The relative costs of proton and X-ray radiation therapy.

AIM: To study the costs of intensity-modulated proton therapy and intensity-modulated X-ray therapy with the particular goal of understanding their relative differences. To analyse the ratio of the cost per fraction of proton therapy to the cost per fraction of X-ray therapy. MATERIALS AND METHODS: We have used a computer spreadsheet tool in which a large number (typically 130) of input parameters characterizing a particular therapeutic modality can be stored. From these parameters a number of derived variables are computed, and from these derived variables the costs of sub-systems, the entire facility, running costs and cost per fraction and per treatment can be computed. The sensitivity of any given variable (e.g. cost/fraction) to any given parameter (e.g. set-up time) can be explored, together with an estimate of the associated confidence interval. The costs of facility construction and facility operation are considered separately. Key data for the input variables regarding the cost of the therapy equipment (a dominant cost for proton beam therapy) were provided by four commercial vendors. Other costs, such as costs for building construction and shielding or personnel costs, are much more standard and our estimates were primarily based on practical experience. We considered two scenarios: (1) both facilities operating under current conditions; and (2) future facilities where foreseeable improvements in efficiency and a 25% reduction in the cost of the proton equipment were assumed. RESULTS: The construction cost of a current two-gantry proton facility, complete with the equipment, was estimated at 62,500 kEE and of a two-linac X-ray facility at 16,800 kEE. In the case of proton therapy the cost of operation of the facility was found to be dominated, by the business cost (42%--primarily the cost of repaying the presumed loan for facility construction), personnel costs (28%) and the cost of servicing the equipment (21%). For X-ray therapy, the cost of operation was seen to be dominated by the personnel cost (51%) and the business costs (28%). The costs per fraction were estimated to be 1.025 kEE for protons and 0.425 kEE for X-rays--for a ratio of costs of 2.4 +/- 0.35 (85% confidence). In a future facility these costs could be reduced to 0.65 kEE and 0.31 kEE respectively, leading to a ratio of costs of 2.1. A number of further improvements could be imagined which could reduce the ratio of costs by some 20%. If, however, the initial capital investment were 'forgiven,' so that the operating costs need not repay the investment, both the costs and the ratio of costs would be significantly less. We estimate that, under this condition, the future costs of proton and X-ray therapies would be 0.37 kEE and 0.23 kEE, respectively, for a cost-per-fraction ratio of 1.6. This ratio could also be susceptible to a further 20% reduction. CONCLUSIONS: Sophisticated (i.e., intensity-modulated) proton therapy is now, and is likely to continue to be, more expensive than sophisticated (i.e., intensity-modulated) X-ray therapy. The ratio of costs is about 2.4 at present and could readily come down to 2.1, and even, perhaps 1.7 over the next 5 to 10 years. If recovery of the initial investment is not required, the ratio of costs would be much lower, in the range of 1.6 to 1.3. The question of whether the greater cost of proton beam therapy is clinically worthwhile is a cost-effectiveness issue. The goal of this study is to contribute to the former arm of this comparison.

Biophysical modelling of proton radiation effects based on amorphous track models.

PURPOSE: To define a photon-equivalent dose in charged particle therapy one needs to know the RBE (Relative Biological Effectiveness) in the target region as well as in the surrounding tissue. RBE estimates are difficult since both the physical input parameters, i.e. LET distributions, and, even more so, the biological input parameters, i.e. cell nucleus size and local response, are not known in general. Track structure theory provides a basis for predicting dose-response curves for particle irradiation. There are (at least) two somewhat different algorithms: the Amorphous Track Partition model (ATP) and the Amorphous Track Local effect model (ATL). Both have been reported to give good agreement with observed radiobiological data. We were interested in a general comparison and in the predictive power of these models for protons. MATERIALS AND METHODS: We compared the principles of the two track structure approaches. The general dependencies of the model predictions on the input parameters are investigated. The model predictions for protons with respect to cell survival of V79 cells are compared with measurements. RESULTS: Although based on similar assumptions, the application of track structure theory in terms of the computational procedure is different for the two models. The ATP model provides a set of equations to predict inter- and intratrack radiation response whereas the ATL model is based on Monte Carlo simulations. One conceptual difference is the use of average doses in subtargets in the ATP model compared with the use of local doses in infinitesimal compartments in the ATL model. The ATP concept introduces an empirical scaling of the cross-section from subcellular to cellular response. The ATL concept inherently requires a critical adjustment of parameters handling the high local dose region near the track centre. The models predict proton survival curves reasonably well but neither shows good agreement with experimental data over the entire range of proton energy and absorbed dose considered. CONCLUSION: Designed for heavy ion applications, the models show weaknesses in the prediction of proton radiation effects. Amorphous track models are based on assumptions about the properties of the biological target and the radiation field that can be questioned. In particular, the assumption of subtargets and the multitarget/single-hit response function on one hand and the parameterization of radial dose and high dose cellular response on the other hand leave question marks.

