The potential for the use of in-silico models of disease in progression monitoring is becoming increasingly recognised, as well as its contribution to the development of complete curative processes. In this paper we report the development of a hybrid cellular automaton model to mimic the growth of avascular tumours, including the infusion of a bioreductive drug to study the effects of protein binding on drug transportation. The growth model is operated within an extracellular tumour microenvironment. An artificial Neural Network based scheme was implemented that modelled the behaviours of each cell (proliferation, quiescence, apoptosis and/or movement) based on the complex heterogeneous microenvironment; consisting of oxygen, glucose, hydrogen ions, inhibitory factors and growth factors. To validate the growth model results, we conducted experiments with multicellular tumour spheroids. These results showed good agreement with the predicted growth dynamics. The outcome of the avascular tumour growth model suggested that tumour microenvironments have a strong impact on cell behaviour. To address the problem of cellular proteins acting as resistive factors preventing efficient drug penetration, a bioreactive drug (tirapazamine) was added to the system. This allowed us to study the drug penetration through multicellular layers of tissue after its binding to cellular proteins. The results of the in vitro model suggested that the proteins reduce the toxicity of the drug, reducing its efficacy for the most severely hypoxic fractions furthest from a functional blood vessel. Finally this research provides a unique comparison of in vitro tumour growth with an intelligent in silico model to measure bioreductive drug availability inside tumour tissue through a set of experiments.