Biomechanical rectal models were generated for 26 patients from the kVCT planning data, and the dose was calculated to the FE-DSM. These patients were a separate cohort to the patients investigated in the motion study in Section 5.2. Different rectal deformation scenarios were simulated in Abaqus, as detailed below. Deformations were applied to the DICOM RT STRUCT contours in MATLAB at the pre-processing stage whilst generating the input file for Abaqus. The model was constructed following the methods described in Section 5.1. Final simulation positions were exported so that resulting delivered dose could be calculated in MATLAB. Due to the different starting contours for each patient, dose differences were reported relative to the baseline dose, and were parameterised using EUD and maximum point dose.
5.3.2.1 Uniform expansion
Rectal contours from the kVCT planning scan were expanded radially, by 1, 2, 3, 5, 8, 10, 15, and 20 mm, and contracted by -1, -2, -3, and -5 mm, uniformly across all planes of the rectal contour. This is illustrated for a sample of contraction and expansions for a single patient in Figure 5.7. Values were selected to incorporate a representative range of rectal motion.
5.3 Sensitivity of dose response to simulated rectal motion 85
The minimum diameter across all rectal contours for all patients was 13 mm, so simulating contractions of the rectal radius by an absolute value greater than 5 mm was not possible. For each patient, the coordinates of the rectal contour were extracted from DICOM structure files, and radially expanded in a polar coordinate system. Expansions were applied uniformly to each slice along the full length of the rectum. This resulted in 13 simulations per patient, including a baseline measurement with zero expansion.
(a)FEM simulation of uniform expansion where dose is shifted by expansion coefficient, scenario (i)
(b)FEM simulation of uniform expansion where no dose shift is applied, scenario (ii) Fig. 5.7
5.3.2.2 Non-uniform expansion
For a separate patient cohort of 76 patients, as defined in Section 5.2, geometric measurements were taken from rectal contours at the reference slice (the slice containing the most anterior point of the kVCT prostate contour) and 7 slices in both the superior and inferior directions, on each of the 37 daily MVCT scans. The number and location of slices within each fraction’s MVCT scans set varies, with a mean of 12 slices per scan [range: 8-17]. Data were included where slice measurements were available for 15 or more patients, each containing 5 or more scan sets (i.e. a combined minimum of 75 contours per slice). The purpose of performing simulations based on extremes of measured patient contours was to determine the maximum dose deviation from baseline for a single fraction, and to explore the approximate accumulated effect based on the mean measured contour position.
Fig. 5.8Radial rectal expansions as measured from 76 patients, as described in Section 5.2. Radius dimensions are mirrored about the origin to mimic the physical cross section of the rectum. Mean radii were measured across all fractions and patients, for each slice of the rectal contour. Maximum and minimum values were the largest measured absolute expansion or contraction from baseline from any fraction or patient. The 95th percentiles (95% max and min) were calculated from the max and min across all patients to remove the effect of outliers. The zero slice is the registration origin, and positive slice number indicates cranial direction, negative slice indicates caudal direction. Slice thickness was 6 mm.
Using MATLAB’s standardregionpropsfunction, the equivalent diameter for each slice was calculated as the diameter of a circle with the same area as the segmented contour. Across all patients and fractions, the mean, global maximum, and global minimum equivalent diameters were measured per slice. Global maximum and minimum represented the most extreme measurements across all patients (with final slicewise values not necessarily from the same fraction or patient). To reduce the effect of outliers, the 95th percentiles of maximum and minimum values across all patients were also calculated for each slice. For each of the 5 sets of parameters (mean, maximum, 95th percentile maximum, minimum, 95th percentile minimum), the differences between MVCT and kVCT equivalent diameters were calculated and halved to find magnitudes of radial expansion to be applied to the rectal simulation. Radial expansions were non-uniformly applied along the length of the rectum, i.e different expansions were applied at each slice as shown in Figure 5.8, to the kVCT planning contours for 26 patients in this sensitivity analysis. An example is shown in Figure 5.9.
5.3 Sensitivity of dose response to simulated rectal motion 87
(a)FEM simulation of non-uniform expansion where dose is shifted by expansion coefficient at the zero slice, scenario (i)
(b)FEM simulation of non-uniform expansion where no dose shift is applied, scenario (ii) Fig. 5.9
5.3.2.3 Dose shifting
Each set of simulations described above (uniform and non-uniform expansions) was per- formed twice in order to model different clinical scenarios in terms of dose delivery; scenario (i) the planned dose is shifted correspondingly, scenario (ii) the planned dose position remains static, unaffected by the rectal deformation. Because daily image guidance was used, target coverage was achieved through matching to the planning target volume (PTV) [81] contour via positional couch shifts or gantry rotations. Both scenarios are illustrated in Figure 5.6.
