PurposeClinical studies in radiation therapy with conventional fractionation show a reduction in the tumor control probability (TCP) with an increase in the total and hypoxic tumor volumes. The main objective of this article is to derive an analytical relationship between the TCP and the hypoxic and total tumor volumes. This relationship is applied to clinical data on the TCP reduction with increasing total tumor volume and, also, dose escalation to target tumor hypoxia.MethodsThe TCP equation derived from the Poisson probability distribution predicts that both (a) an increase in the number of tumor clonogens and (b) an increase in the average cell surviving fraction are the factors contributing to the loss of local control. Using asymptotic mathematical properties of the TCP formula and the linear quadratic (LQ) cell survival model with two levels of hypoxic and oxygenated cells, we separated the TCP dependence on the total and hypoxic tumor volumes. The predicted trends in the local control as a function of total and hypoxic tumor volumes were evaluated in radiotherapy model problems with conventional dose fractionation for head and neck and non‐small cell lung cancers. Tumor‐specific parameters in the LQ model and the density of clonogens in the TCP model were taken from published data on predictive assays and the plating efficiency measurements, respectively.ResultsOur simulations show that, at the dose levels used in conventional radiation therapy for head and neck and non‐small cell lung cancers, the TCP dependence on the total tumor volume is negligible for completely oxygenated tumors. However, the presented results demonstrate that tumor hypoxia introduces a significant volume effect into estimates of the TCP. The extent of tumor hypoxia is a plausible mechanism to explain the TCP reduction with increasing total tumor volume observed in clinical studies. To achieve the same level of tumor control in a hypoxic tumor region relative to well oxygenated tumor regions, the delivered dose should, in principle, be escalated by a factor equal to the oxygen enhancement ratio (OER). The theoretically required hypoxia‐targeted dose escalation could be as large as 100% because it has been estimated that hypoxic tumor regions may have an OER = 2 for conventional fractionation. However, our results indicate that clinically acceptable values of the TCP would require much lower hypoxia‐targeted dose escalation (<50%) when the effects of total and hypoxic tumor volumes are taken into account.ConclusionsThe reported studies and models suggest that the effect of total tumor volume on the TCP is negligible for oxygenated head and neck and non‐small cell lung tumors treated with conventional fractionation. According to our simulations, the volume effects in the TCP observed in clinical studies are defined primarily by the hypoxic volume. This information can be useful for the analysis of treatment outcomes and the dose escalation to target tumor hypoxia.

Purpose:To develop a tumor response model which could be uses to compute tumor hypoxic fraction using serial volumetric tumor This algorithm may be used for treatment response assessment and also for guidance of more expensive PET of hypoxia.Methods:Previously developed two-level cell population tumor response model was modified to include a third cell level describing hypoxic and necrotic cells. This third level was considered constant value during radiotherapy treatment; therefore, inclusion additional parameter did not compromise stability of model fitting to data. Fitting the model to serial volumetric data was performed using a least squares objective function and simulated annealing algorithm. The problem of reconstruction of radiobiological parameters from serial data was considered as inverse ill-posed problem described by the Fredholm integral equation of the first kind. Variational regularization was used to stabilize solutions.Results:To evaluate performance of the algorithm, we used a set of serial CT imaging data on tumor-volume for 14 head and neck cancer patients. The hypoxic fractions were reconstructed for each patient and the distribution of hypoxic fractions was compared to the distribution of initial hypoxic fractions previously measured using histograph. The measured and reconstructed from data distributions of hypoxic fractions are in good agreement. The reconstructed distribution of cell surviving fraction was also in better agreement with in vitro data than previously obtained using the two-level cell population model.Conclusion:Our results indicate that it is possible to evaluate the initial hypoxic tumor fraction using serial volumetric and a tumor response model. This algorithm can be used for treatment response assessment and guidance of more expensive PET imaging.

