1.

(a) Calculate the response function, out(t) for the following input. i(t) ) 2 sec 1 An example of this would be the presentation of a visual image for 2 sec (synchronized to one TR) in a {MRI experiment. (b) Plot the input, htf and output functions on the same graph. (c) What is the lag time for the peak response as compared to the beginning of the input starting at 0 seconds? ( d) If your experiment consisted of a block design how long would you need to wait before the next presentation? t Define the convolution as follows for this problem: out(t) =in(t) htf () = [in(T)htf(t T)dT 0 Hint: One way to do this is by using Laplace transforms again, since convolution is just multiplication in the Laplace space-s. PULSE 90 180 90 180 M. (a) Use the solution for Me from above to calculate its value right before the 180 pulse at t - - TE 2 (b) What is My right after the 180 pulse at f = E ? (Hint: just a simple reversal) (c) Using the differential equations for the Bloch equations in problem 4 solve for the M, right before the second 90 pulse at t = TR. Solve the Bloch differential equations for Me above again except using the initial condition M.(-E) equal to the answer for part (b). (d) The magnetic moment taking into account both longitudinal and transverse relaxation is given by multiplying the solution in (c) by e E/42 . Simplify this expression for TR > > TE