An investigation of entrance surface dose calculationsfor diagnostic radiology using Monte Carlosimulations and radiotherapy dosimetry formalisms
L Ben Omrane1, F Verhaegen2, N Chahed1 and S Mtimet1
1 Centre National de Radio-Protection, Hopital d’Enfants, Place Bab-Saadoun, Tunis, Tunisia2 Medical Physics Unit, Montreal General Hospital, McGill University, Montreal, Canada
Received 31 March 2003Published 3 June 2003Online at stacks.iop.org/PMB/48/1809
AbstractOur aim in this work was to investigate the methodology used in thedetermination of the entrance surface dose (ESD) in diagnostic radiology. In kVx-rays for low-energy photons (tube potential up to 160 kV, HVL: 1–8 mm Al),the ESD is based on the use of the ratio of mass-energy absorption coefficientsand backscatter factors. A full simulation of the photon and electron transportin a kilovoltage x-ray unit, using the Monte Carlo code BEAM/EGS4, wasperformed to obtain an accurate beam phase space for use in dose calculation.The modelled phase space was experimentally validated for the beam qualities(measured HVL: 3.3 mm Al–2.2 mm Cu) and showed good agreement betweencalculated and measured HVLs, air kerma and relative dose distributions. Wehave computed the conversion factors from air kerma to water or soft tissueabsorbed dose at the surface of a phantom for beam qualities (HVL: 3.3–8.35 mm Al). The same model was also used to calculate the ESD in waterand in soft tissue for the low-energy photon range considered. The resultsshow that the numerical differences between the air kerma and the water kermabased backscatter factors are insignificant. The same conclusion was reachedfor the (µen/ρ) ratios, for soft tissue to air, evaluated using either the primaryphoton spectra or the spectra at the surface of a phantom. Furthermore, thegood agreement obtained for the computation of the conversion factors witha full BEAM/EGS4 model confirms the previous studies which are based ondifferent sources for the spectral distribution and different beam geometries(pencil beam or point source assumptions). On the other hand, the ESD inwater or soft tissue is well described either with the Bair or the Bw formalism.Conversion factors from air kerma to ESD in these media are proposed in thiswork for several beam qualities in diagnostic radiology.
Radiation dose measurement in diagnostic radiology is the cornerstone for setting good practicestandards as well as for optimizing radiation protection for both staff and patients. In thiscontext, the ICRP (1990) states that the effective dose is the quantity that most reliablycorrelates with the risk from medical exposures. However, its assessment is not easy toperform in routine examination. An indirect method was proposed by measuring the entrancesurface dose (ESD) or the dose–area-product (DAP) (Hart et al 1993). Effective dose isthen determined using adequate conversion factors, given for each radiological examination(Jones et al 1985). Consequently, the ESD constitutes an important quantity that can bedetermined experimentally in diagnostic radiology. This, in turn, requires access to a national,and preferably international, radiation dosimetry methodology. Remarkably, there is nointernational code of practice in diagnostic radiology to enforce a unified approach for thecalibration and the dosimetry in this field.
In diagnostic radiology, the ESD is generally calculated as tissue (med) absorbed doseaccording to the formula
ESD(med) = KairB
(µen
ρ
)med
air(1)
where Kair is the air kerma reading given by a detector free-in-air at the calibration distance,B is the backscatter factor and (µen/ρ)med
air is the ratio of the absorbed dose in tissue media tothat in air. For the spectral distribution of photon fluence, this ratio is given by
(µen
ρ
)med
air
=∑N
i=1 ϕ(Ei)Ei
(µen
ρ(Ei)
)med�Ei∑N
i=1 ϕ(Ei)Ei
(µen
ρ(Ei)
)air�Ei
(2)
where N is the number of energy bins, Ei is the energy at the mid-point of the energy bini, ϕ(Ei) is the photon fluence in the energy bin i,
(µen
ρ(Ei)
)medand
(µen
ρ(Ei)
)airare the
mass-energy-absorption coefficients for the medium and air, respectively, for the energy Ei
(Hubbell and Seltzer 1995).However, there is a common approach for which three points have to be outlined:
1. The calibration of the dosimeters is generally performed for only one point, by using forexample, an x-ray spectrum generated at around 80 kV and 3.0 mm Al total filtration(NRPB 1992).
2. The backscatter factor B is from Grosswendt (1984), Klevenhagen (1989) or fromPetoussi-Henss et al (1998). The most frequently used one is that derived by Harrison(1982) for x-ray beam qualities with half-value layer (HVL) ranging from 1 to 4 mm Al.
3. The values of (µen/ρ)medair vary by a few per cent (up to 10%) depending on the composition
of the medium that is taken to represent soft tissue (NRPB 1992). All the followinghave been used as tissue substitutes in diagnostic dosimetry: water, striated muscle(ICRU 1970), ICRP reference man soft tissue (ICRP 1975), ICRU sphere ‘soft tissue’(ICRU 1980) and skeletal muscle (ICRU 1989). The most used value for this ratiois 1.06 ± 1% (ICRU striated muscle) for all the diagnostic x-ray spectra encountered(Wagner and Pollock 1999, Fung and Gilboy 2001, Kemerink et al 2001).
Furthermore, some codes of practice (IAEA 1987, IPEMB 1996, NCS 1997, AAPM2001), which are not directly proposed for diagnostic radiology but for kilovoltage radiotherapy(40–300 kV), could have an interesting impact on the determination of the entrance dose. In thisenergy range, the codes are based on air kerma measurements using ion chambers, calibratedfree-in-air. The absorbed dose to water is determined by two methodologies, depending on the
energy of the x-ray beam: low or medium energy. However, if the point of interest is clinicallyat or close to the surface, the AAPM (2001) recommend one unified approach over the entireenergy range to determine the absorbed dose to water at the surface of a water phantom basedon in-air measurements, called ‘the in-air method’. This code was complemented by thework of Ma and Seuntjens (1999), who used Monte Carlo (MC) simulations to calculate themass-energy-absorption coefficient ratios for the primary spectrum and for various biologicaltissues (including skin, muscle, soft tissue, lung and bone) which convert the air kerma totissue kerma, as given in equation (1).
