Numerical calculation of energy deposition by broad high-energy electron beams: II. Multi-layered geometry

Investigation of the added value of high-energy electrons in intensity-modulated radiotherapy: four clinical cases

PURPOSE

Intensity-modulated radiotherapy (IMRT) with photon beams is currently pursued in many clinics. Theoretically, inclusion of intensity- and energy-modulated high-energy electron beams (15-50 MeV) offers additional possibilities to improve radiotherapy treatments of deep-seated tumors. In this study the added value of high-energy electron beams in IMRT treatments was investigated.

METHODS AND MATERIALS

In a comparative treatment planning study, conventional treatment plans and various types of IMRT plans were constructed for four clinical cases (cancer of the bladder, pancreas, chordoma of the sacrum, and breast). The conventional plans were used for the actual treatment of the patients. The IMRT plans were optimized using the Orbit optimization code (Löf et al., 2000) with a radiobiologic objective function. The IMRT plans were either photon or combined electron and photon beam plans, with or without dose homogeneity constraints assuming standard or increased radiosensitivities of organs at risk.

RESULTS

Large improvements in expected treatment outcome are found using IMRT plans compared to conventional plans, but differences in tumor control probability (TCP) and normal tissue complication probabilities (NTCP) values between IMRT plans with and without electrons are small. However, the use of electrons improves the dose-volume histograms for organs at risk, especially at lower dose levels (e.g., 0-40 Gy).

CONCLUSIONS

This preliminary study indicates that addition of higher energy electrons to IMRT can only marginally improve treatment outcome for the selected cases. The dose-volume histograms of organs at risk show improvements for IMRT with higher energy electrons, which may reduce tumor induction but does not substantially reduce NTCP.

Accuracy of the phase space evolution dose calculation model for clinical 25 MeV electron beams

The phase space evolution (PSE) model is a dose calculation model for electron beams in radiation oncology developed with the aim of a higher accuracy than the commonly used pencil beam (PB) models and with shorter calculation times than needed for Monte Carlo (MC) calculations. In this paper the accuracy of the PSE model has been investigated for 25 MeV electron beams of a MM50 racetrack microtron (Scanditronix Medical AB, Sweden) and compared with the results of a PB model. Measurements have been performed for tests like non-standard SSD, irregularly shaped fields, oblique incidence and in phantoms with heterogeneities of air, bone and lung. MC calculations have been performed as well, to reveal possible errors in the measurements and/or possible inaccuracies in the interaction data used for the bone and lung substitute materials. Results show a good agreement between PSE calculated dose distributions and measurements. For all points the differences--in absolute dose--were generally well within 3% and 3 mm. However, the PSE model was found to be less accurate in large regions of low-density material and errors of up to 6% were found for the lung phantom. Results of the PB model show larger deviations, with differences of up to 6% and 6 mm and of up to 10% for the lung phantom; at shortened SSDs the dose was overestimated by up to 6%. The agreement between MC calculations and measurement was good. For the bone and the lung phantom maximum deviations of 4% and 3% were found, caused by uncertainties about the actual interaction data. In conclusion, using the phase space evolution model, absolute 3D dose distributions of 25 MeV electron beams can be calculated with sufficient accuracy in most cases. The accuracy is significantly better than for a pencil beam model. In regions of lung tissue, a Monte Carlo model yields more accurate results than the current implementation of the PSE model.

