Most calculations of the biological effect of radiation on tumours assume that the clonogenic cell density is uniform even if account is taken of non-uniform dose distribution. In practice tumours will almost certainly have a non-uniform clonogenic cell density. This paper extends one particular model of tumour control probability (TCP) to incorporate a variable clonogenic cell density while at the same time assuming a constant 2 Gy fraction size and a uniform radiosensitivity throughout the treatment. Since there are virtually no in vivo data on the variation of density we consider some model situations. One clear conclusion is that a large reduction in clonogenic cell density at the edges of a tumour would permit only a very modest decrease in dose if the TCP is not to be reduced. In general the effect on TCP is a complicated function of the variation in both dose and clonogenic cell density. We give the equations which enable both to be included.

Intensity-modulated radiation therapy (IMRT) can sculpt the high-dose volume around the site of disease with hitherto unachievable precision. Conformal avoidance of normal tissues goes hand in hand with this. Inhomogeneous dose painting is possible. The technique has become a clinical reality and is likely to be the dominant approach this decade for improving the clinical practice of photon therapy. This Series will explore all aspects of the "IMRT chain". Only 15 years ago just a handful of physicists were working on this subject. IMRT has developed so rapidly that its recent past is also its ancient history. This article will review the history of IMRT with just a glance at precursors. The physical basis of IMRT is then described including an attempt to introduce the concepts of convex and concave dose distributions, ill-conditioning, inverse-problem degeneracy, cost functions and complex solutions all with a minimum of technical jargon or mathematics. The many techniques for inverse planning are described and the review concludes with a look forward to the future of image-guided IMRT (IG-IMRT).

The idea of delivering intensity-modulated radiation therapy (IMRT) with a multileaf collimator in a continuous dynamic mode during a single rotation of the gantry has recently gained momentum both in research and industry. In this note we investigate the potential of this Single-Arc IMRT technique at a conceptual level. We consider the original theoretical example case from Brahme et al that got the field of IMRT started. Using analytical methods, we derive deliverable intensity 'landscapes' for Single-Arc as well as standard IMRT and Tomotherapy. We find that Tomotherapy provides the greatest flexibility in shaping intensity landscapes and that it allows one to deliver IMRT in a way that comes close to the ideal case in the transverse plane. Single-Arc and standard IMRT make compromises in different areas. Only in relatively simple cases that do not require substantial intensity modulation will Single-Arc be dosimetrically comparable to Tomotherapy. Compared with standard IMRT, Single-Arc could be dosimetrically superior in certain cases if one is willing to accept the spreading of low dose values over large volumes of normal tissue. In terms of treatment planning, Single-Arc poses a more challenging optimization problem than Tomotherapy or standard IMRT. We conclude that Single-Arc holds potential as an efficient IMRT technique especially for relatively simple cases. In very complex cases, Single-Arc may unduly compromise the quality of the dose distribution, if one tries to keep the treatment time below 2 min or so. As with all IMRT techniques, it is important to explore the tradeoff between plan quality and the efficiency of its delivery carefully for each individual case.

Many studies have been performed to assess correlations between measures derived from dose-volume histograms and late rectal toxicities for radiotherapy of prostate cancer. The purpose of this study was to quantify correlations between measures describing the shape and location of the dose distribution and different outcomes. The dose to the rectal wall was projected on a two-dimensional map. In order to characterize the dose distribution, its centre of mass, longitudinal and lateral extent, and eccentricity were calculated at different dose levels. Furthermore, the dose-surface histogram (DSH) was determined. Correlations between these measures and seven clinically relevant rectal-toxicity endpoints were quantified by maximally selected standardized Wilcoxon rank statistics. The analysis was performed using data from the RT01 prostate radiotherapy trial. For some endpoints, the shape of the dose distribution is more strongly correlated with the outcome than simple DSHs. Rectal bleeding was most strongly correlated with the lateral extent of the dose distribution. For loose stools, the strongest correlations were found for longitudinal extent; proctitis was most strongly correlated with DSH. For the other endpoints no statistically significant correlations could be found. The strengths of the correlations between the shape of the dose distribution and outcome differed considerably between the different endpoints. Due to these significant correlations, it is desirable to use shape-based tools in order to assess the quality of a dose distribution.