Computational Biology and Chemistry 48 (2014) 21–28
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Computational Biology and Chemistry journal homepage: www.elsevier.com/locate/compbiolchem
Research article
Modeling of tumor growth in dendritic cell-based immunotherapy using artificial neural networks Mohammad Mehrian a , Davud Asemani a,∗ , Abazar Arabameri a , Arash Pourgholaminejad b , Jamshid Hadjati b a b
Laboratory of Signals and Electronic Systems, Electrical and Computer Engineering Faculty, K.N. Toosi University of Technology, Tehran, Iran Department of Immunology, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 4 March 2013 Received in revised form 31 August 2013 Accepted 30 September 2013 Keywords: Artificial neural network Dendritic cells Immunotherapy Tumor growth rate
a b s t r a c t Exposure-response modeling and simulation is especially useful in oncology as it permits to predict and design un-experimented clinical trials as well as dose selection. Dendritic cells (DC) are the most effective immune cells in the regulation of immune system. To activate immune system, DCs may be matured by many 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 dynamics of antitumor vaccines using empirical data obtained from the experimentations of different groups of mice treated with DCs matured by bacterial CpG-DNA, LPS and whole lysate of a Gram-positive bacteria 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. Owing to the nonlinearity properties, the proposed ANN model has been able not only to describe the contradictory 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 effective in suppressing the tumor growth. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction To understand and predict the pharmacological behavior of anticancer drugs, it is crucial to quantify the time course of pharmacodynamic responses in relation to the plasma concentration. A fundamental step in the preclinical development of oncology drugs is the in vivo evaluation of the antitumor effect. For this purpose, a series of experiments are performed, in which tumor cells from immortalized cell lines are inoculated into mice. Tumor volumes are measured at different times throughout the experiment for all animals, treated either with a vehicle (control) or with an active drug. The effect of the active molecule is then measured by comparing the average tumor weights in treated and control animals at the end of experiment, or by counting the animals surviving their disease (Fujimoto-Ouchi et al., 2002; Granucci et al., 1999; Hammond et al., 2000; Roose et al., 2007; Rowland et al., 2011; Sharma et al., 2011; Sparano et al., 2008; Tanyi and Chu, 2012; Tod et al., 2008; Van der Graaf and Benson, 2011; Van Kesteren et al., 2000, 2003;
∗ Corresponding author. E-mail addresses: m [email protected] (M. Mehrian), [email protected] (D. Asemani), abazar [email protected] (A. Arabameri), [email protected] (A. Pourgholaminejad), [email protected] (J. Hadjati). 1476-9271/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compbiolchem.2013.09.007
Xie et al., 2009; Yap et al., 2010; Zhang et al., 2002). This approach can be used to select the most potent candidate within a series of vaccines using the same dosing regimen, or the most appropriate dosing regimen among those tested for a specific compound. However, in this way, the whole course of the tumor growth timing is often neglected, so that only a partial use of the information available from the experiment is realized (only final points). Exposure-response modeling and simulation (M&S) has emerged during the last decade as a means to better understand the relationships of drug exposure-clinical outcomes of anticancer therapies (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; Van Kesteren et al., 2003). Contradictory contributions of a large dozens of factors suggest that M&S is a sophisticated tool to transform the data of multiple endpoints into knowledge (Bruno et 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; Roose et 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 the tumor growth process (Roose et al., 2007), without an in-depth mechanistic description of the underlying physiological processes.
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In this context, the dynamics of a drug can be evaluated only in terms of changes of the parameter values describing the tumor growth. These changes depend on the dose level as well as the administration schedule, so that those approaches can be applied only retrospectively and not as predictive tools when used outside the tested regimens. Functional models are nevertheless based on mechanistic, physiology-based hypotheses. In this case, it implies a set of assumptions about the tumor growth, including cell-cycle kinetics and biochemical processes, such as those related to anti-angiogenetic and/or immunological responses (Eftimie et al., 2011). Such models usually represent the cell population in its heterogeneity, splitting it into at least two subpopulations: the proliferating and the quiescent cells. More complex models describe the cell population as age-structured and take into account subpopulations related to specific phases of the cell cycle. These models have a much larger number of parameters compared with the empirical ones. Their development is so time-consuming and a number of quantitative observations (e.g., flow cytometry analyses, biochemical and immunological marker measurements, and so forth) are required to avoid the identifiability problems due to the over-parameterization. The situation becomes even more complicated when the effect of the treatment with an anticancer drug is also considered (Bodnar and Forys, 2007; Bousso, 2008; Bruno et al., 2001; Cabrales et al., 2008; 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; Lanzavecchia and Sallusto, 2001; LoRusso et al., 2008; 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), because of the incomplete knowledge of the mode of action in vivo. As a consequence, these models are rarely used in industrial drug research. Though, several tumor growth models have been proposed so far, a practical and exhaustive tool that supports oncology drug development is still missing. In this regard, the only metrics of success is the compatibility with the experimental data. In this paper, a model is presented associating with an effective compromise between empirical and mechanism-based approaches. It relies on a few identifiable and biologically relevant parameters. The estimation of the related parameters relies only on the data, typically available in the preclinical setting, the pharmacokinetics of the anticancer agents and the tumor growth curves in vivo. Dendritic cells (DCs) represent potent antigen-presenting cells (APC). The most widely emphasized functions of DCs are antigen uptake and processing. DCs activate T lymphocytes to initiate immune responses and also regulate the activation of T lymphocytes (Bousso, 2008; Bruno et 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; Lanzavecchia and Sallusto, 2001). Many factors can influence the development of polarized immune responses such as DC activation status. Many microbial components like bacterial CpG-DNA, Lipopolysaccharide (LPS) and other microbial products have been shown to mature DCs and can regulate the activation of T cell responses (Cornet et al., 2006; Danhof et al., 2008; Eftimie et al., 2011; Fujimoto-Ouchi et al., 2002; Granucci et al., 1999). In oncology, the term tumor immunotherapy embraces a variety of different therapeutic approaches with the shared aim of exploiting effector mechanisms of the immune system to eliminate tumor cells (Sharma et al., 2011). Over the past decade, among the most intensively studied tumor immunotherapies have been DC-based cancer vaccines (Cintolo et al., 2012). Dendritic cells play a pivotal role in anti-tumor immune responses. Therefore, the maturation
