Spatial Encoding: Sub mm from meter sized RF y x y . . z x Excitation: rotating frame y x To Receiver Detection: . RF detection coils z . To Receiver Problem: RF coils are sensitive to transverse component of How do we localize to a spatial location when RF field is sensitive to entire volume?
Field diagram Simplified Drawing of Basic Instrumentation. Body lies on table encompassed by coils for static field Bo, gradient fields (two of three shown), and radiofrequency field B1. Image, caption: copyright Nishimura, Fig. 3.15
Gradient Fields The gradient field is the last magnetic field we have to discuss. - key for imaging - Paul Lauterbur Gradient coils are designed to create an additional B field that varies linearly across the scanner as shown below when current is driven into the coil. The slope of linear change is known as the gradient field and is directly proportional to the current driven into the coil. The value of Bz varies in x linearly. Bz slope = Gz Bo Whole Body Scanners: |G| = 1-4 G/cm (10-40 mT/m) Gz can be considered as the magnitude of the gradient field, or, if you like, as the current level being driven into the coil. z
Putting it all together: The Bloch equation Sums of the phenomena precession, RF excitation transverse magnetization longitudinal magnetization Changes the direction of , but not the length. These change the length of only, not the direction. includes Bo, B1, and
Review: Cosine Theorem (What is a mixer? ) - Consider a pulse A(t) that is multiplied by cos(ot). This is called modulation . A(t) is called the envelope function. o is the carrier frequency. Mixer A(t) cos(ot) A(t) cos(ot) B1(f) Frequency response of RF pulse o = 2fo fo f -fo
Selective Slice Excitation Lets consider 2D imaging Slice excitation or selective excitation We first spoke of B1(t) as a rectangle, an on/off pulse, a) Now modulate the carrier cos(ot) by B1(t) where B1(t) is a sinc . F.T. B1(t) Mixer B1(t) cos(ot) B1(t) cos(ot) B1(f) -fo fo f Create a circularly polarized field
Slice Selection Simultaneously, we apply a gradient Gz. This creates a mapping along z such that only a subset of spins will be within the bandwidth of the RF pulse. z z slope = Gz F.T. B1(t) cos(ot) o Set amplitude of Gz such that bandwidth of where is the desired slice thickness.
Gradient Fields: In Plane Encoding Apply Gx during a FID Frequency is proportional to Bz slope = Gx Bo x
Gradient Fields: In Plane Encoding Signal(t) Sr f t fo The Fourier transform of the signal gives us the projection of the object. The signal detected by the coil, a function of time (t),has spatial information encoded into it. Bz so, slope = Gx Bo x
Gradient Fields: Example Assume a 20 cm wide head. Let Gx = 2 G/cm What is the frequency range across the head?
Gradient Fields: Example Assume a 40 cm wide object. Gx = 0.5 G/cm At 1 T, Bandwidth of interest is small compared to 42.57 MHz.
Gradient Fields: Matlab example sr(t) x m(x) t sr(t) t s(t) m(x) x
Gradient Fields Gy changes field strength of B field in z direction as a function of y Gz changes field strength of B field in z direction as a function of z
Generalized Gradient Fields We can write this all together by looking at G as a vector. Each element refers to the gradient field present at any time ( current in the coil at that time).
Basic Procedure 1) Selectively excite a slice (z) - time? .4 ms to 4 ms - thickness? 2 mm to 1 cm 2) Record FID, control Gx and Gy - time? 1 ms to 50 ms 3) Wait for recovery - time? 5 ms to 3s 4) Repeat for next measurement. - measurements? 128 to 512 - in just 1 flip 5) Next: More on spatial encoding