Scenario (i), assumes that rectal expansion induces prostate motion, i.e. when the rectum expands (or contracts), the prostate is consequently shifted anteriorly (or posteriorly) by the same magnitude. The planned dose would then be shifted and matched to the prostate, which in practice is achieved by altering the height of the treatment couch. This would be the case in the region where the rectum is connected to the prostate via a thin layer of fibrous tissue, the Denonvilliers’ fascia [19]. In this investigation, this effect was achieved for uniform expansion by shifting the dose by the magnitude of the radial expansion, and for non-uniform expansion by shifting the dose by the magnitude of the radial expansion observed at the reference slice.
Scenario (ii) assumes that the rectum moves independently of the prostate, i.e. where the rectum is adjacent to the prostate, and the prostate position remains fixed, the rectum can
expand into ‘prostate space’, effectively compressing the prostate or causing the prostate gland to become ‘dog-eared’ in shape (see Figure 5.6). This would cause the rectum to shift further into the high-dose region, and no adjustment to the planned dose position would necessarily be made as target coverage is priority. Further from the prostate, this assumption allows rectal expansion without affecting the position of the prostate (or planned dose). In the case of contraction in scenario (ii), the assumption is that the rectum contracts away from the prostate without affecting its position. Both scenarios are clinically plausible and represent the extremes of a range in which the real clinical situation lies within.
5.3.2.4 Normal tissue complication probability
To understand the clinical implications of the simulated dose variations caused by rectal expansion and contraction, dose differences were translated into NTCP. A univariate binary logistic regression model was developed using EUD as the input variable, as a predictor of CTCAE Grade 2 rectal bleeding or above. The model was constructed following approaches by Schaake et al. [140], and parameters (Eq. 5.2) were optimised on data from 109 discovery cohort patients (as discussed in Chapter 4) in order to be distinct from the patients used in this study. NTCP was calculated using Eq. 5.1. The resulting sigmoidal relationship between EUD and NTCP is illustrated in Figure 5.10.
NTCP= 1
(1+e−S) (5.1)
whereSis defined as:
S=−19.706+0.302(EU D) (5.2)
Fig. 5.10NTCP model for rectal bleeding based on EUD, developed using univariate logistic regression on 109 patients from the discovery cohort.
5.3 Sensitivity of dose response to simulated rectal motion 89
5.3.3
Results
5.3.3.1 Uniform expansion
Where uniform rectal expansion induced a shift to prostate position, and hence dose po- sitioning (scenario (i)), ∆EUD increased with rectal contraction (+1.8 Gy, SD 0.4 Gy, at -5 mm), and decreased with rectal expansion (-4.0 Gy, SD 0.5 Gy, at +20 mm), as shown in Figure 5.11a. The magnitude of change in EUD was much greater than the change observed for maximum point dose, which was less than±0.15 Gy from baseline across the full range of expansions from -5 to +20 mm (Figure 5.11b). Contractions less than -5 mm were not possible to simulate due to the narrow baseline contour diameters of some kVCT contours (minimum 13 mm). Across the measured range, EUD dose-response was represented using a second-order quadratic line of best fit (LOBF). Using this fit, the predicted change in EUD for a reduction in rectal diameter of -1 cm was +1.6 Gy, and an increase in diameter of +1 cm was -1.4 Gy, across the full course of treatment. This is of the order of magnitude of dose delivered in a single fraction.
Assuming scenario (ii), where rectal expansion did not induce an anterior dose shift, the EUD dose-response is in the opposite direction to scenario (i); as shown in Figure 5.11a, an increase in diameter results in an increase in EUD with respect to baseline, andvice versa. The maximum increase in EUD was +1.1 Gy (SD 0.9 Gy), occurring after +2 cm increase in diameter. After this, there was a reduction in EUD which suggests that the low-dose contribution to the rectal wall begins to dominate as the maximum dose stabilises. Beyond this, the proportion of voxels receiving a lower dose increases relative to voxels receiving a high dose. The LOBF applied to the EUD dose-response was a third order polynomial. Using this fit, a reduction in rectal diameter of -1 cm corresponded to a reduction in EUD of -2.1 Gy, and +1 cm resulted in +1.0 Gy, when the change is held constant across the full course of treatment.
Maximum dose-response was of greater magnitude than scenario (i), and in the same direction as EUD response until around the point of EUD dropoff after an increase of 2 cm in diameter, where the maximum dose reaches a plateau of around 0.6 Gy (Figure 5.11b).
For each patient, the resulting EUDs from the expansion simulations for each scenario were input into the NTCP model (Equation 5.1). These were plotted in Figure 5.12, and both scenarios were modelled using third order polynomials as the LOBF. From simulated measurements, for scenario (i) based on dose shifted results, an average of 1 cm reduction in rectal diameter increased NTCP by +11.8 % (SD 3.6 %) due to a higher proportion of the rectum receiving a higher dose and hence increased NTCP. An average increase of 1 cm in rectal diameter reduced NTCP by -6.0 % (SD 2.1 %).
