The delta-TCP concept: a clinically useful measure of tumor control probability

doi:10.1016/S0360-3016(99)00029-2

International Journal of Radiation OncologyBiologyPhysics

Volume 44, Issue 2, May 1999, Pages 369-380

https://doi.org/10.1016/S0360-3016(99)00029-2 Get rights and content

Abstract

Purpose: The aim of this article is to provide a quantitative tool to evaluate the influence of the different dose regions in a non-uniformly irradiated tumour upon the probability of controlling that tumor.

Methods and Materials: First, a method to generate a distribution of the probability of controlling the cells in a voxel (VCP) is explored and found not to be useful. Second, we introduce the concept of delta-TCP, which represents the gain or loss in the overall TCP as a result of each particular bin in a DVH not receiving the prescribed dose (the same concept is applicable to dose cubes or to a fraction of the bin). The delta-TCP method presented here is based on the Poisson TCP model, but any other model could also be used. Third, using this tool, with parameters appropriate to Stage C prostate tumors, the consequences of “cold” and “hot” dose regions have been explored.

Results: We show that TCP is affected by the minimum dose, even if it is delivered to a very small volume (20% dose deficit to 5% of the volume makes the TCP decrease by 18%), and that a hot region may be “wasted” unless the boost is to the bulk of the volume. An example of the application of the delta-TCP concept to a prostate radiotherapy plan is also given.

Conclusion: The delta-TCP distribution adds more objective information to the original DVH by enabling the clinician or planner to directly evaluate the effects of a non-uniform dose distribution on local control.

Introduction

It is common practice in radiotherapy to evaluate a plan by looking at the isodose encompassing the planning target volume (PTV) (1), with the constraints imposed by the organs at risk (OAR). Dose-volume histograms (DVHs) are becoming widely used to evaluate the complex information produced in 3D treatment planning (2). However, neither dose maps nor dose-volume distributions provide quantitative information on the response of the irradiated volume. Concepts such as the biologically effective dose (BED: the dose that, when delivered continuously, produces the same biologic effect as the dose actually delivered with a given fractionation regime) (3) or the biologic dose inhomogeneity factor (a measurement of the gradient of the log cell kill value, relative to the one which corresponds to the prescribed dose) (4) are attempts to quantify, in some way, the biological effects. Lee et al. (5) gave a lucid presentation on converting physical dose distributions to BED distributions so as to take into account the dependence of the biologic response on the nature of the tissue and fractionation scheme. The concept of equivalent uniform dose (EUD: the dose that, when uniformly delivered, is equivalent [same radiobiological effect] to the actual distribution) has also been recently proposed by Niemierko (6) as a method of summarizing and reporting inhomogeneous dose distributions within the tumor.

Models for tumor control probability (TCP) and normal tissue complication probability (NTCP) have been developed 7, 8 to estimate the response of tumors and OARs to dose distributions expressed in the form of DVHs. Objective score functions based on both physical and biological endpoints and constraints have also been proposed 9, 10. However, none of these concepts provide directly a quantitative tool to evaluate the influence of the different dose regions upon the final outcome. In this article, we put forward a method for doing this for the dose distribution within the tumor volume.

For a fixed integral dose to the PTV (1), the highest TCP arises when the dose is spatially uniform 8, 11, 12. However, uniform dose distributions are not always achievable or even desirable 9, 13, 14, 15, 16, 17. For example, it is possible in principle to increase the TCP without increasing the NTCP by increasing the dose in regions that are distant from the OAR by the use of a partial tumor boost (15). Clearly, one would like to look at the regions of different dose in terms of their contribution to the probability of controlling the tumor. However, it is difficult to deduce the clinical response directly from non-uniform dose distributions as they are expressed today. For example, hot and cold spots do not compensate each other (18); nor will a cold spot necessarily lead to an appreciable decrease in TCP 14, 15.

