Comparison of Compartmental and Minimal PBPK models

for Nonlinear Naproxen Pharmacokinetics in Arthritic Rats

Xiaonan Li (李晓楠), PhD

Clinical Pharmacokinetics Laboratory

China Pharmaceutical University

June 18, 2017

2

Rheumatoid Arthritis (RA)

Chronic, systemic inflammatory autoimmune disease

Joint inflammation, cartilage and bone destruction

Hypoalbuminemia is a common feature associated with RA

Higher serum albumin concentrations in women

Choy EH, Kavanaugh AF and Jones SA (2013) Nat Rev Rheumatol 9:154-163.

Smolen J S, Aletaha D, Mcinnes I B. Rheumatoid arthritis[J]. Lancet, 2016, 388(10055): 2023-2038.

2

PK-PD of highly albumin-bound NSAIDs

3

NSAID-Naproxen (NPX)

NPX

01

02

05

04

03

06

Rapid anti-inflammatory

and analgesic properties

Non-selective COX inhibitor,

blocking PG production

Extensive protein binding (>99.9%),

especially to albumin (>96%)

Concentration-dependent

protein binding

Nonlinear PK in RA patients

(> 500mg)

Inflammatory symptoms control in RA

Ricciotti E et al. Arterioscler Thromb Vasc Biol. 2011 31(5):986-1000.

Aoki T and Narumiya S. Trends Pharmacol Sci. 2012, 33:304-311.

4

Mechanisms Causing Nonlinear PK of NPX

Dose-dependent Clearance

Runkel R (1974) Clinical pharmacology and therapeutics 5:261-266.

Dose-dependent Distribution

Gillette Equation

• Physical volume (Vp & Vt)

• Binding (fu,p & fu,t)

V increases with dose

Saturated binding at high

concentrations/doses,

fu,p , V

CL increases with dose

Total concentration Unbound concentration

Excre

tio

n r

ate CL

5

Research Motivation & Objective

The NPX PK profiles in earlier studies were described using simple

linear clearance models without consideration of the nonlinearity.

Effect of sex differences in albumin concentrations in RA on the

protein binding and disposition of NPX has not yet been well

investigated.

02

01

Objective: Developing PK models incorporating nonlinear binding to account

for the nonlinear PK of NPX in RA and assess the potential influences of sex.

6

Experimental system: Rheumatoid Arthritis in CIA Rats (both sexes)

Determination of plasma albumin concentrations and protein binding

of NPX in arthritic rats

PK studies of NPX in arthritic rats

Development and comparison of extended compartmental and

minimal PBPK (mPBPK) models incorporating nonlinear binding

Outline

7

Males

0 200 400 600 80060

90

120

150

180 Control

Natural growth

Time (h)

Paw

ed

em

a (

mm

2)

Females

0 200 400 600 800

50

100

150 Control

Natural growth

Time (h)

Paw

ed

em

a (

mm

2)

RA in CIA Rats

Day 21 (504 h) Day 16 (384 h)

Natural Growth & Disease Progression

Methods

Protein binding study

• Sandwich ELISA • Ultrafiltration

8

Plasma albumin determination

Animals：CIA rats of both sexes

Sampling time: time to reach peak disease status

Determination of Plasma Albumin & Protein Binding of NPX

9

Plasma Protein Binding of NPX

0 500 1000 1500 20000

50

100

150

200

CM

CF

Cb/C

f

Cb (M)

Rosenthal plots

0 1500 30000

20

40CM

CF

Ct (M)

f u(%

)

Fraction unbound vs. total concentrations

Concentration-dependence Two classes of binding sites

10

Plasma Albumin Concentrations & Protein Binding Data Analysis

Two classes of binding sites

𝐶𝑏𝑝 =𝑛1𝑃𝑡 ∙ 𝐾𝑎1 ∙ 𝐶𝑢𝑝

1 + 𝐾𝑎1 ∙ 𝐶𝑢𝑝+𝑛2𝑃𝑡 ∙ 𝐾𝑎2 ∙ 𝐶𝑢𝑝

1 + 𝐾𝑎2 ∙ 𝐶𝑢𝑝

0 200 400 600 800 1000

0

500

1000

1500

2000CF

CM

Cf (uM)

Cb

( M

)

