Modeling of human tumor xenografts and dose rationale in oncology

TECHNOLOGIES

DRUG DISCOVERY

TODAY

Modeling of human tumor xenograftsand dose rationale in oncologyMonica Simeoni1,*, Giuseppe De Nicolao2, Paolo Magni2,

Maurizio Rocchetti3, Italo Poggesi41Clinical Pharmacology Modelling & Simulation, GlaxoSmithKline, Uxbridge, UB11 1BT, United Kingdom2Dipartimento di Ingegneria Industriale e dell’Informazione, Via Ferrata 1, 27100 Pavia, Italy3Independent Consultant, Via T. Grossi 13, 20017 Rho, Milan, Italy4Advanced PKPD Modeling & Simulation, Janssen Research & Development, Milan, Italy

Drug Discovery Today: Technologies Vol. 10, No. 3 2013

Editors-in-Chief

Kelvin Lam – Simplex Pharma Advisors, Inc., Arlington, MA, USA

Henk Timmerman – Vrije Universiteit, The Netherlands

Translational Pharmacology: From Animal to Man and Back

Xenograft models are commonly used in oncology

drug development. Although there are discussions

about their ability to generate meaningful data for

the translation from animal to humans, it appears that

better data quality and better design of the preclinical

experiments, together with appropriate data analysis

approaches could make these data more informative

for clinical development. An approach based on math-

ematical modeling is necessary to derive experiment-

independent parameters which can be linked with

clinically relevant endpoints. Moreover, the inclusion

of biomarkers as predictors of efficacy is a key step

towards a more general mechanism-based strategy.

Introduction

Xenograft models are the most popular preclinical models for

evaluating the anticancer activity of new compounds under

development in the oncology therapeutic area [1]. Despite

some limitations, their implementation is relatively easy and

requires limited resources. Recently, several mathematical

models have been introduced to describe the relationship

between the drug pharmacokinetic and the dynamics of

tumor growth (PK/PD models) in these experiments (see

for instance the reviews from Bonate [2] and Della Pasqua

[3]). These mathematical models are generally based on

*Corresponding author.: M. Simeoni ([email protected])

1740-6749/$ � 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ddtec.2012

Section editor:Oscar Della Pasqua – Leiden/Amsterdam Center for DrugResearch, Leiden, The Netherlands.

biological and physiological grounds, so that their para-

meters can be associated with biological mechanisms and

processes. Furthermore, these models may be used as predic-

tive tools for anticipating the outcome of new dosing regi-

mens and for the optimization of the preclinical

experimental design. It is of note that the predictive value

of animal models does not only rely on experimental vari-

ables (i.e. what is effectively measured), but also on the ability

to identify the underlying physiological processes. Mathe-

matical models can be the suitable tools for extracting the

descriptors of these processes, which can be translated from

preclinical to clinical setting. The purpose of this paper is to

give a general, although not exhaustive, view of the applica-

tion of mathematical modeling as a translational tool for the

interpretation of experimental tumor growth data in xeno-

graft models.

Tumor xenograft models

The use of animal models for cancer chemotherapy studies

was already reported in late 1940s [4]. The use of human

tumors transplanted into animal models (xenografts) faced

initially the problem of tissue rejection by the immune reac-

tion of the host. The most important advance in human

xenograft models has been the introduction of the athymic

.07.004 e365

http://dx.doi.org/10.1016/j.ddtec.2012.07.004


mailto:[email protected]


Drug Discovery Today: Technologies | Translational Pharmacology: From Animal to Man and Back Vol. 10, No. 3 2013

nude mice: animals resulting from the inheritance of a reces-

sive mutation, hairless and exhibiting the congenital absence

of thymus [5]. The consequent inhibition of T-lymphocytes

with reduced capacity to reject ‘foreign’ tissue allowed the

successful transplantation of human tumors, either by direct

implantation of patient biopsy material or via inoculation of

continuous human tumor cell lines [5,6]. The easiest experi-

ment is the subcutaneous xenograft, in which tumor frag-

ments or tumor cell suspensions are implanted ectopically

into the flanks of athymic mice. When the tumors reach a

pre-specified volume, mice are randomized into control and

treated groups and the tumor growth in the different groups

is evaluated by recording the dimensions of the tumors at

selected time points, for instance using calipers or other

techniques. Experimental results are then summarized using

different metrics, such as the ratio of treated to control tumor

weight at a pre-specified time, or the difference in time

(treated-control; tumor delay) to reach a predefined tumor

weight [7].