(a)
(b)
Fig. 5.11Results of uniform rectal expansion simulations for (a) equivalent uniform dose (EUD) and (b) maximum point dose differences from baseline, over 37 fractions. ‘With dose shift’ shown in blue implies scenario (i) from Section 5.6, and ‘no dose shift’ shown in orange implies scenario (ii). Polynomial lines of best fit (LOBF) and correspondingR2are included in (a). Error bars are standard deviation of mean EUD and maximum point dose measured across all patients and increase with expansion to reflect the reduction in the number of successfully executed simulations.
5.3 Sensitivity of dose response to simulated rectal motion 91
Fig. 5.12Change in NTCP due to uniform rectal expansion scenarios based on changes in EUD over 37 fractions. ‘With dose shift’ shown in navy implies scenario (i) from Section 5.6, and ‘no dose shift’ shown in red implies scenario (ii).
Table 5.1Predicted changes in EUD and NTCP for representative expansions to rectal diameter based on LOBF equations for uniform expansion simulations. Figures are representative assuming stated change is maintained throughout treatment.
With dose shift, scenario (i) No dose shift, scenario (ii)
∆rectal diameter ∆EUD (Gy) ∆NTCP (%) ∆EUD (Gy) ∆NTCP (%)
-1 cm +1.8 +11.8 -2.1 -10.2
+1 cm -1.3 -6 +0.8 +4.0
For scenario (ii) based on no dose shift, an average 1 cm reduction in rectal diameter reduced NTCP by -10.2 % (SD 4.3 %) where the rectum is contracting away from the prostate and hence high dose region. An average increase of 1 cm in rectal diameter increased NTCP by +4.0 % (SD 1.6 %), in contrast to scenario (i). The maximum increase at the point of inflection in scenario (ii) at 2 cm increase to the rectal diameter was +4.9 % (SD 1.6 %) NTCP.
5.3.3.2 Non-uniform expansion
Non-uniform expansions demonstrated similar trends in dose response as results from uniform expansions (Figure 5.13). For scenario (i), where dose was shifted by the magnitude of the radial expansion at the corresponding reference slice,∆EUD increased with rectal contraction to a maximum of +4.0 Gy (SD 0.7), and decreased with rectal expansion to a minimum of -6.9 Gy (SD 1.7). The change in maximum dose also increased with contraction, and reduced with expansion, but effects were less than±0.4 Gy. For scenario (ii) where no dose shift occurred, EUD reduced with rectal contraction to a minimum of -3.7 Gy (SD 2.0), and increased with expansion to a peak of +0.6 Gy (SD 0.9) before reducing to -0.3 Gy (SD 1.3), similar to the behaviour observed in Figure 5.11. Maximum dose changes were greater for scenario (ii), ranging from -2.2 Gy (SD 2.2) at minimum contraction, to +0.8 Gy (SD 0.7) at maximum expansion.
Predicted change in EUD based on rectal expansion was calculated using the LOBF equations derived from uniform expansion results, using the expansion at the reference slice as the input. Predicted values are represented by the dotted line in Figure 5.13a. These generally underestimate the deviation from baseline EUD (by 1.8 Gy at minimum contraction and 2.7 Gy at maximum expansion for scenario (i), and 0.6 Gy at minimum contraction for scenario (ii)). Expansion results for scenario (ii) were within 0.6 Gy of predicted values.
Changes in EUD were input into the NTCP equation 5.1 and plotted in Figure 5.14. The mean NTCP at baseline was 22.9 % (SD 10.7). The change in NTCP with dose shift, scenario (i), ranges from +23.7 % (SD 7.0) at minimum rectal contraction, to -16.1 % (SD 6.2) at maximum expansion. Where no dose shift is applied, scenario (ii), minimum rectal contraction corresponded to a reduction in NTCP of -11.2 % (SD 5.1), with a peak increase at the 95th percentile maximum expansion of +3.2 % (SD 4.8), before reducing to +0.7 % (SD 4.4) at maximum expansion.
5.3 Sensitivity of dose response to simulated rectal motion 93
(a)
(b)
Fig. 5.13Results of non-uniform rectal expansion simulations for (a) equivalent uniform dose (EUD) and (b) maximum dose differences from baseline. ‘With dose shift’ shown in blue implies scenario (i) from 5.6, and ‘no dose shift’ shown in organge implies scenario (ii). Magnitudes of expansions are shown in Figure 5.8. Error
Fig. 5.14Non-uniform rectal expansion scenarios and impact on NTCP, based on changes in EUD. ‘With dose shift’ shown in navy implies scenario (i) from Section 5.6, and ‘no dose shift’ shown in red implies scenario (ii). Error bars indicate standard deviation. Dotted lines indicate predicted change in NTCP using the line of best fit equations, where the magnitude of rectal expansion used as input into the equation was taken at the reference plane. Average NTCP at baseline was 22.9 % (SD 10.7).
