Could someone please complete this homework assignment?

MRD 101 – ASSIGNMENT #2

Date Assigned:
Due Date:

1.

a)

Friday, October 7 2005
Wednesday, October 12 2005

NAME: _________________________

A patient is placed in a 1.58 T static magnetic field.

Determine the linear frequency fo (in MHz) and the angular frequency ωo (in rad/s) of precession of the 1H
atoms.

b) What would be the linear frequency f of an electromagnetic wave have to be in order to absorbed by the 1H
atoms? Determine the wavelength λ of such a wave. The speed of light is 2.998 x 10+8 m/s.

c) What type of electromagnetic wave would have to be used? Refer to the electromagnetic spectrum included
with the assignment.

2. A sample contains 1 000 000 31P atoms. The sample is cooled to the temperature of liquid nitrogen T = -196 ˚C
(77.0 K) and placed in a 9.00 T static magnetic field. The net spin of 31P is the same as that for 1H, S = ½.

Determine the difference in energy between the spin-up and spin-down states when the sample is in the field. a)

b) Determine the spin excess (the excess number of spin-up to spin-down nuclei) for the 31P sample at liquid
nitrogen temperature (77.0 K) and in the 9.00 T static magnetic field

3. The gyromagnetic ratio for the proton has been experimentally determined to be γp= 42.58 MHz/T.

a) Calculate the rate of precession in MHz of a proton in a 1.50 T static magnetic field using the Larmor
equation f = γBo :

b) The gyromagnetic ratio for the electron is 658 times larger than γp. Calculate γe , the gyromagnetic ratio
for the electron:

c) Calculate the precessional frequency in MHz of an electron in a 1.50 T static magnetic field using the
Larmor equation.

d) The calculate precession rate in c) is also equal to the frequency of the RF pulse that must be transmitted
into the patient to elicit an MR signal. Using the precessional frequency from c) and the wave equation

υ = λf calculate the wavelength of the RF pulse required to excite the electrons.

e) Refer to the diagram of the electromagnetic spectrum. What type of radiation would correspond to the
wavelength calculated in d)? Why are protons and not electrons used in MR imaging?

4. In an MRI acquisition, the decay of the transverse magnetization is described by the function:

M trans (t ) = Mo e

Tissue #1
Tissue #2

−t
T2

where T2 is a time constant which depends on type of tissue present.

The T1 values for two particular tissues are:

T2 = 600 ms = 0.600 s
T2 = 300 ms = 0.300 s

Assume the value of Mo is 100.

a) Complete the following table of values. You can omit the blacked out values

time (s)

0.000

0.400

0.800

1.200

1.600

2.000

b) Plot the decay curves for the two tissues on the graph below using the table of values.

M trans (t ) Tissue #1 M trans (t ) Tissue #2

M ⊥ (t )

time (s)

0.4 0.8 1.2 1.6 2.0 2.4

c) Which signal decays faster? How is this decay related to the value of the time constant T2?