706 VOLUME 87 NUMBER 6 | JUNE 2010 | www.nature.com/cpt
ARTICLES nature publishing group
An estimated 170 million people, or ~2.1% of the world popula-
tion, are currently infected with hepatitis C virus (HCV); this
is more than four times the number of people living with HIV.
1

e current standard of care for patients with chronic hepati-
tis C (CHC) is the combination of pegylated interferon- Α and
ribavirin.
2,3
Successful HCV treatment outcome, i.e., sustained
virologic response (SVR), is dened as a patient’s viral load
being below the HCV RNA detection limit at a follow-up evalu-
ation at 24 weeks aer the completion of the treatment. In large,
randomized, multicenter trials, SVR has been attained in up
to 66% of treatment-naive patients by treating with the opti-
mal regimen of peginterferon Α-2a plus ribavirin.
4,5
e HCV
genotype 1 (G1) virus is more dicult to treat. Patients infected
with this genotype—approximately 70% of CHC patients in
the United States
6
—are less likely to achieve an SVR as com-
pared with patients infected with HCV non-genotype 1 (Gn1).
Approximately 50% of the patients with HCV G1 achieved
an SVR when treated with peginterferon Α-2a plus ribavirin,
whereas ~80% of patients with HCV Gn1 achieved an SVR
despite receiving treatment of a shorter duration at a lower
dose of ribavirin.
5
Patients with HCV, therefore, represent a
population with a continued unmet medical need, with many of
them having the potential to attain SVR if optimized treatment
approaches are adopted.
e process of modeling HCV dynamics during therapy has
led to important insights into the life cycle of the virus, elu-
cidating the kinetic parameters governing viral infection and
hepatocyte death, the antiviral eects of interferons, and the
manner in which ribavirin aects HCV treatment.
7
Models
of HCV kinetics have provided a means to compare varied
treatment regimens and outcomes in dierent patient popula-
tions.
8
A model of HCV infection was originally proposed by
Neumann et al.,
9
who adapted a model of HIV infection.
10,11

e Neumann model adequately describes the typical outcome
of short-term therapy, characterized by an initial rapid viral
decline followed by a second, slower decline until HCV RNA
becomes undetectable.
12,13
is model has been frequently used
to describe viral-load proles aer short-term treatment.
8,14,15

However, aer the current long-term standard-of-care treat-
ment, the virus is not eradicated in all CHC patients.
5
In the
patients who do not attain SVR (i.e., patients in whom the virus
is not eradicated), the viral load either rebounds to pretreatment
levels during therapy (breakthrough) or returns to pretreatment
levels upon cessation of therapy (relapse).
13
e Neumann model
cannot describe these two phenomena, and, crucially, it can-
not describe SVR.
13
ese phenomena are the primary reason
that early viral response does not uniformly predict the clinical
end point. Finally, and most important, previous analyses have
1
Exprimo NV, Mechelen, Belgium;
2
F. Hoffmann–La Roche Ltd., Basel, Switzerland;
3
Department of Mathematics, INRIA Saclay, University Paris-Sud, Orsay, France.
Correspondence: NL Jumbe (drshasha@gmail.com)
Received 30 October 2009; accepted 13 February 2010; advance online publication 12 May 2010. doi:10.1038/clpt.2010.35
A Comprehensive Hepatitis C Viral Kinetic
Model Explaining Cure
E Snoeck
1
, P Chanu
2
, M Lavielle
3
, P Jacqmin
1
, EN Jonsson
1
, K Jorga
2
, T Goggin
2
, J Grippo
2
,
NL Jumbe
2
and N Frey
2
We propose a model that characterizes and links the complexity and diversity of clinically observed hepatitis C viral
kinetics to sustained virologic response (SVR)—the primary clinical end point of hepatitis C treatment, defined as an
undetectable viral load at 24 weeks after completion of treatment)—in patients with chronic hepatitis C (CHC) who have
received treatment with peginterferon Α-2a pi ribavirin. The new attributes of our hepatitis C viral kinetic model are (i) the
implementation of a cure/viral eradication boundary, (ii) employment of all hepatitis C virus (HCV) RNA measurements,
including those below the lower limit of quantification (LLOQ), and (iii) implementation of a population modeling
approach. The model demonstrated excellent positive (99.3%) and negative (97.1%) predictive values for SVR as well as
high sensitivity (96.6%) and specificity (99.4%). The proposed viral kinetic model provides a framework for mechanistic
exploration of treatment outcome and permits evaluation of alternative CHC treatment options with the ultimate aim
of developing and testing hypotheses for personalizing treatments in this disease.

