A rapid semi-automated trajectory planning method for non-coplanar interstitial brachytherapy in cervical cancer using a greedy algorithm

Abstract

Purpose

Precise spatial distribution of interstitial needles is critical for 3D-printing-assisted brachytherapy in cervical cancer. This study proposes a greedy algorithm-based needle trajectory planning (GANTP) framework to generate patient-specific needle configurations while ensuring needle collision avoidance and achieving clinically acceptable high-risk clinical target volume (HR-CTV) coverage in compliance with OAR dose constraints.

Methods and materials

The GANTP framework comprises three core steps: (1) Generation of candidate trajectories anchored within clinically viable entry zones; (2) Parameter-driven greedy selection of needle trajectories based on a geometric influence radius (δ) evaluated at three discrete values (12, 15, and 18 mm), where δ serves as a geometric surrogate for dose coverage, together with a geometric coverage-ratio threshold (γ = 98%) and a collision-free margin (d) relative to the tandem; and (3) Dosimetric evaluation and inverse planning with dwell-time optimization. The framework was evaluated using CT datasets from 20 cervical cancer patients. Performance metrics, including HR-CTV coverage, organs-at-risk (OAR) doses (D2cc), needle counts, and efficiency, were compared against manual planning.

Results

GANTP was able to generate clinically acceptable plans for all 20 cases. Based on a final-selection strategy that prioritized clinically acceptable HR-CTV coverage (≥ 90%) and the lowest needle count among the evaluated δ settings, δ = 15 mm was selected for 16 patients and δ = 18 mm for 4 patients as the final selected configurations. Compared to manual planning (HR-CTV coverage: 92.62 ± 1.51%), these Final Selected plans achieved clinically acceptable coverage of 91.96 ± 1.24% (P = 0.024), consistently exceeding the 90% clinical threshold. The OAR sparing was no significant difference to manual planning: D_2cc for the rectum (66.11 ± 3.99 Gy vs. 66.46 ± 4.00 Gy, P = 0.542), bladder (78.28 ± 5.16 Gy vs. 79.45 ± 4.47 Gy, P = 0.201), and sigmoid (63.30 ± 4.86 Gy vs. 62.33 ± 6.84 Gy, P = 0.916). The algorithm significantly reduced the average number of needles from 5.40 ± 0.94 to 4.25 ± 0.55 (P < 0.001). The most substantial improvement was observed in one case (Patient 2), where the needle count was reduced from 7 to 4 while maintaining a coverage of 91.7%. The total planning workflow time was substantially reduced from 2 to 3 h (manual) to 8.2 ± 1.4 min (GANTP), with algorithm execution taking less than 190 s across all δ settings.

Conclusion

GANTP establishes a semi-automated, patient-specific framework for generating collision-free, non-coplanar trajectories that meet clinical dosimetric goals with a reduced mean number of needles. Integrated with 3D-printed templates, this approach demonstrates significant potential for improving the precision and efficiency of interstitial brachytherapy. Future work will include phantom experiments for physical validation.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1186/s13014-026-02881-2.

Introduction

Cervical cancer remains the fourth most common malignancy among women globally, with an estimated incidence rate of 6.8% in 2022 [1]. The combination of external beam radiotherapy (EBRT) and high-dose-rate brachytherapy (HDR-BT) constitutes the cornerstone of curative treatment. HDR-BT offers precise tumor targeting through direct radioactive source placement adjacent to the target volume [2–4]. This procedure relies on applicators, both intracavitary and interstitial, to guide radiation sources to predefined positions.

In combined intracavitary-interstitial (IC/IS) BT, the spatial distribution and placement accuracy of interstitial needles determine the three-dimensional dose distribution, tumor control probability, and the risk of normal tissue complications [5, 6]. Traditional placement methods, including freehand techniques and standardized templates, persist in clinical practice despite inherent limitations in precision and reproducibility [7, 8]. Even with intraoperative imaging guidance, operator-dependent variability leads to sub-optimal trajectories, redundant needles, and compromised dosimetric outcomes [9]. While 3D-printed patient-specific templates have significantly improved anatomical conformity by providing customized guidance channels [10, 11], the critical step of needle trajectory planning remains largely manual. This lack of standardized computational frameworks for automated optimization leads to prolonged planning times and inconsistent plan quality compared with manual planning, particularly in complex anatomical scenarios [12].