Some studies have dealt with the problem of how the TCP depends on the detailed dose distribution. Goitein (19) presented an analysis of the clinical benefit of using CT data in planning by looking at the loss in TCP when part of the tumor volume was outside the treatment field. Brahme (13) gave a quantitative expression for the loss in tumor control probability as a function of the degree of dose variation (relative standard deviation) around the mean dose level, provided that the mean dose was on the linear part of the dose-response curve and that the dose distribution was not too broad; a similar analysis can also be found in Nahum (20). Goitein (14) suggested that, contrary to conventional wisdom, modest dose deficit to small subvolumes of the target volume may not be too deleterious and that modest dose increments to substantial subvolumes of the target volume may be advantageous. However, in a recent editorial, Goitein and Niemierko (15) urge careful quantitative evaluation of dose deficits because their biologic impact depends not only on the magnitude of the deficit but also on its volume. It is clear that a method is needed to explore the influence of subvolumes irradiated to a given dose level on the local tumor control.

We show that voxel-control-probability (VCP) distributions, though superficially attractive, are not useful. Instead, we introduce the concept of delta-TCP as a tool for quantifying the influence of the different dose regions in a heterogeneous dose distribution on the overall TCP. The delta-TCP value is calculated either for each bin (or fraction) in the DVH or for each dose cube and represents the gain or loss in the overall TCP as a result of that particular bin or dose cube not receiving the prescribed dose. Using this tool, we explore the consequences of having cold and hot spots in a tumor, i.e., how large they are able to become before the TCP changes appreciably. One example of the application of delta-TCP to a radiotherapy plan is also given.

The delta-TCP method presented here is based on the Poisson TCP model (8) (see APPENDIX A, APPENDIX B) but any other TCP model (21) could be used to compute delta-TCP values.

Section snippets

Are VCP distributions feasible?

We describe in this section an attempt to convert a dose distribution to a distribution of TCP values. The approach that first suggests itself is a “point-by-point” method that results in a distribution of VCP, i.e., the probability of controlling all the cells in a voxel.

In order to generate a VCP distribution, the VCP values have to be computed for each jth-voxel (j = 1,2 … , number of voxels) inside the tumor. The overall TCP is then given by: $TCP= ∏ j VCP_{j}$ where the VCP_j values can be

ΔTCP features

As an example, ΔTCP calculations have been carried out [using Eq. (5)] for one radiotherapy plan using the selected set of biologic parameters. In Fig. 3a, the DVH corresponding to that plan is shown. In Fig. 3b, the ΔTCP_j numbers are displayed as a distribution. In this fashion, the contribution of each bin in the DVH to the overall TCP is clearly presented. The ΔTCP distribution adds more objective information to the original DVH by revealing the relative (biological/clinical) importance of

Discussion and summary

The aim of this article is to introduce a method (the ΔTCP function) to assess quantitatively the contribution of each dose region in non-uniform dose distributions to the final tumor outcome expressed as TCP.

The first approach was a ‘point-by-point’ method to generate VCP distributions. This idea is not new (e.g. 22) and has found little (if any) support. However, the two examples shown here served to bring up and discuss the problems that ought to be overcome with an alternative approach (i.e.

Acknowledgements

We are grateful to G. Steel and S. Webb for valuable discussions and helpful comments on the manuscript. Comments made by P. Evans, V. N. Hansen, V. Khoo, and the two anonymous referees are also appreciated. This work has been supported by the Spanish Government (Ministry of Education and Science, Programa Sectorial de Formacion de Profesorado y Personal Investigador, Subprograma General en el Extranjero), and by The Institute of Cancer Research, United Kingdom.

