Effects of nuclear interaction corrections and trichrome fragment spectra modelling on dose and linear energy transfer distributions in carbon ion radiotherapy

Highlights

• •Predicting linear energy transfer needed nuclear interaction and trichrome modelling.
• •Rectified carbon dose and linear energy transfer did not affect clinical protocols.
• •Enhanced pencil beam modelling and Monte Carlo simulations agreed within 95%.

Abstract

Background and Purpose

Nuclear interaction correction (NIC) and trichrome fragment spectra modelling improve relative biological effectiveness-weighted dose (D_RBE) and dose-averaged linear energy transfer (LET_d) calculation for carbon ions. The effect of those novel approaches on the clinical dose and LET distributions was investigated.

Materials and Methods

The effect of the NIC and trichrome algorithm was assessed, creating single beam plans for a virtual water phantom with standard settings and NIC + trichrome corrections. Reference D_RBE and LET_d distributions were simulated using FLUKA version 2021.2.9. Thirty clinically applied scanned carbon ion treatment plans were recalculated applying NIC, trichrome and NIC + trichrome corrections, using the LEM low dose approximation and compared to clinical plans (base RS). Four treatment sites were analysed: six prostate adenocarcinoma, ten head and neck, nine locally advanced pancreatic adenocarcinoma and five sacral chordoma. The FLUKA and clinical plans were compared in terms of D_RBE deviations for D_98%, D_50%, D_2% for the clinical target volume (CTV) and D_50% in ring-like dose regions retrieved from isodose curves in base RS plans. Additionally, region-based median LET_d deviations and global gamma parameters were evaluated.

Results

Dose deviations comparing base RS and evaluation plans were within ± 1% supported by γ-pass rates over 97% for all cases. No significant LET_d deviations were reported in the CTV, but significant median LET_d deviations were up to 80% for very low dose regions.

Conclusion

Our results showed improved accuracy of the predicted D_RBE and LET_d. Considering clinically relevant constraints, no significant modifications of clinical protocols are expected with the introduction of NIC + trichrome.

1. Introduction

The advantages of carbon ion radiotherapy (CIRT) lie in its physical and radiobiological properties. Compared to photon and proton beams, carbon ions exhibit a sharper lateral penumbra and a steeper distal fall-off, as well as higher linear energy transfer (LET) and increased relative biological effectiveness (RBE) near the Bragg peak [1], [2], [3], [4]. To fully exploit CIRT properties, treatment planning systems (TPS) for active scanning techniques require accurate physical dose calculation as well as modelling of the biological interactions.

Physical dose calculations in particle therapy employ both Monte Carlo (MC) and analytical algorithms (pencil beam (PB)) in combination with spatial and density information of the treated object [5], [6]. Due to their superior accuracy, MC calculations would be preferable but due to the increased computational power only analytical algorithms are currently available in commercial TPSs for light ions. In a PB algorithm, the dose is computed by convolving Gaussian-modelled lateral fluence by longitudinal integrated depth dose (IDD) curves given in water and scaled for the water equivalent depth of the calculation point [7], [8], [9], [10]. In addition to the limitations of the infinite slab approximation, this approach may result in dose calculation errors due to the water non-equivalence of patient tissues, particularly in terms of nuclear interactions, which can be accounted for by considering the ratio of the probability of nuclear interactions in materials compared to water [9], [11], [8], [12].

In terms of RBE-weighted dose (D_RBE) calculation, a monochrome model is currently clinically used to characterize radiation quality over the beam’s cross-section [13], [14]. The monochrome model assumes that, in regards to the computation of D_RBE and dose-averaged LET (LET_d), the particle composition of the radiation field produced by a spot is homogeneous across the transversal plane and only dependent on depth resulting in a very high LET_d outside of the field. However, due to the different scattering angles of different nuclear reaction fragments, radiation quality is dependent on the distance from the central beam axis [15], [16], [17]. The analytical trichrome model (trichrome) for RBE calculations was developed to improve the accuracy of the biological effectiveness calculation of carbon ions [18]. The trichrome model was originally integrated for the microdosimetric kinetic model (mMKM), whereas the local effective model (LEM) has so far been used with monochrome [12], [14], [19], [20], [21]. With the trichrome model, the particle composition outside of the field only includes lower LET particles of Z ≤ 2, which better matches the actual particle distribution.

