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Question 1

The objective function for TACs is a residual least square sum function or a weighted residual least square sum (WRSS) function. what are the formulas for these functions w.r.t. TACs

Answer 1

sum_t ( [concentration estimate (t) - concentration measured (t)]^2 )

t = mid-time?

in weighted version, weight = duration for mid-time / # measurements

Question 2

The Nonlinear Least Squares Method is regarded as a “golden standard” for parameter estimation

what is the Nonlinear Least Squares Method (fitting).

Answer 2

have initial parameters for estimation model

compare original and estmation using objective function

update estimated parameters

repeat

Question 3

what determines the quality of fitting (Nonlinear Least Squares Method)

Answer 3

dependent on the choice of initial estimates - There may be several local minima, might get stuck at one or may not converge.

Global minimum is the one with the lowest WRSS.

Several initial estimates are required to find global min (optimal result)

Question 4

why is WRSS not reliable

Answer 4

because WRSS would decrease as the model order (degree of freedom) increases ?????????????????????

Question 5

what is a Degree of Freedom

Answer 5

the number of independent pieces of information available to estimate another piece of information.

Here, the number of estimated variables.

Question 6

what are two alternative objective functions that compensate for the number of degrees of freedom (Test of Model Order)

Answer 6

Akaike information criterion (AIC):
AIC = WRSS + 2 p

Schwarz criterion (SC):
SC = WRSS + p ln (p)

p = number of parameters

Question 7

why is the Nonlinear Least Squares Method not suitable for voxel-by-voxel parameter estimation

Answer 7

High Computational cost due to nonlinear iterative procedure with slow converging speed.

Question 8

what is Autoradiography

Answer 8

a well established technique for estimating the distribution of tracer within an organ in animal experiments. fast method to derive rCMRGlc images in vivo. Static scan 45~60 min, duration ~10 min. 6 min in Biograph64 ???

An autoradiograph is an image on an x-ray film or nuclear emulsion produced by the pattern of decay emissions from a distribution of a radioactive substance.

Question 9

describe how Autoradiography works

Answer 9

At a given time point after tracer administration, the
animal is sacrificed and radiation emitted from thin slices of the areas of interest is utilized to directly expose photographic emulsion.

Assumption: mean rate constants used in the estimation. Reason: the accuracy of CMRGlc estimation is rather intensive to variation of the rate constants. ??????????????

Question 10

what is the functional parameter being estimated in Autoradiography

Answer 10

CMRGlc = a x C (T) + b

Question 11

what are some applications of Autoradiography

Answer 11

Acceptable estimation of rCMRGlc for cortex (grey matter)

High bias in pathology
• Tumour
• Stroke