Introduction
Rotational setup errors remain a persistent challenge in radiotherapy centres without access to six-degree-of-freedom (6DoF) couches. Even small angular deviations can compromise target coverage and organ-at-risk sparing. A 1° rotation at 10 cm from the isocentre, for example, results in a positional shift of ∼1.75 mm, which can be clinically relevant in stereotactic and head-and-neck treatments where steep gradients and tight margins are common.Reference Tsujii, Ueda and Isono1–Reference Guckenberger, Meyer and Wilbert3 While 6DoF couches provide direct correction, their high cost limits adoption in many clinics, leaving most departments dependent on three-degree-of-freedom (3DoF) couches that correct only translations.Reference Vanherk4
Modern radiotherapy techniques such as intensity-modulated radiotherapy (IMRT), volumetric-modulated arc therapy (VMAT), stereotactic radiotherapy and stereotactic body radiotherapy rely on highly conformal dose distributions with steep dose gradients. As treatment precision increases, even minor rotational setup deviations may influence target coverage and normal tissue sparing. Although image-guided radiotherapy has improved setup verification, many treatment centres continue to operate without routine access to 6DoF correction systems because of financial and infrastructural limitations. Consequently, practical mitigation approaches for rotational errors remain clinically relevant, particularly in resource-limited radiotherapy environments. In current clinical workflows, uncorrected rotational errors may necessitate time-consuming manual patient repositioning, leading to increased treatment room occupancy and potential patient discomfort. By providing a translational approximation for small rotational deviations, such approaches may help reduce workflow interruptions while maintaining acceptable geometric accuracy in centres without immediate access to advanced rotational correction hardware.
Despite the availability of advanced couch correction systems, practical implementation remains challenging in many high-volume radiotherapy centres because of cost, workflow complexity and infrastructure requirements. As a result, translational compensation strategies for small rotational deviations may offer a clinically useful intermediate solution in situations where full rotational correction is unavailable. The present technical report therefore evaluates a simplified geometric approximation in which rotational setup deviations are represented as equivalent translational displacements, with the aim of assessing their potential dosimetric impact across representative treatment geometries.
Technical Approach
To address this gap, the present technical report evaluated a practical approximation in which small rotational setup errors were represented as equivalent linear displacements using the vector cross-product formulation. For a given point, the displacement (Δ) was estimated as:
$\Delta = {\it{\theta} \times r}$
where θ is the rotation vector (in radians), and r is the positional vector measured from the isocentre. The negative of this displacement was considered as the corrective translational shift. This first-order approximation is exact only at the selected reference point (e.g., isocentre or target centre of mass), but may reduce residual error for small angular deviations (typically ≤3–5°).Reference Fu, Yang and Yue5
Representative treatment scenarios based on common anatomical sites (head-and-neck, breast, lung, pelvis and thorax) were modelled using standard radiotherapy planning geometry. Five representative anatomical site scenarios were evaluated (one per treatment region). Clinical platform context included an Elekta Infinity linear accelerator with Monaco TPS (version 6.1.4.0), which employs a Monte Carlo dose calculation framework. Representative planning geometry was based on modern conformal inverse-planned treatment workflows (IMRT/VMAT-type scenarios). Simulated rotational perturbations were applied, and comparative dosimetric values with and without translation-based correction were assessed using standard DVH endpoints: Dmean, D95 and V95. Rotational perturbations conceptually represented pitch, roll and yaw deviations.
Statistical Analysis
As this technical report was intended as a feasibility demonstration using representative simulated treatment scenarios, results were evaluated descriptively as comparative percentage changes between corrected and uncorrected conditions. Inferential statistical testing was not performed because the study did not involve repeated patient-based datasets or population-level analysis.
Results
Results are summarised in Table 1 and illustrated in Figure 1, which compares D95 values with and without translation-based correction across representative treatment sites. Across all representative treatment sites, translation-based correction consistently improved D95. The largest improvement was observed in head-and-neck geometry (ΔD95 ≈ 2.0%). Pelvis and thorax scenarios showed intermediate gains (1.0–1.5%), while breast and lung cases demonstrated smaller but measurable improvements (0.7–0.8%).
