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[page 12] [Eye Reports 2011; 1:e5]

What are the half-lives 
of ranibizumab and aflibercept
(VEGF Trap-eye) in human
eyes? Calculations with a
mathematical model
Michael W. Stewart
Mayo Clinic School of Medicine,
Jacksonville, FL, USA

Abstract 

The aim of the article is to estimate the
intravitreal half-lives of ranibizumab and
aflibercept (VEGF Trap-eye; VTE) in human
eyes. Using a published mathematical model
for rabbits, the intravitreal half-lives of
ranibizumab and bevacizumab were calculated
and compared to empirical data. The slope coef-
ficient within the model was changed to set the
bevacizumab output equal to experimental val-
ues to meet 3 goals: firstly, to validate the model
in rabbit eyes; secondly, to test the mutability of
the model to monkey eyes; thirdly, to calculate
the half-lives of ranibizumab and the VTE in
human eyes. The half-life calculations for
ranibizumab deviate from published rabbit and
monkey values by only 8.3% and 4.2%. Using
the experimentally determined half-life of
bevacizumab in human eyes (8.25 days) to set
the equation, the half-lives of ranibizumab and
the VTE are calculated to be 4.75 days and 7.13
days in human eyes. The intraocular half-lives
of ranibizumab and the VTE are estimated
using existing published animal and human
data and a mathematical model. The validity of
these half-lives and binding activities, however,
awaits clinical correlation.

Introduction

Antibody based anti-VEGF drugs have
become standard of care for the treatment of
exudative age-related macular degeneration
and are frequently administered for diabetic
retinopathy and retinal vein occlusions. The
VIEW studies showed that ranibizumab and
the aflibercept (VEGF Trap-eye; VTE) had com-
parable peak clinical effects (Heier J, Presen -
tation, Angiogenesis, Miami, FL, February 11,
2011; Smith Urfurth U, Presentation,
Angiogenesis, Miami, FL, February 11, 2011)
suggesting that the maximum clinical
response achievable with anti-VEGF monother-
apy in a study population may have been
reached by the currently available drugs. New
anti-VEGF agents may need to be differentiat-

ed more by their duration of action than by
their peak clinical effect.The duration of clini-
cal action of anti-VEGF drugs is determined by
a combination of binding strength and intraoc-
ular half-life.1,2 The intravitreal half-life of
most drugs is first determined in animal mod-
els, usually rabbit and/or monkey, and then in
humans during phase I-III trials or post-
approval. Pharmacokinetic studies in human
eyes usually consist of intravitreal drug injec-
tions followed several days to weeks later by
sampling of the vitreous or aqueous during a
surgical procedure. For most drugs, pharmaco-
kinetic data in at least 1 animal model has
been determined and some, such as ranibizu -
mab, receive regulatory approval without
human pharmacokinetic studies.3,4

The goal of this study is to estimate the as
yet undetermined intravitreal half-lives of
ranibizumab and the VTE in humans by using
experimental animal and human data com-
bined with a previously published mathemati-
cal model.5

Materials and Methods

A Medline search for studies reporting phar-
macokinetic data on ranibizumab, bevacizum-
ab, the VTE and similar macromolecules in
both animals and humans was performed.
Unique animal models - rabbit and monkey -
that tested both ranibizumab and bevacizumab
or structurally similar molecules were identi-
fied.6-8 The intravitreal half-life of bevacizumab
in humans was calculated by averaging values
from published studies.9-10 A previously pub-
lished mathematical model that calculated
intravitreal drug half-lives in rabbits was
employed.5 The model predicts the half-life of a
drug according to the following equation:

Log t1/2 = -0.32+0.432* (Log MW)-0.157*
(Log P)+0.003* (dose / solubility) at pH 7.4 

where: 
t1/2 is the half-life of the compound.
MW is the molecular weight of the compound.
Log P is the logarithm of P, the partition coeffi-
cient or the ratio of the concentrations of an
un-ionized compound in two immiscible phas-
es at equilibrium. As such, Log P is the
lipophilicity of the compound and P=-0.51 for
macromolecules. 
The ratio of dose/solubility is assumed to be 1
for this data set. 
To test the validity of the model, the half-

lives of ranibizumab and bevacizumab were
calculated. The slope coefficient (0.432) was
changed slightly to set the half-life of beva-
cizumab equal to the published value, the
expected half-life of ranibizumab was re-calcu-
lated, and the deviation, as a percentage from

the published value, was calculated. The muta-
bility of the model to monkey eyes was then
tested. The slope coefficient was changed to
set the bevacizumab half-life equal to the pub-
lished value, the expected ranibizumab half-
life was calculated, and the deviation, as a per-
centage from the published value, was calcu-
lated. Finally the model was used to calculate
the drug half-lives in human eyes. The slope
coefficient was changed to set the bevacizum-
ab half-life equal to the average of the pub-
lished values (8.25 days) and the half-lives of
ranibizumab (MW-48 kD) and the VTE (MW-
110kD) were calculated. To determine the pos-
sible relationship between the size of the eye
and the mutability of the equation, the slope
coefficients were graphed against the intravit-
real volumes and subjected to a regression
analysis.

