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Computational Biology and Chemistry 48 (2014) 21– 28

Contents lists available at ScienceDirect

Computational Biology and Chemistry

jou rn al hom epage : www.elsev ier .com/ locate /compbio lchem

esearch article

odeling of tumor growth in dendritic cell-based immunotherapysing artificial neural networks

ohammad Mehriana, Davud Asemania,∗, Abazar Arabameria,rash Pourgholaminejadb, Jamshid Hadjatib

Laboratory of Signals and Electronic Systems, Electrical and Computer Engineering Faculty, K.N. Toosi University of Technology, Tehran, IranDepartment of Immunology, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran

r t i c l e i n f o

rticle history:eceived 4 March 2013eceived in revised form 31 August 2013ccepted 30 September 2013

eywords:rtificial neural networkendritic cells

a b s t r a c t

Exposure-response modeling and simulation is especially useful in oncology as it permits to predict anddesign un-experimented clinical trials as well as dose selection. Dendritic cells (DC) are the most effectiveimmune cells in the regulation of immune system. To activate immune system, DCs may be matured bymany factors like bacterial CpG-DNA, Lipopolysaccharaide (LPS) and other microbial products.

In this paper, a model based on artificial neural network (ANN) is presented for analyzing the dynamicsof antitumor vaccines using empirical data obtained from the experimentations of different groups ofmice treated with DCs matured by bacterial CpG-DNA, LPS and whole lysate of a Gram-positive bacteria

mmunotherapyumor growth rate

Listeria monocytogenes. Also, tumor lysate was added to DCs followed by addition of maturation factors.Simulations show that the proposed model can interpret the important features of empirical data. Owingto the nonlinearity properties, the proposed ANN model has been able not only to describe the contra-dictory empirical results, but also to predict new vaccination patterns for controlling the tumor growth.For example, the proposed model predicts an exponentially increasing pattern of CpG-matured DC to be

he tu

effective in suppressing t

. Introduction

To understand and predict the pharmacological behavior ofnticancer drugs, it is crucial to quantify the time course of phar-acodynamic responses in relation to the plasma concentration. A

undamental step in the preclinical development of oncology drugss the in vivo evaluation of the antitumor effect. For this purpose,

series of experiments are performed, in which tumor cells frommmortalized cell lines are inoculated into mice. Tumor volumesre measured at different times throughout the experiment for allnimals, treated either with a vehicle (control) or with an activerug. The effect of the active molecule is then measured by compar-

ng the average tumor weights in treated and control animals at thend of experiment, or by counting the animals surviving their dis-ase (Fujimoto-Ouchi et al., 2002; Granucci et al., 1999; Hammond

t al., 2000; Roose et al., 2007; Rowland et al., 2011; Sharma et al.,011; Sparano et al., 2008; Tanyi and Chu, 2012; Tod et al., 2008;an der Graaf and Benson, 2011; Van Kesteren et al., 2000, 2003;

∗ Corresponding author.E-mail addresses: m mehrian@ee.kntu.ac.ir (M. Mehrian),

semani@eetd.kntu.ac.ir (D. Asemani), abazar arabameri@ee.kntu.ac.irA. Arabameri), a.pourgholaminejad@modares.ac.ir (A. Pourgholaminejad),ajatij@tums.ac.ir (J. Hadjati).

476-9271/$ – see front matter © 2013 Elsevier Ltd. All rights reserved.ttp://dx.doi.org/10.1016/j.compbiolchem.2013.09.007

mor growth.© 2013 Elsevier Ltd. All rights reserved.

Xie et al., 2009; Yap et al., 2010; Zhang et al., 2002). This approachcan be used to select the most potent candidate within a seriesof vaccines using the same dosing regimen, or the most appropri-ate dosing regimen among those tested for a specific compound.However, in this way, the whole course of the tumor growth tim-ing is often neglected, so that only a partial use of the informationavailable from the experiment is realized (only final points).