status of administrated DCs could potentially affect the efficacy and 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; Tanyi and Chu, 2012). Apart from general information about tumor behavior in the presence of different vaccines, no further information is available. So, the problem appears to be a black box type according to modeling paradigm. One of the main applications of artificial neural networks (ANN) as modeling tools is in the cases where just the input and output of a system are available and there is no more information about different internal parts of the system (Olden and Jackson, 2002) (black box modeling paradigm). Accordingly, ANN is here used to model the behavior of tumor growth considering different vaccination profiles. 2. Materials 2.1. Animals and cell-lines Six-to-eight week’s old female BALB/c mice were purchased from Lab. Animal Center, Institute of Pasteur of Iran. All of the animal experiments were conducted in accordance with the current best practices and ethical principles. BALB/c-derived fibrosarcoma (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 of female BALB/c mice; 106 cells ml−1 were placed in 24-well plates in RPMI plus 10% FCS, 20 ng ml−1 GM-CSF (R&D systems, USA) and 10 ng ml−1 IL-4 (R&D systems, USA). After 3 days, non-adherent cells were gently collected into a new plate and fresh media was added. On day 5, 100 g ml−1 of tumor lysate (TL) was added to immature DC cultures. After 4–6 h in some wells 10 g CpG, 1 g LPS and 70 mg lysate of Listeria monocytogenes was added. Nonadherent DCs in all wells were harvested on day 7 of the culture and used for tumor immunotherapy. 2.3. Tumor challenge and treatment To generate tumor, mice were injected subcutaneously in the right flank with 200 l of 1.5 × 106 WEHI-164 cells. One, two or three doses of 106 TL-loaded DCs or TL-loaded and three groups of matured DCs (CpG-matured DCs, LPS-matured DCs and Listeria monocytogenes-matured DCs) were injected around tumors in different groups of mice at 7th, 10th and 13th days after tumor implantation (one dose only at 7th day, two doses at 7th and 10th days and alike). When the tumor was palpable, the shortest and longest surface diameters were measured every 2 days using digital calipers. The tumor area was achieved by multiplying the shortest and longest axis of the tumor and then the mean of tumor growth rate per 48 h was calculated. Mice were sacrificed when the tumor size reached above 400 mm2 (>400 mm2 ). Mice were clinically evaluated daily and were weighed every two days. Dimensions of the tumors were measured regularly by caliper during the experiments, and tumor masses were calculated as following: Tumor weight(mg) =
Length(mm) · width2 (mm2 ) 2
assuming density = 1 mg/mm3 for tumor tissue
(1)
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Fig. 1. PK-PD model of cell death. k1 : first order rate constant of transit; k2 : measure of drug potency; and C(t): the plasma concentration of anticancer agent. Table 1 Drug parameters for mice in CpG and Listeria groups.
3. Methods In untreated mice, the experimental data demonstrate that tumor growth rate follows two distinctive and different phases: firstly, an initial phase with exponential growth, secondly a linear growth phase with a smooth transition between two phases. In treated animals, the tumor growth rate is proportionally decreased in terms of both drug concentration and the concentration of proliferating tumor cells. 3.1. Pharmacodynamic model Anticancer treatment influences the dynamics of tumor growth so that the proliferating cells become non-proliferating with a rate depending on the drug concentration in plasma. Invoking immunological principles, the tumor growth rate in the presence of anti-tumor drug may be modeled by a compartment model as shown in Fig. 1 (Koch et al., 2009) with following equations:
x1 =
20 1 x12 (t) (1 + 20 x1 (t))w(t)
x2 = k2 C(t)x1 (t) − k1 x2 (t), xi = k1 (xi−1 (t) − xi (t)), w(t) =
N
− k2 C(t)x1 (t),
x1 (0) = w0
x2 (0) = 0
xi (0) = 0, i = 3, . . ., N
xi (t)
(2) (3) (4)
(5)
i=1
In this model, all tumor cells are assumed to be proliferating. The model assumes that the anti-cancer treatment renders some cells non-proliferating as well (Fig. 1), eventually bringing them to death. For a given time t, x1 (t) indicates the portion of proliferating cells within the total tumor weight w(t) and c(t) demonstrates the plasma concentration of the anticancer agent. x1 (t) represents the portion of w(t) that is actually proliferating. The model assumes that the drug elicits its effect decreasing the tumor growth rate by a factor being proportional to c(t) · x1 (t) multiplied by the constant parameter k2 being an index of the drug efficacy. It is assumed that the cells affected by drug action stop proliferating and pass through n different stages (named x2 , . . ., xn ), characterized by progressive degrees of damage, and, eventually, they die. The dynamics by which the cells proceed through progressive degrees of damage is modulated via a rate constant k1 that can be interpreted in terms of the kinetics of cell death. In practice, the drug absorption function can be replaced as following (Koch et al., 2009):
C(t) =
ˇ ˇ−˛
(e−˛t − e−ˇt )
(6)
That ˇ, ˛ and stand for the absorption and elimination rates and the volume of distribution respectively.
CpG Listeria
˛
ˇ
0.252 0.151
0.651 0.21
1.53 0.82
In the experimental study of this paper, the parameters (0 , 1 , k1 , k2 , ˛, ˇ, ) are supposed to be optimally estimated by Genetic algorithms invoking the experimental data. The drug parameters for those mice in CpG and Listeria groups have been reported in Table 1. The drug concentration of different groups with triple injection on 7th, 10th and 13th days is shown in Fig. 2. It can be seen that after first, second and third injections, the plasma concentration of the drug goes up and then decreases exponentially in consistent with the physiological paradigm. With suitable parameters in different groups of drug injection, a transformation may be obtained to describe the plasma concentration of drug in terms of its injection. To model the behavior of immune system against tumor growth rate, the inputs and outputs for different vaccinations are simply available. Because of the complex behavior of the immune system in response to the different types of vaccines and also to model different feedback paths in the immune system, dynamic Recurrent ANN (RNN) has been used. The ANN output in dynamic case depends on the current input and previous input and output values. Dynamic networks generally model more efficiently than static networks and profit from the feedback loops. However, the training process is often more complex and time-consuming. Noting experimentation data, it is found that in each group of vaccines, only three sets of input-output patterns are available. Nevertheless, a model based on ANN requires in practice much more data to be able to appropriately model the behavior of unknown system. Using a reasonable interpolation scheme for different groups, the data of vaccinations were extended to 21 input–output patterns at each group. Using artificial neural network, it is now possible to model the dynamics of tumor growth in the presence of different doses of vaccines owing to the larger number of input–output patterns.
3.2. NARX neural network Here, a Nonlinear Auto-Regressive network with eXogenous inputs (NARX) is used to simulate the relation between vaccine concentration in plasma and tumor size for different vaccination groups. The desired ANN is a recurrent dynamic network, with feedback connections enclosing several layers of the network. This network can be used as a predictor, to predict the next value of the input signal (Xie et al., 2009).
