In comparison with the approach detailed by van Herk et al [13], we can see that the margin recommendations presented here are similar for some situations. Although the van Herk formula makes no accounting for target size, we can compare the margin recommendations based on the van Herk et al. ‘linear approximation of the random component for 95% dose coverage’. This is a simple formula which approximates the margin required to compensate for target motion as ‘0.7σ’ where σ is the standard deviation of the motion. The approach of van Herk et al. seeks the margin that results in 95% of the prescribed dose covering the target for 90% of patients. These results are presented in Table 6.6.
Standard Deviation (cm) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
van Herk Approximation 0.7 (mm) 1.4 2.1 2.8 3.5 4.2* 4.9* 5.6*
2.6 cm FHWM 0.5 1.5 2.9 4.6 6.8 9.4 12.5 15.9
5.6 cm FWHM 0.3 0.9 1.8 3.1 4.7 6.7 8.9 11.6
10.1 cm FWHM 0.2 0.7 1.4 2.4 3.7 5.3 7.1 9.30
Table 6.6: A comparison of the margin recommendations presented in this work in comparison with the commonly used van Herk recommendations. For small targets, the recommended mar-
gins are similar, but for larger targets D95 can be maintained with less additional margin than
suggested by van Herk et al. Since van Herk et al. only claim accurate approximation of the formula used up to a standard deviation of 0.5 cm, the values marked with an asterisk are noted as an extrapolation.
For small targets, the margin recommendations are similar. For larger targets, the results computed in this study suggest less additional margin is required. The differences in margin recommendations likely arise due to differences in the approach to the problem. The approach of
van Herk et al. is to find margins that satisfy the majority of the population of patients studied. However if a patient specific approach to margin selection is taken, there is opportunity for reduced target margin for patients with larger sized targets. This can be seen in the comparison table above where patients with small target motion (PDF SD < 0.4 cm) have smaller margin recommendations from this work as compared to van Herk et al.
6.10
Summary
Target motion was simulated for a wide range of breathing traces and target sizes in order to determine the loss of target dose coverage. Statistics describing the range of breathing traces were presented. It was shown that breathing trace amplitudes in this large data set ranged from 0.13 to 2.30 cm with an average amplitude of 0.73 cm. The standard deviations of the PDFs in the data set ranged from 0.057 to 1.13 cm with an average standard deviation of 0.34 cm.
A quadratic function used to describe the loss of target dose coverage in terms of the standard deviation of the PDF describing the motion of the target was found to correlate strongly with the
data set (R2 = 0.9821). The size of the target along the direction of motion was also found to
influence the amount of coverage being lost, with larger targets being less susceptible to loss of dose coverage due to motion. The recovery of target dose coverage was also found to correlate with the PDF standard deviation, and these two trends were used to generate margin recommen- dations. A table of margin recommendations based on the PDF standard deviation and target size was presented in Table 6.2. These margins can be applied in a clinical situation to compensate
for the reduction of the target’s D95due to intrafraction motion.
An example application of the use of the methodology and margin recommendation table was presented for a small target and extreme motion. This example demonstrates how the table
can be used to ensure adequate dose coverage of the target volume. The influence of the studied motions on a set of clinical treatment plans was also assessed. This assessment demonstrated the interplay between target size, dose gradient and standard deviation of the target motion.
Finally the margins recommended in this thesis were compared with published recommenda- tions from other authors who also took advantage of the convolution model to assess the impact of target motion on target dose coverage. The margins presented here are comparable to those presented by other authors under some circumstances, however the inclusion of dependence on target size presented in this thesis offers opportunity for smaller margins for some patients, as compared to the other recommendations.
Chapter 7
Convolution Model Sensitivity Analysis
7.1
Introduction
In this thesis a convolution technique has been applied to determine the impact of intrafraction lung motion on absorbed dose. As shown previously, a patient specific lung PDF was derived from 4DCT data, and the gradient of the PDF was convolved with the static dose profile to obtain a blurred or motion-impacted dose gradient along the superior-inferior direction. The blurred dose gradient was then integrated along the superior-inferior direction to obtain the blurred dose profile. This technique was developed in Chapter 4 using Equation 4.8, expanded with clinical examples in Section 4.5, and demonstrated graphically in Figures 4.7 to 4.11. Using a dynamic, tissue equivalent phantom programmed for clinical breathing patterns and radiochromic film for dose measurement, the convolution technique described above was validated experimentally and the results were summarized in Chapter 5.
In Chapter 6, breathing patterns from 502 patients were used to simulate the effect of in- trafraction motion on static dose profiles obtained from a standard treatment plan designed to
cover targets ranging from 2-10 cm in diameter. D95 was selected as the metric for comparing
static and motion-impacted dose profiles based on clinical importance and the relative D95was
defined as the ratio of the blurred D95to the static D95. After analysis it was determined that rel-
ative D95has a quadratic dependence on the standard deviation of the static dose profile and this
is shown in Figures 6.5 and 6.7 and Table 6.1. A program was written in MATLAB to calculate the additional beam width (ABW applied to the static dose profile) that is required to restore the high dose region impacted by lung motion. Table 6.2 shows ABW as a function of the standard deviation of the PDF and also the FWHM of the static dose profile.
In addition to the conformal treatment plan, a 3-field, 4-field and a VMAT plan were also
analyzed with the 502 patient breathing patterns to assess impact on relative D95and the validity
of recommended margins in Table 6.2. The results were shown in Figure 6.9 and the conclu- sion was that Table 6.2 is valid for conformal and more complex planning techniques including multiple beams and arcs.
In Section 6.8, the margin recommendations were tested experimentally using a treatment plan with a single beam of FWHM = 2.6 cm and the dynamic lung phantom programmed for a lung PDF with SD = 0.8 cm. These parameters were chosen to simulate a Stereotactic Radiation Surgery (SRS) treatment and to test the extreme margin recommendations from Table 6.2. The
results from Figure 6.13 show that D95is restored with the recommended margins at the expense
of lower dose spillage adjacent to the target due to a wider field. This effect is shown in Figure 7.1. The intersection points of the blurred dose profiles (with and without ABW) and the static dose profile are highlighted in the figure with ovals.
Figure 7.1: The D95is restored with the additional beam width, however it comes at the expense
of lower dose spillage adjacent to the target. The intersection points of the blurred dose profiles (with and without ABW) and the static dose profile are highlighted in the figure with ovals.