A narrative review: dose calculation algorithms used in external beam radiotherapy planning systems

Introduction

For the treatment of cancer, different treatment modalities are present. Radiation therapy (RT) is one of the major treatment modalities for treating cancer patients. In RT for accurate treatment dose calculation, different dose calculation methods and different treatment planning systems (TPS) are used. In the TPS, dose calculation algorithms play a major role in generating a treatment plan (1). The dose is being calculated based on the algorithms which are used in the TPS. Generation and precision of the treatment plan will be influenced significantly by small uncertainties in dose calculation algorithm (2). Presently, there are many TPS commercially available with different dose calculation engines. This study evaluates Monte Carlo (MC), collapsed cone/superposition (CCS), anisotropic analytical algorithms (AAA), Acuros XB (AXB), and pencil beam (PB) algorithms, representing the current standard for dose calculation in TPS.

During the last 25 years, RT treatment has advanced vastly; treatment options have been upgraded for better patient treatment. Presently available treatment options are stereotactic body RT (SBRT), stereotactic radio surgery (SRS), intensity modulated RT (IMRT), volumetric modulated arc therapy (VMAT), and 3-dimensional conformal radiotherapy (3DCRT) and all these treatment methods rely on more complex treatment delivery and dosimetry. These treatment options are heavily dependent on dose calculation algorithms. This article is a literature review of the various dose calculation algorithms used in TPS.

Objective of the literature review

The purpose of this work is a literature review of published information about the dose calculation algorithms used in the different TPS. The literature review addresses the following research questions: dose calculation algorithms used in the TPS and its limitation, presently available dose calculation algorithms, algorithms used in proton therapy dose calculation, dosimetric verification of dose calculation algorithms, heterogeneous dose calculation accuracy in IMRT/VMAT/SBRT treatment techniques, heterogeneous dose calculation in thorax phantom, dosimetric comparison of different treatment techniques and PB algorithm limitation. We present this article in accordance with the Narrative Review reporting checklist (available at https://tro.amegroups.com/article/view/10.21037/tro-24-10/rc).

Methods

A wide range search through the indexed database “PubMed” was performed. The following search term was used namely “Algorithms”, “Dose calculation”, “Pencil beam algorithms”, “Collapsed Cone Algorithms”, “Superposition algorithms”, “Monte Carlo Algorithms”, “Dose calculation algorithms”. Results relevant to this paper and relevant to the references cited are also included. Papers published in the English language between January 1994 and December 2022 are included in this review article. Table 1 shows the summary of the review search strategy.

Correction-based algorithms

Mazurier et al. clearly explained the correction-based algorithms used for dose calculation in modern 3-dimensional radiotherapy (3). Initial dose measurements for commissioning like output factor, tissue air ratio (TAR), percentage depth dose (PDD), off-axis ratios, and tissue phantom ratio (TPR) were measured on homogenous patients (water phantom) from which the dose will be extrapolated for inhomogeneous patient’s fields, for example, tissue heterogeneous areas and missing tissue will be added for patient surfaces. This type of phenomenon is called “correction-based methods”, which will depend on the scope of measurements.

Model-based algorithms

Direct measurement of dose in a patient requires the use of specific models that describe energy transport. This is accomplished by “dose kernel”, which will give energy transport and deposition in different levels by the interaction of photons in tissue. This model-based algorithm will give the absorbed dose in the heterogeneous area. Model-based algorithms are the currently available algorithms used in different TPS. The simple algorithms in model-based algorithms are the PB algorithm and the superposition algorithms. PB algorithms are very fast and a standard dose engine, whereas superposition algorithms are a more accurate and sophisticated algorithm and one of the most used algorithms. Model-based algorithms depend on approximation and some parts involve physical processes like microscopic absorption.

