Evaluating Correlation between Geometrical Relationship and Dose Difference Caused by Respiratory Motion Using Statistical Analysis

Dong-Seok Shin; Seong-Hee Kang; Dong-Su Kim; Tae-Ho Kim; Kyeong-Hyeon Kim; Min-Seok Cho; Yu-Yoon Noh; Do-Kun Yoon; Tae Suk Suh

doi:10.14316/pmp.2016.27.4.203

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Shin, Kang, Kim, Kim, Kim, Cho, Noh, Yoon, and Suh: Evaluating Correlation between Geometrical Relationship and Dose Difference Caused by Respiratory Motion Using Statistical Analysis

Original Article

Progress in Medical Physics 2016;27(4):203-212.

Published online: 17 December 2016

DOI: https://doi.org/10.14316/pmp.2016.27.4.203

Evaluating Correlation between Geometrical Relationship and Dose Difference Caused by Respiratory Motion Using Statistical Analysis

Dong-Seok Shin^∗, Seong-Hee Kang^∗, Dong-Su Kim^∗, Tae-Ho Kim^∗, Kyeong-Hyeon Kim^∗, Min-Seok Cho^†, Yu-Yoon Noh^∗, Do-Kun Yoon^∗, Tae Suk Suh^∗,

^∗Department of Biomedical Engineering, Research Institute of Biomedical Engineering, College of Medicine, The Catholic University of Korea, Seoul, Korea

^†Department of Radiation Oncology, Asan Medical Center, Seoul, Korea

Correspondence: Tae Suk Suh (suhsanta@catholic.ac.kr) Tel: 82-2-2258-7232, Fax: 82-2-2258-7506

Received 10 November 201619 December 2016 Accepted 20 December 2016

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Dose differences between three-dimensional (3D) and four-dimensional (4D) doses could be varied according to the geometrical relationship between a planning target volume (PTV) and an organ at risk (OAR). The purpose of this study is to evaluate the correlation between the overlap volume histogram (OVH), which quantitatively shows the geometrical relationship between the PTV and OAR, and the dose differences. 4D computed tomography (4DCT) images were acquired for 10 liver cancer patients. Internal target volume-based treatment planning was performed. A 3D dose was calculated on a reference phase (end-exhalation). A 4D dose was accumulated using deformation vector fields between the reference and other phase images of 4DCT from deformable image registration, and dose differences between the 3D and 4D doses were calculated. An OVH between the PTV and selected OAR (duodenum) was calculated and quantified on the basis of specific overlap volumes that corresponded to 10%, 20%, 30%, 40%, and 50% of the OAR volume overlapped with the expanded PTV. Statistical analysis was performed to verify the correlation with the OVH and dose difference for the OAR. The minimum mean dose difference was 0.50 Gy from case 3, and the maximum mean dose difference was 4.96 Gy from case 2. The calculated range of the correlation coefficients between the OVH and dose difference was from −0.720 to −0.712, and the R-square range for regression analysis was from 0.506 to 0.518 (p-value ＜0.05). However, when the 10% overlap volume was applied in the six cases that had OVH value ≤2, the average percent mean dose differences were 34.80±12.42%. Cases with quantified OVH values of 2 or more had mean dose differences of 29.16±11.36%. In conclusion, no significant statistical correlation was found between the OVH and dose differences. However, it was confirmed that a higher difference between the 3D and 4D doses could occur in cases that have smaller OVH value.

Keywords: 4D dose, Overlap volume histogram, Respiratory motion, Geometrical relationship

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Fig. 1.

Ssimple calculation process for four-dimensional doses (4D doses). First, deformable image registration was used to calculate the deformation vector fields (DVFs) for each phase image based on the end-exhalation phase image from four-dimensional computed tomography (4DCT). Second, the calculated DVFs were applied to each dose distribution that was calculated from each phase image to obtain the warped dose distributions. Finally, the warped dose distributions were weighted and summed up to calculate the 4D doses.

Fig. 2.

Example of an overlap volume histogram (OVH). (a) three-dimensional view showing the geometrical relationship between the planning target volume (PTV) and the organ at risk (OAR), (b) two-dimensional view on the given PTV and OAR: r₁ is the maximum expansion distance where the expanded PTV and OAR did not overlap when PTV was expanded by an arbitrary margin. r₂ is the minimum expansion distance where the OAR was perfectly overlapped by the PTV expanded by an arbitrary margin. d is the margin size when the ratio of the overlapped volume (red area) between the expanded PTV and OAR to the volume of OAR was v, (c) OVH of given PTV and OAR.

Fig. 3.

Overlap volume histogram (OVH) for each case. The expansion distance of the horizontal axis represents the size of the margin used when the planning target volume (PTV) was expanded by an arbitrary margin. The vertical axis represents the ratio of the overlapped volume between the organ at risk (OAR) and expanded PTV, which was expanded by an arbitrary margin, to the volume of OAR.

Fig. 4.

Regression line and scatter diagram for the overlap volume histogram (OVH) and the center-of-mass (COM) distance between the planning target volume (PTV) and the organ at risk (OAR), and the mean dose differences between the four-dimensional dose (4D dose) and three-dimensional dose (3D dose) at the OAR. (a) Linear regression line and scatter diagram between the expansion distance and COM distance when the ratio of the OAR volume to the overlapped volume between the OAR and PTV expanded by an arbitrary margin was 50% (OVH₅₀), (b) Linear regression line and the scatter diagram between the mean dose difference and COM distance.

