Some characteristics of tumour control probability for heterogeneous tumours

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Abstract
Some mathematical characteristics of tumour control probability (TCP) have been examined in the light of potential intra-tumour variations in clonogenic cell characteristics. In particular, an explicit expression for the relationship between the dose distribution and the probability of local clonogen eradication is obtained which maximizes the TCP using both general and specific TCP models, for the case of fixed energy deposition into the tumour volume. Characteristics of this expression are considered for the cases of varying clonogen cell density (uniform radiosensitivity) and uniform cell density (uniform radiosensitivity), yielding the `uniform TCP' and `uniform dose' results respectively for TCP maximization. These situations are examined graphically to highlight the possible consequences of neglecting intra-tumour heterogeneity in dose prescription.