Fluctuations induced extinction and stochastic resonance effect in a model of tumor growth with periodic treatment

Abstract We investigate a stochastic model of tumor growth derived from the catalytic Michaelis–Menten reaction with positional and environmental fluctuations under subthreshold periodic treatment. Firstly, the influences of environmental fluctuations on the treatable stage are analyzed numerically. Applying the standard theory of stochastic resonance derived from the two-state approach, we derive the signal-to-noise ratio (SNR) analytically, which is used to measure the stochastic resonance phenomenon. It is found that the weak environmental fluctuations could induce the extinction of tumor cells in the subthreshold periodic treatment. The positional stability is better in favor of the treatment of the tumor cells. Besides, the appropriate and feasible treatment intensity and the treatment cycle should be highlighted considered in the treatment of tumor cells.

[1]  Jacek Waniewski,et al.  Modelling Tumour-Immunity Interactions With Different Stimulation Functions , 2003 .

[2]  S. Rosenberg,et al.  A new approach to the adoptive immunotherapy of cancer with tumor-infiltrating lymphocytes. , 1986, Science.

[3]  N. Goel,et al.  Stochastic models in biology , 1975 .

[4]  B Spagnolo,et al.  Noise-enhanced stability of periodically driven metastable states. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  W Horsthemke,et al.  Bistability in fluctuating environments. Implications in tumor immunology. , 1979, Bulletin of mathematical biology.

[6]  Bartłomiej Dybiec,et al.  Influence of the barrier shape on resonant activation. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Wiesenfeld,et al.  Theory of stochastic resonance. , 1989, Physical review. A, General physics.

[8]  René Lefever,et al.  Stability problems in cancer growth and nucleation , 1980 .

[9]  A. Perelson,et al.  Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. , 1994, Bulletin of mathematical biology.

[10]  Mantegna,et al.  Noise enhanced stability in an unstable system. , 1996, Physical review letters.

[11]  B. Ai,et al.  Stochastic resonance in a stochastic bistable system , 2007 .

[12]  Zhenhui He,et al.  Pure multiplicative stochastic resonance of a theoretical anti-tumor model with seasonal modulability. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Mantegna,et al.  Experimental investigation of resonant activation , 2000, Physical review letters.

[14]  Bernardo Spagnolo,et al.  Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Bernardo Spagnolo,et al.  Noise-enhanced stability in fluctuating metastable states. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  René Lefever,et al.  Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology , 2007 .

[17]  L. D. Pillis,et al.  A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth , 2005 .

[18]  B. Ai,et al.  Mean First-Passage Time in a Bistable Kinetic Model with Stochastic Potentials , 2006 .

[19]  Steffen Trimper,et al.  Stochastic model for tumor growth with immunization. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Properties of resonant activation phenomena , 1997, physics/9712036.

[21]  Cancer immunoediting from immune surveillance to immune escape , 2007 .

[22]  H. Risken.  Fokker-Planck Equation , 1984 .

[23]  P. Allavena,et al.  Tumour-associated macrophages as a prototypic type II polarised phagocyte population: role in tumour progression. , 2004, European journal of cancer.

[24]  Silvano Sozzani,et al.  The chemokine system in diverse forms of macrophage activation and polarization. , 2004, Trends in immunology.

[25]  R. Lefever,et al.  A kinetic approach to the immunology of cancer: stationary states properties of effector-target cell reactions. , 1978, Journal of theoretical biology.

[26]  S. N. Yu,et al.  Effects of random potential on transport. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Bernardo Spagnolo,et al.  Suppression of timing errors in short overdamped josephson junctions. , 2004, Physical review letters.

[28]  B. Spagnolo,et al.  Monitoring noise-resonant effects in cancer growth influenced by external fluctuations and periodic treatment , 2007, 0710.1317.

[29]  R. Schreiber,et al.  Cancer immunoediting: from immunosurveillance to tumor escape , 2002, Nature Immunology.

[30]  I. Derényi,et al.  Intrawell relaxation of overdamped Brownian particles. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[31]  A. Ochab-Marcinek,et al.  Population growth and control in stochastic models of cancer development , 2004, q-bio/0403041.

[32]  P. Hänggi,et al.  Reaction rates when barriers fluctuate: A singular perturbation approach 1 Dedicated to the memory o , 1998 .

[33]  D. Kirschner,et al.  Modeling immunotherapy of the tumor – immune interaction , 1998, Journal of mathematical biology.

[34]  S. Boccaletti,et al.  Signatures of noise-enhanced stability in metastable states. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Gerard C Blobe,et al.  Role of transforming growth factor Beta in human cancer. , 2005, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[36]  B. Ai,et al.  Correlated noise in a logistic growth model. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Y. Zhuo,et al.  Rocking ratchets with stochastic potentials , 2002 .