Unit calculations - DWI MRI (Stejskal-Tanner)

Eowyn
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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.
 
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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
 
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