Spatiotemporal fluctuation-induced transition in a tumor model with immune surveillance

Zhong, Wei-Rong; Shao, Yuanzhi; He, Zhenhui

doi:10.1103/physreve.74.011916

Cited by 39 publications

(27 citation statements)

References 28 publications

(29 reference statements)

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“…In (1), the variable x denotes the tumour population density with an arbitrary unit (au); the parameter r 0 defines the growth rate of tumour cells and K corresponds to the carrying capacity; the term g(x, t) describes some influences on the growth of a tumour, such as immunity, therapy or even fluctuations of patient's body temperature and emotion influenced by surrounding (Zhong et al 2006b(Zhong et al , 2008. In this paper, we consider immunity as an intervention by choosing Bx 2 /(ε 2 + x 2 ) instead of Bx/(ε + x) as derived in Appendix A for the expression of immune intervention.…”

Section: Models and Methodsmentioning

confidence: 99%

“…In order to explore different combinations of the duty-cycle D i of the two therapeutic inter- (Zhong et al 2006a(Zhong et al , 2006b c Values adopted in Byrne (2003) ventions h A (t) and h B (t) against the phase-shift Φ of two interventions, we investigated in every occasion the anti-tumour system for an evolutional time of 10 periods with arbitrary unit (au), and obtained the time-averaged tumour population density x to evaluate the therapeutic effectiveness of the anti-tumour system. According to our computation, the evolutional time of 10 periods (au) allows the anti-tumour system under investigation to attain a steady state.…”

Section: Of Two Therapies a Positive φ Indicates That Intervention Hmentioning

confidence: 99%

See 1 more Smart Citation

In Silico Synergism and Antagonism of an Anti-tumour System Intervened by Coupling Immunotherapy and Chemotherapy: A Mathematical Modelling Approach

Zhong

Wang

et al. 2011

Bull Math Biol

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Based on the logistic growth law for a tumour derived from enzymatic dynamics, we address from a physical point of view the phenomena of synergism, additivity and antagonism in an avascular anti-tumour system regulated externally by dual coupling periodic interventions, and propose a theoretical model to simulate the combinational administration of chemotherapy and immunotherapy. The in silico results of our modelling approach reveal that the tumour population density of an anti-tumour system, which is subject to the combinational attack of chemotherapeutical as well as immune intervention, depends on four parameters as below: the therapy intensities D, the coupling intensity I, the coupling coherence R and the phase-shifts Φ between two combinational interventions. In relation to the intensity and nature (synergism, additivity and antagonism) of coupling as well as the phase-shift between two therapeutic interventions, the administration sequence of two periodic interventions makes a difference to the curative efficacy of an anti-tumour system. The isobologram established from our model maintains a considerable consistency with that of the well-established Loewe Additivity model (Tallarida, Pharmacology 319(1):1-7, 2006). Our study discloses the general dynamic feature of an anti-tumour system regulated by two periodic coupling interventions, and the results may serve as a supplement to previous models of drug administration in combination and provide a type of heuristic approach for preclinical pharmacokinetic investigation.

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Section: Models and Methodsmentioning

confidence: 99%

Section: Of Two Therapies a Positive φ Indicates That Intervention Hmentioning

confidence: 99%

In Silico Synergism and Antagonism of an Anti-tumour System Intervened by Coupling Immunotherapy and Chemotherapy: A Mathematical Modelling Approach

Zhong

Wang

et al. 2011

Bull Math Biol

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“…The term S n is related to the proliferation and death of tumor cells and is formulated by the logistic growth function [60,[62][63][64][65]:…”

Section: Mathematical Modelmentioning

confidence: 99%

Tumor proliferation and diffusion on percolation clusters

et al. 2016

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We study in silico the influence of host tissue inhomogeneity on tumor cell proliferation and diffusion by simulating the mobility of a tumor on percolation clusters with different homogeneities of surrounding tissues. The proliferation and diffusion of a tumor in an inhomogeneous tissue could be characterized in the framework of the percolation theory, which displays similar thresholds (0.54, 0.44, and 0.37, respectively) for tumor proliferation and diffusion in three kinds of lattices with 4, 6, and 8 connecting near neighbors. Our study reveals the existence of a critical transition concerning the survival and diffusion of tumor cells with leaping metastatic diffusion movement in the host tissues. Tumor cells usually flow in the direction of greater pressure variation during their diffusing and infiltrating to a further location in the host tissue. Some specific sites suitable for tumor invasion were observed on the percolation cluster and around these specific sites a tumor can develop into scattered tumors linked by some advantage tunnels that facilitate tumor invasion. We also investigate the manner that tissue inhomogeneity surrounding a tumor may influence the velocity of tumor diffusion and invasion. Our simulation suggested that invasion of a tumor is controlled by the homogeneity of the tumor microenvironment, which is basically consistent with the experimental report by Riching et al. as well as our clinical observation of medical imaging. Both simulation and clinical observation proved that tumor diffusion and invasion into the surrounding host tissue is positively correlated with the homogeneity of the tissue.

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“…to explain periodic recurrences of the earth's ice has attracted much attention [15][16][17][18][19][20]. There are several mathematical functions for describing tumor growth, such as the logistic model [21], Eden model [22] and Gompertzian growth model [23].…”

Section: Introductionmentioning

confidence: 99%

Delay-induced state transition and resonance in periodically driven tumor model with immune surveillance

et al. 2014

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Abstract:The phenomenon of stochastic resonance (SR) in a tumor growth model under the presence of immune surveillance is investigated. Time delay and cross-correlation between multiplicative and additive noises are considered in the system. The signal-to-noise ratio (SNR) is calculated when periodic signal is introduced multiplicatively. Our results show that: (i) the time delay can accelerate the transition from the state of stable tumor to that of extinction, however the correlation between two noises can accelerate the transition from the state of extinction to that of stable tumor; (ii) the time delay and correlation between two noises can lead to a transition between SR and double SR in the curve of SNR as a function of additive noise intensity, however for the curve of SNR as a function of multiplicative noise intensity, the time delay can cause the SR phenomenon to disappear, and the cross-correlation between two noises can lead to a transition from SR to stochastic reverse-resonance. Finally, we compare the SR phenomenon for the multiplicative periodic signal with that for additive periodic signal in the tumor growth model with immune surveillance. PACS

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Spatiotemporal fluctuation-induced transition in a tumor model with immune surveillance

Cited by 39 publications

References 28 publications

In Silico Synergism and Antagonism of an Anti-tumour System Intervened by Coupling Immunotherapy and Chemotherapy: A Mathematical Modelling Approach

In Silico Synergism and Antagonism of an Anti-tumour System Intervened by Coupling Immunotherapy and Chemotherapy: A Mathematical Modelling Approach

Tumor proliferation and diffusion on percolation clusters

Delay-induced state transition and resonance in periodically driven tumor model with immune surveillance

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