Two conceptually different definitions of the backscatter factor B and the mass-energy-absorption ratios are used in the calculation of the ESD(water) in equation (1):
Definition 1. According to the IAEA protocol (1987), B is defined as the ratio of air kermaat the surface of a semi-infinite water phantom to that at the same point in the absence of thephantom, and denoted by Bair. Then, the mass-energy-absorption coefficient ratio, water toair, for the spectrum at the surface of the phantom
[(µen/ρ)wair
]surface is required. The latter
factor is given for only one field size.
Definition 2. According to the other protocols (IPEMB 1996, NCS 1997, AAPM 2001), Bis defined as the ratio of water kerma at the surface of a semi-infinite water phantom to thatat the same point in the absence of the phantom, and denoted by Bw . The mass-energy-absorption coefficient ratio, water to air, averaged over the primary spectrum
[(µen/ρ)wair
]air
is then involved. This factor is independent of field size (Nahum and Knight 1993).
An extensive dataset for the conversion factors to calculate ESD(water) or ESD(tissue) isgiven for the Bw based formalism (IPEMB 1996, NCS 1997, AAPM 2001). Conversely, thereis a lack of data concerning the Bair based formalism and especially for the
[(µen/ρ)tissue
air
]surface.
Also, most of the published conversion factors are derived from MC simulations using differentsources for the spectral distributions: measured spectra (Seelentag 1979) or analyticallycalculated spectra (Birch and Marshall 1979). Different irradiating geometries were used:Knight (1996) used pencil beams whereas others used point sources (Grosswendt 1984, 1990,Petoussi-Henss et al 1998, Ma and Seuntjens 1999).
In this work, we provide a set of air kerma and water kerma based backscatter factors forphoton spectra of our calibration x-ray unit. We also calculate the mass-energy-absorptioncoefficient ratios for two media (med) to air: water and ICRU four element soft tissue (ICRU1984). We used primary spectra to evaluate
[(µen/ρ)med
air
]air and the spectrum at the surface of
a phantom to obtain[(µen/ρ)med
air
]surface for two field sizes. Furthermore, the entrance surface
dose is investigated, for water and for soft tissue, by MC simulations to clarify the situationregarding the effective use of the Bair or the Bw based formalisms.
The BEAM/EGS4 (Rogers et al 1995) Monte Carlo code was used to model the x-raycalibration unit of our SSDL to obtain an accurate beam ‘phase space’ as input for dose calcu-lations, as was done by Verhaegen et al (1999). To our knowledge, this is the first study thatmodels a complete x-ray unit, including the calculation of entrance surface dose conversioncoefficients for a realistic beam. This work could help hospital physicists in the calibrationof dosimeters for the assessment of the entrance absorbed dose in diagnostic radiology.
2. Materials and methods
2.1. Measurements
All measurements (half-value layers, air kerma and percentage depth doses (PDD)) wereperformed in our Secondary Standard Dosimetry Laboratory (SSDL), using an x-ray machine
Table 1. Radiation qualities for the Pantak hf160 x-ray unit. The first and second HVLs weremeasured (in either mm Al or mm Cu). The homogeneity coefficient (HC), for the measured(Al or Cu) HVLs are given.
Tube potential Added filtration First HVL Second HVL(kV) (mm) (mm) (mm) HC
70 0.1 Cu + 1 Al 3.3 Al 4.3 Al 0.7780 0.1 Cu + 1 Al 3.75 Al 5.00 Al 0.75
100 0.1 Cu + 1 Al 4.70 Al–0.170 Cu 6.45 Al–0.309 Cu 0.73 (Al)–0.55 (Cu)120 0.1 Cu + 1 Al 5.50 Al–0.222 Cu 7.60 Al–0.447 Cu 0.72 (Al)–0.50 (Cu)135 0.25 Cu + 1 Al 8.35 Al–0.435 Cu 10.15 Al–0.765 Cu 0.82 (Al)–0.57 (Cu)150 2.5 Sn + 1 Al 2.2 Cu 2.35 Cu 0.94
(Pantak hf160) with a tube potential varying from 40 to 160 kV. The tube has a tungsten targetangled at 20◦ and a focus size of 3 × 3 mm2. The exit window is 1 mm Be. Two collimators,additional filters, a diaphragm to define various circular fields at a focus–surface distance(FSD) of 100 cm and a monitor chamber, were in place.
Table 1 lists the beam qualities, which were originally developed by the InternationalAtomic Energy Agency (IAEA) for our SSDL and the first and second HVLs used in thiswork. The homogeneity coefficient was calculated as the ratio of the first and second HVLs(either for Al or for Cu HVLs).
A 0.6 cc NE2571 cylindrical Farmer ionization chamber (Nuclear Enterprises) was used tomeasure the HVLs. This chamber is recommended by the following codes of practice: IPEMB(1996), NCS (1997), AAPM (2001). HVLs were carefully measured using high-purity Aland Cu sheets, according to the procedure outlined in NCS (1997), AAPM (2001) and IAEA(1994).
For the first five qualities of table 1, air kerma (mGy mAs−1) was measured with the sameionization chamber at an FSD of 100 cm and with a maximum uncertainty of 1.5% (for 95%confidence level). For the 150 kV quality,which is suitable for radiation protection calibrations,a 600 cc NE2575 cylindrical Farmer ionization chamber (Nuclear Enterprises) was used tomeasure the air kerma with a maximum uncertainty of 2.5% (95% confidence level). Thesedetectors were calibrated in terms of air kerma at the IAEA Laboratory (Seibersdorf ).