Currently, commercial TPSs available in Europe for scanned CIRT include neither nuclear interaction correction (NIC) nor trichrome model-based biological dose computation. The current work aims to assess the effects of these two models on D_RBE and LET_d distributions.

The accuracy of D_RBE and LET_d prediction based on NIC and trichrome algorithms was validated with basic treatment plans and target geometries benchmarked against FLUKA MC simulations [22], [23], [24]. Clinical treatment plans for several anatomical districts were analysed to assess clinically relevant variations from the current standard.

2. Material and methods

2.1. Theoretical background

NIC accounted for the elemental composition of the traversed medium and, by that, modified the physical dose calculation. An attenuation correction factor for IDDs was introduced via a relation between the electronic stopping power ratio ${\rho }_S$ (i.e. the ratio of the stopping power in a material to that of water) and the nuclear reaction probability ratio ${\rho }_N$ (i.e. the ratio of a material’s probability of nuclear interaction to that of water) [11]. If ${\rho }_N>{\rho }_S$ (e.g. in adipose tissue), the correction factor predicted more nuclear reactions, while the opposite happened if ${\rho }_S>{\rho }_N$ (e.g. in bone tissue). In the former case, the dose distribution was lower until the Bragg peak due to increased attenuation of primary carbon ions, while the dose in the tail region was higher due to an enlarged fragment production.

The trichrome algorithm for biological dose computation was based on a multiple Gaussian description of the fragments’ contribution to the dose profile: the first Gaussian component was mainly determined by primary carbon ions; the second and the third components were composed of heavy fragments with atomic number Z ≥ 3, and light fragments with Z ≤ 2, respectively. As a result, a greater concentration of carbon ions yielded higher RBE near the central axis, while the opposite happened for regions with a high concentration of light fragments (i.e. far from the central beam axis). Similarly to MKM, the trichrome model was applied to LEM low dose approximation coefficients in mixed radiation fields via the introduction of a radial dependence in the intrinsic LEM parameters [25]. A detailed theoretical description of the theory behind NIC and trichrome corrections can be found in Inaniwa et al [11], [18].

2.2. Reference FLUKA simulations

Single beam plans with a uniform dose of 3 Gy (RBE) to a cubic target of 4 cm side length were optimized with Raystation-V.11B-DTK (RaySearch Laboratories, Sweden) using standard interaction settings (base RS) and employing NIC and trichrome corrections (NIC + trichrome). Slabs of different materials and variable thicknesses were interposed between the beam entrance and the target surface, preceded and followed by 1.5 cm of water (Supplementary Figure S1).

To assess the accuracy of the NIC + trichrome algorithms, reference D_RBE and LET_d distributions were simulated using the FLUKA version 2021.2.9. All plans were calculated with a dose grid resolution of 0.3 cm.

The beam was modelled in FLUKA using a user-defined SOURCE routine which samples beam particles from a phase space according to the RayStation beam model. The HADROTHErapy default settings were enabled, and delta-ray production was disabled. Scoring of LET_d, α and sqrt(β) was achieved with a combination of FLUKA’s built-in scoring card USRBIN and user-defined COMSCW routines where each energy deposition was weighted with its corresponding quantity. The ion-specific α values, given as a function of energy for each particle species, were taken from pre-computed tables of the chordoma cell type according to LEM I [13]. The reference D_RBE was calculated in a separate script using the LEM low-dose approximation [25].

2.3. Clinical dose calculations

Thirty anonymised scanned CIRT plans from patients treated at MedAustron and CNAO (registry trial number GS1-EK-4/350–2015 and CNAO OSS 64 2023) previously optimized with LEM I in Raystation-V.8B (PBv3.0) and 10B (PBv4.2) were imported into Raystation-V.11B-DTK. Keeping the original spot distribution and weights, the final dose was recalculated with the PBv.5.0 carbon ion dose engine (base RS plans), using the LEM low dose approximation [25]. Each plan was reproduced three times (evaluation plans), and the dose distributions were recalculated by applying NIC, trichrome and a combination of both (NIC + trichrome). Treatment plans from four different sites were analysed: six prostate adenocarcinoma (PCA), ten head and neck (H&N), nine locally advanced pancreatic adenocarcinoma (LAPC) and five sacral chordomas (SC).

