Corrections for water attenuation, water concentration, water and metabolites relaxation effects

[Sophie Betka]

Good afternoon (from Brighton, UK),

After having successfully segmented my VOI, I have been able to compute the VOI tissue content for all my subjects.
However, now, I would like to correct for water attenuation, water concentration, water relaxation effects and metabolite relaxation effects.
After a fair amount of reading, I would be very glad if someone could validate what I am doing and answer the questions I still have. :)


1) Water attenuation
I used the tarquin manual and computed my water attenuation (1.5Tesla, TE=40ms, TR=2000ms) so, the taquin default correction  0.7 is ok for me.


2) Water concentration
For each  participant, I am using the fraction of grey matter (pGM), white matter (pWM) and CSF (pCSF) and compute the water concentration like:
waterconcentration_VOI = 35880*pWM + 43300*pGM + 55556* pCSF  (in mM, with NMR visible water concentration for each tissue)

3) Water relaxation effects
here I begin to be very unsure. I read Gasparovic et al., 2006.
I tried to compute myself the water signal, using the equation (cf below).

-First, could you validate or not that, to compute this equation, I am using my tarquin results ?
-If yes, where can I find the observed water signal SH2O_obs? is it the water amplitude in fit diagnostics? is it in mV?
-Do I have then to derive the fully relaxed  water signal SH2O_R from the equation using my SH2O_obs? I am not sure
-----------------------------------------------------------------------
TE=0.040; %in sec
TR= 2;

pGM = 0.4589;                %fraction of grey matter in VOI
pWM = 0.2189;               %fraction of white matter in VOI
pCSF = 0.3222;               %fraction of csf in VOI
              
T1H2O_GM= 1.304;             % T1 and T2 attenuation in tissue, at1.5T
T2h2O_GM= 0.093;              % in sec ; magnetic resonance in medicine; Yymazal et al., 1999 radiology ; Kingsley et al., 1998 magn reson imaging
T1H2O_WM= 0.660;
T2h2O_WM= 0.073;
T1H2O_CSF= 2.93;
T2h2O_CSF= 0.23;

fGM = (pGM*0.78) /((pGM*0.78)+ (pWM*0.65)+(pCSF*0.97));                % fractions of water attributable to tissues, Ernst et al., 1993 magn res ser B
fWM = (pWM*0.65) /((pGM*0.78)+ (pWM*0.65)+(pCSF*0.97));
fCSF = (pCSF*0.97) /((pGM*0.78)+ (pWM*0.65)+(pCSF*0.97));

Rh2O_GM = exp(- TE/T2h2O_GM)*(1- exp(-TR/T1H2O_GM));
Rh2O_WM = exp(- TE/T2h2O_WM)*(1- exp(-TR/T1H2O_WM));
Rh2O_CSF = exp(- TE/T2h2O_CSF)*(1- exp(-TR/T1H2O_CSF));

SH2O_obs = fGM * Sh2O_R * Rh2O_GM + fWM * Sh2O_R * Rh2O_WM + fCSF * Sh2O_R * Rh2O_CSF;             %observed water signal

SH20_GM&WM  = (SH2O_obs *(1- fCSF))/(fGM * Rh2O_GM + fWM * Rh2O_WM + fCSF * Rh2O_CSF);                    %observed water signal for parenchyma


SH2O_obs =??

Sh2O_R = ??;    

--------------------------------------------------------

and then I do similar stuff to correct each concentration of metabolites (glu, naa, ins, cho, lact, in my case).



Should I do other corrections?
Any comment? Suggestions?
Any feedback would be amazing as no one in my team is able to help me.


Thank you

Sophie :)

[Paul Mullins]

Hi Sophie,

I'm traveling and in my phone so not able to provide a full answer, but you could check out a blog post I wrote on this subject a while ago https://wordpress.com/post/pgmm03.wordpress.com/16. This could help get you started.  I will send more once I get back to the UK.

Sent from BlueMail

[Andreas Bartsch]

Hi Paul,

ist the access to

 https://wordpress.com/post/pgmm03.wordpress.com/16

restricted? Do I really have to register to view it?

Cheers,

Andreas

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[Sophie Betka]

Hi Paul,
Thanks for your quick response,

I have already read your blog articles on this topic; "Relax don't do it" is sooo useful! Thanks for that!