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

This work investigates the existing biological models describing the response of tumours and normal tissues to radiation, with the purpose of developing a general biological model of the response of tissue to radiation. Two different types of normal tissue behaviour have been postulated with respect to its response to radiation, namely critical element and critical volume behaviour. Based on the idea that an organ is composed of functional subunits, models have been developed describing these behaviours. However, these models describe the response of an individual, a particular patient or experimental animal, while the clinically or experimentally observed quantity is the population response. There is a need to extend the models to address the population response, based on the ideas we have about the individual response. We have attempted here to summarize and unify the existing individual models. Finally, the population models are investigated by fitting to pseudoexperimental sets of data and comparing them with each other in terms of goodness-of-fit and in terms of their power to recover the values of the population parameters.

Modelling the dose-volume response of the spinal cord, based on the idea of damage to contiguous functional subunits.

PURPOSE: To investigate the response of the spinal cord of experimental animals to homogeneous irradiation, the main purpose being to propose a new version of the Critical Volume Normal Tissue Complication Probability (NTCP) model, incorporating spatial correlation between damaged functional subunits (FSU). METHOD: The standard Critical Volume NTCP model and its modified version, the Contiguous Damage model promoted here, are described in mathematical terms. Also, a fiber-like structure of the spinal cord is considered, which is a more complex structure than the standard Critical Volume NTCP model assumes. It is demonstrated that the Contiguous Damage model predicts different responses to two-segment irradiation and to single-segment irradiation to the same combined length as observed in experiments on rats, a result that cannot be described by the standard Critical Volume NTCP model. RESULTS AND CONCLUSIONS: Both the Critical Volume model and the Contiguous Damage model, are fitted to two sets of canine spinal cord radiation data corresponding to two different fractionation regimes of irradiation. Whole-organ irradiation as well as partial irradiation to different lengths are considered, allowing the investigation of dose-volume effects. Formal goodness-of-fit investigation shows that both models fit the canine spinal cord data equally well.

The general relation between tissue response to x-radiation (alpha/beta-values) and the relative biological effectiveness (RBE) of protons: prediction by the Katz track-structure model.

PURPOSE: Experimental data suggest that the relative biological effectiveness (RBE) of protons compared to x-rays may be determined by the alpha/beta-ratio of the x-ray survival curve. The data are referring to the centre of a spread-out Bragg peak (SOBP) formed to deliver a homogeneous dose to the tumour by modulating the proton energy. In an effort to explore the basis for this observation, calculations were performed to investigate the response of different biological targets through a range of proton energies and doses. MATERIALS AND METHODS: To describe the x-ray survival curve, the parameters of the linear-quadratic equation, alpha and beta, as well as those of the multi-target/single-hit equation, n and D0, were considered. These parameters were varied to investigate the RBE using the Katz track-structure model. Known cell line characterizations, as well as different hypothetical cells assuming different alpha/beta-ratios but similar target size parameters in the framework of the track-structure theory, were considered. RESULTS: The RBE was found to increase with increasing alpha/beta when the parameter n was varied, but to decrease with increasing alpha/beta when D0 was varied. This held when all other radiosensitivity parameters were assumed to stay constant. Thus, the RBE cannot be predicted by the alpha/beta-ratio alone. CONCLUSIONS: Although there is no direct correlation between the proton RBE and the parameters describing the x-ray survival curve, the track-structure model predicts a tendency for late-responding tissues (low alpha/beta) to have higher RBE values than early-responding tissues (high alpha/beta). These calculations reinforce the experimental findings, but also strongly suggest that there are circumstances in which the tendency for RBE to increase with increasing alpha/beta does not occur, or even could be reversed.

Radiobiological significance of beamline dependent proton energy distributions in a spread-out Bragg peak.

Similar target doses can be achieved with different mixed radiation fields, i.e., particle energy distributions, produced by a practical proton beam and a range modulator. The dose delivered in particle therapy can be described as the integral of fluence times the total mass stopping power over the particle energy distributions. We employed Monte Carlo simulations to explore the influence on the relative biological effectiveness (RBE) of the energy and the energy spread of the proton beam incident on a range modulator system. Using different beams, the conditions of beam delivery were adjusted so that similar spread out Bragg peak (SOBP) doses were delivered to a simulated water phantom. We calculated the RBE for inactivation of three different cell lines using the track structure model. The RBE depends on the details of the dose deposition and the biological characteristics of the irradiated tissue. Our calculations show that, for differing beam conditions, the corresponding differences in the total mass stopping power distributions are reflected in differences in the RBE. However, these differences are remarkable only at the very distal edge of the SOBP, for low doses, and/or for large differences in beam setup.