PB algorithms

The PB algorithm assumes that any photon beam hitting the surface of patients will have lots of small, narrow PB. Every PB has a central axis, and dose deposits depend on the intensity of the incident beam. Carolan et al. explain about one narrow PB in isolation (4). When the PB hits the surface of target, each photon beam undergoes basic scattering and absorption due to which dose is spread out on the incident target. This dose distribution will be in the shape of a teardrop or pear shape and the dose from PB is referred to as “dose kernel”.

Superposition/convolution algorithms

Carolan et al. explain how PB calculates dose using a dose kernel for radiotherapy beam (4). Dose kernel will be tabulated from the dose value at each point in the incident PB. To find the dose from the entire beam, the dose contributions from all the beams to each point should be added. The patient volume is divided into dose grid and dose values of each dose kernel will be superimposed on the dose grid. The dose contributions of each beam to the dose grid will be summed to get a total dose (5). This type of dose calculation process is called “superposition” dose calculation.

“Fourier transform convolution” can be used if the patients are considered homogeneous, as the density will be uniform and the dose kernel will be the same. But in reality, patients will have non-uniform density like lung, muscle, bone, etc. For this problem, PB can be used for dose calculation. Computed tomography (CT) images will have the density of each voxel. The dose deposition pattern for the PB was modified according to the density of each voxel. The dose scaling factor is created to “stretch” or “squash”. The dose stretches when the density is reduced, like in lungs, and the dose squashes when the density is increased, like in bones.

In the low-density area, the dose kernel will be elongated, but in the high-density area, the dose kernel will be contracted due to high attenuation. All these are considered for dose calculation in PB algorithm for each voxel of the entire beam. Even after these corrections, PB dose calculation algorithms suffer in the inhomogeneous dose calculation area.

Each TPS will have a slightly different approach to PB dose calculation techniques; the study described the main concept of the elements of the scheme.

MC approach

The most sophisticated approach, which includes all fundamental interactions of radiation with tissue, is the MC approach. The MC approach consists of two independent parts: (I) geometrical design of the treatment head for the machine and characteristics of the electron beam, which serves as input for the respective radiation field; (II) energy transport and absorption inside the patients.

The accuracy and speed are the two main factors in TPS. Jabbari reviewed MC algorithms and inferred that the MC algorithm is accurate in dose calculation of radiotherapy treatment plans (6). The latest advanced version of the MC algorithm dose calculation can be done within a reasonable time.

Key content and findings

Installation and validation of dose calculation algorithms

In 1994, Knöös et al. installed 3CDRT TPS with convolution and superposition algorithms, and the dosimetric verification was performed (7). The results showed that the algorithm model was well-suited for 3DCRT treatment planning. The calculated dose showed a good agreement between measured and calculated data for open and wedge fields. Knöös et al. found that the deviation in the shallow depth for high-energy beams and monitor units (MU) for larger fields had more deviation.

Ma et al. validated the MC user code (MCDOSE) for routine use of the algorithm in treatment planning (8). The MCDOSE code had features of inclusion of beam modifiers in simulation. Beam modifier validation was done by comparing dose distribution between MCDOSE with EGS4 and DOSXYZ user code. The MCDOSE had agreement within 1%, the result showing that MCDOSE was efficient and accurate for clinical use in radiotherapy planning.

Dorje has conducted a study to check the precision of a PB algorithm when inhomogeneous (high-density) material is involved during dose calculation (9). Dorje created an inhomogeneous phantom (30 cm × 30 cm × 17 cm depth), a first 5 cm water equivalent solid phantom in the top layer followed by high-density material polyvinyl chloride (PVC) 5 cm thickness and again 7 cm water equivalent material for the purpose of dose calculation in an inhomogeneous medium. Dose calculation was done for 10×10, 5×5, 20×20 field sizes using the PB convolution algorithm and dose at the same place was measured using an ion chamber. The measured value was compared with calculated values and there were errors in the calculated value of about 4.8–6.9%, 3.7–7.3% and 5.9–7.3%, for the field sizes of 10 cm² × 10 cm², 5 cm² × 5 cm² and 20 cm² × 20 cm², respectively. The result of the study shows that there is no field size dependence but there was a difference in measured dose with calculated dose when high-density inhomogeneity material was involved. The result shows that the PB algorithm has overestimated the dose by about 7.3% beyond high-density material.