Purpose:A standard tool for ensuring the quality of radiation therapy treatments is the initial physics plan review. However, little is known about its performance in practice. The goal of this study is to measure the effectiveness of physics plan review by introducing simulated errors into “mock” treatment plans and measuring the performance of plan review by physicists.Methods:We generated six mock treatment plans containing multiple errors. These errors were based on incident learning system data both within the department and internationally (SAFRON). These errors were scored for severity and frequency. Those with the highest scores were included in the simulations (13 errors total). Observer bias was minimized using a multiple co‐correlated distractor approach. Eight physicists reviewed these plans for errors, with each physicist reviewing, on average, 3/6 plans. The confidence interval for the proportion of errors detected was computed using the Wilson score interval.Results:Simulated errors were detected in 65% of reviews [51–75%] (95% confidence interval [CI] in brackets). The following error scenarios had the highest detection rates: incorrect isocenter in DRRs/CBCT (91% [73–98%]) and a planned dose different from the prescribed dose (100% [61–100%]). Errors with low detection rates involved incorrect field parameters in record and verify system (38%, [18–61%]) and incorrect isocenter localization in planning system (29% [8–64%]). Though pre‐treatment QA failure was reliably identified (100%), less than 20% of participants reported the error that caused the failure.Conclusion:This is one of the first quantitative studies of error detection. Although physics plan review is a key safety measure and can identify some errors with high fidelity, others errors are more challenging to detect. This data will guide future work on standardization and automation. Creating new checks or improving existing ones (i.e., via automation) will help in detecting those errors with low detection rates.

Purpose: To develop a tumor response model which could be uses to compute tumor hypoxic fraction using serial volumetric tumor imaging. This algorithm may be used for treatment response assessment and also for guidance of more expensive PET imaging of hypoxia. Methods: Previously developed two-level cell population tumor response model was modified to include a third cell level describing hypoxic and necrotic cells. This third level was considered constant value during radiotherapy treatment; therefore, inclusion additional parameter did not compromise stability of model fitting to imaging data. Fitting the model to serial volumetric imaging data was performed using a least squares objective function and simulated annealing algorithm. The problem of reconstruction of radiobiological parameters from serial imaging data was considered as inverse ill-posed problem described by the Fredholm integral equation of the first kind. Variational regularization was used to stabilize solutions. Results: To evaluate performance of the algorithm, we used a set of serial CT imaging data on tumor-volume for 14 head and neck cancer patients. The hypoxic fractions were reconstructed for each patient and the distribution of hypoxic fractions was compared to the distribution of initial hypoxic fractions previously measured using histograph. The measured and reconstructed from imaging data distributions of hypoxic fractions are in good agreement. The reconstructed distribution of cell surviving fraction was also in better agreement with in vitro data than previously obtained using the two-level cell population model. Conclusion: Our results indicate that it is possible to evaluate the initial hypoxic tumor fraction using serial volumetric imaging and a tumor response model. This algorithm can be used for treatment response assessment and guidance of more expensive PET imaging.

Purpose:Combination of serial tumor imaging with radiobiological modeling can provide more accurate information on the nature of treatment response and what underlies resistance. The purpose of this article is to improve the algorithms related to imaging‐based radiobilogical modeling of tumor response.Methods:Serial imaging of tumor response to radiation therapy represents a sum of tumor cell sensitivity, tumor growth rates, and the rate of cell loss which are not separated explicitly. Accurate treatment response assessment would require separation of these radiobiological determinants of treatment response because they define tumor control probability. We show that the problem of reconstruction of radiobiological parameters from serial imaging data can be considered as inverse ill‐posed problem described by the Fredholm integral equation of the first kind because it is governed by a sum of several exponential processes. Therefore, the parameter reconstruction can be solved using regularization methods.Results:To study the reconstruction problem, we used a set of serial CT imaging data for the head and neck cancer and a two‐level cell population model of tumor response which separates the entire tumor cell population in two subpopulations of viable and lethally damage cells. The reconstruction was done using a least squared objective function and a simulated annealing algorithm. Using in vitro data for radiobiological parameters as reference data, we shown that the reconstructed values of cell surviving fractions and potential doubling time exhibit non‐physical fluctuations if no stabilization algorithms are applied. The variational regularization allowed us to obtain statistical distribution for cell surviving fractions and cell number doubling times comparable to in vitro data.Conclusion:Our results indicate that using variational regularization can increase the number of free parameters in the model and open the way to development of more advanced algorithms which take into account tumor heterogeneity, for example, related to hypoxia.