CLINICAL PHARMACOLOGY & THERAPEUTICS | VOLUME 87 NUMBER 6 | JUNE 2010 707
ARTICLES
used a naive method of handling the HCV RNA measurements
below the lower limit of quantication (LLOQ) by omitting all
such data, despite the fact that these contain critical information
regarding long-term treatment outcome.
In this article, we propose a novel approach to modeling
the viral kinetics in hepatitis C. First, a nonlinear mixed-
eects model was developed by maximum likelihood estima-
tion (MLE) of the parameters, using the extended stochastic
approximation expectation-maximization (SAEM) algorithm
as implemented in the MONOLIX software (http://www.
monolix.org). Individual long-term HCV kinetic profiles
were simultaneously described for 2,100 patients with CHC
who received treatment with peginterferon Α-2a, alone or in
combination with ribavirin, using a wide spectrum of dosing
regimens. Second, HCV RNA measurements below the LLOQ
were included. e proposed model permits the distinction
between SVR and LLOQ by including censored data resid-
ing between the HCV RNA LLOQ and the irrevocable lower
boundary of zero. ird, cure or complete virion eradication
was determined from viral kinetics via implementation of a
viral eradication boundary. At the time point at which treat-
ment drives the system to less than one infected hepatocyte,
the production of virions was set to zero. e results from the
model, characterizing the dierences between patients who
attain SVR and those in whom treatment fails, were explored in
order to derive hypotheses relating to the mechanisms under-
lying failure or success of treatment.
RESULTS
e parameters of the model were estimated with good precision
(Table 1). e typical value of the basic reproduction number
R
0
was estimated to be 7.2, with an interindividual variability
of 137% coecient of variation. e relatively large interindi-
vidual variability probably reects the large intrinsic biological
dierences in CHC disease. R
0
represents the relative drug-eect
distance from the treatment intervention goal, the goal being
to drive the reproduction number during treatment (R
T
) to <1
(Supplementary Note S2 online), so as to increase the likeli-
hood of attaining SVR (i.e., cure, dened as I <1 infected hepa-
tocyte). Indeed, inspection of the individual parameter estimates
in patients experiencing a breakthrough during therapy showed
that the administered drug therapy failed to decrease the repro-
duction number (R
T
) to <1.
16,17
e maximum hepatocyte pro-
liferation rate (r) was 0.00562/day, and simulations based on this
value of r revealed, in 51 liver gra donors, that predicted extent
of liver regeneration matched well with the observed increases
in liver volumes as measured at 1 year aer the right-lobe liver
gra donation (relative to the respective volumes immediately
aer the surgery) (Supplementary Note S3 online
18
). e typi-
cal value of the virion production rate P was 25.1 virions/day,
and the free virion clearance rate c was estimated to be 4.53/day,
corresponding to a free virion half-life of 3.7 h. is half-life lies
within the previously reported range of 1.5–4.6 h.
12,13
e free
virion clearance rate was found not to be inuenced by HCV
genotype. In contrast, the infected cell death rate (δ) appeared to
Table 1 Population parameters of the HCV viral kinetic model fitted to the individual long-term viral-load profiles of 2,100 patients
with CHC receiving chronic treatment with peginterferon Α-2a, alone or in combination with ribavirin
a
Parameter Description Unit Typical value SE (% CV)
c
IIV (% CV)
T
max
Total number of hepatocytes per ml Hepatocytes/ml 18.5 × 10
6
s Hepatocyte production rate Hepatocytes/ml/day 61.7 × 10
3
D Hepatocyte death rate constant Per day 0.003
r Hepatocyte proliferation rate constant Per day 0.00562 22
R
0
d
Basic reproductive number 7.15 9 137
p Virion production rate Virions·hepatocyte/day 25.1 15
c Virion elimination rate constant Per day 4.53 15 120
∆
HCV non-1
Infected cell death rate constant (HCVGn1) Per day 0.192 16 58
b
∆
HCV-1
Infected cell death rate constant (HCV G1) Per day 0.139 3 58
b
ED
50 HCVnon-1
PEG
ED
50
of peginterferon Α-2a (HCV Gn1) Μg/week 1.19 17 281
b
ED
50 HCV-1
PEG
ED
50
of peginterferon Α-2a (HCV G1) Μg/week 20.9 10 281
b
ED
50
RBV
ED
50
of ribavirin mg/kg/day 14.4 18
K Antiviral-effect decay constant Per day 0.0238 13
σ
2
Residual error 0.260 1
The upper part of the table shows the fixed parameters according to our assumptions, the middle of the table shows system-specific parameters, and the lower part shows the
drug-specific parameters. The SE reflects the precision of the estimated parameters, and IIV represents the interindividual variability (Supplementary Note S5 online).
CHC, chronic hepatitis C; CV, coefficient of variation; G1, genotype 1; Gn1, non-genotype 1; HCV, hepatitis C virus.
a
47% received monotherapy with peginterferon Α-2a at a weekly subcutaneous dose of 45 Μg (20 patients), 90 Μg (114 patients), 135 Μg (210 patients), 180 Μg (596 patients), or
270 Μg (38 patients). The patients with CHC and combination therapy were administered a subcutaneous dose of 180 Μg/week of peginterferon Α-2a and a daily dose of 800 mg
or 1,000/1,200 mg of ribavirin. Almost all patients (93%) received 24 weeks of treatment or more, and 61% of patients received 48 weeks of treatment or more.
b
Assumed to be
similar between patients with HCV genotype 1 and non–genotype 1 infections.
c
Because T
max
, s, and d were fixed, no SE is provided.
d
R
0
is defined as the number of newly infected
cells that arise from one infected cell when almost all cells are uninfected, and therefore has no units.