Generalization of a model of tissue response to radiation based on the idea of functional subunits and binomial statistics

Heterogeneity of absorbed dose distribution in kidney tissues and dose–response modelling of nephrotoxicity in radiopharmaceutical therapy with beta-particle emitters: A review

Absorbed dose heterogeneity in kidney tissues is an important issue in radiopharmaceutical therapy. The effect of absorbed dose heterogeneity in nephrotoxicity is, however, not fully understood yet, which hampers the implementation of treatment optimization by obscuring the interpretation of clinical response data and the selection of optimal treatment options. Although some dosimetry methods have been developed for kidney dosimetry to the level of microscopic renal substructures, the clinical assessment of the microscopic distribution of radiopharmaceuticals in kidney tissues currently remains a challenge. This restricts the anatomical resolution of clinical dosimetry, which hinders a thorough clinical investigation of the impact of absorbed dose heterogeneity. The potential of absorbed dose-response modelling to support individual treatment optimization in radiopharmaceutical therapy is recognized and gaining attraction. However, biophysical modelling is currently underexplored for the kidney, where particular modelling challenges arise from the convolution of a complex functional organization of renal tissues with the function-mediated dose distribution of radiopharmaceuticals. This article reviews and discusses the heterogeneity of absorbed dose distribution in kidney tissues and the absorbed dose-response modelling of nephrotoxicity in radiopharmaceutical therapy. The review focuses mainly on the peptide receptor radionuclide therapy with beta-particle emitting somatostatin analogues, for which the scientific literature reflects over two decades of clinical experience. Additionally, detailed research perspectives are proposed to address various identified challenges to progress in this field.

Effects From Nonuniform Dose Distribution in the Spinal Nerves of Pigs: Analysis of Normal Tissue Complication Probability Models

PURPOSE

Our purpose was to evaluate normal tissue complication probability (NTCP) models for their ability to describe the increase in tolerance as the length of irradiated spinal nerve is reduced in a pig.

METHODS AND MATERIALS

Common phenomenological and semimechanistic NTCP models were fit using the maximum likelihood estimate method to dose-response data from spinal nerve irradiation studies in pigs. Statistical analysis was used to compare how well each model fit the data. Model parameters were then applied to a previously published dose distribution used for spinal cord irradiation in rats under the assumption of a similar dose-response.

RESULTS

The Lyman-Kutcher-Burman model, relative seriality, and critical volume model fit the spinal nerve data equally well, but the mean dose logistic and relative seriality models gave the best fit after penalizing for the number of model parameters. The minimum dose logistic regression model was the only model showing a lack of fit. When extrapolated to a 0.5-cm simulated square-wave-like dose distribution, the serial behaving models showed negligible increase in dose-response curve. The Lyman-Kutcher-Burman model and relative seriality models showed significant shifting of NTCP curves due to parallel behaving parameters. The critical volume model gave the closest match to the rat data.

CONCLUSIONS

Several phenomenological and semimechanistic models were observed to adequately describe the increase in the radiation tolerance of the spinal nerves when changing the irradiated length from 1.5 to 0.5 cm. Contrary to common perception, model parameters suggest parallel behaving tissue architecture. Under the assumption that the spinal nerve response to radiation is similar to that of the spinal cord, only the critical volume model was robust when extrapolating to outcome data from a 0.5-cm square-wave-like dose distribution, as was delivered in rodent spinal cord irradiation research.

Impact of dose heterogeneity in target on TCP and NTCP for various radiobiological models in liver SBRT: different isodose prescription strategy

INTRODUCTION

The impact of dose heterogeneity within the tumor on TCP and NTCP was studied using various radiobiological models. The effect of the degree of heterogeneity index (HI) on TCP was also analyzed.

MATERIALS AND METHODS

Thirty-seven pre-treated liver SBRT cases were included in this study. Two different kinds of treatment techniques were employed. In both arms, the prescribed dose was received by 95% of the PTV. Initially, the inhomogeneous treatment plans (IHTP) were made in which the spatial change of dose within the PTV was high and the maximum dose within the PTV can go up to 160%. Subsequently, in another arm, homogeneous treatment plans (HTP) were generated in which PTV was covered with the same prescription isodose and the maximum dose can go up to 120%. As per RTOG 1112, all organs at risk (OAR's) were considered while optimization of the treatment plans. TCP was calculated using the Niemierko and Poisson model. NTCP was calculated using the Niemierko and LKB fractionated model.

RESULTS

For the IHTP, TCP was decreasing as 'a' value decreased in the Niemierko model whereas, for HTP, TCP was found to be the same. NTCP of the normal liver was less in IHTP as compared to HTP, and the Niemierko model overestimates the NTCP as compared to LKB fractionated model. NTCP for all other OAR's was <1% in both kinds of treatment plans.

CONCLUSION

IHTP is found to be clinically better than HTP because NTCP of the normal liver was significantly less and TCP was more for certain 'a' values of the Niemierko model and the Poisson model. There is not any effect of HI on TCP was observed. Advances in knowledge: IHTP could be used clinically because of the dose-escalation and subsequently, leads to an increase in the TCP.

First-passage times and normal tissue complication probabilities in the limit of large populations

The time of a stochastic process first passing through a boundary is important to many diverse applications. However, we can rarely compute the analytical distribution of these first-passage times. We develop an approximation to the first and second moments of a general first-passage time problem in the limit of large, but finite, populations using Kramers–Moyal expansion techniques. We demonstrate these results by application to a stochastic birth-death model for a population of cells in order to develop several approximations to the normal tissue complication probability (NTCP): a problem arising in the radiation treatment of cancers. We specifically allow for interaction between cells, via a nonlinear logistic growth model, and our approximations capture the effects of intrinsic noise on NTCP. We consider examples of NTCP in both a simple model of normal cells and in a model of normal and damaged cells. Our analytical approximation of NTCP could help optimise radiotherapy planning, for example by estimating the probability of complication-free tumour under different treatment protocols.

