Intensity-modulated radiation therapy (IMRT) was introduced about four decades ago [1] and has proven to produce superior dose distributions to 3D conformal techniques for almost all anatomic sites, particularly those with concave targets [2]. IMRT can deliver tightly conformal dose distributions and have better sparing to organs at risk (OAR) through the generation and realization of non-uniform fluence maps across multiple radiation beams. There is a wide range of literature on IMRT optimization [3–7]. The process of IMRT optimization, as a multi-criteria problem, needs to define an objective function to quantitatively evaluate the deviation between the planned dose and the target dose, including the dose constraints for both target and OARs [8]. To solve the problem, the IMRT optimization process is traditionally classified into two categories: 1) “two-step method”: optimizing the photon fluence map in each field (fluence map optimization, FMO) and then generating sub-field leaf sequences sequentially [9, 10]; 2) direct aperture optimization (DAO): directly optimizing leaf sequences to obtain desired dose distribution [11, 12].

A modern Linac is often equipped with multiple photon energies (usually two photon energies) [13]. The clinically relevant energy range for photons was 6–18 MV. It was known that the physical deposition capability in the medium is energy dependent. Generally, lower energy photon beams (≤6 MV) have limited penetration and are often used to treat superficial or shallow tumors. Due to the benefit of narrow penumbra, the IMRT plan using lower energy photon generated a tighter dose distribution around the target and better preserves the critical structures adjacent to the target volume. However, it results in a higher entrance dose [14]. On the other hand, higher energy photon beams (≥10 MV) are often used to treat deep-seated tumors, such as prostate or gynecological tumors et al, for their higher penetration and better skin-sparing ability. However, the resulting neutron contamination and higher exit dose should be of concern in clinical practice [14].

One challenge in IMRT is the selection of beam energy in traditional treatment planning, which requires the consideration of the overall characteristics of the clinical case. The energy of photon is closely related to the depth of the tumor or the size of the patient. For deep tumor and large size patient, the high energy photon has advantages over the low-energy photon [15]. However, the involvement of many OARs nearby with different dose tolerances and the use of multiple cross-firing beams often makes the selection of optimal energy not obvious. The optimal energy is usually decided on a trial-and-error basis [16], based on the tumor location and clinical experience. Previous papers have shown some energy dependence for different treatment modalities and tumor sites [17–19]. There was a dose increment in regions distant from the target volume when 6 MV photon was used instead of 10 or 18 MV photons in an IMRT plan with less than nine fields [15]. When a sufficient number of fields were used, such dose increment becomes less and the plan quality is no longer sensitive to beam energy, even for exceptionally large patients [15]. However, these observations are only applicable to plans with a single energy.

Recently, some studies have shown the potential dosimetric gains of mixed energy photons (one low-energy and one high-energy photon) [20–23]. In these works, the beam energy is generally assigned based on the one-dimensional effective path length (EPL) of tumor depth. The general findings are that the mixed-energy photon plan has advantages in terms of increasing dose coverage and conformity to PTV, or sparing relevant OARs, but the advantages are not significant. However, these studies simply used two energies available from a Linac and did not fully demonstrate the dose deposition characteristics of different energies. Some works incorporate photon energy as a parameter in the plan optimization. St-Hilaire et al introduced an energy angle concept as an additional, independent degree of freedom for multiple-energy optimization (MEO) using DAO [24]. McGeachy et al provided the algorithm for simultaneously optimizing both beamlet energy and fluence in IMRT and found potential dosimetric benefits in OARs sparing [25]. All these attempts proved that the extra degree of freedom of photon energy can bring some dosimetric gains, and improve the overall plan quality. However, the optimization is more demanding in terms of computation and memory, due to the significantly increased number of variables [24]. Currently, all these studies only selected two energy photons for optimization. If more levels of energy are introduced to the IMRT optimization, the computational complexity and time requirements would increase significantly, which makes the IMRT optimization impracticable [24].

In our previous works [26, 27], it was shown that any intermediate energy photon can be effectively synthesized from a combination of two different energy photons. This technique also enables continuous energy modulation in IMRT, providing another degree of freedom to improve treatment plan quality. Therefore, the purpose of this study was to develop and validate a novel IMRT method that can simultaneously optimize fluence map and beamlet energy, referred to as IMRT with beamlet energy modulated (IMRT-BEM). Based on the energy synthesis principle, the IMRT-BEM was modeled as the optimization of two fluence maps for one low energy and one high energy photon beams, and it was implemented in an in-house inverse planning system. Since the principle showed that any energy photon can be synthesized using two energy photons, it implies that no more than two energy photons are necessary from the same gantry angle. This is fundamentally different from previous studies of trial-and-error that are based on the belief of “more is better”. The IMRT-BEM was analyzed and demonstrated on ten pancreatic cancer cases. To investigate the impact of incorporating an additional degree of freedom in beamlet energy, the dose distributions resulting from IMRT-BEM plans were compared to conventional single energy IMRT plans utilizing either 6 MV beams (IMRT-6MV) or 15 MV beams (IMRT-15MV). To the best of our knowledge, there are no previous works on multi-energy IMRT optimization that validated the method in a large number of clinical cases.