Verification of the alignment of a therapeutic radiation beam relative to its patient positioner.

An easily-used system has been developed for routine measurements of the alignment of beams used for radiation therapy. The position of a beam of circular cross section is measured with respect to a steel sphere fixed to the patient positioning table and which should coincide with the isocenter. Since measurements can be done at all gantry angles (if one is available) and with all possible orientations of the patient table, the system is particularly suited for rapid and accurate measurements of gantry and/or couch isocentricity. Because it directly measures beam-to-positioner offset, the system provides an inclusive alignment verification of the total treatment system. The system has been developed for use with proton beams, but it could equally be used for alignment checks of an x-ray beam from a linear accelerator or other source. The measuring instrument consists of a scintillation screen viewed by a CCD camera, mounted on the gantry downstream of the sphere. The steel sphere is not large enough to stop protons of all energies of interest; however, it will always modify the energy and direction of protons which intersect it, creating a region of lower intensity (a "shadow") in the light spot created by the proton beam hitting the screen. The position of the shadow with respect to the light spot is a measure of the alignment of the system. An image-analysis algorithm has been developed for an automatic determination of the position of the shadow with respect to the light spot. The specifications and theoretical analysis of the system have been derived from Monte Carlo simulations, which are validated by measurements. We have demonstrated that the device detects beam misalignments with an accuracy (1 s.d.) of 0.05 mm, which is in agreement with the expected performance. This accuracy is more than sufficient to detect the maximum allowed misalignment of +/-0.5 mm.

Analysis of the relationship between tumor dose inhomogeneity and local control in patients with skull base chordoma.

PURPOSE: When irradiating a tumor that abuts or displaces any normal structures, the dose constraints to those structures (if lower than the prescribed dose) may cause dose inhomogeneity in the tumor volume at the tumor-critical structure interface. The low-dose region in the tumor volume may be one of the reasons for local failure. The aim of this study is to quantitate the effect of tumor dose inhomogeneity on local control and recurrence-free survival in patients with skull base chordoma. METHODS AND MATERIALS: 132 patients with skull base chordoma were treated with combined photon and proton irradiation between 1978 and 1993. This study reviews 115 patients whose dose-volume data and follow-up data are available. The prescribed doses ranged from 66.6 Cobalt-Gray-Equivalent (CGE) to 79.2 CGE (median of 68.9 CGE). The dose to the optic structures (optic nerves and chiasm), the brain stem surface, and the brain stem center was limited to 60, 64, and 53 CGE, respectively. We used the dose-volume histogram data derived with the three-dimensional treatment planning system to evaluate several dose-volume parameters including the Equivalent Uniform Dose (EUD). We also analyzed several other patient and treatment factors in relation to local control and recurrence-free survival. RESULTS: Local failure developed in 42 of 115 patients, with the actuarial local control rates at 5 and 10 years being 59% and 44%. Gender was a significant predictor for local control with the prognosis in males being significantly better than that in females (P = 0.004, hazard ratio = 2.3). In a Cox univariate analysis, with stratification by gender, the significant predictors for local control (at the probability level of 0.05) were EUD, the target volume, the minimum dose, and the D5cc dose. The prescribed dose, histology, age, the maximum dose, the mean dose, the median dose, the D90% dose, and the overall treatment time were not significant factors. In a Cox multivariate analysis, the models including gender and EUD, or gender and the target volume, or gender and the minimum target dose were significant. The more biologically meaningful of these models is that of gender and EUD. CONCLUSION: This study suggests that the probability of recurrence of skull base chordomas depends on gender, target volume, and the level of target dose inhomogeneity. EUD was shown to be a useful parameter to evaluate dose distribution for the target volume.

Temporal lobe (TL) damage following surgery and high-dose photon and proton irradiation in 96 patients affected by chordomas and chondrosarcomas of the base of the skull.

