Development of Phase Contrast Sequence

Transcription

1 École Polytechnique de Montréal Development of Phase Contrast Sequence Author : Dominique Mathieu Matricule Supervisor : Rick Hoge, PhD September 1 st, 2009

2 Contents 1 Acknowledgements 2 2 Project description 2 3 Working environment IDEA T Scanner Neurolens Theoretical concepts Effect of velocity on spin phase Flow compensation Phase contrast angiography Implementation FLASH.cpp sample Implementation of PCA sequence Preliminary results First scan session : Untriggered PCA acquisition Second scan session : PCA acquisition with ECG triggering Conclusion 13 8 References 14 1

3 1 Acknowledgements I would like to express gratitude to Professor Rick Hoge for this project offer and his integration to the lab team. Getting familiar with pulse programing has helped me understand practical aspects of MRI technique. Also, special thanks to Felipe Tancredi, master student at the Neurovascular Imaging Lab, for his constant support on both technical and theoretical aspects and his knowledge sharing in pulse sequence programming. 2 Project description L Unité de participation et d initiation à la recherche (UPIR) is an academic program from Polytechnique Montreal enabling undergraduate students to get familiar with research activities. Students are invited to collaborate a half day s work for 25 weeks with a Polytechnique teacher or anyone from the biomedical or nuclear institute. During this project, I had the opportunity to work with Rick Hoge s lab team. Professor Rick Hoge is the director of the Neurovascular Imaging Lab 1, a lab developing technology to image blood flow in the brain in order to study physiological regulatory processes during neural activation. The original goal of the project was to analyze the diffusional attenuation during global increases in cerebral blood flow. The objectives were to : 1. Use phase contrast angiography (PCA) sequence available to measure the blood flow in arteries and veins associated with primary motor cortex at rest and during execution of a motor task or during hypercapnia. 2. Perform numerical simulations with Matlab to predict effects of diffusion attenuation gradients on signal in such vessels. At the beginning of the project, we realized that the angiography package required to perform velocity measurements was not available on the scanner. The project goal was redefined and would then be to implement a PCA sequence using a FLASH template. Hence, the new project objectives became to : 1. Get familiar with MRI pulse sequence and object-oriented C++ development. 2. Implement PCA sequence from FLASH template. 3. Perform velocity measurements on the scanner. Table 1 presents in detail the time repartition of the project. Task description Hours Theoretical review 10 Familiarization with IDEA environment 25 Sequence programming 60 Scan test 5 Data analysis 5 Report writing 20 Total 125 Table 1: Time repartition 1 Neurovascular Imaging Lab Rick Hoge Ph.D. 2

4 3 Working environment The working environment provided the equipment required for sequence implementation, data acquisition and image processing. 3.1 IDEA IDEA stands for Integrated Development Environment for Applications. This framework was used for the development of MRI pulse sequence. It contains a shell environment used for sequence programming called the sequence development environment (SDE). This environment enables mutiple tasks such as 1. Sequence testing. 2. Protocol editing. 3. Timing table display. 4. etc. Several source code templates, for instance the FLASH sequence, were included in the software for development. These were useful as a starting point for the implementation of the PCA sequence T Scanner The images were acquired on a Siemens Trio system (3T). Scan tests were performed under the supervison of Carollyn Hurst, radiology technologist of the UNF. 3.3 Neurolens Neurolens is a visualization and analysis platform for quantitative physiological neuroimaging that provides fast image processing. Neurolens was used for flow quantification image analysis. 4 Theoretical concepts This section establishes the theoretical basis which is essential for a complete understanding of PCA sequence implementation. It describes the effects observed when imaging moving objects such as blood flow, and addresses the physical concepts under phase correction using the flow compensation technique. Finally, a discussion on PCA, which uses phase behavior of moving spin to encode velocities, is proposed. 4.1 Effect of velocity on spin phase The phase behavior of spins with constant velocity (as those found in a plug flow) exposed to a gradient magnetic field can be derived from the Newton s laws of motion. Let s define a spin with initial position, x 0, moving in the read encoding direction (ˆx) with constant velocity v x, exposed to a typical readout gradient waveform where 0 t 3τ as shown in Figure 1. x (t) = x 0 + v x t (1) During the application of a gradient magnetic field, Larmor precession becomes time dependent ω(t) = γb 0 + γgz (t). As a result, the phase accumulated by moving spin φ(t) = ω (t) dt varies as a quadratic function of time and doesn t come to zero at the echo time (t = 2τ). 3

