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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)
11
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
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