Exposure-response modeling and simulation (M&S) hasemerged during the last decade as a means to better understandthe relationships of drug exposure-clinical outcomes of anticancertherapies (Danhof et al., 2008; Eftimie et al., 2011; Fujimoto-Ouchiet al., 2002; Granucci et al., 1999; Hammond et al., 2000; Jonssonet al., 2011; Van Kesteren et al., 2003). Contradictory contributionsof a large dozens of factors suggest that M&S is a sophisticated toolto transform the data of multiple endpoints into knowledge (Brunoet al., 2001; Cabrales et al., 2008; Cintolo et al., 2012; Claret et al.,2009; Cornet et al., 2006; Danhof et al., 2008; Eftimie et al., 2011;Fujimoto-Ouchi et al., 2002; Granucci et al., 1999; Hammond et al.,2000; Jonsson et al., 2011; Koch et al., 2009; Lalonde et al., 2007;Morse et al., 2002; Olden and Jackson, 2002; Pili et al., 2001; Rooseet al., 2007; Rowland et al., 2011; Van der Graaf and Benson, 2011;

Van Kesteren et al., 2000, 2003).

Empirical models use mathematical equations to describe thetumor growth process (Roose et al., 2007), without an in-depthmechanistic description of the underlying physiological processes.

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caliper during the experiments, and tumor masses were calculatedas following:

2 M. Mehrian et al. / Computationa

n this context, the dynamics of a drug can be evaluated only inerms of changes of the parameter values describing the tumorrowth. These changes depend on the dose level as well as thedministration schedule, so that those approaches can be appliednly retrospectively and not as predictive tools when used outsidehe tested regimens.

Functional models are nevertheless based on mechanistic,hysiology-based hypotheses. In this case, it implies a setf assumptions about the tumor growth, including cell-cycleinetics and biochemical processes, such as those related tonti-angiogenetic and/or immunological responses (Eftimie et al.,011). Such models usually represent the cell population in itseterogeneity, splitting it into at least two subpopulations: the pro-

iferating and the quiescent cells. More complex models describehe cell population as age-structured and take into account subpop-lations related to specific phases of the cell cycle. These modelsave a much larger number of parameters compared with thempirical ones. Their development is so time-consuming and aumber of quantitative observations (e.g., flow cytometry analy-es, biochemical and immunological marker measurements, ando forth) are required to avoid the identifiability problems due tohe over-parameterization. The situation becomes even more com-licated when the effect of the treatment with an anticancer drug islso considered (Bodnar and Forys, 2007; Bousso, 2008; Bruno et al.,001; Cabrales et al., 2008; Cornet et al., 2006; Danhof et al., 2008;ftimie et al., 2011; Fujimoto-Ouchi et al., 2002; Granucci et al.,999; Hammond et al., 2000; Jonsson et al., 2011; Koch et al., 2009;alonde et al., 2007; Lanzavecchia and Sallusto, 2001; LoRusso et al.,008; Morse et al., 2002; Olden and Jackson, 2002; Pili et al., 2001;oose et al., 2007; Rowland et al., 2011; Sharma et al., 2011; Sparanot al., 2008), because of the incomplete knowledge of the mode ofction in vivo. As a consequence, these models are rarely used inndustrial drug research.

Though, several tumor growth models have been proposed soar, a practical and exhaustive tool that supports oncology drugevelopment is still missing. In this regard, the only metrics ofuccess is the compatibility with the experimental data. In thisaper, a model is presented associating with an effective com-romise between empirical and mechanism-based approaches. Itelies on a few identifiable and biologically relevant parameters.he estimation of the related parameters relies only on the data,ypically available in the preclinical setting, the pharmacokineticsf the anticancer agents and the tumor growth curves in vivo.

