# [FieldTrip] Help with inverse model

Oostendorp, T.F. (Thom) thom.oostendorp at donders.ru.nl
Thu May 2 10:24:07 CEST 2024

```Dear Sara,

As I am the author of the underlying program dipoli that is called by ft_dipolefitting,  I think that I can answer your questions. As I don’t know exactly how that program is used within ft_dipolefitting, somebody might feel the need to comment to my answers.

On 1 May 2024, at 17:01, Sara Cinelli via fieldtrip <fieldtrip at science.ru.nl<mailto:fieldtrip at science.ru.nl>> wrote:

Hello,
I'm writing you because I would like to better understand the the function for the inverse modeling (ft_dipolefitting). Here are some questions I have:
1. how much is big the grid search that the function can do at the start before the non linear search? For example, if  I specified the location of the source using the cfg.sourcemodel, how big will be the area in which it will do the grid search?

There is no “search grid” in ft_dipolefitting. Dipoli will not just allow a limited number of source locations, it searches the continuous space. There are some limitations: by default, the dipole location is constrained to the compartment in which the initial estimate you provide resides. Dipoli allows some other constraining methods:

Control options:
-d [<value>]  Constrain dipoles to remain at such a distance from the
interfaces that the variation of 1/r^2 over any triangle
is less than <value>% (r is the distance from the source
to the surface). The default value of the criterion is 50%
-f            Normally the sources are constrained to remain in the
compartment where they are in the initial estimate.
This options lifts that constraint

The first one served to keep the dipole away from the boundary in order to prevent numerical problems. I’m not sure whether ft_dipolefitting lets you set these options.

aldo, the algorithm which is used here is just the minimization of the L2 norm?

Yes, it is, with the constraints mentioned above.

2. the method for the non linear search is the gradient descent method, is it correct?

No, it is essentially the Marquard method, which combines steepest decent and pseudo-Newton. See T. Oostendorp and A. van Oosterom: Source Parameter Estimation in Inhomogeneous Volume Conductors of Arbitrary Shape. IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 36. NO. 3. MARCH 1989.

3. I see the possibility to choose between a 'moving' model and a 'regional' one. Is it possible to keep fixed both locations and amplitude, so the algorithm changes only the strength of the dipole?

Actually, the choice is between:
- a moving dipole, i.e. at each sample time a new location is fitted
- stationary dipole location and  free orientation, i.e. the best single position is fitted, but dipole orientation is free at each sample time
- stationary dipole location and stationary orientation, i.e. both location at orientation are fixed in time

I am nog quite sure what you mean with "keep fixed both locations and amplitude, so the algorithm changes only the strength of the dipole”. Fixed amplitude and changing the strength sound opposed to me.

Cheers,
Thom

--
dr. T.F. Oostendorp          東村      205 Dept. of Cognitive Neuroscience
route 200, room 02.282                Donders Center for Medical Neuroscience
phone: +31 24 3614240               Radboud University Medical Center
Kapittelweg 29                              6525 EN Nijmegen, the Netherlands

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