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CpG & Tumor Lysate Mean Plasma Concentration
Mean Plasma Concentration
Listeria & LPS 0.25 1 time injection 0.2 0.15 0.1 0.05 0
0
5
10
15 20 Time(day)
25
30
0.4 1 time injection 0.3 0.2 0.1 0
35
0
5
10
3 time injection 0.6 0.4 0.2 0
0
5
10
15
20
25
30
35
CpG & Tumor Lysate
0.8
Mean Plasma Concentration
Mean Plasma Concentration
Listeria & LPS
15 20 Time(day)
25
30
35
0.8 3 time injection 0.6 0.4 0.2 0
0
5
10
Time(day)
15
20
25
30
35
Time(day)
Fig. 2. Mean plasma concentration versus time with one and 3 times injections in different groups.
The input–output relation in the NARX model can be described as follows:
empirical data well. For calculating error between test patterns and empirical data, Mean Absolute Error (MAE) is used as following:
y(t) = f (y(t − 1), . . ., y(t − ny ), u(t − 1), . . ., u(t − nu ))
MAE =
(7)
where the next value of the dependent output y(t) depends on the previous values of output signal as well as the previous values of an independent (exogenous) input signal. Adjustable parameters in a NARX net consist of the number of neurons and the number of input and output delays in the network. To optimally find the number of delays, a sweep has been performed from 0 to 3 delay elements for input/output ones. Besides, the number of neurons has been swept from 5 to 25 to achieve the optimal number of hidden neurons.
1 1 |fi − yi | = |ei | n n n
n
i=1
i=1
(8)
Fig. 4 shows the best training performance for different groups of vaccination using NARX model. According to Table 2, it may be deduced that LPS-matured DCs group exhibits the most complicated data since it requires a larger number of neurons for modeling the empirical data. The same number of output/input delays exhibits that all vaccinations are dealing with the same dynamics (or the same immunological system). 4.2. Model behvaiour for unexperimented vaccination patterns
4. Evaluations and results 4.1. Modeling of experimental data Simulations have been performed using MATLAB and the modeling error in the randomly selected patterns has been used as the selection criteria. The simulations exhibited that the optimal NARX model includes different optimum parameters for various groups of vaccinations. Table 2 demonstrates the optimum NARX parameters for different group of DC-based vaccines. Fig. 3 shows the output of proposed NARX model for test patterns of different groups of vaccinations. According to Fig. 3, it is evident that the proposed NARX model is able to follow up the
As mentioned in the previous section, a NARX model has been established which is able to suitably pursuit the empirical data. Since the proposed NARX model is compatible with the dynamics of immunological system in the extent of experimented cases, it may be exploited to predict the tumor growth rate in the presence of un-experimented vaccination profiles. Then, a series of un-experimented vaccination profiles is applied to the proposed model 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
Table 2 NARX model optimum parameters for different vaccination groups. Group of vaccination
Number of neurons
Number of input delays
Number of output delays
Modeling train error
Listeria LPS CpG Tumor lysate
21 25 15 9
3 3 3 3
1 1 1 1
3.5279 5.1697 3.3963 2.7404
M. Mehrian et al. / Computational Biology and Chemistry 48 (2014) 21–28
Listeria
LPS 150 simulated Empirical
60
Tumor size W(t) cm3
Tumor size W(t) cm3
80
40 20 0 -20
0
10
20
30
50
0
40
simulated Empirical
100
0
10
Time(days) CpG
30
40
Tumor Lysate 150 simulated Empirical
150
Tumor size W(t) cm3
Tumor size W(t) cm3
20 Time(days)
200
100 50 0
25
0
10
20
30
40
Time(days)
simulated Empirical 100
50
0
0
10
20
30
40
Time(days)
Fig. 3. Tumor size versus time using NARX model for different groups of vaccination.
experimented for different groups of mice as well as for different vaccines. Now, four-time injections with the same time interval are to be tested by applying to the proposed NARX model. The input pattern is reconstructed with the same process of the training data and using the same time constants. Applying afore-mentioned input pattern, the proposed NARX model predicts the tumor size evolves as shown in Fig. 5. To evaluate the results, the empirical data in the case of 3-time injections has been shown as well in Fig. 5. Also, the predicted tumor growth rate has been demonstrated for the direct solution of differential equations as well. According to Fig. 5, the differential equations exhibit
very smooth responses. Furthermore, the behavior of predicted responses is more or less compatible with either the empirical data or the differential equations. The compatibility of the responses may be originated from the training data which include three-time injection patterns. From the interpretation viewpoint, the empirical data show that the larger the number of vaccine injections in Listeria-matured DCs group, the size of tumor becomes smaller. The proposed NARX model exhibits the same trend by suppressing the predicted tumor size (Fig. 5). The same process may be observed for the LPS-matured DCs case. CpG-matured DC vaccines group demonstrate a different
Fig. 4. Training and test errors versus epoch number using NARX model for different groups of vaccination.
M. Mehrian et al. / Computational Biology and Chemistry 48 (2014) 21–28
LPS
Listeria
a 50
b Differential Eq NARX net 3 time injection
Tumor size cm3
40 30 20
Tumor size cm3
26
10 0
100 80 60 Differential Eq NARX net 3 time injection
40 20
0
10
20
30
40
0
5
10
15
Time(day)
30
35
Tumor Lysate
d 140
150
Differential Eq NARX net 3 time injection
120 100
Tumor size cm3
Tumor size cm3
25
Time(day)
CpG
c
20
80 60 40
Differential Eq NARX net 3 time injection
100
50
20 0
5
10
15 20 Time(day)
25
30
0
5
10
15 20 Time(day)
25
30
Fig. 5. Predicted tumor size for un-experimented vaccicantion profile with 4-time injections. The results are demosntrated for four groups of vaccinations, and each one exhibits the result of proposed model (red), the solution of differential equations (green) and compared with the experimented case of 3-time injections (blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
mechanism against other three vaccination groups. In this case, the empirical data exhibit a negative effect on the tumor suppression in the presence of CpG-matured DC vaccination. In other words, the size of tumor increases in the presence of CpG-matured DC vaccines. The proposed NARX model exhibits the same behavior with a larger tumor growth rate in the case of four-time CpG-matured DCs injections (Fig. 5).
