Optimal radiation beam profiles considering uncertainties in beam patient alignment

Study of Asymmetric Margins in Prostate Cancer Radiation Therapy Using Fuzzy Logic

PURPOSE

The purpose of present study is to estimate asymmetric margins of prostate target volume based on biological limitations with help of knowledge based fuzzy logic considering the effect of organ motion and setup errors.

MATERIALS AND METHODS

A novel application of fuzzy logic modelling technique considering radiotherapy uncertainties including setup, delineation and organ motion was used in this study to derive margins. The new margin was applied in prostate cancer treatment planning and the results compared very well to current techniques Here volumetric modulated arc therapy treatment plans using stepped increments of asymmetric margins of planning target volume (PTV) were performed to calculate the changes in prostate radiobiological indices and results were used to formulate the rule based and membership function for Mamdani-type fuzzy inference system. The optimum fuzzy rules derived from input data, the clinical goals and knowledge-based conditions imposed on the margin limits. The PTV margin obtained using the fuzzy model was compared to the commonly used margin recipe.

RESULTS

For total displacement standard errors ranging from 0 to 5 mm the fuzzy PTV margin was found to be up to 0.5 mm bigger than the vanHerk derived margin, however taking the modelling uncertainty into account results in a good match between the PTV margin calculated using our model and the one based on van Herk et al. formulation for equivalent errors of up to 5 mm standard deviation (s. d.) at this range. When the total displacement standard errors exceed 5 mm s. d., the fuzzy margin remained smaller than the van Herk margin.

CONCLUSION

The advantage of using knowledge based fuzzy logic is that a practical limitation on the margin size is included in the model for limiting the dose received by the critical organs. It uses both physical and radiobiological data to optimize the required margin as per clinical requirement in real time or adaptive planning, which is an improvement on most margin models which mainly rely on physical data only.

Dosimetric and Radiobiological Evaluation of Patient Setup Accuracy in Head-and-neck Radiotherapy Using Daily Computed Tomography-on-rails-based Corrections

Introduction:

This study evaluates treatment plans aiming at determining the expected impact of daily patient setup corrections on the delivered dose distribution and plan parameters in head-and-neck radiotherapy.

Materials and Methods:

In this study, 10 head-and-neck cancer patients are evaluated. For the evaluation of daily changes of the patient internal anatomy, image-guided radiation therapy based on computed tomography (CT)-on-rails was used. The daily-acquired CT-on-rails images were deformedly registered to the CT scan that was used during treatment planning. Two approaches were used during data analysis (“cascade” and “one-to-all”). The dosimetric and radiobiological differences of the dose distributions with and without patient setup correction were calculated. The evaluation is performed using dose–volume histograms; the biologically effective uniform dose () and the complication-free tumor control probability (P₊) were also calculated. The dose–response curves of each target and organ at risk (OAR), as well as the corresponding P₊ curves, were calculated.

Results:

The average difference for the “one-to-all” case is 0.6 ± 1.8 Gy and for the “cascade” case is 0.5 ± 1.8 Gy. The value of P₊ was lowest for the cascade case (in 80% of the patients).

Discussion:

Overall, the lowest P_I is observed in the one-to-all cases. Dosimetrically, CT-on-rails data are not worse or better than the planned data.

Conclusions:

The differences between the evaluated “one-to-all” and “cascade” dose distributions were small. Although the differences of those doses against the “planned” dose distributions were small for the majority of the patients, they were large for given patients at risk and OAR.

Beyond the margin recipe: the probability of correct target dosage and tumor control in the presence of a dose limiting structure

In the past, hypothetical spherical target volumes and ideally conformal dose distributions were analyzed to establish the safety of planning target volume (PTV) margins. In this work we extended these models to estimate how alternative methods of shaping dose distributions could lead to clinical improvements. Based on a spherical clinical target volume (CTV) and Gaussian distributions of systematic and random geometrical uncertainties, idealized 3D dose distributions were optimized to exhibit specific stochastic properties. A nearby spherical organ at risk (OAR) was introduced to explore the benefit of non-spherical dose distributions. Optimizing for the same minimum dose safety criterion as implied by the generally accepted use of a PTV, the extent of the high dose region in one direction could be reduced by half provided that dose in other directions is sufficiently compensated. Further reduction of this unilateral dosimetric margin decreased the target dose confidence, however the actual minimum CTV dose at 90% confidence typically exceeded the minimum PTV dose by 20% of prescription. Incorporation of smooth dose-effect relations within the optimization led to more concentrated dose distributions compared to the use of a PTV, with an improved balance between the probability of tumor cell kill and the risk of geometrical miss, and lower dose to surrounding tissues. Tumor control rate improvements in excess of 20% were found to be common for equal integral dose, while at the same time evading a nearby OAR. These results were robust against uncertainties in dose-effect relations and target heterogeneity, and did not depend on 'shoulders' or 'horns' in the dose distributions.

A new deconvolution approach to robust fluence for intensity modulation under geometrical uncertainty

This work addresses random geometrical uncertainties that are intrinsically observed in radiation therapy by means of a new deconvolution method combining a series expansion and a Butterworth filter. The method efficiently suppresses high-frequency components by discarding the higher order terms of the series expansion and then filtering out deviations on the field edges. An additional approximation is made in order to set the fluence values outside the field to zero in the robust profiles. This method is compared to the deconvolution kernel method for a regular 2D fluence map, a real intensity-modulated radiation therapy field, and a prostate case. The results show that accuracy is improved while fulfilling clinical planning requirements.

Radiobiological and Dosimetric Analysis of Daily Megavoltage CT Registration on Adaptive Radiotherapy with Helical Tomotherapy

Pre-treatment patient repositioning in highly conformal image-guided radiation therapy modalities is a prerequisite for reducing setup uncertainties. In Helical Tomotherapy (HT) treatment, a megavoltage CT (MVCT) image is usually acquired to evaluate daily changes in the patient's internal anatomy and setup position. This MVCT image is subsequently compared to the kilovoltage CT (kVCT) study that was used for dosimetric planning, by applying a registration process. This study aims at investigating the expected effect of patient setup correction using the Hi-Art tomotherapy system by employing radiobiological measures such as the biologically effective uniform dose ([Formula: see text]) and the complication-free tumor control probability ( P+). A new module of the Tomotherapy software (TomoTherapy, Inc, Madison, WI) called Planned Adaptive is employed in this study. In this process the delivered dose can be calculated by using the sinogram for each delivered fraction and the registered MVCT image set that corresponds to the patient's position and anatomical distribution for that fraction. In this study, patients treated for lung, pancreas and prostate carcinomas are evaluated by this method. For each cancer type, a Helical Tomotherapy plan was developed. In each cancer case, two dose distributions were calculated using the MVCT image sets before and after the patient setup correction. The fractional dose distributions were added and renormalized to the total number of fractions planned. The dosimetric and radiobiological differences of the dose distributions with and without patient setup correction were calculated. By using common statistical measures of the dose distributions and the P+ and [Formula: see text] concepts and plotting the tissue response probabilities vs. [Formula: see text] a more comprehensive comparison was performed based on radiobiological measures. For the lung cancer case, at the clinically prescribed dose levels of the dose distributions, with and without patient setup correction, the complication-free tumor control probabilities, P+ are 48.5% and 48.9% for a [Formula: see text] of 53.3 Gy. The respective total control probabilities, PB are 56.3% and 56.5%, whereas the corresponding total complication probabilities, PI are 7.9% and 7.5%. For the pancreas cancer case, at the prescribed dose levels of the two dose distributions, the P+ values are 53.7% and 45.7% for a [Formula: see text] of 54.7 Gy and 53.8 Gy, respectively. The respective PB values are 53.7% and 45.8%, whereas the corresponding PI values are ~0.0% and 0.1%. For the prostate cancer case, at the prescribed dose levels of the two dose distributions, the P+ values are 10.9% for a [Formula: see text] of 75.2 Gy and 11.9% for a [Formula: see text] of 75.4 Gy, respectively. The respective PB values are 14.5% and 15.3%, whereas the corresponding PI values are 3.6% and 3.4%. Our analysis showed that the very good daily patient setup and dose delivery were very close to the intended ones. With the exception of the pancreas cancer case, the deviations observed between the dose distributions with and without patient setup correction were within ±2% in terms of P+. In the radiobiologically optimized dose distributions, the role of patient setup correction using MVCT images could appear to be more important than in the cases of dosimetrically optimized treatment plans were the individual tissue radiosensitivities are not precisely considered.

