Question

If the difference in resonance frequencies due to the chemical shift between water and fat protons is roughly 210 Hz, and the gradient in a 1.5 Tesla MRI scanner’s main magnet is 1.5 gauss/cm, the fat protons will appear to be in different positions than water protons.

a) Explain why this is true.

b) By how much do their apparent locations differ?

c) By how much would their frequencies differ in a lower field, 0.5 Tesla scanner? Use this result to explain why high fields are used in NMR spectroscopy.

Answer 1

a) Answer-The ¹H protons of fat, for example, are nestled within long-chain triglycerides and covered by electron clouds. These clouds partially shield the fat protons from the full effects of an externally applied magnetic field. The ¹H protons of water, however, are less shielded because their electron clouds are pulled away from them by the highly electronegative oxygen atom.that's why the fat protons will appear to be in different positions than water protons.

b) Answer-

The chemical shift between fat and water has been measured to be approximately 3.5 parts per million (ppm). The suffix ppm is interchangeable with x10−6, just as the symbol % is interchangeable with 1/100, x0.01 or x10−2. The chemical shift is given as a ratio because the actual frequency difference (in Hz) will depend upon the applied magnetic field. Calculating the actual fat-water frequency difference is easy — you simply multiply the Larmor frequency at whatever field strength you are using by 3.5 ppm or 3.5 x 10−6.

Spectral peaks for fat and water over a large anatomic area broadened due to inhomogeneity effects. The average chemical shift difference is about 3.5 ppm.

In a 1.5T scanner (operating at 64 MHz), the fat-water frequency difference (Δf) will therefore be

Δf = (64 MHz)(3.5 ppm) = (64 x 10⁶ Hz)(3.5 x10⁻⁶) ≈ 220 Hz

At 3.0T where the Larmor frequency is 128 MHz, the fat-water frequency shift would be twice as large, or about 440 Hz.

c) Answer- The difference in frequencies is extremely small, on the order of 3.4 parts per million (ppm) or 3.4 x 10^-6. At 1.5 T this corresponds to an absolute frequency difference of approximately 215 Hz. At 3.0 T the difference is twice as large, or about 430 Hz.because in fat and water frequencies is small difference in low field NMR .NMR peak not shown clerly so that's why high magnetic NMR are used in above case.