Ideal needle trajectory configurations must fulfill three essential clinical criteria: (1) Spatial Coverage: Trajectories must be strategically positioned to ensure adequate HR-CTV dose coverage (≥ 90%) while maximizing the dose gradient at the interface between the HR-CTV and adjacent organs-at-risk (OARs); (2) Collision Avoidance: The plan must ensure mechanical safety by avoiding conflicts between needles and the tandem applicator, while maintaining predefined safety margins from critical anatomical structures (rectum, bladder, and sigmoid); (3) Needle Minimization: The total number of needles should be minimized to simplify the procedure and reduce tissue trauma, provided that dosimetric goals are fully met. However, current needle planning is largely constrained by parallel or template-based configurations, with limited systematic exploration of non-coplanar trajectories.

The combinatorial complexity of needle trajectory optimization, categorized as a nondeterministic polynomial (NP)-hard problem with an expansive solution space, demands efficient heuristic approaches. Greedy algorithms offer a promising solution by iteratively selecting locally optimal choices to approximate a clinically acceptable solution, balancing computational speed with dosimetric objectives [13, 14]. Their successful application in external beam radiotherapy [15, 16], including volumetric modulated arc therapy (VMAT) planning [17], suggests their potential for HDR-BT. By sequentially selecting trajectories that maximize incremental target coverage while ensuring physical and anatomical constraints, greedy algorithms could enable rapid convergence toward clinically viable configurations.

This study introduces a semi-automated, greedy algorithm-based needle trajectory planning (GANTP) framework designed to support 3D-printed template-guided BT for cervical cancer. We describe the development of this 3D non-coplanar planning tool and provide a comprehensive validation against traditional manual planning, focusing on dosimetric consistency, OAR sparing, and clinical workflow efficiency.

Methods and materials

Patients’ dataset

Clinical data of cervical cancer patients who underwent brachytherapy at our hospital were retrospectively collected. The inclusion criteria were as follows: (1) aged 18 years or older; (2) with a histologically confirmed malignant tumor of cervix; (3) having undergone brachytherapy guided by 3D-printed patient-specific templates; (4) availability of clear, artifact-free, 3-mm-thick CT images of the pelvis. Patients who did not meet the standard dose coverage requirements, such as those receiving palliative treatment, were excluded. All brachytherapy procedures followed the standardized workflow described in recent studies [18]. All manual plans were clinically approved before this study and were not modified for research comparison.

GANTP optimization method

The GANTP method consists of three key stages: parameter definition and initialization, candidate trajectory generation, screening, and evaluation, and dwell time optimization with dose calculation. The candidate trajectory set consists of a large pre-generated pool of sampled feasible insertion trajectories. Prior to optimization, dose constraints for critical normal tissues are predefined. The optimization process then determines whether the prescribed target coverage can be achieved under these constraints. Final evaluation of the dose distribution is performed to verify whether the selected trajectories meet all dosimetric objectives (Fig. 1). The proposed method is a heuristic greedy planning algorithm rather than a formal mathematical optimization. Given the NP-hard nature of the trajectory optimization problem, the greedy strategy provides a computationally efficient approximation. Candidate trajectories are iteratively evaluated and selected based on coverage and collision constraints.

Fig. 1.

Flowchart of the greedy algorithm-based needle trajectory planning (GANTP) framework. The process integrates three main phases: (1) initialization of geometric and dosimetric parameters, including the definition of coverage radius (δ), geometric coverage-ratio threshold (γ), and collision-free margin (d), based on the reconstructed HR-CTV volume; (2) candidate trajectory generation, screening, and evaluation, in which a candidate trajectory set N is generated once before the greedy loop and then iteratively evaluated to identify the trajectory that maximizes incremental target coverage while satisfying anatomical and collision-free constraints; and (3) decision and update, in which the selected trajectory is added to the selected trajectory set S, covered target points are updated, and the process terminates when the predefined geometric coverage-ratio threshold (γ) is achieved or no further feasible trajectories are available

