Hi Ed,

Please see the comments below...




Edward d'Auvergne wrote:
> Hi,
>
> Sorry for the delayed response, the last few months for me have been
> crazy.  Please see below for more:
>
>
> On Tue, Jun 2, 2009 at 8:36 PM, Sébastien
> Morin<[email protected]> wrote:
>   
>> Hi,
>>
>> This is a fairly old post, but I finally had time to think about these
>> issues... Please see below...
>>
>>
>>
>> Edward d'Auvergne wrote:
>>     
>>> Hi,
>>>
>>> Is the frequency for the reference spectrum necessary?  Isn't
>>> cmpg_delayT set to zero in this case, i.e. the CPMG block is missing?
>>> If it is necessary though, a value of None is probably a better choice
>>> to identify it rather than the frequency of zero Hz.
>>>       
>> I guess recording a reference for each frequency is necessary since the
>> intensity is to be extracted and could vary when changing magnet (along with
>> S/N)...
>>
>> I agree for a value of None for the reference spectrum (which is what is
>> presently in the code).
>>     
>
> Ok, so we need a reference frequency set, but cmpg_delayT set to None.
>   
Fine.

>   
>>> Another question I have is should the nu_cmpg value be given (with Hz
>>> units), or would it be better if the omega_cmpg value was given (with
>>> rad/s units)?  If nu_cmpg is given, this will have to be converted
>>> later to omega.  I think we should have an explanation of both, after
>>> the relevant model equations.  Also the 'frq' arg of
>>> relax_disp.cpmg_frq() might be better named as nu_cmpg or omega_cmpg
>>> for clarity if this is frequency or angular frequency.
>>>       
>> For this part, I am not sure about the units to use... 'cpmg_frq' needs to
>> be of the same units as 'kex' and 'dw' (see equations below). I guess 'kex'
>> and 'dw' should be in rad/s, so 'cpmg_frq' should also be in rad/s...
>>
>> Is it right ?
>>
>> Depending on the answer, 'cpmg_frq' will be renamed (to either 'cpmg_nu' or
>> 'cpmg_omega').
>>     
>
> I think we should use omega units (with the hidden radian unit).  Do
> you know what is normally used?
>   
In the CPMGFit program by Art Palmer, the units seem to be seconds for
both the tcp (with tcp = 1 / 4 cpmg_frq) and Tau (with Tau = 1 / kex)
variables. Accordingly, if using the same approach, the units would be
1/s for both kex and cpmg_frq.

Hence, I still hesitate.

On one hand, the units should maybe be 1/s so the rates extracted with
our approach are the same as obtained using CPMGFit.

On the other hand, the units for kex and cpmg_frq should maybe be rad/s
since they need to be the same as for dw (Hz), the chemical shift
difference between the two states.

I am still confused as you may see...

>
>   
>> --------------------------
>>
>> FAST EXCHANGE
>>
>>                   /              /        kex       \    4 * cpmg_frq \
>> R2eff = R2 + Rex * | 1 - 2 * Tanh | ------------------ | * ------------- |
>>                   \              \ 2 * 4 * cpmg_frq /         kex     /
>>
>> SLOW EXCHANGE
>>                   /     /      dw      \    4 * cpmg_frq \
>> R2eff = R2A + kA - | Sin | -------------- | * ------------- |
>>                   \     \ 4 * cpmg_frq /         dw      /
>>
>> where cpmg_frq = 1 / ( 4 * cpmg_tau ).
>>
>>
>>     
>>> Also note that
>>> we have to convert the cmpg_delayT value too.  Unit analysis of the
>>> equation
>>>
>>> R2eff = ( 1 / T ) * Ln( Icpmg / Iref )
>>>
>>> shows this.  R2 is in units of rad/s.  T is input in seconds.  1/T is
>>> frequency in nu units of Hz.  Therefore we need to convert to the
>>> radian units of angular frequency by multiplying by 2pi as 2pi/T is in
>>> rad/s units.  The natural logarithm of peak intensities is unitless
>>> and dimensionless.
>>>       
>> I just had a look at the reference dataset included in the test suite (from
>> Hansen et al., J. Phys. Chem., 2008)...
>>
>> When treating the delay T as is (in seconds), I get the same values for
>> R2eff as published in the paper (for the FF domain). However, if multiplying
>> the delay T by 2pi, I get values for R2eff that a way too big.
>>     
>
> delay T is in the pulse sequence and should be in seconds.
>   
Fine.

>   
>> I do not want to say that the logic behind unit analysis is deficient. I
>> agree with that logic, but I also think that, in this case, the delay T
>> should stay in seconds in order to get R2eff values of the good size...
>>     
>
> Despite delay T being in seconds, R2eff is in rad/s.  This is the same
> as standard R1 or R2 where the time period in the pulse sequence is in
> seconds whereas the fitted rate is in rad/s.
>   
Fine.

>   
>> What do you think ?
>>     
>
> As long as a number of published results can be replicated, we should be fine.
>   
I agree.

Regards,


Séb

> Regards,
>
> Edward
>
>   


-- 
Sébastien Morin
PhD Student
S. Gagné NMR Laboratory
Université Laval & PROTEO
Québec, Canada


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