2.4. Evaluation and statistics

To examine the effect on healthy/non-target tissues surrounding the clinical target volume (CTV), three ring-like dose regions based on isodose curves calculated in clinical base RS plans were considered, i.e. the region between CTV and 90% isodose (iso90), the region between CTV and 40% isodose (iso40) and the region between 40% and 10% isodose (iso10). For FLUKA simulations iso40 was defined as the region between 90% isodose and 40% isodose instead.

For LET_d additional low-dose regions were defined to investigate the highest expected differences, i.e. the volume between 10% and 2% isodoses (iso2) and the volume between 10% and 0.5% isodoses (iso0.5), for FLUKA simulations and clinical plans, respectively. For the FLUKA simulations, the lower dose limit was selected to avoid significant levels of stochastic fluctuations.

For FLUKA simulations, depth D_RBE and LET_d distributions in water along the beam axis and D_RBE and LET_d profiles in water in the centre of the target were extracted. This was performed among FLUKA, Raystation without NIC + trichrome (base RS) and including NIC + trichrome.

To analyse the dose to the CTV and the defined ring-like dose regions in the clinical plans, near-minimum D_RBE (D_RBE to 98% of the volume (D_98%)), median dose (D_50%) and near-maximum dose (D_2%) were collected for all base RS and evaluation plans. The percentage dose deviations (ΔD) between those D_RBE values of all three evaluation plans (D_eval) concerning base RS plans , were analysed and presented as median dose deviation values [interquartile range]. To assess the outcome for the energy deposition patterns, median LET_d values were collected for the CTVs and above-defined ring-like dose regions, i.e. iso90, iso40, iso10 and iso0.5. Percentage LET_d deviations (ΔLET_d) comparing base RS to the evaluation plans were only reported for the NIC + trichrome combination, which corresponded to the future clinical implementation.

To assess the agreement between the D_RBE and LET_d distributions between different dose computation methods (FLUKA and RayStation) and algorithms (base RS plans and NIC + trichrome), global gamma evaluations were performed [26]. For FLUKA simulations a RayStation codebase using a tailored in-house dose validation framework and for the clinical plans an in-house written Python script, running on the Raystation script framework was used. γ-pass rate criteria of 2%/1 mm and 5%/1 mm were applied for the FLUKA simulations and of 1%/1 mm for the clinical plans. Mean γ-pass rate values will be reported with the respective standard deviation (SD).

For all dose-volume histogram (DVH) and LET-volume histogram (LVH) criteria reported above, the non-parametric Wilcoxon signed-rank test was applied. The statistical significance of D_RBE (comparing NIC, trichrome and NIC + trichrome plans to base RS plans) and LET_d deviations (comparing only NIC + trichrome to base RS plans) was assessed with a significance level of p < 0.02 and p < 0.05, respectively, pooling all treatment sites together.

3. Results

3.1. FLUKA reference simulations

Fig. 1 shows the comparison of D_RBE and LET_d distributions in bone along the beam axis among FLUKA, base RS and NIC + trichrome underlining a sharp LET_d peak at the distal edge of the target that was not fully modelled in Raystation applying NIC + trichrome corrections. The LET_d profile in water (Fig. 1) visualised the trichrome effect, where the monochrome approximation assumed a homogeneous particle composition in the transversal plane, which in reality was dominated by protons with low LET. Percentage deviations in median D_RBE and median LET_d between base RS, NIC + trichrome and the reference FLUKA calculations are reported in Supplementary Table S1.

Fig. 1.

top) Depth D_RBE and LET_d distributions in bone along the beam axis, around the target depth.   bottom) Lateral D_RBE and LET_d profiles in water in the centre of the target; Blue line: RayStation without NIC+trichrome (base RS). Red line: RayStation with NIC+trichrome. Yellow line: FLUKA.