𝑪𝒖𝒑 𝒐𝒓 𝑪𝒖𝒕 = (− 𝑛1𝑃𝑡 ∙ 𝐾𝑎1 + 𝑛2𝑃𝑡 ∙ 𝐾𝑎2 −𝐶𝑡 ∙ 𝐾𝑎1 + 1 +

4 ∙ 𝑛2𝑃𝑡 ∙ 𝐾𝑎2 ∙ 𝐾𝑎1 + 𝐾𝑎1 ∙ 𝐶𝑡 + 𝑛1𝑃𝑡 ∙ 𝐾𝑎1 + 𝑛2𝑃𝑡 ∙ 𝐾𝑎2 − 𝐶𝑡 ∙ 𝐾𝑎1 + 1 2)/2 ∙ 𝑛2𝑃𝑡 ∙ 𝐾𝑎2 ∙ 𝐾𝑎1 + 𝐾𝑎1

𝑃𝑡𝑡𝑖𝑠𝑠𝑢𝑒

𝑃𝑡𝑝𝑙𝑎𝑠𝑚𝑎= 0.9

Equation fittings

Unbound NPX conc. in plasma/tissue

CM CF0

200

400

600

**

Pla

sm

a a

lbu

min

co

ncen

trati

on

(µ

M)

347±19.97

282±12.07

Albumin conc. (Pt)

Parameters Estimates (CV%)

CIA females CIA males

Ka1 (µM-1) 0.28 (3.53) 0.26 (4.00)

Ka2 (µM-1) 0.0041 (4.2) 0.0056 (11.75)

n1 1 (Fixed)

n2 4 (Fixed)

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NPX PK in Arthritic Rats

Groups Administration methods

Female CIA rats（n=3）10, 25 and 50 mg/kg of NPX

Male CIA rats（n=3）

Experimental design

Qhep ~1200 mL/h/kg

12

01

02

03

04The protein binding of NPX in

tissues is considered to occur

primarily in the interstitial fluid

(ISF)

The binding affinities and numbers of binding sites on

each protein molecule in ISF are the same as in

plasma，with a difference in protein concentrations

According to the “free hormone hypothesis”, disposition

processes often operate only on free drug

The binding of NPX is concentration-

dependent and only to albumin in

either plasma or ISF

PK Model Assumptions

13

Two-compartment Model (2CM) with Nonlinear Binding

𝑑𝐴𝑎𝑑𝑡

= −𝑘𝑎 ∙ 𝐴𝑎

𝑑𝐶𝑝

𝑑𝑡=𝑘𝑎𝑉𝑝

∙ 𝐴𝑎 +𝐶𝐿𝑑𝑉𝑝

∙ 𝐶𝑢𝑡−

𝐶𝐿 + 𝐶𝐿𝑑𝑉𝑝

∙ 𝐶𝑢𝑝

𝑑𝐶𝑡𝑑𝑡

=𝐶𝐿𝑑𝑉𝑡

∙ (𝐶𝑢𝑝 − 𝐶𝑢𝑡)

Model Equations Model Structure

14

2CM with Nonlinear Binding

Table 1-3 PK parameter estimates for unbound NPX after IP administration

Parameters Definition Estimates (CV%)

ka (1/h) Absorption rate constant 0.814 (7.54)

CL (mL/h/kg) Unbound plasma clearance 1370 (4.73)

Vp (mL/kg) Central volume of distribution 32.36 (Fixed)

CLd (mL/h/kg) Unbound distribution clearance 647.2 (18.61)

Vt (mL/kg) Peripheral distribution volume 140.7 (9.27)

CIA Females

0 5 10 15 20 250.1

1

10

100

1000

CIA Males

0 5 10 15 20 250.1

1

10

100

1000

Time (h)

NP

X c

on

cen

tra

tio

ns

(µg

/mL

)

Model Fittings PK Parameter Estimates

VISF = 174 mL/kg

15

Extended 2CM Simulations Overlaid with Published Data

From literature:

Healthy female rats (10 mg/kg oral dose), ka=0.4 1/h, F=0.9

0 4 8 120.01

0.1

1

10

100

1000

Time (h)

To

tal c

on

ce

ntr

ati

on

(

g/m

L)

NIALL NS et al., (1977). Ann Rheum Dis. 36(3):244-248.

