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

Abstract

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.

Drug Resistance and the Role of Combination Chemotherapy in Improving Patient Outcomes

“…The majority of current combination regimens have been developed empirically and although patterns of cross-resistance, overlapping drug toxicity, and mechanisms of action are considered when designing such regimens, formal preclinical testing has played only a minor role. A mathematical model has been devised to describe the potency of combining chemotherapy and immunotherapy; however, it remains undefined whether most combinations are effective due to additive or synergistic cytotoxicity [64]. …”

Modelling the Immune Response to Cancer: An Individual-Based Approach Accounting for the Difference in Movement Between Inactive and Activated T Cells

“…These models can be posed on a spatial domain (e.g. a grid), and a set of rules can be given to each cell with certain probabilities to achieve a more detailed description of cancerimmune competition (Chowdhury et al, 1991;Christophe et al, 2015;Hu et al, 2012;Pappalardo et al, 2008).…”

Recognition and learning in a mathematical model for immune response against cancer

“…Since µ I = 0, identities (22) can be proved as in [14] using the result established by Lemma 3.4, assumption (19), upper bound (16) on n 1 (t) and following the strategy proposed in [15].…”

“…The recent scientific literature testifies the development of several mathematical approaches to model the dynamics of immune response, in general, and tumor-immune interactions, in particular. Among others, ODEs [19,5,7,8,13,22,27,36], PDEs [11,26,28,30], integro-differential equations [2,3,4,25], agent-based or cellular automata models [12,23,28,33] and suitable developments of the formal structures pertaining to statistical mechanics [1,9,10]. Mathematical models are usually devoted to enlighten stylized facts, that can emerge from the complex interactions involved in cancer-immune competition, with the aim of achieving a deeper comprehension in the basic mechanisms that allow malignant cells to escape the body multi-layered defenses against tumors.…”