Novel framework based on multi-stage random sampling and differentiable rendering for automated three-dimensional orientation estimation of skull base foramina_Journal of Biomedical Engineering

Authors：

 LI Yonghui ¹ , ZHANG Han ² , GENG Shuai ¹ , TAN Dongliang ¹ , SHI Weili ¹ , MIAO Yu ¹ ,  JIANG Zhengang ¹

1. School of Computer Science and Technology, Changchun University of Science and Technology, Changchun 130022, P. R. China;
2. Hospital of Stomatology, Jilin University, Changchun 130021, P. R. China;

Corresponding?author：

LI Yonghui, Email: lyh_binary@163.com; JIANG Zhengang, Email: jiangzhengang@cust.edu.cn

Keywords：

Trigeminal neuralgia; Skull base foramina; Three-dimensional orientation estimation; Multi stage random sampling; Differentiable rendering

DOI：

10.7507/1001-5515.202512001

Video：

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Abstract Full text Figures/Tables Video References Cited by

The foramen ovale and foramen rotundum of the skull base serve as critical anatomical approaches for percutaneous puncture of the trigeminal ganglion. Their three-dimensional orientation is crucial for designing surgical pathways and avoiding adjacent vital structures. However, this orientation exhibits significant individual variability, and its assessment currently lacks automated quantitative methods. To address this issue, the present study formulates the puncture foramina orientation estimation as a geometric optimization problem and proposes a coarse-to-fine solution framework: first, a coarse estimate is obtained through adaptive multi-stage random sampling to rapidly cover the feasible region, followed by a refined estimate using optimization techniques based on differentiable rendering. Experiments on 64 foraminal structures from 16 subjects demonstrated that the average angular error of the automatically estimated results was 2.21 °, which is smaller than the inter-observer variability among physicians 4.81 °. The method outperforms manual judgment in terms of accuracy, providing an objective anatomical reference for personalized puncture path planning and demonstrating clear potential for clinical translation.

Citation： LI Yonghui, ZHANG Han, GENG Shuai, TAN Dongliang, SHI Weili, MIAO Yu, JIANG Zhengang. Novel framework based on multi-stage random sampling and differentiable rendering for automated three-dimensional orientation estimation of skull base foramina. Journal of Biomedical Engineering, 2026, 43(3): 580-588. doi: 10.7507/1001-5515.202512001 Copy