Step 1: Parameters definition and initialization

The HR-CTV structure was delineated as a set of contour slices in the Varian Eclipse™ treatment planning system (TPS) and exported for further processing. These contours were reconstructed into a 3D volume and discretized via voxelization with a grid resolution of 2 mm, resulting in a uniformly distributed full HR-CTV point cloud P_all={p_i}, where each p_i ∈ P_all represents the center coordinate of voxel i within the discretized HR-CTV. For patients treated with a tandem applicator, the uterine fundus portion of the HR-CTV that was considered to be adequately covered by the tandem was excluded from the needle-driven geometric coverage calculation. The remaining HR-CTV point cloud, denoted as P, represented the target subvolume requiring additional contribution from interstitial needles and was used for greedy trajectory selection and geometric coverage calculation. For patients without a tandem applicator, P was identical to P_all. For each selected trajectory, the dwell positions x_j were defined from the distal endpoint of the trajectory, after excluding the blind tip region, and were discretized at 3-mm intervals along the trajectory until reaching the proximal HR-CTV boundary in the entry-to-tip direction. For a selected needle trajectory n_k, the geometric influence radius (δ) is defined as the maximum allowable Euclidean distance between an HR-CTV point p_i and any dwell position x_j on n_k. This radius δ serves as a geometric surrogate for the high-dose volume surrounding each needle. In this study, δ was tested separately at 12 mm, 15 mm, and 18 mm in independent GANTP runs to evaluate its impact on coverage and needle sparsity, reflecting clinically relevant dose fall-off distances observed in HDR-BT. A point p_i is considered “covered” by a selected trajectory n_k if there exists at least one dwell position x_j on n_k such that the Euclidean distance ∥ p_i - x_j ∥ ≤ δ. The coverage ratio covR(P) quantifies the proportion of the needle-driven HR-CTV point cloud covered by the selected trajectory configuration and is calculated as the ratio of the number of covered p_i points to the total number of p_i within P. A geometric coverage ratio covR(P) greater than 98% was set as the threshold γ for greedy trajectory selection according to Siauw’s study [19]. This threshold was used only for geometric trajectory selection and did not replace the final dosimetric evaluation of the complete HR-CTV. The key parameters involved in the initialization and optimization processes are explicitly defined in the following section and summarized in Table 1 to ensure clarity and reproducibility. In this study, the algorithm was executed separately for each predefined δ value, and the resulting needle configurations were compared to evaluate the impact of δ on coverage and trajectory selection.

Table 1.

Initialization parameters of the proposed framework

Parameter	Symbol	Description	Value
Coverage radius	δ	A point pi is considered covered if its distance to at least one dwell position xj on trajectory nk is less than or equal to δ.	12 / 15/ 18 mm
Collision-free margin	d	Minimum allowable distances for needle–needle and needle–tandem separation	2.4 mm (needle–needle), 3.7 mm (needle–tandem)
Coverage threshold	γ	Minimum required geometric coverage ratio of the needle-driven HR-CTV point cloud P	≥ 98%
Number of initially sampled trajectories	c	Total number of initially sampled candidate trajectories	5000
Selected trajectory set	S	Optimized subset of feasible trajectories selected by the greedy algorithm	Case-dependent solution set
Covered point set	P covered	Voxel points in the needle-driven HR-CTV point cloud P satisfying ∥pi - xj∥ ≤ δ	Derived set

Step 2: Candidate trajectory screening and evaluation

Step 2.1 Candidate trajectory set generation

3D reconstruction and candidate trajectory generation: The HR-CTV, OARs, and tandem applicator were reconstructed. The vaginal cavity was defined as the needle entry zone E, and its convex hull was denoted as ε. To determine the exit zone, the HR-CTV volume was projected onto the transverse plane (X-Y plane) perpendicular to the z-axis at the most superior slice of the target, as previously described in Ref. 19 (Fig. 2). This projection formed region C, and its convex hull, denoted as τ, served as the target area for needle tips. Candidate trajectories were generated once before the greedy selection loop by uniformly sampling entry points from ε and distal target/tip points from τ, with a predefined total number of candidates per patient, as described by Devroye [20]. A fixed random seed was applied to ensure reproducible candidate trajectory generation. These potential trajectories were first filtered to exclude those that: (1) fail to intersect the HR-CTV, or (2) penetrate critical OARs (rectum, bladder, and sigmoid) prior to HR-CTV entry. For the remaining feasible trajectories, a geometric clipping procedure was applied to enforce anatomical safety boundaries. Specifically, each trajectory was truncated according to its intersection with the HR-CTV surface. The distal endpoint was then extended beyond the target boundary by a predefined margin to account for the needle tip (blind end), ensuring adequate coverage of the distal target region. Only the segment from the entry point to this adjusted distal endpoint was retained. After this selection and clipping process, the remaining feasible trajectories constituted the candidate trajectory set N used for subsequent greedy selection.