Elcim et al. have done a study on MC and PB dose calculation algorithms for use in a TPS and compared them using the RANDO LUNG phantom (10). Thermo-luminescent dosimeter (TLD) chips were placed in the RANDO phantom to verify the planned dose. Using the dose volume histogram (DVH), the minimum dose to the target, the maximum dose to the target and the mean dose to the target were compared and the critical structure dose was also compared with the same. The PB algorithm and MC algorithm dose difference for target was 0.3%. It was concluded that planning target volume (PTV) dose coverage obtained using different algorithms had no significant difference from each other in 3DCRT plan. They concluded that significant difference is arises in the mean dose of the lungs due to dose calculation techniques performed by the TPS. This was arising due to the heterogeneity of the medium in the calculation area. They suggest using MC algorithms in a heterogeneous medium.

Asnaashari et al. conducted a study based on International Atomic Energy Agency (IAEA) TECDOC 1583 (11). An inhomogeneous phantom was used for the study, and CT scans were done at different centres, and 7 tests were performed on 3DCRT TPSs. The dose was calculated using TPS and the doses were compared with the measured dose. For an inhomogeneous medium, different algorithms test were conducted. The advanced algorithms will be preferable for an inhomogeneous medium like the lung and bone area for treatment calculation. IAEA TECDOC 1583 dose algorithms comparison for high energy at lower depths has shown that a large deviation was found in measurement-based algorithms, especially in lung and bone materials (11). The model-based algorithms were preferable for clinical implementation (12). Using the algorithms comparison study, we can identify limitations of algorithms in different clinical areas.

Various dosimetric comparisons of different algorithms

Ali & Ahmad studied the accuracy of dose calculation algorithms between MC and PB using BrainLab TPS for different treatment areas such as 2 head neck, 5 prostate, 2 para spinal case, 4 brain and 5 lung cases (13). Treatment planning dose calculation was performed for different treatment techniques such as 3DCRT, conventional and IMRT. Heterogeneity correction was applied for dose calculation of MC and PB algorithms. The treatment plan was analysed using DVH of 95% of PTV coverage and dose distribution.

Dose calculation accuracy was compared with the measured values between MC and PB algorithms using Gafchromic films and ion chamber in different phantoms. The dose distribution and DVH of MC and PB were in good agreement with each other within 5% for all the cases except lung tumours. Dose coverage for lung tumour patients had more discrepancies in DVH. Dose coverage in the PB was acceptable during optimisation, but in the actual calculation using MC algorithm, the dose distribution was less when compared with PB. PB dose calculation for lung cases was highly overestimated up to 40%. The dose measured using EBT3 films in a heterogeneous phantom indicated around 15% less than PB on the junction between heterogeneous media. The dose calculated for small heterogeneous treatment areas agreed within 5% for both PB and MC, but in lung tumours, nearly a 40% difference in coverage was observed in DVH between the two algorithms, which will significantly affect clinical results.

The difference between PB and MC was more for 15 MegaVolt (MV) when compared with 6 MV. The point dose measured may mislead the quality assurance (QA) for assessing the dose calculation algorithms. Ali & Ahmad suggested that for clinical QA verification, algorithms require at least 2- and 3-dimensional measurements for accurate verification of algorithms instead of point dose measurements with heterogeneous phantoms.

Zhao et al. studied the comparison of different algorithms with different treatment techniques for lung tumour cases. Statistical analysis was performed for all the individual patients and a large deviation was found for different algorithms (14). For lung treatment planning, tissue inhomogeneity will be present in the treatment area. The difference between dose to water and dose to medium in lung tissue was around 1%. The author has studied the MC algorithm with convolution collapsed cone (CCC) and PB algorithms for lung tumours and concluded that CCC algorithms overestimate the dose in the IMRT treatment plan, but in the 3DCRT treatment plan, it is within the acceptable limits. 3DCRT and IMRT plans using the PB algorithm show overestimation of the dose to the target.

