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<sebastien.morin.1@xxxxxxxxx> 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.
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?
--------------------------
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.
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.
What do you think ?
As long as a number of published results can be replicated, we should be fine.
Regards,
Edward
Re: r8343 - in /branches/relax_disp: prompt/relax_disp.py specific_fns/relax_disp.py