Fig. 2.

(a) Comparison of HR-CTV prescription dose coverage between manually designed needle trajectories and GANTP-optimized trajectories at δ = 12 mm, 15 mm, and 18 mm across 20 patients. Cases marked with ※ indicate unresolved configurations (no valid solution) at δ = 12 mm. (b) Comparison of needle counts between manual planning (dark blue bars) and GANTP-optimized configurations at δ = 12 mm, 15 mm, and 18 mm. ▽ symbols denote the final selected plans for each patient, chosen as the configuration with clinically acceptable HR-CTV prescription dose coverage (≥ 90%) and the lowest needle count among the evaluated δ settings. Statistically significant reductions in needle counts (P < 0.001) were achieved in the Final Selected plans compared to manual planning

Step 2.2 Candidate trajectory evaluation

The pre-generated candidate trajectory set N is iteratively evaluated to select an optimized trajectory subset S that satisfies HR-CTV coverage requirements, avoids mutual collisions, and minimizes the total number of needles. (1) Iterative selection loop: At the beginning of each greedy iteration, the maximum incremental coverage m_max is reset to 0. The greedy algorithm then iteratively evaluates all remaining candidate trajectories and selects the trajectory that provides the maximum incremental coverage in the current iteration. (2) Candidate trajectory evaluation: (a) Candidate trajectories that have already been added to the selected trajectory set S in previous iterations are excluded from further evaluation. (b) Uncovered point calculation: For every uncovered point p_i, the Euclidean distance to the current candidate trajectory is calculated in 3D space and used to assess whether p_i is covered by that trajectory. (c) Mechanical conflict check: The minimum distance between the current trajectory and all previously selected trajectories is calculated. Specifically, this distance is defined as the shortest Euclidean distance between two 3D line segments, computed using standard vector algebra. If this distance is less than the predefined collision threshold d (2.4 mm), the trajectory is discarded. (d) Tandem conflict check: A similar distance check is performed between the current trajectory and the tandem applicator (threshold: 3.7 mm). (e) Selected trajectory update: The trajectory that covers the maximum number of newly covered points (m_max) without conflicts is selected. In the rare case that multiple candidates provide the same incremental coverage, the first trajectory in the candidate list that meets this criterion is chosen.

Step 2.3: Final trajectory selection and variable Update

(1) Covered-points update: HR-CTV points satisfying ∥p_i - x_j∥ ≤ δ for the newly selected trajectory are added to P_covered. (2) Conflict-record update: collision relationships involving the newly selected trajectory are recorded. (3) The process terminates when the geometric coverage ratio covR(P) reaches the predefined threshold γ = 98%. If γ is not satisfied after all feasible candidate trajectories have been evaluated, or if the resulting needle count exceeds clinically acceptable limits (e.g., > 10 needles), the algorithm reports an infeasible solution and supports re-parameterization followed by re-execution to obtain a feasible solution. The selection of trajectories follows a greedy heuristic: trajectories are chosen iteratively based on maximum incremental coverage.

Step 3: Dwell time optimization and dose calculation

To translate geometric coverage into clinically deliverable dosimetry, the selected trajectories were converted into clinically deliverable needle trajectories and imported into the Varian Eclipse (v13.5) via DICOM. Dwell positions were configured at 3 mm intervals. Although a reduced needle-driven HR-CTV point cloud P was used for greedy trajectory selection in tandem-containing cases, the complete original HR-CTV structure was retained for final visualization, dwell-time optimization, dose calculation, and dosimetric evaluation. The Dose Shaper tool and inverse optimization were employed to maximize prescription coverage of the complete HR-CTV while enforcing strict OAR limits (D2cc for bladder, rectum, and sigmoid) according to EMBRACE II [21]. This step ensures that the final plan satisfies clinically accepted dose limits while maintaining adequate target coverage.

