1. A sample has a T1 of 1.0 seconds. If the net magnetization is set equal to zero, how long will it take for the net magnetization to recover to 98% of its equilibrium value? 2. A sample has a T2 of 100 ms. How long will it take for any transverse magnetization to decay to 37% of its starting value? 3. A hydrogen sample is at equilibrium in a 1.5 Tesla magnetic field. A constant B1 field of 1.17x10-4 Tesla is applied along the +x'-axis for 50 microseconds. What is the direction of the net magnetization vector after the B1 field is turned off? Estimate the spin-lattice relaxation time constant based on the following plot of Mz(t). 4. Sketch the frequency and phase-encoding gradient pulse waveforms necessary to generate the following “single-shot” k-space trajectory. Parts (A) and (B) are used in the so-called spiral and echo-planar imaging, respectively. 5. Consider a MRI session. Assume the static field strength is B_0=1.5Tesla, the z-gradient is Gz=2 gauss/mm, and the gyromagnetic ratio is γ =4.258 kHz/gauss. We would like to image a slice with center position z =10cm, thickness ∆z =1mm. (a) Find the frequency range of the RF waveform required to excite this slice and sketch the desired spectrum of the RF waveform. (b) Write down the mathematical expression for the “ideal” waveform that will yield the desired spectrum. (c) determine the amplitude A of this RF waveform required to induce a flip angle of π/2. 6. Complete the table below to show what choice of TE/TR correspond to T1-weighted, T2 weighted, or Proton-Density-weighted contrast (one of the choice is not useful), in the case of a spin-echo pulse sequence. Explain your answers. 6. Consider an MRI scan using a pulse sequence shown below. There are M readouts total in each slice, and you alternate the direction of the X-gradient between readouts. During each readout duration Ts , N samples are taken. The scan parameters are chosen so that γG yTs / 2 = γG yTy M / 2 . (a) Sketch the corresponding sampling pattern in the Frequency domain. Indicate how the positions of the samples are related to the scan sequence parameters including Gx , G y , Ts , Ty , M , N . (b) (10 pt) If you were to reconstruct the image using inverse 2-D discrete Fourier transform, and you would like to reconstruct an image with M1 rows and N1 columns. How should you choose M and N in your scan sequence? If you would like to have a pixel resolution of ( ∆x, ∆y ), what are the constraints on the scan parameters? (i.e. give the equations that the parameters Gx , G y , Ts , Ty , M , N must satisfy). If you want to cover an image area with size FOVx × FOV y , what are the constraints on the scan parameters? 7. A fast spin-echo (FSE or RARE) sequence employs a series of 180° RF refocusing pulses to generate multiple echoes from each excitation. Consider the diagram below showing a single repetition of a sequence that acquires 4 echoes for each excitation Sketch the corresponding k-space trajectory, using “×” to mark the sampling points. Be sure to label the order of the sampling.