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

Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit

Spatiotemporal fractionation schemes, that is, treatments delivering different dose distributions in different fractions, can potentially lower treatment side effects without compromising tumor control. This can be achieved by hypofractionating parts of the tumor while delivering approximately uniformly fractionated doses to the surrounding tissue. Plan optimization for such treatments is based on biologically effective dose (BED); however, this leads to computationally challenging nonconvex optimization problems. Optimization methods that are in current use yield only locally optimal solutions, and it has hitherto been unclear whether these plans are close to the global optimum. We present an optimization framework to compute rigorous bounds on the maximum achievable normal tissue BED reduction for spatiotemporal plans. The approach is demonstrated on liver tumors, where the primary goal is to reduce mean liver BED without compromising any other treatment objective. The BED-based treatment plan optimization problems are formulated as quadratically constrained quadratic programming (QCQP) problems. First, a conventional, uniformly fractionated reference plan is computed using convex optimization. Then, a second, nonconvex, QCQP model is solved to local optimality to compute a spatiotemporally fractionated plan that minimizes mean liver BED, subject to the constraints that the plan is no worse than the reference plan with respect to all other planning goals. Finally, we derive a convex relaxation of the second model in the form of a semidefinite programming problem, which provides a rigorous lower bound on the lowest achievable mean liver BED. The method is presented on five cases with distinct geometries. The computed spatiotemporal plans achieve 12-35% mean liver BED reduction over the optimal uniformly fractionated plans. This reduction corresponds to 79-97% of the gap between the mean liver BED of the uniform reference plans and our lower bounds on the lowest achievable mean liver BED. The results indicate that spatiotemporal treatments can achieve substantial reductions in normal tissue dose and BED, and that local optimization techniques provide high-quality plans that are close to realizing the maximum potential normal tissue dose reduction.

The emergence of nonuniform spatiotemporal fractionation schemes within the standard BED model

PURPOSE

Nonuniform spatiotemporal radiotherapy fractionation schemes, i.e., delivering distinct dose distributions in different fractions can potentially improve the therapeutic ratio. This is possible if the dose distributions are designed such that similar doses are delivered to normal tissues (exploit the fractionation effect) while hypofractionating subregions of the tumor. In this paper, the authors develop methodology for treatment planning with nonuniform fractions and demonstrate this concept in the context of intensity-modulated proton therapy (IMPT).

METHODS

Treatment planning is performed by simultaneously optimizing (possibly distinct) IMPT dose distributions for multiple fractions. This is achieved using objective and constraint functions evaluated for the cumulative biologically equivalent dose (BED) delivered at the end of treatment. BED based treatment planning formulations lead to nonconvex optimization problems, such that local gradient based algorithms require adequate starting positions to find good local optima. To that end, the authors develop a combinatorial algorithm to initialize the pencil beam intensities.

RESULTS

The concept of nonuniform spatiotemporal fractionation schemes is demonstrated for a spinal metastasis patient treated in two fractions using stereotactic body radiation therapy. The patient is treated with posterior oblique beams with the kidneys being located in the entrance region of the beam. It is shown that a nonuniform fractionation scheme that hypofractionates the central part of the tumor allows for a skin and kidney BED reduction of approximately 10%-20%.

CONCLUSIONS

Nonuniform spatiotemporal fractionation schemes represent a novel approach to exploit fractionation effects that deserves further exploration for selected disease sites.

Adaptive and robust radiation therapy in the presence of drift

Combining adaptive and robust optimization in radiation therapy has the potential to mitigate the negative effects of both intrafraction and interfraction uncertainty over a fractionated treatment course. A previously developed adaptive and robust radiation therapy (ARRT) method for lung cancer was demonstrated to be effective when the sequence of breathing patterns was well-behaved. In this paper, we examine the applicability of the ARRT method to less well-behaved breathing patterns. We develop a novel method to generate sequences of probability mass functions that represent different types of drift in the underlying breathing pattern. Computational results derived from applying the ARRT method to these sequences demonstrate that the ARRT method is effective for a much broader class of breathing patterns than previously demonstrated.