Mixing intensity modulated electron and photon beams: combining a steep dose fall-off at depth with sharp and depth-independent penumbras and flat beam profiles

For application in radiotherapy, intensity modulated high-energy electron and photon beams were mixed to create dose distributions that feature: (a) a steep dose fall-off at larger depths, similar to pure electron beams, (b) flat beam profiles and sharp and depth-independent beam penumbras, as in photon beams, and (c) a selectable skin dose that is lower than for pure electron beams. To determine the required electron and photon beam fluence profiles, an inverse treatment planning algorithm was used. Mixed beams were realized at a MM50 racetrack microtron (Scanditronix Medical AB, Sweden), and evaluated by the dose distributions measured in a water phantom. The multileaf collimator of the MM50 was used in a static mode to shape overlapping electron beam segments, and the dynamic multileaf collimation mode was used to realize the intensity modulated photon beam profiles. Examples of mixed beams were generated at electron energies of up to 40 MeV. The intensity modulated electron beam component consists of two overlapping concentric fields with optimized field sizes, yielding broad, fairly depth-independent overall beam penumbras. The matched intensity modulated photon beam component has high fluence peaks at the field edges to sharpen this penumbra. The combination of the electron and the photon beams yields dose distributions with the characteristics (a)-(c) mentioned above.

Optimal electron and combined electron and photon therapy in the phase space of complication-free cure

The possibility of using intensity-modulated high-energy electrons beams alone or in combination with photon beams to treat tumours located at depths from 5 cm to 25 cm has been investigated. A radiobiologically based optimization algorithm using the probability of complication-free tumour control has been used to calculate the optimal dose distributions. Two different target volumes have been used; one advanced cervical cancer with locally involved lymph nodes and one astrocytoma in the upper brain hemisphere. Treatments with only electron beams and also combinations between electron and photon beams have been investigated. The dependence of the expected treatment outcome on the beam energy and directions was investigated, and to some extent on the number of beam portals. It is shown that the beam direction intervals resulting in a high expected treatment outcome increase with increasing electron energy and also with some electron-photon combinations. For an eccentrically placed, not too deeply situated tumour surrounded by sensitive normal tissue it is shown that the expected treatment outcome can be improved by using electron beams in combination with photon beams compared with using two photon beams, and using two electron beams results in almost as high an expected treatment outcome. The possibility of improving the dose conformity from electron beams by adding photon fields parallel or orthogonal to the electron beams is demonstrated.

Numerical calculation of energy deposition by high-energy electron beams: III. Three-dimensional heterogeneous media

The phase space time evolution model of Huizenga and Storchi and Morawska-Kaczyńska and Huizenga has been modified to accommodate calculations of energy deposition by arbitrary electron beams in three-dimensional heterogeneous media. This is a further development aimed at the use of the phase space evolution model in radiotherapy treatment planning. The model presented uses an improved method to control the evolution of the phase space state. This new method results in a faster algorithm, and requires less computer memory. An extra advantage of this method is that it allows the pre-calculation of information, further reducing calculation times. Typical results obtainable with this model are illustrated with the cases of (i) a 20 MeV pencil beam in a water phantom, (ii) a 20 MeV 5 x 5 cm2 beam in a water phantom containing two air cavities, and (iii) a 20 MeV 5 x 5 cm2 beam in a water phantom containing an aluminium region. The results of the dose distribution calculations are in good agreement with and require significantly less computation time than results obtained with Monte Carlo methods.

Mapping dose distributions

Clinical dose calculations are often performed by scaling distances from a dose distribution measured in one medium to calculate the dose in another. These perturbation calculations have the mathematical form of a mapping. In this paper we identify five conditions required for particle transport to reduce to this form and develop a new mapping for electrons which approximately satisfies these conditions. This continuous scattering mapping is based on two parameters, the scattering power of the medium which determines the shape of the scaling paths, and the stopping power of the medium which determines where the energy is deposited along these paths. Pencil beam dose distributions are calculated with EGS4 in one medium and mapped to other media. The resultant distributions are compared with EGS4 calculations done directly in the second medium. The accuracy of the mapping algorithm is shown to be superior to both linear density scaling and the MDAH electron pencil beam algorithm [Kenneth R. Hogstrom, Michael D. Mills, and Peter R. Almond, "Electron beam dose calculations," Phys. Med. Biol. 26, 445-459 (1981)] for pencil beams in homogeneous media and inhomogeneous phantoms (both slab and nonslab geometries) for a variety of materials of clinical interest.

