A multi-constraint optimal puncture path planning algorithm for percutaneous interventional radiofrequency thermal fusion of the L5/S1 segments

doi:10.12122/j.issn.1673-4254.2024.09.19

Abstract

Abstract:

Objective To minimize variations in treatment outcomes of L5/S1 percutaneous intervertebral radiofrequency thermocoagulation (PIRFT) arising from physician proficiency and achieve precise quantitative risk assessment of the puncture paths. Methods We used a self-developed deep neural network DWT-UNet for automatic segmentation of the magnetic resonance (MR) images of the L5/S1 segments into 7 key structures: L5, S1, Ilium, Disc, N5, Dura mater, and Skin, based on which a needle insertion path planning environment was modeled. Six hard constraints and 6 soft constraints were proposed based on clinical criteria for needle insertion, and the physician's experience was quantified into weights using the analytic hierarchy process and incorporated into the risk function for needle insertion paths to enhance individual case adaptability. By leveraging the proposed skin entry point sampling sub-algorithm and Kambin's triangle projection area sub-algorithm in conjunction with the analytic hierarchy process, and employing various technologies such as ray tracing, CPU multi-threading, and GPU parallel computing, a puncture path was calculated that not only met clinical hard constraints but also optimized the overall soft constraints. Results A surgical team conducted a subjective evaluation of the 21 needle puncture paths planned by the algorithm, and all the paths met the clinical requirements, with 95.24% of them rated excellent or good. Compared with the physician's planning results, the plans generated by the algorithm showed inferior D_Ilium, D_S1, and Depth (P<0.05) but much better D_Dura, D_L5, D_N5, and A_Kambin (P<0.05). In the 21 cases, the planning time of the algorithm averaged 7.97±3.73 s, much shorter than that by the physicians (typically beyond 10 min). Conclusion The multi-constraint optimal puncture path planning algorithm offers an efficient automated solution for PIRFT of the L5/S1 segments with great potentials for clinical application.

Key words: percutaneous intervertebral radiofrequency thermocoagulation, L5/S1, Kambin's triangle, path planning

Hu LIU, Zhihai SU, Chengjie HUANG, Lei ZHAO, Yangfan CHEN, Yujia ZHOU, Hai LÜ, Qianjin FENG. A multi-constraint optimal puncture path planning algorithm for percutaneous interventional radiofrequency thermal fusion of the L5/S1 segments[J]. Journal of Southern Medical University, 2024, 44(9): 1783-1795.

Figures/Tables 20

Fig.1 3D path planning environment.

Fig.2 Overall workflow of the algorithm.

Fig.3 Structural diagram of DWT-UNet model.

Tab.1 Constraints for path planning in radiofrequency ablation for lumbar disc herniation

ID	Hard constraints	Soft constraints
A	To avoid collision with the risk-prone anatomical structures in the L5/S1 segment (including L5, S1, N5, dura mater, and ilium), ensuring a minimum clearance of 0.5mm (considering the outer diameter of a 20G needle is approximately 0.9mm) is crucial to maintain a safety margin during the procedure.^{[14, 16]}	The distance between the puncture path and critical anatomical structures should be maximized as much as possible.^[14]
B	The puncture depth should be less than 150mm (considering the length of the puncture needle is 150mm) to ensure the ablation target can be effectively reached.^{[14, 16]}	The puncture depth should be minimized as much as possible.^[14]
C	To prevent the phenomenon of needle slippage, the angle between the puncture path and the surface of the intervertebral disc should be greater than 20 degrees.^{[14, 16]}	The angle between the puncture path and the surface of the intervertebral disc should be maximized as much as possible.^[14]
D*	The puncture path must traverse the intervertebral foramen.	Utilize a distance field based on bone structures to navigate and avoid densely packed bone regions.
E*	The puncture should be performed from the posterior (back) side.	Utilize a distance field based on neural tissue to navigate and avoid densely populated neural regions.
F*	The entry point of the puncture path must be located on the skin overlying the L5/S1 segment, in order to restrict the insertion range of the ablation needle.	The projected area of the Kambin's triangle should be maximized as much as possible.