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To investigate the possible contribution of indirect damage and damage saturation to tumour control obtained with SBRT/SRS treatments for early-stage NSCLC and brain metastases.
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For each of the 36 plans, UCFCP was computed using eq.1. TCP (Poisson model for GTV as in [18]) and NTCP (LKB model [19,20] for rectum and bladder) values were calculated with BIOPLAN [17] with parameters from [21,22] (Table 2). SPCR was calculated as the summation over risks values, given by the Life Attributable Risk (LAR), of the peripheral organs in BEIR VII PHASE 2 report [23] (lung, stomach, thyroid, red marrow2, colon, bladder, liver, skin, rectum and the remainder).
To perform a systematic and thorough assessment, using the Uncomplicated and Cancer-Free Control Probability (UCFCP) function, of a broad range of photon prostate cancer RT treatments, on the same scenario (a unique pelvic CT set). UCFCP considers, together with the probabilities of local tumour control (TCP) and deterministic (late) sequelae (NTCP), the second primary cancer risk (SPCR) due to photon and neutron peripheral doses.
Thirty-six radiotherapy plans were produced for the same CT. 6, 10, 15 and 18 MV 3DCRT, IMRT and VMAT (77.4 Gy in 43 fractions) and 6 and 10 MV SBRT (36.25 Gy in 5 fractions with flattened and FFF beams) for Elekta, Siemens and Varian Linacs plans were included. DVH and peripheral organ dosimetry were used to compute TCP, NTCP, and SPCR (the competition and LNT models) for further plan ranking.
Biological models (and parameters) used predicted an outcome which is in agreement with epidemiological findings. SBRT plans showed the lowest SPCR and a below average NTCP_rectal. High energy plans did not rank worse than the low energy ones. Intensity modulated plans were ranked above the 3D conformal techniques.
According to UCFCP, the best plans were the10 MV SBRTs. SPCR rates were low and did not show a substantial impact on plan ranking. High energy intensity-modulated plans did not increase in excess the average of SPCR. Even more, they ranked among the best, provided that MU were efficiently managed.
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The radiosensitivity parameters and the repopulation rate are presumed to be log-normally distributed among the population. Corresponding distributions of TCP across the population are built using a Monte-Carlo simulation algorithm. An analytical formula for the TCP distribution is derived for the case of variability in radiosensitivity only and found to be in excellent agreement with the corresponding Monte-Carlo simulations.
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A homogeneity index (HI) measures the uniformity of a dose distribution within a given target volume. Traditional HIs only use a limited number of dose–volume histogram data-points for calculation. A voxel-based homogeneity index (VHI) is proposed which utilizes the entire information of the three-dimensional dose distribution. We compared the VHI with existing HIs and analyzed if VHI results were associated with treatment outcomes in patients who underwent therapeutic WBRT.
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Uncomplicated and Cancer-Free Control Probability (UCFCP) function has been proposed assuming a statistically uncorrelated response for tumour and normal tissues. The Poisson’s and Lyman’s models were chosen for TCP and NTCP calculations, respectively. SCP was modelled as the summation of risks associated to photon and neutron irradiation of radiosensitive organs. For the medium (>4 Gy) and low dose regions, mechanistic and linear secondary cancer risks models were used, respectively. Two conformal and intensity-modulated prostate plans at 15 MV (same prescription dose) were selected to illustrate the UCFCP features.
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A small change in the radiation dose can affect the local response of the tissue largely. It has been reported that a dose reduction of only 20% to 5% of the target volume in prostate cancer can reduce the tumor control probability (TCP) to 18% [5]. Mijnheer et al. recommended an overall dose accuracy of ±3.5% to the ICRU reference point [6].
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Biology ContributionThe delta-TCP concept: a clinically useful measure of tumor control probability

Abstract

Introduction

Section snippets

Are VCP distributions feasible?

ΔTCP features

Discussion and summary

Acknowledgements

Radiother Oncol

Int J Radiat Oncol Biol Phys

Int J Radiat Oncol Biol Phys

Int J Radiat Oncol Biol Phys

Int J Radiat Oncol Biol Phys

Int J Radiat Oncol Biol Phys

Int J Radiat Oncol Biol Phys

Int J Radiat Oncol Biol Phys

Int J Radiat Oncol Biol Phys

Radiother Oncol

Int J Radiat Oncol Biol Phys

Int J Radiat Oncol Biol Phys

Int J Radiat Oncol Biol Phys

ICRU report 50Prescribing, recording and reporting photon beam therapy

Dose-volume histograms

Int J Radiat Oncol Biol Phys

The linear quadratic formula and progress in fractionated radiotherapy

Br J Radiol

Reporting and analysing dose distributionsA concept of equivalent uniform dose

Med Phys

Biology Contribution
The delta-TCP concept: a clinically useful measure of tumor control probability