Advances in dual energy computed tomography approach for proton stopping power ratio computation in radiotherapy

Table 1 Stopping power ratio training and testing root mean square errors (%) using reference ρ_e as presented in Chika[20]

SPR training RMSE (%)	Total	Lung	Soft	Bone	Testing RMSE (%)	Total	Soft	Bone
SPR1,1 continuous	0.32	0.70	0.35	0.13		0.73	0.80	0.62
SPR1,1 piece-wise	0.22	0.02	0.27	0.04		0.92	1.09	0.61
SPR0,3 continuous	0.31	0.14	0.38	0.07		0.71	0.77	0.62
Kanematsu	2.03	0.00	2.08	2.04		1.77	1.80	1.63

Citation: Chika CE. Estimation of Proton Stopping Power Ratio and Mean Excitation Energy Using Electron Density and Its Applications via Machine Learning Approach. J Med Phys 2024; 49: 155-166. Copyright© The Authors 2024. Published by Wolters Kluwer Medknow Publications. This article is available under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike License (CC BY-NC-SA), which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. Permission only needs to be obtained for commercial use. RMSE: Root mean square error; SPR: Stopping power ratio.

Table 2 Stopping power ratio training and testing root mean square error (%) using estimated ρ_e as presented in Chika[20]

SPR training RMSE (%)	Total	Lung	Soft	Bone	Testing RMSE (%)	Total	Soft	Bone
BVM SPR from I1,0	0.26	0.14	0.32	0.06		0.86	0.99	0.63
BVM SPR1,1	0.23	0.07	0.28	0.05		0.98	1.18	0.61
BVM SPR from Ifc	0.29	-0.09	0.31	0.28		1.59	0.61	2.36
BVM SPR from Irc	0.25	0.09	0.30	0.13		1.54	0.61	2.27
H-S SPR from I1,0	0.98	0.94	1.00	0.95		1.40	1.45	1.33
H-S SPR1,1	0.22	0.01	0.27	0.05		0.97	1.15	0.63
H-S Method	0.39	0.28	0.41	0.35		0.85	0.91	0.77

Citation: Chika CE. Estimation of Proton Stopping Power Ratio and Mean Excitation Energy Using Electron Density and Its Applications via Machine Learning Approach. J Med Phys 2024; 49: 155-166. Copyright© The Authors 2024. Published by Wolters Kluwer Medknow Publications. This article is available under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike License (CC BY-NC-SA), which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. Permission only needs to be obtained for commercial use. SPR: Stopping power ratio; RMSE: Root mean square error; BVM: Basis vector method; H-S: Hunemohr’s and Saito.

Table 3 Stopping power ratio modeling and testing root mean square (%) using computed tomography number as presented in Chika[21]

SPR training RMSE (%)	Total	Lung	Soft	Bone	Testing RMSE (%)	Total	Soft	Bone
TSPR,1,0;fr(μ)	1.78	0.04	0.58	2.98		4.72	4.80	4.61
TSPR,1,2;fr(μ)	0.49	0.04	0.58	0.26		5.87	4.82	7.08
TSPR,1,2;fm(μ)	1.04	0.03	1.14	0.87		3.89	3.07	4.80
TSPR,1,2;fL(μ)	0.85	0.00	1.00	0.53		3.14	3.28	3.27
Stochiometric	0.86	0.01	1.00	0.56		3.39	3.35	3.44
Taasti	0.60	0.01	0.22	1.00		6.77	7.19	6.14
H-S method	5.10	0.45	3.42	7.46		4.51	4.47	4.57
TSPR,1,2;fr(μ)4g	0.38	0.04	0.44	0.26		5.87	4.82	7.08

Citation: Chika CE. Machine Learning Approach and Model for Predicting Proton Stopping Power Ratio and Other Parameters Using Computed Tomography Images. J Med Phys 2024; 49: 519-530. Copyright© The Authors 2024. Published by Wolters Kluwer Medknow Publications. This article is available under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike License (CC BY-NC-SA), which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. Permission only needs to be obtained for commercial use. SPR: Stopping power ratio; RMSE: Root mean square; H-S method: Hunemohr’s and Saito model.

Table 4 Stopping power ratio modeling and testing mean error (%) using computed tomography number as presented in Chika[21]

SPR training ME(%)	Total	Lung	Soft	Bone	SPR testing ME(%)	Total	Soft	Bone
TSPR,1,0;fr(μ)	0.28	0.04	0.01	0.84		0.63	1.02	0.09
TSPR,1,2;fr(μ)	0.00	0.04	0.00	0.00		-0.05	1.06	-1.62
TSPR,1,2;fm(μ)	-0.09	-0.03	-0.02	-0.24		-2.08	-1.48	-2.92
TSPR,1,2;fL(μ)	0.00	0.00	-0.01	0.02		-1.04	-0.85	-1.30
Stochiometric	-0.01	-0.01	-0.01	-0.01		-1.15	-0.93	-1.46
Taasti	-0.02	-0.01	-0.01	-0.03		2.19	2.95	1.14
H-S method	0.17	0.45	2.25	-3.84		-0.23	2.66	-4.28
TSPR,1,2;fr(μ)4g	0.00	0.04	0.00	0.00		-0.31	0.62	-1.62

Citation: Chika CE. Machine Learning Approach and Model for Predicting Proton Stopping Power Ratio and Other Parameters Using Computed Tomography Images. J Med Phys 2024; 49: 519-530. Copyright© The Authors 2024. Published by Wolters Kluwer Medknow Publications. This article is available under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike License (CC BY-NC-SA), which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. Permission only needs to be obtained for commercial use. SPR: Stopping power ratio; ME: Mean error; H-S method: Hunemohr’s and Saito model.