Fig.4 Illustration of violations of hard constraints for radiofrequency ablation needle puncture. A: Collision between puncture path and S1. B: Depth greater than the maximum length. C: Entry point out of range. D: Excessively small angle. E: Path misses intervertebral foramen. F: Puncture from anterior approach.

Fig.5 Diagram of the path to the key structures.

Fig.6 Diagram of the XYZ Axis limited perspective of the Kambin's triangle.

Fig.7 Kambin's triangle projection. A: Kambin's triangle projection area. B: Extracted Kambin's triangle region after grayscale conversion.

Fig.8 Diagram of non-feasible puncture area.

Tab.2 Judgment matrix for criterion layer

Decision criteria	W_Ilium	W_Dura	W_L5	W_N5	W_S1	W_Depth	W_Kambin
W_Ilium	1	1/3	1/3	1/3	1/3	3	1/7
W_Dura	3	1	1/3	3	3	5	1/3
W_L5	3	3	1	5	5	7	1/3
W_N5	3	1/3	1/5	1	3	5	1/5
W_S1	3	1/3	1/5	1/3	1	5	1/7
W_Depth	1/3	1/5	1/7	1/5	1/5	1	1/9
W_Kambin	7	3	3	5	7	9	1

Fig.9 Chart of the weight distribution.

Tab.3 Algorithm for skin entry point sampling

Algorithm 1 skin insertion point sampling algorithm

Input:Local 3D model of skin S

Output:Uniform sampling needle insertion point on the skin

1:for triangle ABC in S

2: // calculate the two edge vectors of triangle ABC

3: $V e c t o r A B = P A – P B$

4: $V e c t o r A C = P A – P C$

5: // calculate the area of triangle ABC

6: $A r e a = 12 * A B × A C$

7: s $a m p l e s i z e N = 5 * A r e a$

8: for j = 1, 2, 3, …, N do

9: // generate random numbers $r 1$ and $r 2$ within the range of $[0,1]$

10: if $r 1 + r 2 > 1$ :

11: $r 1 = 1 - r 1$

12: $r 2 = 1 - r 2$

13: end if

14: // sample points in triangle ABC

15: $P j = P A + r 1 * V e c t o r A B + r 2 * V e c t o r A C$

16: add $P j$ to the sampling point list

17: end for

18: end for

19: return sampling point list

Tab.3 Algorithm for skin entry point sampling

Algorithm 1 skin insertion point sampling algorithm

Input:Local 3D model of skin S

Output:Uniform sampling needle insertion point on the skin

1:for triangle ABC in S

2: // calculate the two edge vectors of triangle ABC

3: $V e c t o r A B = P A – P B$

4: $V e c t o r A C = P A – P C$

5: // calculate the area of triangle ABC

6: $A r e a = 12 * A B × A C$

7: s $a m p l e s i z e N = 5 * A r e a$

8: for j = 1, 2, 3, …, N do

9: // generate random numbers $r 1$ and $r 2$ within the range of $[0,1]$

10: if $r 1 + r 2 > 1$ :

11: $r 1 = 1 - r 1$

12: $r 2 = 1 - r 2$

13: end if

14: // sample points in triangle ABC

15: $P j = P A + r 1 * V e c t o r A B + r 2 * V e c t o r A C$

16: add $P j$ to the sampling point list

17: end for

18: end for

19: return sampling point list

Fig.10 Diagram of error.

Tab.4 Core criteria for grading

Level	Core criteria
Excellent	Satisfy all clinical hard constraints and D_Dura, D_N5, D_L5, Depth, A_Kambin all outperforme the manual reference path, where Depth and A_Kambinare allowed to have a downward deviation of no more than 2%.
Good	Satisfy all clinical hard constraints, with D_N5 and Depth required to outperform the manual reference path, while D_Dura, D_L5 and A_Kambin are allowed to have a downward deviation of no more than 5%.
Moderate	Satisfy all clinical hard constraints and at least 3 out of the 7 indicators (D_Dura, D_N5, D_L5, Depth, A_Kambin, Depth, A_Kambin) outperforme the manual reference path.
Pass	Satisfy all clinical hard constraints.
Fail	Violation of any clinical hard constraint condition (Tab.1).