Temporally feathered intensity-modulated radiation therapy: A planning technique to reduce normal tissue toxicity

PURPOSE

Intensity-modulated radiation therapy (IMRT) has allowed optimization of three-dimensional spatial radiation dose distributions permitting target coverage while reducing normal tissue toxicity. However, radiation-induced normal tissue toxicity is a major contributor to patients' quality of life and often a dose-limiting factor in the definitive treatment of cancer with radiation therapy. We propose the next logical step in the evolution of IMRT using canonical radiobiological principles, optimizing the temporal dimension through which radiation therapy is delivered to further reduce radiation-induced toxicity by increased time for normal tissue recovery. We term this novel treatment planning strategy "temporally feathered radiation therapy" (TFRT).

METHODS

Temporally feathered radiotherapy plans were generated as a composite of five simulated treatment plans each with altered constraints on particular hypothetical organs at risk (OARs) to be delivered sequentially. For each of these TFRT plans, OARs chosen for feathering receive higher doses while the remaining OARs receive lower doses than the standard fractional dose delivered in a conventional fractionated IMRT plan. Each TFRT plan is delivered a specific weekday, which in effect leads to a higher dose once weekly followed by four lower fractional doses to each temporally feathered OAR. We compared normal tissue toxicity between TFRT and conventional fractionated IMRT plans by using a dynamical mathematical model to describe radiation-induced tissue damage and repair over time.

RESULTS

Model-based simulations of TFRT demonstrated potential for reduced normal tissue toxicity compared to conventionally planned IMRT. The sequencing of high and low fractional doses delivered to OARs by TFRT plans suggested increased normal tissue recovery, and hence less overall radiation-induced toxicity, despite higher total doses delivered to OARs compared to conventional fractionated IMRT plans. The magnitude of toxicity reduction by TFRT planning was found to depend on the corresponding standard fractional dose of IMRT and organ-specific recovery rate of sublethal radiation-induced damage.

CONCLUSIONS

TFRT is a novel technique for treatment planning and optimization of therapeutic radiotherapy that considers the nonlinear aspects of normal tissue repair to optimize toxicity profiles. Model-based simulations of TFRT to carefully conceptualized clinical cases have demonstrated potential for radiation-induced toxicity reduction in a previously described dynamical model of normal tissue complication probability (NTCP).

A stochastic model for the normal tissue complication probability (NTCP) and applicationss

The normal tissue complication probability (NTCP) is a measure for the estimated side effects of a given radiation treatment schedule. Here we use a stochastic logistic birth-death process to define an organ-specific and patient-specific NTCP. We emphasize an asymptotic simplification which relates the NTCP to the solution of a logistic differential equation. This framework is based on simple modelling assumptions and it prepares a framework for the use of the NTCP model in clinical practice. As example, we consider side effects of prostate cancer brachytherapy such as increase in urinal frequency, urinal retention and acute rectal dysfunction.

Relating the proton relative biological effectiveness to tumor control and normal tissue complication probabilities assuming interpatient variability in α/β

BACKGROUND

Proton therapy uses a constant relative biological effectiveness (RBE) of 1.1. The use of variable RBE values has been suggested but is currently not feasible due to uncertainties. The impact of variable RBE has solely been studied using dosimetric indices. This work elucidates the impact of RBE variations on tumor control and normal tissue complication probabilities (TCP/NTCP).

METHODS

Models to estimate TCP and NTCP were used in combination with an empirical proton RBE model. Variations in outcome as a function of linear-quadratic model parameters for cellular radiosensitivity were determined for TCP in prostate and ependymoma. In addition, NTCP analysis was done for brainstem necrosis.

RESULTS

Considering a variable proton RBE as a dose-modifying factor for prescription doses and dose constraints is misleading, as TCP/NTCP do not simply scale with RBE. The dependency of RBE on α/β cannot be interpreted independent of TCP/NTCP because variations in radiosensitivity affect both photon and proton treatments. Assuming interpatient variability in radiosensitivity results in lower TCP for patients with low α/β. In proton therapy, the magnitude of TCP variations is reduced due to an RBE increase as α/β decreases. The TCP in proton therapy is less affected by interpatient variability in α/β. On the other hand, patients with a lower α/β would have a lower complication probability, which is counteracted by an increase in RBE as α/β decreases. Toxicities in proton therapy would be more affected by α/β variations compared to photon therapy.

CONCLUSIONS

Assessment of variable RBE in proton therapy should be based on TCP and NTCP. Potential interpatient variability in radiosensitivity causes a smaller variance in TCP but a larger variance in NTCP for proton patients. The relative TCP as a function of α/β was found to be higher than the RBE, whereas the relative NTCP was lower than a calculated RBE.

Modeling tumor control probability for spatially inhomogeneous risk of failure based on clinical outcome data

PURPOSE

Objectives of this work are (1) to derive a general clinically relevant approach to model tumor control probability (TCP) for spatially variable risk of failure and (2) to demonstrate its applicability by estimating TCP for patients planned for photon and proton irradiation.

METHODS AND MATERIALS

The approach divides the target volume into sub-volumes according to retrospectively observed spatial failure patterns. The product of all sub-volume TCP_i values reproduces the observed TCP for the total tumor. The derived formalism provides for each target sub-volume i the tumor control dose (D_50,i) and slope (γ_50,i) parameters at 50% TCP_i. For a simultaneous integrated boost (SIB) prescription for 45 advanced head and neck cancer patients, TCP values for photon and proton irradiation were calculated and compared. The target volume was divided into gross tumor volume (GTV), surrounding clinical target volume (CTV), and elective CTV (CTVE). The risk of a local failure in each of these sub-volumes was taken from the literature.

