Evaluation of target dose inhomogeneity in breast cancer treatment due to tissue elemental differences

Five left breast cancer patients were selected from the institutional database. They were considered as a representative sample of the clinical practice. CT datasets were acquired in the supine position with 2 mm slice thickness, adjacent. Clinical target volume (CTV) was contoured on the CT dataset to encompass the whole mammary gland, and cropped 4 mm inside the skin. Additional structures were delineated: CTV_lob and CTV_fat, being the lobular and fat CTV volumes, respectively. These two last structures were contoured using a CT ranger, discriminating the two tissues with the HU = − 59 (CTV_fat where HU < − 59, CTV_lob where HU ≥ − 59, HU: Hounsfield Units). The ratio between the lobular and the fat volumes within the CTV was 0.21 ± 0.13 (range 0.11–0.40).

All the patients were planned with volumetric modulated arc therapy technique (VMAT), in its RapidArc form, on a 6 MV beam from a Varian TrueBeam linac equipped with a multileaf collimator Millennium-120 (Varian Medical Systems, Palo Alto, CA, USA). The arc geometry was of two partial arcs, with the gantry spanning from ~ 300 to ~ 170°, the collimator was of ~ ± 15°, set according to the breast shape and patient anatomy. Total dose prescription was 40.5 Gy in 15 fractions as mean CTV dose.

All the plans were generated with the Varian Eclipse treatment planning system, optimized with the Photon Optimizer (PO) algorithm (version 13.6) and calculated with Acuros XB (version 13.6). The same dose calculation algorithm was used to compute the dose distribution at least once during the plan optimization process (intermediate dose), to improve the optimization result according to an accurate dose estimation, in particular regarding the target dose homogeneity.

Patient CTs, structures and plans were exported in DICOM format from Eclipse and imported in PRIMO (version 0.3.1). PRIMO is a free computer software (http://​www.​primoproject.​net) that simulates clinical linacs and estimates absorbed dose distributions in patient CT datasets (as well as in water phantoms) [12]. It combines a graphical user interface and a computation engine based on the Monte Carlo code PENELOPE [13‐15]. A program for fast Monte Carlo simulation of coupled electron and photon transport, DPM, is also integrated [16], and used in the current work. The linac head was simulated by using the phase-space files made available by the linac vendor (Varian Medical Systems) for research purposes. Those phase-spaces were simulated into a Geant4 Monte Carlo environment and distributed according to the IAEA format [17]. In the current work, a phase-space for TrueBeam linac, 6 MV flattened beam quality, of 49.5e + 09 histories was used. Inside the patient, the transport parameters (to balance the trade-off between speed and accuracy) are predefined for DPM simulations as 50 and 200 keV cut-off energies for photons (bremsstrahlung) and electrons (collision), respectively. A variance reduction technique (splitting in CT with a factor 100) was used to reduce the computing time, that otherwise would be unacceptable if a direct approach was used. With this method, the average statistical uncertainty of all CT voxels accumulating more than 50% of the maximum absorbed dose, and reported by PRIMO at two standard deviations, was around 1% (range over all the simulations 0.99–1.08%).

The same curve to convert HU to mass density was used in PRIMO and Acuros based systems. The material assignment based on the CT number was set in PRIMO as similar as possible to the Acuros setting in Eclipse. Full compatibility of the two assignments is not viable, since Acuros assigns adjacent materials in a smooth way, allowing an overlapping HU range, where the previous and next materials are linearly combined from one to the other. The used materials are summarized in Table 1.

The specific chemical compositions as configured in the two systems, PRIMO and Acuros, are not identical in their defaults, being the hydrogen fraction in PRIMO higher than the corresponding fraction set for Acuros for most of the human tissues. To exclude a systematic error that could arise from this difference, the contribution of the various elements was modified in PRIMO for adipose and muscle tissues, to be more compatible with the Acuros materials. Figure 1 shows the elemental compositions of adipose and muscle tissues according to the PRIMO and Acuros defaults. The Acuros values were hence used in this work.

One of the patients of this study was simulated with the two chemical compositions for adipose and muscle tissues, according to the PRIMO and Acuros defaults. With the PRIMO defaults, the dose to muscle and adipose tissues were estimated higher than using Acuros defaults by about 0.12% and 0.03, respectively. Those differences, although considered negligible, were excluded from the computation by changing the PRIMO tissue composition material defaults.

For each of the five cases, three different Monte Carlo simulations were computed in PRIMO, assigning different materials to the muscle and adipose HU ranges, while keeping the original density:

- AdiMus: as standard, muscle and adipose tissues were assigned to the muscle and adipose HU ranges, respectively;

- Adi: the adipose tissue material was assigned to the HU including both adipose and muscle ranges;

- Mus: the muscle tissue material was assigned to the HU including both adipose and muscle ranges.

Mean doses to CTV, CTV_lob and CTV_fat were computed for all the simulations.

The dose difference generated by the chemical composition of the specific tissue, lobular or fat, was estimated by the difference of the mean doses of the CTV_lob between Adi and AdiMus simulations, and of the difference of the mean doses of the CTV_fat between Mus and AdiMus simulations. Those values give the possible dose estimation error when a different material chemical composition (adipose for lobular tissue, or muscle for fat tissue) is used for calculations, while the surrounding tissue dose is computed with the correct tissue assignment. Calculations were based on the mean dose of the whole structure. Uncertainties were reported at two standard deviations for all the voxels in each specific structure.

