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Distance-adaptive geometric margins for residual rotational uncertainty in single-isocenter multitarget stereotactic radiosurgery.

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The authors' code

Python · 92 lines · 2.8 KB · no license

  1. # -*- coding: utf-8 -*-
  2. import numpy as np
  3. import matplotlib.pyplot as plt
  4. from mpl_toolkits.axes_grid1.inset_locator import inset_axes
  6. def generate_simt_data(n_samples=1000000, sigma_deg=0.5):
  7. np.random.seed(42)
  9. phi = np.random.uniform(0, 2*np.pi, n_samples)
  10. costheta = np.random.uniform(-1, 1, n_samples)
  11. u = np.random.uniform(0, 1, n_samples)
  12. theta = np.arccos(costheta)
  13. r = 200 * (u ** (1/3))
  15. x = r * np.sin(theta) * np.cos(phi)
  16. y = r * np.sin(theta) * np.sin(phi)
  17. z = r * np.cos(theta)
  18. points = np.vstack((x, y, z)).T
  19. distances = np.linalg.norm(points, axis=1)
  22. sigma_rad = np.deg2rad(sigma_deg)
  23. angles = np.random.normal(0, sigma_rad, (n_samples, 3))
  26. cross_prod = np.cross(angles, points)
  27. tre_approx = np.linalg.norm(cross_prod, axis=1)
  30. ca = np.cos(angles[:,0]); sa = np.sin(angles[:,0])
  31. cb = np.cos(angles[:,1]); sb = np.sin(angles[:,1])
  32. cg = np.cos(angles[:,2]); sg = np.sin(angles[:,2])
  34. R00 = cg*cb; R01 = cg*sb*sa - sg*ca; R02 = cg*sb*ca + sg*sa
  35. R10 = sg*cb; R11 = sg*sb*sa + cg*ca; R12 = sg*sb*ca - cg*sa
  36. R20 = -sb; R21 = cb*sa; R22 = cb*ca
  38. px = R00*x + R01*y + R02*z
  39. py = R10*x + R11*y + R12*z
  40. pz = R20*x + R21*y + R22*z
  41. points_prime = np.vstack((px, py, pz)).T
  42. tre_exact = np.linalg.norm(points_prime - points, axis=1)
  44. residuals = np.abs(tre_exact - tre_approx) * 1000
  45. return tre_approx, tre_exact, residuals, distances
  49. approx_05, exact_05, _, dist_05 = generate_simt_data(n_samples=1000000, sigma_deg=0.5)
  52. _, _, res_02, dist_02 = generate_simt_data(n_samples=200000, sigma_deg=0.2)
  53. _, _, res_05, dist_05_sub = generate_simt_data(n_samples=200000, sigma_deg=0.5)
  54. _, _, res_10, dist_10 = generate_simt_data(n_samples=200000, sigma_deg=1.0)
  57. import numpy as np
  58. import matplotlib.pyplot as plt
  61. plt.figure(figsize=(6, 5))
  64. idx = np.random.choice(len(dist_05), 50000, replace=False)
  65. dist_plot = dist_05[idx]
  66. exact_plot = exact_05[idx]
  69. plt.scatter(dist_plot, exact_plot, s=1, c='blue', alpha=0.3, label='Exact Calculation')
  72. slopes = exact_plot / (dist_plot + 1e-6)
  73. max_slope_tight = np.percentile(slopes, 99.99)
  75. x_line = np.linspace(0, 205, 100)
  76. y_line = x_line * max_slope_tight
  77. plt.plot(x_line, y_line, 'r--', linewidth=2.5, label='Linear Model (Upper Bound)')
  80. #plt.title('Figure 1: Error Propagation\n(Standard Scenario: $\sigma=0.5^\circ$)', fontsize=12, fontweight='bold')
  81. plt.xlabel('Distance to Isocenter (mm)', fontsize=11)
  82. plt.ylabel('Target Registration Error (mm)', fontsize=11)
  83. plt.legend(loc='upper left', fontsize=10)
  84. plt.grid(True, linestyle=':', alpha=0.6)
  86. plt.xlim(0, 205)
  88. plt.ylim(0, np.max(y_line) * 1.05)
  90. plt.tight_layout()
  91. plt.savefig('Fig1_ErrorPropagation_Final.png', dpi=300)
  92. plt.show()

