HW6: MRI Imaging Pulse Sequences (7 Problems for 100 ps) GOAL The overall goal of HW6 is o beer undersand pulse sequences for MRI image reconsrucion. OBJECTIVES 1) Design a spin echo pulse sequence o image a poin-like objec (for esing purposes). 2) Image a square-like objec wih differen conras. 3) Image a mysery objec wih differen conras. Your working code will be able o produce T1, T2, or PD weighed images by adjusing he spin echo ime TE and he pulse repeiion inerval TR. DESCRIPTION The basic flow char of he MATLAB-based MRI simulaor is he following: STEP 0: Compue imporan parameers STEP 1: Iniialize he bulk magneizaion. STEP 2: Apply he 90 pulse. STEP 3: Apply phase encode (Gx and Gy) STEP 4: Allow M o evolve unil he 180 pulse. STEP 5: Apply he 180 pulse. STEP 6: Allow M o evolve unil he sar of readou. STEP 7: Apply readou (Gx) STEP 8: Repea Seps 1 o 7 as many imes as necessary o sweep Fourier space. 1
Assumpions 1) The saic polarizing field B o = 1.5 Tesla poins along he z-direcion. 2) o 42.57MHz / Tesla 2. 3) The objec is assumed o be a slice. Therefore, you will no use any selecive exciaion or refocusing (G z ). The image size is 64 x 64 pixels, where dx = dy = 1 mm. 4) All magneic fields are specified in he roaing frame x y z. You mus properly se he componens of he effecive magneic field B eff = (B eff,x, B eff,y, B eff,z ) during he 90 pulse, phase encode, 180 pulse, and readou. 5) The ime sep for he simulaion is d = 1/16 ms. 6) The 90 pulse is applied a = 0 for a duraion d (e.g. one ime sep) along he y axis. 7) The phase encode sars immediaely afer he 90 pulse. The duraion of he encode is Tencode = 4 ms. 8) The 180 pulse duraion is applied a = TE/2 for a duraion d (e.g. one ime sep). 9) The readou is Tread = 8 ms. Remember he spin echo ime TE occurs in he middle of readou! RF 90 180 Gx Gy T ENCODE T READ S() = 0 = TE/2 = TE Fig. 1 Timing diagram for he MRI spin echo pulse sequence. 2
Some oher commens: 1) When he load command is used in he program, i will impor hree 64 x 64 elemen marices called PD, T1, and T2. Remember ha he objec is a 2-D marix consising of 64 x 64 pixels. Each objec pixel has is own value of PD, T1, and T2. Therefore, PD is a 64 x 64 elemen marix. Same for T1 and T2. 2) The magneizaion M is a vecor, so i has hree componens M = (M X, M Y, M Z ). T2 T1 PD Remember ha M depends on x and y. Therefore, he x componen of M is a 64 x 64 elemen marix. Same hing for he oher wo componens. In MATLAB, all hree marices are combined ino a single 3-D marix called M. This can be hough of as a book. The firs, second, and hird pages of his book correspond o he M X, M Y, and M Z marices. 3) In STEP 1, he iniial magneizaion is he value of M Z jus before he 90-pulse is applied. M X M Y M Z In class, we discussed ha M Z () = M 0 (1-exp ( - / T1 )). For MRI, we apply he 90-pulse a a regular ime inerval TR. Therefore, he value of M Z jus before he 90-pulse is applied is M 0 (1-exp ( -TR / T1 )). Noe ha M 0 is he magneizaion value afer full recovery, which depends on proon densiy PD. For his assignmen, we will use he simplified definiion M 0 = PD. Iniial M Z Therefore, your MATLAB program should define he iniial value of M Z as PD (1-exp ( -TR / T1 )). Remember ha PD and T1 are 2-D marices! M Z TR TR TR 4) Remember ha your phase encode involves B eff,z = G X X + G Y Y while readou involves only B eff,z = G X X. Keep in mind ha X and Y are 2-D marices conaining he (x,y) coordinaes of each pixel. Also remember ha G Y is a VECTOR, bu you only need ONE value of G Y for each row in Fourier space. 3
PROBLEM 1 a) Compue he values for B90 and B180 in unis of Tesla. Show all work. Hin: You should ge B90 = 9.3963 x 10-5 Tesla. b) Specify B90 and B180 in vecor forma. For example, B eff = (B90, 0, 0) applies he B90 along he x -direcion in he roaing frame. c) Make separae skeches of he vecor B eff for he 90 and 180 pulses. Include he vecor orienaion of he magneizaion before and afer boh pulses (in he roaing x y z frame). PROBLEM 2 a) Compue he values for Gx and dgy in unis of Tesla/mm. Hin: You should ge Gx = 2.936x10-6 Tesla/mm. and dgy = 9.176x10-8 Tesla/mm. b) Specify all hree componens of B eff during phase encode. Hin: Remember ha we are working in he roaing frame, so you do NOT include he big B 0 field. c) Do he same for readou. PROBLEM 3 Consider a single voxel (sands for volume pixel ) a (x, y) = (8, 4) mm. You can model his objec as a poin impulse locaed a he appropriae posiion. a) Calculae he 2-D Fourier ransform of he objec. You can use sandard Fourier ransform properies and ables. Hin: You should ge F(u,v) = exp(-j2(8u+4v)). b) Skech he real par of F(u,v) over a 2-D region from u = -0.5 o +0.5 mm -1 and v = -0.5 o +0.5 mm -1. Hin: See page 2.4a of he lecure noes. 4