1.	Wang Z M, Su X, Yu Y, et al. A review of literature and meta-analysis of one-puncture success rate in radiofrequency thermocoagulation with different guidance techniques for trigeminal neuralgia. Eur J Med Res, 2022, 27(141): 1-10.
2.	Feng F, Xu Q Q, Wu Q, et al. Radiofrequency thermocoagulation through the foramen rotundum versus the foramen ovale for V2 primary trigeminal neuralgia: a systematic review and meta-analysis. Pain Physician, 2023, 26(6): E627-E633.
3.	Ding Y Y, Yao P, Li H X, et al. Comparison of efficacy and safety of CT-guided radiofrequency thermocoagulation through foramen rotundum versus foramen ovale for V2 primary trigeminal neuralgia. Pain Physician, 2021, 24(8): 587-596.
4.	Qiu T, Guo Q C, Kong T X, et al. A novel mobile C-Arm fluoroscopic imaging of the foramen ovale and its anatomical principles. J Pain Res, 2026, 19: 1-15.
5.	Héréus S, Lins B, Van Vlasselaer N, et al. Morphologic and morphometric measurements of the foramen ovale: comparing digitized measurements performed on dried human crania with computed tomographic imaging. An observational anatomic study. J Craniofac Surg, 2023, 34(1): 404-410.
6.	Bhattarai R, Panthi S, Yadav G K, et al. Morphometric analysis of foramen ovale, foramen spinosum, and foramen rotundum of human skull using computed tomography scan: a cross-sectional study. Ann Med Surg, 2023, 85(5): 1731-1736.
7.	Meng F H, Song Y, Qiao B, et al. Image-guided, surgical robot-assisted percutaneous puncture of the foramen ovale and foramina stylomastoideum: a cadaveric study. Chin Med J, 2021, 134(19): 2362-2364.
8.	Ran B, Wei J, Zhong Q, et al. Long-term follow-up of patients treated with percutaneous radiofrequency thermocoagulation via the foramen rotundum for isolated maxillary nerve idiopathic trigeminal neuralgia. Pain Med, 2019, 20(7): 1370-1378.
9.	Guo Z G, Wang Z J, Li K, et al. Unconventional facial entry points confirmed using a 3D CT reconstruction-guided stereotactic approach to radiofrequency thermocoagulation for the treatment of trigeminal neuralgia: a series of case reports. Pain Med, 2019, 20(8): 1551-1558.
10.	Guo Z G, Wu B S, Du C, et al. Stereotactic approach combined with 3D CT reconstruction for difficult-to-access foramen ovale on radiofrequency thermocoagulation of the gasserian ganglion for trigeminal neuralgia. Pain Med, 2016, 17(9): 1704-1716.
11.	Wu F H W, Cheung C W, Leung Y Y. Neuronavigation-guided percutaneous rhizotomies to trigeminal neuralgia. Clin J Pain, 2024, 40(4): 253-266.
12.	Liu M, Cygler J E, Tiberi D, et al. Dosimetric impact of rotational errors in trigeminal neuralgia radiosurgery using CyberKnife. J Appl Clin Med Phys, 2024, 25(4): 1-10.
13.	Abboud T, Malinova V, Rohde V, et al. Radiofrequency thermocoagulation under neuromonitoring guidance and general anesthesia for treatment of refractory trigeminal neuralgia. Acta Neurochir, 2024, 166(56): 1-4.
14.	Xia Y H, Yu G, Min F X, et al. The focus and new progress of percutaneous balloon compression for the treatment of trigeminal neuralgia. J Pain Res, 2022, 15: 3059-3068.
15.	Tan K, Li J P, Peng Y T, et al. Robot-assisted percutaneous balloon compression in elderly patients with trigeminal neuralgia. J Pain Res, 2023, 16: 1161-1168.
16.	Kim J, Yu J W, Rim J, et al. Intraoperative computed tomography-guided neuronavigation for radiofrequency rhizotomy in trigeminal neuralgia: optimizing cannulation trajectories for individual anatomy. Pain Med, 2025, 27(1): 62-67.
17.	Lv W M, Zheng K, Zhang L W. Three-dimensional CT reconstruction-guided percutaneous balloon compression for trigeminal neuralgia. J Clin Neurosci, 2024, 125: 120-125.
18.	Cheng Y, Yu H Q, Xu S B, et al. A new method of locating foramen rotundum and its anatomic study. J Craniofac Surg, 2015, 26(2): 528-531.
19.	Yang C C, Lee M H, Yang J T, et al. Percutaneous radiofrequency trigeminal rhizotomy benefits in patients with refractory trigeminal neuralgia. Medicine, 2022, 101(25): 1-6.
20.	Sun C L, Zheng W H, Zhu Q, et al. The pros and cons of multiple puncture in percutaneous balloon compression for treatment of trigeminal neuralgia. Front Neurol, 2022, 13: 1-6.
