Accelerated 4D flow MRI

Accelerated 4D flow MRI Comparing SENSE, k-t PCA and Compressed Sensing Tomas Kaandorp 10356169 Patient comfort can be increased by accelerating an MRI scanner to reduce scan time. 4D flow MRI scans can be accelerated by undersampling the k-space. Unfortunately this has a negative effect on the image quality and signal-to-noise ratio. To look at the effects of undersampling on the flow amplitude, SENSE, k-t PCA and Compressed Sensing (CS) are compared for acceleration factors (R): 6, 8, and 10 in five healthy volunteers. The results show that the maximum flow amplitude decreases for all scanning modalities if R increases. The average drop in flow amplitude for SENSE, k-t PCA and CS are respectively: 33 %, 20 %, and 7.5 %. Furthermore CS showed a better image quality for higher R compared to SENSE and k-t PCA, which leads to reliable flow curves and usable image quality up to R10. Thus CS shows promising results for reliable shortening of 4D flow MRI in clinical environments. Report Bachelor Project Physics and Astronomy, size 15 EC, conducted between 01-04 2017 and 01-08 2017 Supervisor: Dr. Ir. A. J. Nederveen Second assessor: Prof. Dr. Ir. G. J. Strijkers Mentor: L. M. Gottwald Department of Radiology and Nucleair medicine Amsterdam Medical Centre University of Amsterdam August 2017

Contents 1 Introduction 2 2 Theory 2 2.1 MRI.................................. 2 2.2 Acceleration methods........................ 3 2.3 Hypothesis.............................. 6 3 Method 7 3.1 Phantom scan............................. 7 3.2 In vivo................................. 8 3.3 SNR.................................. 8 4 Results 8 4.1 Phantom............................... 8 4.2 In vivo................................. 10 4.3 Prospective vs retrospective triggering............... 16 4.4 SNR.................................. 19 5 Discussion 19 6 Conclusion 20 7 References 21 1

1 Introduction The global average life expectancy has tremendously increased for decades. This means that the number of people dying from cardiovascular diseases (CV) is on the rise, and is now even the primary cause of premature deaths (Heissel, 2017). For the correct diagnosis and treatment a 4D flow MRI scan might be beneficial. For example, a 4D flow MRI scan allows physicians to look at blood flow, peak blood flow and wall shear stress. However these scans needed for the diagnosis are high resolution scans which means they take a long time. This in term means that patients have to lie inside the scanner for a prolonged period of time, which can be claustrophobic or uncomfortable. To increase patient well-being it is vital to reduce scanning time of 4D flow MRI. However accelerating an MRI scan has a negative trade-off to the image quality of the scan, this trade-off is expressed in terms of the Signal-to-Noise Ratio (SNR). It is therefor vital to finding a way to shorten the scan time without the drop in image quality. Over the years the scan time of 4D flow has been shortened i.e. by three methods. First by the implementation of multiple receiving coils (Pruessmann et. al., 1999), secondly by the use of k-t Principal Component Analyses (k-t PCA) and more recently by implementing Compressed Sensing (CS). Since the aorta is of interest to diagnose CV, this paper will compare the aorta blood flow for SENSE, k-t PCA and CS to see if the acceleration has an effect on the reliability of the blood flow quantization. 2 Theory 2.1 MRI A MRI scanner uses the 1 H spin of the Nucleus to acquire an image. Firstly a subject (i.e. volunteer or patient) is placed into a homogeneous magnetic field (the scanner). By doing so, all the nuclear spins of the atoms align in to the foot head direction. Once all the spins are aligned, a Radio Frequency (RF) pulse is given with a frequency matching the Larmor frequency of 1 H. This RF-pulse makes the nuclear spin resonate. When resonating the spins send out a RF signal which can be measured with the receiving coil. This can be done via T1 imaging of T2 imaging, depending on what sort of tissue that is scanned. The difference is determined by the time the 1 H nucleus remains resonating. To transfer the frequencies measured during acquisition a Fourier transform is used. The frequencies are measured in the Frequency space, also called k-space. In principle the entire k-space needs to be scanned to get a good image quality. If only parts of the k-space are scanned the image becomes blurry and other artifacts appear. Over the years a number of methods where devised to scan the k-space. Initially k-space was scanned in horizontal row (k x direction) progressing downwards in the vertical direction (k y ) after scanning each horizontal row. 2