b
Listeria-Input 1 Exp injection 3 time injection
0.8 0.6 0.4 0.2 0 0
10
20
30
Mean Plasma Concentration
Mean Plasma Concentration
a
4.3.1. Exponential profile vaccination Now, 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 exponential rise is observed in the plasma vaccine concentration (Figs. 6 and 7). It reflects an increasing doses of vaccination in which the injected doses increase progressively. In practice, it
40
CpG-Input Exp injection 3 time injection
0.6 0.4 0.2
0 0
5
10
Time(days)
40
20
10
20 Time(days)
30
40
3
3 times injection Neural Net
Tumor size W(t) cm
Tumor size W(t) cm
d
Listeria-Output
0 0
20
25
30
35
30
35
Time(days)
60
3
c
15
CpG-Output 250 3 times injection Neural Net
200 150 100 50 0 0
5
10
15
20
25
Time(days)
Fig. 6. The concentration of vaccines in plasma (above) for unexperimented exponential (green) and experimented 3-time (red) injections. The related tumor sizes (below) for Listeria (left) and CpG (right) matured DCs. (For interpretation of the references to color 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
b
LPS-Input 0.8
Mean Plasma Concentration
Mean Plasma Concentration
a
Exp injection 3 time injection
0.6 0.4 0.2 0 0
5
10
15
20
25
30
35
Tumor Lysate-Input Exp injection 3 time injection
0.6 0.4 0.2
0 0
5
10
Time(days) LPS-Output
d
Tumor size W(t) cm 3
100
3 time injection Neural Net
80 60 40 20 0 0
5
10
15 20 Time(days)
15
20
25
30
35
Time(days)
25
30
35
Tumor size W(t) cm 3
c
27
Tumor Lysate-Output 200 3 time injection Neural Net
150 100 50 0 0
5
10
15 20 Time(days)
25
30
35
Fig. 7. The concentration of vaccines in plasma (above) for unexperimented exponential (green) and experimented 3-time (red) injections. The related tumor sizes (below) for LPS (left) and Lysate (right) cases. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
is supposed that the dose of injections is incremented at equal timing intervals. Fig. 6 shows the concentration of vaccines in plasma versus time for two vaccines of Listeria- and CpG-matured DCs. Applying these vaccination profiles to the proposed NARX model, the tumor sizes are predicted as demonstrated in Fig. 6. The results related to LPS and Tumor Lysate groups are shown in Fig. 7. According to Fig. 6, an increasing exponential dose of Listeriamatured DCs vaccine can no longer control the tumor growth and tumor size increases rapidly. In contrast, exponential doses of CpG matured cells can effectively control the tumor growth so that the tumor size is suppressed efficiently.
Fig. 7 demonstrates that both Tumor Lysate and LPS-Matured DCs vaccines worsen the treatment in the increasing exponential injection profile. It may be reflected from the previous findings that the tumor grows faster in the presence of low concentration of these vaccines. Therefore, an exponential injection of CpG matured DCs appear so effective in the control of tumor growth. The result also approves that the treatment procedure is very critical in the initial phase of tumor growth. Besides, it may be deduced that LPSmatured DCs exhibits a bit more effective in varying doses profiles compared to Tumor Lysate-pulsed DCs. It should be reminded that this exponential injection profiles should be experimented to verify in practice the performance of the proposed NARX model.
Fig. 8. The CpG-matured DCs concentration in plasma (above) and injection dosing (below) versus time. The theoretical concentration in plasma (above-green) has been proposed by the ANN model of tumor growth. The approximated concentration in plasma (above-blue) may be achieved by the injection dosing pattern (below) with different doses but regular injection timing pattern. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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5. Discussion
References
According to simulation results, it is found in accordance with the immunological principles that all vaccination procedures such as the ones using matured DCs can only be effective if administered at early stages of tumor growth. Hence, an exponentially increasing concentration of LPS-matured, tumor lysate and Listeria monocytogenes DCs in plasma fail to suppress the tumor growth because of lower concentration at initial stages. In contrary, CpG-matured DCs exhibit more effective response in this profile since CpG ones demonstrated a negative effect at high concentration (according to experimentation data). Besides, an exponentially increasing concentration pattern of CpG-matured DCs in plasma appear to be effective in controlling tumor growth. In practice, this pattern of vaccine concentration in plasma may be approximated by several injections with increasing doses. Fig. 8 demonstrates the proposed injections for achieving mentioned concentration pattern in plasma.
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Enhanced antitumour activity of 6-xenograft hydroxymethylacylfulvene in combination with topotecan or paclitaxel in the MV522 lung carcinoma model. European Journal of Cancer 36, 2430–2436. Jönsson, S., et al., 2011. Contribution of modeling and simulation studies in the regulatory review: a European regulatory perspective. In: Clinical Trial Simulations. Springer, New York, pp. 15–36. Koch, G., et al., 2009. Modeling of tumor growth and anticancer effects of combination therapy. Journal of Pharmacokinetics and Pharmacodynamics 36 (2), 179–197. Lalonde, R.L., et al., 2007. Model-based drug development. Clinical Pharmacology & Therapeutics 82 (1), 21–32. Lanzavecchia, A., Sallusto, F., 2001. Regulation of T cell immunity by dendritic cells. Cell 106 (3), 263–266. LoRusso, P.M., et al., 2008. Phase I and pharmacokinetic study of lapatinib and docetaxel in patients with advanced cancer. Journal of Clinical Oncology 26 (18), 3051–3056. Morse, M.A., et al., 2002. Dendritic cell maturation in active immunotherapy strategies. Expert Opinion on Biological Therapy 2 (1), 35–43. Olden, J.D., Jackson, D.A., 2002. Illuminating the black box: a randomization approach for understanding variable contributions in artificial neural networks. Ecological Modelling 154 (1), 135–150. Pili, R., et al., 2001. Combination of phenylbutyrate and 13-cis retinoic acid inhibits prostate tumor growth and angiogenesis. Cancer Research 61, 1477–1485. Roose, T., et al., 2007. Mathematical models of avascular tumor growth. Siam Review 49 (2), 179–208. Rowland, M., et al., 2011. Physiologically-based pharmacokinetics in drug development and regulatory science. Annual Review of Pharmacology and Toxicology 51, 45–73. Sharma, P., et al., 2011. Novel cancer immunotherapy agents with survival benefit: recent successes and next steps. Nature Reviews Cancer 11 (11), 805–812. Sparano, J.A., et al., 2008. Weekly paclitaxel in the adjuvant treatment of breast cancer. New England Journal of Medicine 358 (16), 1663–1671. Tanyi, J.L., Chu, C.S., 2012. Dendritic cell-based tumor vaccinations in epithelial ovarian cancer: a systematic review. Future Oncology 8 (10), 1273–1299. Tod, M., et al., 2008. Facilitation of drug evaluation in children by population methods and modelling. Clinical Pharmacokinetics 47 (4), 231–243. Van der Graaf, P.H., Benson, N., 2011. Systems pharmacology: bridging systems biology and pharmacokinetics–pharmacodynamics (PKPD) in drug discovery and development. Pharmaceutical Research 28 (7), 1460–1464. Van Kesteren, C.H., et al., 2003. Pharmacokinetic–pharmacodynamic guided trial design in oncology. Investigational New Drugs 21 (2), 225–241. Van Kesteren, C., et al., 2000. Pharmacokinetics and pharmacodynamics of the novel marine-derived anticancer agent ecteinascidin 743 in a phase I dose-finding study. Clinical Cancer Research 6 (12), 4725–4732. Xie, H., et al., 2009. 