PURPOSE: To determine the temporal lobe (TL) damage rate in 96 patients treated with high-dose proton and photon irradiation for chordomas and chondrosarcomas of the base of the skull. METHODS AND MATERIALS: The records of 96 consecutive patients treated at Massachusetts General Hospital (MGH) and Harvard Cyclotron Laboratory (HCL) between June 1984 and 1993, for chordomas and chondrosarcomas of the base of the skull were reviewed. All the patients had undergone some degree of resection of the tumor prior to radiation therapy. Seventy-five patients were classified as "primary tumors" and 21 as recurrent or regrowing tumors after one or more surgical procedures. All the patients were randomized to receive 66.6 or 72 cobalt Gray equivalent (CGE) on a prospective dose-searching study by proton and photon irradiation (Radiation Therapy Oncology Group #85-26) with conventional fractionation (1.8 CGE/day, 5 fractions/week). All treatments were planned using the three-dimensional (3D) planning system developed at the Massachusetts General Hospital, and the dose was delivered using opposed lateral fields for the photon component and a noncoplanar isocentric technique for the proton component. Clinical symptoms of TL damage were classified into 4 grades. Computerized tomography (CT) and magnetic resonance imaging (MRI) scans were evaluated for white matter changes. Abnormalities associated with persistent or recurrent tumor were distinguished from radiation-induced changes. TLs were delineated on the original scans of the 10 patients with damage and those of a group of 33 patients with no clinical or MRI evidence of injury. Dose distributions were calculated and dose-volume histograms were obtained for these patients. RESULTS: Of the patients, 10 developed TL damage, with bilateral injury in 2 and unilateral injury in 8. The cumulative TL damage incidence at 2 and 5 years was 7.6 and 13.2%, respectively. The MRI areas suggestive of TL damage were always separated from the tumor bed. Symptoms were severe to moderate in 8 patients. Several baseline factors, tumor- or host-related, were analyzed to evaluate their predictivity for TL damage: age, gender, tumor site, histology, type of presentation, type and number of surgical procedures, primary tumor volume, prescribed dose, normal tissue involvement, and volume of TL receiving doses ranging between 10 and 50 CGE or more. Only gender, in a univariate analysis (log rank) was a significant predictor of damage (0.0155), with male patients being at significantly higher risk of TL injury. In a stepwise Cox regression that included gender as a variable, no other baseline variable improved the prediction of damage. CONCLUSIONS: The 2- and 5-year cumulative TL damage rates were 7.6 and 13.2%, respectively. Despite the different TL damage rates related to age, tumor volume, number of surgical procedures prior to radiation therapy, and prescribed doses to the tumor, only gender was a significant predictor of damage (p = 0.0155) using a univariate (log rank) test. Chordomas and chondrosarcomas of the base of the skull may represent an interesting model to evaluate the TL damage rates because of their extradural origin, displacing the white matter instead of infiltrating it as gliomas do, because of their longer local recurrence-free survival other than gliomas and other brain tumors and because of the high doses of irradiation delivered to the target volume to obtain local control.

A pencil beam algorithm for proton dose calculations.

The sharp lateral penumbra and the rapid fall-off of dose at the end of range of a proton beam are among the major advantages of proton radiation therapy. These beam characteristics depend on the position and characteristics of upstream beam-modifying devices such as apertures and compensating boluses. The extent of separation, if any, between these beam-modifying devices and the patient is particularly critical in this respect. We have developed a pencil beam algorithm for proton dose calculations which takes accurate account of the effects of materials upstream of the patient and of the air gap between them and the patient. The model includes a new approach to picking the locations of the pencil beams so as to more accurately model the penumbra and to more effectively account for the multiple-scattering effects of the media around the point of interest. We also present a faster broad-beam version of the algorithm which gives a reasonably accurate penumbra. Predictions of the algorithm and results from experiments performed in a large-field proton beam are presented. In general the algorithm agrees well with the measurements.

Tumor and target delineation: current research and future challenges.

In the past decade, significant progress has been made in the imaging of tumors, three dimensional (3D) treatment planning, and radiation treatment delivery. At this time one of the greatest challenges for conformal radiation therapy is the accurate delineation of tumor and target volumes. The physician encounters many uncertainties in the process of defining both tumor and target. The sources of these uncertainties are discussed, as well as the issues requiring study to reduce these uncertainties.

Dose-volume distributions: a new approach to dose-volume histograms in three-dimensional treatment planning.

A new approach to calculating and displaying dose-volume relationships in 3D radiation therapy is presented. We have developed a concept of a dose-volume distribution (DVD) and its corresponding differential dose-volume distribution (DDVD), based on organization of the data in the volume rather than in the dose domain. The new concepts make full use of the information that can be obtained from the dose calculation points and the sampling pattern and are designed to overcome shortcomings of the classical concepts of dose-volume histograms (DVH) and differential dose-volume histograms (DDVH). The new concepts can be applied to any number of dose calculation points, but they are especially advantageous when a small number of points is used. DVDs are particularly well suited to pseudo- and quasi-random sampling of dose distributions. We have developed an error analysis for DVDs and DDVDs in the case of pseudorandom sampling. We also describe an adaptive technique for minimizing the amount of data needed for purposes of display.