But I still have (silly) "practical" questions, especially, concerning water relaxation effects.

Looking forward to hearing from you

S.

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[Paul Mullins]

Sorry sent the wrong link. Will send the  irreconcilable one shortly. You should not need to register to read it.

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Rhif Elusen Gofrestredig 1141565 - Registered Charity No. 1141565 Gall y neges e-bost hon, ac unrhyw atodiadau a anfonwyd gyda hi, gynnwys deunydd cyfrinachol ac wedi eu bwriadu i'w defnyddio'n unig gan y sawl y cawsant eu cyfeirio ato (atynt). Os ydych wedi derbyn y neges e-bost hon trwy gamgymeriad, rhowch wybod i'r anfonwr ar unwaith a dilewch y neges. Os na fwriadwyd anfon y neges atoch chi, rhaid i chi beidio a defnyddio, cadw neu ddatgelu unrhyw wybodaeth a gynhwysir ynddi. Mae unrhyw farn neu safbwynt yn eiddo i'r sawl a'i hanfonodd yn unig ac nid yw o anghenraid yn cynrychioli barn Prifysgol Bangor. Nid yw Prifysgol Bangor yn gwarantu bod y neges e-bost hon neu unrhyw atodiadau yn rhydd rhag firysau neu 100% yn ddiogel. Oni bai fod hyn wedi ei ddatgan yn uniongyrchol yn nhestun yr e-bost, nid bwriad y neges e-bost hon yw ffurfio contract rhwymol - mae rhestr o lofnodwyr awdurdodedig ar gael o Swyddfa Cyllid Prifysgol Bangor. This email and any attachments may contain confidential material and is solely for the use of the intended recipient(s). If you have received this email in error, please notify the sender immediately and delete this email. If you are not the intended recipient(s), you must not use, retain or disclose any information contained in this email. Any views or opinions are solely those of the sender and do not necessarily represent those of Bangor University. Bangor University does not guarantee that this email or any attachments are free from viruses or 100% secure. Unless expressly stated in the body of the text of the email, this email is not intended to form a binding contract - a list of authorised signatories is available from the Bangor University Finance Office.

[Paul Mullins]

Okay, sorry this took me a week to get to Sophie.

To hopefully make things easier to follow I'll address your questions inline below. (Others are free to correct me if they think this is wrong.)

 

1) Water attenuation
I used the tarquin manual and computed my water attenuation (1.5Tesla, TE=40ms, TR=2000ms) so, the taquin default correction  0.7 is ok for me.

Setting this to 1 would be better if you intend to try a full correction for partial volume effects. Hopefully why will become apparent later.

2) Water concentration
For each  participant, I am using the fraction of grey matter (pGM), white matter (pWM) and CSF (pCSF) and compute the water concentration like:
waterconcentration_VOI = 35880*pWM + 43300*pGM + 55556* pCSF  (in mM, with NMR visible water concentration for each tissue)

That is correct.

3) Water relaxation effects
here I begin to be very unsure. I read Gasparovic et al., 2006.
I tried to compute myself the water signal, using the equation (cf below).

-First, could you validate or not that, to compute this equation, I am using my tarquin results ?

Yes you are - although note that part of the calculation has already been done (the referencing of the SMet_obs to SH2O_obs)

-If yes, where can I find the observed water signal SH2O_obs? is it the water amplitude in fit diagnostics? is it in mV?

Yes, it is the water amplitude in the fit diagnostics - however, the metabolite signals in Tarquin have already been normalised by this number (with correction by the Signal Attenuation and water concentration input in the parameter file (or the gui) - so you don't really want to go and put the TARQUIN results directly into the full equation from Gasparovic et al.

-Do I have then to derive the fully relaxed  water signal SH2O_R from the equation using my SH2O_obs? I am not sure
-----------------------------------------------------------------------

TE=0.040; %in sec
TR= 2;

pGM = 0.4589;                %fraction of grey matter in VOI
pWM = 0.2189;               %fraction of white matter in VOI
pCSF = 0.3222;               %fraction of csf in VOI
              