Purpose:To show that a distribution of cell surviving fractions S2 in a heterogeneous group of patients can be derived from tumor‐volume variation curves during radiotherapy for non‐small cell lung cancer.Methods:Our analysis was based on two data sets of tumor‐volume variation curves for heterogeneous groups of 17 patients treated for nonsmall cell lung cancer with conventional dose fractionation. The data sets were obtained previously at two independent institutions by using megavoltage (MV) computed tomography (CT). Statistical distributions of cell surviving fractions S2 and cell clearance half‐lives of lethally damaged cells T1/2 have been reconstructed in each patient group by using a version of the two‐level cell population tumor response model and a simulated annealing algorithm. The reconstructed statistical distributions of the cell surviving fractions have been compared to the distributions measured using predictive assays in vitro.Results:Non‐small cell lung cancer presents certain difficulties for modeling surviving fractions using tumor‐volume variation curves because of relatively large fractional hypoxic volume, low gradient of tumor‐volume response, and possible uncertainties due to breathing motion. Despite these difficulties, cell surviving fractions S2 for non‐small cell lung cancer derived from tumor‐volume variation measured at different institutions have similar probability density functions (PDFs) with mean values of 0.30 and 0.43 and standard deviations of 0.13 and 0.18, respectively. The PDFs for cell surviving fractions S2 reconstructed from tumor volume variation agree with the PDF measured in vitro. Comparison of the reconstructed cell surviving fractions with patient survival data shows that the patient survival time decreases as the cell surviving fraction increases.Conclusion:The data obtained in this work suggests that the cell surviving fractions S2 can be reconstructed from the tumor volume variation curves measured during radiotherapy with conventional fractionation. The proposed method can be used for treatment evaluation and adaptation.

Purpose:To evaluate uncertainties of cell surviving fraction reconstructed from tumor‐volume variation curves during radiation therapy using sensitivity analysis based on linear perturbation theory.Methods:The time dependent tumor‐volume functions V(t) have been calculated using a twolevel cell population model which is based on the separation of entire tumor cell population in two subpopulations: oxygenated viable and lethally damaged cells. The sensitivity function is defined as S(t)=[δV(t)/V(t)]/[δx/x] where δV(t)/V(t) is the time dependent relative variation of the volume V(t) and δx/x is the relative variation of the radiobiological parameter x. The sensitivity analysis was performed using direct perturbation method where the radiobiological parameter x was changed by a certain error and the tumor‐volume was recalculated to evaluate the corresponding tumor‐volume variation. Tumor volume variation curves and sensitivity functions have been computed for different values of cell surviving fractions from the practically important interval S2=0.1‐0.7 using the two‐level cell population model.Results:The sensitivity functions of tumor‐volume to cell surviving fractions achieved a relatively large value of 2.7 for S2=0.7 and then approached zero as S2 is approaching zero Assuming a systematic error of 3‐4% we obtain that the relative error in S2 is less that 20% in the range S2=0.4‐0.7. This Resultis important because the large values of S2 are associated with poor treatment outcome should be measured with relatively small uncertainties. For the very small values of S2<0.3, the relative error can be larger than 20%; however, the absolute error does not increase significantly.Conclusion:Tumor‐volume curves measured during radiotherapy can be used for evaluation of cell surviving fractions usually observed in radiation therapy with conventional fractionation.

