure 1, A and C were qualitatively similar to each other. For a more quantitative comparison, Figure 1D shows the projection profile of the fullview sinogram (solid black line) superimposed over the projection profile of the synthesized (interpolated) fullview sinogram (dashed blue line) at the central detector for one slice location. The 2 projection profiles were comparable to each other, with the profile from the synthesized fullview sinogram slightly smoother than that from the measured fullview sinogram. For reference, the red stars in Figure 1D denote the corresponding projection profile of the sparseview sinogram.
Figure 1.
Sinograms of a pig computed tomography (CT) myocardial perfusion (MP) study acquired with the full 984view (A), sparse 246view (B), and synthesized full 984view protocols (C). The y and xaxis represent the detector and projection numbers, respectively. Projection profile of the fullview sinogram is compared with that of the synthesized fullview sinogram at the central detector (D). The red star marks the evenly subsampled 246 views from the fullview projection set.
Figure 2 shows the DCE heart images reconstructed from the fullview (Figure 2, A and B), sparseview (Figure 2, C and D) and synthesized fullview (Figure 2, E and F) projection sets. Image reconstruction with the sparseview projection set resulted in streak artifacts. Figure 2, G and H show the difference image between the fullview (Figure 2A) and sparseview (Figure 2C) protocols and that between the fullview (Figure 2A) and synthesized fullview (Figure 2E) protocols, respectively. The mean ± standard deviation of CT number in 3 different regions in Figure 2G (lateral wall and apical wall of the left ventricular myocardium and a peripheral soft tissue region) was 8.74 ± 12.71, 10.69 ± 13.84, and 10.14 ± 15.20 Hounsfield unit (HU), which was larger than that of CT number in the 3 different regions in Figure 2H (5.28 ± 8.34, 5.88 ± 8.82, and 7.06 ± 9.32 HU), suggesting that the cubicspline interpolation method was able to reduce the HU errors in the reconstructed images arising from aliasing streak artifacts. As shown in Figure 2I, the image difference metric [equation (8)] between the synthesized fullview and fullview DCE images was consistently <4% at all time points, in comparison to 7.5% between the sparseview and the fullview DCE images.
Figure 2.
Contrastenhanced CT images from a pig heart reconstructed with filtered backprojecton (FBP) from fullview(A, B), sparseview (C, D), and synthesized fullview projections (E, F). These images corresponded to the time when both heart chambers were filled with an iodinated contrast solution. The window width/level was set at 400/40 HU. (G) and (H) depict the difference images between (A) and (C) and between (A) and (E), respectively. Image difference metric for synthesized fullview images (black solid line) is compared with that for sparseview images (dashed blue line) over the whole time course of a dynamic CT MP study (I).
Figure 3 shows the MP maps of a pig with an infarct in the apical myocardium (yellow arrow), derived from the 3 sets of DCE images shown in Figure 2. The MP map generated from the sparseview images (Figure 3B) was clearly noisier than that generated from the fullview images (Figure 3A). After cubicspline view interpolation was applied, the MP map generated from the synthesized fullview images (Figure 3C) was comparable with that generated from the fullview images (Figure 3A).
Figure 3.
CT MP maps derived from dynamic contrastenhanced (DCE) images reconstructed from fullview (A), sparseview (B), and synthesized fullview (C) projections with FBP as shown in Figure 2. The CT MP maps are displayed in a color scale range from 0 (blue) to 400 (red) mL/min/100 g. The yellow arrow in (A) points to the infarcted region within the apical wall of the myocardium.
The Bland–Altman plot shown in Figure 4 showed that the mean bias of absolute MP measurement associated with the synthesized fullview and sparseview protocols was 3.6 (95% CI −8.6 to 15.7) mL/min/100 g and 9.7 (95% CI −12.8 to 32.3) mL/min/100 g, respectively, with respect to the reference fullview protocol. Furthermore, the cubicspline interpolation method led to a 63% decrease in the mean bias of absolute MP measurement when the sparseview DCE heart images were used for perfusion analysis.
Figure 4.
(A) Sparseview and (B) synthesized fullview CT MP measurements in comparison to the reference fullview MP measurements using the Bland–Altman graphical analysis. The solid gray line in each graph represents the mean bias in MP measurement relative to the reference protocol. The dotted gray lines denotes the 95% confidence intervals (CIs) of the estimated mean bias. The numbers in red color in each graph represent the mean bias and corresponding CI values of MP.