RESULTS

Convenient expressions for D_50,i and γ_50,i were provided for the Poisson and the logistic model. Comparable TCP estimates were obtained for photon and proton plans of the 45 patients using the sub-volume model, despite notably higher dose levels (on average +4.9%) in the low-risk CTVE for photon irradiation. In contrast, assuming a homogeneous dose response in the entire target volume resulted in TCP estimates contradicting clinical experience (the highest failure rate in the low-risk CTVE) and differing substantially between photon and proton irradiation.

CONCLUSIONS

The presented method is of practical value for three reasons: It (a) is based on empirical clinical outcome data; (b) can be applied to non-uniform dose prescriptions as well as different tumor entities and dose-response models; and (c) is provided in a convenient compact form. The approach may be utilized to target spatial patterns of local failures observed in patient cohorts by prescribing different doses to different target regions. Its predictive power depends on the uncertainty of the employed established TCP parameters D₅₀ and γ₅₀ and to a smaller extent on that of the clinically observed pattern of failure risk.

Influence of concentration, nanoparticle size, beam energy, and material on dose enhancement in radiation therapy

The purpose of this study was to analyse the effects of the type, concentration, and nanoparticle diameter of dose enhancement materials on the dose enhancement of low- and high-energy megavoltage (MV) X-rays acquired from a medical linear accelerator using Monte Carlo simulation. Monte Carlo simulation was performed with the Monte Carlo N-Particle Transport (MCNPX) code, using the energy spectrum of the linear accelerator and a mathematical Snyder head phantom. A 5-cm-diameter virtual tumour was defined in the centre of the phantom. Gold, gadolinium, iodine and iron oxide were used as dose enhancement materials. Varying concentrations (7, 18 and 30 mg/g) of nanoparticles of different diameters (25, 50, 75, 100 and 125 nm) were applied, and the dose enhancement was comparatively evaluated for 4, 6, 10 and 15 MV X-rays, and a 60Co source. Higher dose enhancement factors (DEFs) were observed when the incident energy was low. Moreover, the dose enhancement effects were greatest with gold nanoparticles, followed by gadolinium, iodine, and iron oxide nanoparticles; the DEFs were 1.011-1.047 (gold), 1.005-1.030 (gadolinium), 1.002-1.028 (iodine) and 1.002-1.014 (iron oxide). The dose enhancement effects increased with increasing nanoparticle diameter and concentration. However, the concentration of the material had a greater impact than the diameter of the nanoparticles. As the concentration and diameter of nanoparticles increased, the DEF also increased. The 4 and 6 MV X-rays demonstrated higher dose enhancement compared with the 10 and 15 MV X-rays.

Modeling Radiotherapy Induced Normal Tissue Complications: An Overview beyond Phenomenological Models

An overview of radiotherapy (RT) induced normal tissue complication probability (NTCP) models is presented. NTCP models based on empirical and mechanistic approaches that describe a specific radiation induced late effect proposed over time for conventional RT are reviewed with particular emphasis on their basic assumptions and related mathematical translation and their weak and strong points.

Big Data Analytics for Prostate Radiotherapy

Radiation therapy is a first-line treatment option for localized prostate cancer and radiation-induced normal tissue damage are often the main limiting factor for modern radiotherapy regimens. Conversely, under-dosing of target volumes in an attempt to spare adjacent healthy tissues limits the likelihood of achieving local, long-term control. Thus, the ability to generate personalized data-driven risk profiles for radiotherapy outcomes would provide valuable prognostic information to help guide both clinicians and patients alike. Big data applied to radiation oncology promises to deliver better understanding of outcomes by harvesting and integrating heterogeneous data types, including patient-specific clinical parameters, treatment-related dose-volume metrics, and biological risk factors. When taken together, such variables make up the basis for a multi-dimensional space (the "RadoncSpace") in which the presented modeling techniques search in order to identify significant predictors. Herein, we review outcome modeling and big data-mining techniques for both tumor control and radiotherapy-induced normal tissue effects. We apply many of the presented modeling approaches onto a cohort of hypofractionated prostate cancer patients taking into account different data types and a large heterogeneous mix of physical and biological parameters. Cross-validation techniques are also reviewed for the refinement of the proposed framework architecture and checking individual model performance. We conclude by considering advanced modeling techniques that borrow concepts from big data analytics, such as machine learning and artificial intelligence, before discussing the potential future impact of systems radiobiology approaches.

Outcome modeling techniques for prostate cancer radiotherapy: Data, models, and validation

Prostate cancer is a frequently diagnosed malignancy worldwide and radiation therapy is a first-line approach in treating localized as well as locally advanced cases. The limiting factor in modern radiotherapy regimens is dose to normal structures, an excess of which can lead to aberrant radiation-induced toxicities. Conversely, dose reduction to spare adjacent normal structures risks underdosing target volumes and compromising local control. As a result, efforts aimed at predicting the effects of radiotherapy could invaluably optimize patient treatments by mitigating such toxicities and simultaneously maximizing biochemical control. In this work, we review the types of data, frameworks and techniques used for prostate radiotherapy outcome modeling. Consideration is given to clinical and dose-volume metrics, such as those amassed by the QUANTEC initiative, and also to newer methods for the integration of biological and genetic factors to improve prediction performance. We furthermore highlight trends in machine learning that may help to elucidate the complex pathophysiological mechanisms of tumor control and radiation-induced normal tissue side effects.