Intensity modulation under geometrical uncertainty: a deconvolution approach to robust fluence

A deconvolution algorithm has been developed to obtain robust fluence for external beam radiation treatment under geometrical uncertainties. Usually, the geometrical uncertainty is incorporated in the dose optimization process for inverse treatment planning to determine the additional intensity modulation of the beam to counter the geometrical uncertainty. Most of these approaches rely on dose convolution which is subject to the error caused by patient surface curvature and internal inhomogeneity. In this work, based on an 1D deconvolution algorithm developed by Ulmer and Kaissl, a fluence-deconvolution approach was developed to obtain robust fluence through the deconvolution of the nominal static one given by any treatment planning system. It incorporates the geometrical uncertainty outside the dose optimization procedure and therefore avoids the error of dose convolution. Robust fluences were calculated for a 4 x 4 cm flat field, a prostate IMRT and a head and neck IMRT plan in a commercial treatment planning system. The corresponding doses were simulated for 30 fractions with the random Gaussian distribution of the iso-centers showing good agreement with the nominal static doses. The feasibility of this deconvolution approach for clinical IMRT planning has been demonstrated. Because it is separated from the optimization procedure, this method is more flexible and easier to integrate into different existing treatment planning systems to obtain robust fluence.

Optimal margin and edge-enhanced intensity maps in the presence of motion and uncertainty

In radiation therapy, intensity maps involving margins have long been used to counteract the effects of dose blurring arising from motion. More recently, intensity maps with increased intensity near the edge of the tumour (edge enhancements) have been studied to evaluate their ability to offset similar effects that affect tumour coverage. In this paper, we present a mathematical methodology to derive margin and edge-enhanced intensity maps that aim to provide tumour coverage while delivering minimum total dose. We show that if the tumour is at most about twice as large as the standard deviation of the blurring distribution, the optimal intensity map is a pure scaling increase of the static intensity map without any margins or edge enhancements. Otherwise, if the tumour size is roughly twice (or more) the standard deviation of motion, then margins and edge enhancements are preferred, and we present formulae to calculate the exact dimensions of these intensity maps. Furthermore, we extend our analysis to include scenarios where the parameters of the motion distribution are not known with certainty, but rather can take any value in some range. In these cases, we derive a similar threshold to determine the structure of an optimal margin intensity map.

Expected clinical impact of the differences between planned and delivered dose distributions in helical tomotherapy for treating head and neck cancer using helical megavoltage CT images

Helical Tomotherapy (HT) has become increasingly popular over the past few years. However, its clinical efficacy and effectiveness continues to be investigated. Pre-treatment patient repositioning in highly conformal image-guided radiation therapy modalities is a prerequisite for reducing setup uncertainties. A MVCT image set has to be acquired to account for daily changes in the patient's internal anatomy and setup position. Furthermore, a comparison should be performed to the kVCT study used for dosimetric planning, by a registration process which results in repositioning the patient according to specific transitional and rotational shifts. Different image registration techniques may lead to different repositioning of the patient and, as a result, to varying delivered doses. This study aims to investigate the expected effect of patient setup correction using the Hi-Art tomotherapy system by employing radiobiological measures such as the biologically effective uniform dose (BEUD) and the complication-free tumor control probability (P+). In this study, a typical case of lung cancer with metastatic head & neck disease was investigated by developing a Helical Tomotherapy plan. For the Tomotherapy HiArt plan, the dedicated Tomotherapy treatment planning station was used. Three dose distributions (planned and delivered with and without patient setup correction) were compared based on radiobiological measures by using the P+ index and the BEUD concept as the common prescription point of the plans and plotting the tissue response probabilities against the mean target dose for a range of prescription doses. The applied plan evaluation method shows that in this cancer case the planned and delivered dose distributions with and without patient setup correction give a P+ of 81.6%, 80.9% and 72.2%, for a BEUD to the planning target volume (PTV) of 78.0Gy, 77.7Gy and 75.4Gy, respectively. The corresponding tumor control probabilities are 86.3%, 85.1% and 75.1%, whereas the total complication probabilities are 4.64%, 4.20% and 2.89%, respectively. HT can encompass the often large PTV required while minimizing the volume of the organs at risk receiving high dose. However, the effectiveness of a HT treatment plan can be considerably deteriorated if an accurate patient setup system is not available. Taking into account the dose-response relations of the irradiated tumors and normal tissues, a radiobiological treatment plan evaluation can be performed, which may provide a closer association of the delivered treatment with the clinical outcome. In such situations, for effective evaluation and comparison of different treatment plans, traditional dose based evaluation tools can be complemented by the use of P+,BEUD diagrams.

The use of spatial dose gradients and probability density function to evaluate the effect of internal organ motion for prostate IMRT treatment planning

The aim of this study is to investigate the effects of internal organ motion on IMRT treatment planning of prostate patients using a spatial dose gradient and probability density function. Spatial dose distributions were generated from a Pinnacle3 planning system using a co-planar, five-field intensity modulated radiation therapy (IMRT) technique. Five plans were created for each patient using equally spaced beams but shifting the angular displacement of the beam by 15 degree increments. Dose profiles taken through the isocentre in anterior-posterior (A-P), right-left (R-L) and superior-inferior (S-I) directions for IMRT plans were analysed by exporting RTOG file data from Pinnacle. The convolution of the 'static' dose distribution D0(x, y, z) and probability density function (PDF), denoted as P(x, y, z), was used to analyse the combined effect of repositioning error and internal organ motion. Organ motion leads to an enlarged beam penumbra. The amount of percentage mean dose deviation (PMDD) depends on the dose gradient and organ motion probability density function. Organ motion dose sensitivity was defined by the rate of change in PMDD with standard deviation of motion PDF and was found to increase with the maximum dose gradient in anterior, posterior, left and right directions. Due to common inferior and superior field borders of the field segments, the sharpest dose gradient will occur in the inferior or both superior and inferior penumbrae. Thus, prostate motion in the S-I direction produces the highest dose difference. The PMDD is within 2.5% when standard deviation is less than 5 mm, but the PMDD is over 2.5% in the inferior direction when standard deviation is higher than 5 mm in the inferior direction. Verification of prostate organ motion in the inferior directions is essential. The margin of the planning target volume (PTV) significantly impacts on the confidence of tumour control probability (TCP) and level of normal tissue complication probability (NTCP). Smaller margins help to reduce the dose to normal tissues, but may compromise the dose coverage of the PTV. Lower rectal NTCP can be achieved by either a smaller margin or a steeper dose gradient between PTV and rectum. With the same DVH control points, the rectum has lower complication in the seven-beam technique used in this study because of the steeper dose gradient between the target volume and rectum. The relationship between dose gradient and rectal complication can be used to evaluate IMRT treatment planning. The dose gradient analysis is a powerful tool to improve IMRT treatment plans and can be used for QA checking of treatment plans for prostate patients.

Evaluation of the reproducibility of lung motion probability distribution function (PDF) using dynamic MRI

Treatment planning based on probability distribution function (PDF) of patient geometries has been shown a potential off-line strategy to incorporate organ motion, but the application of such approach highly depends upon the reproducibility of the PDF. In this paper, we investigated the dependences of the PDF reproducibility on the imaging acquisition parameters, specifically the scan time and the frame rate. Three healthy subjects underwent a continuous 5 min magnetic resonance (MR) scan in the sagittal plane with a frame rate of approximately 10 f s-1, and the experiments were repeated with an interval of 2 to 3 weeks. A total of nine pulmonary vessels from different lung regions (upper, middle and lower) were tracked and the dependences of their displacement PDF reproducibility were evaluated as a function of scan time and frame rate. As results, the PDF reproducibility error decreased with prolonged scans and appeared to approach equilibrium state in subjects 2 and 3 within the 5 min scan. The PDF accuracy increased in the power function with the increase of frame rate; however, the PDF reproducibility showed less sensitivity to frame rate presumably due to the randomness of breathing which dominates the effects. As the key component of the PDF-based treatment planning, the reproducibility of the PDF affects the dosimetric accuracy substantially. This study provides a reference for acquiring MR-based PDF of structures in the lung.