Method evaluation

A total of 5,000 initially sampled trajectories were generated in MATLAB for each patient before geometric filtering. Collision detection was performed using an alphaShape-based geometric modeling approach to avoid primary OARs (rectum, bladder, and sigmoid). After filtering based on HR-CTV intersection and OAR avoidance criteria, an average of 2,078 ± 592 feasible trajectories remained per patient and were used for subsequent greedy selection. Three coverage radii (δ = 12, 15, 18 mm) were evaluated. The algorithm ran on a PC (Intel Core i7-4770 S, 3.10 GHz). Planning time was recorded as the “total workflow time,” encompassing algorithm execution, data I/O, and TPS dose optimization. The reported manual planning time (2–3 h) refers only to the needle trajectory design process performed by physicists and does not include 3D-printed template fabrication time. Robustness was evaluated using repeated simulations with different random seeds.

Dosimetric evaluation and radiobiological modeling

Dosimetric quality was evaluated using cumulative dose-volume histograms (DVH). To account for the biological effectiveness of different fractionation schemes, all physical doses were converted into the equivalent dose in 2 Gy fractions (EQD₂) using the linear-quadratic model:

where D is the total physical dose and d is the dose per fraction. In accordance with the GEC-ESTRO and EMBRACE I/II protocols [3, 9, 21], an ratio of 10 Gy was applied for the HR-CTV, while an ratio of 3 Gy was used for the organs at risk (OARs), including the rectum, bladder, and sigmoid. The reported EQD₂ values represent the cumulative dose from both external beam radiotherapy (EBRT) and the high-dose-rate brachytherapy (HDR-BT) boost. For OAR sparing, the D_2cc (minimum dose to the most irradiated 2 cm³ volume) was recorded.

Results

Patients’ demographics and brachytherapy characteristics

Clinical data from 20 cervical cancer patients were retrospectively analyzed (Table 2). The cohort included 18 patients treated with combined intracavitary-interstitial (IC/IS) brachytherapy (tandem plus needles) and 2 patients treated with interstitial-only techniques. The HR-CTV volumes ranged from 35.1 to 129.8 cm³ (mean: 80.6 cm³), with equivalent spherical diameters (ESD) averaging 5.3 cm (range: 4.1–6.3 cm). The vaginal introitus served as the needle entry zone to minimize vulvar trauma, with a mean entry area of 8.06 ± 3.2 cm². Manual trajectory planning achieved a mean HR-CTV coverage of 92.62 ± 1.51%, requiring 5.40 ± 0.94 needles per patient. This manual process, involving iterative adjustments for collision avoidance and dosimetric compliance, typically required 2–3 h of professional time per case.

Table 2.

Patients’ demographics and brachytherapy characteristics

	N(%)
FIGO 2018 stage
IB	3(15)
Ⅱ	4(20)
Ⅲ	10(50)
ⅣA	3(15)
Number of brachytherapy fractions
4	12(60)
5	8(40)
Average (range) HR-CTV* volume (cm3)	80.6(35.1-129.8)
Average (range) ESD† of HR-CTV (cm)	5.3(4.1–6.3)
Tandem applicator
NO	4(20)
YES	16(80)
Tandem angle degree
15°	7(44)
30°	4(25)
45°	5(31)
Average (range) number of needles by manual	5.40 (4–7)

*High-risk clinical target volume. ^†Equivalent spherical diameters

Development of GANTP algorithm

The GANTP algorithm was successfully implemented as a semi-automated planning tool. Key enhancements included optimized data structures for rapid collision detection and an efficient greedy loop. To evaluate numerical stability, 300 experimental trials (20 patients × 3 δ settings × 5 runs) were conducted. Although the core greedy selection process is deterministic, additional experiments with different random seeds produced similar needle configurations, demonstrating the robustness and stability of the proposed method.

Comparison of GANTP with manual planning

HR-CTV coverage and OAR doses

The GANTP-optimized plans showed δ-dependent performance (Fig. 2a). At δ = 12 mm, the mean HR-CTV coverage was 94.20 ± 1.07% (P < 0.001 vs. manual); however, three cases failed to satisfy the geometric coverage-ratio threshold γ = 98% due to restrictive geometric constraints. At δ = 15 mm, the algorithm achieved a mean HR-CTV coverage of 92.34 ± 1.48%, showing no significant difference compared to manual planning (P = 0.589). Conversely, δ = 18 mm resulted in insufficient coverage (88.90 ± 2.15%, P < 0.001) due to overly sparse needle distributions.

