An Integrated Systems-Based Modelling Framework for Investigating the Effect of Anticancer Drugs On Solid Tumours

An integrated systems-based modelling framework for investigating the effect of anticancer drugs on solid tumours

Cong Liu, J. Krishnan, Xiao Yun Xu

Department of Chemical Engineering, Imperial College London, UK Abstract

Background. The effectiveness of clinical chemotherapy is dependent on the penetration of anticancer agents in tumour tissues and the responsiveness of tumour cells towards exposure to administered drugs. Most blood-borne anticancer drugs gain their access to tumour cells by going through a series of physical and biological processes, including convection in the tumour vasculature, extravasation across the capillary wall, penetration through the tumour interstitium and finally translocation inside tumour cells. However, these transport processes are often impaired by the abnormal tumour microenvironment (i.e. irregular tumour vasculature, elevated interstitial fluid pressure, and extracellular matrix composition), resulting in limited drug concentration available at the target site. Upon interaction with their intracellular targets, anticancer drugs induce multiple cellular signalling pathways, through which they exert therapeutic effects with apoptosis (programmed cell death) being of primary interest. The way by which cellular signalling functions is extremely complex as cellular pathways are carried out in a complex and interconnected network and usually display highly non-linear input-output relationships. Given the complexities associated with drug transport in tumour tissues and intracellular signal transduction, understanding the effect of anticancer drugs on solid tumours presents a highly challenging problem.

Methods. In this study, an integrated systems-based modelling framework is developed which is capable of (i) capturing relevant biological processes and their interconnections, and (ii) providing predictive and mechanistic insight into the effects of chemotherapeutic agents. As a first attempt, the model starts with basic descriptions of the essential elements with a focus on their integration in the system. The essential modules include drug transport, intracellular apoptosis signalling and tumour cell density dynamics.

Drug transport in tumour tissue is described by a diffusion-convection-reaction equation, with doxorubicin as the anti-cancer drug for modelling purpose. Velocity field is obtained by solving tumour blood flow, which is governed by the Navier-Stokes equations in the tumour vasculature, Starling's law for flow across the capillary wall and Darcy's law for flow in the tumour interstitium. Intracellular drug concentration serves as the stress signal triggering apoptosis pathway. Here, two types of coarse-grained intracellular apoptosis models, monostable and bistable apoptosis models, extracted from the systems biology literature are examined. Both simplified models capture key features of apoptosis- threshold effect and irreversibility. The cellular response is reflected on the tissue level in terms of tumour cell density which is described by a sharp decrease in the tumour growth rate in the logistic formulism of tumour growth. Re-distribution of tumour cell density is examined upon different pulse drug injections. The integrated systems-based model is applied to a simplified tumour cord geometry.

Results. Simulation results show that insufficient drug transport in tumour interstitium is a major limiting factor in inducing drug effect. Despite qualitatively different dynamics of signal transduction, the monostable and bistable apoptosis models exhibit similar trends of tumour cell density distribution for most drug stimuli encountered except for a case where drug-induced apoptosis is involved in enhancement in interstitial drug penetration due to lower tumour cell density with the monostable apoptosis model. The sensitivity analysis of drug-specific properties indicates that (a) there exists an optimal drug diffusivity to balance interstitial drug transport and the specific acquirement of apoptosis switch, and (b) higher vascular permeability does not lead to significant improvement in drug effect, demonstrating the interstitial drug transport being a limiting factor.

Conclusion. Despite a number of simplified assumptions employed, the present modelling framework is capable of providing solid conclusions of reasoning-consequence for some aspects of the complex problem and offers clear-cut insights into the effect of various drug injections and other contributing factors on drug efficacy. It serves as a credible platform, which is modular and transparent to allow for systematic incorporation of additional layers of complexities and is expected to bridge the gap between the progress in systems biology of cellular signalling processes and its application in improving the efficacy of anticancer drugs.