The NE2571 chamber was also used to measure the percentage depth dose distribution in awater phantom of 30 × 30 × 30 cm3 dimensions. It should be noted that the first measurementdepth in our phantom is limited to 2.5 cm. So, all the data were normalized to this depth.
2.2. Monte Carlo simulations
2.2.1. The MC x-ray unit model. Monte Carlo simulations were performed using the codeBEAM/EGS4 (Rogers et al 1995) to model the x-ray unit (figure 1). All the interactionswere considered, except Rayleigh (i.e. coherent) scattering. The transport cutoffs were set toAE = ECUT = 0.521 MeV and AP = PCUT = 0.010 MeV in the simulations. The primaryelectron energies were taken as the nominal photon beam energies, without any attempt to fitour model to HVLs, PDDs and profiles. A beam of 3 × 108 mono-energetic electrons wasimpinging on the target. Phase-space information was collected at two levels in the x-rayunit model (see figure 1). The calculation of phase-space1 takes about 120 h of CPU time ona 450 MHz Pentium III computer. The phase-space2 collects the information on about 108
transported particles from the modelled source across the diaphragm. This part takes about2 h of CPU time. Bremsstrahlung splitting is used as a variance reduction technique for thefirst phase-space calculation.
Entrance surface dose investigation 1813
Figure 1. Different components of the modelled x-ray unit. A phase-space file was created justafter the additional filters to collect all the information on the position, direction, energy, etc, ofphotons and electrons emerging from the head of the machine. This phase-space file was thenused as a particle source for the rest of the model. Another phase space was created at an FSD of100 cm (without the phantom) to provide photon spectra in air and to calculate first and second HVLsand air kerma for the simulated beam qualities of table 1. The water phantom was incorporated inthe model to simulate the PDDs.
2.2.2. Characterization of the x-ray beams. To validate our model, we have used MCsimulations to calculate for each beam quality of table 1 the photon spectra in air, the HVL,the air kerma and the PDD.
2.2.2.1. Photon spectra in air. The analysis program BEAMDP (Ma and Rogers 1995) wasused to calculate photon fluence spectra in air and the mean photon energy. All the spectraldistributions of photon fluence were calculated with an energy resolution of 1 keV.
2.2.2.2. HVL. The HVL is the thickness of absorber required to reduce the air kerma to onehalf of its original intensity. Further reduction by a factor of 2 requires additional thicknessof absorber which is termed the second HVL. The first and the second HVLs were calculatedfor each spectrum, by iterating the absorber thickness t:(∑N
i=1 ϕ(Ei)Ei
(µenρ
(Ei))air
e−(µattρ
(Ei))abs medρtj �Ei
)(∑N
i=1 ϕ(Ei)Ei
(µenρ
(Ei))air
�Ei
) = 0.5 (for the first HVL = t1)
= 0.25 (for t2, the second HVL = t2 − t1) (3)
where(
µattρ
(Ei))abs med
is the mass-attenuation coefficient for the absorber medium (Al or Cu)for the energy Ei (Hubbell and Seltzer 1995) and all the other parameters are as for equation (2).The homogeneity coefficient (HC) can be calculated as the ratio of the first and second HVLs.
2.2.2.3. Air kerma. For each calculated photon fluence spectrum (per incident particle perunit energy interval) at an FSD of 100 cm, the air kerma was derived according to
In this part, the air kerma is evaluated in absolute terms in mGy mAs−1 if we assume that thex-ray unit current is obtained from equating one electron hitting the x-ray target with 1.6 ×10−16 mAs.
For each simulation, the number of histories is split up into ten equal batches, so that theresults from each batch could be treated as if they are the results from separate experimentsand are combined to give mean values and measures of dispersion for the calculated quantity.All the results which are based on fluence scoring in this work are given with only statisticaluncertainty derived by the ‘batches’ method and this is taken as equivalent to the overalluncertainty. Hence, the standard deviation (SD) for air kerma and HVL is estimated tobe 0.3%.
2.2.2.4. Percentage depth dose (PDD). From the obtained phase space, the depth dosedistribution in a water phantom of 17 cm radius and 30 cm length was calculated using the MCcode BEAM/EGS4. The scoring volume is 1 cm radius centred at the z-axis. The resolutionwas 0.2 cm until 10 cm depth; then 1 cm for the final 20 cm. The uncertainty in depth dosecalculations is 0.3% (1 SD) at the normalization depth and reaches 2% at a depth of 25 cm.
2.2.3. Calculation of dosimetric quantities
2.2.3.1. The backscatter factor, B. The backscatter factor corresponds to the ratio of thekerma on the surface of a phantom to the kerma free-in-air. The in-air photon spectra resultingfrom our modelled phase space at an FSD of 100 cm were used to determine the kermafree-in-air. A cylindrical water phantom of 17 cm radius and 20 cm depth was simulated toobtain spectra at the surface with the same code BEAM/EGS4. This phantom size was chosento meet the calculation conditions of the AAPM dosimetry protocol (2001). The parametersAP = PCUT were reduced to 1 keV for the photon transport in the phantom.
For the evaluation of Bair and Bw , which are defined in definitions 1 and 2, respectively,in the introduction the general procedure consisted of the determination of the photon fluenceat the centre of the phantom entrance surface, in a circular scoring area of 0.6 cm radius.The air kerma or the water kerma, for the Bair or Bw determination, was then deduced bymultiplying the differential photon fluence with the photon energy and the appropriate mass-energy-absorption coefficient of air or water, respectively.
In this work, Bw and Bair were calculated for two field sizes: 18 cm and 10 cm diameter.Bair was also determined for a field of 11.3 cm diameter to be compared to the methodologyproposed by Petoussi-Henss et al (1998).
2.2.3.2. The mass energy absorption coefficient ratios. The mass-energy-absorption ratiosare also kerma ratios, but for two different media and for the same spectral distribution.Mass-energy-absorption ratios were calculated for our modelled phase space, for water andfor ICRU four element soft tissue to air considering in equation (2):
• the primary spectrum in air, ϕair(Ei), to obtain[(µen/ρ)med
air
]air;
• the spectrum present at the phantom surface, ϕsurface(Ei), for two field sizes (11.3 and18 cm diameter) for
[(µen/ρ)med
air
]surface.