Assessing the Difference between Planned and Delivered Intensity-modulated Radiotherapy Dose Distributions based on Radiobiological Measures

AIMS

Because of the highly conformal distributions that can be obtained with intensity-modulated radiotherapy (IMRT), any discrepancy between the intended and delivered distributions would probably affect the clinical outcome. Consequently, there is a need for a measure that would quantify those differences in terms of a change in the expected clinical outcome.

MATERIALS AND METHODS

To evaluate such a measure, cancer of the cervix was used, where the bladder and rectum are proximal and partially overlapping with the internal target volume. A solid phantom simulating the pelvic anatomy was fabricated and a treatment plan was developed to deliver the prescribed dose to the phantom. The phantom was then irradiated with films positioned in several transverse planes. The racetrack microtron at 50 MV was used in the treatment planning and delivery processes. The dose distribution delivered was analysed based on the film measurements and compared against the treatment plan. The differences in the measurements were evaluated using both physical and biological criteria. Whereas the physical comparison of dose distributions can assess the geometric accuracy of delivery, it does not reflect the clinical effect of any measured dose discrepancies.

RESULTS

It is shown how small inaccuracies in delivered dose can affect the treatment outcome in terms of complication-free tumour cure.

CONCLUSIONS

With highly conformal IMRT, the accuracy of the patient set-up and treatment delivery are critical for the success of the treatment. A method is proposed to evaluate the precision of the delivered plan based on changes in complication and control rates as they relate to uncertainties in dose delivery.

On probabilistically defined margins in radiation therapy

Margins about a target volume subject to external beam radiation therapy are designed to assure that the target volume of tissue to be sterilized by treatment is adequately covered by a lethal dose. Thus, margins are meant to guarantee that all potential variation in tumour position relative to beams allows the tumour to stay within the margin. Variation in tumour position can be broken into two types of dislocations, reducible and irreducible. Reducible variations in tumour position are those that can be accommodated with the use of modern image-guided techniques that derive parameters for compensating motions of patient bodies and/or motions of beams relative to patient bodies. Irreducible variations in tumour position are those random dislocations of a target that are related to errors intrinsic in the design and performance limitations of the software and hardware, as well as limitations of human perception and decision making. Thus, margins in the era of image-guided treatments will need to accommodate only random errors residual in patient setup accuracy (after image-guided setup corrections) and in the accuracy of systems designed to track moving and deforming tissues of the targeted regions of the patient's body. Therefore, construction of these margins will have to be based on purely statistical data. The characteristics of these data have to be determined through the central limit theorem and Gaussian properties of limiting error distributions. In this paper, we show how statistically determined margins are to be designed in the general case of correlated distributions of position errors in three-dimensional space. In particular, we show how the minimal margins for a given level of statistical confidence are found. Then, how they are to be used to determine geometrically minimal PTV that provides coverage of GTV at the assumed level of statistical confidence. Our results generalize earlier recommendations for statistical, central limit theorem-based recommendations for margin construction that were derived for uncorrelated distributions of errors (van Herk, Remeijer, Rasch and Lebesque 2000 Int. J. Radiat. Oncol. Biol. Phys. 47 1121-35; Stroom, De Boer, Huizenga and Visser 1999 Int. J. Radiat. Oncol. Biol. Phys. 43 905-19).

A new method of incorporating systematic uncertainties in intensity-modulated radiotherapy optimization

Uncertainties in tumor position during intensity-modulated radiotherapy (IMRT) plan optimization are usually accounted for by adding margins to a clinical target volume (CTV), or additionally, to organs at risk (OAR). The former approach usually favors target coverage over OAR protection, whereas the latter does not account for correlation in target and OAR movement. We investigate a new approach to incorporate systematic errors in tumor and organ position. The method models a distribution of systematic errors due to setup error and organ motion with displaced replicas of volumes of interest, each representing the patient geometry for a possible systematic error, and maximizes a score function that counts the number of replicas meeting dose or biological constraints for both CTV and OAR. Dose constraints are implemented by logistic functions of Niemierko's generalized model of equivalent uniform dose (EUD). The method is applied to prostate and nasopharynx IMRT plans, in which CTV and OAR each consists of five replicas, one representing no error (the position in the planning CT) and the other four discrete systematic setup displacements in one dimension with equal probability. The resulting IMRT plans are compared with those from two other EUD-based optimizations: a standard planning target volume (PTV) approach consisting of a single replica of each OAR in the planned position and a single PTV encompassing all CTV replicas, and a PTV-PRV approach consisting of a single PTV and a single planning risk volume (PRV) for each OAR encompassing all replicas. When systematic error is present, multiple-replica optimization provides better critical organ protection while maintaining similar target coverage compared with the PTV approach, and provides better CTV-to-OAR therapeutic ratio compared with the PTV-PRV instances where there is substantial PTV-PRV overlap. The method can be used for other systematic errors due to organ motion and deformation.

Incorporating organ movements in IMRT treatment planning for prostate cancer: Minimizing uncertainties in the inverse planning process

We investigate an off-line strategy to incorporate inter fraction organ movements in IMRT treatment planning. Nowadays, imaging modalities located in the treatment room allow for several CT scans of a patient during the course of treatment. These multiple CT scans can be used to estimate a probability distribution of possible patient geometries. This probability distribution can subsequently be used to calculate the expectation value of the delivered dose distribution. In order to incorporate organ movements into the treatment planning process, it was suggested that inverse planning could be based on that probability distribution of patient geometries instead of a single snapshot. However, it was shown that a straightforward optimization of the expectation value of the dose may be insufficient since the expected dose distribution is related to several uncertainties: first, this probability distribution has to be estimated from only a few images. And second, the distribution is only sparsely sampled over the treatment course due to a finite number of fractions. In order to obtain a robust treatment plan these uncertainties should be considered and minimized in the inverse planning process. In the current paper, we calculate a 3D variance distribution in addition to the expectation value of the dose distribution which are simultaneously optimized. The variance is used as a surrogate to quantify the associated risks of a treatment plan. The feasibility of this approach is demonstrated for clinical data of prostate patients. Different scenarios of dose expectation values and corresponding variances are discussed.

Incorporating organ movements in inverse planning: assessing dose uncertainties by Bayesian inference

We present a method to calculate dose uncertainties due to inter-fraction organ movements in fractionated radiotherapy, i.e. in addition to the expectation value of the dose distribution a variance distribution is calculated. To calculate the expectation value of the dose distribution in the presence of organ movements, one estimates a probability distribution of possible patient geometries. The respective variance of the expected dose distribution arises for two reasons: first, the patient is irradiated with a finite number of fractions only and second, the probability distribution of patient geometries has to be estimated from a small number of images and is therefore not exactly known. To quantify the total dose variance, we propose a method that is based on the principle of Bayesian inference. The method is of particular interest when organ motion is incorporated in inverse IMRT planning by means of inverse planning performed on a probability distribution of patient geometries. In order to make this a robust approach, it turns out that the dose variance should be considered (and minimized) in the optimization process. As an application of the presented concept of Bayesian inference, we compare three approaches to inverse planning based on probability distributions that account for an increasing degree of uncertainty. The Bayes theorem further provides a concept to interpolate between patient specific data and population-based knowledge on organ motion which is relevant since the number of CT images of a patient is typically small.

Inclusion of organ movements in IMRT treatment planning via inverse planning based on probability distributions

In this paper, we investigate an off-line strategy to incorporate inter-fraction organ motion in IMRT treatment planning. It was suggested that inverse planning could be based on a probability distribution of patient geometries instead of a single snap shot. However, this concept is connected to two intrinsic problems: first, this probability distribution has to be estimated from only a few images; and second, the distribution is only sparsely sampled over the treatment course due to a finite number of fractions. In the current work, we develop new concepts of inverse planning which account for these two problems.