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6. Conclusion In this paper, the Pharmaco-Dynamics of DC-based immunotherapeutic vaccines have been firstly modeled and characterized using five physiology-relevant parameters. These parameters are simply identifiable using the typical experimental data obtained from nude mice in the drug research and development process. The optimum values have been simply determined using Genetic algorithms. Supposing that the drug concentration in the tumor (at the target) is in rapid equilibrium with plasma, a model of perturbed growth has been sought in terms of plasma drug concentration representing the effect of anticancer compound. The mean plasma concentration of drug has been modeled using three physiologically relevant parameters. Using Genetic algorithm and PK/PD equations, the respective three parameters have been optimally found from experimented laboratory data for 4 different vaccinated groups of mice. To model the effects of different vaccines on tumor growth rate, a black box methodology is invoked considering the available data of drug plasma concentration as input and the tumor growth as the output because the exact information of immune system lacks. A NARX artificial neural network has been used for modeling to cope with the nonlinear and complex behavior of immune system. Simulations show that a dynamic NARX model is able to interpret even the contradictory aspects of the empirical data due to different vaccination groups. Particularly, the proposed NARX model affords to describe the complicated mechanism involved in the case of CpG matured cells. Using the proposed NARX model, a series of un-experimented vaccination profiles have been considered to predict the behavior of immunological system. Simulations demonstrate that the tumor growth is very sensitive to the vaccine concentration in plasma at the initial phase of tumor growth. However, CpG-matured cells behave differently so that an increasing exponential concentration of CpG-matured cells can suppress the tumor growth effectively. Predicted patterns of tumor growth for 4-time and exponential injections need to be verified through laboratory experimentations. It is required to experimentally check the simulation results and predicted profiles, so new effective vaccination can be obtained. According to simulation results for injection profiles of exponential and 4-times injection, contradictory effects are anticipated on the tumor growth. A prospective profile may be sought by merging those schemes in future works.
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Computational Biology and Chemistry journal homepage: www.elsevier.com/locate/compbiolchem
Research article
Modeling of tumor growth in dendritic cell-based immunotherapy using artificial neural networks Mohammad Mehrian a , Davud Asemani a,∗ , Abazar Arabameri a , Arash Pourgholaminejad b , Jamshid Hadjati b a b
Laboratory of Signals and Electronic Systems, Electrical and Computer Engineering Faculty, K.N. Toosi University of Technology, Tehran, Iran Department of Immunology, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 4 March 2013 Received in revised form 31 August 2013 Accepted 30 September 2013 Keywords: Artificial neural network Dendritic cells Immunotherapy Tumor growth rate
a b s t r a c t Exposure-response modeling and simulation is especially useful in oncology as it permits to predict and design un-experimented clinical trials as well as dose selection. Dendritic cells (DC) are the most effective immune cells in the regulation of immune system. To activate immune system, DCs may be matured by many 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 dynamics of antitumor vaccines using empirical data obtained from the experimentations of different groups of mice treated with DCs matured by bacterial CpG-DNA, LPS and whole lysate of a Gram-positive bacteria 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. Owing to the nonlinearity properties, the proposed ANN model has been able not only to describe the contradictory 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 effective in suppressing the tumor growth. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction To understand and predict the pharmacological behavior of anticancer drugs, it is crucial to quantify the time course of pharmacodynamic responses in relation to the plasma concentration. A fundamental step in the preclinical development of oncology drugs is the in vivo evaluation of the antitumor effect. For this purpose, a series of experiments are performed, in which tumor cells from immortalized cell lines are inoculated into mice. Tumor volumes are measured at different times throughout the experiment for all animals, treated either with a vehicle (control) or with an active drug. The effect of the active molecule is then measured by comparing the average tumor weights in treated and control animals at the end of experiment, or by counting the animals surviving their disease (Fujimoto-Ouchi et al., 2002; Granucci et al., 1999; Hammond et al., 2000; Roose et al., 2007; Rowland et al., 2011; Sharma et al., 2011; Sparano et al., 2008; Tanyi and Chu, 2012; Tod et al., 2008; Van der Graaf and Benson, 2011; Van Kesteren et al., 2000, 2003;
∗ Corresponding author. E-mail addresses: m [email protected] (M. Mehrian), [email protected] (D. Asemani), abazar [email protected] (A. Arabameri), [email protected] (A. Pourgholaminejad), [email protected] (J. Hadjati). 1476-9271/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compbiolchem.2013.09.007
Xie et al., 2009; Yap et al., 2010; Zhang et al., 2002). This approach can be used to select the most potent candidate within a series of vaccines using the same dosing regimen, or the most appropriate dosing regimen among those tested for a specific compound. However, in this way, the whole course of the tumor growth timing is often neglected, so that only a partial use of the information available from the experiment is realized (only final points). Exposure-response modeling and simulation (M&S) has emerged during the last decade as a means to better understand the relationships of drug exposure-clinical outcomes of anticancer therapies (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; Van Kesteren et al., 2003). Contradictory contributions of a large dozens of factors suggest that M&S is a sophisticated tool to transform the data of multiple endpoints into knowledge (Bruno et 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; Roose et 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 the tumor growth process (Roose et al., 2007), without an in-depth mechanistic description of the underlying physiological processes.