Implementation of a model for estimating tumor control probability for an inhomogeneously irradiated tumor.

This paper presents the details of a practical implementation of a model for the prediction of the tumor control probability (TCP) when a tumor is irradiated non-uniformly. The implementation is based on a previously published model and represents a simplified version of the model with a limited number (five) of parameters. We show how to derive the model parameters from clinically available data and offer pseudocode for computer implementation. The model should be a useful tool for evaluating and optimizing 3D dose distributions.

Comments on "Sampling techniques for the evaluation of treatment plans" [Med. Phys. 20, 151-161 (1993)].

We believe that, for the purpose of evaluation and optimization of treatment plans, quasirandom sampling is superior to grid sampling and should be the method of choice. We believe it to be on average more efficient than grid sampling (i.e., more accurate for any given number of dose estimates) and, even more importantly, more reliable in that it is subject to less variability due to shape and orientation of the particular VOI--as demonstrated in Fig. 2. As a rule of thumb we recommend using about 400 quasirandom samples per volume of interest. For many situations this number is a conservative estimate; for a few situations more samples might be necessary. Optimal sampling for the purpose of calculation and presentation of the dose distribution is a different story which we have addressed elsewhere.

Late rectal bleeding following combined X-ray and proton high dose irradiation for patients with stages T3-T4 prostate carcinoma.

PURPOSE: Dose escalation for prostate cancer by external beam irradiation is feasible by a 160 MeV perineal proton beam that reduces the volume of rectum irradiated. We correlated the total doses received to portions of the anterior rectum to study the possible relationship of the volume irradiated to the incidence of late rectal toxicity. METHODS: We have randomized 191 patients with stages T3 and T4 prostatic carcinoma to one of two treatment dose arms. These were: 1) 75.6 Cobalt-Gy-equivalent (CGE), 50.4 Gy delivered by 107-25 MV photons followed by 25.2 CGE delivered perineally by protons (Arm 1) or 2) 67.2 CGE delivered by 10-25 MV photons (Arm 2). RESULTS: With a median follow-up of 3.7 years, post-irradiation rectal bleeding (grades 1 and 2 only, none requiring surgery or hospitalization) from telangiectatic rectal mucosal vessels has occurred in 34% of 99 Arm-1 patients and 16% of 92 Arm-2 patients (p = 0.013). Dose-volume histograms (DVHs) for the anterior rectal wall, the posterior rectal wall and the total rectum in 41 patients treated on Arm 1 were calculated from the three dimensional dose distributions. Rectal bleeding has occurred in 14 or 34% of the 41 DVH-analyzed subset of Arm-1 patients. Both the fractional volume of the anterior rectum and the total dose received by fractional volumes of the anterior rectum significantly correlate with the actuarial probability of bleeding. CONCLUSIONS: Clinicians planning dose escalation to men with localized prostate cancer should approve with caution treatment plans raising more than 40% of the anterior rectum to more than 75 CGE without additional effort to protect the rectal mucosa because this late sequela data indicate that more than half of these men will otherwise have rectal bleeding.

Modeling of normal tissue response to radiation: the critical volume model.

PURPOSE: A model for calculating normal tissue complication probability in response to therapeutic doses of radiation is presented. METHODS AND MATERIALS: The model which we call the "critical volume model" is based on a concept of functional subunits defined either structurally (e.g., nephrons) or functionally, and an assumption that normal tissue complication probability is fully determined by the number or fraction of surviving functional subunits composing an organ or tissue. The essential features of the model are that it takes into account variations in tissue radiosensitivity and architecture of an organ for a single patient and for a patient population, and predicts the normal tissue complication probability under conditions of 3-dimensional inhomogeneity of the dose distribution. The model can be used for Integral Response, or "parallel," organs (where all functional subunits are performing the same function in parallel and the output of the organ is the sum of the outputs of the functional subunits and for Critical Element, or "serial," organs (where damage to one functional subunit results in an expression of damage for the whole organ). The model combines into one compact scheme new concepts and several ideas and models which have been previously developed by other investigators. RESULTS: The behavior of the model is presented and discussed for the example of the kidney, with clinical nephritis as the functional endpoint. CONCLUSIONS: The model has the potential to be a useful tool for evaluation and optimization of 3-dimensional treatment plans for a variety of types of normal tissues.