Abstract | U doktorskoj disertaciji su prikazani metoda i rezultati vrednovanja točnosti izračuna apsorbirane doze računalnih algoritama koji se primjenjuju u radijacijskoj onkologiji. Metoda se temelji na primjeni Monte Carlo (MC) simulacije i komplementarna je postojećoj eksperimentalnoj metodologiji. MC simulacija je provedena korištenjem programskog paketa Monte Carlo N-Particle (MCNP). Istraživanje je provedeno za računalni algoritam sustava Elekta Monaco (MCTPS) kao jedan od najnaprednijih algoritama koji se trenutno koriste za planiranje jakosno modulirane radioterapije. Taj algoritam izračun apsorbirane doze dijelom temelji na MC simulaciji. On izračunava apsorbiranu dozu u malom volumenu sredstva koji se nalazi u sredstvu (D_m,m) te pruža mogućnost izračuna apsorbirane doze u vodi (D_w,m). Vrednovanje je provedeno za oba načina izračuna. Da bi se pouzdano utvrdila točnost MCNP izračuna apsorbirane doze bilo je potrebno dozimetrijski vrednovati rezultate MCNP modela 6 MV X-zraka u vodenom fantomu. MCNP simulacije provedene su u 13 postava homogenih fantoma različitih gustoća u rasponu od 0,2 g/cm^3 do 2,17 g/cm^3. Dodatno, vrednovanje je provedeno u složenim geometrijama kojima se nastojalo simulirati stvarne situacije. U heterogenoj geometriji istraživanje je bilo ograničeno na tri materijala gustoća usporedivih s gustoćama pojedinih vrsta tkiva. Osmišljena i simulirana su 4 različita scenarija za ispitivanje utjecaja heterogenosti na točnost izračuna apsorbirane doze u MCTPS, za oba načina izračuna, D_m,m i D_w,m. Korišten je fantom istih dimenzija kao kod izračuna u homogenoj geometriji, s razlikom što su na različitim dubinama dodavani umeci različitih gustoća. Odstupanja su izračunata pomoću korijena srednje vrijednosti kvadrata odstupanja (engl. root mean square deviation, RMS) za krivulje ovisnosti doze o dubini (DD). DD krivulje su izračunate pomoću MCNP programskog paketa te uspoređene s MCTPS izračunima. Također, za svih trinaest materijala ispitivana je točnost uračunavanja doprinosa različitih vrsta međudjelovanja u MCTPS izračunu apsorbirane doze. Prema rezultatima istraživanja, MCTPS način izračuna apsorbirane doze u sredstvu pokazuje RMS odstupanja u odnosu na MCNP izračun manji od 3% za sve materijale, osim za materijal najmanje gustoće (RMS=4,8%). Analiza rezultata između izračuna doza u vodi, nastao pretvorbom iz izračuna doze u sredstvu, i MCNP simulacije izračuna doze u vodi, pokazuje znatna odstupanja za većinu korištenih materijala, do najviše vrijednosti RMS = 13,1% za materijal najveće gustoće. Utvrđeno je da se izračun doze u vodi (D_w,m) koji je nastao pretvorbom iz izračuna doze u sredstvu bitno razlikuje od izračuna doze u vodi (D_w,w) i da ih treba razlikovati. Također, utvrđeno je da za različite materijale apsorbirana doza izračunata kao doza u sredstvu pokazuje bolje slaganje s algoritmima koji izračunavaju apsorbiranu dozu primjenom koncepta Dw,w, pri čemu najveće RMS odstupanje iznosi 3,7% za materijal najveće gustoće. U području gustoća manjih od vode potrebna su poboljšanja izračuna doza u sredstvu (D_m,m) te je predložena korekcija HU-RED krivulje i na taj način je RMS odstupanje smanjeno s 4,8% na 2,8%. Nadalje, s porastom atomskog broja materijala (počevši od materijala gustoće 1,66 g/cm3) utvrđeno je odstupanje u uračunavanju doprinosa fotoelektričnog učinka kao i doprinosa tvorbe para elektron-pozitron. Odstupanja u uračunavanju doprinosa fotoelektričnog učinka u izračunu apsorbirane doze od 1,3% do 1,7% utvrđena su za materijale gustoće od 1,66 g/cm^3 do 2,17 g/cm^3 na dubini od 5 cm. Ispitivanje točnosti uračunavanja doprinosa tvorbe para elektronpozitron na dubini od 10 cm pokazuje trend povećanja odstupanja do maksimalnog odstupanja od 2,3% za materijal gustoće 2,0 g/cm^3. Prikazani rezultati upućuju da MCTPS izračun apsorbirane doze kao doza u sredstvu (D_m,m) predstavlja točniji način izračuna apsorbirane doze. |

Abstract (english) | The most advanced treatment planning systems (TPSs) in radiation oncology have Monte Carlo (MC) based algorithms which facilitate the most accurate calculation of absorbed dose distributions in (external beam) radiotherapy. Such algorithms inherently calculate absorbed dose as dose to medium in medium (D_m,m), but also provide the ability to calculate absorbed dose as dose to water in medium (D_w,m) by converting the calculation from D_m,m to D_w,m using Spencer-Attix's extension of Brag-Gray small cavity theory. According to published data, differences between these two calculation options are noted, particularly in bony structures. Unlike the generalized MC codes (MCNP, EGS, GEANT...) several approximations and simplifications were introduced in such algorithms to speed up the calculation time. Thus, additional validation of calculation accuracy for both abovementioned calculation options is required. This doctoral dissertation presents the method and the results of a verification, complementary to the existing experimental methodology, for the accuracy validation of such algorithms using MC simulations. It was performed using Monte Carlo N-Particle code® (MCNP) by which the transport of photons and electrons is simulated. Algorithms used in radiation oncology calculate the absorbed dose without knowledge of the material chemical composition. Therefore, the investigation of the impact of material chemical composition on calculation accuracy was performed using MCNP calculations. Furthermore, the majority of clinical experience is based on the dose