T1H2O_GM= 1.304;             % T1 and T2 attenuation in tissue, at1.5T
T2h2O_GM= 0.093;              % in sec ; magnetic resonance in medicine; Yymazal et al., 1999 radiology ; Kingsley et al., 1998 magn reson imaging
T1H2O_WM= 0.660;
T2h2O_WM= 0.073;
T1H2O_CSF= 2.93;
T2h2O_CSF= 0.23;

fGM = (pGM*0.78) /((pGM*0.78)+ (pWM*0.65)+(pCSF*0.97));                % fractions of water attributable to tissues, Ernst et al., 1993 magn res ser B
fWM = (pWM*0.65) /((pGM*0.78)+ (pWM*0.65)+(pCSF*0.97));
fCSF = (pCSF*0.97) /((pGM*0.78)+ (pWM*0.65)+(pCSF*0.97));

Rh2O_GM = exp(- TE/T2h2O_GM)*(1- exp(-TR/T1H2O_GM));
Rh2O_WM = exp(- TE/T2h2O_WM)*(1- exp(-TR/T1H2O_WM));
Rh2O_CSF = exp(- TE/T2h2O_CSF)*(1- exp(-TR/T1H2O_CSF));

SH2O_obs = fGM * Sh2O_R * Rh2O_GM + fWM * Sh2O_R * Rh2O_WM + fCSF * Sh2O_R * Rh2O_CSF;             %observed water signa

SH20_GM&WM  = (SH2O_obs *(1- fCSF))/(fGM * Rh2O_GM + fWM * Rh2O_WM + fCSF * Rh2O_CSF);                    %observed water signal for parenchyma

SH2O_obs =??

This is the water amplitude as listed in the diagnostics section for TARQUIN.  However, as mentioned above, TARQUIN has already done a normalisation against this number - and done so using correction factors inout by the user.  I set these correction factors to 1 for signal attenuation and pure water for water concentration, as I will be correcting for relaxation and other factors later.

Basically

Tarquin has done this

 which is basically [Met]_TQ=(S_M_Obs * water_conc * H2O_R * 2)/SH20_obs  (where [Met]_TQ is the metabolite concentration from Tarquin) and H2O_R is an assumed relaxation affect on water.

Whereas Gasparovic et al (2006) basically suggests this

[MET]_G = (S_M_Obs*2*[H2O]/SH20_GM&WM*R_M)  (Where [Met]_G is the metabolite from the Gasparovic equations, and [H2O] denotes the molal concentration (mol/kg of solvent) of MR-visible water in the metabolite solution (9,12) of the parenchyma, assumed here to be that of pure water (55.51 mol/kg) and R_M is relaxation effects for the metabolite.

which is

 

[MET]_G = (S_M_Obs*2*[H2O]/((SH2O_obs *(1- fCSF))/(fGM * Rh2O_GM + fWM * Rh2O_WM + fCSF * Rh2O_CSF))*R_M)

which becomes

[MET]_G = ((S_M_Obs*2*[H2O]*(fGM * Rh2O_GM + fWM * Rh2O_WM + fCSF * Rh2O_CSF))*RM/(SH2O_obs *(1- fCSF))

which you can re-write to

[MET]_G = ((S_M_Obs*2*[H2O]/SH2O_obs)  *  (fGM * Rh2O_GM + fWM * Rh2O_WM + fCSF * Rh2O_CSF))*RM) * 1/(1- fCSF))

So you can see the difference between [MET]_TQ and [MET]_G is the water concentration value used (55510 v's 35880 mMolal), the correction factor used (H2O_R  v's (fGM * Rh2O_GM + fWM * Rh2O_WM + fCSF * Rh2O_CSF))*RM) and correction for the CSF fraction (to get a concentration in the tissue v;s the whole voxel).

As the water attenuation and the water concentration are factors you set, if you set H2O_R as 1 in tarquin it disappears from the equations, and then setting water concentration in tarquin as 55510 (or 55556 to match your numbers) you see that [MET]_TQ = S_M_Obs*[H20]/SH20_obs - so to get to apply the correction for partial volume from Gasparovic et al (2006) all you need to do is take the results from tarquin (assuming you used attenuation of 1 and water conc of 55556) and multiply by (fGM * Rh2O_GM + fWM * Rh2O_WM + fCSF * Rh2O_CSF))*RM) * 1/(1- fCSF)).

(just check my reasoning and equations, but I think they are correct - happy to be told other wise).