Dendritic cells (DCs) represent potent antigen-presenting cellsAPC). The most widely emphasized functions of DCs are anti-en uptake and processing. DCs activate T lymphocytes to initiatemmune responses and also regulate the activation of T lympho-ytes (Bousso, 2008; Bruno et al., 2001; Cabrales et al., 2008; Cintolot al., 2012; Claret et al., 2009; Cornet et al., 2006; Danhof et al.,008; Eftimie et al., 2011; Fujimoto-Ouchi et al., 2002; Granuccit al., 1999; Hammond et al., 2000; Jonsson et al., 2011; Kocht al., 2009; Lalonde et al., 2007; Lanzavecchia and Sallusto, 2001).any factors can influence the development of polarized immune

esponses such as DC activation status. Many microbial compo-ents like bacterial CpG-DNA, Lipopolysaccharide (LPS) and othericrobial products have been shown to mature DCs and can regu-

ate the activation of T cell responses (Cornet et al., 2006; Danhoft al., 2008; Eftimie et al., 2011; Fujimoto-Ouchi et al., 2002;ranucci et al., 1999).

In oncology, the term tumor immunotherapy embraces a varietyf different therapeutic approaches with the shared aim of exploi-ing effector mechanisms of the immune system to eliminate tumor

ells (Sharma et al., 2011). Over the past decade, among the mostntensively studied tumor immunotherapies have been DC-basedancer vaccines (Cintolo et al., 2012). Dendritic cells play a pivotalole in anti-tumor immune responses. Therefore, the maturation

gy and Chemistry 48 (2014) 21– 28

status of administrated DCs could potentially affect the efficacyand outcome of DC-based cancer immunotherapy (Morse et al.,2002; Olden and Jackson, 2002; Pili et al., 2001; Roose et al., 2007;Rowland et al., 2011; Sharma et al., 2011; Sparano et al., 2008; Tanyiand Chu, 2012).

Apart from general information about tumor behavior in thepresence of different vaccines, no further information is available.So, the problem appears to be a black box type according to mod-eling paradigm. One of the main applications of artificial neuralnetworks (ANN) as modeling tools is in the cases where just theinput and output of a system are available and there is no moreinformation about different internal parts of the system (Olden andJackson, 2002) (black box modeling paradigm). Accordingly, ANNis here used to model the behavior of tumor growth consideringdifferent vaccination profiles.

2. Materials

2.1. Animals and cell-lines

Six-to-eight week’s old female BALB/c mice were purchasedfrom Lab. Animal Center, Institute of Pasteur of Iran. All of the ani-mal experiments were conducted in accordance with the currentbest practices and ethical principles. BALB/c-derived fibrosar-coma (WEHI-164) cell-line were maintained in RPMI1640 medium(Gibco-USA), 10% heat inactivated fetal bovine serum (Gibco-USA),antibiotics, and 1% l-glutamine (Sigma-Germany).

2.2. Generation of bone marrow-derived DCs

Bone marrow cells were obtained from the femur and tibia offemale BALB/c mice; 106 cells ml−1 were placed in 24-well platesin RPMI plus 10% FCS, 20 ng ml−1 GM-CSF (R&D systems, USA) and10 ng ml−1 IL-4 (R&D systems, USA). After 3 days, non-adherentcells were gently collected into a new plate and fresh media wasadded. On day 5, 100 �g ml−1 of tumor lysate (TL) was added toimmature DC cultures. After 4–6 h in some wells 10 �g CpG, 1 �gLPS and 70 mg lysate of Listeria monocytogenes was added. Non-adherent DCs in all wells were harvested on day 7 of the cultureand used for tumor immunotherapy.

2.3. Tumor challenge and treatment

To generate tumor, mice were injected subcutaneously in theright flank with 200 �l of 1.5 × 106 WEHI-164 cells. One, two orthree doses of 106 TL-loaded DCs or TL-loaded and three groupsof matured DCs (CpG-matured DCs, LPS-matured DCs and Listeriamonocytogenes-matured DCs) were injected around tumors in dif-ferent groups of mice at 7th, 10th and 13th days after tumorimplantation (one dose only at 7th day, two doses at 7th and 10thdays and alike). When the tumor was palpable, the shortest andlongest surface diameters were measured every 2 days using digitalcalipers. The tumor area was achieved by multiplying the shortestand longest axis of the tumor and then the mean of tumor growthrate per 48 h was calculated. Mice were sacrificed when the tumorsize reached above 400 mm2 (>400 mm2).

