Development and Evaluation of a Physiologically Based Pharmacokinetic Drug-Disease Model of Propranolol for Suggesting Model Informed Dosing in Liver Cirrhosis Patients

Figures & data

Table 1 List of Clinical Studies and Their Demographics Used for the Development and Verification of Propranolol-PBPK-Healthy Population Model

Dose	Sample Size	No. of Females	Age (Years)	Weight (kg)	Race
	(N)		Range	Range
Propranolol IV Administration in the Healthy Population
0.05 mg/kg^Citation65	6	0	20–31	60–90	White American
0.1 mg/kg^Citation66	6	0	24–29	70–100	White American
0.2 mg/kg^Citation27	10	1	22–34	52–86	White American
01 mg^Citation46	15	3	27–67	–––––	European
2.2 mg^Citation26	8	0	23–25	55–85	European
10 mg^Citation28	6	0	23–28	66–81	European
10 mg^Citation47	6	6	24–74	40–67	European
Propranolol Oral Administration in the Healthy Population
05 mg^Citation29	18	4	32–36	–––––	European
10 mg^Citation29	18	4	32–36	–––––	European
40 mg^Citation29	18	4	32–36	–––––	European
40 mg^Citation30	55	31	20–44	–––––	European
40 mg^Citation33	12	0	–––––	–––––	White American
40 mg^Citation48	12	0	20–34	–––––	White American
80 mg^Citation32	6	3	20–28	41–70	European
80 mg^Citation31	18	10	18–26	64.4	White American
80 mg^Citation26	8	0	23–25	55–85	European
80 mg^Citation49	8	2	23–49	–––––	European
80 mg^Citation51	12	6	23–41	62–77	European
80 mg^Citation50	12	0	18–45	54–92	White American
80 mg^Citation52	18	0	18–40	–––––	White American
160 mg^Citation67	24	0	23–44	62–100	European

Table 2 List of Clinical Studies and Their Demographics Used for the Development and Verification of Propranolol- Cirrhosis PBPK Model

Dose	Sample Size (N)				No. of Females				Age (Years)	Weight (kg)	Race
									Range	Range
	Child-Pugh Class				Child-Pugh Class
	A	B	C	Total	A	B	C	Total
Propranolol IV Administration in Cirrhosis Population
0.4 mg/kg^Citation35	1	7	6	14	0	3	4	7	37–78	–––––	European
01 mg^Citation46	6	6	3	15	2	1	0	3	27–67	–––––	European
Propranolol Oral Administration in Cirrhosis Population
40 mg^Citation46	6	6	3	15	2	1	0	3	27–67	–––––	European
80 mg^Citation63	6	6	3	15	0	0	0	0	39–60	48.5–78	European
80 mg^Citation68	9	6	0	15	0	0	0	0	42–60	65.2 ±2.1	Asian
160 mg^Citation62	6	12	6	24	0	0	0	0	–––––	–––––	European

Table 3 Input Parameters Used for the Development of PBPK Model of Propranolol

Input Parameters	Value	Reference
Physicochemical Properties
Major Plasma Protein binding	α1 –Acid Glycoprotein	[^Citation2]
Molecular Weight (g/mol)	259.3
Water Solubility (mg/mL)	61.7	[^Citation69]
pKa (base)	9.45	[^Citation70]
Lipophilicity (Log Units)	3.48	[^Citation71]
Absorption
Specific Intestinal Permeability (cm/min)	5.24×10^−6 (optimized)	Parameter optimization module
Distribution
Fraction Unbound (Fu)	10%	[^Citation72]
Blood to plasma ratio (B/P)	0.89	[^Citation72]
Partition Coefficient Model	Poulin and Theil Standard
Cellular permeability Model	Program Standard
Metabolism
Hepatic plasma Clearance (L/hr)	46
CYP2D6 (µL/min/pmol of enzymes)	15.1249 (Calculated)*	[^Citation73]
CYP1A2 (µL/min/mg of Cyp enzymes)	1.1963 (Calculated)*	[^Citation73]
CYP2C19 (µL/min/mg of Cyp enzymes)	0.3238 (Calculated)*	[^Citation73]
**Additional hepatic clearance (L/hr)	8.06 (calculated)
Excretion
Renal Clearance (L/h/Kg)	0.013	[^Citation22]

Notes: *Back calculated by using the well-stirred model; **17.6% of total hepatic clearance was assigned as additional hepatic clearance.

Figure 1 General workflow of the development of propranolol PBPK model in healthy and cirrhotic populations.

