MRI Gradient Frequency Scan - Biophysical Instrumentation II: From Signals to Genomes Step by Step

Holding position and gamma fixed makes the gradient-to-frequency relation scanable. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A gradient turns position into a field row

The base field is 1 T and the far sample is at position 2 meters. Changing gradient changes the far field.

B_{\text{far}}=B_{\text{base}}+Gz

Three gradients make three far-frequency rows

The gamma value stays fixed. The far position stays fixed. Only the gradient changes, so the far resonance frequency moves row by row.

\begin{array}{c|c|c}G&B_{\text{far}}&f_{\text{far}}\\1&3\ \text{T}&30\ \text{Hz}\\2&5\ \text{T}&50\ \text{Hz}\\3&7\ \text{T}&70\ \text{Hz}\\\end{array}

The steep row gives the largest far frequency

For the steep row, the far field is 7 T and the far frequency is 70 Hz. The values are schematic training values, not real scanner constants.

f_{\text{far}}=\gamma B_{\text{far}}=70\ \text{Hz}