Fundamental properties of the delivery of volumetric modulated arc therapy (VMAT) to static patient anatomy.

PURPOSE: The primary goal of this article is to formulate volumetric modulated arc therapy (VMAT) delivery problem and study interdependence between several parameters (beam dose rate, gantry angular speed, and MLC leaf speed) in the delivery of VMAT treatment plan. The secondary aim is to provide delivery solution and prove optimality (minimal beam on time) of the solution. An additional goal of this study is to investigate alternative delivery approaches to VMAT (like constant beam dose rate and constant gantry angular speed delivery). METHOD: The problem of the VMAT delivery is formulated as a control problem with machine constraints. The relationships between parameters of arc therapy delivery are derived under the constraint of treatment plan invariance and limitations on delivery parameters. The nonuniqueness of arc therapy delivery solutions is revealed from these relations. The most efficient delivery of arc therapy is then formulated as optimal control problem and solved by geometrical methods. A computer program is developed to find numerical solutions for deliveries of specific VMAT plan. RESULTS: Explicit examples of VMAT plan deliveries are computed and illustrated with graphical representations of the variability of delivery parameters. Comparison of delivery parameters with that of Varian's delivery are shown and discussed. Alternative delivery strategies such as constant gantry angular speed delivery and constant beam dose rate delivery are formulated and solutions are provided. The treatment times for all the delivery solutions are provided. CONCLUSION: The investigations derive and prove time optimal VMAT deliveries. The relationships between delivery parameters are determined. The optimal alternative delivery strategies are discussed.

Contamination dose from photoneutron processes in bodily tissues during therapeutic radiation delivery.

Dose to the total body from induced radiation resulting from primary exposure to radiotherapeutic beams is not detailed in routine treatment planning though this information is potentially important for better estimates of health risks including secondary cancers. This information can also allow better management of patient treatment logistics, suggesting better timing, sequencing, and conduct of treatment. Monte Carlo simulations capable of taking into account all interactions contributing to the dose to the total body, including neutron scattering and induced radioactivity, provide the most versatile and accurate tool for investigating these effects. MCNPX code version 2.2.6 with full IAEA library of photoneutron cross sections is particularly suited to trace not only photoneutrons but also protons and heavy ion particles that result from photoneutron interactions. Specifically, the MCNPX code is applied here to the problem of dose calculations in traditional (non-IMRT) photon beam therapy. Points of calculation are located in the head, where the primary irradiation has been directed, but also in the superior portion of the torso of the ORNL Mathematical Human Phantom. We calculated dose contributions from neutrons, protons, deutrons, tritons and He-3 that are produced at the time of photoneutron interactions in the body and that would not have been accounted for by conventional radiation oncology dosimetry.

Radioablación estereotáctica extracraneal. Revisión de las bases biológicas, técnica y experiencia clínica preliminar / Extracranial stereotactic radioablation. Review of biological basis, technique and preliminary clinical experience

La radioablación estereotáctica extracraneal es una nueva y estimulante modalidad de tratamiento en la que se administran dosis grandes hipofraccionadas de irradiación a los tumores extracraneales. En el presente artículo revisamos brevemente el razonamiento, las implicaciones biológicas del hipofraccionamiento “extremo” la técnica de tratamiento y los datos publicados. Además se presentarán los datos de un ensayo clínico fase I en pacientes con cáncer de pulmón de células no pequeñas (NSCLC) inoperable, estadio clínico I, realizado en la Indiana University (AU)

High-dose-rate brachytherapy for vaginal cancer: learning from treatment complications.

Historically, early stage vaginal cancer has been treated with low-dose-rate (LDR) brachytherapy with or without external beam radiation therapy (EBRT). Complication rates have been low and treatment efficacious. Although high-dose-rate (HDR) brachytherapy has been used for cervical cancer in many countries for over a decade, only more recently has it been integrated into treatment plans for vaginal cancer. This paper describes three patients treated with HDR brachytherapy who experienced significant late effects. Given the very limited amount of literature regarding the use of HDR brachytherapy in vaginal cancer, this analysis potentially contributes to an understanding of treatment-related risk factors for complications among patients treated with this modality.A focused review of hospital and departmental treatment records was done on three patients treated with HDR brachytherapy. Abstracted information included clinical data, treatment parameters (technique, doses, volume, combinations with other treatments) and outcomes (local control, survival, early and late effects). A review of the available literature was also undertaken. All patients had significant complications. Although statistical correlations between treatment parameters and complications are impossible given the limited number of patients, this descriptive analysis suggests that vaginal length treated with HDR brachytherapy is a risk factor for early and late effects, that the distal vagina has a lower radiation tolerance than the upper vagina with HDR as in LDR, and that combining HDR with LDR as done in our experience carries a high risk of late toxicity. Integration of HDR brachytherapy techniques into treatment plans for early stage vaginal cancers must be done cautiously. The etiology of the significant side effects seen here is likely to be multifactorial. For users of HDR brachytherapy in vaginal cancer, there is a need to further refine and standardize treatment concepts and treatment delivery. Ideally this will be based on continued careful observation and reporting of both favorable and unfavorable outcomes and experiences.