Figure 1: The Nyquist criterion sets the required k-space coverage, which can be achieved using various sampling trajectories. Image resolution is determined by the extent of the k-space coverage. The supported field of view is determined by the sampling density. Violation of the Nyquist criterion causes artifacts in linear reconstructions, which depend on the sampling pattern. (Lustig et. al., 2008) Although there are multiple ways of scanning the k-space a Cartesian grid is preferred since this can be easily transformed from frequency domain to space domain by a Fourier transform. New techniques such as spiral trajectories based on radial coordinates are gaining popularity since these are less susceptible to motion artifacts and can be more easily under-sampled than Cartesian trajectories (Lustig et. al., 2008). 2.2 Acceleration methods Accelerating MRI scans is mainly done by collecting less data points. Data is collected in the frequency domain (k-space). By collecting less data points in the k-space, i.e. under sampling the k-space, the duration of the scan shortens. However this is where a trade off arises. A fully sampled k-space is needed for high resolution images which physicians like, but this takes time. Under sampling the k-space shortens the scan time but this also means the image quality of the scan deteriorates. This trade off is expressed in the Signal-toNoise Ratio (Formula 1) SN R = Signalintensity SD(N oiseintensity) 3 (1)

In short, if a scan is accelerated, the SNR decreases which means the image quality decreases. One way of accelerating MRI scans is by using a SENSE reconstruction. During a SENSE scan, data is collected using multiple receiver coils. This means there are multiple images created (i. e. 2). These images contain aliasing effects since they are based on only part of the k-space. By later combining these multiple images, one complete image is created and aliasing effects are minimized. This however requires the scanner to save all the images during the scan and to form a reconstructed image by superposition of these saved images weighted by the corresponding coil sensitivity maps. Figure 2: SENSE graphically displayed, two images with aliasing formed by different coils. Afterwards these images are combined using a superposition weighted by coil sensitivity maps (MRIquestions.com, 2017) Another way of reducing scan time is by under sampling the k-space over time, this method is called k-t PCA. Next an adaptive filter is used in the Fourier transformed domain to correct for the aliasing effects that occur due to the under sampling. However, the reconstruction is now under determined since the filter leads to more unknown values than equations. This has a negative effect on the temporal fidelity. To solve this problem k-t BLAST is revised to k-t PCA. Principle Component Analysis (PCA) reduces a multi-dimensional data set to a lower dimensional set by using a training image. PCA constrains the appearance of the object such that the frequency must be a linear combination of predefined basis functions. The basis functions are derived from the training image. The PCA reconstruction separates the overlapped images accurately. Since the temporal fidelity is also separated, there is no negative effect on the fidelity. Therefore, k-t PCA then leads to a shorter 4D flow scan time. Unfortunately this still leads to some aliasing in the image. This means the image quality decreases and it may become difficult to define a correct Region Of Interest (ROI). Thus, limiting the acceleration factor (R). Gwenaël Pagé et. al., 4