Determination and clinical verification of dose-response parameters for esophageal stricture from head and neck radiotherapy

The purpose of this work is to determine the parameters and evaluate the predictive strength of the relative seriality model. This is accomplished by associating the calculated complication rates with the clinical follow-up records. The study is based on 82 patients who received radiation treatment for head and neck cancer. For each patient the 3D dose distribution delivered to the esophagus and the clinical treatment outcome were available. Clinical symptoms and radiological findings were used to assess the manifestation of radiation-induced esophageal strictures. These data were introduced into a maximum likelihood fitting to calculate the best estimates of the parameters used by the relative seriality model (D50 = 68.4 Gy, gamma = 6.55, s = 0.22). The uncertainties of these parameters were also calculated and their individual influence on the dose-response curve was demonstrated. The best estimate of the parameters was applied to 58 patients of the study material and their esophageal stricture induction probabilities were calculated to illustrate the clinical utilization of the calculated parameters. The calculation of the biological effective dose (BED) appeared to be significantly sensitive to the applied fractionation correction for complex treatment plans. The relative seriality model was proved suitable in reproducing the treatment outcome pattern of the patient material studied (probability of finding a worse fit = 61.0%, the area under the ROC curve = 0.84 and chi2 test = 0.95). The analysis was carried out for the upper 5 cm of the esophagus (proximal esophagus) where all the strictures are formed. Radiation-induced strictures were found to have a strong volume dependence (low relative seriality). The uncertainties of the parameters appear to have a significant supporting role on the estimated dose-response curve.

Limitations of a convolution method for modeling geometric uncertainties in radiation therapy. I. The effect of shift invariance

Convolution methods have been used to model the effect of geometric uncertainties on dose delivery in radiation therapy. Convolution assumes shift invariance of the dose distribution. Internal inhomogeneities and surface curvature lead to violations of this assumption. The magnitude of the error resulting from violation of shift invariance is not well documented. This issue is addressed by comparing dose distributions calculated using the Convolution method with dose distributions obtained by Direct Simulation. A comparison of conventional Static dose distributions was also made with Direct Simulation. This analysis was performed for phantom geometries and several clinical tumor sites. A modification to the Convolution method to correct for some of the inherent errors is proposed and tested using example phantoms and patients. We refer to this modified method as the Corrected Convolution. The average maximum dose error in the calculated volume (averaged over different beam arrangements in the various phantom examples) was 21% with the Static dose calculation, 9% with Convolution, and reduced to 5% with the Corrected Convolution. The average maximum dose error in the calculated volume (averaged over four clinical examples) was 9% for the Static method, 13% for Convolution, and 3% for Corrected Convolution. While Convolution can provide a superior estimate of the dose delivered when geometric uncertainties are present, the violation of shift invariance can result in substantial errors near the surface of the patient. The proposed Corrected Convolution modification reduces errors near the surface to 3% or less.

Limitations of a convolution method for modeling geometric uncertainties in radiation therapy. II. The effect of a finite number of fractions

Convolution methods can be used to model the effect of geometric uncertainties on the planned dose distribution in radiation therapy. This requires several assumptions, including that the patient is treated with an infinite number of fractions, each delivering an infinitesimally small dose. The error resulting from this assumption has not been thoroughly quantified. This is investigated by comparing dose distributions calculated using the Convolution method with the result of Stochastic simulations of the treatment. Additionally, the dose calculated using the conventional Static method, a Corrected Convolution method, and a Direct Simulation are compared to the Stochastic result. This analysis is performed for single beam, parallel opposed pair, and four-field box techniques in a cubic water phantom. Treatment plans for a simple and a complex idealized anatomy were similarly analyzed. The average maximum error using the Static method for a 30 fraction simulation for the three techniques in phantoms was 23%, 11% for Convolution, 10% for Corrected Convolution, and 10% for Direct Simulation. In the two anatomical examples, the mean error in tumor control probability for Static and Convolution methods was 7% and 2%, respectively, of the result with no uncertainty, and 35% and 9%, respectively, for normal tissue complication probabilities. Convolution provides superior estimates of the delivered dose when compared to the Static method. In the range of fractions used clinically, considerable dosimetric variations will exist solely because of the random nature of the geometric uncertainties. However, the effect of finite fractionation appears to have a greater impact on the dose distribution than plan evaluation parameters.

The theoretical benefit of beam fringe compensation and field size reduction for iso-normal tissue complication probability dose escalation in radiotherapy of lung cancer

To assess the benefit of beam fringe (50%-90% dose level) sharpening for lung tumors, we performed a numerical simulation in which all geometrical errors (breathing motion, random and systematic errors) are included. A 50 mm diameter lung tumor, located centrally in a lung-equivalent phantom was modeled. Treatment plans were designed with varying number and direction of beams, both with and without the use of intensity modulation to sharpen the beam fringe. Field size and prescribed dose were varied under the constraint of a constant mean lung dose of 20 Gy, which yields a predicted complication probability of about 10%. After numerical simulation of the effect of setup errors and breathing, the resulting dose distribution was evaluated using the minimum dose and the equivalent uniform dose (EUD) in the moving clinical target volume (CTV). When the dose in the CTV was constrained between 95% and 107% of the prescribed dose, the maximum attainable EUD was 71 Gy for a four-field noncoplanar technique with simple conformal beams. When penumbra sharpening was applied using a single beam segment at the edge of the open field, this EUD could be raised to 87 Gy. For a hypothetical infinitely steep penumbra, further escalation to an EUD of 104 Gy was possible. When the dose in the CTV was not constrained, a large escalation of the EUD was possible compared to the constrained case. In this case, the maximum attainable EUD for open fields was 115 Gy, using the four-field noncoplanar technique. The benefit of penumbra sharpening was only modest, with no increase of the EUD for the single-segment technique and a small increase to 125 Gy for the infinitely steep penumbra. From these results we conclude that beam fringe sharpening in combination with field-size reduction leads to a large increase in EUD when a homogeneous target dose is pursued. Further escalation of the EUD is possible when the homogeneity constrained is relaxed, but the relative benefit of beam-fringe sharpening then decreases.

Re-optimization in adaptive radiotherapy

In routine clinical practice, radiotherapy treatment planning is performed based on the patient CT images obtained during the patient setup procedure. However, the actual delivered dose to the patient might be different from the planned dose because of various reasons such as patient motion. Under such situations, it is desirable to modify the original treatment plan in order to partially remedy the dose delivery errors in the subsequent dose delivery process. Such modification can be implemented by modifying the original treatment plan using re-optimization. In this work, issues such as the re-optimization dose prescription, optimization constraints in re-optimization, re-optimization in multiple fractionation schemes and re-optimization procedure with generalized dose-based objective functions were investigated and corresponding mathematical schemes proposed. The derived results were applied to a clinical case study in which it was shown that the proposed re-optimization method is able to remedy the cold spots in tumour while delivering low dose to normal structures. Thus the potential effectiveness of the method was demonstrated.

Dose broadening due to target position variability during fractionated breath-held radiation therapy

Recent advances in Stereotactic Radiosurgery/Conformal Radiotherapy have made it possible to deliver surgically precise radiation therapy to small lesions while preserving the surrounding tissue. However, because of physiologic motion, the application of conformal radiotherapy to extra-cranial tumors is, at present, geared toward slowing the progression of disease rather than obtaining a cure. At the University of Rochester, we are investigating the use of patient breath-holding to reduce respiratory-derived motion in fractional radiotherapy. The primary targeting problem then becomes the small variation in tumor location over repeated breath-holds. This paper describes the effects of residual target position uncertainty on the dose distribution observed by small extra-cranial tumors and their neighboring tissues during fractional radiation treatment using breath holding. We employ two computational methods to study these effects: numerical analysis via Monte Carlo simulation and analytical computation using three-dimensional convolution. These methods are demonstrated on a 2-arc, 10-fraction treatment plan used to treat a representative lung tumor in a human subject. In the same human subject, the variability in position of a representative lung tumor was measured over repeated end-expiration breath-holds using volumetric imaging. For the 7 x 7 x 10 mm margin used to treat this 12 mm diameter tumor and the measured target position variability, we demonstrated that the entire tumor volume was irradiated to at least 48 Gy-well above the tumoricidal threshold. The advantages, in terms of minimizing the volume of surrounding lung tissue that is radiated to high dose during treatment, of using end-expiration breath holding compared with end-inspiration breath-holding are demonstrated using representative tumor size and position variability parameters. It is hoped that these results will ultimately lead to improved, if not curative, treatment for small (5-20 mm diameter) lung, liver, and other extra-cranial lesions.

