Table 4.

Reliability of the proposed optimization method using a single data set

data set used for estimation	data set used for validation	μ	a1	a2	a3	a4	a5	a6	α	MSE
TR 700	TR 800	6.1	0.0934	2.0061	3.0154	0.0546	13.9663	16.2603	21.2708	0.010
TR 1600	TR 1700	4.8	0.0776	2.0115	3.5521	0.0427	14.8203	16.0985	20.0637	0.134
TR 2500	TR 2600	7.2	0.0977	2.0252	2.7860	0.0588	13.4378	16.4564	22.1770	0.0004
data1	data2	7.0	0.0984	2.0208	2.8143	0.0584	13.4949	16.2035	21.8294	0

Note: Rows 1 to 3 list the estimated parameters {a₁ a₂, a₃, a₄, a₅, a₆, α} of the cardiac response function for subject #1 from a single data set for estimation (see first column) and another single data set for validation (see second column). The last row contains the parameters for the full run using datal and data2 (see Fig.1, Table 2). The third column lists the optimum curvature $\mu ={\int }_0^{30s}\mid \frac{d^2{h}_C\left(t\right)}{d{t}^2}\mid dt$ where the minimum of the objective function occurred using the validation data set. The final column list the mean-squared error (MSE) of each estimated cardiac response function to the optimized cardiac response function using all available fMRI data as listed for subject #1 in the last row and Table 2.