The effects of hypoxia on the theoretical modelling of tumour control probability

Figures & data

Figure 1. Theoretical predictions of the tumour response to radiation for a tumour tissue well supplied with oxygen. a) oxygenation of the tissue as histograms (inset–full tissue oxygenation map). b) predicted response to single doses of radiation. c) response from fractionated treatments. Solid lines–predictions for a continuous distribution of oxygen tensions in tumours. Dashed lines–predictions for a ‘black-and-white’ (binary) distribution of oxygen tensions in tumours.

Figure 2. Theoretical predictions of the tumour response to radiation for a tumour tissue with impaired oxygen supply. a) oxygenation of the tissue as histograms (inset–full tissue oxygenation map). b) predicted response to single doses of radiation. c) response from fractionated treatments. Solid lines–predictions for a continuous distribution of oxygen tensions in tumours. Dashed lines–predictions for a ‘black-and-white’ (binary) distribution of oxygen tensions in tumours.

Figure 3. Theoretical predictions of the tumour response to radiation for a tumour tissue with poor oxygenation. a) oxygenation of the tissue as histograms (inset–full tissue oxygenation map). b) predicted response to single doses of radiation. c) response from fractionated treatments. Solid lines–predictions for a continuous distribution of oxygen tensions in tumours. Dashed lines–predictions for a ‘black-and-white’ (binary) distribution of oxygen tensions in tumours.

Table I.  Estimated tumour control probabilities (TCP) after 30 fractions for tissues with various degrees of oxygenation

Tissue type	Percent pO2 values less than 2.5 mmHg	TCP for the full distribution of pO2 values	TCP for the ‘black-and-white’ simplification	ΔTCP
N = 10^7 cells
Good oxygenation	0.0%	97.5%	99.1%	1.6%
Medium oxygenation	3.3%	86.4%	98.5%	12.1%
Poor oxygenation	50.5%	2.2%	0.2%	−2.0%
N = 10^8 cells
Good oxygenation	0.0%	77.8%	91.1%	13.3%
Medium oxygenation	3.3%	23.3%	86.2%	62.9%
Poor oxygenation	50.5%	0.0%	0.0%	0.0%
N = 10^9 cells
Good oxygenation	0.0%	8.1%	39.4%	31.3%
Medium oxygenation	3.3%	0.0%	22.6%	22.6%
Poor oxygenation	50.5%	0.0%	0.0%	0.0%

Table II.  Effects of the temporal variation of the distribution of acute hypoxia in tumours

	Hypoxic fraction (%)	Cell survival predicted by the full distribution (%)	Cell survival predicted by the ‘black-and-white’ simplification (%)
Minimum	2.9	54.1	50.7
Maximum	19.5	56.8	54.7
Mean value	9.7	55.3	52.3
Standard deviation	3.5	0.6	0.8