[Physical and methodological aspects of multimodality imaging and principles of treatment planning in 3D conformal radiotherapy]

The recent evolutions of the imaging modalities, the dose calculation models, the linear accelerators and the portal imaging permit to improve the quality of the conformal radiation therapy treatment planning. With DICOM protocols, the acquired imaging data coming from different modalities are treated by performant image fusion algorithms and yield more precise target volumes and organs at risk. The transformation of the clinical target volumes (CTV) to planning target volumes (PTV) can be realised using advanced probabilistic techniques based on clinical experience. The treatment plans evaluation is based on the dose volume histograms. Their precision and clinical relevance are improved by the multi-modality imaging and the advanced dose calculation models. The introduction of the inverse planning systems permitting to realise modulated intensity radiation therapy generates highly conformal dose distributions. All the previously cited complex techniques require the application of rigorous quality assurance programs.

Using serial imaging data to model variabilities in organ position and shape during radiotherapy

A model is proposed for incorporating the effects of organ motion into the calculation of dose in a statistical fashion based on serial imaging measurements of organ motion. These measurements can either come from a previously studied population of patients, or they can be specific to the particular patient undergoing therapy. The statistical distribution underlying the measurements of organ motion, including the changes in organ shape, is reconstructed non-parametrically without requiring any assumptions about its functional form. The model is thus capable of simulating organ motions that are not present in the original measurements, yet nonetheless come from the same underlying statistical distribution. The present model overcomes two particular limitations of many organ motion models: (a) the fact that they do not account for changes in organ shape, and (b) the fact that they make physically unrealistic assumptions about the functional form of the statistical distribution of organ motion, such as assuming that it is Gaussian. The present model can form the foundation of methods for the more accurate and clinically relevant calculation of the dose to the target volume and normal tissues.

The effect of breathing and set-up errors on the cumulative dose to a lung tumor

BACKGROUND AND PURPOSE

To assess the impact of both set-up errors and respiration-induced tumor motion on the cumulative dose delivered to a clinical target volume (CTV) in lung, for an irradiation based on current clinically applied field sizes.

MATERIALS AND METHODS

A cork phantom, having a 50 mm spherically shaped polystyrene insertion to simulate a gross tumor volume (GTV) located centrally in a lung was irradiated with two parallel opposed beams. The planned 95% isodose surface was conformed to the planning target volume (PTV) using a multi leaf collimator. The resulting margin between the CTV and the field edge was 16 mm in beam's eye view. A dose of 70 Gy was prescribed. Dose area histograms (DAHs) of the central plane of the CTV (GTV+5 mm) were determined using radiographic film for different combinations of set-up errors and respiration-induced tumor motion. The DAHs were evaluated using the population averaged tumor control probability (TCP(pop)) and the equivalent uniform dose (EUD) model.

RESULTS

Compared with dose volume histograms of the entire CTV, DAHs overestimate the impact of tumor motion on tumor control. Due to the choice of field sizes a large part of the PTV will receive a too low dose resulting in an EUD of the central plane of the CTV of 68.9 Gy for the static case. The EUD drops to 68.2, 66.1 and 51.1 Gy for systematic set-up errors of 5, 10 and 15 mm, respectively. For random set-up errors of 5, 10 and 15 mm (1 SD), the EUD decreases to 68.7, 67.4 and 64.9 Gy, respectively. For similar amplitudes of respiration-induced motion, the EUD decreases to 68.8, 68.5 and 67.7 Gy, respectively. For a clinically relevant scenario of 7.5 mm systematic set-up error, 3 mm random set-up error and 5 mm amplitude of breathing motion, the EUD is 66.7 Gy. This corresponds with a tumor control probability TCP(pop) of 41.7%, compared with 50.0% for homogeneous irradiation of the CTV to 70 Gy.

CONCLUSION

Systematic set-up errors have a dominant effect on the cumulative dose to the CTV. The effect of breathing motion and random set-up errors is smaller. Therefore the gain of controlling breathing motion during irradiation is expected to be small and efforts should rather focus on minimizing systematic errors. For the current clinically applied field sizes and a clinically relevant combination of set-up errors and breathing motion, the EUD of the central plane of the CTV is reduced by 3.3 Gy, at maximum, relative to homogeneous irradiation of the CTV to 70 Gy, for our worst case scenario.

Calculation of the uncertainty in complication probability for various dose-response models, applied to the parotid gland

PURPOSE

Usually, models that predict normal tissue complication probability (NTCP) are fitted to clinical data with the maximum likelihood (ML) method. This method inevitably causes a loss of information contained in the data. In this study, an alternative method is investigated that calculates the parameter probability distribution (PD), and, thus, conserves all information. The PD method also allows the calculation of the uncertainty in the NTCP, which is an (often-neglected) prerequisite for the intercomparison of both treatment plans and NTCP models. The PD and ML methods are applied to parotid gland data, and the results are compared.

METHODS AND MATERIALS

The drop in salivary flow due to radiotherapy was measured in 25 parotid glands of 15 patients. Together with the parotid gland dose-volume histograms (DVH), this enabled the calculation of the parameter PDs for three different NTCP models (Lyman, relative seriality, and critical volume). From these PDs, the NTCP and its uncertainty could be calculated for arbitrary parotid gland DVHs. ML parameters and resulting NTCP values were calculated also.

RESULTS

All models fitted equally well. The parameter PDs turned out to have nonnormal shapes and long tails. The NTCP predictions of the ML and PD method usually differed considerably, depending on the NTCP model and the nature of irradiation. NTCP curves and ML parameters suggested a highly parallel organization of the parotid gland.

CONCLUSIONS

Considering the substantial differences between the NTCP predictions of the ML and PD method, the use of the PD method is preferred, because this is the only method that takes all information contained in the clinical data into account. Furthermore, PD method gives a true measure of the uncertainty in the NTCP.

Comparison of conformal radiation therapy techniques within the dynamic radiotherapy project 'Dynarad'

The objective of the dynamic radiotherapy project 'Dynarad' within the European Community has been to compare and grade treatment techniques that are currently applied or being developed at the participating institutions. Cervical cancer was selected as the tumour site on the grounds that the involved organs at risk, mainly the rectum and the bladder, are very close to the tumour and partly located inside the internal target volume. In this work, a solid phantom simulating the pelvic anatomy was used by institutions in Belgium, France, Greece, Holland, Italy, Sweden and the United Kingdom. The results were evaluated using both biological and physical criteria. The main purpose of this parallel evaluation is to test the value of biological and physical evaluations in comparing treatment techniques. It is demonstrated that the biological objective functions allow a much higher conformality and a more clinically relevant scoring of the outcome. Often external beam treatment techniques have to be combined with intracavitary therapy to give clinically acceptable results. However, recent developments can reduce or even eliminate this need by delivering more conformal dose distributions using intensity modulated external dose delivery. In these cases the reliability of the patient set-up procedure becomes critical for the effectiveness of the treatment.

Compensation of x-ray beam penumbra in conformal radiotherapy

In radiotherapy, the gross tumor volume is surrounded by a clinically defined margin to allow for the presence of undetected malignant cells. Additional margins are added to accommodate positioning uncertainties and organ motion, creating a planning target volume, or PTV. Finally, a margin is included in the beam apertures surrounding the PTV to account for the dose fall-off at the beam edges (i.e., the "penumbra"). For higher energy beams and for low density tissues adjacent to the PTV, the beam aperture margin should be increased to account for the increased range of scattered photons and electrons. However, increased margins also increase the volume of normal tissue irradiated. In this work, the beam aperture margin is reduced by using filters and multileaf collimator (MLC) techniques to create compensating rinds of increased beam intensity. These compensation techniques were evaluated for 6 and 18 MV x rays by calculating penumbral widths as a function of the increased beam intensity in the rind, the rind width, and tissue density. Dose calculations were performed using a 3D superposition algorithm, which includes an extrafocal source model. Calculations were validated experimentally with film dosimetry. Results show the distance between the 95%-50% isodose lines is reduced from 11 mm to 4 mm for 6 MV x rays in the lung phantom, when the beam intensity is increased by 20% in a 10 mm wide rind. At 18 MV, this distance is reduced from 16 mm to 6 mm with a 20% increase in rind intensity, but a 15 mm wide rind is required. In all cases, penumbra compensation did not result in any appreciable increase in scatter dose outside the field boundaries. These results suggest that penumbra compensation is a practical means of controlling the beam aperture margin.

