Tumor Control Probability Model Research Articles

Optimum parameters in a model for tumour control probability including interpatient heterogeneity

A model for computing tumour control probability (TCP) is studied which embodies a dependence on the size of the irradiated volume, the density of clonogenic cells and the dose received, together with the alpha and beta parameters of the linear quadratic model of cell kill. The model can be used to describe situations where both the dose and the clonogenic cell densities are inhomogeneously distributed; however there is still uncertainty about its radiobiological parameters and the author aims to establish parameters for four types of tumour. In its simplest form, when the volumes are spherical, the clonogenic cell density is considered constant throughout the volume and the dose is uniform, the model has been used (by D.J. Brenner, 1993) to predict the radiobiological parameter alpha which allows the model to best fit the observed clinical data for four types of tumour. Here a new set of fits to the data presented by Brenner is constructed using a model which includes the distribution of radiosensitivity across a heterogeneous patient population. It is shown that this leads to a different set of optimum radiobiological parameters when the clonogenic cell density is of the order of 107 cells cm-3.

A proof that uniform dose gives the greatest TCP for fixed integral dose in the planning target volume

In this note it is shown that for a fixed integral dose to the planning target volume, the highest tumour control probability (TCP) arises when the dose is spatially uniform. This 'uniform dose theorem' is proved both for (i) a specific TCP model based on Poisson/independent voxel statistics, and (ii) any model for voxel control probability having a specific shape with respect to increasing dose.

Biophysical modelling: implications for conformation radiation treatment

A central theme of this session was the understanding and the modeling of biological phenomenon, and of treatment outcome, with a view to guide the planning and delivery of conformal radiation treatment. Of particular emphasis were discussions on the biological rationale for conformal therapy, the influence of local relapse on the probability of metastasis, the modeling of tumor control probability, and the inclusion of biological indices for the optimization of treatment design. Central to the biological rationale for conformal therapy is the premise that enhanced local control will not be offset by pre-existing metastasis, but will increase cancer cure [&lo]. Added to the plethora of clinical data supporting this hypothesis is the recent work of Yorke et al. modeling metastasis development for prostatic carcinoma and fitting a model to clinical results [18]. This model postulates that the genotypic mutations of tumor cells lead to metastatic phenotypes and ultimately distant disease. Calculated results of this model, using reasonable biological values, were fitted to long-term follow-up results (distant metastasis free survival DMFS of locally controlled patients, local relapse free survival LRFS and DMFS of patients with local relapse) of 679 patients who received 12’1 permanent implants for the treatment of prostatic carcinoma [5]. Then, the model was used to predict DMFS for the hypothetical situation of 100% local control, i.e. if relapses were completely prevented with high dose and high precision conformal radiotherapy. The predicted DMFS result is significantly higher than the clinical results of patients with locally recurrent disease (by about 45 percentage point at 15 years), but slightly below that for patients with local control (by about 10 percentage point at 15 years). Thus, significant gain in prostatic cancer cure may be possible by increasing local control, and the higher metastatic potential of non-responsive tumors may reduce such gain, but only by a small amount. This postulate can probably be extrapolated to disease sites in which metastasis dissemination occurs as a relatively late event, but would be less applicable for cancer with high propensities for early metastatic dissemination. How much would local control be increased with high dose conformal therapy? This question may in part be answered by the continuing efforts to improve methods for calculating tumor control probabilities (TCP), as described by Goitein [7]. Their latest development incorporated intra-tumoral heterogeneity and the size of the tumor in the TCP estimation, and introduce SF2 (the surviving fraction of tumor cells for a dose of 2 Gy) as an explicit reference parameter [8,13]. This last addition brings to mind the prognostic potential of in vitro radiobiological viability assay, with 2 Gy doses, of tumor cells derived from individual patients [2-4,14,15]. Improvement in the accuracy of such assays may yield patient-specific information capable of predicting treatment outcome. In the context of TCP modeling, knowledge of the SF2 of a tumor may permit estimation of patient specific tumor control probability and obviate the need for ‘population-averaging’. These efforts on TCP modeling, and similar attempts by others, have yielded another interesting and challenging insight, that some degree of dose inhomogeneity within the target volume may be beneficial [8]. Specifically, administering ‘a boost within a boost’ (a term used by Herman Suit in a recent conversation) to increase the dose to portions of a tumor may enhance local control, while keeping the original minimum target dose constant to maintain acceptable normal tissue sequelae. It is likely that this postulate will be tested in the clinical arena. It is probable that the TCP and its counterpart for normal tissues, the NTCP [ 171, will be of utility for evaluating the relative merits of rival treatment design. Equally important is the potential of combining TCP and NTCP into an objective function for use in computer-assisted optimization of treatment design [12]. In this regard, Brahme and colleagues incorporated

Some implications of the linear quadratic model for tumor control probability

To define an optimal radiation therapy strategy, the dependence of the probability of cure and of significant complications, on the parameters controlled by the radiotherapist must be determined. The recent success of the Linear Quadratic (LQ model in constructing isoeffect relations for normal tissue damage and in describing in vitro cell survival curves, indicate that this model could be used to determine this dependence. The problem of tumor control is addressed. Using LQ model parameters obtained from human tumor cell lines, the sigmoid dose-response curves for controlling tumors of fixed size but of several histologies, with a fractionated course of radiotherapy is obtained. Except for squamous cell carcinoma, the calculated average tumor control doses (TCD 37 or TCD 50) are unrealistically low, but the model can be made more realistic by including inhomogeneities in the spatial dose distribution and heterogeneous tumor cell populations. The slope of the dose response curves are determined and the significance of the “relative slope” parameter p as a measure of the number of cells in a tumor's most radioresistant clone is noted. The relation of the model's predictions to qualitative features of the experimental animal data for both tumor control and for normal tissue damage is discussed. Experiments to test the validity of this type of model are suggested.