to water in water (D_w,w) concept provided by analytical algorithms and it has represented the standard for dose calculation during the past several decades. Considering that, additional MCNP calculation was performed to simulate the D_w,w concept of absorbed dose calculation. Hence, the deviation between the D_w,w and both calculation options provided by the MC based algorithms was determined. Additionally, the influence of predefined probabilities for X-ray interaction mechanisms and its respective contributions to absorbed dose calculations was validated using MCNP. Futhermore, in order to improve the accuracy of absorbed dose calculation for the D_m,m MCTPS calculation option, a correction for the HU-RED curve was applied. The impact of the proposed corrections on the accuracy of the absorbed dose calculation was also validated. Materials and methods: The calculation algorithm for intensity modulated radiotherapy (IMRT) built in the Elekta Monaco TPS is based on MC simulation. Its absorbed dose calculation has three components: a virtual source model (VSM), a transmission filter, and a patient model. The MC simulation is applied only in the final part of the calculation using X-Ray Voxel Monte Carlo (XVMC). Absorbed dose is calculated as Dm,m, but the conversion from Dm,m to Dw,m is enabled as well. In order to investigate the MCTPS absorbed dose distribution calculation accuracy for 6MV photon beam in various geometries, MCNP simulation was performed. To determine the accuracy of the MCNP absorbed dose calculation in any geometry, it is necessary to dosimetrically validate the results of the MCNP 6 MV X-ray beam model with the values measured using an ionization chamber in a water phantom. A virtual phantom of the same dimensions, 30×30×30 cm^3, as for MCTPS calculations was used. Percentage depth dose curves and dose profiles for various field sizes were calculated at several depths and compared to the measured data. For all MCNP calculations, cut-off energies of 1 keV for electrons (E_CUT) and 1 keV for photons (P_CUT) were applied. Statistical uncertainty for MCNP calculations was less than 1%. The validation criterion was set on the central part of the beam where deviation between calculated and measured data less than 0.5% was taken as acceptable. Initially, comparisons between dose calculation options built in MCTPS and MCNP in 13 different materials with mass densities ranging from 0.2 g/cm^3 to 2.17 g/cm3^3 was performed. The MCNP calculations were performed by assigning elemental chemical composition and mass density (MCNP_MEDIUM) and the absorbed dose is calculated as D_m,m. Additional MCNP simulation was performed to simulate D_w,w absorbed dose calculation (MCNP_WATER). Thus, MC simulation was performed for non-standard conditions, where different materials were represented as water of different densities. Depth dose curves (DDs) calculated by MCNP were compared to D_m,m and D_w,m calculated data using Root Mean Square (RMS) deviation (further in text: deviation). Additionally, similar validation of accuracy of absorbed dose calculations was performed in heterogeneous phantoms. For that reason, 4 different scenarios were designed and simulated. Heterogeneous geometries were simulated by placing inserts of different densities (ρ=0,205 g/cm^3 and ρ=1,6 g/cm^3) at different positions in the virtual water phantom. In this part, the study is limited to three materials used to mimic soft tissue, lungs and bones, respectively. In addition, the influence of the position of the heterogenity in the calculation geometry on the calculation of the absorbed dose was investigated. Due to differences in determination of materials in the respective calculation systems the influence of the chemical composition on the calculation of the absorbed dose in the semi-anthropomorphic phantom was eximened. Potential reasons for deviations were investigated. An improvement of the MCTPS Dm,m calculation accuracy is proposed. Results and discussion: The absorbed dose calculation accuracy is related to the capability of the algorithm to calculate absorbed dose at any point of interest within the patient and correlate it to the beam calibration point dose considered as the reference absorbed dose. In the MCTPS dose calculation engine, the chemical composition of the materials is not taken into account, thus introducing additional uncertainty into the calculation of absorbed dose. Deviations between DDs, for Dm,m and Dw,m in different materials become largest for material of mass density 2.17 g/cm3, up to 13%. Comparison for Dm,m calculation option to the MCNPMEDIUM shows very good agreement, with the deviation less than 3% for the majority of examined materials except for the lowest mass density in this research (ρ=0,2 g/cm^3), where the deviation is 4.8%. For the D_w,m calculation option results are acceptable only in the mass density range from 0.5 g/cm^3 to 1.06 g/cm^3 with deviations less than 2.5%. For the rest of the examined materials, the deviation increases, with a maximal value of 12.4% for mass density 2.17 g/cm3. Absorbed dose calculation comparison between D_w,m and MCNP_WATER shows large deviations for the majority of used materials, up to 13.1% for mass density 2.17 g/cm^3. Deviations between the D_m,m calculation option and MCNP_WATER are lower than one might expect, e.g. for the largest mass density in this research the deviation is 3.7%. Furthermore, the assumption of small cavity conditions applied through stopping power ratios of