Assessment of radiobiological metrics applied to patient-specific QA process of VMAT prostate treatments

VMAT is a powerful technique to deliver hypofractionated prostate treatments. The lack of correlations between usual 2D pretreatment QA results and the clinical impact of possible mistakes has allowed the development of 3D verification systems. Dose determination on patient anatomy has provided clinical predictive capability to patient-specific QA process. Dose-volume metrics, as evaluation criteria, should be replaced or complemented by radiobiological indices. These metrics can be incorporated into individualized QA extracting the information for response parameters (gEUD, TCP, NTCP) from DVHs. The aim of this study is to assess the role of two 3D verification systems dealing with radiobiological metrics applied to a prostate VMAT QA program. Radiobiological calculations were performed for AAPM TG-166 test cases. Maximum differences were 9.3% for gEUD, -1.3% for TCP, and 5.3% for NTCP calculations. Gamma tests and DVH-based comparisons were carried out for both systems in order to assess their performance in 3D dose determination for prostate treatments (high-, intermediate-, and low-risk, as well as prostate bed patients). Mean gamma passing rates for all structures were bet-ter than 92.0% and 99.1% for both 2%/2 mm and 3%/3 mm criteria. Maximum discrepancies were (2.4% ± 0.8%) and (6.2% ± 1.3%) for targets and normal tis-sues, respectively. Values for gEUD, TCP, and NTCP were extracted from TPS and compared to the results obtained with the two systems. Three models were used for TCP calculations (Poisson, sigmoidal, and Niemierko) and two models for NTCP determinations (LKB and Niemierko). The maximum mean difference for gEUD calculations was (4.7% ± 1.3%); for TCP, the maximum discrepancy was (-2.4% ± 1.1%); and NTCP comparisons led to a maximum deviation of (1.5% ± 0.5%). The potential usefulness of biological metrics in patient-specific QA has been explored. Both systems have been successfully assessed as potential tools for evaluating the clinical outcome of a radiotherapy treatment in the scope of pretreatment QA.

Dose volume histogram analysis and comparison of different radiobiological models using in-house developed software

The purpose of this study is to compare Lyman-Kutcher-Burman (LKB) model versus Niemierko model for normal tissue complication probability (NTCP) calculation and Niemierko model versus Poisson-based model for tumor control probability (TCP) calculation in the ranking of different treatment plans for a patient undergoing radiotherapy. The standard normal tissue tolerance data were used to test the NTCP models. LKB model can reproduce the same complication probability data of normal tissue response on radiation, whereas Niemierko model cannot reproduce the same complication probability. Both Poisson-based and Niemierko models equally reproduce the same standard TCP data in testing of TCP. In case of clinical data generated from treatment planning system, NTCP calculated using LKB model was found to be different from that calculated using Niemierko model. When the fractionation effect was considered in LKB model, the calculated values of NTCPs were different but comparable with those of Niemierko model. In case of TCP calculation using these models, Poisson-based model calculated marginally higher control probability as compared to Niemierko model.

Monte Carlo role in radiobiological modelling of radiotherapy outcomes

Radiobiological models are essential components of modern radiotherapy. They are increasingly applied to optimize and evaluate the quality of different treatment planning modalities. They are frequently used in designing new radiotherapy clinical trials by estimating the expected therapeutic ratio of new protocols. In radiobiology, the therapeutic ratio is estimated from the expected gain in tumour control probability (TCP) to the risk of normal tissue complication probability (NTCP). However, estimates of TCP/NTCP are currently based on the deterministic and simplistic linear-quadratic formalism with limited prediction power when applied prospectively. Given the complex and stochastic nature of the physical, chemical and biological interactions associated with spatial and temporal radiation induced effects in living tissues, it is conjectured that methods based on Monte Carlo (MC) analysis may provide better estimates of TCP/NTCP for radiotherapy treatment planning and trial design. Indeed, over the past few decades, methods based on MC have demonstrated superior performance for accurate simulation of radiation transport, tumour growth and particle track structures; however, successful application of modelling radiobiological response and outcomes in radiotherapy is still hampered with several challenges. In this review, we provide an overview of some of the main techniques used in radiobiological modelling for radiotherapy, with focus on the MC role as a promising computational vehicle. We highlight the current challenges, issues and future potentials of the MC approach towards a comprehensive systems-based framework in radiobiological modelling for radiotherapy.

From cell population models to tumor control probability: including cell cycle effects

BACKGROUND

Classical expressions for the tumor control probability (TCP) are based on models for the survival fraction of cancer cells after radiation treatment. We focus on the derivation of expressions for TCP from dynamic cell population models. In particular, we derive a TCP formula for a generalized cell population model that includes the cell cycle by considering a compartment of actively proliferating cells and a compartment of quiescent cells, with the quiescent cells being less sensitive to radiation than the actively proliferating cells.

METHODS

We generalize previously derived TCP formulas of Zaider and Minerbo and of Dawson and Hillen to derive a TCP formula from our cell population model. We then use six prostate cancer treatment protocols as a case study to show how our TCP formula works and how the cell cycle affects the tumor treatment.

RESULTS

The TCP formulas of Zaider-Minerbo and of Dawson-Hillen are special cases of the TCP formula presented here. The former one represents the case with no quiescent cells while the latter one assumes that all newly born cells enter a quiescent cell phase before becoming active. From our case study, we observe that inclusion of the cell cycle lowers the TCP.

CONCLUSION

The cell cycle can be understood as the sequestration of cells in the quiescent compartment, where they are less sensitive to radiation. We suggest that our model can be used in combination with synchronization methods to optimize treatment timing.

Population TCP estimators in case of heterogeneous irradiation: a new discussion of an old problem

PURPOSE

To investigate the capacity of two phenomenological expressions to describe the population tumor response in case of a heterogeneous irradiation of the tumor. The generalization of the individual tumor control probability (TCP) models to include the case of a heterogeneous irradiation is a trivial problem. However, an analytical solution that results in a closed form population TCP formula for the heterogeneous case is, unfortunately, a very complex mathematical problem. Therefore we applied a numerical approach to the problem.

METHOD

Pseudo-experimental data sets are constructed through the generation of dose distributions and population TCP data obtained by a numerical solution of a multi-dimensional integral over an individual TCP model. The capacity of the following two phenomenological - Poisson and equivalent uniform dose (EUD) based - TCP expressions: [Figure: see text] to describe the population tumor response in case of heterogeneous irradiation is investigated through their fitting to the psuedo-experimental data sets. RESULTS AND CONCLUSIONS. While both expressions produce statistically acceptable fits to the pseudo-experimental data within 2% TCP error band, the use of the second expression is preferable since it produces considerably better fits to the data sets.

