4.4 Experiment 2 Temporal Analysis
4.4.3.1 Fast Fourier Transform
Visually the detector appears to be reconstructing the time resolved dose distribu- tions as expected, however a FFT of each of the time series gives a quantitative
Figure 4.15: Temporal response of a DUO pixel with the 15 BPM Sine wave motion applied. When predictive tracking is applied there is a clear benefit after an initial ’learning’ time.
Figure 4.16: Temporal response of a DUO pixel with the prostate motion ap- plied. Predictive tracking shows superior performance until a large irregular peak in the motion pattern at around 30 seconds.
measure of performance. The magnitude response of the FFT of each of the Sine motions was calculated and the frequency peaks are shown in figure 4.17. The peaks correspond to the expected frequencies of 0.17, 0.25 and 0.33 Hz from the 10, 15 and 20 BPM Sine waves, respectively. This proves quantitatively that:
1. The HexaMotion platform is able to accurately reproduce the required motion patterns
2. The temporal response of the detector system is able to reconstruct the mo- tion patterns and correctly recover the expected frequency components of the motion
Figure 4.17: Magnitude response of the FFT of the three Sine wave motions. Peaks occur at the expected frequencies of 0.17, 0.25 and 0.33 Hz, corresponding to the 10, 15 and 20 BPM motions, respectively.
The FFT analysis of the detector temporal response can be used to assess the efficacy of the MLC tracking. Two methods are used to achieve this:
1. Visual inspection of the FFT spectra for each motion modality 2. Calculation of the quality factor for each motion modality
The spectra for the Sine 10 BPM motion are shown in 4.18. It can be seen that passive tracking reduces the height of the characteristic spectrum compared to the
motion case. Predictive tracking reduces this even further, however there is a large DC component in this spectrum which has not beed eliminated after subtracting the no motion spectrum. This is due to the large baseline drift that occurred for the predictive tracking modality as seen in figure 4.13. The baseline drift is not apparent in the no motion case, so the DC component for each of the modalities differs. In addition to the large characteristic peak, the signal is also comprised of secondary resonant peaks (0.34 Hz, 0.51 Hz and 0.68 Hz) and also noise.
Figure 4.18: FFT spectra for each motion modality for the 10 BPM Sine wave.
Similar spectra are produced when the same analysis is performed on the 15 and 20 BPM Sine motions, as shown in figures 4.19 and 4.20. There was no baseline drift during any of the modalities for the 15 and 20 BPM motions, so the DC component is eliminated in each of these acquisitions by subtracting the no motion spectrum.
The peak height and integral area for the peaks in each of the spectra are shown in tables 4.3, 4.4 and 4.5 for the 10, 15 and 20 BPM Sine wave motions, respec- tively.
A similar analysis can be performed on the time response obtained when the prostate motion trace was applied (figure 4.16). The FFT was computed for the temporal
Figure 4.19: FFT spectra for each motion modality for the 15 BPM Sine wave.
Modality
Integral Area
Peak Height
Quality Factor
Motion
0.0423
2.10
11
Passive Tracking
0.0157
1.04
61
Predictive Tracking
0.0142
0.25
279
Table 4.3: FFT peak integral area and height for the 10 BPM Sine wave motion. These metrics are used to calculate the quality factor.
Modality
Integral Area
Peak Height
Quality Factor
Motion
0.0436
1.53
15
Passive Tracking
0.0321
1.13
28
Predictive Tracking
0.0051
0.37
524
Table 4.4: FFT peak integral area and height for the 15 BPM Sine wave motion. These metrics are used to calculate the quality factor.
Figure 4.20: FFT spectra for each motion modality for the 20 BPM Sine wave.
Modality
Integral Area
Peak Height
Quality Factor
Motion
0.049
2.13
10
Passive Tracking
0.0316
1.48
21
Predictive Tracking
0.0126
0.37
214
Table 4.5: FFT peak integral area and height for the 20 BPM Sine wave motion. These metrics are used to calculate the quality factor.
response from each of the tracking modalities. The DC component from the no motion FFT was subtracted from each of the other FFT spectra, shown in figure 4.21.
Figure 4.21: FFT spectra for each motion modality for the prostate motion pattern
The integral area and peak height for each of the motion modalities was calculated and is shown in table 4.6.
Modality
Integral Area
Peak Height
Quality Factor
Motion
0.069
1.672
9
Passive Tracking
0.0453
1.261
18
Predictive Tracking
0.0392
0.6091
42
Table 4.6: FFT peak integral area and height for the prostate motion. These metrics are used to calculate the quality factor.
Quality factors are plotted as a function of modality in figure 4.22. Higher quality factors indicate the treatment delivery is closer to the no motion case. This means
the delivered treatment will more closely match the planned dose from the TPS. Low quality factors indicate potentially large deviations from the planned dose which has impacts on dose tracking and healthy tissue tolerance.
There is a clear trend for each of the sine motion patterns. Passive tracking is better than no tracking, however predictive tracking is far superior. The large difference between the tracking modalities can be attributed to the cyclic nature of the motion patterns. After the initial learning window the predictive algorithm is able to correctly predict the trajectory and amplitude of the Sine waves.
The prostate motion does benefit from tracking; the quality factor increases for each tracking modality. However, the extent of the improvement with predictive tracking is much lower compared to the cyclic sine waves. As discussed previously this is due to a large displacement of the prostate during the delivery that is not cyclic in nature. In this case the predictive algorithm cannot ’learn’ the motion as easily and consequently is not as effective compared to when used with cyclic motion. In this instance predictive tracking would not be recommended.
The temporal resolution offered by the detector system is able to accurately recon- struct the motion patterns provided by HexaMotion. The calculated frequencies of the Sine waves match the expected values and the quality factor can assist in evaluating tracking performance.
Figure 4.22: Quality factors for each of the motion patterns. Tracking provides a clear benefit for all motion patterns. Predictive tracking is best for cyclic motion patterns.