water and different materials for D_w,m calculation was also validated. It could be an acceptable approximation when assumptions of the Bragg-Gray cavity theory are fulfilled. The most probable energy of the secondary electrons for a 6 MV photon beam is below 300 keV. Such electrons have a range of 0.0957 g/cm2, and consequently, the conditions for small cavity when the voxel size of 3×3×3 mm^3 is used, mainly cannot be fulfilled due to the secondary electron range for almost all materials used. To verify the results obtained in simplified geometry, additional validation was performed in more complex geometry. The validation of the MCTPS absorbed dose calculation was performed by comparison with MCNP_MEDIUM calculations, when the conditions for charged particles equilibrium are not met due to heterogeneity. Since the validation was performed in complex geometry, a validation criterion was applied according to which a deviation <5% is considered acceptable. The analysis of deviations in heterogeneous geometry, which mimic real conditions, revealed the same trend as the validation of the calculation of the absorbed dose in a homogeneous phantom. Namely, the deviation in MCTPS D_w,m calculation in heterogeneities is outside the acceptability criterion (<5%). By analysing the deviations for D_m,m, it was found that they follow the trend of deviations found in the calculation of the absorbed dose in a homogeneous phantom with a tendency to increase the deviations in more complex geometries. However, for inserts of high-density medium this deviation is still acceptable. For a low-density medium, the deviation is significantly larger compared to the calculation in a homogeneous phantom, from RMS=6,5% to RMS=12,4% depending on the level of complexity of the examined geometries. Such a trend of deviations suggests that the empirical function used in XVMC calculation of cross sections and stopping power of materials in low density range is not correctly defined and improvements are required. HU-RED conversion curve determines how the algorithm account for materials of different densities. The correction was applied to the HU-RED conversion curve for the low-density region. For the value of HU = -769 the initial RED was 0.198 (corresponding to the material density of 0.2 g/cm^3). Using the aforementioned RED value for the MCTPS D_m,m calculation in homogeneous geometry yielded an deviation of 4.8%. Additionally, a corrected RED value of 0.18 was applied for the same material. Validation of the MCTPS D_m,m calculation option compared to the MCNPMEDIUM in a homogeneous geometry for a material of density 0.2 g/cm^3 resulted in the decrease in deviation of the two DD curves to 2.8%. Furthermore, MCNP simulations were designed and performed in order to examine the contribution of individual energy loss mechanisms to the calculation of the absorbed dose using MCTPS. The results show that for materials of lower atomic number (corresponding to the materials from 0.2 g/cm^3 to 1.16 g/cm^3) the contributions of all three mechanisms are properly included in the absorbed dose calculation. However, with the increase of the atomic number of materials (ρ>1.66 g/cm^3) differences in the calculation of the contribution of the photoelectric effect as well as pair production were observed. Differences in the calculation of the contribution of the photoelectric effect in the calculation of the absorbed dose from 1.3% to 1.7% were determined for materials with densities 1.66 g/cm3-2.17 g/cm^3 at a depth of 5 cm. Within MCTPS, equal stopping powers for positron and electron are applied to electron-positron pair production. However, examination of the deviation in the calculation of the contribution of electronpositron pair production at a depth of 10 cm shows increase of the deviation to a maximum value of 2.3% for the material with a density of 2.0 g/cm^3. The mean free path length, which is one of the parameters defined within the MCTPS when the conditions are met for the electron positron pair production is not correctly defined for the positron within the MCTPS. Conclusion: This doctoral dissertation presents the results of the method for validation of the MC based algorithm calculation accuracy which may be complementary to existing experimental verification methodology. The validation was performed for both options, D_m,m and D_w,m, using MCNP simulations. Although, algorithm built in MCTPS do not take into account the chemical composition of the medium, D_m,m calculation option shows very good agreement with standard MCNP calculations except for low density medium. Furthermore, it is demonstrated that the D_w,m calculation option differs substantially from D_w,w. It was also found that for different materials, absorbed dose calculated as D_m,m shows better agreement to the algorithms that calculate absorbed dose using D_w,w approach. The HU-RED correction was proposed in order to improve the accuracy of D_m,m calculation option built in MCTPS in low density medium. The results indicate that the absorbed dose distribution calculation performed with D_m,m could be preferable in order to allow better consistency with clinical data based on D_w,w dose concept as well as reference dosimetry performed in water. Also, this doctoral dissertation provides additional insight regarding the dilemma which calculation option is more accurate for use in radiation oncology. The results obtained indicate that D_m,m could be regarded as the preferable dose calculation option. |