21.	Rizzi M, Castelli N, Martino D, et al. Neuronavigated percutaneous gasserian radiofrequency thermorhizotomy for trigeminal neuralgia: how I do it. Acta Neurochir, 2024, 166(247): 1-5.
22.	Goel A, Kulkarni G, Cotici A, et al. Volume maximised glycerol rhizolysis for trigeminal neuralgia: a single centre analysis of outcomes. Br J Neurosurg, 2025, 39(2): 191-196.
23.	Liu P J, Qiu K Y, Wang Z X, et al. Automatic extraction of liver vessel centerlines and topology guided by multi-scale vascular features. Signal Image Video Process, 2025, 19(959): 1-8.
24.	Alblas D, Suk J, Brune C, et al. SIRE: scale-invariant, rotation-equivariant estimation of artery orientations using graph neural networks. Med Image Anal, 2025, 101: 1-16.
25.	Yahya-Zoubir B, Hamami L, Saadaoui L, et al. Automatic 3D mesh-based centerline extraction from a tubular geometry form. Inf Technol Control, 2016, 45(2): 156-163.
26.	?etingül H E, Plank G, Trayanova N A, et al. Estimation of local orientations in fibrous structures with applications to the Purkinje system. IEEE Trans Biomed Eng, 2011, 58(6): 1762-1772.
27.	Poznyakovskiy A A, Zahnert T, Kalaidzidis Y, et al. A segmentation method to obtain a complete geometry model of the hearing organ. Hear Res, 2011, 282(282): 25-34.
28.	Ma J Y, Jiang X Y, Fan A X, et al. Image matching from handcrafted to deep features: a survey. Int J Comput Vis, 2021, 129(1): 23-79.
29.	Garifullin A, Maiorov N, Frolov V, et al. Single-view 3D reconstruction via differentiable rendering and inverse procedural modeling. Symmetry-Basel, 2024, 16(2): 1-22.
30.	Wang W Y, Chen Z G, Fang L C, et al. Curved image triangulation based on differentiable rendering. Comput Graph Forum, 2024, 43(7): 1-12.
31.	Gopalakrishnan V, Dey N, Golland P. Intraoperative 2D/3D image registration via differentiable X-ray rendering//Proceedings of the 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition, Seattle: IEEE, 2024: 11662-11672.
32.	Ravi N, Reizenstein J, Novotn D, et al. Accelerating 3D deep learning with PyTorch3D. arXiv, 2020: 2007.08501.
33.	Zhao L, Chen J H, Peng Z W, et al. Radiofrequency thermocoagulation of trigeminal nerve assisted by nerve bundle extraction and image fusion based on Hamilton-Jacobi equation. Comput Methods Programs Biomed, 2021, 209: 1-8.
34.	Guo W C, Wang Y Z, Du Y H, et al. Enhancing visualization of the foramen ovale in percutaneous microcompression: a preoperative image simulation technique. World Neurosurg, 2024, 189: 312-316.
35.	Tian Y C, Tan Y M, Gao W, et al. The quadrant localization technique for percutaneous balloon compression surgery is beneficial for patients with classic trigeminal neuralgia: a retrospective study. Pain Physician, 2024, 27(8): E891-E898.
36.	Ozbek M A, Basak A T, Cakici N, et al. The endoscopic trans-sinusoidal trans-pterygopalatine route to the foramen rotundum approach in trigeminal neuralgia treatment. Turk Neurosurg, 2022, 32(4): 603-611.
37.	Luzzi S, Baldoncini M, Fabozzi G L, et al. Pretemporal anteromedial interdural approach to Meckel's cave: how I do it. Acta Neurochirurgica, 2026, 168(44): 1-6.
38.	Kolakowski L, Pohl H, Stieglitz L, et al. Interdisciplinary strategies for diagnosis and treatment of trigeminal neuralgia. Swiss Medical Weekly, 2024, 154(3460): 1-9.
39.	Fan X C, Fu Z J, Ma K, et al. Chinese expert consensus on minimally invasive interventional treatment of trigeminal neuralgia. Front Mol Neurosci, 2022, 15: 1-9.
40.	Du Y Y, Liu X H, Shi H C, et al. Safety and efficacy of percutaneous radiofrequency thermocoagulation with varying puncture trajectories for recurrent maxillary trigeminal neuralgia: a prospective study. Front Neurol, 2025, 16: 1-8.
41.	Chen Y J, Liu X L, Xu S S, et al. Anatomy of the trigeminal nerve and its clinical significance via fusion of computed tomography and magnetic resonance imagery. Pain Physician, 2022, 25(2): E293-E298.
42.	Huang W C, Chen K T, Kao C H, et al. The impact of needle location on clinical outcome of radiofrequency rhizotomy for trigeminal neuralgia. Acta Neurochir, 2022, 164(6): 1575-1585.