Table 4 Fractions of Physiological Changes, Incorporated in the Propranolol-Cirrhosis-PBPK Model

Parameter	Child-Pugh Class
	A	B	C
Portal Blood flow ^a	0.40	0.36	0.04
Arterial blood flow to liver ^a	1.3	2.3	3.4
Renal Blood flow ^a	0.88	0.65	0.48
Other Organs ^a	1.75	2.25	2.75
Cardiac Output ^a	1.11	1.27	1.36
α1-Acid glycoprotein ^a	0.60	0.56	0.30
Haematocrit ^a	0.39	0.37	0.35
Functional liver mass ^b	0.81	0.65	0.53
GFR ^a	1	0.70	0.36
Hepatic enzymes ^b
CYP2D6	0.76	0.33	0.11
CYP1A2	0.63	0.26	0.12
CYP2C19	0.32	0.26	0.12

Notes:^aFractions of control values as described by Edginton et al 2008;¹⁹ bfractions of control values as described by Johnson et al.¹⁸

Table 5 Mean Observed and Predicted Values of Different Pharmacokinetic Parameters After Intravenous and Oral Administration of Propranolol Among Healthy and Their Ratios (Observed vs Predicted). Average Fold Error (AFE) and Root Mean Square Error (RMSE) of All Predictions of the Developed PBPK Model in Healthy Individuals

PK-Parameters (Unit)
Dose	AUC (µg/L.h)				Cmax. (µg/L)			CL/F (L/h)					AFE	RMSE
	Obs.	Pred.	Ratio Obs/Pred.		Obs.	Pred.	Ratio Obs/Pred.	Obs.	Pred.		Ratio Obs/Pred.
IV Administration
0.05 mg/kg^Citation65	47.04	55.11	0.85		39.41	39.77	0.99	1.06	0.91		1.16		0.86	0.093
0.1 mg/kg^Citation66	121.52	130.95	0.93		30.64	43.64	0.70	0.82	0.76		1.08		0.88	0.113
0.2 mg/kg^Citation27	216.18	215.25	1.004		48.06	89.13	0.53	0.92	0.93		0.99		1.08	0.157
1 mg^Citation46	14.66	9.28	1.58		8.12	11.58	0.70	68.23	107.82		0.63		1.86	0.272
2.2 mg^Citation26	60.23	35.56	1.69		17.56	26.25	0.67	36.53	61.86		0.59		1.22	0.248
10 mg^Citation28	181.75	164.16	1.12		51.2	77.74	0.66	55.02	60.92		0.90		0.86	0.150
10 mg^Citation47	282.51	185.04	1.53		83.53	78.65	1.06	35.4	54.04		0.66		1.56	0.238
Oral Administration
05 mg^Citation29	24.32	25.44	0.96		4.26	3.51	1.21	205.62	196.52		1.05		1.08	0.073
10 mg^Citation29	62.95	50.85	1.28		9.58	7.02	1.36	158.86	196.65		0.81		1.22	0.151
40 mg^Citation48	124.82	170.12	0.73		16.33	24.91	0.66	320.47	235.13		1.36		0.71	0.176
40 mg^Citation29	196.66	200.25	0.98		34.97	28.04	1.25	203.39	199.75		1.02		1.05	0.109
40 mg^Citation30	142.28	213.11	0.67		23.54	29.59	0.80	281.13	187.7		1.50		0.77	0.141
40 mg^Citation46	160.39	251.69	0.64		25.95	24.93	1.04	249.39	158.93		1.56		0.79	0.255
80 mg^Citation50	694.64	500.38	1.39		93.87	48.8	1.92	115.17	159.88		0.72		1.75	1.333
80 mg^Citation51	264.88	433.29	0.61		34.04	56.23	0.61	302.03	184.63		1.64		0.99	0.430
80 mg^Citation52	340.65	502.88	0.68		41.17	48.99	0.84	234.85	159.08		1.48		0.74	1.510
80 mg^Citation31	395.93	606.46	0.65		53.44	67.84	0.79	202.06	131.91		1.53		0.89	0.178
80 mg^Citation26	333.41	449.39	0.74		44.46	51.68	0.86	239.95	178.02		1.35		1.61	0.774
80 mg^Citation49	507.63	411.81	1.23		75.88	51.09	1.49	157.59	194.26		0.81		1.47	0.220
80 mg^Citation32	547.21	450.7	1.21		82.26	56.03	1.47	146.2	177.5		0.82		1.53	0.217
160 mg^Citation67	928.85	833.83	1.11		127.67	98.2	1.30	172.26	191.88		0.90		1.23	0.137
160 mg^Citation74	594.02	811.4	0.73		93.92	101.93	0.92	269.35	197.19		1.37		0.79	0.134

Abbreviations: Obs, observed; Pred, predicted; AFE, average fold error; RMSE, root mean square error.