Kim et al. did a comparison of MC, PB and collapsed cone (CC) algorithms in an inhomogeneous medium for breast and lung treatment plans using 3DCRT planning techniques. The author was trying to find the inaccuracies of algorithms in inhomogeneous areas, such as lung and breast treatment areas (15). The treatment plan was generated using an Oncentra TPS for CC and PB algorithms and Monaco TPS for the MC algorithm. It was followed by treatment planning and dose distributions for critical structures were compared for all 3 algorithms. Kim et al. found that PB gives an adequate dose distribution to the PTV when compared with MC and CC algorithms. The study showed that other algorithms’ MUs were high when compared with PB algorithms. Kim et al. concluded that dose differences were found while comparing all algorithms (15). PB algorithms show overestimated dose for PTV, while comparing with the other two algorithms and MC algorithms give superior accuracy when compared with the other two algorithms.

Kathirvel et al. have studied dosimetric comparison of VMAT treatment plan for head and neck patients (16). Using two superior TPSs (Monaco and Eclipse), head and neck case treatment plans were generated, and the dose distribution of target and normal tissue doses was compared with each other. Kathirvel et al. concluded that both the planning systems generated plans were acceptable. Monaco TPS showed superior results in serial organ sparing, and the Eclipse planning system showed superior results in parallel organ sparing.

Bosse et al. conducted a study to check the dose calculation and comparison of three TPSs (17). The study concluded that small changes in the dose calculation will result in an apparent change in the DVH. The dose calculation has negligible differences in the open field with a homogeneous medium, but a large difference will be observed in different TPS and tissue inhomogeneity interfaces. All these changes are coming from the dose calculation algorithms used in the TPS. After comparing DVHs from different dose calculation algorithms with MC, MC gives a gold standard. AAA and CCS algorithms give an overestimated dose to the PTV and normal structures. The dose calculation accuracy between flattened field (FF) and flattened free field (FFF) is nearly similar in MC algorithm (18). The accuracy of CCC algorithm is more comparable with MC algorithm when comparing with AAA algorithm (19). Pandu et al. studied the dosimetric characteristics of different algorithms with 3DCRT and IMRT treatment plans. The study results showed that PB algorithm overestimates the dose in IMRT treatment plans, whereas in 3DCRT treatment, there is not much difference (20). Table 2 shows the comparison of different dose calculation algorithm results in the different treatment areas.

Effects of dose calculation algorithm in heterogeneous medium

Since the patient’s body has heterogeneous density, the dose calculation needs more attention. Carrasco et al. have studied the different dose calculation algorithms in low-density medium (21). Correction-based algorithms are: Modified Batho, Batho, Cadplan, and PB Helex-TMS TPS. Correction-based algorithms are not successfully correlating with the measured value, but the CCS and MC algorithms are successfully correlating with the measured values in a low-density medium. The dose difference in water equivalent medium, between all the algorithms was very small but in lower field size, the dose difference was very high, up to 24%. When calculating the dose in smaller field size, lateral electronic disequilibrium dose contribution is not considered by most of the algorithms. MC algorithms were very accurate and precise, with very little difference in small field size dose calculation. The MC algorithm accurately represents the penumbra broadening effect in low-density regions, while the CC algorithm’s predictions fall within the expected range.

