Modelling Macrophage Infiltration into Avascular Tumours

Kelly, C. E.; Leek, Russell; Byrne, Helen M.; Cox, Stephen M.; Harris, Adrian L.; Lewis, Claire E.

doi:10.1080/10273660290015242

Cited by 18 publications

(17 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The authors use a simple, spatially uniform model and assume that macrophages have been engineered to destroy cancer cells on contact. Another model, which is more relevant to the work described here, explores the role of macrophage chemotaxis and random motion on tumour size and distribution of macrophages within avascular MTS (Kelly et al, 2002). In an alternative model, Owen et al (2004) found that chemotactic sensitivity is a key determinant of macrophage infiltration and hence tumour size.…”

Section: Introductionmentioning

confidence: 95%

Macrophage-Based Anti-Cancer Therapy: Modelling Different Modes of Tumour Targeting

et al. 2007

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 95%

Macrophage-Based Anti-Cancer Therapy: Modelling Different Modes of Tumour Targeting

et al. 2007

View full text Add to dashboard Cite

show abstract

“…In general, the discretization of advection terms in advection-dominated IBVPs must be handled with caution (Finlayson, 1992;Turner and Perré, 2001;Hundsdorfer and Verwer, 2003). Standard discretization approaches are often inappropriate for this class of problem (Simpson et al, 2005;Simpson et al, 2006), yet they are commonly used in the field of mathematical biology (Pettet et al, 1996b;Byrne et al, 2000;Kelly et al, 2002;Landman et al, 2003).…”

Section: Introductionmentioning

confidence: 98%

Computational Approaches to Solving Equations Arising from Wound Healing

2008

View full text Add to dashboard Cite

In the wound healing process, the cell movement associated with chemotaxis generally outweighs the movement associated with random motion, leading to advection-dominated mathematical models of wound healing. The equations in these models must be solved with care, but often inappropriate approaches are adopted. Two one-dimensional test problems arising from advection-dominated models of wound healing are solved using four algorithms--MATLAB's inbuilt routine pdepe.m, the Numerical Algorithms Group routine d03pcf.f, and two finite volume methods. The first finite volume method is based on a first-order upwinding treatment of chemotaxis terms and the second on a flux limiting approach. The first test problem admits an analytic solution which can be used to validate the numerical results by analyzing two measures of the error for each method: the average absolute difference and a mass balance error. These criteria as well as the visual comparison between the numerical methods and the exact solution lead us to conclude that flux limiting is the best approach to solving advection-dominated wound healing problems numerically in one dimension. The second test problem is a coupled nonlinear three species model of wound healing angiogenesis. Measurement of the mass balance error for this test problem further confirms our hypothesis that flux limiting is the most appropriate method for solving advection-dominated governing equations in wound healing models. We also consider two two-dimensional test problems arising from wound healing, one that admits an analytic solution and a more complicated problem of blood vessels growth into a devascularized wound bed. The results from the two-dimensional test problems also demonstrate that the flux limiting treatment of advective terms is ideal for an advection-dominated problem.

show abstract

“…Consequently, the time derivatives and advection terms in Eqs. (4) and (5) may be neglected and a quasi-steadystate approximation made (Greenspan, 1976;Kelly et al, 2002;Ward and King, 1997). Eliminating n ¼ 1 À l À m; our dimensionless model reads…”

Section: Dimensionless Model and Simplificationmentioning

confidence: 99%

Mathematical modelling of the use of macrophages as vehicles for drug delivery to hypoxic tumour sites

Owen

Byrne

Lewis

2004

Journal of Theoretical Biology

125

View full text Add to dashboard Cite

Poor drug delivery and low rates of cell proliferation are two factors associated with hypoxia that diminish the efficacy of many chemotherapeutic drugs. Since macrophages are known to migrate specifically towards, and localize within, hypoxic tumour regions, a promising resolution to these problems involves genetically engineering macrophages to perform such anti-tumour functions as inducing cell lysis and inhibiting angiogenesis. In this paper we outline a modelling approach to characterize macrophage infiltration into early avascular solid tumours, and extensions to study the interaction of these cells with macrophages already present within the tumour. We investigate the role of chemotaxis and chemokine production, and the efficacy of macrophages as vehicles for drug delivery to hypoxic tumour sites.The model is based upon a growing avascular tumour spheroid, in which volume is filled by tumour cells, macrophages and extracellular material, and tumour cell proliferation and death is regulated by nutrient diffusion. Crucially, macrophages occupy volume, and hence contribute to the volume balance and hence the size of the tumour. We also include oxygen-dependent production of macrophage chemokines, which can lead to accumulations in the hypoxic region of the tumour. We find that the macrophage chemotactic sensitivity is a key determinant of macrophage infiltration and tumour size. Although increased infiltration should be beneficial from the point of view of macrophage-based therapies, such infiltration in fact leads to increased tumour sizes.Finally, we include terms representing the induced death of tumour cells by hypoxic engineered macrophages. We demonstrate that reductions in tumour size can be achieved, but predict that a combination of therapies would be required for complete eradication. We also highlight some counter-intuitive predictions-for example, absolute and relative measures of tumour burden lead to different conclusions about prognosis. In summary, this paper illustrates how mathematical models may be used to investigate promising macrophage-based therapies. r

show abstract

Modelling Macrophage Infiltration into Avascular Tumours

Cited by 18 publications

References 32 publications

Macrophage-Based Anti-Cancer Therapy: Modelling Different Modes of Tumour Targeting

Macrophage-Based Anti-Cancer Therapy: Modelling Different Modes of Tumour Targeting

Computational Approaches to Solving Equations Arising from Wound Healing

Mathematical modelling of the use of macrophages as vehicles for drug delivery to hypoxic tumour sites

Contact Info

Product

Resources

About