Tab.5 DSC of each structure segmented using different models

Model	L5/S1
Model	S1	Disc	L5	Dura mater	N5
nnFormer^[29]	0.9434	0.9219	0.9400	0.9029	0.7933
DeepLabv3^[30]	0.8070	0.8701	0.8427	0.8161	0.5073
U-Net++^[31]	0.9462	0.9225	0.9419	0.9066	0.8012
DWT-UNet (Ours)	0.9491	0.9373	0.9488	0.9197	0.8274

Tab.6 DSC of the ablation experiment

Model	L5/S1
Model	S1	Disc	L5	Dura mater	N5
3D U-Net^[24]	0.9453	0.9231	0.9413	0.9035	0.7981
3D U-Net+DWT	0.9491	0.9373	0.9488	0.9197	0.8274
ResUNet^[32]	0.9429	0.9221	0.9400	0.8974	0.7868
ResUNet+DWT	0.9466	0.9346	0.9477	0.9111	0.8160
V-Net^[33]	0.9404	0.9226	0.9356	0.8944	0.7814
V-Net+DWT	0.9426	0.9269	0.9431	0.9054	0.7974

Tab.7 Parameters of the puncture paths planned by the algorithm in 21 cases

ID	Gender	Age (year)	Initial candidate needle insertion points	Needle insertion points that satisfy hard constraints	Depth (mm)	Clinical level
Case1	Female	53	43 035	22 097	123.71	Good
Case2	Female	54	38 040	18 362	113.90	Good
Case3	Male	39	43 925	11 689	126.46	Good
Case4	Male	40	44 285	12 935	120.15	Good
Case5	Female	26	38 200	8111	109.66	Good
Case6	Female	27	38 995	10 538	103.67	Excellent
Case7	Female	54	45 045	11 346	105.87	Excellent
Case8	Female	32	38 480	18 646	87.22	Excellent
Case9	Female	33	37 370	17 929	88.02	Excellent
Case10	Female	35	35 070	15 663	134.82	Good
Case11	Female	36	34 120	11 825	147.26	Excellent
Case12	Female	63	45 875	12 569	83.74	Moderate
Case13	Female	64	45 250	13 219	84.30	Good
Case14	Female	38	39 495	9911	128.67	Good
Case15	Female	39	38 105	7527	125.40	Good
Case16	Female	41	38 240	6539	112.07	Excellent
Case17	Female	42	36 895	3917	116.50	Good
Case18	Male	33	43 880	11 475	130.13	Excellent
Case19	Male	34	43 725	10 750	122.36	Excellent
Case20	Male	26	39 115	10 094	104.42	Excellent
Case21	Male	27	37 945	11 575	123.99	Excellent

Fig.11 Comparison between algorithmically planned paths and doctor-planned paths.

Tab.8 Comparison of the plans by the algorithm and the physician (Mean±SD)

Soft constraints	Algorithm (ours)	Physician	t/Z	P
D_iliac(mm)	9.44±5.10	11.88±6.14	2.381	0.017
D_Dura(mm)	17.44±2.38	17.23±2.55	2.212	0.039
D_L5(mm)	8.12±1.66	7.20±1.79	3.875	<0.001
D_N5(mm)	6.13±1.84	5.66±1.83	3.980	<0.001
D_S1(mm)	0.58±0.17	1.25±0.18	12.727	<0.001
Depth(mm)	113.92±17.44	119.51±18.60	7.008	<0.001
A_Kambin(mm²)	170.87±59.87	148.70±72.83	2.868	0.004

Tab.9 Algorithm performance comparison of auto-segmented and manually segmented data (Mean±SD)

Soft constraints	Auto segmentation	Manual segmentation	t/Z	P
D_iliac(mm)	7.54±5.54	9.44±5.10	2.958	0.008
D_Dura(mm)	18.43±2.18	17.44±2.38	2.071	0.052
D_L5(mm)	7.99±1.49	8.12±1.66	0.535	0.599
D_N5(mm)	5.94±1.92	6.13±1.84	0.678	0.498
D_S1(mm)	1.07±0.94	0.58±0.17	2.311	0.021
Depth(mm)	111.90±16.97	113.92±17.44	1.477	0.140
A_Kambin(mm²)	154.62±48.07	170.87±59.87	2.066	0.052

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