1. Wang Z M, Su X, Yu Y, et al. A review of literature and meta-analysis of one-puncture success rate in radiofrequency thermocoagulation with different guidance techniques for trigeminal neuralgia. Eur J Med Res, 2022, 27(141): 1-10.
2. Feng F, Xu Q Q, Wu Q, et al. Radiofrequency thermocoagulation through the foramen rotundum versus the foramen ovale for V2 primary trigeminal neuralgia: a systematic review and meta-analysis. Pain Physician, 2023, 26(6): E627-E633.
3. Ding Y Y, Yao P, Li H X, et al. Comparison of efficacy and safety of CT-guided radiofrequency thermocoagulation through foramen rotundum versus foramen ovale for V2 primary trigeminal neuralgia. Pain Physician, 2021, 24(8): 587-596.
4. Qiu T, Guo Q C, Kong T X, et al. A novel mobile C-Arm fluoroscopic imaging of the foramen ovale and its anatomical principles. J Pain Res, 2026, 19: 1-15.
5. Héréus S, Lins B, Van Vlasselaer N, et al. Morphologic and morphometric measurements of the foramen ovale: comparing digitized measurements performed on dried human crania with computed tomographic imaging. An observational anatomic study. J Craniofac Surg, 2023, 34(1): 404-410.
6. Bhattarai R, Panthi S, Yadav G K, et al. Morphometric analysis of foramen ovale, foramen spinosum, and foramen rotundum of human skull using computed tomography scan: a cross-sectional study. Ann Med Surg, 2023, 85(5): 1731-1736.
7. Meng F H, Song Y, Qiao B, et al. Image-guided, surgical robot-assisted percutaneous puncture of the foramen ovale and foramina stylomastoideum: a cadaveric study. Chin Med J, 2021, 134(19): 2362-2364.
8. Ran B, Wei J, Zhong Q, et al. Long-term follow-up of patients treated with percutaneous radiofrequency thermocoagulation via the foramen rotundum for isolated maxillary nerve idiopathic trigeminal neuralgia. Pain Med, 2019, 20(7): 1370-1378.
9. Guo Z G, Wang Z J, Li K, et al. Unconventional facial entry points confirmed using a 3D CT reconstruction-guided stereotactic approach to radiofrequency thermocoagulation for the treatment of trigeminal neuralgia: a series of case reports. Pain Med, 2019, 20(8): 1551-1558.
10. Guo Z G, Wu B S, Du C, et al. Stereotactic approach combined with 3D CT reconstruction for difficult-to-access foramen ovale on radiofrequency thermocoagulation of the gasserian ganglion for trigeminal neuralgia. Pain Med, 2016, 17(9): 1704-1716.
11. Wu F H W, Cheung C W, Leung Y Y. Neuronavigation-guided percutaneous rhizotomies to trigeminal neuralgia. Clin J Pain, 2024, 40(4): 253-266.
12. Liu M, Cygler J E, Tiberi D, et al. Dosimetric impact of rotational errors in trigeminal neuralgia radiosurgery using CyberKnife. J Appl Clin Med Phys, 2024, 25(4): 1-10.
13. Abboud T, Malinova V, Rohde V, et al. Radiofrequency thermocoagulation under neuromonitoring guidance and general anesthesia for treatment of refractory trigeminal neuralgia. Acta Neurochir, 2024, 166(56): 1-4.
14. Xia Y H, Yu G, Min F X, et al. The focus and new progress of percutaneous balloon compression for the treatment of trigeminal neuralgia. J Pain Res, 2022, 15: 3059-3068.
15. Tan K, Li J P, Peng Y T, et al. Robot-assisted percutaneous balloon compression in elderly patients with trigeminal neuralgia. J Pain Res, 2023, 16: 1161-1168.
16. Kim J, Yu J W, Rim J, et al. Intraoperative computed tomography-guided neuronavigation for radiofrequency rhizotomy in trigeminal neuralgia: optimizing cannulation trajectories for individual anatomy. Pain Med, 2025, 27(1): 62-67.
17. Lv W M, Zheng K, Zhang L W. Three-dimensional CT reconstruction-guided percutaneous balloon compression for trigeminal neuralgia. J Clin Neurosci, 2024, 125: 120-125.
18. Cheng Y, Yu H Q, Xu S B, et al. A new method of locating foramen rotundum and its anatomic study. J Craniofac Surg, 2015, 26(2): 528-531.
19. Yang C C, Lee M H, Yang J T, et al. Percutaneous radiofrequency trigeminal rhizotomy benefits in patients with refractory trigeminal neuralgia. Medicine, 2022, 101(25): 1-6.
20. Sun C L, Zheng W H, Zhu Q, et al. The pros and cons of multiple puncture in percutaneous balloon compression for treatment of trigeminal neuralgia. Front Neurol, 2022, 13: 1-6.