Mice were clinically evaluated daily and were weighed everytwo days. Dimensions of the tumors were measured regularly by

Tumor weight(mg) = Length(mm) · width2(mm2)2

�

assuming density � = 1 mg/mm3 for tumor tissue

(1)

M. Mehrian et al. / Computational Biology and Chemistry 48 (2014) 21– 28 23

measure of drug potency; and C(t): the plasma concentration of anticancer agent.

3

tfigtil

3

srios

x

x

x

w

Tcdcpptap

lctgcte

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a

Table 1Drug parameters for mice in CpG and Listeria groups.

�

CpG 0.252 0.651 1.53

Fig. 1. PK-PD model of cell death. k1: first order rate constant of transit; k2:

. Methods

In untreated mice, the experimental data demonstrate thatumor growth rate follows two distinctive and different phases:rstly, an initial phase with exponential growth, secondly a linearrowth phase with a smooth transition between two phases. Inreated animals, the tumor growth rate is proportionally decreasedn terms of both drug concentration and the concentration of pro-iferating tumor cells.

.1. Pharmacodynamic model

Anticancer treatment influences the dynamics of tumor growtho that the proliferating cells become non-proliferating with aate depending on the drug concentration in plasma. Invokingmmunological principles, the tumor growth rate in the presencef anti-tumor drug may be modeled by a compartment model ashown in Fig. 1 (Koch et al., 2009) with following equations:

′1 =

(2�0�1x2

1(t)(�1 + 2�0x1(t))w(t)

)− k2C(t)x1(t), x1(0) = w0 (2)

2 = k2C(t)x1(t) − k1x2(t), x2(0) = 0 (3)

′i = k1(xi−1(t) − xi(t)), xi(0) = 0, i = 3, . . ., N (4)

(t) =N∑

i=1

xi(t) (5)

In this model, all tumor cells are assumed to be proliferating.he model assumes that the anti-cancer treatment renders someells non-proliferating as well (Fig. 1), eventually bringing them toeath. For a given time t, x1(t) indicates the portion of proliferatingells within the total tumor weight w(t) and c(t) demonstrates thelasma concentration of the anticancer agent. x1(t) represents theortion of w(t) that is actually proliferating. The model assumeshat the drug elicits its effect decreasing the tumor growth rate by

factor being proportional to c(t) · x1(t) multiplied by the constantarameter k2 being an index of the drug efficacy.

It is assumed that the cells affected by drug action stop pro-iferating and pass through n different stages (named x2, . . ., xn),haracterized by progressive degrees of damage, and, eventually,hey die. The dynamics by which the cells proceed through pro-ressive degrees of damage is modulated via a rate constant k1 thatan be interpreted in terms of the kinetics of cell death. In practice,he drug absorption function can be replaced as following (Kocht al., 2009):(

ˇ�)

(t) = − ˛

(e−˛t − e−ˇt) (6)

That ˇ, and � stand for the absorption and elimination ratesnd the volume of distribution respectively.

Listeria 0.151 0.21 0.82

In the experimental study of this paper, the parameters (�0, �1,k1, k2, ˛, ˇ, �) are supposed to be optimally estimated by Geneticalgorithms invoking the experimental data. The drug parametersfor those mice in CpG and Listeria groups have been reported inTable 1.

The drug concentration of different groups with triple injectionon 7th, 10th and 13th days is shown in Fig. 2. It can be seen thatafter first, second and third injections, the plasma concentration ofthe drug goes up and then decreases exponentially in consistentwith the physiological paradigm.

With suitable parameters in different groups of drug injection,a transformation may be obtained to describe the plasma concen-tration of drug in terms of its injection. To model the behavior ofimmune system against tumor growth rate, the inputs and outputsfor different vaccinations are simply available. Because of the com-plex behavior of the immune system in response to the differenttypes of vaccines and also to model different feedback paths in theimmune system, dynamic Recurrent ANN (RNN) has been used. TheANN output in dynamic case depends on the current input and pre-vious input and output values. Dynamic networks generally modelmore efficiently than static networks and profit from the feedbackloops. However, the training process is often more complex andtime-consuming.