2.2.3.3. Entrance surface dose. It will be useful to define an overall conversion factorCF(med) to convert the air kerma, free-in-air, to the absorbed dose to medium (water or ICRUfour element soft tissue) at the surface of a phantom made of that medium, given by
CF(med) = ESD(med)
Kair= B
(µen
ρ
)med
air(5)
Entrance surface dose investigation 1815
Table 2. Values of the mean energy of the calculated photon spectra, the first and second HVLin Al and Cu calculated from the modelled phase space. The homogeneity coefficients (HC) aregiven for the calculated HVL. The last column gives the difference between the calculated and themeasured air kerma.
Tube Mean photon Air kermapotential energy First HVL Second HVL (calc/meas)(kV) (keV) (mm) (mm) HC (%)
70 41 3.18 Al 4.16 Al 0.76 2.880 45 3.63 Al 4.87 Al 0.75 2.1
100 50 4.45 Al–0.171 Cu 6.21 Al–0.307 Cu 0.72 (Al)–0.56 (Cu) 1.7120 56 5.26 Al–0.221 Cu 7.40 Al–0.434 Cu 0.71 (Al)–0.51 (Cu) 1.6135 65 8.08 Al–0.436 Cu 9.84 Al–0.746 Cu 0.82 (Al)–0.58 (Cu) 0.1150 117 2.28 Cu 2.39 Cu 0.95 1.6
ESD(med) was determined by two different methods:
• Directly by MC simulations using our modelled phase space: the transport of the photonsand electrons was simulated in a phantom for two media (water and ICRU four-element-soft tissue). The scoring volume was 18 cm diameter centred along the Z-axis and 0.3cm depth. The CF(med)[MC-DIR] were then obtained by using the previously calculatedair kerma (DIR denotes ‘direct’). The statistical uncertainty was estimated to be 0.1%(1 SD) for the ESD(med) and 0.3% (1 SD) for the CF(med)[MC-DIR].
• Calculated indirectly from MC simulations, with equation (1): by using the previouslyevaluated conversion factors of this work (sections 2.2.3.1 and 2.2.3.2) to derive theCF(med)
air [MC-INDIR] (using the calculated Bair) and CF(med)w [MC-INDIR] (using the
calculated Bw), in a first part, or those derived from the AAPM (2001) protocol, todetermine the CF(med)[AAPM] in a second part (INDIR denotes ‘indirect’). The statisticaluncertainty was estimated to be 1% for the CFw
air[MC-INDIR] and the CF(w)w [MC-INDIR].
By using Bw in the expression of the ESD(tissue) instead of the Btissue, an additionaluncertainty of 1% is introduced (Ma and Seuntjens 1999). Uncertainties were addedquadratically to estimate the overall uncertainty of 1.5% (1 SD) for the CF(tissue)
air [MC-INDIR] and the CF(tissue)
w [MC-INDIR]. The AAPM (2001) conversion factors are givenwith an uncertainty of 2% (1 SD) for the backscatter factor and 1.5% for the mass-energy-absorption coefficient, of water to air. The overall uncertainties estimated for theCF(w)[AAPM] and CF(tissue)[AAPM] are then 2.5% and 2.7%, respectively.
3. Results and discussion
3.1. Verification of the x-ray unit model
Figure 2 shows calculated photon fluence spectra in air, for the radiation qualities given intable 1 of the modelled x-ray unit. In a similar study, Verhaegen et al (1999) found a goodagreement between measured and calculated photon spectra by the same Monte Carlo codeBEAM/EGS4. It was noted (Verhaegen et al 1999) that in this code the four characteristicphoton peaks are assigned to only two energy bins: Kα1 (59 keV) and Kα2 (58 keV) lines arebinned together and this is also the case for Kβ1 (67 keV) and Kβ2 (69 keV) lines. Furthermore,the contribution to the characteristic peak is too low, due to the electron impact ionizationprocess not being modelled in EGS4.
For each predicted spectrum, the reported calculated first and second HVLs andhomogeneity coefficient are shown in table 2. These should be compared with the measured
1816 L Ben Omrane et al
0.E+0
1.E-7
2.E-7
3.E-7
4.E-7
5.E-7
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Photon Energy (MeV)
Flu
ence
(/M
eV/in
cide
nt p
artic
le/c
m-2
MeV
-1)
Flu
ence
(/M
eV/in
cide
nt p
artic
le/c
m-2
MeV
-1)
Flu
ence
(/M
eV/in
cide
nt p
artic
le/c
m-2
MeV
-1)
Flu
ence
(/M
eV/in
cide
nt p
artic
le/c
m-2
MeV
-1)
Flu
ence
(/M
eV/in
cide
nt p
artic
le/c
m-2
MeV
-1)
Flu
ence
(/M
eV/in
cide
nt p
artic
le/c
m-2
MeV
-1)
70 kV + 1Al + 0.1 Cu
0.E+0
1.E-7
2.E-7
3.E-7
4.E-7
5.E-7
6.E-7
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Photon Energy (MeV)
80 kV + 1Al + 0.1 Cu
0.0E+0
5.0E-7
1.0E-6
1.5E-6
2.0E-6
0.00 0.02 0.04 0.06 0.08 0.10
Photon Energy (MeV)
100 kV + 1Al + 0.1 Cu
0.E+0
1.E-6
2.E-6
3.E-6
4.E-6
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Photon Energy (MeV)
120 kV + 1Al + 0.1 Cu
0.E+0
1.E-6
2.E-6
3.E-6
4.E-6
5.E-6
0.00 0.03 0.06 0.09 0.12 0.15
Photon Energy (MeV)
135 kV + 0.25 Cu + 1Al
0.E+0
2.E-8
4.E-8
6.E-8
8.E-8
1.E-7
1.E-7
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16
Photon Energy (MeV)
150 kV + 1Al + 2.5 Sn
Figure 2. Photon fluence spectra calculated by the BEAM/EGS4 Monte Carlo code, for somediagnostic x-ray qualities with different kVp and added filtration.