Results

Based upon a review of the literature (Table
1),3,4,6-14 the following animal models were
selected against which to test the validity and
mutability of the modified half-life equation: i)
For rabbits, Bakri et al. determined ranibizum-
ab and bevacizumab half-lives of 2.88 days and
4.32 days respectively;7,8 ii) For monkeys,
Mordenti et al. determined Fab and HER2
(macromolecules structurally similar to
ranibizumab and bevacizumab, respectively)
half-lives of 3.2 days and 5.6 days respectively.6

Using the published half-life equation, the
initially calculated half-lives of ranibizumab
and bevacizumab in rabbit eyes were 2.54 Days
and 4.17 Days. The slope coefficient was
increased from 0.43200 to 0.43564 to set the
output for bevacizumab to equal 4.32 days. The
re-calculated half-life of ranibizumab was 2.64
days, only 8.3% shorter than the experimental

Eye Reports 2011; volume 1:e5

Correspondence: Michael W. Stewart, 4500 San
Pablo Rd., Jacksonville, FL  32224, USA. 
Tel. +1.904.953.2232 - Fax: +1.904.953.7040.
E-mail:  stewart.michael@mayo.edu

Key words: age-related macular degeneration,
ranibizumab, bevacizumab, VEGF Trap, afliber-
cept, half-lives, pharmacokinetics.

Received for publication: 11 June 2011.
Accepted for publication: 31 July 2011.

This work is licensed under a Creative Commons
Attribution NonCommercial 3.0 License (CC BY-
NC 3.0).

©Copyright M.W. Stewart, 2011
Licensee PAGEPress, Italy
Eye Reports 2011; 1:e5
doi:10.4081/eye.2011.e5

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[Eye Reports 2011; 1:e5] [page 13]

value (2.88 days). To establish the mutability
of the half-life equation to monkey eyes, the
slope coefficient was increased to 0.45720 to
set the bevacizumab output to 5.6 days. The
calculated half-life of ranibizumab was 3.34
days, only 4.2% above the experimental value
(3.2 days). To calculate the half-lives of
ranibizumab and the VTE in human eyes the
slope coefficient was changed a third time.
Increasing the coefficient to 0.49000 calculates
the bevacizumab half-life to be 8.25 days, the
average value reported in the literature. By
inputting the molecular weights of ranibizum-
ab and the VTE, their half-lives are calculated
to be 4.75 days and 7.13 days. To determine a
possible relationship between eye size and
mutability of the equation between species,
the 3 slope coefficients used in the previous
calculations were graphed against eye volumes
(Figure 1).
A linear relationship with a high correlation

coefficient (r2 = 0.9956) was determined.

Discussion

Accurate intraocular drug half-lives allow
physicians to create efficacy models to predict
the results of untested clinical situations and
to more accurately predict drug washout peri-
ods when patients change medications or
enter controlled clinical trials. A reliable math-
ematical model would enable physicians to
design better clinical studies and provide
improved patient care. Experimental pharma-
cokinetic data from rabbits, monkeys and
humans has been published for the 3 antibody
based anti-VEGF drugs but only bevacizumab
has been studied in all 3 species.3,4,6-13 Until
human data for ranibizumab and the VTE
become available, half-life calculations based
upon a methodically derived mathematical
model may provide the most accurate values.
Published reports show that intravitreal half-
life differences exist even for the same drug
within a single species. These differences may
be due to several factors including vitreous and
aqueous sampling techniques, drug reflux at
the time of injection, and drug assay technique
and performance. When choosing experimen-
tal models with which to make half-life com-
parisons between different drugs, models that
test at least 2 drugs – Bakri et al.’s rabbit
model and Mordenti et al.’s monkey model –
would minimize artifactual differences. A
mathematical model derived from experimen-
tal rabbit data5 provides the best starting point
for predicting drug half-lives in other species.
This model was created from half-life data of
over 60 drugs, including bevacizumab.
According to the model the most important
determinant of drug half-life is molecular size;
less important factors include lipophilicity,

drug solubility, dose, salt form factor, and eye
pigmentation. The model predicts that macro-
molecules with similar structure (e.g. Fab anti-
body fragments or full length antibodies)
should have similar half-lives within a given
species. Experimental data with rituximab
(MW - 145 kD) – intravitreal half-life of 4.7
days in rabbits - suggests this to be true.14

