Unit calculations - DWI MRI (Stejskal-Tanner)

[Eowyn]

Homework Statement

Calculate the apparent diffusion based on experimental data.

Relevant Equations

I = e^bD
b = gamma^2 * delta^2 * G^2 *(tau - delta/3)

Ok, so basically my task is to calculate the apparent diffusion D based on experimental data, which is kind of easy, BUT the problem is with unit of b...
Gamma is gyromagnetic ratio and can be expressed as: (s*T)^-1 or MHz/T --> but I am not so sure, teacher did not specify
Delta is the pulse length: ms
G is the gradient of magnetic field: Gs/cm
tau - repetition time: ms

So I tried...
b = [(MHz/T)²*(ms)²*(Gs/cm)*ms] = [s/cm² * 10^-5]

How am I supposed to get b in s/cm² from those units? How to let go that 10^-5? Or maybe it's ok, but I'm missing something when it comes to understanding.

 

[Nate810]

The unit for b should be s/cm2, so you need to do some unit conversions to get to that. To convert MHz/T to s/T, you can use the fact that 1 MHz = 10^6 Hz, and 1 Hz = 1 s^(-1). So, 1 MHz/T = 10^6 s^(-1)/T. Similarly, you can convert Gs/cm to T/m by using the fact that 1 Gs = 10^4 A/m, and 1 A/m = 1 T/m. After converting the units, you should have: b = (10^6 s^(-1)/T)^2 * (ms)^2 * (10^4 T/m) * (ms) = 10^4 s/cm^2