Simultaneous optimization of dose distributions and fractionation schemes in particle radiotherapy

PURPOSE

The paper considers the fractionation problem in intensity modulated proton therapy (IMPT). Conventionally, IMPT fields are optimized independently of the fractionation scheme. In this work, we discuss the simultaneous optimization of fractionation scheme and pencil beam intensities.

METHODS

This is performed by allowing for distinct pencil beam intensities in each fraction, which are optimized using objective and constraint functions based on biologically equivalent dose (BED). The paper presents a model that mimics an IMPT treatment with a single incident beam direction for which the optimal fractionation scheme can be determined despite the nonconvexity of the BED-based treatment planning problem.

RESULTS

For this model, it is shown that a small α∕β ratio in the tumor gives rise to a hypofractionated treatment, whereas a large α∕β ratio gives rise to hyperfractionation. It is further demonstrated that, for intermediate α∕β ratios in the tumor, a nonuniform fractionation scheme emerges, in which it is optimal to deliver different dose distributions in subsequent fractions. The intuitive explanation for this phenomenon is as follows: By varying the dose distribution in the tumor between fractions, the same total BED can be achieved with a lower physical dose. If it is possible to achieve this dose variation in the tumor without varying the dose in the normal tissue (which would have an adverse effect), the reduction in physical dose may lead to a net reduction of the normal tissue BED. For proton therapy, this is indeed possible to some degree because the entrance dose is mostly independent of the range of the proton pencil beam.

CONCLUSIONS

The paper provides conceptual insight into the interdependence of optimal fractionation schemes and the spatial optimization of dose distributions. It demonstrates the emergence of nonuniform fractionation schemes that arise from the standard BED model when IMPT fields and fractionation scheme are optimized simultaneously. Although the projected benefits are likely to be small, the approach may give rise to an improved therapeutic ratio for tumors treated with stereotactic techniques to high doses per fraction.

The dependence of optimal fractionation schemes on the spatial dose distribution

We consider the fractionation problem in radiation therapy. Tumor sites in which the dose-limiting organ at risk (OAR) receives a substantially lower dose than the tumor, bear potential for hypofractionation even if the α/β-ratio of the tumor is larger than the α/β-ratio of the OAR. In this work, we analyze the interdependence of the optimal fractionation scheme and the spatial dose distribution in the OAR. In particular, we derive a criterion under which a hypofractionation regimen is indicated for both a parallel and a serial OAR. The approach is based on the concept of the biologically effective dose (BED). For a hypothetical homogeneously irradiated OAR, it has been shown that hypofractionation is suggested by the BED model if the α/β-ratio of the OAR is larger than α/β-ratio of the tumor times the sparing factor, i.e. the ratio of the dose received by the tumor and the OAR. In this work, we generalize this result to inhomogeneous dose distributions in the OAR. For a parallel OAR, we determine the optimal fractionation scheme by minimizing the integral BED in the OAR for a fixed BED in the tumor. For a serial structure, we minimize the maximum BED in the OAR. This leads to analytical expressions for an effective sparing factor for the OAR, which provides a criterion for hypofractionation. The implications of the model are discussed for lung tumor treatments. It is shown that the model supports hypofractionation for small tumors treated with rotation therapy, i.e. highly conformal techniques where a large volume of lung tissue is exposed to low but nonzero dose. For larger tumors, the model suggests hyperfractionation. We further discuss several non-intuitive interdependencies between optimal fractionation and the spatial dose distribution. For instance, lowering the dose in the lung via proton therapy does not necessarily provide a biological rationale for hypofractionation.

