green functions sensitivity

[Alexis Machado]

Dear Dr Fang

I use the MCX algorithm (mcxlab) on a segmented head volume( 5 layers) on a source (Src) then a detector (Det) position to get  the Green's function of the fluence rate (or flux) associated to each optodes.

>fluenceRate_Src=mcxlab(cfg); % cfg.isnormalized=1;
>fluenceRate_Det=mcxlab(cfg); % cfg.isnormalized=1;

I want to compute the sensitivity matrix ( the banana shape) of the nirs measurment between the given Source and the Detector.

sensitivity=fluenceRate_Src.*fluenceRate_Det

It is correct to do it like this or do it need more normalisation ( I have heard it has to be normalized by the fluence rate value at the detector voxel position)

Best regards
Alexis

[Qianqian Fang]

On 6/18/2012 12:05 PM, Alexis Machado wrote:

Dear Dr Fang

I use the MCX algorithm (mcxlab) on a segmented head volume( 5 layers) on a source (Src) then a detector (Det) position to get  the Green's function of the fluence rate (or flux) associated to each optodes.

>fluenceRate_Src=mcxlab(cfg); % cfg.isnormalized=1;
>fluenceRate_Det=mcxlab(cfg); % cfg.isnormalized=1;

I want to compute the sensitivity matrix ( the banana shape) of the nirs measurment between the given Source and the Detector.

sensitivity=fluenceRate_Src.*fluenceRate_Det

hi Alexis

the approach you used here is called the "adjoint method".
The continuous forms of the adjoint method can be found
in many papers, including one from Simon Arridge
[Arridge1999]. The adjoint formulas for a set of FEM meshes
were used in a paper of mine [Fang2009] . The sensitivity
to the absorption and diffusion coeff. can be found as Eqs.
(10) and (11). The former one can be simplified to a form
I called a "nodal adjoint" [Fang2010]. The form for a uniform
3D grid is also described in this paper.

In short, the sensitivity to mu_a equals

J(ri)=v_i*Phi_s(ri)*Phi_d(ri)
(unit of J is 1/m, same as d(Phi)/d(mu_a))

where ri is a discrete position in a 3D mesh or grid,
v_i is the associated volume to this node (voxel size
for grid, or element volume/4 for an FEM mesh) ; Phi_s
and Phi_d are the forward and adjoint Green's functions.

Qianqian

[Arridge1999] Arridge SR, “Optical tomography in
medical imaging,” Inv. Problems, vol. 5, pp. R41–R93, 1999

[Fang2009] Fang Q, et al, “Combined optical Imaging and
mammography of the healthy breast: optical contrast
derives from breast structure and compression,”
 IEEE TMI, 28(1): 30 – 42, 2009.

[Fang2010] Fang Q, Meaney PM, Paulsen KD, “Viable
three-dimensional microwave imaging, theory and
experiments,” IEEE Trans Antennas and Propagation,
vol. 58, issue 2, Feb. 2010.

It is correct to do it like this or do it need more normalisation ( I have heard it has to be normalized by the fluence rate value at the detector voxel position)

Best regards
Alexis

--
You received this message because you are subscribed to the Google Groups "mcx-users" group.
To view this discussion on the web visit https://groups.google.com/d/msg/mcx-users/-/hl6GvZiLWiQJ.
To post to this group, send email to mcx-...@googlegroups.com.
To unsubscribe from this group, send email to mcx-users+...@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/mcx-users?hl=en.

The information in this e-mail is intended only for the person to whom it is
addressed. If you believe this e-mail was sent to you in error and the e-mail
contains patient information, please contact the Partners Compliance HelpLine at
http://www.partners.org/complianceline . If the e-mail was sent to you in error
but does not contain patient information, please contact the sender and properly
dispose of the e-mail.

[Qianqian Fang]

On 6/19/2012 5:18 AM, Qianqian Fang wrote:

On 6/18/2012 12:05 PM, Alexis Machado wrote:

Dear Dr Fang

I use the MCX algorithm (mcxlab) on a segmented head volume( 5 layers) on a source (Src) then a detector (Det) position to get  the Green's function of the fluence rate (or flux) associated to each optodes.

oh, I forgot to mention, the default output of mcx is
flux (1/mm^2/s), you need to convert it to fluence
first by multiplying delta_t - your time gate width.
Then you can use the formulas I mentioned previously.

Qianqian