values of table 1. The overall agreement is good to within 3.7%, except for the qualitiesof 100 and 120 kV, both with the same filtration (0.1 mm Cu + 1 mm Al), for which themeasured HVLs for Al sheets are about 5.3% higher than for the calculated ones. This is notthe case for Cu filters for which the agreement is good. Additionally, the difference betweencalculated and measured air kerma, free-in-air, is given in table 2. The results show that MCcalculated air kerma are slightly higher than measured ones. The agreement is very good,differing by at most 2.8% across the 70–150 kVp tube potential range, especially consideringthat the comparisons were performed for lightly filtered beams with a large low-energy x-raycomponent and also for heavily filtered beams. This result demonstrates that an MC model ofan x-ray unit can be used to calculate air kerma in absolute units (i.e. per mAs).
The relative dose distribution in water is shown in figure 3 for the first four beam qualitiesof table 1. Generally, good agreement is found between calculated and measured PDD: for120 kV, the deviation is less than 1.5% until 12.5 cm depth in the water phantom and reaches
Entrance surface dose investigation 1817
0
20
40
60
80
100
120
140
0 5 10 15 20 25 30Depth (cm)
PD
D (
%)
calculatedmeasured
70 kV + 1 Al + 0.1 Cu
0
20
40
60
80
100
120
140
0 5 10 15 20 25 30Depth (cm)
PD
D (
%)
calculatedmeasured
80 kV + 1 Al + 0.1 Cu
0
20
40
60
80
100
120
140
0 5 10 15 20 25 30Depth (cm)
PD
D (
%)
calculatedmeasured
100 kV + 1 Al + 0.1 Cu
0
20
40
60
80
100
120
140
0 5 10 15 20 25 30Depth (cm)
PD
D (
%)
calculatedmeasured
120 kV + 1 Al + 0.1 Cu
Figure 3. Percentage depth dose (PDD) for an added filtration of 1 mm Al + 0.1 mm Cu anddifferent kVp, with a field size of 18 cm diameter at an FSD of 100 cm. Normalization is performedat a depth of 2.5 cm.
4% at maximum at some depths. For the qualities less than 120 kV, the deviation is up to 3%until 12.5 cm and reaches 5%. It is known that accurate measurements of relative depth dosecurves for low and medium energy x-rays are very difficult due to the sharp dose gradient andthe energy dependence of most practical detectors. However, the NE2571 ionization chamberhas a fairly flat energy response in this energy range and allows accurate axial measurementsfor doses in regions where the dose rate is not changing rapidly (Seuntjens and Verhaegen1996, Ma and Nahum 1995). Consequently, the normalization depth in this work (2.5 cm),which is very close to the reference point (2 cm) recommended for medium energies in therecent codes of practice for kilovoltage x-rays beams, seems to give accurate results.
3.2. Calculation of dosimetric quantities
Figure 4 illustrates the comparison between the calculated backscatter factors Bw of thiswork for two field sizes: 18 and 10 cm diameter at an FSD of 100 cm, and the interpolatedbackscatter factors derived from the AAPM (2001) code of practice, for the same geometricconditions. The AAPM factors have been derived from the results of Grosswendt (1984, 1990,1993) and have independently been checked using the experimental data from Klevenhagen(1989) and the Monte Carlo data from Knight (1996). The agreement is excellent betweenthese two sets of values, i.e. generally within 0.4% with a maximum deviation of 0.7%.
Figure 5 presents a comparison between the calculated Bair of this work for a field size of11.3 cm diameter with the results from Petoussi-Henss et al (1998) for the equivalent squarefield size (10 × 10 cm2). Petoussi-Henss et al (1998) have calculated the air kerma basedbackscatter factors for some spectral beams typical in diagnostic radiology. These spectra,characterized by tube voltage, added filtration and HVL, were simulated by the method of
1818 L Ben Omrane et al
1.0
1.1
1.2
1.3
1.4
1.5
0 1 2 3 4 5 6 7 8 9
HVL (mm Al)
Bac
ksca
tter
fact
or, B
wwater, d=18 cm : AAPM
water, d=18 cm : this work
water, d=10 cm : AAPM
water, d=10 cm : this work
Figure 4. Comparison of the backscatter factors Bw calculated with BEAM/EGS4 for two fieldsizes: 18 and 10 cm diameter at an FSD of 100 cm with the values incorporated in the AAPM(2001) code of practice.
1.1
1.2
1.3
1.4
1.5
1 2 3 4 5 6 7 8 9
HVL (mm Al)
Bac
ksca
tter
fact
or, B
air
10x10 cm2 : Petoussi et al (1998)
d=11.3 cm : mono-energetic BSF
d=11.3 cm : this work
Figure 5. Backscatter factors Bair calculated with BEAM/EGS4 for a field size of 11.3 cmdiameter (10 × 10 cm2) at an FSD of 100 cm. For comparison, the values from Petoussi-Hensset al (1998) are plotted for some photon beams typical in diagnostic radiology. The backscatterfactors obtained from the combination of our modelled spectral distribution with the correspondingmono-energetic BSF values for the same field size, are also incorporated.
Birch and Marshall (1979) and combined with the monochromatic backscatter factor valuescalculated also by MC simulations. For comparison, we have also plotted the values obtainedfrom the calculated spectral energy distribution of this work combined with the monochromaticbackscatter factor values of Petoussi-Henss et al (1998). Good agreement to within 0.7% withthe calculated Bair for our modelled phase space is found, except for the lowest energy wherethe deviation reaches 1%. Furthermore, it was shown in this work that the Bair and the Bw
are numerically equivalent for low-energy photon x-ray beams (up to 160 kV and HVL up to8 mm Al).