Comparisons of treatment optimization directly incorporating systematic patient setup uncertainty with a margin-based approach

PURPOSE

To develop a probabilistic treatment planning (PTP) method which is robust to systematic patient setup errors and to compare PTP plans with plans generated using a planning target volume (PTV) margin optimized to give the same target coverage probability as the PTP plan.

METHODS

Plans adhering to the RTOG-0126 protocol are developed for 28 prostate patients using PTP and margin-based planning. For PTP, an objective function that simultaneously considers multiple possible patient positions is developed. PTP plans are optimized using clinical target volume (CTV) structures and organ at risk (OAR) structures. The desired CTV coverage probability is 95%. Plans that cannot achieve a 95% CTV coverage probability are re-optimized with a desired CTV coverage probability reduced by 5% until the desired CTV coverage probability is achieved. Margin-based plans are created which achieve the same CTV coverage probability as the PTP plans by iterative adjustment of the CTV-to-PTV margin. Postoptimization, probabilistic dose-volume coverage metrics are used to compare the plans.

RESULTS

For equivalent target coverage probability, PTP plans significantly reduce coverage probability for rectum objectives (-17% for D(35) < 65 Gy, p = 0.0010; -23% for D(25) < 70 Gy, p < 0.0001; and -27% for D(15) < 75 Gy, p < 0.0001). Physician assessment indicates PTP plans are entirely preferred 71% of the time while margin-based plans are entirely preferred 7% of the time.

CONCLUSIONS

For plans having the same target coverage probability, PTP has potential to reduce rectal doses while maintaining CTV coverage probability. In blind comparisons, physicians prefer PTP plans over optimized margin plans.

A population-based model to describe geometrical uncertainties in radiotherapy: applied to prostate cases

Local motions and deformations of organs between treatment fractions introduce geometrical uncertainties into radiotherapy. These uncertainties are generally taken into account in the treatment planning by enlarging the radiation target by a margin around the clinical target volume. However, a practical method to fully include these uncertainties is still lacking. This paper proposes a model based on the principal component analysis to describe the patient-specific local probability distributions of voxel motions so that the average values and variances of the dose distribution can be calculated and fully used later in inverse treatment planning. As usually only a very limited number of data for new patients is available; in this paper the analysis is extended to use population data. A basic assumption (which is justified retrospectively in this paper) is that general movements and deformations of a specific organ are similar despite variations in the shapes of the organ over the population. A proof of principle of the method for deformations of the prostate and the seminal vesicles is presented.

Coverage optimized planning: probabilistic treatment planning based on dose coverage histogram criteria

This work (i) proposes a probabilistic treatment planning framework, termed coverage optimized planning (COP), based on dose coverage histogram (DCH) criteria; (ii) describes a concrete proof-of-concept implementation of COP within the PINNACLE treatment planning system; and (iii) for a set of 28 prostate anatomies, compares COP plans generated with this implementation to traditional PTV-based plans generated with planning criteria approximating those in the high dose arm of the Radiation Therapy Oncology Group 0126 protocol. Let Dv denote the dose delivered to fractional volume v of a structure. In conventional intensity modulated radiation therapy planning, Dv has a unique value derived from the static (planned) dose distribution. In the presence of geometric uncertainties (e.g., setup errors) Dv assumes a range of values. The DCH is the complementary cumulative distribution function of D(v+). DCHs are similar to dose volume histograms (DVHs). Whereas a DVH plots volume v versus dose D, a DCH plots coverage probability Q versus D. For a given patient, Q is the probability (i.e., percentage of geometric uncertainties) for which the realized value of Dv exceeds D. PTV-based treatment plans can be converted to COP plans by replacing DVH optimization criteria with corresponding DCH criteria. In this approach, PTVs and planning organ at risk volumes are discarded, and DCH criteria are instead applied directly to clinical target volumes (CTVs) or organs at risk (OARs). Plans are optimized using a similar strategy as for DVH criteria. The specific implementation is described. COP was found to produce better plans than standard PTV-based plans, in the following sense. While target OAR dose tradeoff curves were equivalent to those for PTV-based plans, COP plans were able to exploit slack in OAR doses, i.e., cases where OAR doses were below their optimization limits, to increase target coverage. Specifically, because COP plans were not constrained by a predefined PTV, they were able to provide wider dosimetric margins around the CTV, by pushing OAR doses up to, but not beyond, their optimization limits. COP plans demonstrated improved target coverage when averaged over all 28 prostate anatomies, indicating that the COP approach can provide benefits for many patients. However, the degree to which slack OAR doses can be exploited to increase target coverage will vary according to the individual patient anatomy. The proof-of-concept COP implementation investigated here utilized a probabilistic DCH criteria only for the CTV minimum dose criterion. All other optimization criteria were conventional DVH criteria. In a mature COP implementation, all optimization criteria will be DCH criteria, enabling direct planning control over probabilistic dose distributions. Further research is necessary to determine the benefits of COP planning, in terms of tumor control probability and/or normal tissue complication probabilities.