Figure 2 Comparison of observed and predicted systemic propranolol plasma concentration versus time profile in healthy subjects after IV dose of (A) 0.05 mg/kg,⁶⁵ (B) 0.1 mg/kg,⁶⁶ (C) 0.2 mg/kg,²⁷ (D) 1 mg⁴⁶ (E) 2.2 mg²⁶ (F) and (G) 10 mg^28,47 respectively. Solid line (―) are indicating arithmetic mean, dash line (---------) minimum and maximum concentrations, dotted line (.............) 10th and 90th percentile.

Figure 3 Comparison of observed and predicted systemic propranolol plasma concentration versus time profile in healthy subjects after oral dose of (A) 5 mg,²⁹ (B) 10 mg,²⁹ (C–F) 40 mg,^29,30,46,48 (G–M) 80 mg^{26,31,32,49–52} (N) and (O) 160 mg^67,68 respectively. Solid line (―) are indicating arithmetic mean, dash line (---------) minimum and maximum concentrations, dotted line (.............) 10th and 90th percentile.

Table 6 Mean Observed and Predicted Values of Different Pharmacokinetic Parameters After Intravenous and Oral Administration of Propranolol Among Cirrhosis Populations and Their Ratios (Observed vs Predicted). Average Fold Error (AFE) and Root Mean Square Error (RMSE) of All Predictions of the Developed PBPK Model in Healthy Individuals

PK-Parameters (Unit)
Dose	AUC (µg/L.h)			Cmax. (µg/L)			CL/F (L/h)			AFE	RMSE
	Obs.	Pred.	Ratio Obs/Pred.	Obs.	Pred.	Ratio Obs/Pred.	Obs.	Pred.	Ratio Obs/Pred.
IV Administration in Cirrhosis
0.4 mg/Kg^Citation35	1236.3	743.48	1.66	127.86	273.89	0.47	0.32	0.54	0.60	0.53	0.21
01 mg^Citation46	26.52	31.56	0.84	6.94	7.19	0.97	37.7	31.69	1.19	0.71	0.29
Oral Administration in Cirrhosis
40 mg^Citation46	807.08	582.98	1.38	56.02	40.55	1.38	49.56	68.61	0.72	1.93	0.44
80 mg^Citation68	832.87	1270.32	0.66	59.32	91.88	0.65	96.05	62.98	1.53	0.82	0.30
80 mg^Citation63	2631.5	5482.68	0.48	199.41	169.26	1.18	14.59	30.40	0.48	1.43	0.17
160 mg^Citation62	2272.3	2311.29	0.98	119.35	146.59	0.81	70.41	69.22	1.02	0.98	0.08

Abbreviations: Obs, observed; Pred, predicted; AFE, average fold error; RMSE, root mean square error.

Figure 4 Comparison of observed and predicted systemic propranolol plasma concentration versus time profile in Cirrhosis population (CP-A–C) subjects after IV dose of (A) 1 mg⁴⁶ (B) 0.4 mg/kg,³⁵ an oral dose of (C) 40 mg,⁴⁶ (D) 80 mg,⁶⁹ (E) 80 mg twice daily (b.i.d)⁶³ and (F) 160 mg⁶² respectively. Solid line (―) indicating Arithmetic mean, dash line (---------) minimum and maximum concentrations, dotted line (................) 10th and 90th percentile.

Figure 5 Box-Whisker plots compare the AUC_total and AUC_unbound after oral doses of propranolol among healthy, CP-A, CP-B, and CP-C populations. (A) AUC_total after 40 mg oral dose of propranolol in healthy adults and CP-A–C populations. (B) AUC_unbound after 40 mg oral dose of propranolol among healthy adults and CP-A–C populations. (C) AUC _total up to 20%, 10%, and 5% reduction in oral doses of propranolol in CP-A, CP-B, and CP-C populations respectively as compared to 40 mg oral dose in the healthy population. (D) AUC _unbound up to 20%, 10%, and 5% reduction in oral doses of propranolol in CP-A, CP-B, and CP-C populations respectively as compared to 40 mg oral dose in the healthy population. (E) AUC _total after further 25%, 50%, and 25% reduction in oral doses of propranolol among CP-A, CP-B, and CP-C populations respectively (F) after further 25%, 50%, and 25% reduction in oral doses of propranolol among CP-A, CP-B, and CP-C populations respectively.

Abbreviations: AUC, area under the curve; CP-A, Child-Pugh class A; CP-B, Child-Pugh class B; CP-C, Child-Pugh class C.

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