Entrance surface dose investigation 1819
0.90
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
0 1 2 3 4 5 6 7 8 9
HVL (mm Al)
[(µ e
n/ ρ
) me
d, a
ir] a
ir
water : AAPM
ICRU tissue : AAPM
water : this work
ICRU tissue : this work
Figure 6. Free-in-air mass-energy-absorption coefficient ratios, of water to air and of soft tissue toair, for photon beams 70–135 kV (3.18–8.08 mm Al). For comparison, the values from the AAPM(2001) protocol are included.
0.90
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
0.07 0.17 0.27 0.37 0.47
HVL (mm Cu)
[(µ e
n/ ρ
) med
,air] S
urfa
ce
water : IAEA
water: this work
ICRU tissue : this work
Figure 7. Ratios of mass-energy-absorption coefficient, of water to air and of soft tissue to air, atthe surface of a phantom are plotted as a function of HVL in mm Cu. The field size of 11.3 cmdiameter defined at an FSD of 100 cm. The values from the IAEA (1987) protocol are also givenfor water.
Figure 6 shows the free-in-air mass-energy-absorption coefficient ratios for water and forICRU four-element soft tissue to air, calculated for the modelled primary energy photonspectrum of this work. For comparison, the AAPM (2001) recommendations for thecorresponding HVL, which represent a global fit of data from Ma and Seuntjens (1999)and the IPEMB (1996) code of practice, are plotted. It can be seen that the agreement is verygood; the highest discrepancy is found for the lowest energy: 0.5% for water and 0.8% forICRU soft tissue.
Figure 7 presents the mass-energy-absorption coefficient ratios, averaged over the photonspectrum at the surface of a phantom, for water and for ICRU tissue to air. The field size is
1820 L Ben Omrane et al
11.3 cm diameter at an FSD of 100 cm. These irradiating conditions were selected to fitthe situation of Grosswendt (1984) most closely who calculated the (µen/ρ)wair at the surface,at 2 and 5 cm depths of a water phantom to be used by the IAEA (1987) code of practice.Grosswendt calculated this quantity for only one field size and represented the values asa function of HVL in mm Cu. The agreement shown is excellent, i.e. generally within0.2% with a maximum deviation of 0.3% for the lowest energy. Also, in this figure, the[(µen/ρ)tissue
air
]surface are plotted for the five beam qualities (70–135 kV) and for the same field
size. There are no data available in the literature for an adequate comparison. It is noted inthis part that the difference in the mass-energy-absorption coefficient ratios between ‘in-air’and at the surface of a phantom is very small (within 0.3% for water and 0.5% for soft tissue)for this energy range (figures 6 and 7).
To study the field size dependence of[(µen/ρ)med
air
]surface, we simulated the photon
spectrum at the surface of the phantom for field sizes of 11.3 cm and 18 cm diameter atan FSD of 100 cm for the five beam qualities. The
[(µen/ρ)wair
]surface and
[(µen/ρ)tissue
air
]surface
vary by no more than 0.1% for the two field sizes.All these results mentioned so far such as the small field size dependence and the small
differences in the µen/ρ ratios between the ‘in-air’ and at the surface of a phantom, areconsistent with older studies. Knight and Nahum (1993) have considered the effect of theseparameters on the
[(µen/ρ)wair
]2 cm ratios and Ma and Seuntjens (1999) on the
[(µen/ρ)med
w
]2 cm
ratios for human tissues to water. They found that the variation of the µen/ρ ratios with depthdoes not show a discernible trend for the softer qualities. In this context it seems adequate touse, for low energy (tube potential up to 160 kV, HVL: 1–8 mm Al) and for human tissues(except for bone), the µen/ρ ratios averaged at 2 cm depth or those calculated for the free-in-airspectra as an appropriate approximation for the µen/ρ ratios at the surface of the phantom.
It should be mentioned that the µen/ρ ratios in the works cited above and in our own workwere derived using different computational methods through the utilization of:
• The reciprocity theorem for a circular plane parallel beam incident on a very broad waterphantom which corresponds to scoring fluence for a pencil beam impinging on the surfaceof the phantom (Knight 1996).
• A point source of photons with variable field sizes defined at a specified SSD and impingingon a broad phantom (Ma and Seuntjens 1999). In-air photon spectra have been calculatedusing a program called XRAYBEAM, which was based on the initial work by Birch andMarshall (1979) and improved by Nahum and Knight (1993) and Knight (1996).
• A realistic MC model of the x-ray unit in the present work, providing a full determinationof the energy, angular and spatial distribution of both photons and electrons in the beam.
Thus, regarding the good agreement, the calculation time becomes an important criterion forthe choice of one of the different techniques for the computation of these quantities. However,an MC model allows calculations of air kerma in absolute terms and allows a straightforwarddetermination of the influence of, e.g., collimators on dose distributions and photon spectra.
Figure 8 gives the HVL dependence of the overall conversion factor CF(w) from air kermato absorbed dose in water at the surface of a water phantom for an FSD of 100 cm and a fieldsize of 18 cm diameter. For the MC calculation of the entrance surface dose in water whichwas incorporated in the modelled geometry of this work, the CF(w)[MC-DIR] are derived usingequation (5). To investigate the calculation of the ESD(w) via the backscatter factors Bair andBw and the appropriate mass-energy-absorption ratios, of water to air, the CF(w)
air [MC-INDIR]and CF(w)
w [MC-INDIR] are plotted for the calculated (Al) HVLs. It can be seen that theoverall agreement is good to within 0.7% for the two methods except for the lowest and thehighest energies, where the discrepancy is up to 1%. For comparison, we have also plotted
Entrance surface dose investigation 1821
1.35
1.40
1.45
1.50
1.55
1.60
3 4 5 6 7 8 9 HVL (mm Al)
CF(water)
CF [MC-DIR]CF[AAPM] CFair[MC-INDIR]CFw[MC-INDIR]
Figure 8. Variation of the overall conversion factor CF(w) of air kerma to the entrance surfaceabsorbed dose in water with HVL (mm Al). The range of the x-ray photon beams considered isfrom 70 to 135 kV. The MC calculated factor CF(w)[MC-DIR] is compared with the CF(w)[AAPM]factor which is obtained by using the conversion factors provided by the AAPM (2001). TheCF(w)
air [MC-INDIR] and CF(w)w [MC-INDIR] which are calculated using the conversion factors of
this work are also represented.