PROBLEM 4 You mus fill in he key pars (i.e. TE, TR, B90, ec.) of he MATLAB emplae program. The following MATLAB files are available on he course websie: 1) A MATLAB emplae for he simulaor called MRI_Imaging_simulaor_emplae.m. 2) A MATLAB funcion MRI_Evolve_M.m ha evolves he magneizaion according o he applied magneic fields for a specific number of ime seps. 3) A MATLAB funcion MRI_Bloch.m ha is used by he MRI_Evolve_M.m funcion. 4) A daa se for a single waer spin MRI_daa_single_spin1.ma conaining T1, T2, gamma, and PD. 5) A daa se for a square objec MRI_daa_square.ma. 6) A daa se for a mysery objec MRI_daa_mysery.ma. a) Reconsruc he image of a single waer spin using TE = 25 ms and TR = 3500 ms. Se case_num=1 in he beginning of your code. Submi he image. You should ge an image of a single whie pixel a (x,y)=(8,4) surrounded by a black background (see Fig. 2). If you do no ge his image, hen your code is no working properly. Image of poin-like objec Real componen of daa Imag componen of daa 30 0.4 0.4 20 0.3 0.3 10 0.2 0.1 0.2 0.1 y (mm) 0 v (1/mm) 0-0.1 v (1/mm) 0-0.1-10 -0.2-0.2-20 -0.3-0.3-0.4-0.4-30 -30-20 -10 0 10 20 30 x (mm) -0.5-0.4-0.2 0 0.2 0.4 u (1/mm) -0.5-0.4-0.2 0 0.2 0.4 u (1/mm) Fig. 2: The reconsruced poin-objec (lef) and raw daa (middle and righ) should look like he images shown above. The middle figure should resemble your skech from Problem 3! b) Submi images of he real and imaginary componens of he daa. Explain he appearance of he wo componens. Are hey idenical? NOTE: Once your code works for his poin-objec, Problems 5 and 6 will go very quickly. 5
PROBLEM 5 a) Reconsruc he image of he square objec wih TE = 25 ms and TR = 3500 ms. The square objec is whie brain maer, while he background is waer. Submi he image. Wha ype of weighing is he resuling image? NOTE: The proon densiy, T2, and T1 values of whie maer, gray maer, and cerebrospinal fluid are shown below. Tissue Type Relaive PD T2 (ms) T1 (ms) Whie maer 0.61 67 510 Gray maer 0.69 77 760 Cerebrospinal fluid 1.0 280 2650 b) Reconsruc an image of he square objec wih TE = 25 ms and TR = 500 ms. Submi he image. Wha ype of weighing is he resuling image? Explain differences beween he wo images. PROBLEM 6 a) Now implemen hree differen pulse sequences o reconsruc images of he mysery daa. Use he TE and TR values shown o he righ. Submi all hree hree images. Sequence TE (ms) TR (ms) 1 25 500 2 25 3500 3 100 3500 b) Wha ype of weighing is performed by each sequence? For a paricular sequence, idenify he brighes and faines porions of he image. Wha can you conclude abou he issue properies of hese porions? 6
PROBLEM 7 v Echo planar imaging (EPI) is an MRI echnique allowing fas image acquisiion. An enire image can be acquired in less han 30 ms, as opposed o he usual duraion of several minues. This is paricularly useful in imaging dynamic evens (i.e. blood flow in he brain). The enire Fourier space (also called k-space) is acquired in a single sho acquisiion. Therefore, daa acquisiion for an enire image involves: (1) A single 90 pulse followed by (2) An iniial phase encode followed by (3) G x and G y waveforms ha produce a zig-zag Fourier rajecory shown o he righ. The following assumpions can be made: 1) B 0 = 3 Tesla and /2 = 42.58 MHz/Tesla for all issue. Finish Sar u 2) Boh G x and G y are T read /2 in duraion during he iniial phase encode. 3) During he zig-zag pah, he readou ime for each row is T read = 300 s. 4) During he zig-zag pah, each G y pulse is 30 s in duraion. 5) No 180 pulse is used his is a gradien echo EPI pulse sequence. 6) Oupu images are 64 x 64 pixels wih a pixel spacing of x = y = 4 mm. (a) Compue G x and G y during he iniial phase encode (i.e. before he zig-zag readou is performed). Express your answer in Gauss/cm. (remember ha 1 Tesla = 10 4 Gauss). Hin: You should ge G x = -1.96 G/cm and G y = -1.96 G/cm. (b) Compue he ampliude of G x and dg y during he zig-zag readou (unis = Gauss/cm). Hin: You should ge dg y = 0.31 G/cm. (c) Skech he RF, G x, G y, and G z fields for your pulse sequence. Obviously, you do no need o skech he enire G x and G y waveform jus skech a porion of he waveforms ha span he firs FOUR rows of he zig-zag pah. You can assume he readou sars immediaely afer he iniial phase encode. 7