We present extensions to our quasi-2D cellular automata spheroid model that add a cellular kinetics module together with an irradiation and repair module. Significantly, our approach is not based on the Linear Quadratic (LQ) model, instead, we propose a simple two-parameter, algorithmic model which captures the essential biological features of irradiation-induced cell death, repair and associated cell cycle delays. This approach allows us to estimate directly the underlying irradiation-induced cell survival probability. We present the calibration of this extended model both with and without the application of single irradiation doses to the commonly studied (in vitro) EMT6/Ro (mammary carcinoma) cell line. A comparison of the estimated underlying cell survival probability with the in vitro survival probability data confirms the expected differences in the measures.