2017 showed that it is possible to accelerate the scan using R = 8 and retain a good image quality. However the flow amplitude decreases significantly above R6. Thus limiting 4D flow MRI. Figure 3: An example of k-t PCA. Firstly the training image is made (a), then the data is under sampled (b). By using a filter to correct for the aliasing effect, the image becomes under determined which is solved with the training image(c). (Petersen et. al., 2009) A more recent development is called Compressed Sensing (CS). CS also under samples the k-space but has some more requirements. Firstly the data has to be under sampled in a random way. Secondly, transform sparsity is needed and lastly, to acquire the best image quality, an iterative reconstruction method is needed. There are again a number of ways to scan the k-space, a Poisson distribution in Cartesian coordinates can be used. However a spiral shape with more data points in the centre than on the outer radius shows promising results in scan time reduction and image quality(l. M. Gottwald et. al., 2017). The collected data has to be incoherent/sparse to make it possible to separate noise from the signal. Via a wavelet transform, the data is made sparse which is necessary to do the further data analyses. In the sparse data set, the strongest signal is identified and abstracted from the whole signal. In the next iteration of data process, the signal then allows for the identification of a signal with a lower intensity. After multiple iterations only the noise remains and the complete spectrum of signals is identified. In Figure 2, the CS reconstruction is graphically 5

displayed. After the separation of the signals, the image can be reconstructed through the regular methods i.e. a Fast Fourier transform(fft). Because all signals are deduced from the under sampled k-space, the image quality remains acceptable for clinical use (Lustig et. al., 2008). Figure 4: Heuristic procedure for reconstruction from under sampled data. A sparse signal (a) is 8-fold under sampled in its 1-D k-space domain (b). Equispaced under sampling results in signal aliasing (d) preventing recovery. Pseudorandom under sampling results in incoherent interference (c). Some strong signal components stick above the interference level, are detected and recovered by thresholding (e) and (f). The interference of these components is computed (g) and subtracted (h), thus lowering the total interference level and enabling recovery of weaker components.(lustig et. al., 2008 2.3 Hypothesis Based on the paper from Gwenaël Pagé et. al., 2017, it is expected that for SENSE and k-t PCA the amplitude of the flow curves decrease if the acceleration factor (R) is higher then R6. Secondly, since the SNR decreases if the acceleration rate increases, it is to be expected that the image quality decreases. Since this effect is greater for SENSE than for k-t PCA or CS, it is expected that SENSE has the worst image quality and thus lowest SNR, followed by k-t PCA. Since the CS reconstruction is better in determining the signals with low intensity because it uses an iterative reconstruction method, CS should have a better image quality. Therefore the average SNR of CS should be higher than the average SNR of k-t PCA and SENSE. 6

3 Method 3.1 Phantom scan Firstly, an exploratory scan was made with a carotid bifurcation phantom (LifeTec, Eindhoven, Netherlands). A pulsating water flow with a simulated heart rate of 60 bpm and a variability of 5 bpm created a temporal mean flow of 300 ml/min. A time stamp from the pump signal was used for retrospective triggering. A schematic overview of the experimental setup and all measurement parameters are shown in Figure 5. Figure 5: Experimental setup used for the Phantom scans, (L. M. Gottwald, 2017) All experiments were conducted on a 3T MRI scanner (Philips Healthcare, Best, Netherlands) using an 8-channel neck coil. A total matrix size(fov) of 64x64x64 mm 3 and a voxel size of 1x1x1 mm 3 was acquired in three flow encoding directions using a VENC of 150 cm/s. Profile lists of different lengths were created with a nominal acceleration factor (R) of 2, 4, 6, 8 and 10 per acceleration method i.e. SENSE and k-t PCA. The acquired data was processed by ReconFrame (Gyrotools, Zurich, Zwiterland) and retrospectively absolute binned in 24 cardiac frames. For the flow analysis the return artery was used since this was the largest phantom artery and thus yields the highest signal. Next Matlab(The Math- Works Inc, r2016b) was used to draw Regions Of Interest (ROI). Based on these ROI, a Black and White (BW) mask was created. This BW mask was then used to make the flow curves since it multiplies the data in the aorta with 1 and all other areas with 0. The flow curves are compared to the pre-set maximum flow and pulsation of the phantom. The flow was quantified using the Phase image. The phase data was multiplied with the BW mask so only the Aorta was selected. Next the flow data was scaled to the voxel size and the preset VENC. This was done using Formula 2 and 3. V elocityroi = mean(bw mask Dataset) (2) AverageF lowroi = mean( V elocityroi BW Area ) (3) 100 7