Comparisons of treatment optimization directly incorporating random patient setup uncertainty with a margin-based approach

The purpose of this study is to incorporate the dosimetric effect of random patient positioning uncertainties directly into a commercial treatment planning system's IMRT plan optimization algorithm through probabilistic treatment planning (PTP) and compare coverage of this method with margin-based planning. In this work, PTP eliminates explicit margins and optimizes directly on the estimated integral treatment dose to determine optimal patient dose in the presence of setup uncertainties. Twenty-eight prostate patient plans adhering to the RTOG-0126 criteria are optimized using both margin-based and PTP methods. Only random errors are considered. For margin-based plans, the planning target volume is created by expanding the clinical target volume (CTV) by 2.1 mm to accommodate the simulated 3 mm random setup uncertainty. Random setup uncertainties are incorporated into IMRT dose evaluation by convolving each beam's incident fluence with a sigma = 3 mm Gaussian prior to dose calculation. PTP optimization uses the convolved fluence to estimate dose to ensure CTV coverage during plan optimization. PTP-based plans are compared to margin-based plans with equal CTV coverage in the presence of setup errors based on dose-volume metrics. The sensitivity of the optimized plans to patient-specific setup uncertainty variations is assessed by evaluating dose metrics for dose distributions corresponding to halving and doubling of the random setup uncertainty used in the optimization. Margin-based and PTP-based plans show similar target coverage. A physician review shows that PTP is preferred for 21 patients, margin-based plans are preferred in 2 patients, no preference is expressed for 1 patient, and both autogenerated plans are rejected for 4 patients. For the PTP-based plans, the average CTV receiving the prescription dose decreases by 0.5%, while the mean dose to the CTV increases by 0.7%. The CTV tumor control probability (TCP) is the same for both methods with the exception of one case in which PTP gave a slightly higher TCP. For critical structures that do not meet the optimization criteria, PTP shows a decrease in the volume receiving the maximum specified dose. PTP reduces local normal tissue volumes receiving the maximum dose on average by 48%. PTP results in lower mean dose to all critical structures for all plans. PTP results in a 2.5% increase in the probability of uncomplicated control (P+), along with a 1.9% reduction in rectum normal tissue complication probability (NTCP), and a 0.7% reduction in bladder NTCP. PTP-based plans show improved conformality as compared with margin-based plans with an average PTP-based dosimetric margin at 7100 cGy of 0.65 cm compared with the margin-based 0.90 cm and a PTP-based dosimetric margin at 3960 cGy of 1.60 cm compared with the margin-based 1.90 cm. PTP-based plans show similar sensitivity to variations of the uncertainty during treatment from the uncertainty used in planning as compared to margin-based plans. For equal target coverage, when compared to margin-based plans, PTP results in equal or lower doses to normal structures. PTP results in more conformal plans than margin-based plans and shows similar sensitivity to variations in uncertainty.