The gamma evaluation comparing dose distributions in RayStation and FLUKA with 5%/1mm criterion showed a very good agreement between both, base RS and NIC + trichrome and FLUKA calculations (Table 1). γ-passing rates with 2%-1mm criterion in the water showed small deviations (passing rate around or higher than 99%) for adipose and bone cases and larger deviations for the lung and titanium cases (around 97% passing rate, down to 83% for titanium in the iso10 region). NIC + trichrome overall improved the γ-passing rate compared to base RS, except in the lung case.

Table 1.

Global γ-pass rates of the D_RBE and LET_d computed in RayStation with (NIC + trichrome) and without (base RS), with D_RBE computed in FLUKA as the reference. Data is presented for each one of the plans with different slab materials, for both 2%/1mm and 5%/1mm criteria and for each of the dose regions.

DRBE		2%/1mm γ-pass rate [%]				5%/1mm γ-pass rate [%]
Material	Algorithm	Target	iso40	iso10		Target	iso40	iso10
Water	base RS	98.9	100.0	99.6		100.0	100.0	100.0
	NIC + trichrome	99.9	99.9	99.8		100.0	100.0	100.0
Lung	base RS	97.3	99.0	99.6		100.0	100.0	100.0
	NIC + trichrome	96.9	99.0	98.4		100.0	100.0	100.0
Adipose	base RS	99.0	97.8	99.8		100.0	100.0	100.0
	NIC + trichrome	99.7	98.7	99.9		100.0	99.99	100.0
Bone	base RS	98.0	100.0	99.6		100.0	100.0	100.0
	NIC + trichrome	99.9	99.9	99.9		100.0	100.0	100.0
Titanium	base RS	0.0	81.9	59.2		99.1	100.0	100.0
	NIC + trichrome	97.1	96.1	83.1		100.0	100.0	100.0

LETd		2%/1mm γ-pass rate [%]				5%/1mm γ-pass rate [%]
Material	Algorithm	Target	iso40	iso10	iso2	Target	iso40	iso10	iso2
Water	base RS	96.9	98.2	79.3	75.6	100.0	99.8	94.9	88.9
	NIC + trichrome	97.6	98.4	98.0	68.4	100.0	99.8	100.0	99.5
Lung	base RS	91.4	99.2	76.8	83.6	95.8	99.6	90.4	91.2
	NIC + trichrome	92.8	99.3	91.6	91.6	95.7	99.8	95.7	99.1
Adipose	base RS	96.4	99.4	79.0	73.7	100.0	100.0	97. 9	77.7
	NIC + trichrome	98.5	99.6	97.3	67.8	100.0	100.0	99.8	99.6
Bone	base RS	89.5	97.6	75.0	86.6	92.9	98.8	85.0	92.6
	NIC + trichrome	92.5	98.3	91. 9	90.8	92.9	98.8	94.0	99.3
Titanium	base RS	90.4	93.5	80.7	89.2	100.0	95.6	89.4	94.6
	NIC + trichrome	99.9	95.6	97.8	96.4	100.0	95.6	99.2	99.7

The gamma evaluation for LET_d distributions with 2%/1mm criterion showed an improved γ-passing rate in all materials and dose regions when using NIC + trichrome, except in the iso2 region in the water and adipose cases (Table 1). The results with γ-pass criteria 5%/1mm at the iso2 dose region showed large deviations when comparing base RS to FLUKA, whereas the γ-passing rates for all cases were higher than 99% when using NIC + trichrome. For the target and the iso40 regions, the LET_d γ-passing rates with 5%/1mm criterion were comparable for base RS and NIC + trichrome, but some of them had a significant number of fails (around 5% fail rate or higher).