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In this context, the dynamics of a drug can be evaluated only in terms of changes of the parameter values describing the tumor growth. These changes depend on the dose level as well as the administration schedule, so that those approaches can be applied only retrospectively and not as predictive tools when used outside the tested regimens. Functional models are nevertheless based on mechanistic, physiology-based hypotheses. In this case, it implies a set of assumptions about the tumor growth, including cell-cycle kinetics and biochemical processes, such as those related to anti-angiogenetic and/or immunological responses (Eftimie et al., 2011). Such models usually represent the cell population in its heterogeneity, splitting it into at least two subpopulations: the proliferating and the quiescent cells. More complex models describe the cell population as age-structured and take into account subpopulations related to specific phases of the cell cycle. These models have a much larger number of parameters compared with the empirical ones. Their development is so time-consuming and a number of quantitative observations (e.g., flow cytometry analyses, biochemical and immunological marker measurements, and so forth) are required to avoid the identifiability problems due to the over-parameterization. The situation becomes even more complicated when the effect of the treatment with an anticancer drug is also considered (Bodnar and Forys, 2007; Bousso, 2008; Bruno et al., 2001; Cabrales et al., 2008; 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; Lanzavecchia and Sallusto, 2001; LoRusso et al., 2008; 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), because of the incomplete knowledge of the mode of action in vivo. As a consequence, these models are rarely used in industrial drug research. Though, several tumor growth models have been proposed so far, a practical and exhaustive tool that supports oncology drug development is still missing. In this regard, the only metrics of success is the compatibility with the experimental data. In this paper, a model is presented associating with an effective compromise between empirical and mechanism-based approaches. It relies on a few identifiable and biologically relevant parameters. The estimation of the related parameters relies only on the data, typically available in the preclinical setting, the pharmacokinetics of the anticancer agents and the tumor growth curves in vivo. Dendritic cells (DCs) represent potent antigen-presenting cells (APC). The most widely emphasized functions of DCs are antigen uptake and processing. DCs activate T lymphocytes to initiate immune responses and also regulate the activation of T lymphocytes (Bousso, 2008; Bruno et 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; Lanzavecchia and Sallusto, 2001). Many factors can influence the development of polarized immune responses such as DC activation status. Many microbial components like bacterial CpG-DNA, Lipopolysaccharide (LPS) and other microbial products have been shown to mature DCs and can regulate the activation of T cell responses (Cornet et al., 2006; Danhof et al., 2008; Eftimie et al., 2011; Fujimoto-Ouchi et al., 2002; Granucci et al., 1999). In oncology, the term tumor immunotherapy embraces a variety of different therapeutic approaches with the shared aim of exploiting effector mechanisms of the immune system to eliminate tumor cells (Sharma et al., 2011). Over the past decade, among the most intensively studied tumor immunotherapies have been DC-based cancer vaccines (Cintolo et al., 2012). Dendritic cells play a pivotal role in anti-tumor immune responses. Therefore, the maturation
status of administrated DCs could potentially affect the efficacy and 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; Tanyi and Chu, 2012). Apart from general information about tumor behavior in the presence of different vaccines, no further information is available. So, the problem appears to be a black box type according to modeling paradigm. One of the main applications of artificial neural networks (ANN) as modeling tools is in the cases where just the input and output of a system are available and there is no more information about different internal parts of the system (Olden and Jackson, 2002) (black box modeling paradigm). Accordingly, ANN is here used to model the behavior of tumor growth considering different vaccination profiles. 2. Materials 2.1. Animals and cell-lines Six-to-eight week’s old female BALB/c mice were purchased from Lab. Animal Center, Institute of Pasteur of Iran. All of the animal experiments were conducted in accordance with the current best practices and ethical principles. BALB/c-derived fibrosarcoma (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 of female BALB/c mice; 106 cells ml−1 were placed in 24-well plates in RPMI plus 10% FCS, 20 ng ml−1 GM-CSF (R&D systems, USA) and 10 ng ml−1 IL-4 (R&D systems, USA). After 3 days, non-adherent cells were gently collected into a new plate and fresh media was added. On day 5, 100 g ml−1 of tumor lysate (TL) was added to immature DC cultures. After 4–6 h in some wells 10 g CpG, 1 g LPS and 70 mg lysate of Listeria monocytogenes was added. Nonadherent DCs in all wells were harvested on day 7 of the culture and used for tumor immunotherapy. 2.3. Tumor challenge and treatment To generate tumor, mice were injected subcutaneously in the right flank with 200 l of 1.5 × 106 WEHI-164 cells. One, two or three doses of 106 TL-loaded DCs or TL-loaded and three groups of matured DCs (CpG-matured DCs, LPS-matured DCs and Listeria monocytogenes-matured DCs) were injected around tumors in different groups of mice at 7th, 10th and 13th days after tumor implantation (one dose only at 7th day, two doses at 7th and 10th days and alike). When the tumor was palpable, the shortest and longest surface diameters were measured every 2 days using digital calipers. The tumor area was achieved by multiplying the shortest and longest axis of the tumor and then the mean of tumor growth rate per 48 h was calculated. Mice were sacrificed when the tumor size reached above 400 mm2 (>400 mm2 ). Mice were clinically evaluated daily and were weighed every two days. Dimensions of the tumors were measured regularly by caliper during the experiments, and tumor masses were calculated as following: 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
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Fig. 1. PK-PD model of cell death. k1 : first order rate constant of transit; k2 : measure of drug potency; and C(t): the plasma concentration of anticancer agent. Table 1 Drug parameters for mice in CpG and Listeria groups.
3. Methods In untreated mice, the experimental data demonstrate that tumor growth rate follows two distinctive and different phases: firstly, an initial phase with exponential growth, secondly a linear growth phase with a smooth transition between two phases. In treated animals, the tumor growth rate is proportionally decreased in terms of both drug concentration and the concentration of proliferating tumor cells. 3.1. Pharmacodynamic model Anticancer treatment influences the dynamics of tumor growth so that the proliferating cells become non-proliferating with a rate depending on the drug concentration in plasma. Invoking immunological principles, the tumor growth rate in the presence of anti-tumor drug may be modeled by a compartment model as shown in Fig. 1 (Koch et al., 2009) with following equations:
x1 =
20 1 x12 (t) (1 + 20 x1 (t))w(t)
x2 = k2 C(t)x1 (t) − k1 x2 (t), xi = k1 (xi−1 (t) − xi (t)), w(t) =
N
− k2 C(t)x1 (t),
x1 (0) = w0
x2 (0) = 0
xi (0) = 0, i = 3, . . ., N
xi (t)
(2) (3) (4)
(5)
i=1
In this model, all tumor cells are assumed to be proliferating. The model assumes that the anti-cancer treatment renders some cells non-proliferating as well (Fig. 1), eventually bringing them to death. For a given time t, x1 (t) indicates the portion of proliferating cells within the total tumor weight w(t) and c(t) demonstrates the plasma concentration of the anticancer agent. x1 (t) represents the portion of w(t) that is actually proliferating. The model assumes that the drug elicits its effect decreasing the tumor growth rate by a factor being proportional to c(t) · x1 (t) multiplied by the constant parameter k2 being an index of the drug efficacy. It is assumed that the cells affected by drug action stop proliferating and pass through n different stages (named x2 , . . ., xn ), characterized by progressive degrees of damage, and, eventually, they die. The dynamics by which the cells proceed through progressive degrees of damage is modulated via a rate constant k1 that can be interpreted in terms of the kinetics of cell death. In practice, the drug absorption function can be replaced as following (Koch et al., 2009):
C(t) =
ˇ ˇ−˛
(e−˛t − e−ˇt )
(6)
That ˇ, ˛ and stand for the absorption and elimination rates and the volume of distribution respectively.