Coverage-based treatment planning: optimizing the IMRT PTV to meet a CTV coverage criterion

This work demonstrates an iterative approach-referred to as coverage-based treatment planning-designed to produce treatment plans that ensure target coverage for a specified percentage of setup errors. In this approach the clinical target volume to planning target volume (CTV-to-PTV) margin is iteratively adjusted until the specified CTV coverage is achieved. The advantage of this approach is that it automatically compensates for the dosimetric margin around the CTV, i.e., the extra margin that is created when the dose distribution extends beyond the PTV. When applied to 27 prostate plans, this approach reduced the average CTV-to-PTV margin from 5 to 2.8 mm. This reduction in PTV size produced a corresponding decrease in the volume of normal tissue receiving high dose. The total volume of tissue receiving > or =65 Gy was reduced on average by 19.3% or about 48 cc. Individual reductions varied from 8.7% to 28.6%. The volume of bladder receiving > or =60 Gy was reduced on average by 5.6% (reductions for individuals varied from 1.7% to 10.6%), and the volume of periprostatic rectum receiving > or =65 Gy was reduced on average by 4.9% (reductions for individuals varied from 0.9% to 12.3%). The iterative method proposed here represents a step toward a probabilistic treatment planning algorithm which can generate dose distributions (i.e., treated volumes) that closely approximate a specified level of coverage in the presence of geometric uncertainties. The general principles of coverage-based treatment planning are applicable to arbitrary treatment sites and delivery techniques. Importantly, observed deviations between coverage implied by specified CTV-to-PTV margins and coverage achieved by a given treatment plan imply a generic need to perform coverage probability analysis on a per-plan basis to ensure that the desired level of coverage is achieved.

Tumor trailing strategy for intensity-modulated radiation therapy of moving targets

Internal organ motion during the course of radiation therapy of cancer affects the distribution of the delivered dose and, generally, reduces its conformality to the targeted volume. Previously proposed approaches aimed at mitigating the effect of internal motion in intensity-modulated radiation therapy (IMRT) included expansion of the target margins, motion-correlated delivery (e.g., respiratory gating, tumor tracking), and adaptive treatment plan optimization employing a probabilistic description of motion. We describe and test the tumor trailing strategy, which utilizes the synergy of motion-adaptive treatment planning and delivery methods. We regard the (rigid) target motion as a superposition of a relatively fast cyclic component (e.g., respiratory) and slow aperiodic trends (e.g., the drift of exhalation baseline). In the trailing approach, these two components of motion are decoupled and dealt with separately. Real-time motion monitoring is employed to identify the "slow" shifts, which are then corrected by applying setup adjustments. The delivery does not track the target position exactly, but trails the systematic trend due to the delay between the time a shift occurs, is reliably detected, and, subsequently, corrected. The "fast" cyclic motion is accounted for with a robust motion-adaptive treatment planning, which allows for variability in motion parameters (e.g., mean and extrema of the tidal volume, variable period of respiration, and expiratory duration). Motion-surrogate data from gated IMRT treatments were used to provide probability distribution data for motion-adaptive planning and to test algorithms that identified systematic trends in the character of motion. Sample IMRT fields were delivered on a clinical linear accelerator to a programmable moving phantom. Dose measurements were performed with a commercial two-dimensional ion-chamber array. The results indicate that by reducing intrafractional motion variability, the trailing strategy enhances relevance and applicability of motion-adaptive planning methods, and improves conformality of the delivered dose to the target in the presence of irregular motion. Trailing strategy can be applied to respiratory-gated treatments, in which the correction for the slow motion can increase the duty cycle, while robust probabilistic planning can improve management of the residual motion within the gate window. Similarly, trailing may improve the dose conformality in treatment of patients who exhibit detectable target motion of low amplitude, which is considered insufficient to provide a clinical indication for the use of respiratory-gated treatment (e.g., peak-to-peak motion of less than 10 mm). The mechanical limitations of implementing tumor trailing are less rigorous than those of real-time tracking, and the same technology could be used for both.

