In total, 15 patients were included in this study, their ages ranged from 23 to 56 year with a mean of 43 year. The mammary basal diameter (D) ranged from 17.32 to 22.53 cm with a mean of 19.72cm and with the mammary height axis (H) ranging from 3.58 to 6.82cm with a mean of 4.79 cm and with the D×H ranging from 66.69 to 148.70 cm2 with a mean of 95.29 cm2.
The fiducial motions
Our study analyzed clinical data from 372 fractions of 39 fiducials. The distributions of the displacements of all individual fiducials are shown in Fig. 2. Both the one-dimensional displacements per fiducial and the combined three-dimensional displacements per fiducial are shown. It could be seen that the fiducial motions conform to the Gaussian distribution. MLR, MAP, MSI and M3D are shown as follows (average ± standard deviation): 2.2 ± 3.0 mm, -1.1 ± 3.6 mm, 0.8 ± 4.7 mm, 6.5 ± 2.7 mm. According to the Gaussian curve, the one-dimensional displacements all concentrate in the range of -5 ~ 5 mm, out of which MLR accounts for 81.6%, MAP accounts for 81.5%, and MSI accounts for 70.4%. The fiducial migration is anisotropic, and tend to move to the right, dorsal and caudal.
Correlation with breast size
Due to the insufficient quantity of fiducials located in the second and third quadrants in this study, they were not included in the analysis. When D < mD and D×H < mD×H, MLR, MAP and MSI all have a statistically significant but weak correlation with D and D×H (p < 0.05) both in the first and fourth quadrants, except for MAP located in the first quadrant, which is significantly positively correlated with D, H and D×H (r = 0.517,0.691,0.805). For M3D, there is no correlation with D, H and D×H in the first quadrant, however it had a negatively weak correlation with H and D×H in the fourth quadrant only when H ≥ mHand D×H ≥ mD×H, and the Pearson correlation coefficient r is -0.353 and − 0.312 (p < 0.05).
Correlation with fiducial position
When D ≥ mD, H ≥ mH, D×H ≥ mD×H, the linear fitting diagrams are shown in Fig. 3. It could be seen that in the first quadrant, MSI show a strong linear negative correlation with DSSI both in H and D×H classifications(r<-0.7, R2 = 0.55 VS 0.77 ). For M3D, it's strongly linearly negatively correlated with DSLR in D and D×H classifications(r<-0.7, R2 = 0.87 VS 0.50). While in the fourth quadrant, only under the D classification, MAP and DSSI show a strong linear negative correlation (r<-0.9, R2 = 0.76).
When D < mD, H < mH, D×H < mD×H, the linear fitting diagrams are shown in Fig. 4. it can be seen that under D and D×H classifications, MLR and MAP located in the first quadrant all have a strong linear positive correlation with DSLR, DSAP and DSSI(r > 0.8). In the D×H classification the R2 values of MLR and DSLR, DSAP are all greater than that in the D classification(R2 = 0.87,0.86 VS 0.74,0.75), which is as the same as MAP(R2 = 0.76,0.80 VS 0.64,0.67). For MSI, whether it's D, H or D×H classification, MSI and DSLR, DSAP all show a significant linear positive correlation(R2 = 0.53,0.62 VS 0.68,0.74 VS 0.80,0.87). The one-dimensional displacements of fiducials located in the fourth quadrant is correlated with the fiducial position only in the H and D×H classifications. As explained below: MAP and DSLR, MSI and DSAP all show a strong linear negative correlation (r<-0.9), the corresponding R2 values are 0.91 and 0.87 both in H and D×H classification. However MLR is strongly linearly positively correlated with DSLR, and the r(R2) value is 0.91(0.77). For M3D, it's all significantly linearly positively correlated with DSLR in the three classifications(r > 0.7), and the R2 values are 0.54,0.71 and 0.71.
The correlation coefficient (r) and linear goodness of fit (R2) between fiducial migration and the fiducial position are shown in Table 1. It is not difficult to see that for the linear fitting analysis between the fiducial motion and the fiducial position, the D×H classification(R2 > 0.7) is generally better than D(R2 > 0.6) and H classification(R2 > 0.5).