The probability of correct target dosage: dose-population histograms for deriving treatment margins in radiotherapy

PURPOSE

To provide an analytical description of the effect of random and systematic geometrical deviations on the target dose in radiotherapy and to derive margin rules.

METHODS AND MATERIALS

The cumulative dose distribution delivered to the clinical target volume (CTV) is expressed analytically. Geometrical deviations are separated into treatment execution (random) and treatment preparation (systematic) variations. The analysis relates each possible preparation (systematic) error to the dose distribution over the CTV and allows computation of the probability distribution of, for instance, the minimum dose delivered to the CTV.

RESULTS

The probability distributions of the cumulative dose over a population of patients are called dose-population histograms in short. Large execution (random) variations lead to CTV underdosage for a large number of patients, while the same level of preparation (systematic) errors leads to a much larger underdosage for some of the patients. A single point on the histogram gives a simple "margin recipe." For example, to ensure a minimum dose to the CTV of 95% for 90% of the patients, a margin between CTV and planning target volume (PTV) is required of 2.5 times the total standard deviation (SD) of preparation (systematic) errors (Sigma) plus 1.64 times the total SD of execution (random) errors (sigma') combined with the penumbra width, minus 1.64 times the SD describing the penumbra width (sigma(p)). For a sigma(p) of 3.2 mm, this recipe can be simplified to 2.5 Sigma + 0.7 sigma'. Because this margin excludes rotational errors and shape deviations, it must be considered as a lower limit for safe radiotherapy.

CONCLUSION

Dose-population histograms provide insight into the effects of geometrical deviations on a population of patients. Using a dose-probability based approach, simple algorithms for choosing margins were derived.

Dosimetric effects of patient displacement and collimator and gantry angle misalignment on intensity modulated radiation therapy

PURPOSE AND OBJECTIVE

The primary goal of this study was to examine systematically the dosimetric effect of small patient movements and linear accelerator angular setting misalignments in the delivery of intensity modulated radiation therapy. We will also provide a method for estimating dosimetric errors for an arbitrary combination of these uncertainties.

MATERIALS AND METHODS

Sites in two patients (lumbar-vertebra and nasopharynx) were studied. Optimized intensity modulated radiation therapy treatment plans were computed for each patient using a commercially available inverse planning system (CORVUS, NOMOS Corporation, Sewickley, PA). The plans used nine coplanar beams. For each patient the dose distributions and relevant dosimetric quantities were calculated, including the maximum, minimum, and average doses in targets and sensitive structures. The corresponding dose volumetric information was recalculated by purposely varying the collimator angle or gantry angle of an incident beam while keeping other beams unchanged. Similar calculations were carried out by varying the couch indices in either horizontal or vertical directions. The intensity maps of all the beams were kept the same as those in the optimized plan. The change of a dosimetric quantity, Q, for a combination of collimator and gantry angle misalignments and patient displacements was estimated using Delta=Sigma(DeltaQ/Deltax(i))Deltax(i). Here DeltaQ is the variation of Q due to Deltax(i), which is the change of the i-th variable (collimator angle, gantry angle, or couch indices), and DeltaQ/Deltax(i) is a quantity equivalent to the partial derivative of the dosimetric quantity Q with respect to x(i).

RESULTS

While the change in dosimetric quantities was case dependent, it was found that the results were much more sensitive to small changes in the couch indices than to changes in the accelerator angular setting. For instance, in the first example in the paper, a 3-mm movement of the couch in the anterior-posterior direction can cause a 38% decrease in the minimum target dose or a 41% increase in the maximum cord dose, whereas a 5 degrees change in the θ(1)=20 degrees beam only gave rise to a 1.5% decrease in the target minimum or 5.1% in the cord maximum. The effect of systematic positioning uncertainties of the machine settings was more serious than random uncertainties, which tended to smear out the errors in dose distributions.

CONCLUSIONS

The dose distribution of an intensity modulated radiation therapy (IMRT) plan changes with patient displacement and angular misalignment in a complex way. A method was proposed to estimate dosimetric errors for an arbitrary combination of uncertainties in these quantities. While it is important to eliminate the angular misalignment, it was found that the couch indices (or patient positioning) played a much more important role. Accurate patient set-up and patient immobilization is crucial in order to take advantage fully of the technological advances of IMRT. In practice, a sensitivity check should be useful to foresee potential IMRT treatment complications and a warning should be given if the sensitivity exceeds an empirical value. Quality assurance action levels for a given plan can be established out of the sensitivity calculation.

Treatment planning algorithm corrections accounting for random setup uncertainties in fractionated stereotactic radiotherapy

A number of relocatable head fixation systems have become commercially available or developed in-house to perform fractionated stereotactic radiotherapy (SRT) treatment. The uncertainty usually quoted for the target repositioning in SRT is over 2 mm, more than twice that of stereotactic radiosurgery (SRS) systems. This setup uncertainty is usually accounted for at treatment planning by outlining extra target margins to form the planning target volume (PTV). It was, however, shown by Lo et al. [Int. J. Radiat. Oncol., Biol., Phys. 34, 1113-1119 (1996)] that these extra margins partly offset the radiobiological advantages of SRT. The present paper considers dose calculations in SRT and shows that the dose predictions could be made at least as accurate as in SRS with no extra margins required. It is shown that the dose distribution from SRT can be calculated using the same algorithms as in SRS, with the measured off-axis ratios (OARs) replaced by "effective" OARs. These are obtained by convolving the probability density distribution of the isocenter positions (assumed to be normal) and the original OARs. An additional output correction factor has also been introduced accounting for the isocenter dose reduction (2.4% for a 7 mm collimator) due to the OARs "blurring." Another correction factor accommodates for the reduced (by 1% for 6 MV beam) dose rate at the isocenter due to x-ray absorption in the relocatable mask. Mean dose profiles and the standard deviations of the dose (STD) were obtained through simulating SRT treatment by a combination of normally distributed isocenters. These dose distributions were compared with those calculated using the convolution approach. Agreement of the dose distributions was within 1%. Since standard deviation reduces with the number of fractions, N, as STD/square root(N), the planning predictions in fractionated stereotactic radiotherapy can be made more accurate than in SRS by increasing N and using "effective" OARs along with corrected dose output.

Biologically based treatment planning

The classical way of quantifying dose-response relations for tumors and normal tissues and their dependence on the genetic make up of the patient is briefly reviewed. Response quantifiers such as quality of life and the probability of achieving a complication-free cure are helpful in solving many of the problems of radiation therapy planning. It is shown, through the use of these quantifiers, that by introducing radiobiologically optimized, intensity-modulated dose delivery, the treatment outcome can be improved by as much as 20%, and more in cases with a complex spread of the disease. The real strength of the radiobiological models is to serve as a scientific tool for the development of treatment optimization so that the models are modified when the clinical response systematically deviates from the predictions of the models. In this way, the biological models serve as a continuously updated historical database that later on may replace the control arm in clinical trials and allow all patients to benefit from the latest developments in radiobiologically optimized treatment techniques.

