A mathematical model of the impact of infused targeted cytotoxic agents on brain tumours: implications for detection, design and delivery - PubMed (original) (raw)

A mathematical model of the impact of infused targeted cytotoxic agents on brain tumours: implications for detection, design and delivery

Lawrence M Wein et al. Cell Prolif. 2002 Dec.

Abstract

Motivated by the recent development of highly specific agents for brain tumours, we develop a mathematical model of the spatio-temporal dynamics of a brain tumour that receives an infusion of a highly specific cytotoxic agent (e.g. IL-4-PE, a cytotoxin comprised of IL-4 and a mutated form of Pseudomonas exotoxin). We derive an approximate but accurate mathematical formula for the tumour cure probability in terms of the tumour characteristics (size at time of detection, proliferation rate, diffusion coefficient), drug design (killing rate, loss rate and convection constants for tumour and tissue), and drug delivery (infusion rate, infusion duration). Our results suggest that high specificity is necessary but not sufficient to cure malignant gliomas; a nondispersed spatial profile of pretreatment tumour cells and/or good drug penetration are also required. The most important levers to improve tumour cure appear to be earlier detection, higher infusion rate, lower drug clearance rate and better convection into tumour, but not tissue. In contrast, the tumour cure probability is less sensitive to a longer infusion duration and enhancements in drug potency and drug specificity.

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Figures

Figure 1

Figure 1

The spatial profiles of (a) the initial tumour cell density, (b) the steady‐state drug concentration, (c) the probability of tumour cell survival, and (d) the final tumour cell density.

Figure 2

Figure 2

The spatial profiles for the initial tumour cell densityfor the three lower grade tumours in Burgess et al. (1997 ): (a) the high proliferation, and (b) the high diffusion and low grade tumours.

Figure 3

Figure 3

The impact of time of detection on (a) TCP and (b) the detectable tumour radius.

Figure 4

Figure 4

TCP versus drug design parameters: (a) drug potency, (b) drug specificity, (c) drug penetration into tumour, (d) drug penetration into normal brain cells, and (e) loss rate.

Figure 5

Figure 5

TCP versus drug delivery parameters: (a) infusion rate for a fixed infusion volume, and (b) time duration of infusion.

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