In general, different issues should be considered to describe

the predictivity of the outcome in xenograft models. One

aspect concerns the assessment of active vs. nonactive com-

pounds. Several experimental factors need to be identified

and controlled to make the xenograft models effective for the

screening of new compounds, for instance, the appropriate

choice of tumor models, the experimental conditions, the

dosing regimens and the exposure achieved during the

experiments, the experimental endpoints and an accurate

statistical assessment to compare the experimental groups

[8]. A retrospective study of National Cancer Institute on 39

cytotoxic anticancer drugs showed that 45% of the 33 agents

with activity in one-third or more of tested pre-clinical xeno-

graft models (median 12 xenograft models per agent) had also

clinical activity (P = 0.04) [9]. However, activity within a

particular histological type of xenograft generally did not

predict clinical activity in the same tumor, with the exception

of non-small cell lung cancer. Several considerations may

explain the examples in which the xenograft model was not

able to identify the active compounds. One potential reason

for the of lack of predictivity may be found in the fact that

tumors are implanted subcutaneously in the animal flank

(ectopically), so these models may not mimic tumors of other

origins. Furthermore, these models, in contrast to the clinical

scenario, do not develop metastases. This motivated the

development of xenograft orthotopic models where

the tumor is implanted in the originary tissue in which the

primary tumor developed [1]. A new promising and sophis-

ticated class of animal models of human cancer are the

genetically engineered models [10], either transgenic or

endogenous. Many experimental models now exist that accu-

rately mimic the pathophysiological and molecular features

of human malignancies, but further investigations are

required to assess if they can replace the xenograft models,

e366 www.drugdiscoverytoday.com

or if the two classes have validity in different diagnostic

applications [1].

Most of the tumor growth inhibition metrics are not

invariant with respect to the experimental conditions. For

instance, the time to maximal value of the tumor growth

inhibition was shown to be dose-, time- and dosing regimen-

dependent [11]. Only mathematical models that are able to

describe tumor growth by dissecting the system-specific prop-

erties can provide compound-specific and experiment-inde-

pendent model parameters. These models can help improve

the experimental design (e.g. predicting the effect of untested

dose levels and dosing regimens) before setting up a confir-

matory experiment, thus contributing to reduce costs of

experiments and number of animals used. It is indeed our

opinion that in many cases, the failure to correlate animal

and clinical results [12] could be attributed to inappropriate

experimental conditions and/or parameter representation of

compound potency.

Mathematical models for tumor growth

In the past 40 years different mathematical models were built

on xenograft animal model data in an attempt to predict the

exposures at different doses and regimens in animals. On one

hand, mathematical modeling provides a more robust way to

summarize pharmacokinetic and pharmacodynamic proper-

ties; on the other hand, it can be even more important as a

translational tool able to provide rational predictions of

clinical findings from the outcome of preclinical experi-

ments. Mathematical models can be grouped into three main

categories: descriptive (empirical), mechanistic and large

scale/system biology models.

The first proposed models were of a descriptive nature like

the logistic function, the von Bertalanffy growth equation

and the Gompertz function [13] which describe the growth

processes of biological organisms, but are based on para-

meters lacking a full biological basis.

Anna Kane Laird in 1964 [14] was the first scientist to use

the Gompertz curve to fit in vitro data of tumor growth

successfully. The same model was subsequently utilized in

animals [15] and humans [16–19]. To be potentially valid for

translational purposes, a model should be able to predict the

expected outcome at different dosing levels and schedules

from the tested regimens in terms of few meaningful para-

meters amenable to being extrapolated to humans. In this

respect, although these models were able to describe and

compare studies, nevertheless, they had difficulties to allow

for changes of dose levels and schedules.

Although the boundary between empirical and mechan-

istic models is not always sharp, a distinctive feature is that

the latter models account for the physiology underlying the

interplay between the tumor growth process and the drug

action without necessarily going into deeper details about the

involved biological mechanism. Two examples are given by

Vol. 10, No. 3 2013 Drug Discovery Today: Technologies | Translational Pharmacology: From Animal to Man and Back

the models of Simeoni et al. [20,21] and Lobo and Balthazar

[22]. Notably, the existence of specific model parameters

representative of drug potency is a key opportunity for trans-

lational purposes. These models were also called Cell Distri-

bution Model (CDM) and Signal Distribution Model (SDM)

respectively [23]. The first one describes the unperturbed

tumor growth with an exponential phase, followed by a

linear one; the drug acts hitting the tumor cells that even-

tually go to death through a transit compartment model

which takes into account the delayed drug response. It has

also been shown that Simeoni’s model can be formally

derived from a minimal set of basic assumptions formulated

at cellular level [24]. By contrast, in the SDM the drug acts

upon a receptor which initiates a signal transduction cascade

whose final product is a modulation of the killing effect

against tumor cells. The necessity to introduce a transit

compartment model to describe the chemotherapeutic effect

was confirmed in the subsequent modifications of the model

by Jumbe et al. [25] and by Sung et al. [26].

The CDM [20] has also been modified to cope with combi-

nation therapies, to serve as a guide in the selection of clinical

doses and the optimal timing of administration of anticancer

agents so as to maximize tumor suppression [27]. To take into

account possible drug interactions, Koch et al. [28] intro-

duced a multiplicative factor on the action of one of the

two drugs. Both models were proposed for drugs with the

same mechanism of action. Rocchetti et al. [29] proposed a

null-interaction model that combines two single drug tumor

growth inhibition (TGI) models (essentially applying the Bliss

independence criterion in a dynamic context). The proposed

model can simulate the behavior of non-interacting drugs,

whereas synergistic or antagonistic behaviors are highlighted

as deviations from the simulated one.