3.2. Clinical dose calculations

The introduction of NIC led to a median reduction of D_50% below 1% in the CTV, iso90 and iso40, for all considered treatment plans. A sign variation was reported only for sacral chordomas (increase by median 0.9% [interquartile range 0.7%]) in the lower dose region (iso10). Trichrome modelling resulted in a median dose increase of D_98%, D_50% and D_2% in the CTV; the trend was variable for iso10 depending on the treatment site, where negative variations of D_50% up to −0.9% [0.2%] for sacral chordomas cases were observed. ΔD_50% never exceeded ± 1%. The median ΔD values for each indication for all three evaluation doses are reported in Supplementary Table S2. A D_RBE and LET_d comparison is exemplified for a prostate patient in Fig. 2.

Fig. 2.

Base RS vs NIC+trichrome plan for a prostate adenocarcinoma case; left) D_RBE distribution right): LET_d distributions.

The combination of NIC + trichrome led to overall smaller dose deviations compared to the evaluation of the NIC and tri-chrome alone with a median increase < 0.5%. This trend was observed in all the analysed dose regions, except iso10 in H&N where ΔD_50% was −0.8% [0.7]. Fig. 3 shows box plots of the median ΔD values and interquartile ranges comparing NIC + trichrome to base RS plans for the CTV (D_98%, D_50% and D_2%) and the ring-like dose regions (D_50%) for the different anatomical districts. Dose deviations comparing base RS and evaluation plans were not statistically significant for any dose/volume metrics that were considered (p > 0.02). The mean γ-pass rate restricted to CTV and ring-like dose regions was > 97% for all NIC + trichrome plans averaged over all patients within an anatomical district (Table 2).

Fig. 3.

Percentage median dose deviations and interquartile ranges comparing base RS and NIC+trichrome plans. D_98%, D_50% and D_2% (upper part) for the CTV and D_50% for iso90, iso40 and iso10 (lower part) are plotted in the different diagrams. All plans included in this boxplot were recalculated with NIC+trichrome and plotted for each anatomical district separately. The boxplots show the median and 25th to 75th percentile, with the whiskers displaying 1.5 times inter-quartile range.

Table 2.

Average γ-pass rates (1%/1mm criteria) and standard deviations (SD) restricted to the CTV and the defined ring-like dose regions comparing base RS plans with the NIC + trichrome plans; the values were averaged over anatomical district defining the standard deviation (SD).

γ-pass rates (1%/1mm) [%] (SD)
	PCA	H&N	LAPC	SC
CTV	100.0 (0.1)	99.7 (0.9)	100.0 (0.0)	100.0 (0.0)
Iso-90%	100.0 (0.1)	99.9 (0.0)	100.0 (0.0)	100.0 (0.3)
Iso-40%	99.8 (0.1)	100.0 (0.1)	100.0 (0.0)	100.0 (0.0)
Iso-10%	97.1 (1.6)	100.0 (0.5)	99.5 (0.1)	99.9 (0.1)

When considering the CTV, the LET_d analysis showed deviations ≤ 1% comparing base RS and NIC + trichrome plans for all treatment sites, except prostate adenocarcinoma (median ΔLET_d > 1% (1.71 [1.81]%)). Considering the different treatment sites, the trend of a ΔLET_d increase/decrease was consistent for the iso90 and iso0.5 rings. For the iso40 and iso10, the median ΔLET_d showed an increase for the PCA cases, while the other anatomical districts exhibited a median ΔLET_d decrease. The most relevant variations in LET_d distribution were observed in iso0.5, where a statistically significant negative median deviation of up to 80% was reported for PCA and LAPC cases (p < 0.05). The corresponding box plots comparing ΔLET_d values between base RS and NIC + trichrome plans are illustrated in Fig. 4.

Fig. 4.

Percentage median LET_d deviations and interquartile ranges in ring-like dose regions, namely iso90, iso40, iso10 and iso0.5, comparing base RS and NIC+trichrome plans stratified by anatomical districts analysed. The boxplots show the median and 25th to 75th percentile, with the whiskers displaying 1.5 times inter-quartile range.

4. Discussion

The effect of nuclear interaction correction and trichrome modelling on carbon ion dose and LET_d distributions was validated and compared against reference FLUKA MC simulations. Investigations in a phantom geometry and analysing 30 clinical treatment plans for various anatomical districts revealed that enhancing PB modelling did not affect the clinical dose distributions, while LET_d prediction was significantly improved.

