Pavel Stavrev

A TCP-NTCP estimation module using DVHs and known radiobiological models and parameter sets

Radiotherapy treatment plan evaluation relies on an implicit estimation of the tumor control probability (TCP) and normal tissue complication probability (NTCP) arising from a given dose distribution. A potential application of radiobiological modeling to radiotherapy is the ranking of treatment plans via a more explicit determination of TCP and NTCP values. Although the limited predictive capabilities of current radiobiological models prevent their use as a primary evaluative tool, radiobiological modeling predictions may still be a valuable complement to clinical experience. A convenient computational module has been developed for estimating the TCP and the NTCP arising from a dose distribution calculated by a treatment planning system, and characterized by differential (frequency) dose‐volume histograms (DDVHs). The radiobiological models included in the module are sigmoidal dose response and Critical Volume NTCP models, a Poisson TCP model, and a TCP model incorporating radiobiological parameters describing linear‐quadratic cell kill and repopulation. A number of sets of parameter values for the different models have been gathered in databases. The estimated parameters characterize the radiation response of several different normal tissues and tumor types. The system also allows input and storage of parameters by the user, which is particularly useful because of the rapidly increasing number of parameter estimates available in the literature. Potential applications of the system include the following: comparing radiobiological predictions of outcome for different treatment plans or types of treatment; comparing the number of observed outcomes for a cohort of patient DVHs to the predicted number of outcomes based on different models/parameter sets; and testing of the sensitivity of model predictions to uncertainties in the parameter values. The module thus helps to amalgamate and make more accessible current radiobiological modeling knowledge, and may serve as a useful aid in the prospective and retrospective analysis of radiotherapy treatment plans. PACS number: 87.53.Tf

A study on the magnetic resonance imaging (MRI)-based radiation treatment planning of intracranial lesions.

The aim of this study is to develop a magnetic resonance imaging (MRI)-based treatment planning procedure for intracranial lesions. The method relies on (a) distortion correction of raw magnetic resonance (MR) images by using an adaptive thresholding and iterative technique, (b) autosegmentation of head structures relevant to dosimetric calculations (scalp, bone and brain) using an atlas-based software and (c) conversion of MR images into computed tomography (CT)-like images by assigning bulk CT values to organ contours and dose calculations performed in Eclipse (Philips Medical Systems). Standard CT + MRI-based and MRI-only plans were compared by means of isodose distributions, dose volume histograms and several dosimetric parameters. The plans were also ranked by using a tumor control probability (TCP)-based technique for heterogeneous irradiation, which is independent of radiobiological parameters. For our 3 T Intera MRI scanner (Philips Medical Systems), we determined that the total maximum image distortion corresponding to a typical brain study was about 4 mm. The CT + MRI and MRI-only plans were found to be in good agreement for all patients investigated. Following our clinical criteria, the TCP-based ranking tool shows no significant difference between the two types of plans. This indicates that the proposed MRI-based treatment planning procedure is suitable for the radiotherapy of intracranial lesions.

Breast radiotherapy with inclusion of internal mammary nodes: a comparison of techniques with three-dimensional planning.

PURPOSE To compare the partially wide tangent (PWT) technique of breast and internal mammary chain irradiation with photon/electron (P/E) and standard tangent (ST) techniques in terms of dose homogeneity within breast and the dose to critical structures such as the heart and lung. METHODS AND MATERIALS Sixteen left breast cancer patients underwent CT simulation. The breasts, lungs, heart, and internal mammary chain were contoured and treatment plans generated on a three-dimensional planning system (Helax-TMS). RESULTS The mean dose to the left breast volume with the ST, P/E, and PWT techniques was 94.7%, 98.4%, and 96.5%, respectively (p = 0.029). The left lung received the lowest mean dose with the ST technique (13.9%) compared with PWT (22.8%) and P/E (24.3%). The internal mammary chain volume was most consistently treated with the PWT (mean dose 99%) vs. P/E (86%) and ST (38.4%) techniques. The heart received the least dose with ST (mean dose 6.7%) vs. PWT (10.3%) and P/E (19%). The PWT treated the greatest amount of contralateral breast (mean dose 5.8%) vs. ST (3.2%) vs. P/E (2.8%). CONCLUSION The PWT technique treats the internal mammary chain with acceptable toxicity to major organs, especially the heart, and with reasonable dose homogeneity in patients with mastectomy or intact breasts.