Sharpening the penumbra of high energy electron beams with low weight narrow photon beams

BACKGROUND AND PURPOSE

High energy (20-50 MeV) electron beams, available from the MM50 Racetrack Microtron, can be used for the treatment of deep-seated tumors. A disadvantage is the increasing penumbra width as a function of depth. By the addition of a narrow (typically 1 cm wide) photon beam near the field edge, the 50-90% penumbra width of the electron beam is reduced, yielding a significantly increased effective field size.

MATERIALS AND METHODS

For rectangular electron beams in a water phantom (energies 25 and 40 MeV, field sizes 5 x 5-15 x 15 cm2) a computer program was used to optimize the photon beam parameters (position, weight and width) to obtain a combined beam with the sharpest penumbra at the optimization depth and a beam flatness within certain constraints. The study furthermore included penumbra sharpening of an irregular multileaf collimator-shaped field.

RESULTS AND CONCLUSION

At optimization depths near R90, photon beam addition reduces the penumbra width by 40-50% (from 15-20 mm to 8-10 mm). Beam flatness at the optimization depth is within +/-5% and hot-spots are < or =120% for all depths. By the addition of narrow photon beams around the rectangular or irregular field, the electron field width can be reduced by 1-3 cm, while the effective field size is maintained.

Optimization of 3D conformal electron beam therapy in inhomogeneous media by concomitant fluence and energy modulation

The possibilities of using simultaneous fluence and energy modulation techniques in electron beam therapy to shape the dose distribution and almost eliminate the influences of tissue inhomogeneities have been investigated. By using a radiobiologically based optimization algorithm the radiobiological properties of the tissues can be taken into account when trying to find the best possible dose delivery. First water phantoms with differently shaped surfaces were used to study the effect of surface irregularities. We also studied water phantoms with internal inhomogeneities consisting of air or cortical bone. It was possible to improve substantially the dose distribution by fluence modulation in these cases. In addition to the fluence modulation the most suitable single electron energy in each case was also determined. Finally, the simultaneous use of several preselected electron beam energies was also tested, each with an individually optimized fluence profile. One to six electron energies were used, resulting in a slow improvement in complication-free cure with increasing number of beam energies. To apply these techniques to a more clinically relevant situation a post-operative breast cancer patient was studied. For simplicity this patient was treated with only one anterior beam portal to clearly illustrate the effect of inhomogeneities like bone and lung on the dose distribution. It is shown that by using fluence modulation the influence of dose inhomogeneities can be significantly reduced. When two or more electron beam energies with individually optimized fluence profiles are used the dose conformality to the internal target volume is further increased, particularly for targets with complex shapes.

Numerical calculation of energy deposition by high-energy electron beams: III-B. Improvements to the 6D phase space evolution model

The phase space evolution model of Huizenga and Storchi, Morawska-Kaczyńska and Huizenga and Janssen et al has been modified to (i) allow application on currently available computer equipment with limited memory (128 Megabytes) and (ii) allow 3D dose calculations based on 3D computer tomographic patient data. This is a further development aimed at the use of the phase space evolution model in radiotherapy electrons beam treatment planning. The first modification regards the application of depth evolution of the phase space state combined with an alternative method to transport back-scattered electrons. This depth evolution method requires of the order of 15 times less computer memory than the energy evolution method. Results of previous and new electron transport methods are compared and show that the new electron transport method for back-scattered electrons hardly affects the accuracy of the calculated dose distributions. The second modification regards the simulation of electron transport through tissues with varying densities by applying distributed electron transport through similarly composed media with a limited number of fixed densities. Results of non-distributed and distributed electron transport are compared and show that the distributed electron transport method hardly affects the accuracy of the calculated dose distributions. It is also shown that the results of the new dose distribution calculations are still in good agreement with and require significantly less computation time than results obtained with the EGS4 Monte Carlo method.