Discussion
Quantitative CT MP imaging is useful for the functional assessment of coronary artery disease (17) but high radiation dose is a major hurdle for its implementation in routine clinical practice. This study aimed to demonstrate the feasibility of reducing the radiation dose of a quantitative CT MP study with the sparseview dynamic acquisition and image reconstruction. CT image reconstruction with sparsely sampled projections has been of great interest lately. Although compressed sensing is the primary algorithmic choice for sparseview CT image reconstruction with promising results reported in a number of preclinical studies (18, 19), it can lead to loss of image details in aspects of contrast and spatial resolution. Although more advanced compressed sensing–based algorithms have been recently developed to improve these aspects (20–22), they remain computationally demanding, which may limit their clinical applications. In contrast, FBPbased image reconstruction methods are faster, making the sparseview CT MP imaging more feasible in realworld clinical settings.
To the best of our knowledge, the application of cubicspline interpolation for sparseview CT MP measurement has not been previously investigated. The main challenge of this approach is the aliasing streak artifacts in reconstructed DCE images that can significantly affect the accuracy of MP measurement. A cubicspline interpolation method was used in our studies conducted in pigs to estimate the missing projections before FBP image reconstruction to minimize the aliasing streak artifacts in DCE images. Our findings showed that the number of projections required for reconstructing relatively streakfree DCE heart images with the conventional FBP algorithm could be reduced to 25% of the fullview projection set (from 984 to 246 views), as evident by the subtle image difference with respect to the reference fullview protocol (<4% for all time points, Figure 2I). The accuracy of MP measurement was also minimally affected, as reflected by the small bias in MP measurement with respect to the fullview protocol (<4 mL/min/100 g; Figure 4B). Without view interpolation, the corresponding image difference and bias in MP measurement were 2 and 3 times higher, respectively.
The effective dose of a quantitative CT MP study covering 8 cm of the heart with the fullview dynamic acquisition protocol, estimated from the doselength product reported on the scanner, was 8 mSv. With a 4fold reduction in projection views (from 984 to 246), the effective dose of the sparseview dynamic acquisition protocol was reduced to 2 mSv.
The same magnitude of radiation dose reduction can be achieved by reducing the xray tube current from 80 mA to 20 mA while keeping all the projection views (984). However, such an approach leads to much poorer signaltonoise ratio in each measured projection, and the system electronic noise may exert a greater impact at low mA which is difficult to correct for with Poisson statistics. By contrast, the signaltonoise ratio of each measured projection in the sparseview dynamic acquisition is maintained. As such, the sparseview acquisition may be a better option for radiation dose reduction than lowmilliampere acquisition in this regard.
It is noteworthy to mention that the use of interpolated projection views introduced the blurring of sharp edges in the reconstructed DCE heart images, as depicted in Figure 2, E and F. However, extremely high spatial resolution is not necessary for CT MP imaging, as MP maps are typically generated with onehalf of the spatial resolution of the source images. The noise in the synthesized fullview images was also lower than the fullview images and was contributed by the lowpass filtering effect inherent to interpolation.
In addition to the cubicspline interpolation applied in our studies, other advanced algorithms such as directional sinogram interpolation (23, 24) and deeplearningbased interpolation (25) have been recently developed for generating additional projections to minimize streak artifacts in the sparseview CT image reconstruction. In the directional sinogram interpolation, the measured projections are first combined to generate the sinogram, which is then downsized with a specialized filter along the axis in parallel to the plane of gantry rotation. The purpose of sinogram downsizing is to eliminate the disconnected traces of the sinogram as a result of sparseview acquisition before the calculation of the structure tensor. Weighted pixel interpolation is then performed after estimation of the sinogram orientation. The entire interpolation process can be executed iteratively to generate more projections to further minimize the streak artifacts (24). In the deeplearningbased interpolation, the sinogram sampled from the sparseview acquisition is first upsampled with a linear interpolation. Then, a synthesized sinogram with quality superior to the linearly interpolated sinogram is generated with a pretrained convolution neural network followed by image reconstruction (25). Preliminary results have suggested that both the directional sinogram interpolation and the deeplearningbased interpolation are promising to generate streakfree CT images from the sparseview acquisition. Further research should focus on comparing the image quality (such as contrast and spatial resolution) and computation efficiency among different projection interpolation methods available for the sparseview CT image reconstruction in dynamic perfusion imaging.