CpG Listeria
˛
ˇ
0.252 0.151
0.651 0.21
1.53 0.82
In the experimental study of this paper, the parameters (0 , 1 , k1 , k2 , ˛, ˇ, ) are supposed to be optimally estimated by Genetic algorithms invoking the experimental data. The drug parameters for those mice in CpG and Listeria groups have been reported in Table 1. The drug concentration of different groups with triple injection on 7th, 10th and 13th days is shown in Fig. 2. It can be seen that after first, second and third injections, the plasma concentration of the drug goes up and then decreases exponentially in consistent with the physiological paradigm. With suitable parameters in different groups of drug injection, a transformation may be obtained to describe the plasma concentration of drug in terms of its injection. To model the behavior of immune system against tumor growth rate, the inputs and outputs for different vaccinations are simply available. Because of the complex behavior of the immune system in response to the different types of vaccines and also to model different feedback paths in the immune system, dynamic Recurrent ANN (RNN) has been used. The ANN output in dynamic case depends on the current input and previous input and output values. Dynamic networks generally model more efficiently than static networks and profit from the feedback loops. However, the training process is often more complex and time-consuming. Noting experimentation data, it is found that in each group of vaccines, only three sets of input-output patterns are available. Nevertheless, a model based on ANN requires in practice much more data to be able to appropriately model the behavior of unknown system. Using a reasonable interpolation scheme for different groups, the data of vaccinations were extended to 21 input–output patterns at each group. Using artificial neural network, it is now possible to model the dynamics of tumor growth in the presence of different doses of vaccines owing to the larger number of input–output patterns.
3.2. NARX neural network Here, a Nonlinear Auto-Regressive network with eXogenous inputs (NARX) is used to simulate the relation between vaccine concentration in plasma and tumor size for different vaccination groups. The desired ANN is a recurrent dynamic network, with feedback connections enclosing several layers of the network. This network can be used as a predictor, to predict the next value of the input signal (Xie et al., 2009).
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CpG & Tumor Lysate Mean Plasma Concentration
Mean Plasma Concentration
Listeria & LPS 0.25 1 time injection 0.2 0.15 0.1 0.05 0
0
5
10
15 20 Time(day)
25
30
0.4 1 time injection 0.3 0.2 0.1 0
35
0
5
10
3 time injection 0.6 0.4 0.2 0
0
5
10
15
20
25
30
35
CpG & Tumor Lysate
0.8
Mean Plasma Concentration
Mean Plasma Concentration
Listeria & LPS
15 20 Time(day)
25
30
35
0.8 3 time injection 0.6 0.4 0.2 0
0
5
10
Time(day)
15
20
25
30
35
Time(day)
Fig. 2. Mean plasma concentration versus time with one and 3 times injections in different groups.
The input–output relation in the NARX model can be described as follows:
empirical data well. For calculating error between test patterns and empirical data, Mean Absolute Error (MAE) is used as following:
y(t) = f (y(t − 1), . . ., y(t − ny ), u(t − 1), . . ., u(t − nu ))
MAE =
(7)
where the next value of the dependent output y(t) depends on the previous values of output signal as well as the previous values of an independent (exogenous) input signal. Adjustable parameters in a NARX net consist of the number of neurons and the number of input and output delays in the network. To optimally find the number of delays, a sweep has been performed from 0 to 3 delay elements for input/output ones. Besides, the number of neurons has been swept from 5 to 25 to achieve the optimal number of hidden neurons.
1 1 |fi − yi | = |ei | n n n
n
i=1
i=1
(8)
Fig. 4 shows the best training performance for different groups of vaccination using NARX model. According to Table 2, it may be deduced that LPS-matured DCs group exhibits the most complicated data since it requires a larger number of neurons for modeling the empirical data. The same number of output/input delays exhibits that all vaccinations are dealing with the same dynamics (or the same immunological system). 4.2. Model behvaiour for unexperimented vaccination patterns
4. Evaluations and results 4.1. Modeling of experimental data Simulations have been performed using MATLAB and the modeling error in the randomly selected patterns has been used as the selection criteria. The simulations exhibited that the optimal NARX model includes different optimum parameters for various groups of vaccinations. Table 2 demonstrates the optimum NARX parameters for different group of DC-based vaccines. Fig. 3 shows the output of proposed NARX model for test patterns of different groups of vaccinations. According to Fig. 3, it is evident that the proposed NARX model is able to follow up the
As mentioned in the previous section, a NARX model has been established which is able to suitably pursuit the empirical data. Since the proposed NARX model is compatible with the dynamics of immunological system in the extent of experimented cases, it may be exploited to predict the tumor growth rate in the presence of un-experimented vaccination profiles. Then, a series of un-experimented vaccination profiles is applied to the proposed model 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
Table 2 NARX model optimum parameters for different vaccination groups. Group of vaccination
Number of neurons
Number of input delays
Number of output delays
Modeling train error
Listeria LPS CpG Tumor lysate
21 25 15 9
3 3 3 3
1 1 1 1
3.5279 5.1697 3.3963 2.7404
M. Mehrian et al. / Computational Biology and Chemistry 48 (2014) 21–28
Listeria
LPS 150 simulated Empirical
60
Tumor size W(t) cm3
Tumor size W(t) cm3
80
40 20 0 -20
0
10
20
30
50
0
40
simulated Empirical
100
0
10
Time(days) CpG
30
40
Tumor Lysate 150 simulated Empirical
150
Tumor size W(t) cm3
Tumor size W(t) cm3
20 Time(days)
200
100 50 0
25
0
10
20
30
40
Time(days)
simulated Empirical 100
50
0
0
10
20
30
40
Time(days)
Fig. 3. Tumor size versus time using NARX model for different groups of vaccination.
experimented for different groups of mice as well as for different vaccines. Now, four-time injections with the same time interval are to be tested by applying to the proposed NARX model. The input pattern is reconstructed with the same process of the training data and using the same time constants. Applying afore-mentioned input pattern, the proposed NARX model predicts the tumor size evolves as shown in Fig. 5. To evaluate the results, the empirical data in the case of 3-time injections has been shown as well in Fig. 5. Also, the predicted tumor growth rate has been demonstrated for the direct solution of differential equations as well. According to Fig. 5, the differential equations exhibit
very smooth responses. Furthermore, the behavior of predicted responses is more or less compatible with either the empirical data or the differential equations. The compatibility of the responses may be originated from the training data which include three-time injection patterns. From the interpretation viewpoint, the empirical data show that the larger the number of vaccine injections in Listeria-matured DCs group, the size of tumor becomes smaller. The proposed NARX model exhibits the same trend by suppressing the predicted tumor size (Fig. 5). The same process may be observed for the LPS-matured DCs case. CpG-matured DC vaccines group demonstrate a different
Fig. 4. Training and test errors versus epoch number using NARX model for different groups of vaccination.