Vanderstraeten et al. stated that the performance of dose calculation algorithm strongly influences the accuracy of dose computation in the lungs, especially in the areas of electronic disequilibrium, which arises due to tissue inhomogeneity and density variations (22). Vanderstraeten et al. compared MC calculation MC dose engine (MCDE) along with the other two algorithms, Pinnacle convolution/superposition (CS) and Helex TMS PB. For all the treatment, algorithms DVH of target and organ at risk (OAR) doses was compared and statistical analysis was performed. The Pinnacle CS algorithm demonstrated a strong correlation with the MC algorithm (MCDE) within the PTV. However, for critical structures (OARs), the CC algorithm exhibited better agreement with MCDE. The Helex PB algorithm showed discrepancies for both PTV and critical structures. When analysing patient-specific doses, Pinnacle CS consistently maintained a deviation of less than 5% from MCDE within the target volume. Conversely, for OARs, both CC and CS algorithms exceeded the 5% deviation threshold compared to MCDE. Vanderstraeten et al. concluded that not even one pair of algorithms provided the results within 5% for all 10 patients. This study found that both the algorithms (CC and CS) significantly differ. MC algorithm gives a point of reference for evaluating patient dose with other algorithms.

Kry et al. did a retrospective study which was conducted in 221 institutes and did 304 irradiations as a clinical trial in a Radiotherapy Oncology Group to find the accuracy of TPS algorithms on heterogeneous medium using Radiological Physics Center (RPC) thorax phantom (23). For this clinical trial, 3DCRT and IMRT treatment plans were generated using a 6 MV X-ray beam on RPC thorax phantom. The different treatment plans were generated using different algorithms such as AAA, PB, MC and CS. The absolute dose measured using TLD chips in the lung area was compared with the TPS calculated dose. The dose difference between calculated and measured was examined. The results of this study show that PB algorithms overestimate dose to the PTV by 4.9%. Similarly, AAA and CS were found to overestimate dose to PTV by 3.7%. The MC algorithms’ dose calculation gives good agreement; the dose estimation was within 0.6%. For both planning 3DCRT and IMRT, there was no difference found. Kry et al. concluded that an advanced TPS system using AAA and CS algorithms overestimated dose to the PTV target (23). These calculation algorithms require attention for homogeneous correction for clinical use.

Chetty et al. studied the clinical implementation problem with MC-based treatment planning American Association of Physicists in Medicine (AAPM) Task group no 105 (24). The MC algorithm’s performance was good and more accurate for dose distribution in heterogeneous patient treatment planning. In heterogeneous tissue area, electron distribution cannot give more accurate dose calculation than other algorithms. MC simulation algorithms take a long time for dose calculation, which was the issue with the MC algorithms, but currently the calculation time problem has been reduced when compared with other algorithms due to the fastest development in computer technology. For a small field size dose calculation 0.5 cm² × 0.5 cm², AXB algorithm results gives within 3% of deviation (25). The dose calculation accuracy using AXB algorithm will be better than AAA algorithm in high heterogeneity treatment area (26-28). During dose calculation, the AXB algorithm takes into account heterogeneities (29). When the AXB algorithm was compared with AAA algorithm for lung tumours, the AAA algorithms overestimate the dose to the PTV (30-33). Table 3 shows the different dose calculation algorithm results in the inhomogeneous treatment area.

Proton beam therapy dose calculation algorithms

Paganetti et al. has studied about dose distribution of MC and PB for proton therapy (35). The PB algorithm depends on the kernel to model and the proton range in water equivalent material is scaled in density. MC algorithm’s dose calculation takes the theoretical model using physics of particle interaction and MC, considering the tissue inhomogeneities by the material properties, for example, electron density, material composition and mass density. In proton therapy, the dose difference between MC and PB algorithms will be more significant because of the dose gradient (35).

The dose calculation in an inhomogeneous treatment area needs to be studied, because proton beam will undergo multiple scattering. Sorriaux et al. studied the proton dose calculation in an inhomogeneous treatment area using the inhomogeneous phantom. The results of this study showed that MC algorithm gives better results compared to PB algorithm (36). Dose calculation of treatment area, such as the skull, using PB will be more challenging due to bonier regions and air cavities. The proton treatment plan for both cases was done using MC and PB algorithms. The agreement between the algorithms was good. For head and neck tumours, there were differences near the spinal cord between MC and PB dose algorithms. In proton beam also the MC algorithms also show good accuracy and precise treatment plan when compared with PB algorithms.

