Table 1.

Correction Factor

The values of correction factors based on P(t, a) are listed for t =TMD1 and t =TMD2. The correction factor for C(t) is P(t, a). The correction factor for $\frac{d}{dt}C(t)$ is $\frac{d}{dt}P(t,a)$. The correction factor for $\frac{d^2}{dt}C(t)$ is $\frac{d^2}{dt}P(t,a)$. The following results are reported by Table 1: The correction factors for the signal intensity at TMD1 and for the first derivative value at TMD2 are relatively insensitive to the value a, or equivalently the shape of the gamma-variate function AIF. In contrast, correction factors for the first derivative at TMD1 and the second derivative at TMD2 are more sensitive to a. The second derivative of C(t) at TMD1 is naturally zero so the correction factor $\frac{d^2}{dt}P(t,a)$ is also zero at TMD1.

t	Value a of P(t, a)	Correction Factor P(t, a) for Signal Intensity of tissue curve	Correction Factor $\frac{d}{dt}P(t,a)$ for first Derivative of tissue curve	Correction Factor $\frac{d^2}{dt}P(t,a)$ for second Derivative of tissue curve
TMD1	3	0.3233	0.2707	0
	4	0.3528	0.2240	0
	5	0.3712	0.1954	0
TMD2	3	0.02174	0.0955	0.2306
	4	0.04	0.0956	0.1306
	5	0.05265	0.0902	0.0902