1. Oct 13, 2009

### johnq2k7

Suppose you would like to detect the NMR signal from water within an area of the brain using a 2 Tesla Magnet. Intially, the magnetization from the protons in water has a magnitude (length) represented by Mo and oriented in a direction parallel to the z-axis (defined as the direction of the external magnetic field (Bo)). In order to observe the NMR signal this magnetization is rotated into the x,y plan (using the B1 magnetic field).

a.) At what frequency in (MHz) does the magnetization (now in the x,y plane) precess about the external magnetic field (Bo).

b.) If the magnitude of B1 is 1.5 mT, how long does it take for the magnetization to rotate into the x,y plane from it's intial position parallel to the z-axis?

My work:

f0= (y/2pi) (Bo)

since (y/2pi) is equal to 42.6 MHz/T for H1

therefore, f0= (42.6 MHz/T) (2T)= 85.2 MHz

exp (-t_(1/2)/ T2*)= 1/2

-t_(1/2) / T2*= -ln 2
t_(1/2)= T2*(ln(2))

# of cycles= t_(1/2)/ T_period = t_(1/2)*(f0)= T2*(ln(2))*f0= 50x10^3 us (ln 2) (85.2 MHz)
= 3 x10^6 cycles

b.) B1= 1.5mT
# of cycles = 3 x 10^6

f0= 85.2 x 10^6 =8.52 x 10^7 Hz= 8.52 x 10^7 cycles/sec

# of cycles/f0= 3x 10^6 cycles/ (8.52 x 10^7 cycles/sec)
= 3.52 x 10^-2 sec

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 14, 2009

### Ygggdrasil

85.2 MHz is the correct answer.

I'm not quite sure what you're trying to do here.

I'm not quite sure what you're trying to do here. Basically, when you turn on the B1 field, your magnetization will precess about B1. Because you know the strength of the field, you can calculate the frequency of precession as well as the period. From this information, you should be able to calculate the time needed to move the magnetization by 90o (from the z-axis into the x,y-plane).

3. Oct 14, 2009

### johnq2k7

since i know the value of B1, i can find the frequency and period .. how do i determine the time, i understand if the magnetization is rotated into the x,y plane from the z plane that is equal to angle of 90 degrees... which formula do i use to compute the time?

4. Oct 14, 2009

### Ygggdrasil

If it takes T seconds to rotate one cycle, how much time will it take to rotate 90o (1/4 of a cycle)?

5. Oct 14, 2009

### johnq2k7

Suppose you acquire the 31P NMR signal from a region of muscle of a healthy subject using a 3 Tesla magnet. Assume that the signal has contributions from ATP,PCR, Pi, and from an unknown phosphorous containing biochemical. Assume that all decay shapes are exponential.

Note: H1- 42.575 MHz/T for y/2pi , 31P- 17.235 MHz/T for y/2pi, and 13C- 10.705 for y/2pi

31P- nucleus (chemical shifts), ATP-alpha= -7.52 ppm
ATP-beta= -16.26 ppm
ATP-gamma= -2.48 ppm
PCr= 0 ppm
Pi= 5.02 ppm
a.) Determine the ratio S_PCr@0/ S_ATP@0, where S_PCr@0 is the contribution to the intial signal amplitude from PCr, and S_ATP@0 is the contribution to the initial signal amplitude from ATP.

b.) If the peak in the spectrum from the unknown biochemical is centered at a frequency 100 Hz to the left of the Pi peak (where PCr is on the right of the Pi peak), determine the value of the chemical shift for the peak from the unknown chemical, with PCR as the reference peak.

c.) If the full width at half maximum (FWHM) of the peak from the unknown chemical is 10 Hz and its height s half that of the PCr peak, determine the concentration of the unknown chemical assuming that there is only one phosphorous nucleus per molecule.