Following a hierarchical strategy that prioritized the largest δ associated with lower needle density while maintaining an HR-CTV coverage of at least 90%, the Final Selected plans (comprising 16 cases at δ = 15 mm and 4 cases at δ = 18 mm) achieved an average HR-CTV coverage of 91.96 ± 1.24%. Although this was statistically lower than manual planning 92.62 ± 1.51%, (P = 0.024), it consistently exceeded the clinical requirement of 90%. Individualized results and the specific configuration selected for each of the 20 patients are detailed in Supplementary Table S1. As shown in Table 3, the OAR sparing of the Final Selected plans was no significant difference to manual planning. The D_2cc values for the rectum, bladder, and sigmoid were 66.11 ± 3.99 Gy, 78.28 ± 5.16 Gy, and 63.30 ± 4.86 Gy, respectively, compared to 66.46 ± 4.00 Gy, 79.45 ± 4.47 Gy, and 62.33 ± 6.84 Gy in manual plans (all P > 0.05). 95% confidence intervals were calculated using a paired t-distribution. The detailed D_2cc values for each OAR across all evaluated δ configurations for each patient are provided in Supplementary Table S2. Dose distributions and DVH comparisons for Patients 2 and 6 are provided in the Supplementary Materials (Supplementary Figures S1–2).

Table 3.

Dosimetric and efficiency comparison between manual planning and GANTP optimization at different coverage radius (δ)

Parameters	Manual (n = 20)	GANTP (δ = 12)†	P a	GANTP (δ = 15)	P b	GANTP (δ = 18)	P c	Final selected (n = 20)*	P d	Mean difference	95% CI
HR-CTV coverage (%)	92.62 ± 1.51	94.20 ± 1.07	< 0.001	92.34 ± 1.48	0.589	88.90 ± 2.15	< 0.001	91.96 ± 1.24	0.024	-0.66	(-1.21, -0.11)
Number of needles	5.40 ± 0.94	6.06 ± 1.14	0.016	4.55 ± 0.83	0.004	3.35 ± 0.75	< 0.001	4.25 ± 0.55	< 0.001	-1.15	(-1.53, -0.77)
Organ D2cc (Gy)
Rectum	66.46 ± 4.00	65.57 ± 5.87	0.543	65.48 ± 3.72	0.504	66.54 ± 5.13	0.947	66.11 ± 3.99	0.542	-0.35	(-3.32, 2.63)
Bladder	79.45 ± 4.47	75.02 ± 8.04	0.103	76.77 ± 6.24	0.124	78.73 ± 3.58	0.553	78.28 ± 5.16	0.201	-1.17	(-4.54, 2.20)
Sigmoid	62.33 ± 6.84	61.18 ± 3.48	0.830	62.47 ± 4.07	0.949	64.15 ± 3.95	0.304	63.30 ± 4.86	0.916	+ 0.97	(-3.44, 5.38)

Note: * The Final Selected column represents the selected clinical plans, where δ = 15 mm was used for 16 patients and δ = 18 mm for 4 patients to optimize target coverage and needle count. Data are presented as mean ± SD (standard deviation). Significant P-values (P < 0.05) are highlighted in bold.

Abbreviations: GANTP, Greedy algorithm-based needle trajectory planning; HR-CTV, high-risk clinical target volume; D2cc, minimum dose to the most irradiated 2 cm³ volume. All doses are reported as equivalent doses in 2 Gy fractions EQD₂ calculated using the linear-quadratic model, representing the cumulative dose from external beam radiotherapy and brachytherapy. ɑ/β = 3 Gy for OARs. 

^† For the δ = 12 group, three cases were excluded due to non-viable planning trajectories; statistical analysis for this column was performed using 17 matched pairs. P_a GANTP (δ = 12) vs. Manual; P_b GANTP (δ = 15) vs. Manual; P_c GANTP (δ = 18) vs. Manual. P_d Final Selected vs. Manual. All P-values were calculated using the paired t-test. Mean differences and 95% confidence intervals (CI) were calculated based on paired differences between the Final Selected GANTP plans and manual planning (Final Selected − Manual, n = 20) using a two-sided t-distribution (df = 19)

Needles counts

The candidate trajectory generation phase produced an average of 2,078 ± 592 feasible trajectories per patient after filtering the initially sampled trajectories (N = 5000) based on HR-CTV intersection and OAR avoidance criteria. GANTP significantly optimized needle utilization (Fig. 2b). In the Final Selected plans, the mean needle count was reduced to 4.25 ± 0.55, representing a significant decrease compared to 5.40 ± 0.94 in manual planning (with a mean reduction of 1.15 needles, P < 0.001). Specifically, 16 out of 20 patients required fewer needles, while 4 patients maintained equivalent counts. The most substantial improvement was observed in Patient 2, where the needle count was reduced from 7 in manual planning to 4 in the Final Selected plan (a reduction of 3 needles), while maintaining an HR-CTV coverage of 91.7%. The 3D spatial distributions for all 20 cases confirm the algorithm’s ability to maintain dosimetric integrity while significantly reducing procedural complexity (Fig. 3).