To include also the positional dose difference, the 3D gamma evaluation available in PRIMO software was analysed. The gamma index [18] was evaluated between AdiMus simulation (the best approximation of the true patient), and Adi or Mus simulations for CTV_lob and CTV_fat, respectively (i.e. assigning the “erroneous” material to the two portions, respectively). For the gamma criteria, the distance to agreement (DTA) was set to 2.5 mm, equal to the simulation grid, as well as to half of this value, 1.25 mm; the delta dose was varied from 0.5 to 3.0% of the maximum dose. No threshold dose value was limiting the evaluation, that was performed only inside the target (close to the prescription dose level). However, the analysis was restricted to the points with reference dose having uncertainty below 70%.

For one patient, two additional simulations were run, assigning to the HU range of the CTV the cartilage and the cortical bone tissues, keeping the original density. This would emphasize the importance of properly assigning the correct tissue (elemental composition) to the HU ranges.

Comparison of the PRIMO computed results was performed with Acuros calculations, as implemented in Eclipse (version 13.6). Acuros explicitly solve the Linear Boltzmann Transport Equation, while Monte Carlo methods (as PENELOPE in PRIMO) generate a stochastic solution by simulating a large finite number of particles. In principle, the two methods should lead to the same solution. However, non-negligible approximations are used in the radiotherapy planning practice. One of the most crucial is the material composition and assignment to pre-defined HU ranges, which is not modifiable in Acuros. This reason prevented the calculations in settings similar to the above-described Monte Carlo simulations (AdiMus, Adi, Mus). Nonetheless, to evaluate the dose difference generated by the elemental composition of tissues estimated by Acuros, dose calculations were performed also with AAA (Anisotropic Analytical Algorithm) implemented in Eclipse. The two algorithms used the same machine configuration data, and are based on the same concepts of the beam source model [19]. AAA does not take into account the specific tissue composition, and inhomogeneities are managed by rescaling the density according to HU, with no differentiation in the energy deposition for different materials (no medium differentiation). The differences arose in Acuros due to the chemical composition of the tissues were evaluated through the differences of the mean doses in CTV_lob and CTV_fat for Acuros and AAA calculations, once the two plans were renormalized to the same mean dose to CTV. This is clearly a very crude approximation to isolate the medium composition effect on the calculated dose.

The analysed patients presented a mean HU of − 14 ± 10 and − 103 ± 3 in the lobular and fat portions of CTV, respectively. The Standard Deviations of the HU distributions inside CTV_lob and CTV_fat were 26 ± 2, and 21 ± 9, respectively. To notice is the quite stable HU values in the lobular and fat portions of breast among patients.

In Fig. 2 the average (over the analysed patients) HU histograms is presented, where the two peaks are well separated, although an overlap is present, due most probably to the structure contours inaccuracy (the CTV_lob was defined as the CTV voxels with HU larger than − 59).

A cumulative dose-volume histogram example of one of the selected patients is presented in Fig. 3. Here, the CTV, CTV_lob and CTV_fat were presented for AdiMus, Adi, and Mus simulations. As expected, the AdiMus and Adi simulations estimated the same dose distributions in CTV_fat, while in CTV_lob this happens for AdiMus and Mus simulations.

Table 2 reports the percentage dose differences between the mean dose of the specific CTV portions of the test simulation, and the CTV mean dose from AdiMus simulations. The AdiMus CTV mean dose can be considered the standard condition for planning and dose prescription. The reported errors are the average statistical uncertainties in each specific structure, at 2 standard deviations, propagated for all the patients.

The possible dose overestimation in the lobular breast region, relative to the prescribed dose, when adipose tissue is there assigned, is of 1.25 ± 0.45% (considering the difference of the mean doses from AdiMus and Adi simulations in the lobular fraction). Conversely, the possible dose underestimation in the fat region of the breast if muscle tissue is assigned is of 1.14 ± 0.51% (the differences of the mean doses from AdiMus and Mus simulations in the fat fraction). In the case of cartilage and bone assignments, a dose underestimation was evaluated of 0.6% and 2.8, respectively in the lobular fraction, and of 1.8% and 4.1 in the fat fraction.

All those differences are generated by the lone difference in elemental composition of the tissues, since the specific density of each voxel is allocated from the HU value.

The gamma evaluation analysis was summarized in Fig. 4, where the percentage of points fulfilling the criteria is shown for CTV_lob and CTV_fat comparing AdiMus vs. Adi and AdiMus vs. Mus simulations, respectively. From those graphs, a large amount of the structure volume is shown not to fulfil the criteria below a dose difference compatible with the difference estimated just above, between 1 and 1.5%.

The computed gamma evaluation presented an agreement for DTA = 2.5 mm and delta dose of 0.5% exceeding the 90–95% of the CTV_lob and CTV_fat volumes for AdiMus vs. Mus and AdiMus vs. Adi comparisons, respectively (that is between the simulations with muscle in the CTV_lob, and adipose in the CTV_fat, not shown in Fig. 4). This is consistent with the average uncertainty of the simulations, around 1% at two standard deviations.

Concerning the clinical use of tissue differentiation in Acuros, the results showed a dose overestimation of the AAA (where no chemical composition is taken into account) in the lobular portion of breast of 0.98 ± 0.06%, and an underestimation of 0.21 ± 0.14% in the fat portion. Interesting to note is a better homogeneity between doses in the lobular and fat regions of the CTV found for the Acuros calculated plans, while the AAA recalculation presented an overdose to the lobular region of about 1%. The reason of an increased homogeneity in the Acuros calculated plan resides in the optimization process, which used Acuros calculation as intermediate dose to refine the optimization and improve the target dose homogeneity. If the optimization process uses a less accurate dose calculation algorithm for intermediate dose estimation (AAA), in these specific cases of breast planning, the lobular portion of then breast will be underdosed by 1%.