Using the LOBF equations derived from uniform expansion results, the predicted change in NTCP was calculated for non-uniform expansions, based upon the change in rectal radius at the reference slice (dotted lines, Figure 5.13a). For scenario (i) where a dose shift is applied, the predicted dose underestimated the measured simulated change in NTCP (closer to baseline by 7.8 % and 5.8 % at minimum and maximum expansions, respectively).
5.3.4
Discussion
Rectal models for 26 patient were simulated in the FEA environment Abaqus based on manually segmented contours from the kVCT planning scan. Models were expanded (and contracted) either uniformly, where incremental expansions were applied to all slices of the rectal simulation, or non-uniformly, where expansions varied in the z-direction according to the measured deformations from patient data at each slice. Expansions were applied radially, but in practice the rectal diameter is measured on the IGRT image at the time of treatment, so to discuss in terms of diameter is more clinically relevant.
For each simulation, two dose scenarios were investigated; (i) where rectal expansion resulted in a dose-shift, (ii) where no dose shift was applied. These scenarios were designed to
5.3 Sensitivity of dose response to simulated rectal motion 95
investigate the extremes of a clinical IGRT scenario and demonstrate different dose-response behaviours. However, within each scenario the direction of the dose and NTCP responses agreed for uniform and non-uniform expansions.
Scenario (i) suggests that where rectal expansion causes the prostate to move, and the dose to be shifted accordingly, that rectal expansion causes EUD to reduce, and rectal contraction causes EUD to increase. Hence, a narrower rectal diameter with respect to the planning scan would be associated with an increased likelihood of developing toxicity. This result implies that achieving as narrow a rectal diameter as possible at the time of the kVCT planning scan is therefore desirable, as further narrowing throughout the course of treatment would be less probable. On-treatment clinical imaging protocols often define tolerances for the maximum acceptable rectal diameter, but do not specify a minimum diameter. Furthermore, often patients will be instructed to empty their bowels if the rectum is deemed outwith the maximum tolerance. Results for scenario (i) suggest this practice may need revising, as larger rectal diameters are associated with decreased dose and NTCP, whereas narrower rectums should be monitored. Thor et al. [155] reported findings that narrower rectums on the planning CT scan were associated with higher rates of morbidity. However, VoxTox results presented in Section 5.2 showed that kVCT diameter was not indictive of MVCT diameter, and hence delivered dose. Maximum dose appeared to be fairly independent of rectal wall expansion or contraction, varying by less than±0.4 Gy.
The results for scenario (ii) are more intuitive, whereby the EUD increases as the rectum expands into the static high-dose region, and reduces as the rectum contracts away from it. The EUD reaches a peak and begins to reduce as the maximum dose begins to plateau. This response suggests that at this point, as the rectal radius increases, the proportion of the rectum receiving a lower dose is increasing greater than the proportion of the rectum receiving a higher dose, resulting in a reduction in EUD.
The direction of the dose response for each scenario agreed between uniform and non- uniform expansions. For scenario (i), rectal expansion resulted in a reduction in dose and NTCP. This suggests that with an increase in rectal diameter, the proportion of rectal wall receiving a high dose level is reduced, and the risk of toxicity is lowered. Rectal contraction resulted in an increase in dose and NTCP, at a greater rate than expansion results. For uniform expansion with a corresponding dose shift, dose response was modelled using polynomials and can be interpreted for clinical purposes as approximately: a reduction of -1 cm in rectal diameter results in an increase of +1.5 Gy (or +10 % NTCP), and an increase in rectal diameter of 1 cm corresponds to a reduction of -1.5 Gy (or -5 %), where the rectum remains abutting the prostate maintained over the course of treatment. The results
for non-uniform expansion suggest that these may be under-estimations of the magnitude of the dose/NTCP-effects.
When comparing simulated dose measurements for non-uniform rectal expansions with predicted dose measurements from the equations derived for uniform rectal expansion simulations for scenario (i), the predicted values underestimate the absolute effect on EUD, but are within the bounds of the standard deviation error bars (with the exception of minimum expansion). The differences may be due to expansions only being applied to the central 15 slices, and slices outwith this range, where the dose is equal to the original planning dose, may be negatively influencing the EUD calculation. Additionally, radial expansions used in the prediction calculation, were from the reference slice, but the magnitude of the expansion at each slice varied, which was not accounted for in the prediction model.
For scenario (ii), the trend of the dose response with expansion and contraction from uniform simulations were generally in agreement with non-uniform simulations. The changes