Fig. 5.

Regression line and scatter diagram for the mean dose difference between three-dimensional doses (3D doses) and four-dimensional doses (4D doses); expansion distance according to each volume ratio standard when the ratio of the overlapped volume between the organ at risk (OAR) and the planning target volume (PTV) expanded by an arbitrary margin to the OAR volume ranges from 10% to 50% (OVH₁₀, OVH₂₀, OVH₃₀, OVH₄₀, OVH₅₀). (a) Standard at OVH₁₀, (b) standard at OVH₂₀, (c) standard at OVH₃₀, (d) standard at OVH₄₀, (e) standard at OVH₅₀.

Table 1.

Therapy plan and characteristics of each case. The center-of-mass (COM) distance is the distance from the planning target volume (PTV) to the organ at risk (OAR), which is the duodenum.

Case No.	Plan	PTV volume (cm³)	COM distance (cm)	Prescription dose (Gy)
1	SBRT	83.37	7.35	40
2	SBRT	53.63	3.89	40
3	SBRT	54.59	5.43	40
4	SBRT	141.07	5.04	30
5	3DCRT	267.34	5.71	40
6	3DCRT	74.71	6.90	40
7	3DCRT	71.71	5.07	40
8	3DCRT	78.74	9.25	40
9	SBRT	36.30	2.97	30
10	3DCRT	67.20	4.34	40

SBRT: stereotactic body radiation therapy, 3DCRT: three conformal radiation therapy.

Table 2.

Expansion distance of each case according to the ratio of the overlapped volume between the organ at risk (OAR and the planning target volume (PTV), which was expanded by an arbitrary margin to the OAR volume.

Case No.	Expansion Distance (a.u.)
Case No.	OVH₁₀	OVH₂₀	OVH₃₀	OVH₄₀	OVH₅₀
1	3.38	4.01	4.43	4.79	5.10
2	0.54	1.66	0.76	0.92	1.11
3	2.13	2.42	2.69	2.95	3.34
4	1.42	1.67	1.88	2.08	2.25
5	1.34	1.68	1.95	2.16	2.36
6	1.33	1.59	1.78	1.95	2.11
7	2.10	2.36	2.59	2.76	2.94
8	4.05	4.52	4.99	5.34	5.71
9	0.41	0.54	0.63	0.72	0.80
10	0.20	0.58	0.93	1.27	1.59

OVH_x: Standard where the ratio between the overlapped volume of expanded PTV and the OAR to OAR volume is x%.

Table 3.

Mean three-dimensional dose (3D dose), mean four-dimensional dose (4D dose) and mean dose differencecalculated for the duodenum, which was the organ at risk (OAR) for each case.

Case No.	3D_mean (Gy)	4D_mean (Gy)	Mean dose difference (Gy)
1	12.74	11.04	1.70
2	12.79	7.83	4.96
3	1.64	1.14	0.50
4	7.21	3.80	3.41
5	14.09	11.15	2.94
6	7.57	3.76	3.81
7	5.16	3.48	1.68
8	2.31	1.38	0.93
9	9.87	7.31	2.56
10	12.83	9.55	3.28

3D_mean: mean dose for 3D dose, 4D_mean: mean dose for 4D dose.

Table 4.

Regression analysis results of the quantified overlap volume histogram (OVH) and the center-of-mass (COM) distance between the planning target volume (PTV) and the organ at risk (OAR).

	R²	Regression coefficient	Standard error	p–value	95% Confide	ence interval
	R²	Regression coefficient	Standard error	p–value	Lower	Upper
OVH₁₀–COM distance	0.763	1.296	0.250	0.001	0.693	1.845
OVH₂₀–COM distance	0.779	1.175	0.221	0.001	0.665	1.685
OVH₃₀–COM distance	0.789	1.102	0.201	0.001	0.638	1.566
OVH₄₀–COM distance	0.792	1.057	0.192	0.001	0.615	1.499
OVH₅₀–COM distance	0.786	1.009	0.186	0.001	0.580	1.438

OVH_x: Standard where the ratio of overlapped volume between expanded PTV and OAR to OAR volume is x%, Standard error: the error value for regression coefficient.

Table 5.

Regression analysis results for the mean dose differences between three-dimensional doses (3D doses) and four-dimensional doses (4D doses), and the center-of-mass (COM) distance between the quantified overlap volume histogram (OVH), the organ at risk (OAR), and the planning target volume (PTV).

	Correlation coefficient R	R²	Regression coefficient	Standard error	p-value	95% Confidence interval
	Correlation coefficient R	R²	Regression coefficient	Standard error	p-value	Lower	Upper
OVH10–MDD	−0.717	0.514	−0.784	0.270	0.020	−1.407	−0.162
OVH20–MDD	−0.713	0.508	−0.715	0.249	0.021	−1.288	−0.142
OVH30–MDD	−0.715	0.511	−0.668	0.231	0.020	−1.201	−0.135
OVH40–MDD	−0.712	0.506	−0.637	0.222	0.021	−1.150	−0.124
OVH50–MDD	−0.720	0.518	−0.617	0.210	0.019	−1.103	−0.132
COM distance–MDD	0.460	0.212	−0.347	0.237	0.181	−0.892	0.198

OVH_x: Standard where the ratio of overlapped volume between expanded PTV and OAR to OAR volume is x%, MDD: mean dose difference, Standard error: the error value for regression coefficient.

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