A promising extension of the mechanistic models is repre-

sented by the inclusion of biomarkers. For instance, Bueno

et al. considered the percentage of phosphorylated Smad2 and

Smad3 (pSmad) as biomarkers that drive the inhibition of

tumor growth, described by a CDM [30]. Yamazaki et al. linked

the inhibitory response of cMet phosphorylation in tumor to

the plasma concentration of an anticancer agent, a competi-

tive ATP-binding of cMet kinase, using an effect-compartment

model. They found that the EC90 of the PK-biomarker model

corresponds to the EC50 of the indirect model describing the

tumor growth, suggesting that near-complete inhibition of

cMet phosphorylation is required to significantly inhibit

tumor growth [31]. An analogous approach was implemented

by Salphati et al. [32] who obtained similar IC50 values with

separate indirect response models relating the pharmacoki-

netics of a PI3K inhibitor and the inhibition of Akt and PRAS40

phosphorylation. Using an integrated pharmacokinetic-bio-

marker-tumor growth model, the authors claimed that 30%

continuous inhibition of phosphorylated Akt signal would be

required to achieve tumor stasis.

Another interesting problem is to understand how the

mathematical models developed for in vivo preclinical

experiments can be applied to the in vitro settings. In most

cases, the analyses of in vitro experiments are limited to the

calculation of EC50 values at a given exposure duration [33]

or the description of the inhibition surfaces as a function of

concentrations and exposure times [34,35]. Mechanistic

models were used (signal transduction model vs. phase-

specific and phase-nonspecific model) to describe the delay

between methotrexate exposure and observable tumor

growth inhibition [22]. A more recent investigation, cover-

ing ten commercial anticancer drugs and four compounds in

early discovery phase, demonstrated that the CDM [20] can

be effectively applied also to in vitro data [36]. Differently

from its in vivo version, the cell proliferation did not slow

down to linear but remained exponential for all observed

sizes of cell cultures in the conditions adopted in these

experiments.

Large scale/system biology models try to mimic in fine

detail the biological pathways and physiological processes

involved. We can group them in continuum, and discrete

cell-based models [37,38]. In continuum models the tumor is

treated as a continuous mass, few cell populations are iden-

tified, subcellular processes are not considered and, usually,

stochastic methods are not used [39,40]. By contrast, discrete

cell-based models see the tumor as a collection of interacting

cells (e.g. [40–43]) and are more suitable to describe phenom-

ena like metastases. Large scale/system biology models make

a set of assumptions about tumor growth, involving cell-cycle

kinetics and biochemical processes, such as those related to

antiangiogenetic and/or immunological responses [44,45].

The simplest heterogeneous models split tumor cells into

proliferating and quiescent ones, while more complex mod-

els describe the cell population as age-structured and take

into account subpopulations related to specific phases of the

cell cycle [46–48]. These models have a much larger number

of parameters compared with the empirical and mechanistic

ones, so that extensive quantitative observations (e.g. flow

cytometry analyses, biochemical and immunological marker

measurements, and so forth) are needed to avoid identifia-

bility problems. A compromise between large scale and the

mechanistic models is the ‘model of spheroid growth’

recently proposed by Ribba et al. [49].

Different techniques can be used in a model-based data

analysis depending on the quality of the data, the collection

scheme and the number of subjects. Estimates of the indi-

vidual PK/PD parameters can be obtained from each indivi-

dual profile, or the mean study parameters can be estimated

either from the average treatment profiles [20,22], or from a

population of profiles using a non-linear mixed effect mod-

eling approach [50]. The last technique has the benefit to

evaluate the inter-individual variability of the parameters

within and across studies [51,52]. Designing the studies for

www.drugdiscoverytoday.com e367


Table 1. Variety of experimental conditions and designs used in some xenograft studies. (Lines separate different studies.)

Ref Drug Cell line n per

group

Route Dose (mg/kg) Dose

scheme

Start

day

Sampling times (days)

[20] CPT11 HCT116 5 IV bolus Control, 45, 60 qd1 13 qd 13–22, qd 25–28,

32, 36

Paclitaxel A2780 8 IV bolus Control, 30 q4dx3 8 qd 9–20, 22, 24, 27, 35

Paclitaxel A2780 8 IV bolus Control, 30 q4dx3 13 eod 9–19, 23, 28, 31

5-FU HCT116 8 IV bolus Control, 50 qwx2 8 8, 12, 15, 19, 22, 26

5-FU HCT116 8 IV bolus Control, 50 qwx4 8 10, 14, 17, 21, 24, 28, 31

A A2780 8 IV bolus Control, 60 tidx1, bidx4,

qdx11

9 8, qd 10–23, eod

23–29, 33

B A2780 8 IV bolus Control, 15, 30 bidx5 13 15, 17, 19, 23, 28, 31

B A2780 8 IV inf Control, 83/day 7 days 9 7, 10, 12, 14, 15, 16, 17

[21] A A2780 8 IV bolus Control, 45 qd10 13 13, 15, 19, 21, 23, 26,

29, 33, 37, 42

[22] MTX Ehrlich

ascites cells

10,000 cell/ml In vitro Control, 0.19, 2,

14, 140 mg/ml

24 h Days 1, 3, 5, 7, 9, 11,

13, 15, 17, 20, 22, 24

MTX Sarcoma

180 cells

5000 cell/ml In vitro Control, 0.19, 2,

14, 140 mg/ml

25 h Days 1, 2, 3, 5, 7, 9, 11,

13, 14, 15, 17, 19, 21

[23] Paclitaxel

(Taxol-SUV)

Murine

Colon-26

10 IV Control, 10, 40, 60 (qdx3)qwx3 8 qd 8–13, 15–18,

20–25, 28, 30

[24] Docetaxel A2780 8 IV bolus Control, 10 qd1, q4dx1 8 7, 9, 10, 12, 13, 15, 17,

19, 21, 23, 26, 28, 30

Drug B A2780 7 IV inf Control, 15/day 5 days 7.5 eod 7–19

Drug C A2780 8 Gastric

gavage

Control, 20, 30, 40 10 days 8 8, 10, 14, 16, 18,

21, 24, 28, 31

[25] TDM-1 MMTV-HER2 Fo5 IV 1, 3, 10, 15, 30 q3wx3 biwx10, qw from 11w

TDM-1 MMTV-HER2 Fo5 IV 3.3, 5, 10 qwx9 biwx10, qw from 11w

TDM-1 MMTV-HER2 Fo5 IV 15 q3wx3 biwx10, qw from 11w

TDM-1 BT474EEI IV 0.3, 1, 3, 10, 15 q3wx3 biwx10, qw from 11w

TDM-1 BT474EEI IV 3.3, 5, 10 qwx9 biwx10, qw from 11w

TDM-1 BT474EEI IV 6, 9, 18 q2wx5 biwx10, qw from 11w

TDM-1 BT474EEI IV 15 q3wx3 biwx10, qw from 11w

Trastuzumab BT474EEI IV 15 q3wx3 biwx10, qw from 11w

[26] 5-FU HCT116 In vitro Control, 1,

10, 50, 100 ng/ml

144 h 0, 24, 48, 72, 144 h

5-FU SW480 In vitro Control, 10,

100, 500,

1000 ng/ml

144 h 0, 24, 48, 72, 144 h

5-FU COLO320DM In vitro 100, 1000 ng/ml 144 h

UFT Colon cancer Oral 60/day 28 days qd 0–14, eod 14–26

[30] LY2157299 Human Calu6 10 Oral Control, 75 bidx20 7–10 6, 10, 13, 17, 20, 24, 26

LY2157299 Human Calu6 36 Oral Control bidx 7–10 Once a week for

one month

LY2157299 Human Calu6 10 Oral 75 bidx10 7–10 4, 10, 14

LY2157299 Human Calu6 10 Oral 75 bidx15 7–10 4, 10, 14, 17, 21

LY2157299 Human Calu6 20 Oral 75 bidx20 7–10 4, 10, 14, 17, 21, 24, 28

LY2157299 Human MX1 10 Oral Control, 75 tidx20 7–10 4, 7, 10, 14, 17,

19, 21, 24, 27, 32

[31] PF02341066 GTL16 Oral

gavage

8.5, 17, 34 9–11



Table 1 (Continued )

Ref Drug Cell line n per

group

Route Dose (mg/kg) Dose

scheme

Start

day

Sampling times (days)

[32] GDC-0941 MCF7.1 10 Oral Control, 12.5, 25,

50, 75, 100, 200

qd (16–21 days) 0, 4, 10, 18, 24,

32, 38 after dose

GDC-0941 MCF7.1 10 Oral Control, 12.5, 25,

37.5, 50, 100

bid (16–21days) 0, 6, 12, 16, 26,

32 after dose

GDC-0941 MCF7.1 10 Oral Control, 200 qd, eod, e3d

(16–21 days)

0, 6, 12, 16, 26, 32,

40 after dose

IV: intravenous; q: every; qd: once a day; q#d: every # days; eod: every other day; bid: twice a day; tid: three times a day; qw: every week; biw: twice a week.

being suitable for the selected modeling technique should be

the recommended way to proceed. This could result in a

reduction in the number of animals involved in the study

and in a more accurate estimate of the model parameters,

In vitro data

Biomarker data

Co

Preclinical tumor gr

Time (h)

% p

Sm

ad

Time (h)

0.001 0.01

1000

10

120

100

80

60

40

20

00 4 8

controls

0.0390625 µM

0.3125 µM

2.5 µM

0.009765625 µM

0.078125 µM

0.625 µM

5 µM

1.25 µM

0.15625 µM

0.01953125 µM

0 24 48 72

105

104

103

102

Nº

of c

ells

(a)

(b)

Sys

tem

ic e

xpos

ure

(mg×

h/L)

Figure 1. In this cartoon, the application of model-based approaches is proposed

structure of the Simeoni’s tumor growth inhibition model (upper boxes) and the re

anticancer agents (lower graph) is reported [54,55]. At the periphery of the circl

oncology therapeutic area are shown: from bottom left, in clockwise order: model

[30], modeling of combination data in xenograft experiments [29], modeling of t

improving their ability to translate clinically. Indeed, so far,

preclinical studies have been designed without applying

optimal design strategies (some study designs are shown

in Table 1).

mbinations

Clinical tumor growth

Survival

owth

observed

observed

individualprediction

populationprediction

3

2

1

00 7

fitting of single agents

simulation of combinationassuming additivity

14 21 28 35 42 49 56 63

0 7 14 21 28 35 42 49 56 63

90% predicted

Time (arbitrary units)

k2 (L/mg×h)

Time (arbitrary units)

Time (days)

Time (days)

TW

(g)

3

2

1

0

TW

(g)

tum

or w

eigh

t (ar

bitr

ary

units

)

prob

abili

ty o

vera

ll su

rviv

al 1

25

20

15

10

5

00 200 400 600 800 1000

0.75

0.5

0.250.1 1 10

00 0.5 1 1.5 2 2.5 3 3.5 4

Drug Discovery Today: Technologies

in the continuum of oncology drug development. In the central panel, the

lationship between the potency parameter k2 and the clinical dose of known

e, some of the achievements to support the model-based development in

ing of in vitro data [49], modeling of biomarkers connected to tumor growth

umor growth in human patients and prediction of overall survival [60].



Dose rationale in the clinics

Until a few years ago, the approaches used to anticipate the

clinical dose from the information gained in xenograft mod-

els were very empirical. ‘A new drug should at a minimum

achieve an AUC in humans that equals the effective AUC in

animals’ [53]: this was considered the condition necessary

(but not sufficient) for a new compound to enter into phase

III clinical stage. More recently, it has been shown that the

model-based approach can provide rational quantitative

guidelines based on specific parameters of the mathematical

model estimated in the preclinical experimental model. In

general, the availability of experiment-independent, drug-

specific, model-based parameters is key to translate the pre-

clinical knowledge into the clinical setting [54]. For instance,

a parameter of Simeoni’s model describes the anticancer

potency of a compound [20]. Then, a significant correlation

was found between this potency parameter and the systemic

exposures (area under the drug plasma concentration–time

curve) of well-established anticancer drugs associated with

standard therapies in clinics (see central portion of Fig. 1)

[55]. In drug development, this correlation could anticipate

the dose levels that need to be reached in future clinical

studies to observe a clinical benefit. In fact, for a compound

whose development was interrupted due to lack of efficacy,

we retrospectively found that its maximum tolerated dose

was much lower than the model-predicted clinical dose. This

example suggests that this correlation – besides anticipating

the clinical dose for a new compound – could be used to kill

faster (or, alternatively, minimize the resources for further

development of) a compound with low probability of success.

As already mentioned, the mathematical models of tumor

growth have been recently integrated within mechanism-

based models incorporating the relationship between drug

exposure and biomarkers modulation. This approach,

together with a deeper understanding of the preclinical set-

ting, aims to identify biomarker levels that correlate with

therapeutic response. Referring to the examples previously

quoted, an integrated model may help predict the likelihood

of tumor growth inhibition in humans from the inhibition of

cMet phosphorylation [31], or the extent of suppression of

the PI3K pathway measured by pAkt inhibition [32].

Although such extrapolations assume that the relationship

between PD marker response and antitumor activity is similar

in human and xenograft models, this approach may help find

the appropriate dosing regimen and guide the dose escalation

to rapidly achieve efficacious systemic exposure in the clinic.

Based on the outcome of these integrated preclinical models,

rapid turnaround of the analysis of biomarker modulation

data in the clinical trials can be treated in a more quantitative

manner, defining the path forward for the development of

new anticancer compounds and designing study adaptations

(as the adoption of different dose levels and dosing regimen)

in early clinical trials. In addition, in-target and off-target


effects can be more thoroughly examined and evaluated in

terms of risk–benefit ratio, providing the basis for the assess-

ment of the utility curves of a new compound.

Conclusions

In this brief review we have described what information can

be achieved from the modeling of xenograft data, especially

with regard to the dose rationale to be used in the clinics.

An interesting question is the possibility of extending in

vivo modeling approaches also to the earlier in vitro studies.

Indeed, the possibility of predicting the time course of the

effect may be very helpful both for candidate ranking pur-

poses and the design of experimental protocols in preclinical

species. It has been shown that CDM can be effectively

applied also to in vitro data [30]. At this time, the major open

challenge is demonstrating whether and how in vitro models

could be used to predict results of in vivo studies.

Another area that is booming is the application of models

to combination therapy. Some modeling attempts were

recently reported in the literature [27–29]. The definition

of a general combination model able to predict the inhibition

of the tumor growth curve in response to interacting drugs

given in combination is still an open issue. Although the

main rationale to combine anticancer agents in the clinic is to

obtain better or similar responses in comparison to single

agent therapies but with reduced adverse effects, the integra-

tion of safety and tolerability issues in the mathematical

approaches has still to be realized [56].

Modeling approaches similar to those so far illustrated

within the preclinical setting have also been developed for

describing and, potentially, predicting growth of tumor in

patients. Some of these approaches have been used to gen-

erate hypotheses to be tested in the clinics. For instance, the

Norton–Simon hypothesis [19] indicated that the regression

rate of tumor mass after a chemotherapeutic agent is directly

proportional to the rate of growth for an unperturbed tumor

of that size. This suggested that in clinical practice dose-dense

regimens may be more effective than alternative regimens

and this was demonstrated in two different clinical settings

[57,58]. Tumor growth models are becoming more and more

popular to describe clinical data, for instance in non-small

cell lung cancer patients [59]. In other cases, the tumor

growth models have been used in late clinical phases as

significant covariates for describing relevant clinical end-

points such as overall survival [60]. In other model-based

approaches, markers such as PSA were proposed for modeling

using PKPD approaches [61]: within such models which

consider the potential effect of anticancer agents, these mar-

kers may be also used to assess the potential effect on the

clinical endpoint (e.g. progression-free survival, overall sur-

vival), in turn validating the clinical relevance of the bio-

marker itself. Thus, finding an appropriate, quantitative

translational link between the compound effects in xenograft


experimental models and the corresponding effects of tumor

reduction in the clinical situation, and further resorting to

the approaches linking tumor growth (or, more generally,

intermediate markers of antitumor effects) with survival end-

points would allow to have a full end-to-end description of

the potential development paths of new anticancer treat-

ments.

Oncology is a very active area for the investigation of

model-based approaches: this may be due to the fact that

the mechanisms of tumor generation, development and

spread – although heterogeneous and not fully understood

– are very active areas of basic research. While there are several

model-based approaches available for addressing specific

issues in the oncology therapeutic area, it seems that we

are still moving in the ‘model-aided’ and not in the

‘model-based’ paradigm [62]. The use of the model-based

approach could become more widespread in the presence

of the consensus on behalf of the regulatory authorities. The

new regulatory framework provides recommendations for

nonclinical evaluations supporting the development of antic-

ancer pharmaceuticals [63,64] and recognizes the value of the

model-based approach [65–67]. Consequently new qualifica-

tion pathways for the integration of novel methodologies,

including modeling and simulation have recently been made

available [68]. Indeed model-based drug development

appears particularly suited to integrate in vitro and in vivo,

preclinical and clinical data to allow a better characterization

of new compounds and provide elements for their differen-

tiation from the anticancer drugs already available [62,69]. A

more thorough characterization of the mechanisms of cel-

lular proliferation and metastasis, the adoption of appropri-

ate modeling tools for interpreting the experimental

outcomes and a better understanding of the relationship

between molecular markers and relevant clinical endpoints

can be integrated in a modeling approach centered on tumor

growth modeling (Fig. 1). This approach – discriminating

between the biological system characteristics and drug action

– can pave the way of drug development in the oncology

therapeutic area (Fig. 1).

References1 Liu, M. and Hicklin, D. (2011) Human tumor xenograft efficacy models. In

Tumor Models in Cancer Research, Cancer Drug Discovery and Development

(Teicher, B.A., ed.), Springer Science+Business Media

2 Bonate, P.L. (2011) Modeling tumor growth in oncology. In

Pharmacokinetics in Drug Development (Bonate, P.L. and Howard, D.R.,

eds), American Association of Pharmaceutical Scientists, LLC

3 Della Pasqua, O.E. (2011) PKPD and disease modeling: concepts and

applications to oncology. In Clinical Trial Simulations (Kimko, H.H.C. and

Peck, C.C., eds), AAPS Advances in the Pharmaceutical Sciences Series 1,

Springer Science + Business Media, LLC

4 Woodhouse, D.L. (1947) Chemotherapy investigations in cancer; with

reference to the influence of certain organic dibasic acids, diamino

compounds and nitro compounds on tumors in mice. Cancer Res. 7,

398–401

5 Mattern, J. et al. (1988) Human tumor xenografts as model for drug testing.

Cancer Metastasis Rev. 7, 263–284

6 Rygaard, J. et al. (1969) Heterotransplantation of a human malignant

tumour to the mouse mutant ‘nude’. Acta Pathol. Microbiol. Scand. 77, 758–

760

7 Bissery, M.C. et al. (1996) Experimental antitumor activity and

pharmacokinetics of camptothecin analog irinotecan (CPT-11) in mice.

Anticancer Drugs 7, 437–460

8 Hollingshead, M.G. (2008) Antitumor efficacy testing in rodents. J. Natl.

Cancer Inst. 100, 1500–1510

9 Kelland, L.R. (2004) Of mice and men: values and liabilities of the athymic

nude mouse model in anticancer drug development. Eur. J. Cancer 40, 827–

836

10 Walrath, J.C. et al. (2010) Genetically engineered mouse models in cancer

research. Adv. Cancer Res. 106, 113–164

11 Rocchetti, M. et al. (2005) Pharmacokinetic-pharmacodynamic model for

predicting tumour growth inhibition in mice: a useful tool in oncology

drug development. Basic Clin. Pharmacol. Toxicol. 265–268

12 Voskoglou-Nomikos, T. et al. (2003) Clinical predictive value of the in vitro

cell line, human xenograft, and mouse allograft preclinical cancer models.

Clin. Cancer Res. 9, 4227–4239

13 Marusic, M. (1996) Mathematical models of tumor growth. The Lecture

Presented at the Mathematical Colloquium in Osijek Organized by Croatian

Mathematical Society – Division Osijek, June 7, 1996

14 Laird, A.K. (1964) Dynamics of tumor growth. Br. J. Cancer 18, 490–502

15 Simpson-Herren, and Lloyd, (1970) Kinetic parameter and growth curves

for experimental tumor systems. Cancer Chemotherapy Rep. 54, 143–174

16 Sullivan, P.W. and Salmon, S.E. (1972) Kinetics of tumor growth and

regression in IgG multiple myeloma. J. Clin. Invest. 51, 1697–1708

17 Norton, L. et al. (1976) Predicting the course of Gompertzian growth.

Nature (Lond.) 264, 542–545

18 Norton, L. and Simon, R. (1977) Growth curve of an experimental solid

tumor following radiotherapy. J. Natl. Cancer Inst. (Bethesda) 58, 1735–

1741

19 Simon, R. and Norton, L. (2006) The Norton-Simon hypothesis: designing

more effective and less toxic chemotherapeutic regimens. Nat. Clin. Pract.

Oncol. 3, 406–407

20 Simeoni, M. et al. (2004) Predictive pharmacokinetic–pharmacodynamic

modeling of tumor growth kinetics in xenograft models after

administration of anticancer agents. Cancer Res. 64, 1094–1101

21 Magni, P. et al. (2006) A mathematical model to study the effects of drug

administration on tumor growth dynamics. Math. Biosci. 200, 127–151

22 Lobo, E.D. and Balthasar, J.P. (2002) Pharmacodynamic modeling of

chemotherapeutic effects: application of a transit compartment model to

characterize methotrexate effects in vitro. AAPS PharmSci. 4, E42

23 Yang, J. et al. (2010) Comparison of two pharmacodynamic transduction

models for the analysis of tumor therapeutic responses in model systems.

AAPS J. 12, 1–10

24 Magni, P. et al. (2008) A minimal model of tumor growth inhibition. IEEE

Trans. Biomed. Eng. 55, 2683–2690

25 Jumbe, N.L. et al. (2010) Modeling the efficacy of trastuzumab-DM1, an

antibody drug conjugate, in mice. J. Pharmacokinet. Pharmacodyn. 37, 221–

242

26 Sung, J.H. et al. (2009) A combined pharmacokinetic–pharmacodynamic

(PK–PD) model for tumor growth in the rat with UFT administration. J.

Pharm. Sci. 98, 1885–1904

27 Goteti, K. et al. (2010) Preclinical pharmacokinetic/pharmacodynamic

models to predict synergistic effects of co-administered anti-cancer agents.

J. Cancer Chemother. Pharmacol. 66, 245–254

28 Koch, G. et al. (2009) Modeling of tumor growth and anticancer effects of

combination therapy. J. Pharmacokinet. Pharmacodyn. 36, 179–197

29 Rocchetti, M. et al. (2009) Testing additivity of anticancer agents in pre-

clinical studies: a PK/PD modelling approach. Eur. J. Cancer 45, 3336–3346

30 Bueno, L. et al. (2008) Semi-mechanistic modelling of the tumour growth

inhibitory effects of LY2157299, a new type I receptor TGF-beta kinase

antagonist, in mice. Eur. J. Cancer 44, 142–150

31 Yamazaki, S. et al. (2008) Pharmacokinetic–pharmacodynamic modeling

of biomarker response and tumor growth inhibition to an orally available



cMet kinase inhibitor in human tumor xenograft mouse models. Drug Met.

Disp. 36, 1267–1274

32 Salphati, L. et al. (2010) Pharmacokinetic–pharmacodynamic modeling of

tumor growth inhibition and biomarker modulation by the novel

phosphatidylinositol 3-kinase inhibitor GDC-0941. Drug Met. Disp. 38,

1436–1442

33 Kalns, J.E. et al. (1995) Design and analysis of in vitro antitumor

pharmacodynamic studies. Cancer Res. 55, 5315–5322

34 Millenbaugh, N.J. et al. (2000) A pharmacodynamic analysis method to

determine the relative importance of drug concentration and treatment

time on effect. Cancer Chemother. Pharmacol. 45, 265–272

35 Germani, M. et al. (2003 Dec) In vitro cell growth pharmacodynamic

studies: a new nonparametric approach to determining the relative

importance of drug concentration and treatment time. Cancer Chemother.

Pharmacol. 52, 507–513

36 Del Bene, F. et al. (2009) A model-based approach to the in vitro evaluation

of anticancer activity. Cancer Chemother. Pharmacol. 63, 827–836

37 Roose, T. et al. (2008) Mathematical models of avascular tumor growth.

SIAM Rev. 49, 179–208

38 Lowengrub, J.S. et al. (2010) Nonlinear modelling of cancer: bridging the

gap between cells and tumours. Nonlinearity 23, R1–R91

39 Byrne, H.M. (2010) Dissecting cancer through mathematics: from the cell

to the animal model. Nat. Rev. Cancer 10, 221–230

40 Owen, M.R. et al. (2004) Mathematical modelling of the use of

macrophages as vehicles for drug delivery to hypoxic tumour sites. J.

Theor. Biol. 226, 377–391

41 Jiang, Y. et al. (2005) A multiscale model for avascular tumor growth.

Biophys. J. 89, 3884–3894 Erratum in: Biophys J. 91(2): 775

42 Ribba, B. et al. (2006) A multiscale mathematical model of avascular tumor

growth to investigate the therapeutic benefit of anti-invasive agents. J.

Theor. Biol. 243, 532–541

43 Ribba, B. et al. (2006) A multiscale mathematical model of cancer, and its

use in analyzing irradiation therapies. J. Theor. Biol. 3, 7

44 Bajzer, Z. et al. (1996) Conceptual frameworks for mathematical modeling

of tumor growth dynamics. Math. Comput. Model. 23, 31–46

45 Bellomo, N. and Preziosi, L. (2000) Modeling and mathematical problems

related to tumor evolution and its interaction with the immune system.

Math. Comput. Model. 32, m413–m452

46 Basse, B. and Ubezio, P. (2007) A Generalised age- and phase-structured

model of human tumour cell populations both unperturbed and exposed

to a range of cancer therapies. Bull. Math. Biol. 69, 1673–1690

47 Wang, Z. et al. (2007) Simulating non-small cell lung cancer with a

multiscale agent-based model. Theor. Biol. Med. Model. 4, 50

48 Zhang, L. et al. (2009) Multiscale agent-based cancer modeling. J. Math.

Biol. 58, 545–559

49 Ribba, B. et al. (2011) A model of vascular tumour growth in mice

combining longitudinal tumour size data with histological biomarkers.

Eur. J. Cancer 47, 479–490

50 Sheiner, L.B. et al. (1977) Estimation of population characteristics of

pharmacokinetic parameters from routine clinical data. J. Pharmacokin.

Pharmacodyn. 5, 445–479

51 Poggesi, I. et al. (2004). Population modeling of tumor growth in untreated

xenografted mice. Abstracts of the Annual Meeting of the Population


Approach Group in Europe, Uppsala PAGE 13, Abstr 535 [http://

www.page-meeting.org/?abstract=535]

52 Simeoni, M. et al. Population modeling of tumor growth inhibition in

vivo: application to anticancer drug development. Abstracts of the Annual

Meeting of the Population Approach Group in Europe, Uppsala PAGE 13,

PAGE 13 (2004) Abstr 503 [http://www.page-meeting.org/?abstract=503]

53 Roberts, T.G. et al. (2003) The phase III trial in the era of targeted therapy:

unraveling the go and no go decision. J. Clin. Oncol. 19, 3683–3695

54 Poggesi, I. et al. (2009) Antitumor efficacytesting in rodents. J. Natl. Cancer

Inst. 101, 1592–1593

55 Rocchetti, M. et al. (2007) Predicting the active doses in humans from

animal studies: a novel approach in oncology. Eur. J. Cancer 12, 1862–1868

56 Ouellet, D. (2010) Benefit–risk assessment: the use of clinical utility index.

Expert Opin. Drug Safety 9, 289–300

57 Bonadonna, G. et al. (2004) Clinical relevance of different sequencing of

doxorubicin and cyclophosphamide, methotrexate and fluorouracil in

operable breast cancer. J. Clin. Oncol. 22, 1614–1620

58 Citron, M.L. et al. (2003) Randomized trial of dose-dense versus

conventionally scheduled and sequential versus concurrent combination

chemotherapy as postoperative adjuvant treatment of node-positive

primary breast cancer: first report of Intergroup trial C9741/Cancer and

Leukemia Group B trial 9741. J. Clin. Oncol. 21, 1431–1439

59 Wang, Y. et al. (2009) Elucidation of relationship between tumor size and

survival in non-small-cell lung cancer patients can aid early decision

making in clinical drug development. Clin. Pharmacol. Ther. 86, 167–174

60 Claret, L. et al. (2009) Model-based prediction of phase III overall survival

in colorectal cancer on the basis of phase II tumor dynamics. J. Clin. Oncol.

27, 4103–4108

61 Hedican, E.B. et al. (2007) Modeling biomarker dynamics with

implications for the treatment of prostate cancer. Comput. Math. Methods

Med. 8, 77–92

62 Zhang, L. et al. (2008) Concepts and challenges in quantitative

pharmacology and model-based drug development. AAPS J. 10, 552–559

63 International Conference on Harmonisation of Technical Requirements

for Registration of Pharmaceuticals for Human Use (ICH). S9 Nonclinical

Evaluation for Anticancer Pharmaceuticals; March 2010

64 Jones, P.S. and Jones, D. (2012) New regulatory framework for cancer drug

development. Drug Discov. Today 17, 227–231

65 US Food and Drug Administration, (2004) Innovation or Stagnation:

Challenge and Opportunity on the Critical Path to New Medical Products. p. 24.

http://www.fda.gov/downloads/ScienceResearch/SpecialTopics/

CriticalPathInitiative/CriticalPathOpportunitiesReports/ucm113411.pdf

66 End-of-phase 2a meetings. FDA guidance for Industry; September 2009

67 European Medicines Agency-European Federation of Pharmaceutical

Industries and Associations modelling and simulation workshop; 30/11/

2011-01/12/2011, London (UK); http://www.ema.europa.eu/ema/

index.jsp?curl=pages/news_and_events/events/2011/07/

event_detail_000440.jsp&mid=WC0b01ac058004d5c3

68 Manolis, E.E. et al. (2011) New pathway for qualification of novel

methodologies in the European Medicines Agency. Proteomics Clin. Appl. 5,

248–255

69 Lalonde, R.L. et al. (2007) Model-based drug development. Clin. Pharmacol.

Ther. 82, 21–32

http://www.page-meeting.org/%3Fabstract=535



http://www.fda.gov/downloads/ScienceResearch/SpecialTopics/CriticalPathInitiative/CriticalPathOpportunitiesReports/ucm113411.pdf

http://www.fda.gov/downloads/ScienceResearch/SpecialTopics/CriticalPathInitiative/CriticalPathOpportunitiesReports/ucm113411.pdf

http://www.ema.europa.eu/ema/index.jsp?curl=pages/news_and_events/events/2011/07/event_detail_000440.jsp&mid=WC0b01ac058004d5c3



Documents

Modeling of human tumor xenografts and dose rationale in oncology