PURPOSE:Volumetric tumor response to radiotherapy is an integrated process which includes several radiobiological mechanisms, such as cell killing, cell proliferation, dead-cell removal and tumor reoxygenation. Our goal is to reconstruct the information about these underlying radiobiological processes and specifically the cell survival fractions by fitting a 2-level cell-population tumor-volume model to imaging-derived tumor-volume variation curves obtained during radiotherapy for head-and-neck cancer.METHODS:Modeling tumor-volume during radiotherapy is a challenging problem because it is described by a sum of exponentials; therefore, the problem of accurately fitting a model to measured data is ill-posed. As an initial point of this research, we utilize a simplest 2-level cell-population tumor-volume model which separates the entire tumor-cell population into oxygenated viable cells and oxygenated lethally damaged cells. The 2-level cell population tumor model has the advantage of being conditionally well-posed. We integrated this parameterized radiobiological model with a least squares objective function and a simulated annealing optimization algorithm to characterize individual patients' time-dependent tumor-volume regression rates. The measured tumor-volume variation curves were taken from a clinical study on tumor-volume variation during radiotherapy for 14 head-and-neck cancer patients in which an integrated CT/linac system was used for tumor-volume measurements.RESULTS:The 2-level tumor volume modeling is able to predict tumor behavior throughout an entire treatment for 8 of 14 patients. The average survival fraction 0.44 agrees very well with the published survival fraction of 0.45 for the head-and-neck squamous cell carcinoma. However, the 2-level model cannot describe the variation of the cell disintegration rate which is observed at the end of treatment for some of the head-and-neck cancer patients.CONCLUSIONS:The 2-level cell population model is an acceptable approximation for the tumor-volume for some clinical cases, but it cannot describe all tumor-volume regression cases. This may be explained by omitting hypoxia in the 2-level model.

PURPOSEIn vivo dosimetry (IVD) assessment of treatment dose is important when delivering total body irradiation (TBI). One method is to average AP and PA surface diode measurements and compare them to prescribed midline doses. We designed phantom studies to examine the impact of patient thickness on surface IVD measurements under TBI conditions.METHODSPhantom studies were designed to assess the effects of patient thickness on diode IVD. Sun Nuclear QED diodes with inherent buildup were placed on anterior and posterior surfaces of a solid water phantom. Phantom thickness was varied between 20 and 40 cm. A PTW farmer chamber was inserted in the center of the phantom at 425 SSD to reflect prescribed midline dose, and 50 cGy was delivered to midline with 18 MV photons. Averaged entrance and exit diode doses were then compared to farmer chamber measurements of phantom midline dose.RESULTSA trend of increased deviation with increasing umbilicus thickness was observed between averaged surface diodes and midline farmer chamber measurements. Averaged surface diode dose ranged from 49.6 cGy (20 cm thickness) to 52.1 cGy (40 cm thickness). Interpolation of diode measurements to midline resulted in linear overestimation of delivered dose relative to farmer chamber measurements at midline, up to 6.8% at 40 cm umbilicus thickness.CONCLUSIONAccurate in vivo dosimetry at time of patient TBI is important to allow individual correction of MU exposure and tissue compensation. Without patient thickness correction, overresponse of surface diodes may lead to unnecessary clinical intervention to treatment MU or compensation and insufficient midline dose. Additionally, SAD setup is preferable to SSD setup to minimize thickness non-linearity. In conclusion, thickness correction factors should be used to generate expected diode readings for patients with thickness greater than 30 cm.

Purpose: To develop a technique for proton beam dose simulation in a random medium where geometry or density may change stochastically. An example of such a random medium can be found in a rectum during fractionated proton therapy for prostate cancer because of air bubbles of random size and location. Method and Materials: The proton range in a random medium can be considered as a random parameter. The distribution of random proton ranges is given by the probability density function (PDF). The total dose distribution during fractionated radiotherapy may be described by a sample range PDF if we assume that the each fractional radiotherapy treatment is a single statistical trial. To verify this hypothesis we have computed the range PDFs in the random medium which simulates the proton beam transport through the rectum. The rectum was simulated as a cylindrical region with an air bubble randomly placed in the upper semicircle. A random number generator was utilized to simulate the random bubble location and radius. The range of a 200 MeV monoenegetic proton beam was computed using continuous slowing down approximation. Results: We have computed the proton range PDF in the model rectum problem using different number of histories. The range PDF consists of two henor parts describing the total probability notto hit the bubble. and total probability not to hit the bubble. The convergence of the range PDF in the “hit bubble” region was seen at 1000 histories; however, even with 40 histories the PDF shape can be predicted. The depth-dose distributions in the “hit bubble” region agree within 10% for converged PDF and sample PDFs with 40 histories. Conclusions: The proton range PDF in a random medium as rectum with air bubbles can be potentially used for evaluation of total dose distributions in fractionated proton therapy.