In this work, a new IMRT optimization algorithm for continuous photon beamlet energy modulation was developed and demonstrated in 10 pancreatic cancer cases, to show the effect of an additional degree of freedom of beamlet energy on plan quality. IMRT-BEM simultaneously optimizes the photon fluence and energy in each beamlet, which is theoretically different from the traditional single-energy IMRT optimization method. In contrast to the traditional IMRT optimization, where the photon energy was fixed at a pre-selected value, the photon energy of each beamlet in the IMRT-BEM plan could continuously vary within the range of min 6)—max (15) MV, and the photon energy of the beamlet is a free variable in optimization.

It is widely recognized that high-energy photon beams with energies of 10 MV or higher are commonly used in radiation therapy for deep-seated tumors. They offer excellent penetration power and protect the skin during treatment. However, it should be noted that these high-energy beams may lead to an increase in the range of secondary electrons, which can result in greater lateral scattering [34]. This can cause blurring of dose boundaries and potentially inadequate delivery of the required dose to the target area. Additionally, there is a concern regarding neutron contamination [35]. In light of these challenges, there has been a growing interest in exploring the potential dosimetric advantages of lower energy photons, such as, Cobalt-60 and low-energy X-rays (<6 MV). By utilizing lower energy photons, it may be possible to mitigate some of the issues associated with high-energy beams. Lower energy photons exhibit reduced secondary electron ranges, which can result in sharper dose boundaries and improved delivery of the desired dose to the target area. One notable advantage of low-energy photon beams is their ability to create a smaller penumbra, resulting in a more precise and tightly-focused dose distribution around the target volume [36]. Furthermore, the use of lower energy photons can potentially address concerns related to neutron contamination.

Exploring the benefits of lower energy photons opens up new possibilities in radiation therapy planning and treatment. However, it is important to thoroughly evaluate the specific requirements of individual cases and consider factors such as tumor depth, target volume, and surrounding critical structures when determining the optimal photon energy for treatment. Consequently, in future research, the IMRT-BEM algorithm can use energies lower than 6 MV, such as 2 MV, to continue exploring the advantages of low-energy photon beams in radiotherapy. However, it is important to acknowledge that there are also some drawbacks associated with low-energy beams. These include a lower output dose rate, limited maximum dose depth, and reduced penetration capabilities. Additionally, careful planning is required when using low-energy photons to avoid higher dose deposition in the tissue at the entrance of the beam.

In conventional practice, the optimal beam energy is often selected according to the effective path length at a given gantry angle through the body, assigning higher energy to beams with longer path lengths [21]. Although this processing method seems intuitive, it ignores the dose accumulation effect of multiple radiation beams and the complex three-dimensional dosimetric distribution [25]. It was proved that the mixed energy technique is a practical way to generate a homogenous dose distribution for the target or reduce the dose to the OARs while maintaining adequate target coverage. A hybrid photon energy technology is only a simple linear combination of two energy photon plans, which is commonly used for breast and prostate cancers [21, 37, 38]. Obviously, The results obtained by this method are not optimal, and the arbitrariness of the photon energy of a beam increases the possibility of optimization to obtain a suboptimal plan [39]. The optimal and possibly unintuitive plan can be found through energy modulation in inverse planning. However, limited by computing power and system memory, all these studies only selected two photon energies for IMRT optimization research and failed to explore the continuous modulation of photon energy as we did [24, 25]. Besides, their methods all were verified on a small number of clinical cases or ideal water phantom data with the conclusion lacking sufficient clinical statistical data support.

It is a new way to realize energy-modulated IMRT based on two levels of energy photon on a medical linear accelerator with conventional configuration. In theory, compared to conventional single-energy IMRT plans, a beam in IMRT-BEM plans is composed of multiple small sub-beams with different photon energies, allowing separate optimization of different beamlet energies for different parts of the target volume. This may lead to clinical dosimetric improvements in some complex cases with off-center targets or concave tumors adjacent to many OARs of serial or parallel tissue. In this work, we pioneered the application of the concept of continuous photon energy modulation in IMRT planning and showed some advantages of the proposed method. In the future, we will study other tumor sites to identify the scenarios where this method is more useful. The results of this study show that the IMRT-BEM could improve the CI and HI of the plan, and provided a significant reduction of high-dose irradiation volume of the PTV(PTV_105%), at least 24.7%. Compared with the single-energy IMRT plan (IMRT-6MV or IMRT-15MV), the irradiation volumes of the medium dose (V_20Gy and V_40Gy) to the duodenum and V_20Gy of the stomach were reduced significantly than the other solutions, which may decrease the late toxicity of the duodenum. Research has shown that radiation dose escalation for pancreatic cancer is limited by the proximity of the sensitive surrounding OARs, in particular, gastrointestinal organs which are directly adjacent to the pancreas [40]. Therefore, the reduction of the bowel and the duodenum dose may help to further escalate the dose of PTV in IMRT-BEM, which requires further research to verify.