Investigating the effect of cell repopulation on the tumor response to fractionated external radiotherapy

In this work we study the descriptive power of the main tumor control probability (TCP) models based on the linear quadratic (LQ) mechanism of cell damage with cell recovery. The Poisson, binomial, and a dynamic TCP model, developed recently by Zaider and Minerbo are considered. The Zaider-Minerbo model takes cell repopulation into account. It is shown that the Poisson approximation incorporating cell repopulation is conceptually incorrect. Based on the Zaider-Minerbo model, an expression for the TCP for fractionated treatments with varying intervals between two consecutive fractions and with cell survival probability that changes from fraction to fraction is derived. The models are fitted to an experimental data set consisting of dose response curves that correspond to different fractionation regimes. The binomial TCP model based on the LQ mechanism of cell damage solely was unable to fit the fractionated response data. It was found that the Zaider-Minerbo model, which takes tumor cell repopulation into account, best fits the data.

Fundamental form of a population TCP model in the limit of large heterogeneity.

A population tumor control probability (TCP) model for fractionated external beam radiotherapy, based on Poisson statistics and in the limit of large parameter heterogeneity, is studied. A reduction of a general eight-parameter TCP equation, which incorporates heterogeneity in parameters characterizing linear-quadratic radiosensitivity, repopulation, and clonogen number, to an equation with four parameters is obtained. The four parameters represent the mean and standard deviation for both clonogen number and a generalized radiosensitivity that includes linear-quadratic and repopulation descriptors. Further, owing to parameter inter-relationship, it is possible to express these four parameters as three ratios of parameters in the large heterogeneity limit. These ratios can be directly linked to two defining features of the TCP dose response: D50 and gamma50. In the general case, the TCP model can be written in terms of D50, gamma50 and a third parameter indicating the ratio of the levels of heterogeneity in clonogen number and generalized radiosensitivity; however, the third parameter is unnecessary when either of these two sources of heterogeneity is dominant. It is shown that heterogeneity in clonogen number will have little impact on the TCP formula for clinical scenarios, and thus it will generally be the case that the fundamental form of the Poisson-based population TCP model can be specified completely in terms of D50 and gamma50: TCP= 1/2 erfc[square root of pi(gamma50)(D50/D-1)]. This implies that limited radiobiological information can be determined by the analysis of dose response data: information about parameter ratios can be ascertained, but knowledge of absolute values for the fundamental radiobiological parameters will require independent auxiliary measurements.

Derivation of the expressions for γ50 and D50 for different individual TCP and NTCP models

This paper presents a complete set of formulae for the position (D50) and the normalized slope (gamma50) of the dose-response relationship based on the most commonly used radiobiological models for tumours as well as for normal tissues. The functional subunit response models (critical element and critical volume) are used in the derivation of the formulae for the normal tissue. Binomial statistics are used to describe the tumour control probability, the functional subunit response as well as the normal tissue complication probability. The formulae are derived for the single hit and linear quadratic models of cell kill in terms of the number of fractions and dose per fraction. It is shown that the functional subunit models predict very steep, almost step-like, normal tissue individual dose-response relationships. Furthermore, the formulae for the normalized gradient depend on the cellular parameters alpha and beta when written in terms of number of fractions, but not when written in terms of dose per fraction.

