TABLE 3

Fitted parameters [estimate and (CV%)] obtained from mPBPK-PD and full PBPK-PD models with TM and SFM nested within the models

Fitted Parameters	Definition	mPBPK(TM)-PD	mPBPK(SFM)-PD	Full PBPK(TM)-PD	Full PBPK(SFM)-PD
f_Q	Fraction of intestinal flow to enterocyte region	1	0.114 (2.26)	1	0.105 (0.533)
f_d	Fraction of cardiac output to peripheral compartment	0.0021 (0.021)	0.0032 (0.025)	0.0035 (0.002)	0.0048 (0.001)
k_a (h⁻¹)	Absorption rate constant of 1,25(OH)₂D₃	1.43 (0.011)	1.26 (0.013)	1.50 (0.004)	1.61 (0.0021)
k_deg (h⁻¹)	Degradation rate constant of 1,25(OH)₂D₃ in lumen	0.0042 (6.06)	0.0013 (11.6)	0.0017 (2.34)	0.0012 (6.65)
K_peri or K_others	Partition coefficient of peripheral/other compartment	0.117 (0.025)	0.161 (0.032)	0.272 (0.003)	0.335 (0.003)
R_syn (fmol × h⁻¹)	Endogenous synthesis rate of 1,25(OH)₂D₃	50.9 (0.26)	23.0 (0.238)	31.0 (0.247)	21.5 (0.116)
	Turnover rate constants of renal Cyp27b1	—	—	0.220 (11.5)	0.245 (9.72)
(h⁻¹)	Turnover rate constants of renal Cyp27b1	—	—	0.220 (11.5)	0.245 (9.72)
	Hill coefficient for indirect response of renal Cyp27b1 function	—	—	3.57 (14.0)	2.71 (12.1)
(mL×h⁻¹)^{^a}	Hepatic metabolic intrinsic clearance of 1,25(OH)₂D₃ via hepatic Cyp24a1	0.031 (0.841)	0.0782(2.82)	0.0043 (1.78)	0.0010 (3.03)
(mL×h⁻¹)^{^a}	Intestinal metabolic intrinsic clearance of 1,25(OH)₂D₃ via intestinal Cyp24a1	0.229 (0.348)	0.220 (0.196)	0.0011 (0.038)	0.0014 (0.412)
(mL×h⁻¹)^{^a}	Renal metabolic intrinsic clearance of 1,25(OH)₂D₃ via renal Cyp24a1	0.053 (0.435)	0.0641 (0.782)	0.0242 (0.008)	0.0280 (0.0066)
(mL×h⁻¹)^{^a}	Brain metabolic intrinsic clearance of 1,25(OH)₂D₃ via brain Cyp24a1	0.030 (15.0)	0.0345 (3.37)	0.0006 (8.30)	0.0003 (0.412)
	Hill coefficient for indirect response function of hepatic Cyp24a1	—	—	1.24 (2.45)	1.75 (0.020)
	Hill coefficient for indirect response function of renal Cyp24a1	—	—	2.64 (0.665)	3.59 (0.081)
	Hill coefficient for indirect response function of intestinal Cyp24a1	—	—	0.985 (1.22)	2.09 (0.002)
	Hill coefficient for indirect response function of brain Cyp24a1	—	—	0.878 (0.148)	0.576 (0.076)
or (h⁻¹)	Turnover rate constant of hepatic Cyp24a1	0.0413 (0.052)	0.044 (0.708)	0.045 (0.006)	0.047 (0.008)
or (h⁻¹)	Turnover rate constant of intestinal Cyp24a1	0.218 (0.278)	0.174 (0.485)	0.489 (0.005)	0.287 (0.067)
or (h⁻¹)	Turnover rate constant of renal Cyp24a1	0.0256 (0.038)	0.0238 (0.026)	0.012 (0.065)	0.047 (0.008)
or (h⁻¹)	Turnover rate constant of brain Cyp24a1	1.20 (2.73)	2.10 (4.52)	1.28 (0.051)	1.87 (5.10)
	Power coefficient on renal Cyp24a1 enzyme turnover	0.931 (0.112)	0.766 (0.933)	—	—
	Power coefficient on hepatic Cyp24a1 enzyme turnover	1.27 (0.120)	1.33 (0.056)	—	—
	Power coefficient on brain Cyp24a1 enzyme turnover	0.804 (0.389)	0.800 (0.498)	—	—
	Power coefficient on intestinal Cyp24a1 enzyme turnover	1.40 (0.116)	1.42 (0.160)	—	—
HK	Power coefficient on renal intrinsic clearance	0.828 (0.0622)	0.784 (0.0372)	—	—
HL	Power coefficient on hepatic intrinsic clearance	1.86 (0.0769)	0.470 (2.23)	—	—
HBr	Power coefficient on brain intrinsic clearance	0.142 (17.8)	0.374 (5.68)	—	—
HI	Power coefficient on intestinal intrinsic clearance	0.230 (0.246)	0.054 (7.82)	—	—
AIC	Akaike information criteria	9367	9270	10,006	9993
WSSR	Weighted sum of squared residuals	1684	1644	1664	1478
df^{^b}	Degrees of freedom	989	988	986	985
F value^{^c}	(critical F = 3.84)	Calculated F score	24.0^{^d} versus mPBPK(TM)-PD	5.93^{^d} versus mPBPK(TM)-PD	55.3^{^d} versus mPBPK(SFM)-PD
F value^{^c}	(critical F = 3.84)	Calculated F score	24.0^{^d} versus mPBPK(TM)-PD	5.93^{^d} versus mPBPK(TM)-PD	124^{^d} versus PBPK(TM)-PD

↵^a Fitted CL_int,met,T values were adjusted by corresponding unbound fraction of 1,25(OH)₂D₃ in tissue (f_T).
↵^b Degrees of freedom are the number of data points (n = 1010) used in the model minus the number of parameters being fitted.
↵^c F score was calculated using , where df_j > df_i.
↵^d F score suggests a significant improvement in goodness of fit (critical F = 3.84) (Boxenbaum et al., 1974); the rank order of goodness of fit (from poorest to best for optimal fit): mPBPK(TM)-PD < mPBPK(SFM)-PD < full PBPK(TM)-PD < full PBPK(SFM)-PD model.