Regarding cancer cells that do not have a full recovery in response to a radiation exposure based on their radiosensitivity, some cells will undergo cell death by apoptosis and the remaining will undergo cell death depending on the amount of division-associated death. The LQ model for cell death by apoptosis is the following.

If the term that describes division-associated cell death in the nLQT model in equation (3) is set to f_{cont} [ t, t _{i} ] , the formula of f_{cont} [ t, t _{i} ] is described as follows;

If the proportion of cells subject to apoptosis is k%, then the probability of division-associated cell death will be p = (100 − k)%. Therefore, the following formula was generated as a general LQ model (GLQ model) for showing time-dose-fractionation relationships.

When radiotherapy of 60 Gy/30 Fr is started on Wednesday with the usual 2 Gy/Fr and 5 Fr/w, the time-survival relationships for 30% and 1% as the proportion of apoptotic cell death are shown in Fig. 7.