×

Ordinary differential equation models for adoptive immunotherapy. (English) Zbl 1394.92066

Summary: Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here, we explore four previous approaches that have used ordinary differential equations to model this type of therapy, compare their properties, and modify the models to address their deficiencies. Although the four models treat the workings of the immune system in slightly different ways, they all predict that adoptive immunotherapy can be successful to move a patient from the large tumor fixed point to an equilibrium with little or no tumor.

MSC:

92C50 Medical applications (general)
34D20 Stability of solutions to ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Pillis, L; Radunskaya, AE, Mixed immunotherapy and chemotherapy of tumors: modeling, appplications and biological interpretations, J Theor Biol, 238, 841-862, (2006) · Zbl 1445.92135 · doi:10.1016/j.jtbi.2005.06.037
[2] de Pillis L, Radunskaya AE, Wiseman CL (2005) A validated mathematical model of cell-mediated immune response to tumor growth. Cancer Res 65:7950-7958
[3] Dong, Y; Miyazaki, R; Takeuchi, Y, Mathematical modeling on helper T cells in a tumor immune system, Discrete Continuous Dyn Syst B, 19, 55-71, (2014) · Zbl 1309.92043 · doi:10.3934/dcdsb.2014.19.55
[4] Eshhar, Z; Waks, T; Gross, G; Schindler, DG, Specific activation and targeting of cytotoxic lymphocytes through chimeric single chains consisting of antibody-binding domains and the \(γ \) or \(ζ \) subunits of the immunoglobulin and T-cell receptors, Proc Natl Acad Sci, 90, 720-724, (1993) · doi:10.1073/pnas.90.2.720
[5] Grupp, SA; etal., Chimeric antigen receptor-modified T cells for acute lymphoid leukemia, N Engl J Med, 368, 1509-1518, (2013) · doi:10.1056/NEJMoa1215134
[6] Janeway CA, Travers P, Walport M, Shlomicki MJ (2001) Immunobiology: the immune system in health and disease. Garland Publishing Company, New York
[7] Kirschner, D; Panetta, JC, Modeling immunotherapy of the tumor-immune interaction, J Math Biol, 37, 235-252, (1998) · Zbl 0902.92012 · doi:10.1007/s002850050127
[8] Kuznetsov VA, Makalkin IA, Taylor MA, Perleson AS (1994) Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull Math Biol 56:295-321 · Zbl 0789.92019
[9] Maude, SL; etal., Chimeric antigen receptor T cells for sustained remission in leukemia, N Engl J Med, 371, 1507-1517, (2014) · doi:10.1056/NEJMoa1407222
[10] Mohri, H; etal., Increased turnover of \(T\) lymphocytes in HIV-1 infection and its reduction by anti-viral therapy, J Exp Med, 194, 1277-1287, (2001) · doi:10.1084/jem.194.9.1277
[11] Moore, HN; Li, NK, A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction, J Theor Biol, 227, 513-523, (2004) · Zbl 1439.92068 · doi:10.1016/j.jtbi.2003.11.024
[12] Park, TS; Rosenberg, SA; Morgan, RA, Treating cancer with genetically engineered T cells, Trends Biotechnol, 29, 550-557, (2011) · doi:10.1016/j.tibtech.2011.04.009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.