As for:

Sh2O_R = ??; 

Note You don't really need to use this figure, but it can be derived from equation [3] in Gasparovic et al (2006) which can first be re-written as

SH2O_obs = Sh2O_R * (fGM * Rh2O_GM + fWM * Rh2O_WM + fCSF * Rh2O_CSF)

then 

SH2O_R =SH2O_obs/(fGM * Rh2O_GM + fWM * Rh2O_WM + fCSF * Rh2O_CSF).  

  

--------------------------------------------------------

and then I do similar stuff to correct each concentration of metabolites (glu, naa, ins, cho, lact, in my case).

Yes, you just need to update the R_M for each taking into account differing T2 and T1 values (not sure if they are available for Glutamate and Lactate at 1.5T).

Should I do other corrections?
Any comment? Suggestions?
Any feedback would be amazing as no one in my team is able to help me.


Thank you

Sophie :)

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----------------------------------------------------
----------------------------------------------------
Paul Mullins PhD
Director, Senior MRI Physicist
Bangor Imaging Center,
Reader, School of Psychology, Bangor University.

Adeilad Brigantia
Penrallt Road
Gwynedd LL57 2AS
United Kingdom

Ph: ++44 (0) 1248 383631
email: p.mu...@bangor.ac.uk
----------------------------------------------------
----------------------------------------------------

[Sophie Betka]

Thank you so much Paul!
 It is very clear!

I have a last tiny question.

You are right, I have not found any T1 and T2 relaxation time for glutamate at 1.5T.

Is it ok to ignore the correction for glutamate but to do the correction for NAA etc when I have the correct info?

(I imagine that it is not a problem, but I just need to specify it, right?)

thanks again,

S.

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----------------------------------------------------
----------------------------------------------------
Paul Mullins PhD
Director, Senior MRI Physicist
Bangor Imaging Center,
Reader, School of Psychology, Bangor University.

Adeilad Brigantia
Penrallt Road
Gwynedd LL57 2AS
United Kingdom

Ph: ++44 (0) 1248 383631
email: p.mu...@bangor.ac.uk
----------------------------------------------------
----------------------------------------------------

 

Rhif Elusen Gofrestredig 1141565 - Registered Charity No. 1141565 Gall y neges e-bost hon, ac unrhyw atodiadau a anfonwyd gyda hi, gynnwys deunydd cyfrinachol ac wedi eu bwriadu i'w defnyddio'n unig gan y sawl y cawsant eu cyfeirio ato (atynt). Os ydych wedi derbyn y neges e-bost hon trwy gamgymeriad, rhowch wybod i'r anfonwr ar unwaith a dilewch y neges. Os na fwriadwyd anfon y neges atoch chi, rhaid i chi beidio a defnyddio, cadw neu ddatgelu unrhyw wybodaeth a gynhwysir ynddi. Mae unrhyw farn neu safbwynt yn eiddo i'r sawl a'i hanfonodd yn unig ac nid yw o anghenraid yn cynrychioli barn Prifysgol Bangor. Nid yw Prifysgol Bangor yn gwarantu bod y neges e-bost hon neu unrhyw atodiadau yn rhydd rhag firysau neu 100% yn ddiogel. Oni bai fod hyn wedi ei ddatgan yn uniongyrchol yn nhestun yr e-bost, nid bwriad y neges e-bost hon yw ffurfio contract rhwymol - mae rhestr o lofnodwyr awdurdodedig ar gael o Swyddfa Cyllid Prifysgol Bangor. This email and any attachments may contain confidential material and is solely for the use of the intended recipient(s). If you have received this email in error, please notify the sender immediately and delete this email. If you are not the intended recipient(s), you must not use, retain or disclose any information contained in this email. Any views or opinions are solely those of the sender and do not necessarily represent those of Bangor University. Bangor University does not guarantee that this email or any attachments are free from viruses or 100% secure. Unless expressly stated in the body of the text of the email, this email is not intended to form a binding contract - a list of authorised signatories is available from the Bangor University Finance Office.

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[Andreas Bartsch]

Hi Paul,

can you send the worldpress link again (that I had issues to open without registering)?

Thanks!

Cheers,

Andreas

[Paul Mullins]

Try this one

https://pgmm03.wordpress.com/2015/05/01/relax-dont-do-it/

----------------------------------------------------
----------------------------------------------------
Paul Mullins PhD
Director, Senior MRI Physicist
Bangor Imaging Center,
Reader, School of Psychology, Bangor University.