Fig_2A.py at commit 947ec2f, no license · at the source

Overview

Authors: Jiaxin Deng1,2, Zun Piao1, Xinyu Song3, Danyang Li1, Jiang Hu1, Shouliang Ding1, Yanfei Liu4, Li Chen1, Guanqun Zhou1, Ying Sun1, Xiaoyan Huang1, Guangyu Wang1
  1. State Key Laboratory of Oncology in South China, Guangdong Key Laboratory of Nasopharyngeal Carcinoma Diagnosis and Therapy, Guangdong Provincial Clinical Research Center for Cancer, Sun Yat-sen University Cancer Center, Guangzhou 510060, PR China
  2. School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, PR China
  3. Department of Radiation Oncology, Cancer Center, The First Affiliated Hospital, Sun Yat-sen University, Guangzhou 510080, PR China
  4. Radiotherapy Laboratory, Shenzhen United Imaging Research Institute of Innovative Medical Equipment, Shenzhen 518048, PR China
Institutions: Sun Yat-sen University (China); Sun Yat-sen University Cancer Center (China); State Key Laboratory of Oncology in South China; Southern Medical University (China); The First Affiliated Hospital, Sun Yat-sen University (China)
Journal: Physics and imaging in radiation oncology, volume 39, article 101012
Dates: received 10 February 2026; accepted 31 May 2026; published online 1 June 2026
Type: Research article · Language: English
License: CC BY-NC-ND
Identifiers: DOI 10.1016/j.phro.2026.101012 · PMID 42293113 · PMCID PMC13264242 · OpenAlex W7162995708
Open access: gold, a free copy (OpenAlex)
Status: code verified
Keywords: Single-isocenter multitarget, Stereotactic radiosurgery, Error propagation, Distance-adaptive geometric margin
Topic: Advanced Radiotherapy Techniques (Radiation, Physics and Astronomy), according to OpenAlex
Funding: National Natural Science Foundation of China; Key Technologies Research and Development Program
Citations: not cited yet (Europe PMC); 23 references in the paper

Abstract

The abstract is not reproduced here: the paper's license (CC BY-NC-ND) does not allow it. Read it in the paper, at the publisher or on Europe PMC.

Repository

Its files are read in the Code ↔ Paper reader above.

Xina359/SIMT-DAGM-Calculator

License: none: the authors keep all their rights
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: 947ec2f247085dd50f6df628eccf72d3fa69ff83, 8 January 2026
Languages: Python (16)
Size: 20 files, 16 scripts
Software Heritage: not checked
Found in: “Data availability”
Holds: README, environment (requirements.txt)
Not found: license file, CITATION.cff, tests, continuous integration, documentation
Tools: NumPy (16 files), Matplotlib (15 files), seaborn (9 files), SciPy (2 files), pandas (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
17 files
At the source: github.com/Xina359/SIMT-DAGM-Calculator

The paper's code and data availability statement is in the Data section.

Tracing map

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  • 16 scripts, each with its path and the digest of its content;
  • no match between paragraphs and code yet;
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Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

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Code and data availability statement

The paper has a code and data availability statement. Its license (CC BY-NC-ND) does not allow reproducing it here; in short, from what the harvester recognized in it:

Read it in the paper: doi.org/10.1016/j.phro.2026.101012.

Versions

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, pages, dates, 12 authors, 4 keywords, 2 funders, 23 references.

Cite

This paper

Deng, J., Piao, Z., Song, X., Li, D., Hu, J., Ding, S., Liu, Y., Chen, L., Zhou, G., Sun, Y., Huang, X., & Wang, G. (2026). Distance-adaptive geometric margins for residual rotational uncertainty in single-isocenter multitarget stereotactic radiosurgery. Physics and imaging in radiation oncology, 39, 101012. https://doi.org/10.1016/j.phro.2026.101012

BibTeX

@article{deng2026distance,
author = {Deng, Jiaxin and Piao, Zun and Song, Xinyu and Li, Danyang and Hu, Jiang and Ding, Shouliang and Liu, Yanfei and Chen, Li and Zhou, Guanqun and Sun, Ying and Huang, Xiaoyan and Wang, Guangyu},
title = {{Distance-adaptive geometric margins for residual rotational uncertainty in single-isocenter multitarget stereotactic radiosurgery}},
journal = {Physics and imaging in radiation oncology},
year = {2026},
month = may,
volume = {39},
pages = {101012},
publisher = {Elsevier},
issn = {2405-6316},
doi = {10.1016/j.phro.2026.101012},
url = {https://doi.org/10.1016/j.phro.2026.101012},
pmid = {42293113},
pmcid = {PMC13264242}
}

RIS

TY - JOUR
AU - Deng, Jiaxin
AU - Piao, Zun
AU - Song, Xinyu
AU - Li, Danyang
AU - Hu, Jiang
AU - Ding, Shouliang
AU - Liu, Yanfei
AU - Chen, Li
AU - Zhou, Guanqun
AU - Sun, Ying
AU - Huang, Xiaoyan
AU - Wang, Guangyu
TI - Distance-adaptive geometric margins for residual rotational uncertainty in single-isocenter multitarget stereotactic radiosurgery
T2 - Physics and imaging in radiation oncology
J2 - Phys Imaging Radiat Oncol
PY - 2026
DA - 2026/05/01
VL - 39
SP - 101012
SN - 2405-6316
PB - Elsevier
DO - 10.1016/j.phro.2026.101012
UR - https://doi.org/10.1016/j.phro.2026.101012
LA - en
ER -

CSL-JSON

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"id": "10.1016/j.phro.2026.101012",
"type": "article-journal",
"title": "Distance-adaptive geometric margins for residual rotational uncertainty in single-isocenter multitarget stereotactic radiosurgery",
"container-title": "Physics and imaging in radiation oncology",
"author": [
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"family": "Deng",
"given": "Jiaxin"
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"PMCID": "PMC13264242",
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