● Plasma

○ ISF

16

Basic Minimal PBPK model

Cao Y, et al. J Pharmacokinet Pharmacodyn 2013; 40: 597-607.

mPBPK ModelWhole Body PBPK Model

Lumping

17

Fick’s Laws of perfusion

Rapid equilibrium of tissue : venous blood

Basic Minimal PBPK model

18

Basic mPBPK Model with Nonlinear Binding

𝑑𝐴𝑎𝑑𝑡

= −𝑘𝑎 ∙ 𝐴𝑎

𝑉𝑝 ∙𝑑𝐶𝑝𝑑𝑡

= 𝑘𝑎 ∙ 𝐴𝑎 + 𝑓𝑑 ∙ 𝑄𝑐𝑜 ∙ (𝐶𝑢𝑡 − 𝐶𝑢𝑝) − 𝐶𝐿𝑝 ∙ 𝐶𝑢𝑝

𝑉𝑡 ∙𝑑𝐶𝑡𝑑𝑡

= 𝑓𝑑 ∙ 𝑄𝑐𝑜 ∙ (𝐶𝑢𝑝 − 𝐶𝑢𝑡)

Model Equations Model Structure

𝒇𝒅 ≤ 1，Vp + Vt = ECF (206.29 ml/kg)

ISF

Kp = fu,p/fu,t

19

Possible Tissue Distribution of NPX

NPX is a weak acid (pKa=4.5)

Henderson-Hasselbalch equation for acids：

pH = pKa + log ([ionized]/[unionized])

The unionized fraction of NPX in ISF/plasma (pH 7.4) is much less than that in

cell water (pH 7.0).

pH Partition Hypothesis: only the unbound unionized drug is able to permeate

cell membranes in vivo.

Therefore, it is very likely that NPX distributes mainly into the extracellular

space with minimal cell distribution.

Poulin P. J Pharm Sci, 2015, 104(7): 2359-68.

• VNPX (Human) ~ 0.14 L/kg

• VECF (Human) ~ 0.26 L/kg

20

Basic mPBPK Model with Nonlinear Binding

Table 1-4 PK parameter estimates for NPX in CIA rats after IP administration

Parameter (units) Definition Estimates (CV%)

ka (1/h) Absorption rate constant 0.98 (8.3)

fd Fraction of cardiac plasma flow 0.15 (12.9)

CL (mL/h/kg) Unbound plasma clearance 1438 (3.2)

Vp (mL/kg) Plasma volume 32.36 a

Vt (mL/kg) ISF volume 173.93 a

Qco (mL/h/kg) Cardiac plasma flow 7650 a

CIA Females

0 5 10 15 20 250.1

1

10

100

1000

CIA Males

0 5 10 15 20 250.1

1

10

100

1000

Time (h)

NP

X c

on

cen

trati

on

s (µ

g/m

L)

Model Fittings PK Parameter Estimates

Model Simulations Overlaid with Published Data

21

Model Simulations

0 5 100

5

10

15

0 5 10

0

50

100

150

200

NP

X c

on

cen

tra

tio

n (µ

g/m

L)

Time (h)

Total NPX Total NPX

Unbound NPX Unbound NPX

Female CIA Male CIA

—— Plasma

------ ISFPlasmaSynovial fluid

Published Human Data

Basic mPBPK Model with Nonlinear Binding

● Plasma○ ISF

Doherty et al., (1977) Ann Rheum Dis. 36:244.

Huntjens DR et al., (2006) Br J Pharmacol. Jun;148(4):396-404.

Day RO et al., (1999) Clin Pharmacokinet 36:191-210.

22

Model Comparison

Compartmental model mPBPK model

Model structure Limited physiologic or anatomic reality Physiological and anatomical properties

Model fittings Similar fitting results for the plasma PK data of NPX

PK parametersDepend highly on the quality of the PK

data;

Unclear physiologic relevance

Physiological-relevant PK parameters;

Separates system- and drug- specific

parameters

Assessment of

tissue

distribution

Drug concentrations outside of

plasma, especially when protein

binding is nonlinear, cannot be

reasonably predicted

Allows reasonable calculation of total

and unbound NPX concentrations in ISF

Concentration–dependent protein binding was incorporated into a classic type of 2CM

and the basic mPBPK model to account for the nonlinearity of NPX PK in arthritic rats.

Both models operated distribution and elimination processes using unbound drug and

allowed a global analysis of all PK data over a range of doses simultaneously.

However, there are advantages to be gained by use of the extended mPBPK model for

describing the PK of NPX, particularly for describing unbound NPX in ISF and SF,

adjacent to the site of action. This serves as the prelude for establishing more

reasonable PK-PD relationship of NPX in RA.

Sex differences in albumin concentrations did not produce differences in PK, suggesting

that other factors (e.g., drug metabolism) are involved. However, the underlying

mechanisms still need further investigations.

23

Summary

24

Compartmental model mPBPK model

Related Published Papers

25

Dr. William J. Jusko

Dr. Debra C. DuBois

Dr. Richard R. Almon

Dr. Yanguang Cao

NIH Grant GM 24211

Acknowledgements

Thank you!

Dr. Xijing Chen