Though the advantage of the IMRT-BEM plan over the 15 MV plan may not be as pronounced as that over the IMRT-6MV plan, it is important to note that even modest improvements resulting from energy modulation contribute to the development of a more favorable treatment plan. Besides, our study also indicates that, in comparison to the IMRT-15MV plan, the IMRT-BEM plan exhibits a significantly lower monitor unit (MU) value contributed by the 15 MV photon, which reduces the neutron generated.

The focus of this study is to evaluate the effect of beamlet energy modulation. To exclude the dosimetric effect of other factors, the same optimization objectives and constraints were used across all plans for each patient. However, in radiotherapy practice, the optimization goals and constraints can be appropriately adjusted during the optimization to meet the individual dose-volume constraints of different cases. Therefore, the plan quality of IMRT-BEM may be further improved.

In this study, five beams were used. One may ask whether the dosimetric advantages of the IMRT-BEM technique still be valid when the number of beams increases. Therefore, some additional explorations were done in this regard. We found that IMRT-BEM can obtain the lowest objective value when the number of beams is less than 9, as shown in Figure 6. When the number of beams increased, the objective function values of different plans are close to the same, consistent with previous research [15]. Therefore, for some complex cases, we can reduce the dependence of the plan on energy by increasing the number of beams. In radiotherapy practice, the number of beams is generally selected to be 5-7, and the IMRT-BEM technology could be used to deal with some complex cases.

The findings of this study illustrate the different contributions of photons with varying energies to the fluence intensity of the IMRT-BEM plan. Although the synthesized beams cannot perfectly replicate real beams with identical energy levels, they do exhibit dose equivalence in terms of measurable dose effects. Nevertheless, disparities exist in their energy spectral distributions. For instance, a real 10 MV photon beam possesses a maximum photon energy of 10 MeV, whereas a synthesized 10 MV beam has a maximum photon energy equivalent to the highest energy photon employed during synthesis, which could be 15 MeV or 18 MeV. However, when comparing two treatment plans utilizing photons with different energies within the clinically utilized energy range, the primary emphasis lies on their respective doses rather than disparities in beam spectra and energies. However, the differences in other beam modification devices were not taken into consideration in energy modulation, such as leaf transmission and dosimetric leaf gap, which are photon energy dependent. However, they are monotonically changing with energy, these negligible differences may not be observed in our plan comparisons due to the “interpolation” nature of the energy synthesis.

After the optimization of IMRT-BEM, the fluence map of continuous photon energy in each beam was converted into two separate fluence maps corresponding to the low and high photon energies. Then, using a subfield segmentation algorithm, the fluence of each energy was divided into multiple dynamic subfield sequences. Each beam defines two sets of MLC shapes and their respective weights (MUs) for high and low energy, respectively. Ultimately, the IMRT-BEM plan is transformed into two single-energy photon plans, one with energy E l o w and the other with energy E h i g h , for delivery. This approach, which utilizes a continuous photon energy modulation optimization strategy, effectively increases the total number of beamlets only by a factor of two in all beam directions, without significantly adding complexity to IMRT optimization and calculation processes. Thus, the algorithm can be efficiently implemented. As for MLC sequencing itself, the sequencing for 6 MV and 15 MV photon beams does not differ from that for single energy beams and can be performed using existing algorithms.

For the IMRT-BEM plan, each beam needs to be converted to two MLC sequences with 6 MV and 15 MV photon beams respectively with two possible delivery strategies. One strategy is to deliver all beams at one energy first and then the other energy. In this case, only one energy switch needs to be performed but the gantry rotation time (field switch time) is doubled. The other strategy is to deliver the beam angle by angle, which involves as much energy switch as the number of beams. The delivery strategy can be chosen by the characteristics of the linac. For Linac with the ability of quick energy switch, ex. less than 20 s on a Varian TrueBeam linac, the second delivery strategy would be preferred.

Certainly, there are shortcomings in this optimization method. One obvious limitation is the extended treatment time caused by the requirement for delivery at two photon energies and increased plan MUs compared with single energy plans (Figure 3). However, this may not be a serious issue because the delivery time is taking less portion of the time slot compared with other steps such as patient setup and image guidance, and the continued development in the linac delivery automation will improve the efficiency of IMRT-BEM. Another limitation is 15 MV photon was used in the IMRT-BEM and neutrons will be produced which may lead to an increased incidence of secondary cancers after photon radiotherapy [35]. However, recent studies have shown that the high-energy neutron component may have been overestimated in the past [41]. More studies are needed to evaluate the effect of using the 15 MV photon beam in radiotherapy.

We developed a novel optimization algorithm to include continuous photon beamlet energy modulation in IMRT through the use of photon energy synthesis and validated it in pancreatic cancers. The dosimetric properties of both PTV and some OARs are superior to single-energy IMRT plans. The integral dose of IMRT-BEM is lower than that of IMRT-6MV but slightly higher than IMRT-15MV. The preliminary results demonstrate that the IMRT-BEM algorithm can improve plan quality, especially for complex cases with off-center and concave tumors adjacent to many OARs of serial or parallel tissue.