Accelerating IMRT optimization by voxel sampling

This paper presents a new method for accelerating intensity-modulated radiation therapy (IMRT) optimization using voxel sampling. Rather than calculating the dose to the entire patient at each step in the optimization, the dose is only calculated for some randomly selected voxels. Those voxels are then used to calculate estimates of the objective and gradient which are used in a randomized version of a steepest descent algorithm. By selecting different voxels on each step, we are able to find an optimal solution to the full problem. We also present an algorithm to automatically choose the best sampling rate for each structure within the patient during the optimization. Seeking further improvements, we experimented with several other gradient-based optimization algorithms and found that the delta-bar-delta algorithm performs well despite the randomness. Overall, we were able to achieve approximately an order of magnitude speedup on our test case as compared to steepest descent.

A comparison between 2-Step IMRT and conventional IMRT planning

BACKGROUND AND PURPOSE

2-Step intensity modulated radiation therapy (2-Step IMRT) is an IMRT segmentation procedure based on analytical approximations [Bratengeier K. 2-Step IMAT and 2-Step IMRT: a geometrical approach. Med Phys 2005;32:777-785; Bratengeier K. 2-Step IMAT and 2-Step IMRT in three dimensions. Med Phys 2005;32:3849-3861]. The aim was to benchmark it with other IMRT algorithms and to establish it as planning tool for fast IMRT application with a reduced number of segments.

MATERIALS AND METHODS

2-Step IMRT plans were compared with IMRT-solutions obtained with methods from a commercial planning system (Pinnacletrade mark TPS). The four clinical cases chosen were: paraspinal tumour, carcinoma of the prostate, head and neck carcinoma and breast carcinoma. In addition the "Quasimodo" phantom study was used to compare the quality of the 2-Step IMRT method with respect to other planning procedures in the ESTRO study.

RESULTS

The number of segments (and - to a minor degree - the monitor units per dose) of the majority of 2-Step IMRT plans was lower than for the commercial algorithms. The quality of the 2-Step IMRT-plan was comparable. In the Quasimodo comparison 2-Step IMRT plans with nine beams would place in the mid-range of all participants, whereas the 15-beam arrangements could compete with the best results.

CONCLUSIONS

2-Step IMRT is a valuable IMRT segmentation method, especially if the number of segments is to be limited (e.g. for reasons of precision, speed and leakage radiation).

Self-consistent tumor control probability and normal tissue complication probability models based on generalized EUDa)

Traditional methods to compute the tumor control probability (TCP) or normal tissue complication probability (NTCP) typically require a heterogeneous radiation dose distribution to be converted into a simple uniform dose distribution with an equivalent biological effect. Several power-law type dose-volume-histogram reduction schemes, particularly Niemierko's generalized equivalent uniform dose model [Med. Phys. 26, 1000 (1999)], have been proposed to achieve this goal. In this study, we carefully examine the mathematical outcome of these schemes. We demonstrate that (1) for tumors, with each tumor cell independently responding to local radiation dose, a closed-form analytical solution for tumor survival fraction and TCP can be obtained; (2) for serial structured normal tissues, an exponential power-law form relating survival to functional sub-unit (FSU) radiation is required, and a closed-form analytical solution for the related NTCP is provided; (3) in the case of a parallel structured normal tissue, when NTCP is determined solely by the number of the surviving FSUs, a mathematical solution is available only when there is a non-zero threshold dose and/or a finite critical dose defining the radiotherapy response. Some discussion is offered for the partial irradiation effect on normal tissues in this category; (4) for normal tissues with alternative architectures, where the radiation response of FSU is inhomogeneous, there is no exact global mathematical solution for SF or NTCP within the available schemes. Finally, numerical fits of our models to some experimental data are also presented.

