1. Introduction o Microscopic property responsible for MRI Show and discuss graphics that go from macro to H nucleus with N-S pole

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1 Page 1 Very Quick Itroductio to MRI The poit of this itroductio is to give the studet a sufficietly accurate metal picture of MRI to help uderstad its impact o image registratio. The two major aspects are (1) the ability of MRI to produce more tha oe type of image of the same aatomy ad (2) the iheret geometrical distortio i MRI. This is a qualitative discussio oly. Detailed quatitative courses are available, e.g., BME 395, Special Topics: Magetic Resoace Imagig by Aderso. This itroductio is based o a o-lie resource: This is a electroic book writte by Joseph P. Horak. His biosketch is at the begiig. This book has roughly 1000 times as much iformatio as we eed. My itroductio utilizes some graphics ad aimatios that are there. 1. Itroductio o Microscopic property resposible for MRI Show ad discuss graphics that go from macro to H ucleus with N-S pole 2. [SKIP] 3. Spi Physics o Spi Packets: Show last two graphics (lots of spis oe M vector) o Pulsed Magetic Fields 1 st ad 2 d graphic shows RF coil (oly oe, but all scaers have two). 5 th graphic shows M spiralig dow to the XY plae from a 90-deg pulse o Bloch Equatios: The oly graphic shows them. T1 ad T2 gover how log the Mxy vector is. This is the oly compoet of the vector that produces a sigal. 4. [SKIP] 5. [SKIP] 6. Imagig Priciples o Itroductio: 1 st ad 2 d graphics: all sigal at oe frequecy o Magetic Field Gradiet: oly graphic shows gradiet (o frequecy plot) o Frequecy Ecodig: 1 st ad 2 d graphics: sigals at two frequecies o Slice Selectio 1 st graphic shows perfect slice selectio 3 rd graphic shows slice selectio whe profile is ot rectagular (first problem of geometrical distortio it is really a covolutio) 7. Fourier Trasform Imagig Priciples o Phase Ecodig Gradiet 1 st graphic shows three spis precessig at same frequecy 2 d graphic shows them while a phase-ecodig gradiet i o

2 Page 2 o 3 rd graphic shows them after the phase-ecodig is tured off all precessig at the same frequecy but with differet phases FT Tomographic Imagig Graphics 1 through 6 show a typical pulse sequece (do t show the 7 th yet). It is good ow to start a ew browser, leave this oe showig the pulse sequece, ad advace oly the secod oe. 8 th ad 9 th graphics (just after the Table labeled Gradiet, which skip) shows slice selectio 11 th graphic shows a 3 by three array of spis precessig at the same frequecy after slice selectio but before other gradiets are o 12 th graphic shows the situatio while the phase-ecodig gradiet is o 13 th graphic shows the situatio after the phase-ecodig is off 14 th graphic shows the situatio while the frequecy-ecodig gradiet, also kow as the readout gradiet is o Back to 7 th graphic, which shows the pulse sequece for multiple phase ecodigs ( P) For each of the three phase ecodig gradiets G m, m = 1,2,3, we sample the sigal at three chose times t1, t2, t durig readout, givig a total of 9 samples. The time t 3 is ( R) usually measured from the ceter of the iterval durig which the readout gradiet, G, is tured o, so there are both positive ad egative time values. There are two sigals received simultaeously with two RF coils or chaels, ad by meas of mathematical operatios o these two sigals, it is possible to costruct the MR image.

3 Page 3 To see how this is miracle is performed, we represet these two sigals as a complex umber with oe chael desigated as the real chael ad oe the imagiary chael. The received sigal is the sum of sigals cotributed from each spi packet, which have oe compoet cotributig to each chael. We write the two compoets of each idividual sigal also as the real ad imagiary part of a complex umber. Here is the math. The sigal produced at sample time by a sigle spi packet at positio k,l with the impositio of a phase-ecodig gradiet G m is proportioal to the compoet of the spi packet s magetic vector that is lyig i the x-y plae at that time, which, like ay complex umber, has the form ( ) ( ) i ( m,, k, l) Mm, k, l = M k, l e θ, (1) It ca be show that, by correctly choosig the three phase-ecodig gradiets, the readout gradiet, ad the three samplig times, we have the followig simple formula for the complex agle: θ ( mkl,,, ) 2 π ( mk/3 l/3) = + (2) So the sigal produced at that time by that spi packet has the form (,, ) (,) m m, i2π( km 3+ l 3) s k l t = c M k l e (3) The scaer s receiver coil receives the sum of all ie sigals, so the received sigal has the form 3,3 Sm( t) = sm( k,, l t) (4) k= 1, l= 1 where S is the total sigal, s is the sigal from oe spi packet, ad all sigals are complex. It is easy to geeralize to larger arrays of spi-packets. If we had a K by L array of spi packets (typical values are K = 256 = L), the we d replace the 3,3 by K,L i the sum. Agai by correctly choosig the gradiets ad the times, we fid that m (,, ) (,) i2π( km K+ l L) s k l t = c M k l e (5) Therefore, KL, Sm( t) = c M( k, l) e k= 1, l= 1 i2π( km K+ l L) (6)