3.2 In vivo Secondly the flow was compared in vivo. This was also done on a 3T MRI scanner (Phillips Healthcare, Best, Netherlands) using a 16-channel Torso and an 8-channel posterior coil. Five healthy volunteers, aged between 20-25 years where scanned. A total FOV size of 315x275x60 mm 3 and a VENC of 150 cm/s was used, the resolution was set to 2.5x2.5x2.5 mm 3. Data was collected in three different flow encoding directions for each acceleration method(sense, k-t PCA and CS). Scanning R2 and R4 would lead to a longer scanning time then 1.5 hours. It becomes very uncomfortable for a volunteer to lay inside the scanner longer then 1.5 hours, therefor R2 and R4 are not included in this paper. The ROI was drawn on the Ascending Aorta (AAO) for all 24 cardiac frames. next this was scaled for the phase offset. To calculate the flow Equation 2 and 3 where used again. Next the mean flow is determined over all volunteers. The flow curves are compared based on the acceleration rate (R) with fixed modality and also compared per modality with fixed R. Furthermore it was investigated if retrospective cardiac synchronization differs from prospective cardiac synchronization. This is done by comparing data, for a fixed R, between retrospective and prospective gating for CS and k-t PCA. This can be interesting since it may occur that data is not binned correctly in retrospective binning than with prospective binning (triggering). 3.3 SNR Lastly, the SNR is compared. This is done by making two extra ROI. The first one is inside the body but on a location where there should be no significant change in the signal intensity. The second ROI is then drawn outside the body where only noise is expected. By using Formula 1 the SNR is calculated. In contrary to the flow, the SNR is calculated based on the magnitude image and not on the phase image. This is done since the intensity in a phase image can change around the blood vessels due to blood flow. 4 Results 4.1 Phantom Firstly, a Phantom was examined for k-t PCA and SENSE, the flow curves per acceleration rate are displayed in Figure 6. As Pagé et. al., 2017, predicted, the amplitude of the flow curves declines as the acceleration rate (R) increases. Furthermore it can be seen that the lines become less smooth for increased R. Both these observations are due to the undersampling of the data. 8

Figure 6: Flow comparison in the Phantom, expressed for fixed R. Notice the drop in maximum flow amplitude. 9

4.2 In vivo First the image quality of the magnitude images are compared to see if the data is usable and how the undersampling effects the image quality. This comparison is done by eye based on Figure 7 Figure 7: on the x-axis R 6, 8, and 10 are displayed. On the y-axis CS, k-t PCA and Sense are displayed. On the top row it is visible that SENSE is very noisy and unclear. Below kt-pca shows a good image quality for all R although some streaking appears. On the bottom CS also shows good image quality. The image is a bit blurry due to scaling. CS is scaled by multiplying with 0.2 and SENSE by multiplying with 2 10

During the drawing of the ROI it became clear that the aorta was very difficult to locate on the accelerated SENSE scans. Since the volunteers where scanned for multiple scanning modalities, sometimes k-t PCA or CS scans where used to draw the ROI. Firstly, the differences in the flow curves is compared within each scanning modality, in Figure 8 the flow for all R is plotted for SENSE. Figure 8: Mean flow for SENSE. R 6, 8, and 10 are compared. R6 shows no real flow. This may be due to a small and incorrect data set. The max flow amplitude of R10 is lower then R8. It can be seen that the flow curves are very rough, also R6 preforms very bad compared to R8 and R10. This might be because the mean R6 flow is determined on less than five volunteers due to some failed scans. The decrease in amplitude between R8 and R10 is neatly visible. In Figure 9, k-t PCA is compared between acceleration rate (R). The flow curves preform better and are smoother compared to SENSE. Again the drop in amplitude is visible as predicted by Pagé et. al. On the x-axis the cardiac frames are displayed. In all flow curves we can see when the heart makes a beat. First a peak is visible since the heart is pumping, next the a slow relaxation occurs. During the relaxation some low peaks are still caused by the relaxation 11