5 This phase behavior during the rephasing lobe (τ t 3τ ) can be expressed in terms of stationary and velocity components (Figure 1) φ(t ) = φ s (t ) + φ v (t ) (2) where φ s (t ) and φ v (t ) are respectively position and velocity dependent φ s (t ) = γgx 0 t (3) with t = t 2τ and τ t τ. φ v (t ) = 1 2 γgv x ( t 2 + 4τt + 2τ 2) (4) Figure 1: Phase behavior of static and mobile spins during typical readout gradient application Solving Equation 2 at the echo time (t = 0) indicates that the phase acquired by moving spin is proportional to the velocity φ(t ) = φ v (0) = γgv x τ 2 (5) t =0 This demonstration can be extended to a laminar flow which can be decomposed over a short period of time and a tiny dot of space (pixel) as the sum of multiple plug flows at different velocities. To avoid non-zero phase at the echo, it is possible to add flow compensation gradients to the typical gradient waveform as discussed in the next section. 4.2 Flow compensation Flow compensation is a technique used to correct phase dispersion caused by motion or to reduce flow artifacts such as ghosting due to periodic flow. It is based on the principle of even-echo rephasing and consists in the addition of extra gradient lobes along the motion direction. Particular flow compensation waveform can be used to correct both constant velocity or accelerated spin. 4

6 One solution is here proposed to correct phase acquired by spins with constant velocity moving in the read encoding direction, as discussed in the previous section. For this scheme, two preparatory lobes G 1 and G 2 must be added prior to the readout gradient G. To facilitate the resolution, the duration τ of each three lobes is set (Figure 2). The third lobe added to the traditional readout gradients must ensure that phase is zero at echo time for both stationary and moving spins. For the stationary spins, this condition leads to the first equation on the zeroth moment M 0 of the gradient waveform G (t) which leads to M 0 (te) = ˆ te 0 G 1 t τ + G 2t 0 2τ τ G (t) dt = 0 (6) + Gt 3τ = 0 (7) 2τ G 1 τ + G 2 τ + Gτ = 0 (8) Zero phase at the echo for moving spins leads to the second condition on the first moment M 1 of G (t) leading to ˆ te M 1 (te) = v x G (t) dt = 0 (9) t 2 τ G G t τ τ + G t2 2 3τ 2τ = 0 (10) 1 2 G 1τ G ( 2 4τ 2 τ 2) G ( 9τ 2 4τ 2) = 0 (11) Solving this two-equation-two-unknown system guides to the appropriate gradient waveform { G 1 + G 2 + G = 0 (12) G 1 + 3G 2 + 5G = 0 which has for solution { G 1 = G G 2 = 2G Figure 2 presents the phase behavior as a function of time of both stationary and constant velocity spins in a velocity compensated readout gradient waveform. (13) 5

7 Figure 2: Phase behavior of static and mobile spins during flow compensated readout gradient application As predicted, phase comes to zero at the echo time for both stationary and moving spins, independently of the speed of flow. Sometimes, the second gradient amplitude ( 2G) cannot be performed, in which case the time application must be increased. Usually, velocity compensated sequences are designed to minimize the echo time to avoid T2 signal loss or flow acceleration effects. This demonstration addressed velocity compensation in the read direction, but the same rational reasoning can be used to obtain the gradient waveform for compensation in the slice selection direction. In this case, the zeroth and first moment of the slice selection gradient must be zero at the end of the slice select gradient, with t = 0 fixed at the center of the radio frequency pulse. Further development leads to a (G, 2G, G) gradient scheme. 4.3 Phase contrast angiography PCA uses the effect of motion on spin phase in order to encode velocities. Square bipolar pulses are added prior to the data collection to the flow compensated gradient scheme found in Figure 2. With an analysis similar to the one found in Section 4.2, it is seen that spin moving in the gradient axe develops a phase proportional to their velocity. At the end of the bipolar pulses, the phase φ acquired by moving spins becomes where τ stands for the duration of each two bipolar gradient lobes. φ = γgv z τ 2 (14) Note that there are other sources of phase alteration due to field inhomogeneities. To suppress these background phases, two images are collected in a standard PCA Kernel with an inversion of the polarity of the bipolar gradient lobes. The corresponding phase images are then subtracted and velocity can be extracted using φ = 2γGv z τ 2 (15) 6

8 In order to get proper velocity measurements, the range of phase must stand between π and π to avoid aliasing effects. This condition must be transposed to Equation 14 γgv z τ 2 < π In a PCA sequence, velocity encoding bipolar lobes are determined from a maximum velocity venc parameter set by the user venc = π /γgτ 2 For accurate velocity measurements, experimentator must set venc parameter nearest to the maximum velocity expected. Also it is essential to ensure that flow arises strictly perpendicular to the encoding plane to avoid partial volume effects or to underevaluate velocity. Velocity maps obtained with PCA sequences have found multiple application such as evaluation of blood volume in human vessel with 2D acquisition. Velocity maps can be used straightforwardly to determine the actual flow through a vessel ˆ F = v z da Rigourous blood flow quantification requires cardiac triggering and can lead to a good approximation of blood volume. A series of transverse images are generally collected during cardiac cycle across great vessels like the aorta or the vena cava. 7