1.20
1.30
1.40
1.50
1.60
3 4 5 6 7 8 9 HVL (mm Al)
CF(tissue) CF[MC-DIR]
CF[AAPM]
CFair[MC-INDIR]
CFw[MC-INDIR]
Figure 9. Variation of the overall conversion factor CF(tissue) of air kerma to the entrance surfaceabsorbed dose in soft tissue, with HVL (mm Al) for photon beams 70–135 kV. The MC calculatedfactor CF(tissue)[MC-DIR] is compared with the CF(tissue)[AAPM] factor which is calculated using
the AAPM (2001) conversion factors. The CF(tissue)air [MC-INDIR] and CF(tissue)
w [MC-INDIR]performed using the conversion factors of this work are plotted.
the values of the overall conversion factors which are obtained from the AAPM protocol andcarefully interpolated for the appropriate HVLs and field sizes. The agreement between theCF(w)[AAPM] and the CF(w)[MC-DIR] is excellent: 0–0.4%. The ESD(w) determinations,either using the Bair, Bw or the AAPM conversion factors, are equivalent if we consider theuncertainties estimated for each procedure.
Similarly, the overall conversion factor CF(tissue)[MC-DIR], derived from equation (5),is plotted as a function of calculated HVL (Al) in figure 9. Values of the CF(tissue)
air [MC-INDIR] and CF(tissue)
w [MC-INDIR] which are derived from the calculated backscatter factorsand mass-energy coefficient ratios, tissue to air, of this work are included. These data are
1822 L Ben Omrane et al
Table 3. Values of the conversion factor CF(w) [MC-DIR] and CF(tissue) [MC-DIR], from air kermato entrance surface dose absorbed in water or soft tissue calculated by MC simulations for the HVLencountered in diagnostic radiology qualities.
generally in good agreement to within 0.2–0.8%, except for the lowest and highest energieswhere the discrepancy is up to 1.2%. This shows that the direct and indirect MC calculationsessentially yield the same results. This implies that the indirect method, which is faster, is moreappropriate. For comparison, we have also plotted the values of the CF(tissue)[AAPM] whichare calculated with the interpolated AAPM conversion factors. The agreement is excellent,mostly within 0.3%. An exception occurs at only one beam quality (100 kV) with a differenceof up to 1%.
In table 3, we present a set of conversion factors from air kerma to entrance surface doseabsorbed in water or in soft tissue medium. These MC calculated values for the qualitiesencountered in diagnostic radiology and for a field size of 18 cm diameter can be used tocalibrate diagnostic dosimeters. It seems adequate to upgrade the dosimetry in diagnosticradiology with the use of the
[(µen/ρ)tissue
air
]air which were recently presented by Ma and
Seuntjens (1999) for low-energy (tube potential up to 160 kV, HVL: 1–8 mm Al) photons.With the consideration of the appropriate backscatter factor to be used, the AAPM (2001)formalism is also recommended.
4. Conclusions
In this work, the phase space of the x-ray calibration unit (Pantak hf160) has been modelledusing the Monte Carlo code BEAM/EGS4. For the (70–150 kV) range, good agreement wasfound between the MC simulations and the experimental results, either for relative quantitiessuch as HVL and PDDs, or for the absolute dosimetric quantities, such as air kerma. Theresults show that the modelled phase space is acceptable for dose calculations.
We have investigated the conversion coefficient from air kerma to water or soft tissueabsorbed dose at the surface of a phantom for low-energy photons (tube potential up to 160 kVand HVL up to 8 mm Al). The results show that there are no significant numerical differencesbetween Bw and Bair or between
[(µen/ρ)tissue
air
]air and
[(µen/ρ)tissue
air
]surface but that they only
differ from a theoretical point of view for the application considered here. Also, the goodresults obtained for the calculation of these factors by using spectral distributions obtainedfrom either simplified assumptions or a full MC model by BEAM/EGS4 confirm the previousstudies. Consequently, the benefit of simple models should be in the consideration of thecalculation time.
In general, the ESD is adequately determined either via the Bair or the Bw formalism andwell described using an appropriate interpolation for the AAPM code of practice factors.
Finally, the MC calculated conversion factors presented in this work, which convert theair kerma to the entrance surface absorbed dose in water or in soft tissue, can be used in thediagnostic radiology field.
Entrance surface dose investigation 1823
Acknowledgments
Our gratitude is extended to Dr D Rogers and Dr J P Seuntjens for their assistance in the use ofthe code BEAM/EGS4. We also thank Drs A Nahum, P Andreo, H Palmans, A Meghzifeneand H Zaidi for their instructive discussions. The authors would like to thank the referees fortheir constructive comments. Mrs M Mekhnini and A Metoui are thanked for their assistancewith Linux. We wish to thank the dosimetry staff for their help with the experiments. Also, the‘Ministere de l’Enseignement Superieur et a la Recherche Scientifique—SERST’ of Tunisia,the IAEA and the WHO are acknowledged for their support.
