Incorporating biological modeling into patient‐specific plan verification

Abstract Purpose Dose–volume histogram (DVH) measurements have been integrated into commercially available quality assurance systems to provide a metric for evaluating accuracy of delivery in addition to gamma analysis. We hypothesize that tumor control probability and normal tissue complication probability calculations can provide additional insight beyond conventional dose delivery verification methods. Methods A commercial quality assurance system was used to generate DVHs of treatment plan using the planning CT images and patient‐specific QA measurements on a phantom. Biological modeling was performed on the DVHs produced by both the treatment planning system and the quality assurance system. Results The complication‐free tumor control probability, P +, has been calculated for previously treated intensity modulated radiotherapy (IMRT) patients with diseases in the following sites: brain (−3.9% ± 5.8%), head‐neck (+4.8% ± 8.5%), lung (+7.8% ± 1.3%), pelvis (+7.1% ± 12.1%), and prostate (+0.5% ± 3.6%). Conclusion Dose measurements on a phantom can be used for pretreatment estimation of tumor control and normal tissue complication probabilities. Results in this study show how biological modeling can be used to provide additional insight about accuracy of delivery during pretreatment verification.

hot or cold spots in the target. 10,11 Furthermore, studies have shown that gamma-based analysis can be insensitive to detect errors or correlate dose errors in anatomic regions of interest. 12,13 Results derived from the usual individualized pretreatment QA tools have not been related with clinically relevant dosimetric errors on patient dose delivery. A more robust QA than the gamma index would be needed to quantify the clinical impact of dose measured prior to treatment in comparison to planned dose distribution, in addition to estimating the radiobiological implications of any dose differences.
A new approach for plan verification compares independently measured dose-volume histograms (DVHs) to that computed by a treatment planning system (TPS). There are commercially available solutions that incorporate dose measurements on phantom with the CT images of patient to compute pretreatment DVH. The capabilities of producing DVH of the Delta4DVH Anatomy 3D QA system (Scandidos, Uppsala), and both MapCHECK 2 and the ArcCHECK with 3DVH system (Sun Nuclear, Melbourne) have been evaluated in previous studies. [14][15][16] New metrics for IMRT QA verification were explored in a study that utilized the COMPASS system (IBA Dosimetry, Bartlett, Tennessee) to incorporate pretreatment DVH into tumor control probability (TCP) and normal tissue complication probability (NTCP) models. 17 TCP provides additional insight to plan quality as it is associated with the clinically observed tumor control rates. Similar association exists between NTCP and radiation-induced toxicity to organs at risk (OAR). These radiobiological metrics offers accountability for the response of specific tissues to dose and dose per fraction, which is not considered in the gamma index. 18 In previous studies, the complication-free tumor control probability, P + , has demonstrated value in approximating complication rates of patients treated. 19 The aim of this work is to demonstrate the value of incorporating P + as a pretreatment verification metric for IMRT plans.

2.A | Patient cohort
Fifty-four previously treated VMAT patient plans were used in this study. Prescribed doses and fraction schedules were dependent on the treatment site; however, no patients in the cohort received stereotactic body radiotherapy or radiosurgery. The patients were treated for 5 different anatomical sites consisting of 10 brain, 10 head-neck, 10 lung, 14 pelvis, and 10 prostate patients. There was a variation in the dose, number of fractions, and modalities incorporated in the treatment plans (Table 1)   shows DVH produced with Pinnacle 3 overlaid with VeriSoft's DVH for the patient.

2.C | TCP/NTCP modeling
where P(D) is the probability of response of a voxel irradiated by uniform irradiation of dose D, D 50 is the dose that induces response to 50% of the patients, and γ is the maximum normalized dose-response gradient. In Eq. (1), the fractionation correction of dose is handled by using the quantity D 2 Gy , which is the equivalent dose at 2 Gy per fraction. 26 The D 2Gy is calculated by the following expression: where D x Gy is the total dose when x Gy is the dose per fraction. To estimate normal tissue complications (NTCP) from nonuniform dose distributions, the relative seriality model was used: The overall probability of injury, P I , for several OARs is expressed by the following equation 24,25 : where N organs is the total number of vital OARs, and NTCP j is the response probability of the organ j having the reference volume and been irradiated by a dose D i as given by Eq. (1). Furthermore, Δv i is the fractional subvolumes of the organ being irradiated, M is the total number of voxels or subvolumes in the considered organ, and s is relative seriality parameter of that organ. In tumors, for estimating tumor control probability from nonuniform dose distributions, the following model was used: The overall probability of benefit, P B , can be quantified by the following expression: where N tumors is the total number of tumors or targets involved in the clinical case. The effectiveness of different treatment plans were evaluated by the radiobiological concept of complication-free tumor control probability, P + , which represents the probability of achieving tumor control without causing damage to normal tissues. 27,28 The radiobiological analysis was based on the DVH from Pinnacle 3 Table 6 summarizes the resulting values for gamma analysis of all cohorts. Γ 3D is the average 3D gamma score, σ Γ 3D is the uncertainty in gamma 3D scores, μ arith is the arithmetic mean, σ μ arith is the uncertainty of the arithmetic mean, μ med is the mean of the medians, and σ μ med is the uncertainty of the mean of medians.   Table A4).

3.B | TCP/NTCP results
Similarly, the delivered dose to patient eight in the prostate cohort in