9 5 Implementation This section describes the approach used for the implementation of the PCA sequence. 5.1 FLASH.cpp sample All implementations were achieved using the FLASH sample (Figure 3) provided with IDEA installation. This sample proposes a typical gradient echo sequence with multiple acquisition options (preparation pulses, reconstruction options, physiological triggering, etc.). GSlice GSliceSpoil GS GSliReph GPhase GPhaseRew GP GRead GReadSpoil GR GReadDeph Figure 3: Flash sample kernel diagram which consists in a standard 2D gradient echo with spoiler gradients added in the slice and read encoding directions The sample s sequence library provided four mandatory points implemented as C++ member functions which were slightly modified to perform PCA : 1. fseqinit : Set the hard limits of the sequence (maximum gradient amplitude, minimum rising time, etc.). 2. fseqprep : Verify if protocol is consistent, perform calculations before measurement. 3. fseqrun : Handle sequence timing, provide Image Calculation Environment (ICE) programs with information. 4. fseqcheck : Support the gradient overflow check. Next section describes succinctly the changes made in the sample source code for the PCA sequence. 8

10 5.2 Implementation of PCA sequence Before starting the implementation, the desired sequence kernel (Figure 4) was drawn to get a general view of the problem. GSlice GSFQOuter GSlice -GSFQInner GS GSFQInner -GSFQOuter GPhase GPhaseRew GPhase GPhaseRew GP GRFCOuter GRFCOuter GRead GReadSpoil GRead GReadSpoil GR GRFCInner GRFCInner Figure 4: PCA kernel diagram Comparing Figure 3 and Figure 4 lead to the following modifications in the FLASH sample source code : 1. In fseqinit : Allow two images calculation (There are two different acquisitions for each phase step). 2. In fseqprep : Create and prepare flow quantification/compensation gradients in the slice selection and read encoding directions. 3. In fseqprep : Adapt Echo Time (TE) calculation to incorporate new gradient objects. 4. In fseqrun : Adapt sequence timing. To allow two images calculation, sequence contrast parameter was set to two as in a Double Echo sequence. This procedure ensured Image Calcul Environment (ICE) programs to expect two different set of measurement data headers (Mdh) and reconstruct two images. Flow quantification was performed in the slice selection direction and read encoding direction was flow compensated to avoid phase alteration caused by non-perpendicular field of view (FOV) positioning. As discussed in the theoretical section, flow compensation requires a (G, 2G, G) gradient scheme. Since gradient calculation is generally restricted by amplitude and minimum timing, it can be arduous 9

11 to get the perfect compromise between maximum amplitude and minimum TE. Implementation of such optimization from scratch could have been delicate, but fortunately flow quantification and compensation functions were supported in the sequence utility library. The IDEA library contained two functions for both flow quantification and compensation : 1. fsugslflowcalc : Function returning the appropriate bipolar gradient pair characteristics to fill all the time available before TE (Figure 5). 2. fsucalcshortestflowcomp : Calculates a gradient pair in the shortest possible time. These functions require general information about the gradient to be compensated and return the pair of compensating gradients. Functions could be called with multiple variable input or with pointers to the gradient pulses. Function fsugslflowcalc was used in the implementation. One of the key input parameters of fsugslflowcalc was the maximum velocity encoded, venc. For full flow compensation, venc had to be set to 0. For flow quantification gradients calculation, this parameter had to be modified in the protocol by the user. There were several ways to enable venc parameter adjustement in the user interface. For learning purposes, the sequence special card, which is specially designed for sequence programmers, was used. A special venc parameter could be find in this sub-card of the sequence card for the expected maximum velocity in the slice direction. This venc could admit values from 0 to 5000 mm /s with increment of 100 mm /s. F0S R0S R1 F1 ΔG GS G0 G1 G2 ΔG R2 F2 Time available Flow quantification bipolar Gradient ΔG ΔG Figure 5: Approach behind flow quantificaton gradient calculation with fsugslflowcalc Flow sensitive gradient pair G are added to the flow compensated gradients G 1 and G 2. A greater venc parameter leads to a smaller G. The user has to be aware that there is a minimum 10

