Ho+△Ho Pulse Data collection window Transmit/Receive Coil IGURE 116.3 Concept of magnetic resonance imaging. The static magnetic field Ho has a gradient such that excitation at frequency fo excites only the plane P Gradient G, in the y direction is applied for time tyi causing a phase shift along the ydirection Gradient G in the x direction is applied for time t, causing a frequency shift along the x direction. Repetition of this process for different yi allows the receive coil to pick up a signal which is the two-dimensional Fourier transform of the magnetic resonance effect within the slice. f o=YH where fo is the Larmour frequency, y is the gyromagnetic ratio which is a property of the atomic element, and the magnitude of the external magnetic field. For example, given a gyromagnetic ratio of 42. 7 MHz/tesla for hydrogen and a field strength of I tesla(10 kilogauss), the Larmour frequency would be 42.7 MHz, which falls into the radio frequency range The magnetic resonance effect occurs when nuclei in a static magnetic field H are excited by a rotating magnetic field H, in the x,y plane, resulting in a total vector field M given by M=HZ+ H,(x coS Oo t+y sin @, t) pon cessation of excitation, the magnetic field decays back to its original alignment with the static field H, emitting electromagnetic radiation at the Larmour frequency, which can be detected by the same coil that Imaging As shown in Fig. 116.3, one method for imaging utilizes a transmit/receive coil to emit a magnetic field at uency fo which is the Larmour frequency of plane P. Subsequently, magnetic gradients are applied in the y and x directions. The detected signal during the data collection window can be expressed as ∫J4xy)ep-Gx+x,由 where s(x,y)represents the magnetic resonance signal at position(x,y)(GnG)are the x and y gradients, t is time within the data collection window, ty is the y direction gradient application times, and y is the gyromagnetic ratio. The two-dimensional spatial integration is obtained by appropriate geometry of the detection coil. Collecting a number of such signals for a range of tr, we can obtain the two-dimensional function S(t, t) Comparing this to the two-dimensional Fourier transform relation F(u,v)=f(x, y)exp[-i2n(ux vy )]dx dy e 2000 by CRC Press LLC© 2000 by CRC Press LLC f0 = gH where f0 is the Larmour frequency, g is the gyromagnetic ratio which is a property of the atomic element, and H is the magnitude of the external magnetic field. For example, given a gyromagnetic ratio of 42.7 MHz/tesla for hydrogen and a field strength of 1 tesla (10 kilogauss), the Larmour frequency would be 42.7 MHz, which falls into the radio frequency range. The magnetic resonance effect occurs when nuclei in a static magnetic field H are excited by a rotating magnetic field H1 in the x,y plane, resulting in a total vector field M given by M = H z + H1(x cos w0 t + y sin w0t) Upon cessation of excitation, the magnetic field decays back to its original alignment with the static field H, emitting electromagnetic radiation at the Larmour frequency, which can be detected by the same coil that produced the excitation [Macovski, 1983]. Imaging As shown in Fig. 116.3, one method for imaging utilizes a transmit/receive coil to emit a magnetic field at frequency f0 which is the Larmour frequency of plane P. Subsequently, magnetic gradients are applied in the y and x directions. The detected signal during the data collection window can be expressed as where s(x,y) represents the magnetic resonance signal at position (x,y) (Gx,Gy) are the x and y gradients, tx is time within the data collection window, tyi is the y direction gradient application times, and g is the gyromagnetic ratio. The two-dimensional spatial integration is obtained by appropriate geometry of the detection coil. Collecting a number of such signals for a range of tyi, we can obtain the two-dimensional function S(tx,ty). Comparing this to the two-dimensional Fourier transform relation FIGURE 116.3 Concept of magnetic resonance imaging. The static magnetic field H0 has a gradient such that excitation at frequency f0 excites only the plane P. Gradient Gy in the y direction is applied for time tyi, causing a phase shift along the y direction. Gradient Gx in the x direction is applied for time tx, causing a frequency shift along the x direction. Repetition of this process for different tyi allows the receive coil to pick up a signal which is the two-dimensional Fourier transform of the magnetic resonance effect within the slice. S t t s x y i G xt G yt dx dy x yi x x y yi ( , ) ( , ) exp[– ( )] – – = + • • • • Ú Ú g Fuv ( , ) f(x, y) exp[–i (ux vy )]dx dy – – = + • • • • Ú Ú 2p