Development of a Pharmacokinetic Model That Accounts for the Plasma Concentrations of Conjugated and Unconjugated Bilirubin Observed in a Variety of Disease States

Figures & data

Table 1 Representative Human Plasma Bilirubin Values in Normal and Pathological Conditions. Concentrations are in μmole/Liter and (in Parenthesis) mg/dl. Analytic Chromatographic (HPLC) Values Were Used When They Were Available; Otherwise, the Standard Diazo Assay Values are Used

	Total	Unconjugated	Conjugated	% Conjugated
Healthy (HPLC)^Citation3	6.2 (0.36)	6.0 (0.35)	0.2 (0.012)	3.2
Reference Range (HPLC)^Citation3	2.0 (0.1) −13 (0.7)	2.0(0.1) –13 (0.7)	0.06(0.003)- 0.5(03)
Reference Range (Diazo)^Citation4	3.5 (0.2) - 20 (1.2)	3(0.15) – 15(0.9)	0.35(0.02) - 4.8(0.28)
Gilbert’s (HPLC)^Citation3	32 (1.8)	31.5 (1.84)	0.29 (0.017)	0.9
Crigler-Najjar I (HPLC)^Citation3	316 (18.5)	316 (18.4)	0.7 (0.04)	0.2
Hemolytic (HPLC)^Citation3	26 (1.52)	25 (1.46)	1 (0.058)	3.8
Chronic alcoholic cirrhosis (Diazo)^Citation5	101 (5.9)	49.6 (2.9)	51.4(3.0)	51
Chronic viral hepatitis (Diazo)^Citation6	75 (4.4)	27 (1.6)	48 (2.8)	64
Dubin-Johnson (Diazo)^Citation7	69 (4.0)	28 (1.64)	40 (2.34)	59
Rotor syndrome (Diazo)^Citation8	102 (6.0)	34.2 (2.0)	68 (4.0)	66
Common duct stone (HPLC)^Citation9	150 (8.8)	10 (0.58)	140 (8.18)	93
Biliary Atresia (Diazo)^Citation10	340 (20)	85 (5)	260 (15)	75
Cholestasis of pregnancy (Diazo)^Citation11	14.2 (0.83)	7.4 (0.43)	6.8 (0.4)	48
Primary biliary cirrhosis (Diazo)^Citation12	170 (10)	51 (3.0)	120 (7)	70

Figure 1 Kinetic model of hepatic bilirubin transport and metabolism. M=rate of bilirubin production. UBp, UBc = Unconjugated plasma and cell concentration, respectively. CBp, CBc = Conjugated plasma and cell concentration, respectively. J_UB, J_CB = OATP mediated influx rate of UB and CB, respectively. Concentrations (UB, CB) are in units of mg/dl and fluxes (M, J) are in units of mg/day.

Abbreviations: J_P, diffusive bidirectional flux rate of UB; J_MRP, protein-mediated efflux rate of CB; J_R, renal excretion of CB; J_Glu, rate of glucuronidation of UB; J_Bile, rate of biliary secretion of CB.

Table 2 Summary of the Normal Human Quantitative Model Parameters and Rate Constants

Symbol	Description	Value	Source
M	Rate of UB synthesis	250 mg/day	Measurement
ClR	CB renal clearance	12 dL/day	Measurement
UBpo	Normal plasma UB	0.35 mg/dl	Measurement
CBpo	Normal plasma CB	0.012 mg/dl	Measurement
UBco	Normal cell UB	= Upo	Assumption
CBco	Normal cell CB	= 10 x Cpo	Assumption
UBpr	Rotor plasma UB	2 mg/dl	Measurement
CBpr	Rotor plasma CB	4 mg/dl	Measurement
RGlu	Normal UB glucuronidation	714 dL/day	Calculation
RBile	Normal CB bile excretion	2082 dL/day	Calculation
P	Passive UB permeability	151 dL/day	Calculation
RMRP	CB MRP efflux rate	495 dL/day	Calculation
KCB	OATP Km for CB	0.2 mg/dl	Estimate
KUB	OATP Km for UB	1.382 mg/dl	Calculation
VM	OATP Vmax	1296 mg/day	Calculation

Table 3 Model Plasma UB and CB Concentrations for Different Pathological Fractional Decreases in the Biliary Secretion Rate Constant (R_Bile)

Fractional Decrease in RBile	Plasma UB (mg/dl)	Plasma CB (mg/dl)
1.0 (Normal)	0.35	0.012
0.1	0.59	0.23
0.05	1.27	1.77
0.046	1.39	2.42
0.04	1.58	3.82
0.03	1.72	7.1
0.02	1.81	12.9

Figure 2 Plasma UB (black) and CB (red) concentration as function of the relative decrease in biliary secretion rate (R_Bile, green). The normal condition is for x=1 fold reduction, and x = 50 corresponds to a R_Bile of 1/50th of normal. The fractional reduction of the biliary secretion rate (green) is indicated on the right side of the graph.

Table 4 Model Plasma UB and CB Concentrations for Different Pathological Fractional Decreases in the Rate of UB Glucuronidation (RGlu)

Fraction Decrease in RGlu	Plasma UB (mg/dl)	Plasma CB (mg/dl)
1.0 (Normal)	0.35	0.012
0.2	0.69	0.014
0.1	1.25	0.018
0.072	1.84	0.022
0.05	3.03	0.03
0.03	6.57	0.054
0.014	19.0	0.137

Table 5 Model Plasma UB and CB Concentration for Pathological Increases in the Rate of Bilirubin Production (M)

Fraction Increase in M	Plasma UB (mg/dl)	Plasma CB (mg/dl)
1.0 (Normal)	0.35	0.012
1.50	0.60	0.021
2.0	0.91	0.033
2.7	1.49	0.058
3.0	1.81	0.07
4.0	3.13	0.145
5.0	4.85	0.26
6.0	6.81	0.44

Table 6 Increase in Plasma UB and CB (mg/dl) Concentration as the Functional Impairment Parameter FR Decreases from 1 (Normal) to 0.025, Simulating Alcoholic Cirrhosis. The Corresponding Reductions in the 5 Model Rate Constants (V_M, R_Bile, P, R_Glu, R_MRP) are Listed in the Second and Third Columns

Functional Impairment (FR)	Fractional Reduction of VM and RBile	Fractional Reduction of P, RGlu, and RMRP	Plasma UB (mg/dl)	Plasma CB (mg/dl)
1.0 (Normal)	1.0	1.0	0.35	0.02
0.5	0.5	0.89	0.79	0.060
0.2	0.2	0.67	2.45	1.125
0.15	0.1	0.58	3.15	3.08
0.1	0.1	0.47	4.1	6.45
0.05	0.05	0.30	6.62	10.17
0.025	0.025	0.17	11.6	12.0

Figure 3 Model simulation of alcoholic cirrhosis. The plasma unconjugated (black) or conjugated (red) bilirubin (mg/dl) is plotted as a function of the inverse of the functional impairment parameter (F_R). The value of F_R =1 corresponds to the normal state.

Figure 4 Plot of the conjugated bilirubin versus total bilirubin for increasing severity of alcoholic cirrhosis. The black line is the model prediction, and the red dashed line is the clinical regression relation of Hur and Park.

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