[Homer-users] FW: MBLL Missing ln(10)

Wed Jul 3 11:56:41 EDT 2013

Hi Robert thank you for you response
This is indeed very confusing

If i look in the header of GetExtinction.m it is sais clearly thatµa = (2.303) e  x /(66,500)   or in other terms µa = ln(10).e.[X]  where [X] denotes molar concentration and e is the specific extinction coeff

Therefore i think that  GetExtinction returns the specific extinction coefficients and not the specific absorption coefficient.
Moreover it seems confirmed in [1] See Important Note

Now, If i look in the HOmer's article [2]  equation 2ln (I/Io)=Dmua.L=(eps1.D[HbO]+eps2.D[HbR]) .L  Because It seems that HOMer use the  specific molar extinction coefficient provided in [1] in the function GetExtinction.m and calculated using a base 10 logarithm. The Biomedical optic research laboratory website states that the ln(10) scale factor should be considered for the calculation of DmuaSo , I think there is a  MISSING ln(10) scale factor in equation 2 of this article and in any articles which use the extinction coefficients provided by reference [2] instead of specific absorption coefficients.

[1] http://www.medphys.ucl.ac.uk/research/borg/research/NIR_topics/spectra/spectra.htm

[2] P: HomER: a review of time-series analysis methods for near-infrared spectroscopy of the brain; Theodore J. Huppert, Solomon G. Diamond Maria A. Franceschini and David A. Boas,
best regardsAlexis

From: robert.cooper at ucl.ac.uk
To: alexis.machado at hotmail.fr
Subject: RE: [Homer-users] MBLL Missing ln(10)
Date: Wed, 3 Jul 2013 14:39:13 +0000

Hi Alexis,

This is  a little confusing.  I think the explanation is the difference between specific extinction coefficient (which is defined base 10, such that I = Io*10^(-Extinction*concentration))
 and specific absorption coefficient (which is defined base e, such that I = Io*exp(absorption*concentration).  I think that the homer function GetExtinctions, counter-intuitively, outputs specific absorption coefficients.  The functions hmrIntensity2OD and
 hmrOD2Conc are then all base e.  Homer is therefore internally consistent, although the function GetExtinctions should perhaps be renamed.

Rob

Rob J Cooper PhD.
Research Associate
Biomedical Optics Research Laboratory
Malet Place Engineering Building, Rm 3.18
University College London
Gower Street
London WC1E 6BT
T: +44 (0)20 7679 0275

From: homer-users-bounces at nmr.mgh.harvard.edu [mailto:homer-users-bounces at nmr.mgh.harvard.edu]
On Behalf Of alexis machado

Sent: 02 July 2013 18:36

To: homer-users at nmr.mgh.harvard.edu

Subject: [Homer-users] MBLL Missing ln(10)

Hi

I am a PhD student in NIRS.

I have a doubt on the definition of the Modified Beer Lambert Law as used in the sofware HOMER version1. Indeed HOmer uses a natural logarithm to define the absorbance  ( also known as optical density) whereas the extinction coefficients values provided were
 calculated with a log base 10 definition of  the absorbance. 

Let me explain much: 

Let see the definition : REF  HomER: a review of time-series analysis methods for near-infrared  spectroscopy of the brain  Theodore J. Huppert  Solomon G. Diamond Maria A. Franceschini and David A. Boas you define the delta optical density or delta absorbance
 as 

equation: 1b

DOD=-ln(I/Io)=eps_1*D[HbO] +eps_2*D[HbR] *L   % it is a natural logarithm definition

where D stands for variation from a baseline period, and OD the absorbance

where I is the detected fluence and Io the detected baseline fluence

where eps_1 is the molar extinction coeff of HbO and eps_2 the molar extinction coeff of HbR and L is the mean total optical pathlength

Because the beer lamber law states that I/Io=exp(-mua*L)  equation 1.b implies that  Dmua the absorption coeff  variation= eps_1*D[HbO] +eps_2*D[HbR] 

However according to the  header explanation of the GetExtinctions.m function located in /HOMER/GeneralSubs/   the provided eps where measured using a different definition of the absorbance which is DOD=-log10(I/Io) . Indeed  they say clearly that  mua =ln(10)*(
 eps_1*[HbO] +eps_2*[HbR])

Therefore, I think the equation 1.b should be corrected as in REF  A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology Scholkmann F, Kleiser S, Metz AJ, Zimmermann R, Mata Pavia J, Wolf U, Wolf M.

equation 1

DOD=-log10(I/Io) = eps_1*D[HbO] +eps_2*D[HbR] *L

Please correct me if i am wrong !!

best regards

Alexis

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