Mechanistic simulation of normal-tissue damage in radiotherapy--implications for dose-volume analyses

A radiobiologically based 3D model of normal tissue has been developed in which complications are generated when 'irradiated'. The aim is to provide insight into the connection between dose-distribution characteristics, different organ architectures and complication rates beyond that obtainable with simple DVH-based analytical NTCP models. In this model the organ consists of a large number of functional subunits (FSUs), populated by stem cells which are killed according to the LQ model. A complication is triggered if the density of FSUs in any 'critical functioning volume' (CFV) falls below some threshold. The (fractional) CFV determines the organ architecture and can be varied continuously from small (series-like behaviour) to large (parallel-like). A key feature of the model is its ability to account for the spatial dependence of dose distributions. Simulations were carried out to investigate correlations between dose-volume parameters and the incidence of 'complications' using different pseudo-clinical dose distributions. Correlations between dose-volume parameters and outcome depended on characteristics of the dose distributions and on organ architecture. As anticipated, the mean dose and V(20) correlated most strongly with outcome for a parallel organ, and the maximum dose for a serial organ. Interestingly better correlation was obtained between the 3D computer model and the LKB model with dose distributions typical for serial organs than with those typical for parallel organs. This work links the results of dose-volume analyses to dataset characteristics typical for serial and parallel organs and it may help investigators interpret the results from clinical studies.

A comparison of HDR brachytherapy and IMRT techniques for dose escalation in prostate cancer: a radiobiological modeling study

A course of one to three large fractions of high dose rate (HDR) interstitial brachytherapy is an attractive alternative to intensity modulated radiation therapy (IMRT) for delivering boost doses to the prostate in combination with additional external beam irradiation for intermediate risk disease. The purpose of this work is to quantitatively compare single-fraction HDR boosts to biologically equivalent fractionated IMRT boosts, assuming idealized image guided delivery (igIMRT) and conventional delivery (cIMRT). For nine prostate patients, both seven-field IMRT and HDR boosts were planned. The linear-quadratic model was used to compute biologically equivalent dose prescriptions. The cIMRT plan was evaluated as a static plan and with simulated random and setup errors. The authors conclude that HDR delivery produces a therapeutic ratio which is significantly better than the conventional IMRT and comparable to or better than the igIMRT delivery. For the HDR, the rectal gBEUD analysis is strongly influenced by high dose DVH tails. A saturation BED, beyond which no further injury can occur, must be assumed. Modeling of organ motion uncertainties yields mean outcomes similar to static plan outcomes.

Analyzing adjuvant radiotherapy suggests a non monotonic radio-sensitivity over tumor volumes

BACKGROUND

Adjuvant Radiotherapy (RT) after surgical removal of tumors proved beneficial in long-term tumor control and treatment planning. For many years, it has been well concluded that radio-sensitivities of tumors upon radiotherapy decrease according to the sizes of tumors and RT models based on Poisson statistics have been used extensively to validate clinical data.

RESULTS

We found that Poisson statistics on RT is actually derived from bacterial cells despite of many validations from clinical data. However cancerous cells do have abnormal cellular communications and use chemical messengers to signal both surrounding normal and cancerous cells to develop new blood vessels and to invade, to metastasis and to overcome intercellular spatial confinements in general. We therefore investigated the cell killing effects on adjuvant RT and found that radio-sensitivity is actually not a monotonic function of volume as it was believed before. We present detailed analysis and explanation to justify above statement. Based on EUD, we present an equivalent radio-sensitivity model.

CONCLUSION

We conclude that radio sensitivity is a sophisticated function over tumor volumes, since tumor responses upon radio therapy also depend on cellular communications.

Analytic investigation into effect of population heterogeneity on parameter ratio estimates

PURPOSE

A homogeneous tumor control probability (TCP) model has previously been used to estimate the alpha/beta ratio for prostate cancer from clinical dose-response data. For the ratio to be meaningful, it must be assumed that parameter ratios are not sensitive to the type of tumor control model used. We investigated the validity of this assumption by deriving analytic relationships between the alpha/beta estimates from a homogeneous TCP model, ignoring interpatient heterogeneity, and those of the corresponding heterogeneous (population-averaged) model that incorporated heterogeneity.

METHODS AND MATERIALS

The homogeneous and heterogeneous TCP models can both be written in terms of the geometric parameters D(50) and gamma(50). We show that the functional forms of these models are similar. This similarity was used to develop an expression relating the homogeneous and heterogeneous estimates for the alpha/beta ratio. The expression was verified numerically by generating pseudo-data from a TCP curve with known parameters and then using the homogeneous and heterogeneous TCP models to estimate the alpha/beta ratio for the pseudo-data.

RESULTS

When the dominant form of interpatient heterogeneity is that of radiosensitivity, the homogeneous and heterogeneous alpha/beta estimates differ. This indicates that the presence of this heterogeneity affects the value of the alpha/beta ratio derived from analysis of TCP curves.

CONCLUSIONS

The alpha/beta ratio estimated from clinical dose-response data is model dependent--a heterogeneous TCP model that accounts for heterogeneity in radiosensitivity will produce a greater alpha/beta estimate than that resulting from a homogeneous TCP model.

Reverse mapping of normal tissue complication probabilities onto dose volume histogram space: the problem of randomness of the dose volume histogram sampling

A very important issue in contemporary inverse treatment radiotherapy planning is the specification of proper dose-volume constraints limiting the treatment planning algorithm from delivering high doses to the normal tissue surrounding the tumor. Recently we have proposed a method called reverse mapping of normal tissue complication probabilities (NTCP) onto dose-volume histogram (DVH) space, which allows the calculation of appropriate biologically based dose-volume constraints to be used in the inverse treatment planning. The method of reverse mapping requires random sampling from the functional space of all monotonically decreasing functions in the unit square. We develop, in this paper, a random function generator for the purpose of the reverse mapping. Since the proposed generator is based on the theory of random walk, it is therefore designated in this work, as a random walk DVH generator. It is theoretically determined that the distribution of the number of monotonically decreasing functions passing through a point in the dose volume histogram space follows the hypergeometric distribution. The proposed random walk DVH generator thus simulates, in a random fashion, trajectories of monotonically decreasing functions (finite series) that are situated in the unit square [0, 1] X [1,0] using the hypergeometric distribution. The DVH generator is an important tool in the study of reverse NTCP mapping for the calculation of biologically based dose-volume constraints for inverse treatment planning.