Equivalent uniform dose concept evaluated by theoretical dose volume histograms for thoracic irradiation

BACKGROUND AND PURPOSE

The goal of our study was to quantify the limits of the EUD models for use in score functions in inverse planning software, and for clinical application.

MATERIALS AND METHODS

We focused on oesophagus cancer irradiation. Our evaluation was based on theoretical dose volume histograms (DVH), and we analyzed them using volumetric and linear quadratic EUD models, average and maximum dose concepts, the linear quadratic model and the differential area between each DVH.

RESULTS

We evaluated our models using theoretical and more complex DVHs for the above regions of interest. We studied three types of DVH for the target volume: the first followed the ICRU dose homogeneity recommendations; the second was built out of the first requirements and the same average dose was built in for all cases; the third was truncated by a small dose hole. We also built theoretical DVHs for the organs at risk, in order to evaluate the limits of, and the ways to use both EUD(1) and EUD/LQ models, comparing them to the traditional ways of scoring a treatment plan. For each volume of interest we built theoretical treatment plans with differences in the fractionation.

CONCLUSION

We concluded that both volumetric and linear quadratic EUDs should be used. Volumetric EUD(1) takes into account neither hot-cold spot compensation nor the differences in fractionation, but it is more sensitive to the increase of the irradiated volume. With linear quadratic EUD/LQ, a volumetric analysis of fractionation variation effort can be performed.

The IMRT information process—mastering the degrees of freedom in external beam therapy

The techniques and procedures for intensity-modulated radiation therapy (IMRT) are reviewed in the context of the information process central to treatment planning and delivery of IMRT. A presentation is given of the evolution of the information based radiotherapy workflow and dose delivery techniques, as well as the volume and planning concepts for relating the dose information to image based patient representations. The formulation of the dose shaping process as an optimization problem is described. The different steps in the calculation flow for determination of machine parameters for dose delivery are described starting from the formulation of optimization objectives over dose calculation to optimization procedures. Finally, the main elements of the quality assurance procedure necessary for implementing IMRT clinically are reviewed.

Estimation of the delivered patient dose in lung IMRT treatment based on deformable registration of 4D-CT data and Monte Carlo simulations

The purpose of this study is to accurately estimate the difference between the planned and the delivered dose due to respiratory motion and free breathing helical CT artefacts for lung IMRT treatments, and to estimate the impact of this difference on clinical outcome. Six patients with representative tumour motion, size and position were selected for this retrospective study. For each patient, we had acquired both a free breathing helical CT and a ten-phase 4D-CT scan. A commercial treatment planning system was used to create four IMRT plans for each patient. The first two plans were based on the GTV as contoured on the free breathing helical CT set, with a GTV to PTV expansion of 1.5 cm and 2.0 cm, respectively. The third plan was based on the ITV, a composite volume formed by the union of the CTV volumes contoured on free breathing helical CT, end-of-inhale (EOI) and end-of-exhale (EOE) 4D-CT. The fourth plan was based on GTV contoured on the EOE 4D-CT. The prescribed dose was 60 Gy for all four plans. Fluence maps and beam setup parameters of the IMRT plans were used by the Monte Carlo dose calculation engine MCSIM for absolute dose calculation on both the free breathing CT and 4D-CT data. CT deformable registration between the breathing phases was performed to estimate the motion trajectory for both the tumour and healthy tissue. Then, a composite dose distribution over the whole breathing cycle was calculated as a final estimate of the delivered dose. EUD values were computed on the basis of the composite dose for all four plans. For the patient with the largest motion effect, the difference in the EUD of CTV between the planed and the delivered doses was 33, 11, 1 and 0 Gy for the first, second, third and fourth plan, respectively. The number of breathing phases required for accurate dose prediction was also investigated. With the advent of 4D-CT, deformable registration and Monte Carlo simulations, it is feasible to perform an accurate calculation of the delivered dose, and compare our delivered dose with doses estimated using prior techniques.