Dear David,


On 1 Sep 2010, at 19:01, David Roalf wrote:

> I am working on a project that has acquired DTI (in 64 directions) and DWI (in one direction at 4 b-values: b0 and three other values under 1200, based on previous literature--this paper did NOT use FSL to process the data). I am familiar with DTI analysis and this data is not a problem to analyze using FSL FDT Toolbox. However, I am having issues with the DWI data.
>
> First, part of my confusion is nomenclature. I've seen numerous uses of ADC, diffusivity and Trace (D). I've also seen the following in a previous post:
>
> "- ADC is defined along a single orientation (hence it is not L1+L2+L3).
> - MD is the mean of ADC across all orientations (though, again, some people might use the terms interchangeably)
> - The trace is L1+L2+L3 (math definition), hence MD=Trace/3."
>

As you said the ADC is a quantity that can be estimated when you have one DW and one b=0 measurement, and it depends on the direction of the DW measurement Sk and the b value. It is:
ADC=-(1/b)ln(Sk/So)

The mean diffusivity gives the mean of many ADCs measured along many directions on the sphere and can be estimated using the mean of three orthogonal ADCs.

Both ADC and MD are valid for DWI in general, there is no need to calculate a tensor. On the other hand, the trace of the tensor and the eigenvalues are quantities tied to DTI analysis and the tensor model. The eigenvalues give three orthogonal ADCs and their mean give the MD.




> Based on this I would like to create the ADC maps in the x, y, and z direction, an average of those maps (which I am assuming is the MD) and the Trace image (which I am assuming would be: MD*3=Trace OR L1+L2+L3). **Please correct me if my descriptions are incorrect.


To get maps of ADC in specific directions (e.g. x,y,z) you either a) need to have measured the signal in this directions and use the formula ADC=-(1/b)ln(Sk/So) or b) you need a model to infer these quantities. If you fit the DTI model and calculate a tensor D, then the ADC along any direction g, can be given as ADC=g*D*gT, where gT is the transpose of the vector g. Doing that for many directions on the sphere, will give what is known as the ADC peanut.



> If this is correct I could try to use the FDT Toolbox-DTIFIT to create the MD. In order to do this I would have duplicate the 4 volumes and append them to the original 4 volumes for a total of 8 volumes. I am making this assumption since DTIFIT require a minimum of 6 volumes to run (at least in my experience). Is this method appropriate?
>
> If this method is okay, the FA map will essentially be binary (since the data was collected in only one direction), but the MD output should be correct. Yes/No?
>
> If so, I should then be able to use fslmaths to multiply the MD by 3 and output the Trace image. Yes/No?
>
> The ADC maps are then L1, L2, L3? Or does some calculation need to be made to generate these maps?
>
> This method seems straight forward, if considered valid
>

Based on what I have mentioned before, you need to fit a tensor to estimate the ADC in arbitrary directions. You cannot fit a tensor with 3 co-linear measurements.



> ***Alternatively, I could use the diffusion formula to calculate the ADC maps from the raw volumes since I have the b0 and the b-weighted images? Correct?
>

Again, using the formula and your measurements will give you ADC estimates along the direction of the measurements, you cannot infer from these estimates ADCs in other directions.



> With the help of my colleague Yossi Berlow at OHSU I post these steps to manually determine the ADC:
>
> S=signal with diffusion
> So=signal without diffusion
>
> D=-(1/b)ln(S/So)
>
> rearranged
>
> D=-(lnS-lnSo)/b
>
>
> if b=1000
>
> fslmaths S -log lnS
> fslmaths So -log lnSo
> fslmaths lnS -sub lnSo lnS_sub_lnSo
> fslmaths lnS_sub_lnSo -div -1000 D
>
> I should be able to implement this for each b-value, average the images together using fslmaths for the MD, and divide the MD by 3 to get the Trace? I don't know if the above steps are correct so please advise or if should be able to compare them to the output from DTIFIT. I've tried comparing results between the two methods to no avail, which leads me to believe that I am forgetting to do something (or many things)!!!
>

As mentioned above, you need ADCs measured along 3 orthogonal directions to estimate the MD.

> I apologize for the long post, but I appreciate any effort in helping with this issue
>
> David
>


Hope this is helpful,
Stam