12 venc available in the scanner restricted by the maximum gradient amplitude. If flow quantification gradient exceeds these hard limits all gradients are automatically set to 0 for safety purposes. All flow quantification and compensation gradient objects were incorporated in the timing table to obtain the desired sequence kernel. The new gradient durations were also included in the time available calculation to calculate the proper TE. All the lines added in the original sample code can be found in the PCAngio.cpp source code and are commented with \\DOMINIQUE to facilitate research. 6 Preliminary results Two scan sessions were organized on the MRI platform during the project to confirm that the implementation could produce results. 6.1 First scan session : Untriggered PCA acquisition This session was performed the 12 th March 2009 on a 22 year-old male subject. The test purpose was to ensure that the PCA sequence could generate two different phase images with proper bipolar gradient inversion. Plane of study was positioned around the carotid junction level using a 2D multislice FLASH acquisition. Magnitude and phase reconstruction images were obtained with this set of parameters : T E = 10ms, T R = 35ms, F lipangle = 35, SliceT hickness = 5mm, M atrixsize = Maximum velocity was set to venc = 1500 mm/s to avoid aliasing. Table 2 presents the results. Table 2: PCA images with V max set to 1500 mm /s (Left : Modulus ; Center : Positive bipolar acquisition ; Right : negative bipolar acquisition) The sequence implemented could be used to reconstruct two different phase images with opposite flow encoding bipolar gradients. Both phase images revealed that there was an obvious phase pattern caused by the magnetic field inhomogeneities. This field pattern was not affected by the gradient inversion. The phase images were subtracted after the scan session using Neurolens to spot phase modifications in the blood flowing regions. In Table 3, the image to the left shows the basic subtraction, the middle one shows the subtraction with adapted intensity level to mask noise, and the right one shows the superposition of the second image and the modulus image. 11

13 Table 3: PCA phase images subtraction with V max set to 1500 mm /s With appropriate intensity adjustments as shown in the third image, at least two blood vessels with opposite flowing directions were vizualised. On the other hand, there was a lot of flow artifacts caused by the blood flow pulsativity and possibly the plane orientation which could have not been strictly perpendicular to the vessels. These artifacts caused periodic repetition of vessel regions along phase encoding direction corrupting dramatically the velocity maps. 6.2 Second scan session : PCA acquisition with ECG triggering To remove flow artifacts, an other scan test was performed the 29 th May 2009 on a 21 year-old female subject. The test purpose was to certify the PCA sequence implemented could handle ECG triggering. Plane of study was positioned around the carotid junction level using a 2D multislice FLASH acquisition. Magnitude and phase reconstruction images were obtained with the same set of parameters defined in Section 6.1. Maximum velocity was fixed to venc = 1500 mm/s and venc = 1000 mm/s to observe how phase varied with bipolar gradient amplitude. Scan session was performed with prospective ECG triggering. Acquisition window was reduced in order to acquire one k-space line per R wave. Table 4 shows the results for venc = 1500 mm/s. Table 4: PCA images with venc set to 1500 mm /s (Left : Modulus ; Center : Basic subtraction ; Right : Subtraction with adapted intensity) With the triggered method, phase variations were much more condensed in the expected vessel regions. Also, ghosting along the phase encoding direction due to flow pulsativity was reduced. To verify the dependence between venc and phase accumulation, another set of images was obtained 12

14 with venc = 1000 mm/s. Table 5 displays the maps obtained with the same intensity adjustments as those used in the previous Table. Table 5: PCA images with venc set to 1000 mm /s As predicted by the theory, subtracted phase images revealed a greater phase accumulation in the vessel regions with venc = 1000 mm/s. The relation among flow encoding gradient amplitude, phase accumulation and velocity was observed practically. 7 Conclusion To conclude, this challenging project was an excellent opportunity to get more familiar with sequence programming and to see how physics principles could be integrated in a source code. The final version of the PCA sequence is not ready to perform accurate velocity measurements, but it can still be used to observe practically how moving spin exposed to bipolar gradients can accumulate a phase term. Optimization of the sequence could include implementation of flow compensation gradient lobes in the phase encoding direction to avoid mismeasurements due to inacurate plane of study positioning. Calculation of such gradients was not supported in the IDEA library and would have to be implemented from scratch. Also, ICE programs could be modified to perform the basic subtraction of phase images and the velocity map normalization. 13

15 8 References BERNSTEIN M. A. et al. Handbook of MRI pulse sequences. Elsevier, p. HAACKE E. M. et al. Magnetic Resonance Imaging. New-York : Wiley-Liss, p. HOA D. et al. L IRM pas à pas. Paris : Campus Medica, p. MATHIEU D. Rapport de stage. Grenoble : Institut des Neurosciences, 42 p. POPE J. M. et YAO S. Quantitative NMR Imaging of Flow. Conceptis in Magnetic Resonance, 1993, vol. 5, issue 4, pp IDEA Manual. Integrated Development Environment for Applications p. 14