Hi John/Guillaume
I would like to use the Jacobian of the deformation field estimated by Shoot to determine the local volume change of a given brain when it goes from subject space to common space. I am interested in the local volume change over time, i.e. I have longitudinal measurements of the same brain which changes its volume. Could you refer me to a paper (or explain shortly in this email) how the Jacobian is related to the volume change?
I think that the basic math is clear to me – to be sure, I am describing below what I understand and how I would like to estimate the local volume change:
If I have a volume “V1” and perform a volume-changing transformation “T”, the resulting volume can be linearly approximated as “V2=Jac(T)xV1, where V2 is the local volume of the transformed image and V1 the local volume of the image in subject space.
I am wondering whether the Jacobian of the deformation field (estimated by Shoot and generated by the SPM-Util-Module “Deformations”) gives me “V2/V1”?
Here, my concrete problem:
I would like to determine the relative volume change in subject space at timepoint t_k: rV1(t_k)=(V1(t_1)-V1(t_k))/V1(t_1)=1-V1(t_k)/V1(t_1),
If I assume that the volume in common space is the same (V2(t_k)=V2(t_1)), I obtain on of the two equations for the relative volume change as an expression of the Jacobians:
rV1(t_k)=1-Jac(T_t_k)/Jac(T_t_1) ,
or:
rV1(t_k)=1-Jac(T_t_1)/Jac(T_t_k) ,
depending on whether Jac(T)=V2/V1 or Jac(T^-1)=V1/V2 is the Jacobian of the Shoot deformation field generated by the SPM-Util-Module “Deformations”.
PS: Could you also refer me to one or more papers that I can cite when using the above mentioned SPM tools to calculate the desired volume changes?
Thanks for your help!
Greetings from Hamburg,
Siawoosh
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Dr. Siawoosh Mohammadi
Emmy Noether Group "QMRI & in vivo histology"
Department of Systems Neuroscience
University Medical Center Hamburg-Eppendorf
Martinistraße 52, Geb. W34 (Room 210)
20246 Hamburg, Germany
Phone: +49-40-7410-59859
Email: [log in to unmask]
Website: https://goo.gl/NKCgKn
Twitter: @siawooshmn
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