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Delay and Dispersion Correction
Since the blood samples used to estimate C_{a}(t) are taken from the
subject's arm, the activity data gathered from them must be corrected
for delay and dispersion within the body. In order to perform the
delay correction, we used the technique of Iida, by performing a
least squares fitting of the equation:

(11) 
where A^{*}(t) in this case is the average activity over grey
matter,
represents integration over frames,
,
,
and
are the fitting parameters, and
C_{a}(t) is the blood data. The delay itself enters this equation by
generating C_{a}(t) from:

(12) 
The function
is the result of performing dispersion
correction on the blood sample data. This is represented by the
equation:

(13) 
which is an implicit deconvolution of the equation:

(14) 
Next: MATLAB Implementation
Up: Mathematical Analysis
Previous: TripleWeighted Integration Method
Mark Wolforth
<wolforth@bic.mni.mcgill.ca>
Greg Ward
<greg@bic.mni.mcgill.ca>
Sean Marrett
<sean@bic.mni.mcgill.ca>