Adeilad Brigantia
Penrallt Road
Gwynedd LL57 2AS
United Kingdom

Ph: ++44 (0) 1248 383631
email: p.mu...@bangor.ac.uk
----------------------------------------------------
----------------------------------------------------

[Andreas Bartsch]

thanks - yes, this works.

cheers,

andreas

[Ben Rowland]

Dear Paul et al.

Sorry to resurrect a dead thread but I have been working through these equations today and just wanted to check my interpretation of the parameters.

Assuming a fixed T1/T2 for all metabolites, we can set the water attenuation in Tarquin as:

(fGM * Rh2O_GM + fWM * Rh2O_WM + fCSF * Rh2O_CSF)) / RM * (1- fCSF))

which reduces to the default Tarquin equation if T1/T2 is constant for water across tissue types, plus the partial volume correction.

Setting the water concentration to pure water (55556) gives us the molal concentration of the metabolites as it implicitly scales the water peak by the water fraction in the voxel to give us a ratio to amount of solvent, whereas setting the water concentration to the visible water of the voxel (35880*pWM + 43300*pGM + 55556* pCSF) will give a molar concentration as the amount of metabolite in the voxel volume rather than in the fraction of the voxel that is water.

Does that sound right?

Ben

[Paul Mullins]

Okay, initial thoughts inline (always happy to be corrected if my thinking is wrong) 

On 2 May 2018, at 15:56, Ben Rowland <bennyr...@mac.com> wrote:

Dear Paul et al.

Sorry to resurrect a dead thread but I have been working through these equations today and just wanted to check my interpretation of the parameters.

Assuming a fixed T1/T2 for all metabolites,

Not a safe assumption unless at TE = 0 (or very short) and TR very long, (and not correct for T2 of the big three at least, let alone other metabolites)

we can set the water attenuation in Tarquin as:

(fGM * Rh2O_GM + fWM * Rh2O_WM + fCSF * Rh2O_CSF)) / RM * (1- fCSF))

which reduces to the default Tarquin equation if T1/T2 is constant for water across tissue types, plus the partial volume correction.

 yes, you could use this - if correcting for metabolite relaxation outside of TARQUIN - to account for relaxation varying with metabolite, (and possibly with tissue type - and maybe even voxel composition). Not sure how it would work putting it into TARQUIN as a default as your concentration estimates would only be valid for one metabolite, unless TARQUIN sets different RMs for each metabolite.

Setting the water concentration to pure water (55556) gives us the molal concentration of the metabolites as it implicitly scales the water peak by the water fraction in the voxel to give us a ratio to amount of solvent,

Yes, that is right

whereas setting the water concentration to the visible water of the voxel (35880*pWM + 43300*pGM + 55556* pCSF) will give a molar concentration as the amount of metabolite in the voxel volume rather than in the fraction of the voxel that is water.

Does that sound right?

To be honest - I'm not sure at this point - I need to think a bit more on this.  Anyone else have a comment?

Mae croeso i chi gysylltu gyda'r Brifysgol yn Gymraeg neu Saesneg You are welcome to contact the University in Welsh or English

[Bhattacharyya, Pallab]

Dear Ben,

 

Your formulation looks right. I usually do this offline following the series of equations described in https://www.ncbi.nlm.nih.gov/pubmed/16688703 by Chuck Gasparovic et al. You may have already referred to that publication but if you have not, I would highly encourage you to do so.

 

Best regards.

 

Pallab K Bhattacharyya, PhD

Imaging Institute, Cleveland Clinic

Radiology, Cleveland Clinic Lerner College of Medicine

Tel.: (216)444-5364

Fax: (216)636-2397

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[Vuong Truong]

Dear Paul,

I realized that you did not put the #H_M(number of proton that gives rise to the metabolite peak) in the formula. The Gasparovic paper did include that in their formula. Am I correct that we should also take that into account if we use their formula on Tarquin results?

Thank you for very useful info,

Vuong

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----------------------------------------------------
----------------------------------------------------
Paul Mullins PhD
Director, Senior MRI Physicist
Bangor Imaging Center,
Reader, School of Psychology, Bangor University.

Adeilad Brigantia
Penrallt Road
Gwynedd LL57 2AS
United Kingdom

Ph: ++44 (0) 1248 383631
email: p.mu...@bangor.ac.uk
----------------------------------------------------
----------------------------------------------------