4 Page 4 From Eq. (6) it is possible to determie each value of cm( kl, ) image., which gives us the MR Eq. (6) is the Fourier trasform of the 2D fuctio cm( kl, ). So, by takig the iverse Fourier trasform of S ( t ), we get a image of M ( kl, ) : m KL, cm( kl, ) = image ( kl, ) = Sm( t) e m= 1, = 1 + i2π( km K+ l L) (7) TR ad TE TR is the time that elapses betwee repetitios of the pulse sequece from oe phaseecodig gradiet to the ext. TE is the time elapsed betwee the tippig of the spis durig excitatio to the begiig of sigal collectio. 8. Basic Imagig Techiques o Image Cotrast: I iclude this because of the table showig T1 ad T2 values ad example images (ear the ed of this sectio) Cosider two tissue types, say gray matter of the brai ad white matter. Let M a ( kl, ) ad M (, ) b kl be their respective magetic vector legths at equilibrium. Because these legths are proportioal to spi desity, ρ, ad because of temporary chages i these legths durig imagig that deped o the iteractios betwee the spi-packets ad the electros i the surroudig molecules ad the iteractios amog the spi-packets themselves, the values of these vector legths durig the acquisitio of the sigal deped o ρ, TR, ad TE. The strogest depedece is summarized by two parameters for each tissue type: T1 ad T2. These parameters appear i the Bloch equatios, which gover all the behavior that we ve described here. Example values are give by Horak i Chapter 8, i the sectio called Image Cotrast i a table ear the ed. By adjustig TR ad TE it is possible to chage the relative brightess of these tissues i the image. It is this adjustmet that makes it possible for MRI to produce differet images of the same aatomy. Examples of the chages ca be see i the table i that same sectio called Spi-Echo Images. For the most commo sequece, which is a Spi-Echo the itesity of the sigal has the form:

5 ( ) ρ ( )( ) image kl, c kl, 1 e e Page 5 TR /T1 = TE /T2 (8) where ρ ( kl, ) = cm( kl, ) is the spi desity or proto desity, ad c ad c are costats that deped o the scaer amplificatio system. This relatioship alog with those for other popular sequeces, such as Iversio Recovery ad Gradiet Recalled Echo are give i this same sectio (i.e., Basic Imagig Techiques/Image Cotrast). Note that for values of T1 ad T2 that reduce the magitude of the image, the sigal-tooise ratio suffers, ad the images look oisy. Three parameters affect the image itesity i Eq. (8): spi desity, T1, ad T2. It is possible to emphasize the effect of oe or two of these parameters by chagig the TR ad TE of the pulse sequece. Because most tissue is made primarily of water, the spi desity is quite similar for most tissues, but T1 ad T2 may be quite differet. Thus, sequeces are typically chose to emphasize T1 ad/or T2 differeces. The two most commo modes are give below. Note that the appearaces are relative. The brightess is adjusted o the scree so that there is visible structure, so for three levels of itesity i the raw image, the middle oe is always gray: T1 weighted images: TR is short (e.g., 500 ms) ad TE is short (e.g., 20 ms): o Gray matter appears gray o White matter appears white o CSF appears dark T2 weighted images: TR is log (e.g., 2000 ms) ad TE is log (e.g., 80 ms) o Gray matter appears gray o White matter appears dark gray o CSF appears white Proto-desity weighted images: TR is log ad TE is short o Gray matter appears white o White matter appears gray o CSF appears gray The Matlab script, TR_TE_effect explores the behavior of Eq. (8) as T1 ad T2 are varied for reasoable values of T1 ad T2 for gray, white, ad CSF. The values for gray ad white come from a paper i RadiologyI that plot the regios of T1-weightig, T2- weightig, ad proto-desity weightig are show. The images i Horak s Chapter 8, Image Cotrast, Spi-Echo Images show examples. They agree well with the Matlab script. Spi-Echo versus Gradiet-Echo The huma body becomes magetized whe it is placed ito a magetic field, ad the result is a spatial variatio i the field that was ot iteded. A spatially varyig field is said to be ihomogeeous ad the ihomogeeity of the field has a very oticeable effect. Because of variatio of the field across a spi packet, spis withi the spi packet