Deoxynivalenol in barley samples from Uruguay

A survey of the natural occurrence of deoxynivalenol (DON) in barley harvested in Uruguay from 1996 to 2002 was conducted. A total of 292 samples were analyzed for DON by an immunochemical method using inmunoaffinity columns and fluorimetric detection. Between 26 and 100% of the samples were positive for DON while mean DON contents varied between the quantification limit (500 mug/kg) to 6349 mug/kg. Annual maximum levels in individual samples ranged from 1900 mug/kg to 10,000 mug/kg. The mean DON contents were similar from 1996 to 1999 increasing markedly from 2000 to 2002. The percentage of the samples with DON were highest in 1997, 2000, 2001 and 2002 (67, 90, 100 and 100%) as was the accumulated precipitation during the flowering period. A positive correlation between DON levels and precipitation was seen. These results suggest that monitoring for DON barley crops, particularly in years with heavy rainfall during the flowering period, must be regularly performed.

Dose response explorer: an integrated open-source tool for exploring and modelling radiotherapy dose–volume outcome relationships

Radiotherapy treatment outcome models are a complicated function of treatment, clinical and biological factors. Our objective is to provide clinicians and scientists with an accurate, flexible and user-friendly software tool to explore radiotherapy outcomes data and build statistical tumour control or normal tissue complications models. The software tool, called the dose response explorer system (DREES), is based on Matlab, and uses a named-field structure array data type. DREES/Matlab in combination with another open-source tool (CERR) provides an environment for analysing treatment outcomes. DREES provides many radiotherapy outcome modelling features, including (1) fitting of analytical normal tissue complication probability (NTCP) and tumour control probability (TCP) models, (2) combined modelling of multiple dose-volume variables (e.g., mean dose, max dose, etc) and clinical factors (age, gender, stage, etc) using multi-term regression modelling, (3) manual or automated selection of logistic or actuarial model variables using bootstrap statistical resampling, (4) estimation of uncertainty in model parameters, (5) performance assessment of univariate and multivariate analyses using Spearman's rank correlation and chi-square statistics, boxplots, nomograms, Kaplan-Meier survival plots, and receiver operating characteristics curves, and (6) graphical capabilities to visualize NTCP or TCP prediction versus selected variable models using various plots. DREES provides clinical researchers with a tool customized for radiotherapy outcome modelling. DREES is freely distributed. We expect to continue developing DREES based on user feedback.

A theoretical approach to the problem of dose-volume constraint estimation and their impact on the dose-volume histogram selection

This paper outlines a theoretical approach to the problem of estimating and choosing dose-volume constraints. Following this approach, a method of choosing dose-volume constraints based on biological criteria is proposed. This method is called "reverse normal tissue complication probability (NTCP) mapping into dose-volume space" and may be used as a general guidance to the problem of dose-volume constraint estimation. Dose-volume histograms (DVHs) are randomly simulated, and those resulting in clinically acceptable levels of complication, such as NTCP of 5 +/- 0.5%, are selected and averaged producing a mean DVH that is proven to result in the same level of NTCP. The points from the averaged DVH are proposed to serve as physical dose-volume constraints. The population-based critical volume and Lyman NTCP models with parameter sets taken from literature sources were used for the NTCP estimation. The impact of the prescribed value of the maximum dose to the organ, D(max), on the averaged DVH and the dose-volume constraint points is investigated. Constraint points for 16 organs are calculated. The impact of the number of constraints to be fulfilled based on the likelihood that a DVH satisfying them will result in an acceptable NTCP is also investigated. It is theoretically proven that the radiation treatment optimization based on physical objective functions can sufficiently well restrict the dose to the organs at risk, resulting in sufficiently low NTCP values through the employment of several appropriate dose-volume constraints. At the same time, the pure physical approach to optimization is self-restrictive due to the preassignment of acceptable NTCP levels thus excluding possible better solutions to the problem.

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

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

Limitations of a TCP model incorporating population heterogeneity

The variation between individuals in their dose-response characteristics complicates attempts to extract estimates of radiobiological parameters (e.g. alpha, beta, etc) from fits to clinical dose-response data. The use of 'population' dose-response models that explicitly account for this variability is necessary to avoid obtaining skewed parameter estimates. In this work, we evaluated an example of a 'population' tumour control probability (TCP) model in terms of its ability to provide reliable parameter estimates. This was accomplished by performing fits of this population model to 'pseudo' data sets, which were generated with Monte Carlo techniques and based on preset values for the various radiobiological parameters. The fitting exercises illustrated considerable correlations between the model parameters. Especially significant was the large correlation observed between the parameter mu=alpha/sigmaalpha used to characterize the level of population heterogeneity in radiosensitivity and the alpha/beta parameter typically used to describe the response to fractionation. The results imply that fits to clinical data may not be able to distinguish between tumours exhibiting a high degree of heterogeneity and a strong beta-mechanism and those containing little heterogeneity and having a weak beta-mechanism. One implication is that basing the design of optimal fractionation regimes on such fitting results may be error-prone. If in vitro assays are to be used to independently determine biologically reasonable ranges for parameter values, an accurate knowledge of the relationship between in vitro and in vivo dose-response characteristics is required.