How well are clinical gross tumor volume DVHs approximated by an analytical function

How well are clinical gross tumor volume DVHs approximated by an analytical function? The dose heterogeneity in the tumor is often described as being normally distributed. Besides the normal distribution we propose the Fermi function describing Fermi statistics as a possible dose heterogeneity descriptor. In order to demonstrate the adequacy of the proposed functions as dose distribution descriptors 30 clinical gross tumor volume (GTV) dose-volume histograms (DVHs) are gathered and fit with the examined functions.

Radiation damage, repopulation and cell recovery analysis of in vitro tumour cell megacolony culture data using a non-Poissonian cell repopulation TCP model

The effects of radiation damage, tumour repopulation and cell sublethal damage repair and the possibility of extracting information about the model parameters describing them are investigated in this work. Previously published data on two different cultured cell lines were analysed with the help of a tumour control probability (TCP) model that describes tumour cell dynamics properly. Different versions of a TCP model representing the cases of full or partial cell recovery between fractions of radiation, accompanied by repopulation or no repopulation were used to fit the data and were ranked according to statistical criteria. The data analysis shows the importance of the linear-quadratic mechanism of cell damage for the description of the in vitro cell dynamics. In a previous work where in vivo data were analysed, the employment of the single hit model of cell kill and cell repopulation produced the best fit, while ignoring the quadratic term of cell damage in the current analysis leads to poor fits. It is also concluded that more experiments using different fractionation regimes producing diverse data are needed to help model analysis and better ranking of the models.

Analytical investigation of the possibility of parameter invariant TCP-based radiation therapy plan ranking

Abstract Purpose. To analytically investigate the possibility of a parameter invariant ranking of radiotherapy (RT) plans based on comparing the tumor control probabilities (TCPs) produced by the competing plans for different values of the radiobiological model parameters determining the radiation response. Method. Individual TCP models based on the Single hit model of cell kill and on the linear-quadratic (LQ) model of cell damage, with and without repopulation, are considered. The tumor dose distributions in case of heterogeneous dose irradiation are described by a Gaussian distribution function on the basis of which a TCP expression is derived depending only on the mean dose to the tumor and its standard deviation and the TCP model parameters. Results. It is shown that in case of homogeneous dose to the tumor the plan ranking in terms of TCP is parameter invariant. In case of heterogeneous dose to the tumor there are cases when the plan ranking is parameter invariant and cases when the parameter invariance is violated. An interesting dependence of the extent of the parameter invariance violation on the model of cell kill as well as on the size and repopulation rate of the tumor is noted. Conclusion. We conclude that in many cases RT plan ranking in terms of TCP is parameter invariant. However, since there exist cases where the parameter invariance is lost an investigation of the specific plans to be ranked should be performed applying the proposed approach.

Applying radiobiological plan ranking methodology to VMAT prostate SBRT

The impact of a rectal spacer and an increased near maximum target dose in VMAT prostate SBRT is studied. For a group of 11 patients (35Gy-in-five-fractions VMAT prostate SBRT) a set of 4 plans were generated, namely two VMAT plans, with D2%⩽37.5Gy (Hom) and with D2%⩽40.2Gy (Het), were created for each of two CT scans taken before (NoSpc) and after (Spc) transperineal spacer insertion. Consequently the methodology for parameter invariant TCP (tumor control probability) plan ranking was applied for comparison of the plans in terms of tumor control. NTCPs (normal tissue complication probabilities) were calculated for rectum and bladder using Lymans model. For all 11 patients the TCP plan ranking has shown that the Het plans would perform considerably better in TCP terms than the Hom ones. The plans without rectal spacer were ranked worse compared to those with rectal spacer except for one set of Hom plans. The calculated NTCPs for rectum produced by the Het plans were quite similar to the NTCPs of the Hom ones. The rectal NTCPs of the Hom Spc plans were always lower than the NTCPs of the Hom NoSpc plans. The NTCP values for bladder were extremely low in all cases. The use of rectal spacer leads in general to lower risk of rectal complications, as expected, and even to better tumor control. Plans with increased near maximum target dose (D2%⩽40.2Gy) are expected to perform much better in terms of tumor control than those with D2%⩽37.5Gy.