of the slightly expanded aorta due to the blood pressure. On the y-axis, the Mean blood flow is given in ml/s. Figure 9: Mean flow for k-t PCA. R 6, 8, and 10 are compared. The drop in amplitude is visible and for low R the graphs are smoother due to less undersampling. Figure 10 shows the mean flow curves of CS. Here it can be seen that the max amplitude is almost constant. Again as expected the amplitude does drop, the difference between the highest peak (R6) and the lowest peak (R8) is 14.75 ml/s. The amplitude difference between R8 and R10 can not be calculated due to a difference in cardiac frames. However since the peak flow amplitude of R10 lies between the peak flow of R8 and R6 this is still smaller then 14.75 ml/s. 12

Figure 10: Mean flow for CS. R 6, 8, and 10 are compared. The difference in max flow between R8 and R6 is 14.75 ml/s Next the differences per modality are compared. 13

Figure 11: Mean flow for SENSE, k-t PCA, and CS for R6 Figure 12: Mean flow for SENSE, k-t PCA, and CS for R8 14

Figure 13: Mean flow for SENSE, k-t PCA, and CS for R10. Again CS preforms stable with a maximum flow around 160 ml/s SENSE preforms well for R8 but decreases signifcantly compared to CS for R10. For k-t PCA a steady drop can be seen in maximum amplitude for all R compared to SENSE and CS. Also the curve remains reasonably smooth. The maximum difference in flow amplitude between R6 and R10 for SENSE, k-t PCA and CS are respectively: 33%, 20%, and 7.5%. 15

4.3 Prospective vs retrospective triggering It can be seen in Figures 14, 15, 16, and 17 that retrospective binning leads to a binning error at the end of the flow curves. A ascending line can be seen which should actually be at the beginning of the flow curve. Furthermore it can be seen that the amplitude for retrospective binning matches more to the amplitude of CS and SENSE. Figure 14: Mean flow for retrospective and prospective binning in the AAo accelerated to R8. A small binning error can be seen at the end of the flow curve for retrospective binning. 16

Figure 15: Velocity for retrospective and prospective binning in the AAo accelerated to R8. A small binning error can be seen at the end of the flow curve for retrospective binning. Figure 16: Mean flow for retrospective and prospective binning in the DAo accelerated to R8. A small binning error can be seen at the end of the flow curve for retrospective binning. 17

Figure 17: Velocity for retrospective and prospective binning in the DAo accelerated to R8. A small binning error can be seen at the end of the flow curve for retrospective binning. 18

4.4 SNR As the acceleration rate (R) increases, the increased under sampling of the k- space leads to a decrease in signal intensity. Therefor, the SNR calculated with Formula 1 should drop. Since the image quality for CS is also better then for SENSE or k-t PCA, it is also expected that the SNR is higher for CS than for SENSE and k-t PCA. However this is not what is seen in the data. The SNR values are given below in Table 1. SENSE k-t PCA CS R6 3.45 3.39 48.17 R8 4.09 4.09 54.15 R10 2.67 2.62 58.70 Tabel 1: average SNR expressed per method and R As seen in the table, CS has an higher average SNR than k-t PCA or SENSE over all volunteers. Furthermore there is an unexpected peak in the average SNR for R8 in SENSE and k-t PCA. As expected the SNR value for R10 are below R6 for k-t PCA and SENSE as should be based on the fact that the signal decreases if the undersampling increases. 5 Discussion Not all scans could be performed one after the other due to a software change during the examination, resulting in a scan break. Moreover, some exams had to be spitted into two exams, when the gating efficiency of the subject had been very poor. The composition of the subject scans and masks are shown in Table 2. 19