Monte Carlo based phase-space evolution for electron dose calculation

A system of computer codes based on phase-space evolution is developed and applied to low energy therapeutic electron beams. Monte Carlo (EGS4) is used to pre-calculate the electron transport and dose deposition in a 0.5 cm width cubic voxel. Dose calculations at larger scales are computed from the pre-calculated data using phase-space evolution. This approach has the theoretical accuracy of Monte Carlo with potentially significant speed gains resulting from the pre-calculation. This study demonstrates the accuracy of this technique while providing a preliminary assessment of the calculation time. For a 4.3 MeV electron beam in water with a 0.5 cm thick slab of either water (homogeneous), air, or aluminum at 1 cm depth, we observe differences relative to Monte Carlo of less than 3% along the central axis for a pencil-beam. For a 3.5 cm x 3.5 cm field we observe a maximum difference on the central axis of 4% in the build-up region and less than 0.1 cm in the fall-off region for all three phantoms. Calculation times are disappointing; however, there is high potential for their reduction to values comparable to or better than condensed history Monte Carlo while retaining clinically acceptable accuracy.

The role of phantom and treatment head generated bremsstrahlung in high-energy electron beam dosimetry

An analytical expression has been derived for the phantom generated bremsstrahlung photons in plane-parallel monoenergetic electron beams normally incident on material of any atomic number (Be, H2O, Al, Cu and U). The expression is suitable for the energy range from 1 to 50 MeV and it is solely based on known scattering power and radiative and collision stopping power data for the material at the incident electron energy. The depth dose distribution due to the bremsstrahlung generated by the electrons in the phantom is derived by convolving the bremsstrahlung energy fluence produced in the phantom with a simple analytical energy deposition kernel. The kernel accounts for both electrons and photons set in motion by the bremsstrahlung photons. The energy loss by the primary electrons, the build-up of the electron fluence and the generation, attenuation and absorption of bremsstrahlung photons are all taken into account in the analytical formula. The longitudinal energy deposition kernel is derived analytically and it is consistent with both the classical biexponential relation describing the photon depth dose distribution and the exponential attenuation of the primary photons. For comparison Monte Carlo calculated energy deposition distributions using ITS3 code were used. Good agreement was found between the results with the analytical expression and the Monte Carlo calculation. For tissue equivalent materials, the maximum total energy deposition differs by less than 0.2% from Monte Carlo calculated dose distributions. The result can be used to estimate the depth dependence of phantom generated bremsstrahlung in different materials in therapeutic electron beams and the bremsstrahlung production in different electron absorbers such as scattering foils, transmission monitors and photon and electron collimators. By subtracting the phantom generated bremsstrahlung from the total bremsstrahlung background the photon contamination generated in the treatment head can be determined to allow accurate dosimetry of heavily photon contaminated electron beams.

Phase space evolution distribution functions for high energy electron beams

The phase space evolution (PSE) model is a 3D electron beam dose calculation model for radiation oncology. The PSE model is based upon the transport of electrons with a specific energy and direction over short distances (typically 0.3-1 cm). The result of the transport of these electrons is described by an energy and direction distribution of the electrons, which is stored in a database. The database is used by the PSE model at the time of the actual electron transport simulation. A good agreement between dose distributions calculated by the PSE model and EGS4 Monte Carlo code for mono-energetic, mono-directional electron beams was found. The differences in point dose are within 1-2% of the maximum dose. These differences can be caused by errors in the database used, or by assumptions made in the PSE model. The aim of this paper is to get more insight into the possible errors introduced by the database. Results show that the data in the database are in good agreement with EGS4 calculated data. Also the influence of the database on a PSE calculated dose distribution has been investigated. The differences between a PSE calculated dose distribution and an EGS4 calculated dose distribution can be reduced to < 0.5% if the database is replaced by a database partly created by EGS4. This shows that small errors in the database have a distinct effect on the dose distribution, and that this dose distribution can be calculated accurately by the PSE model if the right database is used.