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Mathematical modeling of tumor therapy with oncolytic viruses: effects of parametric heterogeneity on cell dynamics.

Karev GP, Novozhilov AS, Koonin EV - Biol. Direct (2006)

Bottom Line: We also demonstrate that, within the applied modeling framework, to overcome the adverse effect of tumor cell heterogeneity on the outcome of cancer treatment, a heterogeneous population of an oncolytic virus must be used.It should be straightforward to apply these techniques to mathematical modeling of other types of anticancer therapy.Leonid Hanin (nominated by Arcady Mushegian), Natalia Komarova (nominated by Orly Alter), and David Krakauer.

View Article: PubMed Central - HTML - PubMed

Affiliation: National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD 20894, USA. karev@ncbi.nlm.nih.gov

ABSTRACT

Background: One of the mechanisms that ensure cancer robustness is tumor heterogeneity, and its effects on tumor cells dynamics have to be taken into account when studying cancer progression. There is no unifying theoretical framework in mathematical modeling of carcinogenesis that would account for parametric heterogeneity.

Results: Here we formulate a modeling approach that naturally takes stock of inherent cancer cell heterogeneity and illustrate it with a model of interaction between a tumor and an oncolytic virus. We show that several phenomena that are absent in homogeneous models, such as cancer recurrence, tumor dormancy, and others, appear in heterogeneous setting. We also demonstrate that, within the applied modeling framework, to overcome the adverse effect of tumor cell heterogeneity on the outcome of cancer treatment, a heterogeneous population of an oncolytic virus must be used. Heterogeneity in parameters of the model, such as tumor cell susceptibility to virus infection and the ability of an oncolytic virus to infect tumor cells, can lead to complex, irregular evolution of the tumor. Thus, quasi-chaotic behavior of the tumor-virus system can be caused not only by random perturbations but also by the heterogeneity of the tumor and the virus.

Conclusion: The modeling approach described here reveals the importance of tumor cell and virus heterogeneity for the outcome of cancer therapy. It should be straightforward to apply these techniques to mathematical modeling of other types of anticancer therapy.

Reviewers: Leonid Hanin (nominated by Arcady Mushegian), Natalia Komarova (nominated by Orly Alter), and David Krakauer.

No MeSH data available.


Related in: MedlinePlus

Solutions of system (5)–(6) with gamma distributed parameter β on [1.5, ∞). Uninfected cells, X(t), infected cells, Y(t), and the total tumor load, X(t) + Y(t), are shown in blue, green and black, respectively. The initial conditions X(0) = 0.5, Y(0) = 0.1, parameter values γ = 1, δ = 2. The initial mean of distribution Eβ (0) = 2.5, the initial variances 0.06 (a), 0.1(b), 0.3(c), 0.4(d).
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Figure 2: Solutions of system (5)–(6) with gamma distributed parameter β on [1.5, ∞). Uninfected cells, X(t), infected cells, Y(t), and the total tumor load, X(t) + Y(t), are shown in blue, green and black, respectively. The initial conditions X(0) = 0.5, Y(0) = 0.1, parameter values γ = 1, δ = 2. The initial mean of distribution Eβ (0) = 2.5, the initial variances 0.06 (a), 0.1(b), 0.3(c), 0.4(d).

Mentions: Results of several numerical simulations of system (5)–(6) are shown in Fig. 2. The parameter values were chosen such that we start in domain VIII (Fig. 1) (eradication of the tumor), cross domain VII (bistable situation), and end up in domain I (no effect of virus therapy). The solutions shown in Fig. 2 reflect the fact that the degree of heterogeneity plays an important role in the model dynamics. The parameter values and initial conditions are the same for all four simulations; the difference comes from different initial variances of β ; the greater the initial variance the faster we reach the unfavorable domain I. Conversely, the initial variance of the distribution can be small enough such that the time during which the size of the tumor remains negligible (X + Y is close to zero) is comparable with the life-time of a patient; this emphasizes that we need to know not only the final state of Eβ (t) but also its transient behavior.