Stochastic optimization of intensity modulated radiotherapy to account for uncertainties in patient sensitivity

The aim of the present work is to better account for the known uncertainties in radiobiological response parameters when optimizing radiation therapy. The radiation sensitivity of a specific patient is usually unknown beyond the expectation value and possibly the standard deviation that may be derived from studies on groups of patients. Instead of trying to find the treatment with the highest possible probability of a desirable outcome for a patient of average sensitivity, it is more desirable to maximize the expectation value of the probability for the desirable outcome over the possible range of variation of the radiation sensitivity of the patient. Such a stochastic optimization will also have to consider the distribution function of the radiation sensitivity and the larger steepness of the response for the individual patient. The results of stochastic optimization are also compared with simpler methods such as using biological response 'margins' to account for the range of sensitivity variation. By using stochastic optimization, the absolute gain will typically be of the order of a few per cent and the relative improvement compared with non-stochastic optimization is generally less than about 10 per cent. The extent of this gain varies with the level of interpatient variability as well as with the difficulty and complexity of the case studied. Although the dose changes are rather small (<5 Gy) there is a strong desire to make treatment plans more robust, and tolerant of the likely range of variation of the radiation sensitivity of each individual patient. When more accurate predictive assays of the radiation sensitivity for each patient become available, the need to consider the range of variations can be reduced considerably.

Optimization of the dose level for a given treatment plan to maximize the complication-free tumor cure

During the past decade, tumor and normal tissue reactions after radiotherapy have been increasingly quantified in radiobiological terms. For this purpose, response models describing the dependence of tumor and normal tissue reactions on the irradiated volume, heterogeneity of the delivered dose distribution and cell sensitivity variations can be taken into account. The probability of achieving a good treatment outcome can be increased by using an objective function such as P+, the probability of complication-free tumor control. A new procedure is presented, which quantifies P+ from the dose delivery on 2D surfaces and 3D volumes and helps the user of any treatment planning system (TPS) to select the best beam orientations, the best beam modalities and the most suitable beam energies. The final step of selecting the prescribed dose level is made by a renormalization of the entire dose plan until the value of P+ is maximized. The index P+ makes use of clinically established dose-response parameters, for tumors and normal tissues of interest, in order to improve its clinical relevance. The results, using P+, are compared against the assessments of experienced medical physicists and radiation oncologists for two clinical cases. It is observed that when the absorbed dose level for a given treatment plan is increased, the treatment outcome first improves rapidly. As the dose approaches the tolerance of normal tissues the complication-free cure begins to drop. The optimal dose level is often just below this point and it depends on the geometry of each patient and target volume. Furthermore, a more conformal dose delivery to the target results in a higher control rate for the same complication level. This effect can be quantified by the increased value of the P+ parameter.

Beam intensity modulation to reduce the field sizes for conformal irradiation of lung tumors: a dosimetric study

PURPOSE

In conformal radiotherapy of lung tumors, penumbra broadening in lung tissue necessitates the use of larger field sizes to achieve the same target coverage as in a homogeneous environment. In an idealized model configuration, some fundamental aspects of field size reduction were investigated, both for the static situation and for a moving tumor, while maintaining the dose homogeneity in the target volume by employing a simple beam-intensity modulation technique.

METHODS AND MATERIALS

An inhomogeneous phantom, consisting of polystyrene, cork, and polystyrene layers, with a 6 x 6 x 6 cm3 polystyrene cube inside the cork representing the tumor, was used to simulate a lung cancer treatment. Film dosimetry experiments were performed for an AP-PA irradiation technique with 8-MV or 18-MV beams. Dose distributions were compared for large square fields, small square fields, and intensity-modulated fields in which additional segments increase the dose at the edge of the field. The effect of target motion was studied by measuring the dose distribution for the solid cube, displaced with respect to the beams.

RESULTS

For the 18-MV beam, the field sizes required to establish a sufficient target coverage are larger than for the 8-MV beam. For each beam energy, the mean dose in cork can significantly be reduced (at least a factor of 1.6) by decreasing the field size with 2 cm, while keeping the mean target dose constant. Target dose inhomogeneity for these smaller fields is limited if the additional edge segments are applied for 8% of the number of monitor units given with the open fields. The target dose distribution averaged over a motion cycle is hardly affected if the target edge does not approach the field edge to within 3 mm.

CONCLUSIONS

For lung cancer treatment, a beam energy of 8 MV is more suitable than 18 MV. The mean lung dose can be significantly reduced by decreasing the field sizes of conformal fields. The smaller fields result in the same biological effect to the tumor if the mean target dose is kept constant. Intensity modulation can be employed to maintain the same target dose homogeneity for these smaller fields. As long as the target (with a 3 mm margin) stays within the field portal, application of a margin for target motion is not necessary.

Computerized design of target margins for treatment uncertainties in conformal radiotherapy

PURPOSE

We describe a computerized method of determining target margins for beam aperture design in conformal radiotherapy plans.

MATERIALS AND METHODS

The method uses previously measured data from a population of patients to simulate setup error and organ motion in the patient currently being planned. Starting with a clinical target volume (CTV) and nontarget organs from the patient's planning CT scan, the simulation is repeated many times to produce a spatial probability distribution for each organ in the treatment machine coordinate system. This is used to determine a prescribed dose volume (PDV), defined as the volume to receive the prescribed dose, which encompasses the CTV while restricting the volume of nontarget organs within it, according to planner-specified values. The PDV is used to design beam apertures using a conventional margin for beam penumbra.

RESULTS

The method is applied to 6-field prostate conformal treatment plans, in which the PDV encloses the prostate and seminal vesicles while limiting the enclosed rectal wall volume. The effect of organ motion is assessed by applying the plans on subsequent CT scans of the same patients, calculating probabilities for tumor control (TCP) and normal tissue complication (NTCP), and comparing with plans designed from a physician-drawn planning target volume (PTV). Although prostate TCP and rectal wall NTCP are found to be similar in the two sets of plans, TCP for the seminal vesicles is significantly higher in the PDV-based plans.

CONCLUSIONS

The method can improve the dose conformality of treatment plans by incorporating population-based measurements of treatment uncertainties and consideration of nontarget tissues in the design of nonuniform target margins.

Optimized radiation therapy based on radiobiological objectives

In the broad field of radiation therapy optimization, both simple and complex problems have their origins in the interaction of the radiation beams with the biological structures of normal and malignant tissues of the human body. Therefore, it is no great surprise that many treatment optimization problems are best handled by the use of well-designed radiobiological models. The classic way of quantifying dose-response relations for tumors and normal tissues as well as their cross-correlation with each other and their dependence on the underlying genetic and molecular biology of the cell are first briefly reviewed. Radiobiological objective functions, such as the probability of achieving complication-free cure and its expectation value under influence of stochastic processes during the course of treatment, are defined and shown to solve many of the problems of radiation therapy planning. Finally, it is shown through the use of these quantifiers that, simply by introducing biologically optimal intensity modulated dose delivery, the treatment outcome can be improved by about 20% or more in cases with a complex spread of the disease. Once radiobiological optimal plans have been developed, they can be approximated by ordinary physical planning, but the biological objective functions are still needed to have a figure of merit for the quality of the treatment.

Beam characteristics and clinical possibilities of a new compact treatment unit design combining narrow pencil beam scanning and segmental multileaf collimation

Not until the last decade has flexible intensity modulated three-dimensional dose delivery techniques with photon beams become a clinical reality, first in the form of heavy metal transmission blocks and other beam compensators, then in dynamic and segmented multileaf collimation, and most recently by scanning high-energy narrow electron and photon beams. The merits of various treatment unit and bremsstrahlung target designs for high-energy photon therapy are investigated theoretically for two clinically relevant target sites, a cervix and a larynx cancer both in late stages. With an optimized bremsstrahlung target it is possible to generate photon beams with a half-width of about 3 cm at a source to axis distance (SAD) of 100 cm and an initial electron energy of 50 MeV. By making a more compact treatment head and shortening the SAD, it is possible to reduce the half-width even further to about 2 cm at a SAD of 70 cm and still have sufficient clearance between the collimator head and the patient. One advantage of a reduced SAD is that the divergence of the beam for a given field size on the patient is increased, and thus the exit dose is lowered by as much as 1%/cm of the patient cross section. A second advantage of a reduced SAD is that the electron beam on the patient surface will be only about 8 mm wide and very suitable for precision spot beam scanning. It may also be possible to reduce the beamwidth further by increasing the electron energy up to about 60 MeV to get a photon beam of around 15 mm half-width and an electron beam as narrow as 5 mm. The compact machine will be more efficient and easy to work with, due to the small gantry and the reduced isocentric height. For a given target volume and optimally selected static multileaf collimator, it is no surprise that the narrowest possible scanned elementary bremsstrahlung beam generates the best possible treatment outcome. In fact, by delivering a few static field segments with individually optimized scan patterns, it is possible to combine the advantage of being able to fine tune the fluence distribution by the scanning system with the steeper dose gradients that can be delivered by a few static multileaf collimator segments. It is demonstrated that in most cases a few collimator segments are sufficient and often a single segment per beam portal may suffice when narrow scanned photon beams are employed, and they can be delivered sequentially with a negligible time delay. A further advantage is the increase of therapeutically useful photons and improved patient protection, since the pencil beam is only scanned where the leaf collimator is open. Consequently, some of the problems associated with dynamic multileaf collimation such as the tongue and groove and edge leakage effects are significantly reduced. Fast scanning beam techniques combined with good treatment verification systems allow interesting future possibilities to counteract patient and internal organ motions in real time.