For the phantom geometries, an improved agreement of the PB algorithm with FLUKA reference simulations was observed for the LET_d calculations when applying NIC + trichrome instead of monochrome (base RS). One exception was found for calculations in the iso2 region with the 2%/1mm criteria in pure water and adipose tissue where NIC had no impact [11], [12]. Especially in the low dose region, (iso2 and iso10) comprising the lateral fall-off and the tail region, NIC + trichrome outperformed monochrome achieving γ-pass rates of 99% for almost all tissue slabs for the 5%/1mm criteria. Even though LET_d values in low-dose regions far away from the target might not be clinically relevant, actual high LET_d regions are more easily discerned. For lung and bone, the LET_d γ-pass rates in the target region were lower than for the rest of the materials with only a slight improvement by the introduction of NIC and trichrome. In these cases, the RayStation PB algorithm did not capture the sharpness of the distal LET_d peak (Fig. 1), which was unaffected by trichrome.

D_RBE calculation could be improved by employing NIC + trichrome for all tissue material slabs and dose regions except for the target region with lung material in the beam path. For the elemental composition of the lung, the NIC algorithm had a negligible effect because ${\rho }_S$ nearly equals ${\rho }_N$ [11], [12]. The slightly worse γ-pass rate for NIC + trichrome for the 2%/1mm criteria resulted from the fact that lower physical dose and higher RBE factor predicted in FLUKA averaged out in base RS. In the remaining cases (adipose, bone and titanium slabs), both NIC and trichrome played a significant role resulting in moderately improved D_RBE and LET_d passing rates in the target region for adipose and bone to dramatically increase γ-pass rates for titanium in all dose regions. The largest improvements in D_RBE were observed in the bone and titanium cases since the effects of both NIC and trichrome contributed to an increase of the dose inside the target and a decrease in the dose outside, which was not well predicted with base RS [11], [12], [18].

For the clinical cases, the introduction of NIC and trichrome in the PB dose calculation algorithm did not affect the clinical acceptability, as all DVH parameter deviations (D_98%, D_50% and D_2%) were considered negligible and were not statistically significant. This was further confirmed by the excellent γ-pass rate (1%/1mm) with a median value larger than 99% in the target region and surrounding dose regions.

Nuclear interaction correction alone accounted for the water-non-equivalence of the irradiated tissues [27]. The cross-section adjustment decreased the physical dose inside the target as the additional elastic scatter of the primary ions was accounted for and resulted in a minor median decrease (<1%) of D_50% in the target region for all anatomical districts. Adding solely trichrome stratified the incident particles into three halos, with the dominating particles being primary ions in the centre and light ion fragments in the lateral periphery [18]. Also, this change in particle type and LET_d resulted in a minor median increase (<1%) of D_50% in the target region. The observed deviations in the clinical plans confirm the previous non-clinical examinations in the frame of the algorithm development and phantom studies [28].

Notable changes between the LET_d NIC + trichrome and base RS plans were observed, particularly in regions far from the central beam axis (iso0.5). With little contribution from the primary ions, light fragments dominated the energy deposition, which drastically lowered the LET_d in the edge-of-field regions. With increasing ion energies e.g. in PCA and LAPC cases, the lateral fall-off of LET_d increased compared to the monochrome approximation [13], [14], [18]. Thus, reported differences grew more pronounced, compared to shallower targets in H&N and SC cases. NIC altered the physical dose, which caused LET_d changes, while NIC + trichrome scaled the halos according to the particle spectra assigned by trichrome. All studies investigating the association between LET_d and clinical outcomes in carbon ion radiotherapy will benefit from a more accurate calculation of the clinical LET_d distribution.

In conclusion, the results showed a general improvement in the accuracy of the predicted RBE-weighted dose and LET_d. Considering clinically relevant goals and constraints, no significant modifications of clinical protocols are expected with the introduction of NIC and trichrome.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Lars Glimelius, Daniel Simon Colomar, Walter Ikegami Andersson reports financial support was provided by RaySearch Laboratories AB. Barbara Knäusl is associate editor in phiRO. The remaining authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following are the Supplementary data to this article: