Table 2.

Parameters of cardiac response functions

	a₁	a₂	a₃	a₄	a₅	a₆	α
#1	0.0984 (0.641)	2.02 (2.20)	2.81 (1.88)	0.0584 (0.682)	13.5 (33.2)	16.2 (14.3)	21.8 (3.59)
#2	0.000949 (0.218)	4.47 (4.37)	1.89 (1.14)	0.00917 (1.50)	14.8 (42.0)	12.7 (11.1)	73.4 (0.303)
#3	0.00121 (0.255)	4.91 (4.47)	1.53 (1.07)	0.0183 (1.99)	13.4 (22.7)	13.0 (9.82)	55.4 (0.241)
#4	0.00300 (0.564)	3.69 (3.64)	2.21 (1.19)	0.0115 (1.22)	16.7 (56.3)	11.4 (11.4)	66.3 (0.323)
#5	0.000374 (0.256)	4.34 (4.27)	1.94 (1.14)	0.00333 (1.51)	15.9 (44.0)	12.5 (11.2)	219 (0.304)
#6	0.000761 (0.362)	4.58 (4.11)	1.62 (1.12)	0.00876 (2.04)	14.5 (23.6)	12.8 (9.69)	130 (0.252)
fit of mean function (MSE=6×10⁻³)	0.667	2.97	1.53	1.83	32.5	10.4	0.336
Chang et.al.	0.6/1.0167	2.7	1.6	2.128/1.0167	18.0	12.0	0.0

Note: The obtained cardiac response function was parameterized as $h_{C} (t) = h_{C}^{(0)} (t) + α \frac{d}{d t} h_{C}^{(0)} (t)$ where $h_{C}^{(0)} (t) = a_{1} t^{a_{2}} e^{- \frac{t}{a_{3}}} - a_{4} e^{- \frac{1}{a_{5}} {(t - a_{6})}^{2}}$ . The function h_c(t) was scaled such that var(h_c(t)) = 1. We have also calculated approximations to the cardiac response function where the coefficient for α is smaller such that the approximate cardiac response function (with small α coefficient) is similar to the exact cardiac response function for most time points (t< 30 s). The numbers in parenthesis give coefficients of approximate wave forms with a small α coefficient. The mean squared error (MSE) between the approximate cardiac response function and the exact cardiac response function (which is the solution of the optimization problem) is less than 7×10⁻³.