Fogliata et al. studied the comparison of algorithms with proton and VMAT treatment plans for soft tissue sarcoma in extremities (37). The radiotherapy side effects will be stiffness in the joints of the bone, skin toxicity and oedema. To overcome this bone fracture, the treatment plan should provide adequate coverage to the target while delivering reduced doses to the nearby bone and other normal structures. The author has investigated two plans: (I) VMAT treatment plan with different algorithms; (II) proton plan IMPT (intensity-modulated proton therapy). For the VMAT plan, dose calculation of two algorithms (AAA and Acuros-XB) were performed using two options, dose to water and dose to medium. For the proton treatment plan, IMPT convolution superposition algorithms were used. Plan evaluations were performed with DVH analysis. In the proton plan, dose homogeneity was significantly found. For normal tissues, low-dose was lower with a proton treatment plan and integral dose also half reduced for VMAT plans. Dose distribution in AAA and AXB both are similar, no difference found. In bone, dose calculation has no significant difference between these algorithms for the dose to the medium. For lung tumours, analytic algorithms calculated dose in proton therapy, but not up to the mark. For efficient treatment dose calculation in proton therapy treatment, MC or other advanced algorithms need to be used (34). Table 4 shows the different algorithms used in proton dose calculation.

Limitation of PB algorithms

Whenever the photons travel in the heterogeneous medium, the electron transport and photon scatter will be ignored by most of the dose calculation algorithms. The study was conducted to find out the limitations in mediastinum geometry for the different ranges of beam quality by comparing the results of PB algorithms with the MC algorithms (38). The deviation was found for PB algorithms when increasing the beam energy from lower to higher energy.

Ahnesjö & Aspradakis have published a review article on external beam dose calculation for the radiotherapy beams (39). Ahnesjö & Aspradakis concluded that the pencil kernel model was simpler and faster than the point dose kernel models. They suggested that, in the future, the pencil kernel model can be used for optimisation algorithms for finding the beam shape and optimal beam modulation. Presently, we are using PB as initial dose optimisation in MC algorithms. PB algorithms can create a treatment plan for different treatment techniques, but in air tissue, the treatment area needs attention before using this algorithm (40).

Conclusions

This review emphasises the crucial role of accurate dose calculation algorithms in effective and safe radiotherapy. MC and AXB consistently demonstrate superior accuracy, particularly in complex, heterogeneous tissues like the lung. Superposition/convolution algorithms also perform commendably, closely aligning with MC-based calculations in these challenging scenarios. Conversely, traditional PB and other correction-based algorithms, despite their speed, frequently overestimate target volume doses and often fail to accurately account for tissue heterogeneity, especially in the lungs and near tissue interfaces. This can lead to clinically significant errors. Multiple studies have shown substantial deviations between PB algorithms and measured doses in heterogeneous regions, with MC algorithms serving as the established gold standard for validation.

Fortunately, technological advancements have significantly reduced MC calculation times, making their routine clinical use more feasible. Furthermore, clinical evidence supports the enhanced performance of newer model-based algorithms like AXB over older methods, including PB and AAA, particularly when high accuracy is paramount in heterogeneous regions for both photon and proton therapy. In essence, careful algorithm selection is vital, especially for cases involving pronounced tissue inhomogeneity or small field sizes. MC and AXB are the preferred choices when uncompromising accuracy is required, while PB may only be suitable for simpler, homogeneous cases. A thorough understanding of each algorithm’s strengths and limitations empowers physicists to optimise treatment plans and ultimately enhance patient treatment plan outcomes in modern radiotherapy.

Acknowledgments

None.

Footnote

Reporting Checklist: The authors have completed the Narrative Review reporting checklist. Available at https://tro.amegroups.com/article/view/10.21037/tro-24-10/rc

Funding: None.

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://tro.amegroups.com/article/view/10.21037/tro-24-10/coif). The authors have no conflicts of interest to declare.

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