brachytherapy procedures have been used for treatment of cancer patients by radiation emitted from small encapsulated sources . in this treatment modality ,
the common radionuclides of brachytherapy sources are co , cs , ir , au , i , and pd [ 14 ] .
ir can be accounted as the most commonly radionuclide used for both low - dose - rate ( ldr ) and high - dose - rate ( hdr ) brachytherapy sources .
recently , new radionuclides have been considered as alternatives to the above noted sources in brachytherapy treatments .
these sources include cs , yb , co , gd , and tm [ 512 ] .
radial dose function of cs is similar to those of i sources but it has radiobiological advantages in permanent brachytherapy implants over other sources due to its shorter half - life [ 5 , 6 ] .
yb and tm with average energies of 93 kev and 66.39 kev and half - lives of 32 days and 128.6 days , respectively , are interesting for use as hdr brachytherapy sources [ 710 ] .
co emits photons with energies of 122 and 136 kev and half - life of 272 days .
two dimensional ( 2d ) anisotropy function of co is comparable to that of ir and its radial dose function has an increasing trend in some distances , which could lead to larger dose to deeper tissue .
gd radionuclide with average energy of 60.9 kev was proposed as a low dose rate or pulsed dose rate brachytherapy source .
have shown that this source can be used for interstitial brachytherapy with rotating shield in needle .
these new radionuclides , despite having average energies lower than ir , have high enough energy to minimize photoelectric interactions in soft tissue . with these sources , a smaller shielding
the drawbacks of some of the new hypothetical isotopes can be related to their short half - life , beta contamination , and bremsstrahlung contributions .
for example , the yield of the photons emission of tm is lower than the yield its electron emission ( 6 photons per 100 electrons emitted ) .
the energy of the photon emission and half - life of rhodium-101 ( rh ) make this radionuclide a possible candidate as a brachytherapy source .
rh can be produced by nuclear reactions of ru(d , 2n)rh or ru(d , 3n)rh in a cyclotron .
prototype radionuclides have been produced at the isochronous cyclotron at the hiskp ( helmholtz - instituts fr strahlen - und kernphysik ) of the university of bonn ( germany ) .
a natural ruthenium foil ( with 20 mm cross - section and 0.3 mm thickness ) was applied as target , which included ru and ru isotopes .
a number of typical factors used in this nuclear reaction are : 1 ) deuteron energy : 27 mev ; cross section : 1000 mbarn ; deuteron beam intensity : 1 a ; 2 ) irradiation time : 2 days ; rh activity after cool - down period of 43 days : 1 mbq .
advantages of rh over the existing ir may be due to its relatively longer half - life of 3.3 years , higher specific activity of 397 tbq / g , and lower mean photon energy of 121.5 kev as shown in tables 1 and 2 .
these adequate physical characteristics made this radioisotope interesting for this project for evaluation as a possible alternative for the hdr brachytherapy source .
the purpose of this work is to evaluate the dosimetric parameters of a hypothetical rh source using task group no .
43 ( tg-43 ) recommendations and verify if it would be a potential hdr brachytherapy source . 
  the photon energy spectrum emitted by rh radionuclide 
  characteristics of the co , rh and ir sources
in this project , the geometric structure of the hypothetical rh source was designed to be similar to the flexisource ir hdr source , just for the ease of the comparison of the dosimetric parameters between the two sources .
the active core of the source is a pure rh cylinder ( density of 12.41 g / cm ) with an active length of 3.5 mm and an active diameter of 0.6 mm .
the active core is covered by a 304 stainless steel capsule ( composition by weight  fe : 67.92% , cr : 19% , ni : 10% , mn : 2% ,
si : 1% and c : 0.08% ; density : 8.0 g / cm ) .
the outer dimensions of the source are 0.85 mm in diameter and 4.6 mm in total length .
the 304 stainless steel cable ( density of 8.0 g / cm ) has been considered as a cylinder with a length of 5 mm and a diameter of 0.5 mm .
the energy spectrum of the rh photons considered in this study is listed in table 1 , .
this figure is not to scale based on updated tg-43 formalism , dose rate at a point is calculated from the following formula:1d.(r,)=skg(r,)g(r0,0)g(r)f(r, ) 
  in the above formula , s 
 k ,  , g(r, ) , g(r ) and f(r, ) present air kerma strength , dose rate constant , geometry function , radial dose function , and 2d anisotropy function , respectively . the mcnpx monte carlo ( mc ) code ( version 2.4.0 )   was used for obtaining dosimetric parameters of the new source design . in the calculations , only photons emitted by the rh were defined in the source definition card .
it was assumed that the beta particles emitted by the source ( ranging 118.78 - 541 kev with the most probable energy of 215.77 ) are absorbed by the encapsulation of source , therefore they were ignored . for estimation of air kerma strength ,
a torus with a minor diameter of 0.5 mm and major radii of 20 cm was defined on the transverse plane of the hypothetical source .