Critical volume model analysis of lung complication data from different strains of mice

The critical volume (CV) normal tissue complication probability (NTCP) model was used to fit experimental data on radiation pneumonitis in mice to test the model and determine the values of the model parameters characterizing the lung structure: relative critical volume and cell radiosensitivity. The entire lungs of mice from ten different strains were irradiated acutely and homogeneously to different doses. The experimental animals from the different strains expressed different radiation sensitivities, forming ten well-defined dose-response curves. The most widely accepted biological NTCP model (the individual CV NTCP) readily applicable to cases of acute uniform irradiation was used to fit all the individual dose-response curves simultaneously. To account for the apparent difference in the response of the different strains, it was assumed that the strains differed in their (cell) radiosensitivity. The maximum likelihood method of fitting was used. The obtained fit was statistically highly acceptable. The best-fit value of the relative critical volume, mu, was 78%, which is extremely close to the histologically observed value of around 72%. The values of radiosensitivity, alpha, ranged between 0.26 and 0.37 Gy(-1) for the different strains. The best-fit numbers of functional subunits (FSU) constituting the lung, N, and the number of cells in an FSU, N(o), were implausibly low: N = 9 and N(o) = 23, respectively. The best-fit value of N(o)N was a very small number that was unlikely to correspond to the total number of cells comprising the lung, suggesting that a different interpretation of N and N(o) was required. The individual CV model provided a simultaneous description of the individual responses of different mouse strains through assumed interindividual variability in alpha only. A new interpretation is given to the entities corresponding to N(o) and N. N(o)N is interpreted as the number of certain elementary structures. These structures are considered to be equivalent to the classical functional subunit, which is much larger than a cell and plays a fundamental role in determining the radiation response of the organ. N is identified as the number of the few large subdivisions of the lungs, M = microN is the number that have to be damaged for the lung to fail. N(o) is interpreted as the mean number of elementary structures (FSU) per large subdivision. This imposes a picture of damage to large, contiguous subdivisions containing many FSU, which is consistent with the histological appearance of the lungs of mice in respiratory distress. This picture is in marked contrast to the random distribution of small areas of damage expected for the small size of an FSU. This random distribution is characteristic of earlier stages of the development of radiation pneumonitis, suggesting that some additional process spreads injury from damaged FSU to adjacent, undamaged FSU during the terminal phase.

Radiation damage, repopulation and cell recovery analysis ofin vitrotumour cell megacolony culture data using a non-Poissonian cell repopulation TCP model

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

Mechanism and modification of gastrointestinal soft tissue response to radiation: role of growth factors

PURPOSE

The negative effects of radiation on the bowel critically limit the treatment doses possible for tumors in the abdomen. The purpose of the present study was to measure mRNA levels of inflammatory cytokines in abdominally irradiated mouse bowel.

METHODS AND MATERIALS

Eight- to 12-week-old DBA mice were irradiated to the whole bowel in single fractions of 0 (mock irradiation), 12.5, or 13.5 Gy, and sacrificed 18-25 weeks thereafter. Gross bowel reactions were scored for bowel retraction, bowel wall thickening, mesenteric telangiectasia, and petechia. Tissues were snap frozen and processed for RNase protection assay or reverse transcription polymerase chain reaction assay, or both. Transforming growth factor beta1 (TGFbeta1), TGFbeta2, TGFbeta3, tumor necrosis factor alpha, interleukin-6, and interferon gamma mRNA were measured.

RESULTS

Radiation at 12.5 Gy and at 13.5 Gy produced significant bowel damage. Levels of all cytokines in irradiated mice were significantly increased (p < 0.05).

CONCLUSIONS

Late radiation-related bowel fibrovascular toxicity includes cytokine signal pathways that parallel those of many other normal tissues. These cytokine responses include elevations of tumor necrosis factor alpha, TGFbeta1, and interleukin-6. There exist approaches for lowering these cytokine levels that do not also protect tumor, and thus a therapeutic gain is expected. Opportunities to use these cytokine measurements both to predict clinical toxicity and to develop interventions are discussed.

Characterization of rectal normal tissue complication probability after high-dose external beam radiotherapy for prostate cancer

PURPOSE

Conformal radiotherapy (RT) has allowed radiation dose escalation to improve the outcome of prostate cancer. With higher doses, concern exists that rectal injury may increase. This study analyzed the utility and limitations of the widely used Lyman-Kutcher- Burman (LKB) normal tissue complication probability model in projecting the hazards of rectal complication with high-dose RT.

METHODS AND MATERIALS

A total of 128 patients were included in this study. These patients were treated with three-dimensional conformal RT alone at the University of Texas M.D. Anderson Cancer Center between 1992 and 1999. Patients were treated to 46 Gy with a four-field box technique followed by a six-field arrangement to boost the total dose to 78 Gy. All doses were delivered at 2 Gy/fraction to the isocenter. The minimal follow-up was 2 years. The end point for analysis was Grade 2 or worse rectal bleeding by 2 years. The LKB model was fitted to the data using the maximal likelihood method.

RESULTS

Of the 128 patients, 29 experienced Grade 2 or worse rectal bleeding by 2 years. For the entire cohort, the parameters obtained from the fit of the LKB model were as follows: the volume factor was n = 3.91 (95% confidence interval [CI] 0.031 to infinity ), dose associated with 50% chance of complication for uniform whole rectal irradiation [TD50(1)] was 53.6 Gy (95% CI 50.0-75.1), and a determinant of the steepness of the dose-response curve, (m), was 0.156 (95% CI 0.036-0.271). A statistically significant difference was found in the rate of postradiation rectal bleeding in patients with hemorrhoids vs. those without hemorrhoids. The parameters obtained for the patients without hemorrhoids were as follows: n = 0.746 (95% CI 0.026 to infinity ), TD50(1) 56.7 Gy (95% CI 49.9-75.2), and m 0.092 (95% CI 0.019-0.189).

CONCLUSION

Our analysis suggests a dose response for rectal bleeding probability along with a volume effect. We found that the LKB model might have limited utility in determining a large volume effect. We further suggest that LKB model should be used with caution in clinical practice.