Noting experimentation data, it is found that in each groupof vaccines, only three sets of input-output patterns are avail-able. Nevertheless, a model based on ANN requires in practicemuch more data to be able to appropriately model the behav-ior of unknown system. Using a reasonable interpolation schemefor different groups, the data of vaccinations were extended to 21input–output patterns at each group. Using artificial neural net-work, it is now possible to model the dynamics of tumor growthin the presence of different doses of vaccines owing to the largernumber of input–output patterns.

3.2. NARX neural network

Here, a Nonlinear Auto-Regressive network with eXogenousinputs (NARX) is used to simulate the relation between vaccineconcentration in plasma and tumor size for different vaccinationgroups. The desired ANN is a recurrent dynamic network, with

feedback connections enclosing several layers of the network. Thisnetwork can be used as a predictor, to predict the next value of theinput signal (Xie et al., 2009).

24 M. Mehrian et al. / Computational Biology and Chemistry 48 (2014) 21– 28

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3 ti me injecti on 3 time injecti on

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with

a

y

wpa

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4

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muttoc

te

TN

Time(day)

Fig. 2. Mean plasma concentration versus time

The input–output relation in the NARX model can be describeds follows:

(t) = f (y(t − 1), . . ., y(t − ny), u(t − 1), . . ., u(t − nu)) (7)

here the next value of the dependent output y(t) depends on therevious values of output signal as well as the previous values ofn independent (exogenous) input signal.

Adjustable parameters in a NARX net consist of the number ofeurons and the number of input and output delays in the network.o optimally find the number of delays, a sweep has been per-ormed from 0 to 3 delay elements for input/output ones. Besides,he number of neurons has been swept from 5 to 25 to achieve theptimal number of hidden neurons.

. Evaluations and results

.1. Modeling of experimental data

Simulations have been performed using MATLAB and theodeling error in the randomly selected patterns has been

sed as the selection criteria. The simulations exhibited thathe optimal NARX model includes different optimum parame-ers for various groups of vaccinations. Table 2 demonstrates theptimum NARX parameters for different group of DC-based vac-

ines.

Fig. 3 shows the output of proposed NARX model for test pat-erns of different groups of vaccinations. According to Fig. 3, it isvident that the proposed NARX model is able to follow up the

able 2ARX model optimum parameters for different vaccination groups.

Group of vaccination Number of neurons Number of input d

Listeria 21 3

LPS 25 3

CpG 15 3

Tumor lysate 9 3

Time(day)

one and 3 times injections in different groups.

empirical data well. For calculating error between test patterns andempirical data, Mean Absolute Error (MAE) is used as following:

MAE = 1n

n∑i=1

|fi − yi| = 1n

n∑i=1

|ei| (8)

Fig. 4 shows the best training performance for different groupsof vaccination using NARX model.

According to Table 2, it may be deduced that LPS-matured DCsgroup exhibits the most complicated data since it requires a largernumber of neurons for modeling the empirical data. The samenumber of output/input delays exhibits that all vaccinations aredealing with the same dynamics (or the same immunological sys-tem).

4.2. Model behvaiour for unexperimented vaccination patterns

As mentioned in the previous section, a NARX model has beenestablished which is able to suitably pursuit the empirical data.Since the proposed NARX model is compatible with the dynamicsof immunological system in the extent of experimented cases, itmay be exploited to predict the tumor growth rate in the pres-ence of un-experimented vaccination profiles. Then, a series ofun-experimented vaccination profiles is applied to the proposedmodel to predict the related tumor growth rate.

4.3. 4-Time injections

According to the experiments conducted in the laboratory,a pattern of triple injections on 7th, 10th and 13th days was

elays Number of output delays Modeling train error

1 3.52791 5.16971 3.39631 2.7404

M. Mehrian et al. / Computational Biology and Chemistry 48 (2014) 21– 28 25

0 10 20 30 40-20

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simulatedEmpirical

RX m

evtpa

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Fig. 3. Tumor size versus time using NA

xperimented for different groups of mice as well as for differentaccines. Now, four-time injections with the same time interval areo be tested by applying to the proposed NARX model. The inputattern is reconstructed with the same process of the training datand using the same time constants.