The cubicspline view interpolation method allows the standard FBP algorithm to be used for sparseview image reconstruction without the need of implementing iterative reconstruction algorithms such as compressed sensing, which is more computationally demanding. Moreover, our previous studies revealed that the minimum number of projections required to produce streakfree DCE heart images with compressed sensing was 328 (26). In comparison, the cubicspline view interpolation method permits FBP image reconstruction with merely 246 views, which results in a greater degree of dose reduction for quantitative CT MP imaging.
Conclusion
The findings of this study suggest that ultralowdose quantitative CT MP measurement can be attained with sparseview dynamic contrastenhanced acquisition, provided the missing projections can be properly estimated using a cubicspline interpolation method before image reconstruction. The number of projections required for generating the DCE heart images can be reduced to just 25% of the conventional fullview setting without affecting the absolute MP measurements. The cubicspline interpolation method allows the conventional FBP algorithm to be used for the sparseview image reconstruction in CT MP imaging, avoiding the need of implementing the more computationally demanding algorithms such as compressed sensing. The substantial reduction in radiation exposure associated with the sparseview dynamic acquisition may lead to a wider clinical application of quantitative CT MP imaging for functional assessment of coronary artery disease.
Acknowledgments
We sincerely thank Jennifer Hadway, Laura Morrison, Dave Gaskin, and Anna MacDonald from Lawson Health Research Institute and St. Joseph's Healthcare London for assisting the animal imaging studies. The project was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant.
Disclosures: No disclosures to report.
Conflict of Interest: The authors have no conflict of interest to declare.
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Research Articles
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TOMOGRAPHY, September 2019, Volume 5, Issue 3:300307
DOI: 10.18383/j.tom.2019.00013
CubicSpline Interpolation for SparseView CT Image Reconstruction With Filtered Backprojection in Dynamic Myocardial Perfusion Imaging
Esmaeil Enjilela^{1}, TingYim Lee^{1}, Gerald Wisenberg^{3}, Patrick Teefy^{3}, Rodrigo Bagur^{3}, Ali Islam^{4}, Jiang Hsieh^{5}, Aaron So^{1}
Abstract
We investigated a projection interpolation method for reconstructing dynamic contrastenhanced (DCE) heart images from undersampled xray projections with filtered backprojecton (FBP). This method may facilitate the application of sparseview dynamic acquisition for ultralowdose quantitative computed tomography (CT) myocardial perfusion (MP) imaging. We conducted CT perfusion studies on 5 pigs with a standard fullview acquisition protocol (984 projections). We reconstructed DCE heart images with FBP from all and a quarter of the measured projections evenly distributed over 360°. We interpolated the sparseview (quarter) projections to a fullview setting using a cubicspline interpolation method before applying FBP to reconstruct the DCE heart images (synthesized fullview). To generate MP maps, we used 3 sets of DCE heart images, and compared mean MP values and biases among the 3 protocols. Compared with synthesized fullview DCE images, sparseview DCE images were more affected by streak artifacts arising from projection undersampling. Relative to the fullview protocol, mean bias in MP measurement associated with the sparseview protocol was 10.0 mL/min/100 g (95%CI: −8.9 to 28.9), which was >3 times higher than that associated with the synthesized fullview protocol (3.3 mL/min/100 g, 95% CI: −6.7 to 13.2). The cubicsplineview interpolation method improved MP measurement from DCE heart images reconstructed from only a quarter of the full projection set. This method can be used with the industrystandard FBP algorithm to reconstruct DCE images of the heart, and it can reduce the radiation dose of a wholeheart quantitative CT MP study to <2 mSv (at 8cm coverage).
Introduction
Computed tomography (CT) myocardial perfusion (MP) imaging is a technique used to quantitatively measure myocardial blood flow (perfusion) through tracer kinetic modeling of the timeenhancement curves acquired from dynamic contrastenhanced (DCE) CT scanning of the heart. As this technique requires repeated scanning of the heart following a short bolus injection of contrast solution, the associated radiation dose is higher than that required for a standard chest CT scan. A straightforward strategy to minimize radiation exposure is to lower the tube current setting (measured in milliampere or mA) for dynamic scanning, and that to correct for excessive projection noise is to use postprocessing techniques such as highly constrained backprojection local reconstruction (HYPRLR) (1–3), multiband filtering (4), sinogram smoothing (5), or statisticsbased iterative reconstruction (6, 7). However, there are 2 main challenges associated with the ultralowmilliampere approach. First, photon starvation could lead to inaccurate sampling of the arterial and myocardial timeenhancement curves and sequentially the measurement of MP. Second, the CT detector electronic noise becomes dominant at the extremely low milliampere level, which is difficult to model and correct for with Poisson statistics alone.
