Computational Visualization of Tumor Virotherapy. X.F. Gao1, M. Tangney2 and S. Tabirca1. 1 Computing Resources for Life Sciences Research, University ...
Computational Visualization of Tumor Virotherapy X.F. Gao1 , M. Tangney2 and S. Tabirca1 1
Computing Resources for Life Sciences Research, University College Cork, Cork, Ireland 2 Cork Cancer Research Center, Cork, Ireland
Abstract— Recent research has indicated that replicationcompetent viruses are being tested as tumor therapy agents. The fundamental premise of this therapy is based on the viruses infecting tumor cells and replicating inside them. Spread of the virus in the tumor ultimately should lead to eradication of the cancer. The outcome of tumor virotherapy depends on the dynamics that arise from the interaction between the virus and tumor cell populations both of which change in time. Motivated by this novel cancer treatment, we simulate the dynamical process of the interactions between tumor cells and viruses. We have developed a computational model based on mathematical models that captures the essential factors involved in cellular dynamics. By analyzing and adjusting the essential parameters, we reconstruct and visualize the process and outcomes of cancer virotherapy in a dynamical system. By comparing with in vivo experiments, we validate our simulations to keep a high similarity with the three typical types of experimental observations - tumor eradication, therapeutic failure and oscillations. Keywords— Virotherapy simulation; Computational visualization; Cellular dynamics; Population dynamics
I. I NTRODUCTION Virotherapy is an experimental method of cancer treatment using biotechnology to convert viruses into cancer-fighting agents by reprogramming viruses to selectively lyse and destroy tumour cells, while healthy cells remained relatively undamaged [1]. Over the last few years, several viruses have been altered to selectively infect cancer cells. Viruses such as Newcastle disease virus (NDV), vesicular stomatitis virus (VSV), reovirus and measles virus (MV) seem to have a natural tropism for tumor cells due to a variety of mechanisms [2–6]. In the present study, the recombinant MV has significant in vitro and in vivo oncolytic activity against various types of cancer. Tumor cells infected with MV that exerts its cytopathic effect (CPE) by formation of multinucleated cell aggregates (syncytia) via cell-cell fusion. The giant cell syncytia ultimately die after a few days [7]. Infected cells that have been incorporated into syncytia stop replicating and do not contribute to further growth of the tumor population. Moreover, once infected cells die, they might release free virus particles that can infect surrounding cells. This cellcell fusion is regarded as an important therapeutic advantage
of MV as it provides a significant bystander effect that eliminates uninfected cells that are incorporated in syncytia. Fig 1 shows the three types of tumor cells under MV-NIS injection.
Fig. 1: In vivo MV-NIS infection of prostate cancer xenografts. (a) Uninfected tumor cell; (b) Infected tumor cell; (c) Syncytia
An underlying premise of tumor virotherapy is that the infected tumor cells become factories that generate new virus particles which proceed to infect additional tumor cells in a series of waves [6]. Such a system may have different outcomes including the potential for chaotic behavior, which are highly dependent on the interactions between between the tumor, virus and immune system cells as well as their populations. Hence, modeling these dynamic interactions is essential to understand therapeutic outcomes and optimize therapy. To visualize these experimental observations, we need to build a dynamical system based on mathematical models. Rigorous mathematics play important roles in the computational modeling of cell biology [8]. In the development of the techniques and algorithms, mathematics composes the tools of numerical and statistical analysis. A process of estimations is the foundation of the computational solutions to mathematical problems, and the accuracy and efficiency of these methods of estimation are the subjects of much study. In addition, mathematics helps to identify certain key parameters that play a central role in defining the overall behavior of the system, and thus lead to new predictions and informative experiments. Several mathematical models have been created to understand and characterize the dynamical system by (Wu et al. 2004 [9]; Tao and Guo 2005 [10]; Dingli et al. 2006a [11]; Friedman et al., 2006 [12]). These mathematical models are useful to describe the populations of tumor cells and viruses, as well as how infected cells and syncy-
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tia contributing to tumour growth under different combinations. They do not, however, account for active cell motility or how macroscopic behavior of tumor cells being affected by the presence of viruses at the microscopic level. In this article, we design a two-dimensional computational simulation based on a mathematical model that has been developed by David Dingli et al., to visualize the dynamic interactions between the viruses and tumor cells as well as identify the vital parameters and their promising ranges. Another important question concerns the role of immune responses for the outcome of therapy, for example immune response that directly reduces the replication rate of the virus. Our model does not consider the potential interactions between immune system and viruses and/or the tumor cells that could introduce additional complexity in the dynamics.