Incorporation of functional imaging data in the evaluation of dose distributions using the generalized concept of equivalent uniform dose

Advances in the fields of IMRT and functional imaging have greatly increased the prospect of escalating the dose to highly active or hypoxic tumour sub-volumes and steering the dose away from highly functional critical structure regions. However, current clinical treatment planning and evaluation tools assume homogeneous activity/function status in the tumour/critical structures. A method was developed to incorporate tumour/critical structure heterogeneous functionality in the generalized concept of equivalent uniform dose (EUD). The tumour and critical structures functional EUD (FEUD) values were calculated from the dose-function histogram (DFH), which relates dose to the fraction of total function value at that dose. The DFH incorporates flouro-deoxyglucose positron emission tomography (FDG-PET) functional data for tumour, which describes the distribution of metabolically active tumour clonogens, and single photon emission computed tomography (SPECT) perfusion data for critical structures. To demonstrate the utility of the method, the lung dose distributions of two non-small cell lung cancer patients, who received 3D conformal external beam radiotherapy treatment with curative intent, were evaluated. Differences between the calculated lungs EUD and FEUD values of up to 50% were observed in the 3D conformal plans. In addition, a non-small cell lung cancer patient was inversely planned with a target dose prescription of 76 Gy. Two IMRT plans (plan-A and plan-B) were generated for the patient based on the CT, FDG-PET and SPECT treatment planning images using dose-volume objective functions. The IMRT plans were generated with the goal of achieving more critical structures sparing in plan-B than plan-A. Results show the target volume EUD in plan-B is lower than plan-A by 5% with a value of 73.31 Gy, and the FEUD in plan-B is lower than plan-A by 2.6% with a value of 75.77 Gy. The FEUD plan-B values for heart and lungs were lower than plan-A by 22% and 18%, respectively. While EUD values show plan-A is marginally better than plan-B in terms of target volumetric coverage, the FEUD plan-B values show adequate target function coverage with significant critical structure function sparing. In conclusion, incorporating functional data in the calculation of EUD is important in evaluating the biological merit of treatment plans.

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

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

PACS number: 87.53.Tf

Exploring the effect of marked normal structure volume on normal tissue complication probability

Radiation therapy dosimetry software now frequently incorporates biological predictions of the probability of normal tissue complications. This study investigates whether the length of normal structure outlined affects a normal tissue complication probability (NTCP) for that structure. It also researches the effect of any change in the dose parameter used to produce a 50% probability of a complication (the TD50) on the calculated NTCP, as this is related to the clinical observations. An NTCP was calculated for rectum and bladder on a sample of prostate cases receiving external beam radiation therapy. The length of the organs at risk was varied and the NTCP recalculated for each different length using the same treatment plan. Large variations of up to 80% in NTCP for different delineated lengths of organ for a given TD50 were observed. Changing the TD50 dose altered the calculated NTCP and the relative size of the variation in the values. This parameter will need further investigation; a standardized delineated length of 2 cm beyond the beam edge for normal structures is recommended. Interpatient and interinstitution plan comparison using dose volume histograms and/or normal tissue complication probabilities will be compromised until such standardization occurs.

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

PURPOSE

To compare the partially wide tangent (PWT) technique of breast and internal mammary chain irradiation with photon/electron (P/E) and standard tangent (ST) techniques in terms of dose homogeneity within breast and the dose to critical structures such as the heart and lung.

METHODS AND MATERIALS

Sixteen left breast cancer patients underwent CT simulation. The breasts, lungs, heart, and internal mammary chain were contoured and treatment plans generated on a three-dimensional planning system (Helax-TMS).

RESULTS

The mean dose to the left breast volume with the ST, P/E, and PWT techniques was 94.7%, 98.4%, and 96.5%, respectively (p = 0.029). The left lung received the lowest mean dose with the ST technique (13.9%) compared with PWT (22.8%) and P/E (24.3%). The internal mammary chain volume was most consistently treated with the PWT (mean dose 99%) vs. P/E (86%) and ST (38.4%) techniques. The heart received the least dose with ST (mean dose 6.7%) vs. PWT (10.3%) and P/E (19%). The PWT treated the greatest amount of contralateral breast (mean dose 5.8%) vs. ST (3.2%) vs. P/E (2.8%).

CONCLUSION

The PWT technique treats the internal mammary chain with acceptable toxicity to major organs, especially the heart, and with reasonable dose homogeneity in patients with mastectomy or intact breasts.

Derivation of the expressions for gamma50 and D50 for different individual TCP and NTCP models

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

Direct aperture optimization: a turnkey solution for step-and-shoot IMRT

IMRT treatment plans for step-and-shoot delivery have traditionally been produced through the optimization of intensity distributions (or maps) for each beam angle. The optimization step is followed by the application of a leaf-sequencing algorithm that translates each intensity map into a set of deliverable aperture shapes. In this article, we introduce an automated planning system in which we bypass the traditional intensity optimization, and instead directly optimize the shapes and the weights of the apertures. We call this approach "direct aperture optimization." This technique allows the user to specify the maximum number of apertures per beam direction, and hence provides significant control over the complexity of the treatment delivery. This is possible because the machine dependent delivery constraints imposed by the MLC are enforced within the aperture optimization algorithm rather than in a separate leaf-sequencing step. The leaf settings and the aperture intensities are optimized simultaneously using a simulated annealing algorithm. We have tested direct aperture optimization on a variety of patient cases using the EGS4/BEAM Monte Carlo package for our dose calculation engine. The results demonstrate that direct aperture optimization can produce highly conformal step-and-shoot treatment plans using only three to five apertures per beam direction. As compared with traditional optimization strategies, our studies demonstrate that direct aperture optimization can result in a significant reduction in both the number of beam segments and the number of monitor units. Direct aperture optimization therefore produces highly efficient treatment deliveries that maintain the full dosimetric benefits of IMRT.