Macrophage-tumour interactions: In vivo dynamics

Abstract

Abstract. Experimentalists are developing new therapies that exploit the tendency of macrophages, a type of white blood cell, to localise within solid tumours. The therapy studied here involves engineering macrophages to produce chemicals that kill tumour cells. Accordingly, a simple mathematical model is developed that describes interactions between normal cells, tumour cells and infiltrating macrophages. Numerical and analytical techniques show how the ability of the engineered macrophages to eliminate the tumour changes as model parameters vary. The key parameters are m * , the concentration of engineered macrophages injected into the vasculature, and k 1 , the rate at which they lyse tumour cells. As k 1 or m * increases, the average tumour burden decreases although the tumour is never completely eliminated by the macrophages. Also, the stable solutions are oscillatory when k 1 and m * increase through well-defined bifurcation values. The physical implications of our results and directions for future research are also discussed.

"Bifurcation Analysis and Optimal Control of the Tumor Macrophage Interactions"

“…They verified that the proportion of macrophages in tumors increases with the chemotactic activity of the mutant cell line. Byrne, et al [11] proposed a mathematical model that describes the interactions between normal cells, tumor cells and infiltrating macrophages, to evaluate the ability of the engineered macrophages to eliminate the tumor changes as model parameters vary Owen, et al [12] investigated the role of chemotaxis, chemokine production and the efficacy of macrophages as vehicles for drug delivery to hypoxic tumor sites.…”

Addressing current challenges in cancer immunotherapy with mathematical and computational modelling

“…s Models with a relatively small number of equations can be analysed in this way and have consistently shown that knowledge of system parameters can help lead to tumour classification for treatment via bifurcation and stability analysis (e.g. [20][21][22][23]). Identification of parameters where thresholds exist with respect to system response to therapy can aid in the identification of effective therapies.…”

Nonlinear dynamics in tumor-immune system interaction models with delays

“…In order to simulate the host's own immune response to destroy and eliminate tumor cells, various types of mathematical models have been proposed, see for example Adam and Bellomo [3], Arciero et al [8], Byrne et al [24], de Pillis et al [35], Dritschel et al [43], Frascoli et al [52], Hu and Jang [64], Kirschner and Panetta [70], Kuznetsov et al [74], Lejeune et al [78], Nani and Freedman [92], Nikolopoulou et al [93], Owen and Sherratt [94], Robertson-Tessi et al [100], Stepanova [109], and the references cited therein. We refer to reviews by Anderson and Maini [7], Cristini et al [31], dePillis et al [34], Eftimie et al [47], Freedman [53], Friedman [54], Konstorum et al [72], Mahlbacher et al [84], Szymańska et al [110], Wilkie [120] and the references cited therein on modeling tumor-immune system interactions and tumor growth, proceedings of d'Onofrio et al [41] and Figure 1.…”