Sparseview dynamic acquisition, where only a small number of xray projections are acquired in each gantry rotation, is an alternative solution to achieve ultralowdose CT MP imaging. This approach is not restricted by the electronic noise barrier and hence could achieve more dose reduction than the lowmilliampere approach. Furthermore, the feasibility of the sparseview acquisition with a clinical CT scanner capable of rapid xray pulsing has been demonstrated (8). However, sparseview acquisition can induce aliasing streak artifacts in the reconstructed images (9, 10), which could have a significant impact on the measurements of timeenhancement curves and MP.
In this paper, we investigated whether reconstruction of streakfree DCE heart images from undersampled projections by using the standard filtered backprojection (FBP) algorithm is feasible if the missing projections are estimated from neighboring ones. The performance of this view interpolation method was evaluated in CT MP studies of pigs, in which a subset of measured projections was used to generate DCE heart images and MP maps with and without the view interpolation applied, and the image quality and MP measurement against the reference fullview technique were compared.
Methods and Materials
Animal Model
DCECT imaging was performed on 5 farm pigs that weighed 40–50 kg. The animal studies were approved by the institutional animal research ethics review board. Two pigs had acute myocardial infarction induced in the apical wall of the left ventricular myocardium from a transient occlusion of the distal left anterior descending (LAD) artery with a balloon catheter for 1 h followed by reperfusion. The other 3 pigs were normal and without infarction. These pigs collectively provided a wide spectrum of myocardial tissue, from normal to abnormal (ischemic or infarcted), for the validation of the cubicsplineview interpolation method for the sparseview image reconstruction with FBP.
Projection Data Acquisition
In each CT MP study, the pig was intubated and mechanically ventilated, and they were placed in either a supine or lateral position on the CT scanner table. Before each DCECT acquisition, iodinated contrast solution (Iohexol 300 mgI/mL) was injected into a peripheral vein at 3 mL/s and at a dosage of 0.7 mL/kg body weight, followed by saline flush at the same injection rate. The ventilator was turned off to minimize breathing motion during the short acquisition (∼30 s). Using a 64row CT750 HD scanner (GE Healthcare, Waukesha, WI) operating in a prospective electrocardiogramgated acquisition mode, a 4cm section of the heart covering the largest crosssection of the left ventricle in the axial tomographic plane was scanned at 3–4 s after contrast injection over 20–25 heart beats at middiastole. For each full (360°) gantry rotation at 140kV tube voltage, 80mA tube current, 8 × 5mm collimation width, and 0.35s gantry rotation period, the fullview projection set consisted of 984 projections. From each fullview projection set, 1 out of every 4 consecutive projections was selected to generate the sparseview set of 246 projections distributed evenly over 360°.
Image Reconstruction
For each pig, the following 3 sets of DCE heart images were reconstructed from the 3 projection sets with FBP: (a) fullview (984 views), (b) sparseview (246 views), and (c) synthesized fullview (984 views). The synthesized fullview projection set was generated by applying a cubicspline interpolation of the sparseview projection set in (b).
Different algorithms are available to generate missing projections from a discrete set of sampled projections. Generally speaking, with n measured data points, a single (n − 1)^{th} order polynomial can be used for the interpolation. Although polynomial interpolation is a common choice of interpolants, the associated error of interpolation can be large when a highorder polynomial function is used for data fitting. Such an interpolation error can be minimized by using spline interpolation which applies loworder polynomials to subsets of data points (11). Let us denote f(x) as a function between the sampled data points, x_{i − 1} and x_{i,} with i = [1, …, n]. A spline S(x) is a piecewise (composite) function formed by n loworder polynomials P(x) each fitting f(x).
(1)
Compared with a single highorder polynomial function, spline interpolation should provide a more accurate approximation of f(x), particularly if there exists local abrupt changes (such as the edges between high and lowcontrast regions). A cubic spline is a spline constructed of piecewise thirdorder polynomials (12, 13). Let us consider 3 consecutive data points, namely, x_{i−1}, x_{i}, x_{i+1}. Mathematically, a thirdorder polynomial P(x) on the interval between data points x_{i − 1} and x_{i} can be expressed as follows:
(2)
(3)
(4)
(5)
(6)
(7)
Image Analysis
Comparison of MP measurement.