where n is the number of neighboring cells (range from 0-8 in 0 is the base probability that a sina 2D square lattice), and PDiv gle cell will divide. During interphase and division states, a normal tumor cell can be infected by free viruses/neighboring infected cells or fuse into a syncytia. Cells may die when they receive a death signal (e.g. infection) or fail to receive a lifemaintaining signal (e.g. failed to divide), namely Apoptosis. In our model, if a cell’s age over TApopotosis (18 h in our simulation), it enters a programmed cell death (PCD) phase, with its activity progressively decreasing and will die by a probability Pdie F(Age) Age ≤ TApoptosis Pdie = 1.0 TApoptosis < Age ≤ TDeath (2) 0 F(T ) = Pdie +
II. M ODELING There have already been some interesting modeling and observations of recombinant viruses based on the Edmonston vaccine strain of MV as these vectors have potent and selective oncolytic activity against a wide range of tumors [13–16]. To model the observations of virotherapy, we consider about modeling the cellular dynamics of the system, kinetics of multiplication of tumor cells, the amplification of virus, and the interactions between different components(e. g. virus, cell and syncytia). To model the infection of tumour cells, one approach is to simulate the interactions between tumour cells and recombinant viruses during their movements. We have presented a 3D computational model that successfully captures many of the cell behaviors that play important roles in cell aggregation and cell sorting [17]. We extend this multicellular dynamic system by introducing new factors that found to be important in virotherapy. A cell passes through different stages during its life, namely Quiescent, Interphase, Division and Apoptosis. Cell cycle operates continuously during growth, with newly formed daughter cells immediately embarking on their own path to mitosis. In our model, each virtual cell is designed as a discrete unit with the ability of dividing, aging, dying, being infected and fusing with other cells into syncytia. A cell’s life cycle and behaviors are implemented as a set of actions which are performed during each simulation time step.After a cell is created by cell division, it enters quiescent phase where its biological machinery is not fully functional. We assume these cells can not perform mitosis or be infected by viruses. Following this period a cell in interphase state becomes most active, and is able to divide with a probability PDiv that calculated as 0 PDiv = e−n ∗ PDiv
(T − TApoptosis (TDeath − TApopotosis )2 )2
0 is the base probability of cell death. The probabilwhere Pdie ity of dying is increasing after Apoptosis state and up to 1.0 when the cell’s age reaches TDeath (24 h in our simulation). A dead cell will be removed from the system, and if it was infected, the infectious viruses can be released into surrounding environment by a possibility α, whereas by probability (1 − α) die with their host cell. The virus in this model is designed as a smaller particle with the ability of randomly floating, dividing inside of cell and infecting a uninfected cell. When referring to cells infected by infectious viruses, the term multiplicity of infection (MOI) is the ratio of infectious agents (e.g. virus) to infection targets (e.g. cell). The actual number of viruses that will enter any given cell can be regarded as a statistical process: some cells may absorb more than one virus particle while others may not absorb any. The probability that a cell will absorb n virus particles when inoculated with an MOI of m can be calculated for a given population using a Poisson distribution.
P(n) = α.
mn .e−m n!
