Use of radiobiology in medical jurisprudence, with particular reference to delays in diagnosis and therapeutic onset

Abstract

Objective: This paper considers aspects of radiobiology and cell and tissue kinetics applicable to legal disputations concerned with diagnostic and treatment onset delays.

Methods: Various models for tumour volume changes with time are reviewed for estimating volume ranges at earlier times, using ranges of kinetic parameters. Statistical cure probability methods, using Poisson statistics with allowances for parameter heterogeneity, are also described to estimate the significance of treatment delays, as well as biological effective dose (BED) estimations of radiation effectiveness.

Results: The use of growth curves, based on parameters in the literature but with extended ranges, can identify a window of earlier times when such tumour volumes would be amenable to a cure based on the literature for curability with stage (and dimensions). Also, where tumour dimensions are not available in a post-operative setting, higher cure probabilities can be achieved if treatment had been given at earlier times.

Conclusion: The use of radiobiological modelling can provide useful insights, with quantitative assessments of probable prior conditions and future outcomes, and thus be of assistance to a Court in deciding the most correct judgement.

Advances in knowledge: This study collates prior knowledge about aspects of radiobiology that can be useful in the accumulation of sufficient proof within medicolegal claims involving diagnostic and treatment days.

Figure 1.

Four examples of exponential tumour growth with increasing time for volume doubling times of 60–180 days, and one Gompertz(sigmoidal) growth curve which matches the volume of the 180 doubling time example at just over 3 years

Figure 2.

Time is now reversed, but using the same doubling times and Gompertz parameters, for volumes at earlier times than a reference volume of 100 cm³

Figure 3.

Tumour diameter at earlier times for respective assumed volume doubling times, with a linear approximation of a Gompertz curve trio provide a further boundary. Longer doubling times than shown here would predict even larger tumour diameters at earlier times

Figure 4.

The effect of improving tumour cure probability for earlier treatment onset times for an individual tumour that would otherwise follow the black dose response curve for the actual treatment start time. Radiobiological characteristics: α = 0.25 Gy⁻¹, b = 0.025 Gy⁻², cellular population doubling time = 60 days, 5 × 10⁵ cells present when actual treatment started

Figure 5.

The effect of improving tumour cure probability for earlier treatment onset times for a population of 100 patients which would follow the black dose response curve for the actual treatment start time. Radiobiological characteristics: mean α = 0.25 Gy⁻¹(σ = 0.025), b = 0.03 Gy⁻², cellular population doubling time mean = 60 days (σ = 1.25 days, log-normal distribution), 5 × 10⁵ cells present when actual treatment started

FigureA.1 Plot of the doubling time (w) at any timepoint, the average doubling time (w_av) during Gompertzian growth. The equivalent doubling time (w_eq), when used with the standard exponential growth equation, provides the same volume over a specified time as would a Gompertzfunction.

Figure C1. Tumour Control Probability dose response curves for seven different simulated tumours of different radiosensitivities (grey curves) with the averaged population value for all seven tumour shown as the black line which is shallower.