The 3 sets of DCE heart images of each pig were analyzed with the CT Perfusion software (GE Healthcare, Waukesha, Wisconsin) to generate MP maps with a modelbased deconvolution algorithm (15). The mean MP value in the lateral, apical, and septal walls of the left ventricular myocardium in the axial view over 8 consecutive 5mm slices were compared between the 3 image reconstruction schemes. In total, 120 ischemic and nonischemic myocardial segments from 5 pigs were available for comparison. Bland–Altman graphical analysis was used to determine the mean bias of the sparseview and synthesized fullview MP measurements with respect to that of the reference fullview MP measurements. The limits of agreement were presented as 95% confidence intervals.
Comparison of Image Difference.
We used an image difference metric described by Busono and Hussein (16) to determine which between the sparseview and the synthesized fullview FBP reconstruction produced DCE heart images best matched with images from the fullview FBP reconstruction. The image difference at time point t, δ_{Dif}^{t}, is defined as follows:
(8)
Results
Figure 1A shows the sinogram of a fullview projection set acquired at one slice location. This fullview sinogram was then subsampled to generate a sparseview set of 246 projections evenly distributed over 360° as shown in Figure 1B. The dark vertical lines in Figure 1B are projections in the fullview set that were left out in the sparseview set. The sinogram of the corresponding synthesized fullview projection set is shown in Figure 1C for comparison. The 2 sinograms in Figure 1, A and C were qualitatively similar to each other. For a more quantitative comparison, Figure 1D shows the projection profile of the fullview sinogram (solid black line) superimposed over the projection profile of the synthesized (interpolated) fullview sinogram (dashed blue line) at the central detector for one slice location. The 2 projection profiles were comparable to each other, with the profile from the synthesized fullview sinogram slightly smoother than that from the measured fullview sinogram. For reference, the red stars in Figure 1D denote the corresponding projection profile of the sparseview sinogram.
Figure 1.
Sinograms of a pig computed tomography (CT) myocardial perfusion (MP) study acquired with the full 984view (A), sparse 246view (B), and synthesized full 984view protocols (C). The y and xaxis represent the detector and projection numbers, respectively. Projection profile of the fullview sinogram is compared with that of the synthesized fullview sinogram at the central detector (D). The red star marks the evenly subsampled 246 views from the fullview projection set.
Figure 2 shows the DCE heart images reconstructed from the fullview (Figure 2, A and B), sparseview (Figure 2, C and D) and synthesized fullview (Figure 2, E and F) projection sets. Image reconstruction with the sparseview projection set resulted in streak artifacts. Figure 2, G and H show the difference image between the fullview (Figure 2A) and sparseview (Figure 2C) protocols and that between the fullview (Figure 2A) and synthesized fullview (Figure 2E) protocols, respectively. The mean ± standard deviation of CT number in 3 different regions in Figure 2G (lateral wall and apical wall of the left ventricular myocardium and a peripheral soft tissue region) was 8.74 ± 12.71, 10.69 ± 13.84, and 10.14 ± 15.20 Hounsfield unit (HU), which was larger than that of CT number in the 3 different regions in Figure 2H (5.28 ± 8.34, 5.88 ± 8.82, and 7.06 ± 9.32 HU), suggesting that the cubicspline interpolation method was able to reduce the HU errors in the reconstructed images arising from aliasing streak artifacts. As shown in Figure 2I, the image difference metric [equation (8)] between the synthesized fullview and fullview DCE images was consistently <4% at all time points, in comparison to 7.5% between the sparseview and the fullview DCE images.
Figure 2.
Contrastenhanced CT images from a pig heart reconstructed with filtered backprojecton (FBP) from fullview(A, B), sparseview (C, D), and synthesized fullview projections (E, F). These images corresponded to the time when both heart chambers were filled with an iodinated contrast solution. The window width/level was set at 400/40 HU. (G) and (H) depict the difference images between (A) and (C) and between (A) and (E), respectively. Image difference metric for synthesized fullview images (black solid line) is compared with that for sparseview images (dashed blue line) over the whole time course of a dynamic CT MP study (I).