Fig. 3.

Three-dimensional spatial distribution of needle trajectories selected for 20 patients based on the GANTP framework. For each patient, the final configuration was selected as the plan achieving clinically acceptable HR-CTV prescription dose coverage (≥ 90%) with the lowest needle count among the evaluated δ settings. Each visualization illustrates the algorithm’s ability to balance target volume irradiation with OAR avoidance

Workflow efficiency

The GANTP algorithm demonstrated high computational efficiency, with algorithm execution taking less than 190 s across δ settings. The total workflow time—encompassing algorithm execution, data I/O, and final dwell-time optimization in the TPS—averaged approximately 8.2 ± 1.4 min. This represents a reduction compared to the 2–3 h required for manual planning, which involves an iterative workflow including needle trajectory design, intersection checking, trajectory adjustment, dwell-time optimization, and repeated dose calculation and evaluation until clinically acceptable plans are achieved.

Discussion

Automated needle trajectory planning in cervical cancer brachytherapy remains limited due to the reliance on fixed template-based systems and constrained solution spaces [22–27]. Recent attempts using 3D-printed templates have improved anatomical adaptability but still face challenges in computational efficiency and planning robustness [28–33]. Our GANTP framework addresses these limitations by providing a rapid, patient-specific solution for non-coplanar trajectory optimization. By dynamically balancing anatomical adaptability with dosimetric integrity, GANTP harmonizes the need for high-quality target coverage with the clinical imperative of minimizing invasive trauma through reduced needle utilization. Compared to random trajectory selection, the greedy approach ensures systematic coverage improvement through incremental optimization.

A significant finding of this study is that GANTP achieved comparable dosimetric outcomes to manual planning while significantly reducing procedural complexity. As evidenced by Table 3, the Final Selected GANTP plans showed no significant difference in OAR sparing (all P > 0.05), while HR-CTV coverage was slightly but significantly lower than manual planning (P = 0.024). These results indicate that OAR sparing with the proposed method is similar to manual planning, while HR-CTV coverage remains clinically acceptable despite being marginally lower.

The algorithm reduced the required number of needles in 80% of cases (16/20), with a mean reduction of 1.15 needles (P < 0.001). The most substantial improvement was observed in Patient 2, where the needle count was reduced from 7 to 4 while maintaining a coverage of 91.7%. This reduction may be attributed to differences in planning strategy, where manual planning is more experience-driven and tends to adopt conservative and sometimes redundant needle placement to ensure robust target coverage, whereas GANTP selects trajectories based on incremental coverage efficiency, thereby reducing unnecessary overlap. In the clinical setting of HDR brachytherapy, reducing the number of interstitial insertions is directly linked to a lower risk of hemorrhage, infection, and procedural trauma. These results demonstrate that GANTP can effectively navigate the complex trade-off between target coverage and OAR protection, maintaining the therapeutic ratio while simplifying the surgical procedure.

However, it should be acknowledged that to maintain high computational efficiency, this study evaluated only three discrete δ settings (12, 15, and 18 mm). While these intervals were sufficient to generate clinically acceptable plans for all cases in our cohort, they represent a heuristic approximation that balances optimization granularity and execution speed. There may exist even more individualized δ values that could further fine-tune the needle-to-target relationship for specific patient anatomies. Future developments of GANTP will explore more granular or adaptive searching strategies for δ to further enhance the precision of individualized planning.

One of the primary concerns regarding idealized trajectory models is needle deflection and its impact on clinical reproducibility. While our model assumes straight needle trajectories, the integration of rigid 3D-printed patient-specific templates serves as a critical bridge between computational optimization and clinical execution. These customized templates provide robust mechanical guidance that significantly minimizes trajectory deviation compared to freehand techniques. Furthermore, the high efficiency of GANTP—with a total workflow time of approximately 8.2 ± 1.4 min—directly addresses the challenge of intraoperative anatomical shifts. Manual planning requires 2–3 h, a window during which physiological changes, such as bladder filling or rectal peristalsis, can render the initial plan sub-optimal. The reduction in planning time enabled by GANTP (8.2 ± 1.4 min vs. 2–3 h) enables a near-real-time adaptive workflow, improving synchronization with patient anatomy and potentially enhancing procedural precision and safety.