Improved leaf sequencing reduces segments or monitor units needed to deliver IMRT using multileaf collimators.

Leaf sequencing algorithms may use an unnecessary number of monitor units or segments to generate intensity maps for delivery of intensity modulated radiotherapy (IMRT) using multiple static fields. An integer algorithm was devised to generate a sequence with the fewest possible segments when the minimum number of monitor units are used. Special hardware related restrictions on leaf motion can be incorporated. The algorithm was tested using a benchmark map from the literature and clinical examples. Results were compared to sequences given by the routine of Bortfeld that minimizes monitor units by treating each row independently, and the areal or reducing routines that use fewer segments at the price of more monitor units. The Bortfeld algorithm used on average 58% more segments than provided by the integer algorithm with bidirectional motion and 32% more segments than did an integer algorithm admitting only unidirectional sequences. The areal algorithm used 48% more monitor units and the reducing algorithm used 23% more monitor units than did the bidirectional integer algorithm, while the areal and reducing algorithms used 23% more segments than did the integer algorithm. Improved leaf sequencing algorithms can allow more efficient delivery of static field IMRT. The integer algorithm demonstrates the efficiencies possible with an improved routine and opens a new avenue for development.

CPP calculation of multiple scattering distributions for charged particles penetrating compounds or mixtures.

Charged particle multiple scattering distributions may be constructed from individual atomic scattering events on the basis of compound Poisson process (CPP) theory. We present a CPP method for computing multiple scattering transition probability densities from charged particles penetrating compounds and mixtures. Water as a scattering medium provides here an example of the calculation method which is applicable to compounds or mixtures. Electrons are chosen as examples of charged particle beams. The Rutherford single scattering cross section and a partial wave analysis single scattering cross section are chosen as example cross sections. Transition probability densities predicted on the basis of CPP theory can be calculated with great accuracy for the improvement of radiation dose calculations. The advantages of the CPP method are (a) an effective atomic number need not be defined for the scattering medium, (b) it can be applied in both spherical and planar coordinate systems, and (c) it does not require any specific form for the single scattering cross section.

150-250 meV electron beams in radiation therapy.

High-energy electron beams in the range 150-250 MeV are studied to evaluate the feasibility for radiotherapy. Monte Carlo simulation results from the PENELOPE code are presented and used to determine lateral spread and penetration of these beams. It is shown that the penumbra is comparable to photon beams at depths less than 10 cm and the practical range (Rp) of these beams is greater than 40 cm. The depth dose distribution of electron beams compares favourably with photon beams. Effects caused by nuclear reactions are evaluated, including increased dose due to neutron production and induced radioactivity resulting in an increased relative biological effectiveness (RBE) factor of < 1.03.

On the equivalence of rotational and concentric therapy.

The aim of this work is to analyse the equivalence of two classes of radiation therapy. One class of therapy is characteristic of Gamma Knife type irradiations and is defined by pencil beam concentric irradiation converging on multiple centres throughout the patient's body. The other class of treatment is characteristic of accelerator based, beam intensity modulated type irradiation defined by a rotation of wide beams around a single centre. We focus our attention on deriving formulae that relate treatments in these two classes and characterize conditions under which they are valid.

The clinical application of dynamic shielding and imaging in moving table total body irradiation.

The moving table technique for total body irradiation (MTT TBI) has some advantages in regard to dose homogeneity, patient positioning and comfort. However, divergence of the radiation field coupled with patient motion necessitates corresponding motion of the shielding blocks and verification film so that penumbra is minimized. MTT TBI system is presented, together with dose calculations, incorporating moving trays for shields and film to ensure dose delivery with minimal penumbra of the blocked field.

Contamination of the pleural surfaces in childhood sarcoma. Use of colloidal P-32 to reduce radiation dose to the whole lung.

