Macrophage-based anti-cancer therapy: modelling different modes of tumour targeting

S.D. Webb, M.R. Owen, H.M. Byrne, C. Murdoch, C.E. Lewis

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

Tumour hypoxia is associated with poor drug delivery and low rates of cell proliferation, factors that limit the efficacy of therapies that target proliferating cells. Since macrophages localise within hypoxic regions, a promising way to target hypoxic tumour cells involves engineering macrophages to express therapeutic genes under hypoxia. In this paper we develop mathematical models to compare the responses of avascular tumour spheroids to two modes of action: either the macrophages deliver an enzyme that activates an externally applied prodrug (bystander model), or they deliver cytotoxic factors directly (local model). The models we develop comprise partial differential equations for a multiphase mixture of tumour cells, macrophages and extracellular fluid, coupled to a moving boundary representing the spheroid surface. Chemical constituents, such as oxygen and drugs, diffuse within the multiphase mixture. Simulations of both models show the spheroid evolving to an equilibrium or to a travelling wave (multiple stable solutions are also possible). We uncover the parameter dependence of the wave speed and steady-state tumour size, and bifurcations between these solution forms. For some parameter sets, adding extra macrophages has a counterintuitive deleterious effect, triggering a bifurcation from bounded to unbounded tumour growth. While these features are common to the bystander and local models, the crucial difference is where cell death occurs. The bystander model is comparable to traditional chemotherapy, with poor targeting of hypoxic tumour cells; however, the local mode of action is more selective for hypoxic regions. We conclude that effective targeting of hypoxic tumour cells may require the use of drugs with limited mobility or whose action does not depend on cell proliferation.
LanguageEnglish
Pages1747-1776
Number of pages29
JournalBulletin of Mathematical Biology
Volume69
Issue number5
DOIs
Publication statusPublished - Jul 2007

Fingerprint

Macrophage
Macrophages
tumor
targeting
Therapy
Tumors
Tumor
cancer
Cancer
macrophages
therapeutics
neoplasms
Modeling
Cell
modeling
Neoplasms
drugs
Hypoxia
hypoxia
mechanism of action

Keywords

  • bifurcation
  • bystander effect
  • cancer
  • gene therapy
  • hypoxia
  • macrophage
  • parameter continuation

Cite this

Webb, S.D. ; Owen, M.R. ; Byrne, H.M. ; Murdoch, C. ; Lewis, C.E. / Macrophage-based anti-cancer therapy: modelling different modes of tumour targeting. In: Bulletin of Mathematical Biology. 2007 ; Vol. 69, No. 5. pp. 1747-1776.
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Macrophage-based anti-cancer therapy: modelling different modes of tumour targeting. / Webb, S.D.; Owen, M.R.; Byrne, H.M.; Murdoch, C.; Lewis, C.E.

In: Bulletin of Mathematical Biology, Vol. 69, No. 5, 07.2007, p. 1747-1776.

Research output: Contribution to journalArticle

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