Despite its advantages, this study has several limitations. First, the greedy strategy prioritizes locally optimal decisions at each iteration, which may result in slight variations in needle count compared with global optimization methods. In our cohort, this difference remained limited (mean reduction of 1.15 needles compared with manual planning), indicating that its impact on clinical feasibility is modest while maintaining high computational efficiency.

Second, the use of discrete δ values (12, 15, and 18 mm) introduces a coarse sampling of the solution space. As demonstrated in the results, this discretization influenced both coverage and needle selection patterns, with HR-CTV coverage varying from 88.90% to 94.20% across δ settings. However, the final selection strategy ensured that all clinically adopted plans exceeded the 90% coverage threshold, indicating that the impact of this discretization on clinical acceptability was minimal.

Third, as a heuristic method, it relies on surrogate geometric coverage criteria rather than an explicit global objective function. It nevertheless achieves clinically satisfactory coverage with high reproducibility and stable performance. This study should be interpreted as an initial feasibility study, given its retrospective single-center design and limited sample size.

Finally, future iterations will incorporate additional anatomical structures, such as major vessels and nerves, to further enhance surgical safety. We are also exploring the use of deep learning models to adaptively and continuously tune δ and other geometric parameters based on individual patient anatomy. This study focuses on geometric planning and dosimetric evaluation, while insertion accuracy was not directly assessed. Future work will include phantom and clinical validation.

Conclusion

The GANTP framework establishes a robust, semi-automated pipeline for generating patient-specific, non-coplanar needle trajectories in cervical cancer brachytherapy. By bridging geometric spatial optimization with formal dosimetric validation, this approach consistently achieves clinically acceptable target coverage while reducing the mean number of needles compared with traditional manual planning. When integrated with 3D-printing-guided templates, GANTP streamlines the planning workflow from hours to minutes (averaging approximately 8 min) and minimizes operator-dependent variability, thereby enhancing procedural standardization. The successful balance between dosimetric integrity and reduced procedural complexity, evidenced by the significant reduction in needle count without compromising clinical thresholds, provides a scalable foundation for the transition toward real-time, adaptive brachytherapy planning. Future work will focus on physical validation using phantom experiments and prospective clinical studies to evaluate insertion accuracy and generalizability.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

J.S. and Z.X. designed the research and developed the GANTP algorithm. S.S. collected the clinical data and performed the dosimetric comparisons. X.W., C.X. , H.L. and H.Q. provided clinical guidance and revised the manuscript. J.S. supervised the study and secured funding. J.S. and S.S. wrote the main manuscript text and prepared Figs. 1, 2 and 3. All authors reviewed and approved the final manuscript.

Funding

The work was supported by the National Natural Science Foundation of China (Grant No. 12405394), Clinical research and development projects of Zhongnan Hospital (Grant No. LCYFMS2024004), Hubei Provincial Natural Science Foundation (Grant No. 2023AFB204), Hubei Provincial Natural Science Foundation Innovation Development Joint Fund (Grant No. 2025AFD772).

Data availability

The datasets generated and analyzed during the current study are not publicly available due to patient privacy and institutional data protection policies. However, the data are available from the corresponding author on reasonable request.

Code availability

The protected MATLAB implementation of the GANTP-basic framework described in this study is provided as Supplementary Software S1. The package includes a public wrapper script, Step 1 data-preparation module, protected Step 2 trajectory-generation and greedy-selection engine, Step 3 output and visualization module, de-identified example TXT contour files, and a README file describing the input format, parameter settings, execution workflow, and expected outputs. Due to patient privacy and institutional regulations, the original clinical CT images and RT Structure DICOM files are not publicly available. The provided example data are de-identified geometric contour files intended to facilitate reproduction of the algorithmic workflow.

Declarations

Ethics approval

This study was approved by the Ethics Committee of Zhongnan Hospital of Wuhan university. All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards.

Consent to participate

Informed consent was obtained from all individual participants included in the study.

Competing interests

The authors declare no competing interests.