Purpose: To evaluate the uncertainty of computed proton range in radiotherapy treatment planning which is attributed to random component in CT numbers. Method and Materials: We utilize a random number generator to simulate a white Gaussian noise in CT numbers along the proton pathlength. The proton range is computed using continuous slowing down approximation which is valid for most of proton range. To simulate the statistical straggling of computed proton range, this procedure is iteratively repeated to obtain convergence of proton range PDF which is approaching a Gaussian. The FWHM (full-width at half maximum) of the range PDF is used as a measure of uncertainty. Results: We investigate parameters which affect the proton range uncertainty in the presence of CT image noise. These parameters may include 1) initial proton energy, 2) noise period and 3) noise amplitude. The FWHM of range PDF increases linearly with the noise period. These results indicate that low frequency fluctuations in CT image noise can significantly increase the range uncertainty. We have also computed the range PDF as a function of initial proton energy. The FWHM of range PDF increases linearly with the initial proton energy. For the maximum proton energy of 250 MeV, the FWHM of proton range PDF can achieve a value of 5 mm in the presence of CT image noise. We note that the ratio FWHM/range increases as the proton range decreases; therefore, the relative range uncertainty is larger for smaller ranges. Conclusions: Range uncertainties due to CT image noise can be significant and comparable to the uncertainties attributed to the calibration of CT numbers. The relative range uncertainty increases as the range decreases. Noise reduction in CT images using smoothing and denoising algorithms can be recommended to reduce the standard deviation of range PDF.

Purpose: To validate the four‐level population tumor model using tumor volumetric changes obtained using on‐board imaging techniques during fractionated radiotherapy for non‐small‐cell lung cancer. Method and Materials: The four‐level population tumor model is based on separation of tumor cell population into four subpopulations: 1) oxygenated viable cells, 2) oxygenated lethally damaged cells, 3) hypoxic viable cells, and 4) hypoxic lethally damaged cells. The oxygenated lethally damaged cells are removed from tumor using an exponential decay model. The hypoxic lethally damaged cells stay in tumor for unlimited time; therefore, their removal is governed by reoxygenation process. The model utilizes the following six radiobiological parameters: alpha, beta, potential doubling time Tpot, half‐life T1/2 of lethally damaged cells, initial hypoxic fraction R and reoxygenation rate A. To test the model, we use the clinical data on volumetric tumor changes during fractionated radiotherapy for non‐small‐cell lung cancer obtained using Tomotherapy and Cone‐Beam CT at different institutions. Results: Our preliminary data indicate that adenocarcinoma and squamous cell carcinoma demonstrate different rate of tumor volume variation after irradiation; therefore only cases have been selected where adenocarcinoma o squamous cell carcinoma diagnosis was available. Another problem of accurate tumor‐volume simulation for lung tumors is a significant hypoxic tumor fraction according to the experimental data obtained using fluoromisonidazole PET imaging. The hypoxic tumor fraction can be between 1.3% and 94.7.9% with a median value of 47.6%. Our model with average values of radiobiological parameters describes majority of lung squamous carcinoma cases. However, significant discrepancies have been observed between the model and clinical data for lung adenocarcinoma. Conclusions: The proposed radiobiological model with average values of parameters can be used for simulation of tumor‐volume for lung squamous cell carcinoma with acceptable accuracy. However, this approach does not describe the tumor volume variation for significant fraction of lung adenocarcinoma cases.