M. Mehrian et al. / Computational Biology and Chemistry 48 (2014) 21–28
LPS
Listeria
a 50
b Differential Eq NARX net 3 time injection
Tumor size cm3
40 30 20
Tumor size cm3
26
10 0
100 80 60 Differential Eq NARX net 3 time injection
40 20
0
10
20
30
40
0
5
10
15
Time(day)
30
35
Tumor Lysate
d 140
150
Differential Eq NARX net 3 time injection
120 100
Tumor size cm3
Tumor size cm3
25
Time(day)
CpG
c
20
80 60 40
Differential Eq NARX net 3 time injection
100
50
20 0
5
10
15 20 Time(day)
25
30
0
5
10
15 20 Time(day)
25
30
Fig. 5. Predicted tumor size for un-experimented vaccicantion profile with 4-time injections. The results are demosntrated for four groups of vaccinations, and each one exhibits the result of proposed model (red), the solution of differential equations (green) and compared with the experimented case of 3-time injections (blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
mechanism against other three vaccination groups. In this case, the empirical data exhibit a negative effect on the tumor suppression in the presence of CpG-matured DC vaccination. In other words, the size of tumor increases in the presence of CpG-matured DC vaccines. The proposed NARX model exhibits the same behavior with a larger tumor growth rate in the case of four-time CpG-matured DCs injections (Fig. 5).
b
Listeria-Input 1 Exp injection 3 time injection
0.8 0.6 0.4 0.2 0 0
10
20
30
Mean Plasma Concentration
Mean Plasma Concentration
a
4.3.1. Exponential profile vaccination Now, 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 exponential rise is observed in the plasma vaccine concentration (Figs. 6 and 7). It reflects an increasing doses of vaccination in which the injected doses increase progressively. In practice, it
40
CpG-Input Exp injection 3 time injection
0.6 0.4 0.2
0 0
5
10
Time(days)
40
20
10
20 Time(days)
30
40
3
3 times injection Neural Net
Tumor size W(t) cm
Tumor size W(t) cm
d
Listeria-Output
0 0
20
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Fig. 6. The concentration of vaccines in plasma (above) for unexperimented exponential (green) and experimented 3-time (red) injections. The related tumor sizes (below) for Listeria (left) and CpG (right) matured DCs. (For interpretation of the references to color 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
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Fig. 7. The concentration of vaccines in plasma (above) for unexperimented exponential (green) and experimented 3-time (red) injections. The related tumor sizes (below) for LPS (left) and Lysate (right) cases. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
is supposed that the dose of injections is incremented at equal timing intervals. Fig. 6 shows the concentration of vaccines in plasma versus time for two vaccines of Listeria- and CpG-matured DCs. Applying these vaccination profiles to the proposed NARX model, the tumor sizes are predicted as demonstrated in Fig. 6. The results related to LPS and Tumor Lysate groups are shown in Fig. 7. According to Fig. 6, an increasing exponential dose of Listeriamatured DCs vaccine can no longer control the tumor growth and tumor size increases rapidly. In contrast, exponential doses of CpG matured cells can effectively control the tumor growth so that the tumor size is suppressed efficiently.
Fig. 7 demonstrates that both Tumor Lysate and LPS-Matured DCs vaccines worsen the treatment in the increasing exponential injection profile. It may be reflected from the previous findings that the tumor grows faster in the presence of low concentration of these vaccines. Therefore, an exponential injection of CpG matured DCs appear so effective in the control of tumor growth. The result also approves that the treatment procedure is very critical in the initial phase of tumor growth. Besides, it may be deduced that LPSmatured DCs exhibits a bit more effective in varying doses profiles compared to Tumor Lysate-pulsed DCs. It should be reminded that this exponential injection profiles should be experimented to verify in practice the performance of the proposed NARX model.
Fig. 8. The CpG-matured DCs concentration in plasma (above) and injection dosing (below) versus time. The theoretical concentration in plasma (above-green) has been proposed by the ANN model of tumor growth. The approximated concentration in plasma (above-blue) may be achieved by the injection dosing pattern (below) with different doses but regular injection timing pattern. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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5. Discussion
References
According to simulation results, it is found in accordance with the immunological principles that all vaccination procedures such as the ones using matured DCs can only be effective if administered at early stages of tumor growth. Hence, an exponentially increasing concentration of LPS-matured, tumor lysate and Listeria monocytogenes DCs in plasma fail to suppress the tumor growth because of lower concentration at initial stages. In contrary, CpG-matured DCs exhibit more effective response in this profile since CpG ones demonstrated a negative effect at high concentration (according to experimentation data). Besides, an exponentially increasing concentration pattern of CpG-matured DCs in plasma appear to be effective in controlling tumor growth. In practice, this pattern of vaccine concentration in plasma may be approximated by several injections with increasing doses. Fig. 8 demonstrates the proposed injections for achieving mentioned concentration pattern in plasma.
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6. Conclusion In this paper, the Pharmaco-Dynamics of DC-based immunotherapeutic vaccines have been firstly modeled and characterized using five physiology-relevant parameters. These parameters are simply identifiable using the typical experimental data obtained from nude mice in the drug research and development process. The optimum values have been simply determined using Genetic algorithms. Supposing that the drug concentration in the tumor (at the target) is in rapid equilibrium with plasma, a model of perturbed growth has been sought in terms of plasma drug concentration representing the effect of anticancer compound. The mean plasma concentration of drug has been modeled using three physiologically relevant parameters. Using Genetic algorithm and PK/PD equations, the respective three parameters have been optimally found from experimented laboratory data for 4 different vaccinated groups of mice. To model the effects of different vaccines on tumor growth rate, a black box methodology is invoked considering the available data of drug plasma concentration as input and the tumor growth as the output because the exact information of immune system lacks. A NARX artificial neural network has been used for modeling to cope with the nonlinear and complex behavior of immune system. Simulations show that a dynamic NARX model is able to interpret even the contradictory aspects of the empirical data due to different vaccination groups. Particularly, the proposed NARX model affords to describe the complicated mechanism involved in the case of CpG matured cells. Using the proposed NARX model, a series of un-experimented vaccination profiles have been considered to predict the behavior of immunological system. Simulations demonstrate that the tumor growth is very sensitive to the vaccine concentration in plasma at the initial phase of tumor growth. However, CpG-matured cells behave differently so that an increasing exponential concentration of CpG-matured cells can suppress the tumor growth effectively. Predicted patterns of tumor growth for 4-time and exponential injections need to be verified through laboratory experimentations. It is required to experimentally check the simulation results and predicted profiles, so new effective vaccination can be obtained. According to simulation results for injection profiles of exponential and 4-times injection, contradictory effects are anticipated on the tumor growth. A prospective profile may be sought by merging those schemes in future works.