Children with pulmonary sarcomas who have diffuse contamination of the pleural cavity present a difficult management problem for the radiation oncologist. Doses required to control even microscopic disease exceed lung tolerance. We report on the use of intracavity colloid P-32 in an attempt to treat the pleural surface and spare normal lung parenchyma and tissues of the chest wall. Three children--18 months, 12 years, and 3 years of age--had spillage of pulmonary sarcomas into the chest cavity. All children were treated with systemic chemotherapy. Initially, 0.5 mCi of technetium sulfur colloid (99mTc-sulfur colloid) was instilled into the pleural space to ascertain even distribution of isotope. This was then followed by installation of 5.0 mCi of colloidal P-32. Uniform distribution was then confirmed by bremsstrahlung scanning. All three patients are in complete remission 3.5 years, 3 years, and 1 year after treatment, respectively. The major toxicity was asymptomatic pleural thickening, which could be confused with disease. This was confirmed histologically to be fibrous in the first patient. The process diminished or stabilized with time in all 3 patients over the period of observation. In this small series, intrapleural colloidal P-32 appeared to be safe and well tolerated and would be expected to be less toxic than wide-field external beam in the treatment of spilled pulmonary sarcomas.

Extension of a numerical algorithm to proton dose calculations. I. Comparisons with Monte Carlo simulations.

A numerical algorithm originally developed for electron dose calculations [Med. Phys. 21, 1591 (1994)] has been modified for use with proton beams. The algorithm recursively propagates the proton distribution in energy, angle, and space from one level in an absorbing medium to another at slightly greater depth until all protons stop. Vavilov's theory is used to predict, at any point in the absorber, the broadening of the primary proton energy-spectrum. Moliere's theory is applied to describe the angular distribution, and it is shown that the Gaussian first term of Moliere's series expansion is of sufficient accuracy for dose calculations. These multiple scattering and energy loss distributions are sampled using equal probability spacing to optimize computational speed while maintaining calculational accuracy. Inelastic nuclear collisions along the proton trajectories are modeled by a simple exponential extinction. Predictions of the algorithm for absolute dose deposition by a 160 MeV initially monoenergetic proton beam are compared with the results of Monte Carlo simulations performed with the PTRAN code. The excellent level of agreement between the results of these two methods of dose calculation (< 5% dose and < 3 mm spatial deviations) demonstrate that dose deposition from proton beams may be computed to high accuracy using this algorithm without the need for extensive empirical measurement as input.

Optimization of rotational radiotherapy treatment planning.

PURPOSE: Rotational therapy treatment planning for rotationally symmetric geometry of tumor and healthy tissue provides an important example of testing various approaches to optimizing dose distributions for therapeutic x-ray irradiations. In this article, dose distribution optimization is formulated as a variational problem. This problem is solved analytically and numerically. METHODS AND MATERIALS: The classical Lagrange method is used to derive equations and inequalities that give necessary conditions for minimizing the mean-square deviation between the ideal dose distribution and the achievable dose distribution. The solution of the resulting integral equation with Cauchy kernel is used to derive analytical formulas for the minimizing irradiation intensity function. RESULTS: The solutions are evaluated numerically and the graphs of the minimizing intensity functions and the corresponding dose distributions are presented. CONCLUSIONS: The optimal solutions obtained using the mean-square criterion lead to significant underdosage in some areas of the tumor volume. Possible solutions to this shortcoming are investigated and medically more appropriate criteria for optimization are proposed for future investigations.

Inclusion of energy straggling in a numerical method for electron dose calculation.

Energy straggling along electron trajectories has been incorporated into a numerical algorithm for electron beam dose calculations. Landau's theory is used to predict, at any point in the absorber, the broadening of the primary electron energy spectrum due to energy loss straggling. Numerical calculations have been performed for electron beams with energies of 10-30 MeV incident upon water in order to determine the variation of dose with depth and variation of energy spectra with pathlength. These calculations are compared with the results of Monte Carlo simulations performed with the EGS4 code. The inclusion of energy loss straggling in the numerical calculations leads to predictions of energy spectra and dose deposition that are in good agreement with modified Monte Carlo simulations in which bremsstrahlung is ignored and the energy given to knock-on electrons is deposited at the site of their creation. Less satisfactory agreement was achieved when these calculations were compared to full Monte Carlo simulations that included the bremsstrahlung events and transported the knock-on electrons. It is concluded that bremsstrahlung energy loss must also be included into this algorithm, if an acceptable dose computation accuracy is to be achieved for clinical applications.

A solution to the Yang equation with electron energy loss following Harder's formula.