6 Page 6 will ot all precess at the same rate. As a result, they will get out of phase with each M kl, of the other a processes called dephasig. Dephasig causes the size ( ) magetic vector for the packet to be reduced i some cases to zero! As a result, after image recostructio, packets that should appear bright will appear dim or black. A solutio to this problem of lost sigal due to field ihomogeeity is the spi-echo acquisitio techique. I this techique, a RF pulse is applied at the time half way betwee slice selectio ad the ceter of the readout iterval. This pulse is set so that it that will rotate all the spis by 180 about a axis lyig i the xy plae. Thus, they rotate out of the xy plae ad back ito the xy plae. The result is that, after the spis withi each packet have dephased for a time, they the re-phase for the same time ad the sigal is restored. Thus, this additioal pulse is alterately called the 180-degree pulse or the rephasig pulse. This rephasig idea was discovered by accidet before MRI came alog, whe people were usig magetic resoace o small samples. As i MRI, they applied a excitatio pulse ad the they measured the sigal that came back. Ulike i MRI, they did ot apply ay gradiets, ad they moitored the sigal the etire time from iitial excitatio whe it was at its peak util the sigal died out. By accidet, they foud that, if they applied a pulse that was twice as strog as the optimum excitatio pulse (evetually revealed to be a 180-degree pulse ad 90-degree pulse, respectively) at a time T after the excitatio, the eve if the sigal had died out completely, the sigal would icrease to a peak at a time T after the 180-degree pulse. They called the secod peak the echo or spi-echo ad soo figured out that it was caused by rephasig. As a result, MRI images acquired with a rephasig gradiet are called Spi-Echo images. Images acquired without a rephasig gradiet also have a echo. That echo is caused by a rephasig gradiet (as opposed to a rephasig pulse). Rephasig is ecessary because durig the time over which the slice selectio gradiet is applied spis withi a packet get out of phase with each other because the gradiet causes the field to vary across the packet. As i the case described above whe the field is perturbed by the magetizatio of the patiet, this gradiet cotributes to field ihomogeeity. However, a differece is that this is cotrolled homogeeity, ad its effect ca be udoe by meas of a opposite homogeeity. After the slice-selectio gradiet is applied, a secod gradiet i the opposite directio is applied resultig i a rephasig. This rephasig gradiet is used i Spi-Echo images ad o-spi echo images, but it is metioed oly i the ame of o-spi-echo images. Such images are called Gradiet-Echo images. Despite this echo, the loss of sigal due to the compoet of ihomogeeity caused by magetizatio of the patiet is still there. As a result the itesity ca be reduced cosiderably below that give by Eq. (8). The effect ca be approximated by replacig T2 i that equatio by a smaller umber. The smaller umber is called T2* (proouced T2 star ), ad i regios were the ihomogeeity is larger the differece betwee T2 ad T2* is larger. Thus, for gradiet-echo images, we have the followig equatio: TR/T1 ( ) ρ ( )( ) image kl, c kl, 1 e e TE/T2* = (9)

7 Page 7 I regios where the ihomogeeity is larger T2* is smaller: Gradiet-Echo (GE) images are ofte acquired with a excitatio pulse that tips the magetic vector of the spi packets by less tha 90 degrees. The image itesity is smaller, but the sigal regeerates more quickly, makig it possible to acquire images more quickly. The trade-offs are that GE images ca be acquired more quickly, but because there is o rephasig pulse, TE must be kept very short. Therefore, it is ot possible to acquire T2-weighted images with GE. Furthermore, because there is a loss of sigal, the sigal-to-oise ratio will i geeral be smaller, ad that effect is made stroger i images with smaller excitatio agles. There is a lot more to MRI! This itroductio gives you a basis to start studyig MR imagig, but it barely scratches the surface of the MRI field. There are may other acquisitio methods i additio to the basic Spi-Echo ad Gradiet-Echo. A method, which is i fact quite old, but has bee popularized over the last 10 years is echo-plaar imagig This method makes it possible to reduce the acquisitio time for a MR image volume from a miute or two to a couple secods albeit with may artifacts ad reduced sigal-to-oise. Acosequece of the magetizatio of the huma body ot metioed above is geometric ad itesity distortio. There are methods to deal with these problems, icludig origid registratio approaches. There are hardware optios i particular hardware that permits so-called parallel acquisitio that make it possible to acquire images more quickly, albeit with a sacrifice i sigal-to-oise, there are chages i T1 ad T2 due to chages i the stregth of the maget, there are effects from motio of the head that cause artifacts ad methods to reduce those artifacts, there are effects from motio withi the body blood flow primarily that allow MRI to detect it. There are may, may more effects, problems, approaches, ad acquisitio techiques. The varieties of problems ad solutios that fall uder the ame MRI are probably edless.