Comparative dosimetric parameters with and without translation-based correction across representative treatment sites
Table 1. Long description
The table presents a comparison of dosimetric parameters with and without translation-based correction across various treatment sites. It includes columns for mean dose (Dmean) and dose received by 95% of the volume (D95) both without correction (No Corr) and with correction (With Corr), along with the differences between these values (Delta Dmean, Delta D95). The sites compared are head and neck, breast, lungs, pelvis, and thorax. Notable improvements in D95 are observed with correction, particularly in head and neck geometry with a 2.04 percentage point increase. Other sites show varying degrees of improvement, with pelvis and thorax showing intermediate gains, and breast and lung cases demonstrating smaller improvements.
Comparison of D95 with and without translation-based correction across representative treatment sites.
Figure 1. Long description
The bar graph compares D95 percentage values with and without translation-based correction for different body parts. The x-axis lists body parts: Head and Neck, Breast, Lungs, Pelvis, and Thorax. The y-axis measures D95 percentage, ranging from 0 to 70. There are two sets of bars for each body part: one in gray representing ‘No Correction’ and one in black representing ‘With Correction’. The bars are grouped vertically for each body part. The graph shows that translation-based correction generally increases the D95 percentage across all body parts. The increase is most noticeable in the Head and Neck region, while the Thorax region shows the least difference. All values are approximated.
Dmean increased modestly (0.2–0.4%), suggesting improved dose uniformity, whereas V95 remained essentially unchanged (<0.03% variation). These findings indicate that translation-based compensation may improve target coverage while preserving volumetric conformity under small rotational setup deviations.
Discussion
The present technical evaluation suggests that minor rotational setup errors may be partially compensated on 3DoF couches through equivalent translational correction. Although the approximation is not exact, simulations demonstrated consistent dosimetric improvements across multiple anatomical sites. The greatest benefit was observed in head-and-neck cases, with D95 improving by nearly 2%, reflecting the high sensitivity of these treatments to geometric deviations due to complex anatomy and steep dose gradients.Reference Guckenberger, Meyer and Wilbert3,Reference Fu, Yang and Yue5 Pelvic and thoracic plans showed intermediate gains of 1.0–1.5%, while breast and lung plans demonstrated smaller improvements of 0.7–0.8%, consistent with their larger target volumes and more generous margins.
Even modest improvements in D95 may be clinically meaningful in high-precision radiotherapy, where small residual errors often require patient repositioning.Reference Stroom and Heijmen2,Reference Guckenberger, Meyer and Wilbert3 By reducing the dosimetric consequences of minor rotations, this approach offers a low-cost option to enhance treatment quality and reduce workflow disruptions in centres without access to 6DoF couches.
Alternative mitigation approaches include improved immobilisation, margin expansion and dedicated 6DoF couch correction systems.
Several limitations should be noted. The method is approximate and less accurate for rotations exceeding 5°. Validation was limited to simulations, and residual errors persist at points distant from the isocentre. Future studies should include phantom-based evaluation, integration into image-guided radiotherapy workflows and automated correction tools for clinical implementation.
Limitations
The translation-based correction used in this study represents a first-order geometric approximation in which small rotational setup errors are converted into equivalent linear displacements at a chosen reference point, such as the isocentre or target centre of mass. This approximation is most valid for small rotations (typically ≤3–5°), where higher-order nonlinear effects remain negligible. The correction is exact only at the selected reference point; residual errors increase with distance from this point and with increasing rotation magnitude. Consequently, this method does not replace 6DoF couch corrections, particularly for larger rotations or highly off-axis structures. Instead, it should be viewed as a pragmatic mitigation strategy that can reduce the dosimetric impact of minor rotational errors in centres limited to 3DoF couch corrections.
Conclusion
In summary, translation-based correction is not a substitute for 6DoF couch technology, but may provide a practical, low-cost mitigation strategy for centres limited to 3DoF correction capability.
Data availability and statement
All data generated or analyzed during this study are available from the corresponding author upon reasonable request.
Authors’ Contributions
Subhrendu Ghosh: Conceptualisation, methodology, data analysis, manuscript preparation and final approval of the version to be published.
Financial support
This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.
Competing interests
The author declares no conflicts of interest related to this work.
Ethical approval
Not applicable (simulation-based technical study).
Consent to participate
Not applicable.
Consent for publication
Not applicable.
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