Applying afore-mentioned input pattern, the proposed NARXodel predicts the tumor size evolves as shown in Fig. 5. To evalu-

te the results, the empirical data in the case of 3-time injections haseen shown as well in Fig. 5. Also, the predicted tumor growth rateas been demonstrated for the direct solution of differential equa-ions as well. According to Fig. 5, the differential equations exhibit

Fig. 4. Training and test errors versus epoch number usin

Time(days)

odel for different groups of vaccination.

very smooth responses. Furthermore, the behavior of predictedresponses is more or less compatible with either the empirical dataor the differential equations. The compatibility of the responsesmay be originated from the training data which include three-timeinjection patterns.

From the interpretation viewpoint, the empirical data show thatthe larger the number of vaccine injections in Listeria-matured

DCs group, the size of tumor becomes smaller. The proposed NARXmodel exhibits the same trend by suppressing the predicted tumorsize (Fig. 5). The same process may be observed for the LPS-maturedDCs case. CpG-matured DC vaccines group demonstrate a different

g NARX model for different groups of vaccination.

26 M. Mehrian et al. / Computational Biology and Chemistry 48 (2014) 21– 28

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Differential EqNARX net3 time injection

Differential EqNARX net3 time injection

Differential EqNARX net3 time injection

Differential EqNARX net3 time injection

a b

dc

F injece s (grei to the

metscaD

Ff

ig. 5. Predicted tumor size for un-experimented vaccicantion profile with 4-timexhibits the result of proposed model (red), the solution of differential equationnterpretation of the references to color in this figure legend, the reader is referred

echanism against other three vaccination groups. In this case, thempirical data exhibit a negative effect on the tumor suppression inhe presence of CpG-matured DC vaccination. In other words, the

ize of tumor increases in the presence of CpG-matured DC vac-ines. The proposed NARX model exhibits the same behavior with

larger tumor growth rate in the case of four-time CpG-maturedCs injections (Fig. 5).

0 10 20 30 400

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3 times injectionNeural Net

a

c

ig. 6. The concentration of vaccines in plasma (above) for unexperimented exponential

or Listeria (left) and CpG (right) matured DCs. (For interpretation of the references to col

tions. The results are demosntrated for four groups of vaccinations, and each oneen) and compared with the experimented case of 3-time injections (blue). (For

web version of the article.)

4.3.1. Exponential profile vaccinationNow, a different scheme of vaccination profile is applied to

the proposed NARX model. It is assumed that there exists a

trend in the vaccinations doses versus time so that an expo-nential rise is observed in the plasma vaccine concentration(Figs. 6 and 7). It reflects an increasing doses of vaccination inwhich the injected doses increase progressively. In practice, it

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(green) and experimented 3-time (red) injections. The related tumor sizes (below)or in this figure legend, the reader is referred to the web version of the article.)

M. Mehrian et al. / Computational Biology and Chemistry 48 (2014) 21– 28 27

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a b

c d

F ential

f n this

itpDmTF

mtmt

Fpd

ig. 7. The concentration of vaccines in plasma (above) for unexperimented exponor LPS (left) and Lysate (right) cases. (For interpretation of the references to color i

s supposed that the dose of injections is incremented at equaliming intervals. Fig. 6 shows the concentration of vaccines inlasma versus time for two vaccines of Listeria- and CpG-maturedCs. Applying these vaccination profiles to the proposed NARXodel, the tumor sizes are predicted as demonstrated in Fig. 6.

he results related to LPS and Tumor Lysate groups are shown inig. 7.

According to Fig. 6, an increasing exponential dose of Listeria-

atured DCs vaccine can no longer control the tumor growth and

umor size increases rapidly. In contrast, exponential doses of CpGatured cells can effectively control the tumor growth so that the

umor size is suppressed efficiently.

ig. 8. The CpG-matured DCs concentration in plasma (above) and injection dosing (belroposed by the ANN model of tumor growth. The approximated concentration in plasma (oses but regular injection timing pattern. (For interpretation of the references to color in

(green) and experimented 3-time (red) injections. The related tumor sizes (below)figure legend, the reader is referred to the web version of the article.)

Fig. 7 demonstrates that both Tumor Lysate and LPS-MaturedDCs vaccines worsen the treatment in the increasing exponentialinjection profile. It may be reflected from the previous findings thatthe tumor grows faster in the presence of low concentration ofthese vaccines. Therefore, an exponential injection of CpG maturedDCs appear so effective in the control of tumor growth. The resultalso approves that the treatment procedure is very critical in theinitial phase of tumor growth. Besides, it may be deduced that LPS-

matured DCs exhibits a bit more effective in varying doses profilescompared to Tumor Lysate-pulsed DCs. It should be reminded thatthis exponential injection profiles should be experimented to verifyin practice the performance of the proposed NARX model.

ow) versus time. The theoretical concentration in plasma (above-green) has beenabove-blue) may be achieved by the injection dosing pattern (below) with different

this figure legend, the reader is referred to the web version of the article.)

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8 M. Mehrian et al. / Computationa

. Discussion

According to simulation results, it is found in accordance withhe immunological principles that all vaccination procedures suchs the ones using matured DCs can only be effective if adminis-ered at early stages of tumor growth. Hence, an exponentiallyncreasing concentration of LPS-matured, tumor lysate and Lis-eria monocytogenes DCs in plasma fail to suppress the tumorrowth because of lower concentration at initial stages. In contrary,pG-matured DCs exhibit more effective response in this profileince CpG ones demonstrated a negative effect at high concentra-ion (according to experimentation data). Besides, an exponentiallyncreasing concentration pattern of CpG-matured DCs in plasmappear to be effective in controlling tumor growth. In practice, thisattern of vaccine concentration in plasma may be approximatedy several injections with increasing doses. Fig. 8 demonstrates theroposed injections for achieving mentioned concentration pattern

n plasma.

. Conclusion

In this paper, the Pharmaco-Dynamics of DC-basedmmunotherapeutic vaccines have been firstly modeled andharacterized using five physiology-relevant parameters. Thesearameters are simply identifiable using the typical experi-ental data obtained from nude mice in the drug research and

evelopment process. The optimum values have been simplyetermined using Genetic algorithms. Supposing that the drugoncentration in the tumor (at the target) is in rapid equilibriumith plasma, a model of perturbed growth has been sought

n terms of plasma drug concentration representing the effectf anticancer compound. The mean plasma concentration ofrug has been modeled using three physiologically relevantarameters. Using Genetic algorithm and PK/PD equations, theespective three parameters have been optimally found fromxperimented laboratory data for 4 different vaccinated groupsf mice.

To model the effects of different vaccines on tumor growth rate, black box methodology is invoked considering the available dataf drug plasma concentration as input and the tumor growth ashe output because the exact information of immune system lacks.

NARX artificial neural network has been used for modeling toope with the nonlinear and complex behavior of immune system.imulations show that a dynamic NARX model is able to interpretven the contradictory aspects of the empirical data due to differentaccination groups. Particularly, the proposed NARX model affordso describe the complicated mechanism involved in the case of CpG

atured cells.Using the proposed NARX model, a series of un-experimented

accination profiles have been considered to predict the behaviorf immunological system. Simulations demonstrate that the tumorrowth is very sensitive to the vaccine concentration in plasmat the initial phase of tumor growth. However, CpG-maturedells behave differently so that an increasing exponential con-entration of CpG-matured cells can suppress the tumor growthffectively. Predicted patterns of tumor growth for 4-time andxponential injections need to be verified through laboratoryxperimentations.

It is required to experimentally check the simulation results andredicted profiles, so new effective vaccination can be obtained.

ccording to simulation results for injection profiles of exponentialnd 4-times injection, contradictory effects are anticipated on theumor growth. A prospective profile may be sought by merginghose schemes in future works.

gy and Chemistry 48 (2014) 21– 28

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