Purpose: To develop a fast computational radiobiological model for qualitative and quantitative analysis of tumor volume variation during fractionated radiotherapy. This model can be used in 4D treatment planning for evaluation of dose variations due to time-dependent density variations in highly conformal radiotherapeutic modalities as IMRT and proton therapy. Method and Materials: The analysis is performed using two approximations: 1) tumor volume is a linear function of total cell number in tumor and 2) tumor cell population is separated into four subpopulations: oxygenated live and dead cells and hypoxic live and dead cells. The “dead” cells are lethally damaged by radiation and not able to proliferate; however, they stay in the tumor and contribute to the tumor volume until they disintegrate and their debris is removed. The number of living oxygenated and hypoxic cells is governed by the radiobiological mechanisms as LQ survival model, exponential repopulation and reoxygenation. The oxygenated dead cells are removed from the tumor using an exponential decay model. Results: We have computed tumor volume variation during fractionated radiotherapy for the head-and-neck cancer. The computational results have been compared to the clinical data previously obtained for the head-and-neck cancer using an integrated CT/linear accelerator system. We show that the model predicts the tumor volume variation for the majority of head-and-neck cases. Largest discrepancies between the model and clinical data are obtained during the first days of treatment. Conclusion: The tumor volume during radiotherapy can be qualitatively described using a relatively simple radiobiological model. The potential impact on the tumor volume of other radiobiological processes which have not been included into the current model as cell cycle analysis, accelerated repopulation and chemotherapy should be studied in the future. Research sponsored by Elekta corporation.

The purpose of this study is to evaluate and compare image quality characteristics for two commonly used and commercially available CBCT systems: the X‐ray Volumetric Imager and the On‐Board Imager. A commonly used CATPHAN image quality phantom was used to measure various image quality parameters, namely, pixel value stability and accuracy, noise, contrast to noise ratio (CNR), high‐contrast resolution, low contrast resolution and image uniformity. For the XVI unit, we evaluated the image quality for four manufacturer‐supplied protocols as a function of mAs. For the OBI unit, we did the same for the full‐fan and half‐fan scanning modes, which were respectively used with the full bow‐tie and half bow‐tie filters. For XVI, the mean pixel values of regions of interest were found to generally decrease with increasing mAs for all protocols, while they were relatively stable with mAs for OBI. Noise was slightly lower on XVI and was seen to decrease with increasing mAs, while CNR increased with mAs for both systems. For XVI and OBI, the high‐contrast resolution was approximately limited by the pixel resolution of the reconstructed image. On OBI images, up to 6 and 5 discs of 1% and 0.5% contrast, respectively, were visible for a high mAs setting using the full‐fan mode, while none of the discs were clearly visible on the XVI images for various mAs settings when the medium resolution reconstruction was used. In conclusion, image quality parameters for XVI and OBI have been quantified and compared for clinical protocols under various mAs settings. These results need to be viewed in the context of a recent study that reported the dose‐mAs relationship for the two systems and found that OBI generally delivered higher imaging doses than XVI.(1)PACS numbers: 85.57.C‐, 85.57.cj, 85.57.cm, 85.57.cf

Purpose: To evaluate image quality on the X‐ray Volumetric Imager (XVI®, Elekta Medical Systems) and the On‐Board Imager (OBI®, Varian Medical Systems) using a CatPhan® phantom in a single institution setting. Method and Materials: We evaluated four major image quality indices, including high and low contrast resolution, noise, and contrast‐to‐noise (CNR) ratio. For the XVI unit, the four manufacturer‐supplied protocols were measured. For the OBI unit, full bow‐tie and half bow‐tie filters were used in combination with the “full‐fan” and “half‐fan” modes. The mAs was varied for each protocol. High contrast resolution was evaluated using number of line pairs visible per cm and low contrast resolution was evaluated using the visibility of low resolution disks. Noise was computed over circular regions of interest (ROIs) on the uniformity module. CNR was calculated using a polystyrene insert and the background of module CTP404. The images were analyzed using MATLAB. Results: Up to 10 line pairs per cm are visible on OBI for high mAs settings and so are most low contrast discs. 2 line pairs per cm and none of the low contrast discs are visible on XVI. Noise values fall from 35 to 6 on OBI and vary between 10 and 3 for “prostate” protocol on XVI with increasing mAs. On OBI, CNR steadily increased from 4 to 20 with increasing mAs. For the “prostate” protocol on XVI, CNR varies from 10 to 23 and generally increases with mAs. For the four XVI protocols evaluated, mean pixel values in ROIs are found to decrease with mAs. Conclusion: Image quality parameters are generally found to be better on OBI as compared with XVI for clinical protocols. However, this is important to be viewed in the context of the observation that OBI generally delivered higher doses than XVI.Research sponsored by Elekta Inc.