Table 1
linear fit between the fiducial motion and the fiducial position (R2/r values)
Quadrant
|
Motion
|
D
|
H
|
D×H
|
DSLR
|
DSAP
|
DSSI
|
DSLR
|
DSAP
|
DSSI
|
DSLR
|
DSAP
|
DSSI
|
First
|
M3D
|
0.87/
-0.76a
|
/
|
/
|
/
|
/
|
/
|
0.50/
-0.71a
|
/
|
/
|
MLR
|
0.74/
0.88
|
0.75/
0.88
|
0.82/
0.91
|
/
|
/
|
/
|
0.87/
0.94
|
0.86/
0.94
|
0.80/
0.91
|
MAP
|
0.64/
0.83
|
0.67/
0.84
|
0.84/
0.93
|
/
|
0.59/
0.81
|
/
|
0.76/
0.87
|
0.80/
0.91
|
0.83/
0.92
|
MSI
|
0.53/
0.77
|
0.62/
0.82
|
/
|
0.68/
0.86
|
0.74/
0.88
|
0.55/
-0.77a
|
0.80/
0.91
|
0.87/
0.94
|
0.77/
-0.89a
|
Fourth
|
M3D
|
0.54/
0.77
|
/
|
/
|
0.71/
0.89
|
/
|
/
|
0.71/
0.89
|
/
|
/
|
MLR
|
/
|
/
|
/
|
0.77/
0.91
|
|
|
0.77/
0.91
|
|
|
MAP
|
/
|
/
|
0.76/
-0.91a
|
0.91/
-0.96
|
/
|
/
|
0.91/
-0.96
|
/
|
/
|
MSI
|
/
|
/
|
/
|
/
|
0.87/
-0.95
|
/
|
/
|
0.87/
-0.95
|
/
|
a Linear fitting results for patients with the larger breast. |
The individualed PTV margins
we calculated the PTV margin according to the Van Herk margin recipe 2.5Σ་0.7σ[13]. In the first quadrant, when D×H < 99.89 cm2, the margin in the left, right, ventral, dorsal, cranial and caudal directions are 0.63, 0.73, 0.68, 1.06, 0.93, 0.64 (cm) in turn, which is statistically significantly different from that when D×H ≥ 99.89 cm2, except for the ventral and dorsal directions (p < 0.05), and when D×H ≥ 99.89 cm2, the corresponding margins are 0.69,1.01, 0.64, 0.81, 1.05, 1.24 (cm). In the fourth quadrant, because of the small sample size, the margins have no statistical difference between the D×H < 90.71 cm2 and the D×H ≥ 90.71 cm2 classifications, but it shows a smaller margin than that in the first quadrant. And the PTV margins in the ventral, dorsal, cranial and caudal directions have a statistically significant difference between the first and fourth quadrants (p < 0.05).
Table 2
PTV margins based on different breast size and quadrant position of lesion
Quadrant
|
Direction
|
D (cm)
|
H (cm)
|
D×H (cm2)
|
D < mD
|
D ≥ mD
|
H < mH
|
H ≥ mH
|
D×H < mD×H
|
D×H ≥ mD×H
|
First
|
LR(+/−)
|
0.71/0.64
|
1.04/0.69
|
0.69/0.56
|
0.89/0.77
|
0.73/0.63
|
1.01/0.69
|
AP(+/−)
|
0.65/1.02
|
0.63/0.82
|
0.40/1.05
|
0.69/0.81
|
0.68/1.06
|
0.64/0.81
|
SI(+/−)
|
0.73/0.65
|
1.29/1.21
|
1.29/0.96
|
0.97/0.99
|
0.64/0.93
|
1.24/1.05
|
Fourth
|
LR(+/−)
|
0.68/0.46
|
0.91/0.38
|
0.75/0.40
|
0.83/0.49
|
0.76/0.39
|
0.80/0.46
|
AP(+/−)
|
0.23/0.73
|
0.82/0.63
|
0.62/0.71
|
0.90/0.70
|
0.66/0.73
|
0.82/0.68
|
SI(+/−)
|
0.73/0.99
|
1.26/1.11
|
1.05/1.08
|
0.89/0.26
|
0.70/1.11
|
1.02/0.50
|
The positive signals in the LR, AP and SI directions indicate the right, ventral and caudal direction in turn, and the negative signals mean the opposite directions.