References
AAPM (American Association of Physicists in Medicine) 2001 Task Group 61 Ma C M, Coffey C W, DeWerd L A,Liu C, Nath R, Seltzer S M and Seuntjens J P A APM protocol for 40–300 kV x-rays beam dosimetry inradiotherapy and radiobiology Med. Phys. 28 868–93
Birch R and Marshall M 1979 Computation of bremsstrahlung x-ray spectra and comparison with spectra measuredwith Ge(Li)detector Phys. Med. Biol. 24 505–17
Fung K K L and Gilboy W 2001 The effect of beam tube potential variation of gonad dose to patients during chestradiography investigated using high sensitivity LiF:Mg, Cu, P thermoluminescent dosimeters Br. J. Radiol.74 358–67
Grosswendt B 1984 Backscatter factors for x-rays generated at voltages between 10 and 100 kV Phys. Med. Biol.29 579–91
Grosswendt B 1990 Dependence of the photon backscatter factor for water on source-to-phantom distance andirradiation field size Phys. Med. Biol. 35 1233–45
Grosswendt B 1993 Dependence of the photon backscatter factor for water on irradiation field size and source-to-phantom distances between 1.5 and 10 cm Phys. Med. Biol. 38 305–10
Harrison R M 1982 Backscatter factors for diagnostic radiology (1–4 mm Al HVL) Phys. Med. Biol. 27 1465–74Hart D and Wall B F 1993 Estimating of effective dose in diagnostic radiology from entrance surface dose and
dose-area products measurements National Radiological Protection Board–R262 (London: HMSO)Hubbell J and Seltzer S 1995 Tables of x-ray mass-attenuation coefficients and mass-energy-absorption coefficients
1 keV to 20 MeV for elements Z = 1 to Z = 92 and 48 additional substances of dosimetric interest InternationalInstitute for Standards and Technology Report NISTIR 5632 (Gaithersburg: NIST)
IAEA (International Atomic Energy Agency) 1987 Absorbed dose determination in photon and electron beams: aninternational code of practice Technical Report Series No 277 (Vienna: IAEA)
IAEA 1994 Calibration of dosimeters used in radiotherapy TEC-DOC-Series No 374ICRP (International Commission on Radiological Protection) 1975 Reference Man: Anatomical Physiological and
Metabolic Characteristics (Oxford: Pergamon)ICRP 1990 Recommendations of the International Commission on Radiological Protection ICRP Publication 60
(Ann. ICRP)ICRU (International Commission on Radiation Measurements and Units) 1970 Radiation dosimetry: X-ray generated
at potentials of 5 to 150 kV ICRU Report No 17ICRU 1980 Radiation quantities and units ICRU Report No 33ICRU 1984 Stopping powers for electrons and positrons ICRU Report No 37ICRU 1989 Tissue substitutes in radiation dosimetry and measurements ICRU Report No 44IPEMB (Institution of Physicists and Engineers in Medicine and Biology) 1996 Code of practice for the determination
of absorbed dose for x-rays below 300 kV generating potential Phys. Med. Biol. 41 2605–25Jones D G and Wall B F 1985 Organ doses from medical x-ray examinations calculated using Monte Carlo techniques
NRPB-R186 (London: HMSO)Kemerink G J, Borstlap A C W, Frantzen M J, Schultz F W, Zoetelief J and Engelshoven J M A 2001 Patient and
occupational dosimetry in double contrast barium enema examinations Br. J. Radiol. 74 420–8Klevenhagen S C 1989 Experimentally determined backscatter factors for x-rays generated at voltages between 16
and 140 kV Phys. Med. Biol. 34 1871–82Knight R T 1996 Absorbed dose conversion factors for therapeutic kilovoltage and megavoltage x-ray beams,
calculated by Monte Carlo method PhD Thesis London University ICR-PHYS-1/96Knight R T and Nahum A E 1993 Depth and field size dependence of ratios of mass-energy absorption coefficients
water to air for kV x-ray dosimetry Proc. IAEA Int. Symp. on Measurement Assurance in Dosimetry (Vienna:IAEA) pp 361–70
1824 L Ben Omrane et al
Ma C M and Nahum A E 1995 Calculations of ion chamber displacement effect corrections for medium-energy x-raydosimetry Phys. Med. Biol. 40 45–62
Ma C M and Rogers D W O 1995 BEAMDP users manual NRCC Report PIRS-0509C (Ottawa: NRC)Ma C M and Seuntjens J P 1999 Mass-energy-absorption coefficient and backscatter factor ratios for kilovoltage x-ray
beams Phys. Med. Biol. 44 131–43Nahum A E and Knight R T 1993 Consistent formalism for kilovoltage x-ray dosimetry Proc. IAEA Int. Symp. on
Measurement Assurance in Dosimetry (Vienna: IAEA) pp 451–9NCS (Netherlands Commission on Radiation Dosimetry) 1997 Dosimetry of low and medium energy x-rays, a code
of practice for use in radiotherapy and radiobiology NCS Report 10 NCS Delft, The NetherlandsNRPB (National Radiological Protection Board) 1992 National protocol for patient dose measurements in diagnostic
radiologyPetoussi-Henss N, Zankl M, Drexler G, Panzer W and Regulla D 1998 Calculation of backscatter factors for diagnostic
radiology using Monte Carlo methods Phys. Med. Biol. 43 2237–50Rogers D W O, Fadeggon B A, Ding G X, Ma C M, Wei T and Mackies T R 1995 BEAM: a Monte Carlo code to
simulate radiotherapy treatment units Med. Phys. 22 503–24Seelentag W W, Panzer W, Drexler G, Platz L and Santner F 1979 A catalogue of spectra used for the calibration of
dosimeters (Munich: Gesellschaft fur Strahlen-und Umweltforschung mbH)Seuntjens J P and Verhaegen F 1996 Dependence of overall correction factor of a cylindrical ionisation chamber on
field size and depth in medium energy x-ray beams Med. Phys. 23 1789–96Verhaegen F, Nahum A E, Van De Putte S and Namito Y 1999 Monte Carlo modelling of kV x-ray units Phys. Med.
Biol. 44 1767–89Wagner L K and Pollock J J 1999 Real time portal monitoring to estimate dose to skin of patients from high dose