Figure 3 shows the MP maps of a pig with an infarct in the apical myocardium (yellow arrow), derived from the 3 sets of DCE images shown in Figure 2. The MP map generated from the sparseview images (Figure 3B) was clearly noisier than that generated from the fullview images (Figure 3A). After cubicspline view interpolation was applied, the MP map generated from the synthesized fullview images (Figure 3C) was comparable with that generated from the fullview images (Figure 3A).
Figure 3.
CT MP maps derived from dynamic contrastenhanced (DCE) images reconstructed from fullview (A), sparseview (B), and synthesized fullview (C) projections with FBP as shown in Figure 2. The CT MP maps are displayed in a color scale range from 0 (blue) to 400 (red) mL/min/100 g. The yellow arrow in (A) points to the infarcted region within the apical wall of the myocardium.
The Bland–Altman plot shown in Figure 4 showed that the mean bias of absolute MP measurement associated with the synthesized fullview and sparseview protocols was 3.6 (95% CI −8.6 to 15.7) mL/min/100 g and 9.7 (95% CI −12.8 to 32.3) mL/min/100 g, respectively, with respect to the reference fullview protocol. Furthermore, the cubicspline interpolation method led to a 63% decrease in the mean bias of absolute MP measurement when the sparseview DCE heart images were used for perfusion analysis.
Figure 4.
(A) Sparseview and (B) synthesized fullview CT MP measurements in comparison to the reference fullview MP measurements using the Bland–Altman graphical analysis. The solid gray line in each graph represents the mean bias in MP measurement relative to the reference protocol. The dotted gray lines denotes the 95% confidence intervals (CIs) of the estimated mean bias. The numbers in red color in each graph represent the mean bias and corresponding CI values of MP.
Discussion
Quantitative CT MP imaging is useful for the functional assessment of coronary artery disease (17) but high radiation dose is a major hurdle for its implementation in routine clinical practice. This study aimed to demonstrate the feasibility of reducing the radiation dose of a quantitative CT MP study with the sparseview dynamic acquisition and image reconstruction. CT image reconstruction with sparsely sampled projections has been of great interest lately. Although compressed sensing is the primary algorithmic choice for sparseview CT image reconstruction with promising results reported in a number of preclinical studies (18, 19), it can lead to loss of image details in aspects of contrast and spatial resolution. Although more advanced compressed sensing–based algorithms have been recently developed to improve these aspects (20–22), they remain computationally demanding, which may limit their clinical applications. In contrast, FBPbased image reconstruction methods are faster, making the sparseview CT MP imaging more feasible in realworld clinical settings.
To the best of our knowledge, the application of cubicspline interpolation for sparseview CT MP measurement has not been previously investigated. The main challenge of this approach is the aliasing streak artifacts in reconstructed DCE images that can significantly affect the accuracy of MP measurement. A cubicspline interpolation method was used in our studies conducted in pigs to estimate the missing projections before FBP image reconstruction to minimize the aliasing streak artifacts in DCE images. Our findings showed that the number of projections required for reconstructing relatively streakfree DCE heart images with the conventional FBP algorithm could be reduced to 25% of the fullview projection set (from 984 to 246 views), as evident by the subtle image difference with respect to the reference fullview protocol (<4% for all time points, Figure 2I). The accuracy of MP measurement was also minimally affected, as reflected by the small bias in MP measurement with respect to the fullview protocol (<4 mL/min/100 g; Figure 4B). Without view interpolation, the corresponding image difference and bias in MP measurement were 2 and 3 times higher, respectively.
The effective dose of a quantitative CT MP study covering 8 cm of the heart with the fullview dynamic acquisition protocol, estimated from the doselength product reported on the scanner, was 8 mSv. With a 4fold reduction in projection views (from 984 to 246), the effective dose of the sparseview dynamic acquisition protocol was reduced to 2 mSv.
The same magnitude of radiation dose reduction can be achieved by reducing the xray tube current from 80 mA to 20 mA while keeping all the projection views (984). However, such an approach leads to much poorer signaltonoise ratio in each measured projection, and the system electronic noise may exert a greater impact at low mA which is difficult to correct for with Poisson statistics. By contrast, the signaltonoise ratio of each measured projection in the sparseview dynamic acquisition is maintained. As such, the sparseview acquisition may be a better option for radiation dose reduction than lowmilliampere acquisition in this regard.