(3)
where m is MOI, n is the number of infectious agents that enter the infection target, al pha is some scale and P(n) is the probability that an infection target (a cell) will get infected by n infectious agents. This relationship will be affected by the infectivity of the virus in different situations, such as the type of cells. In our simulation, we test the range of MOI from 1 to 8 in order to generate different treatment results. In principle, an infected cell or syncytium may transfer the virus to an neighboring uninfected cell, which by certain probability λ becomes a single infected cell, whereas by
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under certain conditions. Table 1: Font sizes and styles
(a)
Parameter
Range tested
Not cured
Oscillation
Cured
0 Pdiv
0.001-0.01
0.0031
0.023
0.0026
0 Pdie
0.0001-0.0005
0.01
0.0015
0.0011
α
0.01-0.1
0.052
0.03
0.038
λ
0.035-0.1
0.05
0.003
0.035
MOI
1-8
2
3
4
III. V ISUALIZATION AND R ESULT
(b)
(c)
Fig. 2: Three representative examples of therapy with MV-NIS are shown. In (a), is an example of a tumor that initially responds and then regrows while in (b), the tumor is eradication after, and in (c) treated tumor that exhibit oscillations in size as a function of time.
probability (1 − λ ) fuses with the infected cell to form a syncytium or fuses to the already existing syncytium. We assume a syncytia can not be broken apart, and the invasion viruses inside of it can duplicate and be released into environment
The simulation environment is presented as a 500 × 500 × 500 ηm3 cubic space which contains randomly mixed tumor cells and viruses with the ratio of 1 : 10. Each cell has a radius of 6ηm and is initialized with a randomly assigned age between 0 to 24 h. Our mathematical model has accounted for three populations: uninfected tumor cells, virus-infected tumor cells (single or incorporated into syncytia), and free viruses. We assume that a tumor was considered cured if the total population was reduced to less than one cell. Three types of virotherapy outcome were exhibited: tumor eradication, therapeutic failure or oscillations in tumor size. Numerous groups of simulations were performed with our model in order to identify which of its components are most critical for this system and their best combinations for successfully simulating the different outcomes. During parametric studies, we found a promising range for each parameter as well as the optimal value that produced simulation results best matching the three types of outcomes (see Table 1). During each simulation the size distribution of the the total tumor cells, uninfected cells, infected cells and cells incorporated in syncytium are saved, and we averaged several best simulations to outline the three typical preservations ranging from tumor eradication to oscillatory behavior (see Fig 2). We found that tumor eradication occurred mostly with a small λ which can lead to high efficiency of syncytium formation. In addition, another feature that accompanies with the tumor eradication is the population of uninfected cells drop faster than the cells incorporated in syncytia. This is compatible with the findings by D Dingli et al.. We also saved the state of the simulation system at regular intervals to generate animations of the virotherapy process, from which we can clearly visualize the dynamic interactions between the tumor cell and virus (see Fig 3).
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cells proliferation rate which is controlled directly by the dividing probability in our model and the infection probability. In the future, we aim to develop a multicellular engine that can be used to facilitate understanding experimental observations, exploring alternative therapeutic scenarios, predicting experiments result and optimizing therapy. (a)
R EFERENCES
(b)
(c)
Fig. 3: Three representative examples: (a) Not cured, (b) Cured; (c) Oscillation. Red : Uninfected cells; Blue: Discrete infected cells; Yellow: Syncytium
IV. C ONCLUSION Virotherapy using replication-competent viruses is an exciting approach for cancer treatment since many viruses preferentially infect and destroy tumor cells. Visualization of interactions between tumor cells and viruses at cellular level by using computational models can greatly facilitate understanding the virotherapy process. In this paper, a 2D computational model was created to simulate the interactions between tumor cells and recombinant viruses injected. This model is driven by the population dynamics of tumour cells and viruses. We demonstrated the tumour growth behavior and the interactions between tumor cells and viruses as dynamics simulation progress, and also presented the outcomes in quantitative approaches fitting the experimental observations. Our simulations successfully captured therapy outcomes including tumor eradication, oscillatory and therapy failure. During the parameters modifications, we validated this computational model by fitting with experimental data. It is clear that tumor virotherapy is a highly non-linear process, and very sensitive to many factors such as the tumor
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