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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: There is no unifying theoretical framework in mathematical modeling of carcinogenesis that would account for parametric heterogeneity.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.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

Eβ (t) versus time for the cases presented in Fig. 2. The curves from top to bottom correspond to panels (a)–(d) in Fig. 2.
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Figure 3: Eβ (t) versus time for the cases presented in Fig. 2. The curves from top to bottom correspond to panels (a)–(d) in Fig. 2.

Mentions: The change of the mean parameter value for the cases presented in Fig. 2 is shown in Fig. 3. It can be seen that higher rate of change corresponds to greater values of the initial variance; in addition, in none of the analyzed cases Eβ (t) reaches the final value η, because the speed of movement is determined by two simultaneously acting factors: the characteristics of the mgf and the equation for the auxiliary variable q(t) for which dq(t)/dt ≈ 0 starting from some time t.


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

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

Eβ (t) versus time for the cases presented in Fig. 2. The curves from top to bottom correspond to panels (a)–(d) in Fig. 2.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: Eβ (t) versus time for the cases presented in Fig. 2. The curves from top to bottom correspond to panels (a)–(d) in Fig. 2.
Mentions: The change of the mean parameter value for the cases presented in Fig. 2 is shown in Fig. 3. It can be seen that higher rate of change corresponds to greater values of the initial variance; in addition, in none of the analyzed cases Eβ (t) reaches the final value η, because the speed of movement is determined by two simultaneously acting factors: the characteristics of the mgf and the equation for the auxiliary variable q(t) for which dq(t)/dt ≈ 0 starting from some time t.

Bottom Line: There is no unifying theoretical framework in mathematical modeling of carcinogenesis that would account for parametric heterogeneity.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.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