It is noteworthy to mention that the use of interpolated projection views introduced the blurring of sharp edges in the reconstructed DCE heart images, as depicted in Figure 2, E and F. However, extremely high spatial resolution is not necessary for CT MP imaging, as MP maps are typically generated with onehalf of the spatial resolution of the source images. The noise in the synthesized fullview images was also lower than the fullview images and was contributed by the lowpass filtering effect inherent to interpolation.
In addition to the cubicspline interpolation applied in our studies, other advanced algorithms such as directional sinogram interpolation (23, 24) and deeplearningbased interpolation (25) have been recently developed for generating additional projections to minimize streak artifacts in the sparseview CT image reconstruction. In the directional sinogram interpolation, the measured projections are first combined to generate the sinogram, which is then downsized with a specialized filter along the axis in parallel to the plane of gantry rotation. The purpose of sinogram downsizing is to eliminate the disconnected traces of the sinogram as a result of sparseview acquisition before the calculation of the structure tensor. Weighted pixel interpolation is then performed after estimation of the sinogram orientation. The entire interpolation process can be executed iteratively to generate more projections to further minimize the streak artifacts (24). In the deeplearningbased interpolation, the sinogram sampled from the sparseview acquisition is first upsampled with a linear interpolation. Then, a synthesized sinogram with quality superior to the linearly interpolated sinogram is generated with a pretrained convolution neural network followed by image reconstruction (25). Preliminary results have suggested that both the directional sinogram interpolation and the deeplearningbased interpolation are promising to generate streakfree CT images from the sparseview acquisition. Further research should focus on comparing the image quality (such as contrast and spatial resolution) and computation efficiency among different projection interpolation methods available for the sparseview CT image reconstruction in dynamic perfusion imaging.
The cubicspline view interpolation method allows the standard FBP algorithm to be used for sparseview image reconstruction without the need of implementing iterative reconstruction algorithms such as compressed sensing, which is more computationally demanding. Moreover, our previous studies revealed that the minimum number of projections required to produce streakfree DCE heart images with compressed sensing was 328 (26). In comparison, the cubicspline view interpolation method permits FBP image reconstruction with merely 246 views, which results in a greater degree of dose reduction for quantitative CT MP imaging.
Conclusion
The findings of this study suggest that ultralowdose quantitative CT MP measurement can be attained with sparseview dynamic contrastenhanced acquisition, provided the missing projections can be properly estimated using a cubicspline interpolation method before image reconstruction. The number of projections required for generating the DCE heart images can be reduced to just 25% of the conventional fullview setting without affecting the absolute MP measurements. The cubicspline interpolation method allows the conventional FBP algorithm to be used for the sparseview image reconstruction in CT MP imaging, avoiding the need of implementing the more computationally demanding algorithms such as compressed sensing. The substantial reduction in radiation exposure associated with the sparseview dynamic acquisition may lead to a wider clinical application of quantitative CT MP imaging for functional assessment of coronary artery disease.
Notes
[1] Abbreviations:
DCE
Dynamic contrastenhanced
FBP
filtered backprojecton
CT
computed tomography
MP
myocardial perfusion
Acknowledgments
We sincerely thank Jennifer Hadway, Laura Morrison, Dave Gaskin, and Anna MacDonald from Lawson Health Research Institute and St. Joseph's Healthcare London for assisting the animal imaging studies. The project was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant.
Disclosures: No disclosures to report.
Conflict of Interest: The authors have no conflict of interest to declare.
References
Journal Information
Journal ID (nlmta): tom
Journal ID (publisherid): TOMOG
Title: Tomography
Subtitle: A Journal for Imaging Research
Abbreviated Title: Tomog.
ISSN (print): 23791381
ISSN (electronic): 2379139X
Publisher: Grapho Publications, LLC (Ann Abor, Michigan)
Article Information
Self URI: media/vol5/issue3/pdf/tomo05300.pdf
Copyright statement: © 2019 The Authors. Published by Grapho Publications, LLC
Copyright: 2019, Grapho Publications, LLC
License (openaccess, http://creativecommons.org/licenses/byncnd/4.0/):
This is an open access article under the CC BYNCND license (http://creativecommons.org/licenses/byncnd/4.0/).
Publication date (print): September 2019
Volume: 5
Issue: 3
Pages: 300307
Publisher ID: TOMO201900013
DOI: 10.18383/j.tom.2019.00013
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