Since lipophilicity, drug solubility, and salt
form factor are independent of the vitreous vol-
ume, the model was altered by changing only
the slope coefficient. Bevacizumab data exists
for all 3 species so its half-lives were used to
guide changes of the slope coefficient within
the mathematical model. These changes were
made with 3 goals in mind: i) To establish
validity of the model in rabbits; ii) To establish
mutability of the model to monkeys; iii) To cal-
culate half-lives of ranibizumab and VTE in
humans.
The bevacizumab guided changes in the

model produced ranibizumab values of 2.64
days in the rabbit and 3.34 days the monkey,
differing from the experimental values by only
8.3% and 4.2%. This finding suggested that the
model was accurate for macromolecule half-
lives in rabbit eyes and mutable to monkey
eyes. Given these findings, the model was used
to calculate the half-lives of ranibizumab (4.75
days) and the VTE (7.13 days) in humans. Both
published experimental results and the half-
life calculations obtained with this adapted
model are consistent with 2 commonly held
principles of intraocular drug pharmacokinet-
ics. Firstly, the intravitreal half-life of a given
drug increases with the size of the eye. When
the slope coefficient is graphed against the
size of the eye a highly correlated (r2=0.9956)
linear relationship is seen. This limited exper-
imental data suggests that the half-life of a
drug in one species may be predicted based
upon experimental data in other species. More
work, however, needs to be done to determine

the validity of such a mathematical relation-
ship. Secondly, the half-lives of drugs with sim-
ilar structures increase according to the loga-
rithm of molecular weight. This suggests that
for the anti-VEGF drugs the intravitreal half-
lives should rank as follows: bevacizumab >
VTE > ranibizumab.
The major weakness of this model concerns

the mutability of the rabbit-determined model
between species. Though changing the slope
coefficient seems a logical transformation, the
validity of this strategy must await confirma-
tion with experimental data.

References

1. Stewart MW. Predicted biologic activity of
intravitreal bevacizumab. Retina 2007;27:
1196-200.

2. Stewart MW, Rosenfeld P. Predicted biolog-
ical activity of intravitreal VEGF Trap. Br J
Ophthalmol 2008;92:667-8.

3. Gaudreault J, Webb W, Van Hoy M, et al.
Pharmacokinetics and retinal distribution
of AMD rhuFab V2 after intravitreal admin-
istration in rabbits. AAPS Pharm Sci
1999;Suppl 1:2142.

Article

Figure 1. Intravitreal volume is graphed
against the slope coefficient of the mathe-
matical model, as determined by beva-
cizumab half-lives.

Table 1. Intraocular half-lives of ranibizumab, VTE, bevacizumab and similar macromol-
ecules are listed.

Authors Drug Species Half-life

Bakri8 Ranibizumab Rabbit 2.88 days
Gaudreault11 Ranibizumab Rabbit 2.89 days
Regeneron VTE Rabbit 4.79  days
Bakri7 Bevacizumab Rabbit 4.32 days
Nomoto12 Bevacizumab Rabbit 5.95 days
Miyake13 Bevacizumab Rabbit 2.8 days (aqueous)
Kim14 Infliximab Rabbit 4.7  days
Gaudreault4 Ranibizumab Monkey 2.63 days (0.5 mg)0
Gaudreault4 Ranibizumab Monkey 3.9 days (2.0 mg)
Mordenti6 Fab Monkey 3.2  days
Mordenti6 HER2 Monkey 5.6  days
Zhu10 Bevacizumab Human 6.7  days
Krohne9 Bevacizumab Human 9.82 days (aqueous)

Intravitreal volume (mL)

S
lo

p
e
 c

o
e
ff
ic

ie
n

t 0.5

0.49

0.48

0.47

0.46

0.45

0.44

0.43
0 0.5 1 1.5 2 2.5 3 .3.5 4 4.5 5

y= 0.0178x+0.4107

R2=0.9956

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[page 14] [Eye Reports 2011; 1:e5]

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11. Gaudreault J, Fei D, Beyer JC, et al.
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12. Nomoto H, Shiraga F, Kuno N, et al. Phar -
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