21. Rizzi M, Castelli N, Martino D, et al. Neuronavigated percutaneous gasserian radiofrequency thermorhizotomy for trigeminal neuralgia: how I do it. Acta Neurochir, 2024, 166(247): 1-5.
22. Goel A, Kulkarni G, Cotici A, et al. Volume maximised glycerol rhizolysis for trigeminal neuralgia: a single centre analysis of outcomes. Br J Neurosurg, 2025, 39(2): 191-196.
23. Liu P J, Qiu K Y, Wang Z X, et al. Automatic extraction of liver vessel centerlines and topology guided by multi-scale vascular features. Signal Image Video Process, 2025, 19(959): 1-8.
24. Alblas D, Suk J, Brune C, et al. SIRE: scale-invariant, rotation-equivariant estimation of artery orientations using graph neural networks. Med Image Anal, 2025, 101: 1-16.
25. Yahya-Zoubir B, Hamami L, Saadaoui L, et al. Automatic 3D mesh-based centerline extraction from a tubular geometry form. Inf Technol Control, 2016, 45(2): 156-163.
26. ?etingül H E, Plank G, Trayanova N A, et al. Estimation of local orientations in fibrous structures with applications to the Purkinje system. IEEE Trans Biomed Eng, 2011, 58(6): 1762-1772.
27. Poznyakovskiy A A, Zahnert T, Kalaidzidis Y, et al. A segmentation method to obtain a complete geometry model of the hearing organ. Hear Res, 2011, 282(282): 25-34.
28. Ma J Y, Jiang X Y, Fan A X, et al. Image matching from handcrafted to deep features: a survey. Int J Comput Vis, 2021, 129(1): 23-79.
29. Garifullin A, Maiorov N, Frolov V, et al. Single-view 3D reconstruction via differentiable rendering and inverse procedural modeling. Symmetry-Basel, 2024, 16(2): 1-22.
30. Wang W Y, Chen Z G, Fang L C, et al. Curved image triangulation based on differentiable rendering. Comput Graph Forum, 2024, 43(7): 1-12.
31. Gopalakrishnan V, Dey N, Golland P. Intraoperative 2D/3D image registration via differentiable X-ray rendering//Proceedings of the 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition, Seattle: IEEE, 2024: 11662-11672.
32. Ravi N, Reizenstein J, Novotn D, et al. Accelerating 3D deep learning with PyTorch3D. arXiv, 2020: 2007.08501.
33. Zhao L, Chen J H, Peng Z W, et al. Radiofrequency thermocoagulation of trigeminal nerve assisted by nerve bundle extraction and image fusion based on Hamilton-Jacobi equation. Comput Methods Programs Biomed, 2021, 209: 1-8.
34. Guo W C, Wang Y Z, Du Y H, et al. Enhancing visualization of the foramen ovale in percutaneous microcompression: a preoperative image simulation technique. World Neurosurg, 2024, 189: 312-316.
35. Tian Y C, Tan Y M, Gao W, et al. The quadrant localization technique for percutaneous balloon compression surgery is beneficial for patients with classic trigeminal neuralgia: a retrospective study. Pain Physician, 2024, 27(8): E891-E898.
36. Ozbek M A, Basak A T, Cakici N, et al. The endoscopic trans-sinusoidal trans-pterygopalatine route to the foramen rotundum approach in trigeminal neuralgia treatment. Turk Neurosurg, 2022, 32(4): 603-611.
37. Luzzi S, Baldoncini M, Fabozzi G L, et al. Pretemporal anteromedial interdural approach to Meckel's cave: how I do it. Acta Neurochirurgica, 2026, 168(44): 1-6.
38. Kolakowski L, Pohl H, Stieglitz L, et al. Interdisciplinary strategies for diagnosis and treatment of trigeminal neuralgia. Swiss Medical Weekly, 2024, 154(3460): 1-9.
39. Fan X C, Fu Z J, Ma K, et al. Chinese expert consensus on minimally invasive interventional treatment of trigeminal neuralgia. Front Mol Neurosci, 2022, 15: 1-9.
40. Du Y Y, Liu X H, Shi H C, et al. Safety and efficacy of percutaneous radiofrequency thermocoagulation with varying puncture trajectories for recurrent maxillary trigeminal neuralgia: a prospective study. Front Neurol, 2025, 16: 1-8.
41. Chen Y J, Liu X L, Xu S S, et al. Anatomy of the trigeminal nerve and its clinical significance via fusion of computed tomography and magnetic resonance imagery. Pain Physician, 2022, 25(2): E293-E298.
42. Huang W C, Chen K T, Kao C H, et al. The impact of needle location on clinical outcome of radiofrequency rhizotomy for trigeminal neuralgia. Acta Neurochir, 2022, 164(6): 1575-1585.

Journal of Biomedical Engineering

Novel framework based on multi-stage random sampling and differentiable rendering for automated three-dimensional orientation estimation of skull base foramina

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