The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth
Abstract
Mathematical models of tumor-immune interactions provide an analytic framework in which to address specific questions about tumor-immune dynamics. We present a new mathematical model that describes tumor-immune interactions, focusing on the role of natural killer (NK) and CD8+ T cells in tumor surveillance, with the goal of understanding the dynamics of immune-mediated tumor rejection. The model describes tumor-immune cell interactions using a system of differential equations. The functions describing tumor-immune growth, response, and interaction rates, as well as associated variables, are developed using a least-squares method combined with a numerical differential equations solver. Parameter estimates and model validations use data from published mouse and human studies. Specifically, CD8+ T-tumor and NK-tumor lysis data from chromium release assays as well as in vivo tumor growth data are used. A variable sensitivity analysis is done on the model. The new functional forms developed show that there is a clear distinction between the dynamics of NK and CD8+ T cells. Simulations of tumor growth using different levels of immune stimulating ligands, effector cells, and tumor challenge are able to reproduce data from the published studies. A sensitivity analysis reveals that the variable to which the model is most sensitive is patient specific, and can be measured with a chromium release assay. The variable sensitivity analysis suggests that the model can predict which patients may positively respond to treatment. Computer simulations highlight the importance of CD8+ T-cell activation in cancer therapy.
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Cites
Cancer Regression and Autoimmunity in Patients After Clonal Repopulation with Antitumor Lymphocytes
Dudley, M. E., Wunderlich, J. R., Robbins, P. F., Yang, J. C., Hwu, P., Schwartzentruber, D. J., Topalian, S. L., Sherry, R., Restifo, N. P., Hubicki, A. M., et al. (2002) · Science · doi:10.1126/science.1076514 · Cited by 2,823
Rae1 and H60 ligands of the NKG2D receptor stimulate tumour immunity
Diefenbach, A., Jensen, E. R., Jamieson, A. M., & Raulet, D. H. (2001) · Nature · doi:10.1038/35093109 · Cited by 1,083
Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis
Kuznetsov, V. A., Makalkin, I. A., Taylor, M. A., & Perelson, A. S. (1994) · Bulletin of Mathematical Biology · doi:10.1007/bf02460644 · Cited by 1,061
Modeling immunotherapy of the tumor - immune interaction
Kirschner, D., & Panetta, J. C. (1998) · Journal of Mathematical Biology · doi:10.1007/s002850050127 · Cited by 915
Dynamics of T Lymphocyte Responses: Intermediates, Effectors, and Memory Cells
Lanzavecchia, A., & Sallusto, F. (2000) · Science · doi:10.1126/science.290.5489.92 · Cited by 796
Essential Mathematical Biology
Britton, N. F. (2003) · Springer Undergraduate Mathematics Series · doi:10.1007/978-1-4471-0049-2 · Cited by 506
A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach
De Pillis, L. G., & Radunskaya, A. (2001) · Computational and Mathematical Methods in Medicine · doi:10.1080/10273660108833067 · Cited by 425
Self-citationThe dynamics of an optimally controlled tumor model: A case study
De Pillis, L. G., & Radunskaya, A. (2003) · Mathematical and Computer Modelling · doi:10.1016/s0895-7177(03)00133-x · Cited by 413
Self-citationBellomo, N., & Preziosi, L. (2000) · Mathematical and Computer Modelling · doi:10.1016/s0895-7177(00)00143-6 · Cited by 301
Mathematical Models in Cell Biology and Cancer Chemotherapy
Eisen, M. (1979) · Lecture Notes in Biomathematics · doi:10.1007/978-3-642-93126-0 · Cited by 197
Cited by
The mathematics of cancer: integrating quantitative models
Altrock, P. M., Liu, L. L., & Michor, F. (2015) · Nature Reviews Cancer · doi:10.1038/nrc4029 · Cited by 685
Nonlinear modelling of cancer: bridging the gap between cells and tumours
Lowengrub, J. S., Frieboes, H. B., Jin, F., Chuang, Y.-L., Li, X., Macklin, P., Wise, S. M., & Cristini, V (2010) · Nonlinearity · doi:10.1088/0951-7715/23/1/r01 · Cited by 553
Zhang, X., Trame, M., Lesko, L., & Schmidt, S. (2015) · CPT: Pharmacometrics & Systems Pharmacology · doi:10.1002/psp4.6 · Cited by 467
ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES
BELLOMO, N., LI, N. K., & MAINI, P. K. (2008) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s0218202508002796 · Cited by 420
Baleanu, D., Jajarmi, A., Sajjadi, S. S., & Mozyrska, D. (2019) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.5096159 · Cited by 357
Metadata
- Authors
- de Pillis, L. G., Radunskaya, A. E., & Wiseman, C. L.
- Venue
- Cancer Research
- Published
- 2005-09-01
- Volume
- 65
- Issue
- 17
- Pages
- 7950-7958
- ISSN
- 0008-5472 (ISSN-L)
- 1538-7445
- OpenAlex
- W2169169493
- Cited by
- 649
- References
- 17
- FWCI
- 11.49
- Type
- journal article
- Language
- en
- Open access
- closed
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- de Pillis, L. G., Radunskaya, A. E., & Wiseman, C. L. (2005). A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth. Cancer Research. https://doi.org/10.1158/0008-5472.can-05-0564
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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