Volunteer: 1 2 3 4 5 Mask 1 SENSE + kt-pca 4 SENSE + k-t PCA SENSE 2.45 + k-t PCA SENSE + k-t PCA Kt-PCA Mask 2 CS CS CS + SENSE 2.8, 3.2 CS CS + SENSE Mask 3 k-t PCA: 6, 8 Table 2: Composition of scanned volunteer and corresponding BW masks The drawing of the ROI remains a human task. This means it is susceptible to flaws such as drawing the ROI to big or to small. Drawing the ROI wrong can lead to misguided flow curves. One other solution is to only look at the velocity since this is not scaled for the area of the ROI. Furthermore, in determining the Signal-to-Noise Ratio (SNR), it was assumed that the signal outside of the body would only contain noise. It may be possible that the signal outside the body is also scaled depending on the scan modality used. Thus the used baseline of noise would differ per modality and it would not be able to make a good comparison. The average SNR for CS is about 20 times higher than the SNR for SENSE and k-t PCA. This might be explained by a scaling factor. There are also strong indications that the SNR is influenced by the multiple scanning sessions of volunteers and the software update of the scanner. For example the CS SNR for volunteer two is around 17 while all the other SNR are around 50. Volunteer two was scanned with CS before the scanner update whilst all other volunteers where scanned with CS after the scanner update. Therefore it is clear the scanner update has influenced either the scaling of the reconstruction method. 6 Conclusion Just like Pagé Et. Al. showed, the amplitude of the flow curves drops for all modalities if the acceleration rate increases. However the drop in flow amplitude for CS is limited to 14.75 ml/s between R6 and R8. Since R10 lies between R6 and R8 the difference of 14.75 ml/s is a maximum difference. The image quality does decrease if R increases. For SENSE the decrease in image quality means that it is no longer possible to draw the correct ROI. For k-t PCA the image quality remains acceptable but the max flow amplitude decreases significantly. For CS the image quality also remains acceptable and the decrease in max flow amplitude is limited to 14.75 ml/s up to R = 10. This is roughly 7 % of the maximum flow for R6 whilst the drop in amplitude for SENSE and k-t PCA are respectively 33% and 20%. Therefore CS shows promising results for reliably shortening the scan time of a 4D flow MRI. However there are still other limiting factors such as the gating efficiency. It is advisable to do some further research into 4d flow MRI but also into the gating efficiency. 20

7 References Heiddel W, Deaths from cardiovasculair disease increase globally while mortality rates decrease, Healthdata, www.healthdata.com, 2017, retrieved 17-08-2017. Gottwald L. M, Peper E. S, Zang Q, Pronk V, Coolen B. F, Strijkers G. J, Nederveen A. J, Compressed Sensing accelerated 4D flow MRI using a pseudo spiral Cartesian sampling technique with random undersamling in time, Unknown, 2017 Lustig M, Donoh D, Santos J, Compressed sensing MRI, IEEE SIGNAL PROCESSING MAGAZINE,] MARCH 2008, 72-82. MRI questions, retrieved 17-08-2017. www.mriquestions.com/senseasset Pagé G, Bettoni J, Salsac A.V, Balédent O, Influence of the k-t Principal Component Analysis acceleration factor on the accuracy of flow measurement in 4D PC-MRI, Proc. Intl. Soc. Mag. Reson. Med. 25 (2017) Pedersen H, Kozerke S, Ringgaard S, Nehrke K, and Kim W, k-t PCA: Temporally Constrained k-t BLAST Reconstruction Using Principal Component Analysis, Magnetic Resonance in Medicine, 2009, 62, 706-716. Pruessmann K. P, Weiger M, Scheidegger M. B, Boesiger P, SENSE: Sensitivity Encoding for Fast MRI, Magnetic Resonance in Medicine, 1999, 42, 952-962. 21