Mathematical modeling of tumor therapy with oncolytic viruses: effects of parametric heterogeneity on cell dynamics.

Karev GP, Novozhilov AS, Koonin EV - Biol. Direct (2006)

Solutions of system (5)–(6) with gamma distributed parameter β on [1.5, ∞). Uninfected cells, X(t), infected cells, Y(t), and the total tumor load, X(t) + Y(t), are shown in blue, green and black, respectively. The initial conditions X(0) = 0.5, Y(0) = 0.1, parameter values γ = 1, δ = 2. The initial mean of distribution Eβ (0) = 2.5, the initial variances 0.06 (a), 0.1(b), 0.3(c), 0.4(d).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC1622743&req=5

Figure 2: Solutions of system (5)–(6) with gamma distributed parameter β on [1.5, ∞). Uninfected cells, X(t), infected cells, Y(t), and the total tumor load, X(t) + Y(t), are shown in blue, green and black, respectively. The initial conditions X(0) = 0.5, Y(0) = 0.1, parameter values γ = 1, δ = 2. The initial mean of distribution Eβ (0) = 2.5, the initial variances 0.06 (a), 0.1(b), 0.3(c), 0.4(d).
Mentions: Results of several numerical simulations of system (5)–(6) are shown in Fig. 2. The parameter values were chosen such that we start in domain VIII (Fig. 1) (eradication of the tumor), cross domain VII (bistable situation), and end up in domain I (no effect of virus therapy). The solutions shown in Fig. 2 reflect the fact that the degree of heterogeneity plays an important role in the model dynamics. The parameter values and initial conditions are the same for all four simulations; the difference comes from different initial variances of β ; the greater the initial variance the faster we reach the unfavorable domain I. Conversely, the initial variance of the distribution can be small enough such that the time during which the size of the tumor remains negligible (X + Y is close to zero) is comparable with the life-time of a patient; this emphasizes that we need to know not only the final state of Eβ (t) but also its transient behavior.

Bottom Line: We also demonstrate that, within the applied modeling framework, to overcome the adverse effect of tumor cell heterogeneity on the outcome of cancer treatment, a heterogeneous population of an oncolytic virus must be used.It should be straightforward to apply these techniques to mathematical modeling of other types of anticancer therapy.Leonid Hanin (nominated by Arcady Mushegian), Natalia Komarova (nominated by Orly Alter), and David Krakauer.

View Article: PubMed Central - HTML - PubMed

Affiliation: National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD 20894, USA. karev@ncbi.nlm.nih.gov

ABSTRACT

Background: One of the mechanisms that ensure cancer robustness is tumor heterogeneity, and its effects on tumor cells dynamics have to be taken into account when studying cancer progression. There is no unifying theoretical framework in mathematical modeling of carcinogenesis that would account for parametric heterogeneity.

Results: Here we formulate a modeling approach that naturally takes stock of inherent cancer cell heterogeneity and illustrate it with a model of interaction between a tumor and an oncolytic virus. We show that several phenomena that are absent in homogeneous models, such as cancer recurrence, tumor dormancy, and others, appear in heterogeneous setting. We also demonstrate that, within the applied modeling framework, to overcome the adverse effect of tumor cell heterogeneity on the outcome of cancer treatment, a heterogeneous population of an oncolytic virus must be used. Heterogeneity in parameters of the model, such as tumor cell susceptibility to virus infection and the ability of an oncolytic virus to infect tumor cells, can lead to complex, irregular evolution of the tumor. Thus, quasi-chaotic behavior of the tumor-virus system can be caused not only by random perturbations but also by the heterogeneity of the tumor and the virus.

Conclusion: The modeling approach described here reveals the importance of tumor cell and virus heterogeneity for the outcome of cancer therapy. It should be straightforward to apply these techniques to mathematical modeling of other types of anticancer therapy.

Reviewers: Leonid Hanin (nominated by Arcady Mushegian), Natalia Komarova (nominated by Orly Alter), and David Krakauer.

No MeSH data available.


Related in: MedlinePlus