Gradient Position Encoding - Physics for Biophysics Step by Step

MRI uses field gradients so samples at different positions resonate at different frequencies. 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 makes position change the field

The base field is 1 tesla and the gradient index is 1 tesla per meter.

B(z)=B_{\text{base}}+Gz,\quad B_{\text{base}}=1\ \text{T},\quad G=1

Three positions have three exact fields

At positions 0 meters, 1 meters, and 2 meters, the fields are 1 tesla, 2 tesla, and 3 tesla.

B_a=1\ \text{T},\quad B_b=2\ \text{T},\quad B_c=3\ \text{T}

Position becomes a frequency code

The matching frequencies are 10 hertz, 20 hertz, and 30 hertz.

f_a=10\ \text{Hz},\quad f_b=20\ \text{Hz},\quad f_c=30\ \text{Hz}