An adaptive control algorithm for optimization of intensity modulated radiotherapy considering uncertainties in beam profiles, patient set-up and internal organ motion

A new general beam optimization algorithm for inverse treatment planning is presented. It utilizes a new formulation of the probability to achieve complication-free tumour control. The new formulation explicitly describes the dependence of the treatment outcome on the incident fluence distribution, the patient geometry, the radiobiological properties of the patient and the fractionation schedule. In order to account for both measured and non-measured positioning uncertainties, the algorithm is based on a combination of dynamic and stochastic optimization techniques. Because of the difficulty in measuring all aspects of the intra- and interfractional variations in the patient geometry, such as internal organ displacements and deformations, these uncertainties are primarily accounted for in the treatment planning process by intensity modulation using stochastic optimization. The information about the deviations from the nominal fluence profiles and the nominal position of the patient relative to the beam that is obtained by portal imaging during treatment delivery, is used in a feedback loop to automatically adjust the profiles and the location of the patient for all subsequent treatments. Based on the treatment delivered in previous fractions, the algorithm furnishes optimal corrections for the remaining dose delivery both with regard to the fluence profile and its position relative to the patient. By dynamically refining the beam configuration from fraction to fraction, the algorithm generates an optimal sequence of treatments that very effectively reduces the influence of systematic and random set-up uncertainties to minimize and almost eliminate their overall effect on the treatment. Computer simulations have shown that the present algorithm leads to a significant increase in the probability of uncomplicated tumour control compared with the simple classical approach of adding fixed set-up margins to the internal target volume.

Variations of tumor control and rectum complication probabilities due to random set-up errors during conformal radiation therapy of prostate cancer

BACKGROUND AND PURPOSE

The effect of random set-up errors on tumor control probability (TCP) and rectum complication probability (NTCP) on 3D conformal treatment planning of prostate cancer has been investigated by applying the convolution method originally proposed by Leong (Leong, J. Implementation of random positioning error in computerized radiation treatment planning systems as a result of fractionation. Phys. Med. Biol. 32: 327-334, 1987).

MATERIALS AND METHODS

The combined influence of the standard deviation of the random shifts probability distribution (sigma) of the dose and of the Beam's-eye-view margin (M) between the clinical target volume (CTV) and the edge of the blocks have been investigated in two patients.

RESULTS AND CONCLUSIONS

Random set-up error has been found to decrease TCP (for a typical 70 Gy CTV mean dose) by up to 6% for a 1 cm margin (sigma = 7 mm). When M is equal to or larger than 1.5 cm, no relevant effects on TCP are obtained. Maximum acceptable TCP values (corresponding to a rectum NTCP equal to 5%) have been derived and the dependence on sigma and M has been investigated.

Automatic calculation of three-dimensional margins around treatment volumes in radiotherapy planning

Following the publication of ICRU Report 50, the concepts of GTV (gross tumour volume). CTV (clinical target volume) and PTV (planning target volume) are being used in radiotherapy planning with increasing frequency. In 3D planning, the GTV (or CTV) is normally outlined by the clinician in CT or MRI slices. The PTV is determined by adding margins to these volumes. Since manual drawing of an accurate 3D margin in a set of 2D slices is extremely time consuming, software has been developed to automate this step in the planning. The target volume is represented in a 3D matrix grid with voxel values one inside and zero outside the target volume. It is expanded by centering an ellipsoid at every matrix element within the volume. The shape of the ellipsoid reflects the size of the margins in the three main orthogonal directions. Finally, the PTV contours are determined from the 50% iso-value lines of the expanded volume. The software tool has been in clinical use since the end of 1994 and has mostly been applied to the planning of prostate irradiations. The accuracy is better than can be achieved manually and the workload has been reduced considerably (from 4 h manually to approximately 1 min automatically).

A numerical simulation of organ motion and daily setup uncertainties: implications for radiation therapy

PURPOSE

In radiotherapy planning, the clinical target volume (CTV) is typically enlarged to create a planning target volume (PTV) that accounts for uncertainties due to internal organ and patient motion as well as setup error. Margin size clearly determines the volume of normal tissue irradiated, yet in practice it is often given a set value in accordance with a clinical precedent from which variations are rare. The (CTV/PTV) formalism does not account for critical structure dose. We present a numerical simulation to assess (CTV) coverage and critical organ dose as a function of treatment margins in the presence of organ motion and physical setup errors. An application of the model to the treatment of prostate cancer is presented, but the method is applicable to any site where normal tissue tolerance is a dose-limiting factor.

METHODS AND MATERIALS

A Monte Carlo approach was used to simulate the cumulative effect of variation in overall tumor position, for individual treatment fractions, relative to a fixed distribution of dose. Distributions of potential dose-volume histograms (DVHs), for both tumor and normal tissues, are determined that fully quantify the stochastic nature of radiotherapy delivery. We introduce the concept of Probability of Prescription Dose (PoPD) isosurfaces as a tool for treatment plan optimization. Outcomes resulting from current treatment planning methods are compared with proposed techniques for treatment optimization. The standard planning technique of relatively large uniform margins applied to the CTV, in the beam's eye view (BEV), was compared with three other treatment strategies: (a) reduced uniform margins, (b) nonuniform margins adjusted to maximize normal tissue sparing, and (c) a reduced margin plan in which nonuniform fluence profiles were introduced to compensate for potential areas of reduced dose.

RESULTS

Results based on 100 simulated full course treatments indicate that a 10 mm CTV to PTV margin, combined with an additional 5 mm dosimetric margin, provides adequate CTV coverage in the presence of known treatment uncertainties. Nonuniform margins can be employed to reduce dose delivered to normal tissues while preserving CTV coverage. Nonuniform fluence profiles can also be used to further reduce dose delivered to normal tissues, though this strategy does result in higher dose levels delivered to a small volume of the CTV and normal tissues.

CONCLUSIONS

Monte Carlo-based treatment simulation is an effective means of assessing the impact of organ motion and daily setup error on dose delivery via external beam radiation therapy. Probability of Prescription Dose (PoPD) isosurfaces are a useful tool for the determination of nonuniform beam margins that reduce dose delivered to critical organs while preserving CTV dose coverage. Nonuniform fluence profiles can further alter critical organ dose with potential therapeutic benefits. Clinical consequences of this latter approach can only be assessed via clinical trials.

A new method for optimum dose distribution determination taking tumour mobility into account

A method for determining the optimum dose distribution in the planning target volume is proposed when target volumes are deliberately enlarged to account for tumour mobility in external beam radiotherapy. The optimum dose distribution is a dose distribution that will result in an acceptable level of tumour control probability (TCP) in most of the arising cases of tumour dislocation. An assumption is made that the possible shifts of the tumour are subject to a Gaussian distribution with mean zero and known variance. The idea of a reduced (mean in ensemble) tumour cell density is introduced. On this basis, the target volume and dose distribution in it are determined. The tumour control probability as a function of the shift of the tumour has been calculated. The Monte Carlo method has been used to simulate TCP distributions corresponding to tumour mobility characterized by different variances. The obtained TCP distributions are independent of the variance of the mobility because the dose distribution in the planning target volume is prescribed so that the mobility variance is taken into account. For simplicity a one-dimensional model is used but three-dimensional generalization can be done.