The Yang diffusion transport equation for charged particles was modified to allow the linear angular scattering power to vary with penetration depth in the scattering medium. Assuming charged particle energy loss to be a linear function of depth, conditional solutions to this transport equation have been found for the two cases of interest specified by Yang. The normalized excess path length distributions predicted for a 10-MeV electron beam show a shift toward larger excess path lengths compared to Yang's solutions.

Radiance and particle fluence.

The concepts of radiance and fluence are fundamental to the description of a radiation field. The International Commission on Radiological Units and Measurements (ICRU) has defined fluence in terms of the number of the radiation particles crossing a small sampling sphere. A second definition has been proposed in which the length of track segments contained within any sampling volume are used to calculate the incident fluence. This approach is often used in Monte Carlo simulations of individual particle tracks, allowing the fluence to be scored in small volumes of any shape. In this paper we stress that the second definition generalizes the classical (ICRU) concept of fluence. We also identify the assumptions inherent in the two definitions of fluence and prove their equivalence for the case of straight-line particle trajectories.

A method for the calculation of electron energy-straggling spectra.

To calculate electron beam dose distributions accurately, numerical methods of electron transport calculations must account for the statistical variation (or "straggling") in electron energy loss. This paper shows that the various energy straggling theories that are applicable to short path lengths all derive from a single statistical model, known as the compound Poisson process. This model in turn relies on three assumptions: (1) the number of energy-loss events in a given path length is Poisson distributed; (2) events are mutually independent; and (3) each event has the same probability distribution for energy loss (i.e., the same energy-loss cross section). Applying the principles of the compound Poisson process and using fast Fourier transforms, a new method for calculating energy-loss spectra is developed. The spectra calculated using this method for 10, 20, and 30 MeV electrons incident on graphite and aluminum absorbers agreed with Monte Carlo simulations (EGS4) within 1% in the spectral peak. Also, stopping powers derived from the calculated spectra agreed within 1.2%, with stopping powers tabulated by the International Commission on Radiation Units and Measurements. Several numerical transport methods "propagate" the electron distribution (in position, direction, and energy) over small discrete increments of path length. Thus the propagation of our calculated spectra over multiple path length increments is investigated. For a low atomic number absorber (graphite in this case), calculated spectra agreed with EGS4 Monte Carlo simulations over the full electron range, provided the path length increments were sufficiently small (less than 0.5 g/cm2). It is concluded from these results that numerical methods of electron transport should restrict the size of path length increments to less than 0.5 g/cm2 if energy straggling is to be modeled accurately.

A numerical method for electron transport calculations.

A numerical algorithm for calculating the penetration of electrons in dense media is presented. The numerical algorithm is intended for future application to radiotherapy dose calculations. The method is generic in the sense that it may be used with different theoretical models describing the angular scattering of electrons with depth. It is also general enough that it may be applied to electron dose calculations in heterogeneous as well as homogeneous media. The assumptions used in the algorithm are examined and equations describing the evolution of the distribution of electrons with depth are presented. Calculations have been performed for 10 MeV broad beams and pencil beams incident on water. It is shown that the Fermi-Eyges analytical solutions are recovered if the angular scattering process is assumed to be a Gaussian Markov process and the cumulative angle of electron travel remains small. In the case where the small angle approximation is not imposed, the numerical method qualitatively reproduces, at large depths, the wide angle scattering 'tails' seen in Monte Carlo generated profiles.

A restricted angular scattering model for electron penetration in dense media.

A restricted angular scattering model for electron penetration in dense media is presented. In the model, the Fermi-Eyges transport equation is modified through the addition of an extra term which may be interpreted as representing an apparent force opposing the scattering of electrons into wider angles. The introduction of this extra term allows the modeling of the measured saturation in the mean square angular spread of electrons with depth. The restricted scattering model retains the Gaussian features of the Fermi-Eyges model and, therefore, may be readily incorporated into existing dose computation algorithms. Good agreement is obtained with measured angular electron distribution data for a point monodirectional beam over a wide range of incident electron energies (5-20 MeV) and scattering media (atomic numbers of 6 to 82). Also, a comparison of the restricted scattering model predictions with measurements of the lateral pencil beam spread shows an improvement over the predictions of Fermi-Eyges model close to the end of the electron range. Broad beam profiles were generated using both the Fermi-Eyges and restricted scattering models. A comparison of predicted and measured beam profiles shows that the restricted scattering model is a significant improvement over the Fermi-Eyges model for the prediction of beam penumbra shape in homogeneous media.