the positive value in Jacobian

[zhiguan wang]

Hi Prof. Fang,

Thank you for building such a wonderful toolkit.

When using the replay mode to obtain the Jacobian of mu_a, I noticed that the result is always a positive value both in my own code and in the example 'demo_mcxlab_replay.m' . 

However, in my mind I thought Jacobian of mu_a should always contain negative value. Besides, in your paper (https://doi.org/10.1364/BOE.9.004588) there is a negative symbol in Eq. (8).

Best regards,

Zhiguan Wang

[Fang, Qianqian]

Hi Zhiguan,

You are correct that the Jacobian of mua should have negative values. This is because when mua increases, the surface fluence should decrease.

The volumetric output of mcx for outputtype='jacobian' or 'wl' is not the Jacobian, but L-bar, as shown in Eq. 8 of the replay paper. L-bar is the average pathlengths of photons traveling in each voxel, which is the negative of the mua Jacobian.

Similarly, the output of cfg.outputtype='wp' is also not the Jacobian for mus, instead it is p-bar, shown as part of the right-hand-side in Eq. 9 of our paper.

In order to compute J_mua or J_mus, one must use the L-bar and p-bar terms

J_mua = - L_bar

J_mus = p_bar/mus - L_bar

I agree that this is confusing. The outputtype flag 'jacobian' is a historic one and the use of 'wl' and 'wp' are more accurate and recommended.

The conversion between L-bar/p-bar to J_mua/J_mus are implemented in these two mmc functions. I remember at some point we have a similar version for mcx, but I could not find those

https://github.com/fangq/mmc/blob/master/matlab/mmcjmua.m

https://github.com/fangq/mmc/blob/master/matlab/mmcjmus.m

Qianqian

---

From: mcx-...@googlegroups.com <mcx-...@googlegroups.com> on behalf of zhiguan wang <qiqiwa...@gmail.com>
Sent: Friday, February 28, 2025 7:36 AM
To: mcx-users <mcx-...@googlegroups.com>
Subject: [mcx-users] the positive value in Jacobian

 

You don't often get email from qiqiwa...@gmail.com. Learn why this is important

--
You received this message because you are subscribed to the Google Groups "mcx-users" group.
To unsubscribe from this group and stop receiving emails from it, send an email to mcx-users+...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/mcx-users/1d0722b5-abc5-483f-b1c2-02fea545ed86n%40googlegroups.com.

[zhiguan wang]

Hi Prof. Fang,

Thank you for your quick response and detailed explanation.

Best regards

Zhiguan

'Fang, Qianqian' via mcx-users <mcx-...@googlegroups.com> 于2025年3月5日周三 22:42写道：

You received this message because you are subscribed to a topic in the Google Groups "mcx-users" group.
To unsubscribe from this topic, visit https://groups.google.com/d/topic/mcx-users/p_rB5Y07qbU/unsubscribe.
To unsubscribe from this group and all its topics, send an email to mcx-users+...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/mcx-users/BYAPR06MB4103F56A5BE412F79B1949D3E4CB2%40BYAPR06MB4103.namprd06.prod.outlook.com.

[Vytautas Gradauskas]

Hi all,

This reminded me of a video that Prof Fang has on mcx.space about absorption and scattering Jacobians (video: https://mcx.space/tutorials/mmc/replay.htm). I think this is the perfect thread to post it here