f6 tally , which is a commonly used tally in mcnp simulations , was used for these calculations and the results were obtained in terms of kerma of the source in mev/(g.photon ) .
this torus is composed of air and the surrounding phantom material is composed of vacuum .
air kerma strength then was calculated from the air kerma strength formula presented in the updated tg-43 formalism using the kerma value and the corresponding units and other conversion factors ( such as ev to joule , grams to kilograms , photon yields , etc . ) . for determination of dose rate constant
, the hypothetical source was positioned at the center of a spherical water phantom with radius of 50 cm in the simulations .
a torus with 0.5 mm minor diameter and major radii of 1.0 cm was defined on the transverse plane and * f8 tally was calculated .
this torus was also composed of water . using * f8 tally ( in terms of mev ) in mcnp it is feasible to score the absorbed energy inside a tally cell .
therefore , dose rate is output of * f8 tally divided by the mass of the torus considering the units for conversion factors ( for example , ev to joule , grams to kilograms , yields , etc . ) .
dose rate constant then was obtained as the dose rate divided by the air kerma strength . as an example for conversion of the mc output ( for * f8 tally divided per mass in terms of : mev / g per photon ) to absorbed dose rate in units of cgy/(h.mci ) the following formula can be used:2dose rate(cgy / h)=mc output(mev / g per photon)106(ev / mev)1.60210 - 19(j / ev)103(g / kg)1.0mci10 - 3(ci / mci)3.71010(bq / ci)1(dis / s per bq)photon yield of101rh(photon
/ dis)100(cgy / gy)3600(s / h ) 
  with this regard , the value of photon yield of the rh radionuclide is equal to 2.37 photons / dis .
this value can be obtained from summation and normalization of the prevalences listed in table 1 .
the activity of rh source , used in this conversion was equal to 1.0 mci . in order to calculate radial dose function of the new source design , a spherical water phantom with 50 cm radius
torus voxels were considered at distances of 0.1 - 15.0 cm on the transverse plane of the source in the phantom .
the thicknesses of the tori were 0.4 mm at distances up to 1.0 cm , and 1.0 mm for other distances up to 15.0 cm .
the outputs of * f4 tally was used for calculation of dose rate at various radial distances . to have an acceptable level of uncertainty
, this type of tally was used to speed up the calculations in the mcnp simulations .
finally , radial dose function was calculated from dose rate and geometry function values at various distances . for calculation of 2d anisotropy function ,
the same phantom ( i.e. spherical water phantom with 50 cm radius ) was defined as that described in calculation of radial dose function .
for these simulations , the calculation points were located on a circular path around the source with the same radial distances , and different polar angles , ranging from 0 to 180 angles at 5 degrees intervals .
these points were divided into two groups , those that were along the longitudinal axis of the source , and those that were off the longitudinal axis .
spherical voxels with 0.1 cm diameter were utilized to score the dose on the longitudinal axis of the source . for the other points , tori with minor diameter of 0.4 mm
the minor diamaters of these tori were 1 mm for larger distances ( larger than 1.0 cm , up to 15.0 cm ) .
the reason for different tally voxel sizes at various distances is due to the presence of steep dose gradient as a function of distance from the source , which is an inherent effect in brachytherapy .
therefore , using larger voxel size at shorter distances may introduce artifacts in the calculations by volume - averaging .
the outputs of * f4 was used for calculation of 2d anisotropy functions . from the selected tallies at various distances ,
the 2d anisotropy function values were calculated for distances ranging between 0.5 - 15.0 cm and for angles between 0 to 180 with 5.0 degrees intervals . in calculation of tg-43 parameters ,
an attempt was also made to use toroid cells not having large dimensions at various reference directions to avoid volume - averaging artifacts .
as an example , for calculation of anisotropy function at 2.0 cm distance and 30 angle , a torus with minor diameter of 1 mm at horizontal and vertical directions was utilized . it should be noticed that in these calculations , the source delivery cable is coincident on the angle of 180 degrees . in all calculations , the energy cut off of 1 kev was defined for photons and electrons .
for calculation of tg-43 dosimetric parameters , except for 2d anisotropy function , the input files were run for 2.5  10 particles . for calculation of 2d anisotropy function , in order to reduce the calculation uncertainties at larger distances from the source , the input file was run for 10 photons . the maximum type a errors or statistical uncertainties in monte carlo calculations for air kerma strength , dose rate constant and radial dose function over all the evaluated distances were 0.3% , 3.32% and 0.44% , respectively .
the reason for having larger uncertainty in dose rate constant than the other two parameters was due to the use of * f8 tally in this case compared to f6 or * f4 tallies for the others . for similar particle scoring numbers , using * f8 tally in mcnp normally incorporates to larger uncertainty compared to the other tallies . the maximum type a uncertainty in calculation of 2d anisotropy function was 4.42% .
it should be noted that these values are type a uncertainties , by having ignored type b uncertainties and with a coverage factor ( k ) of 2.0 , the expanded uncertainties ( u ; u = ku 
 c , in which u 
 c is the combined uncertainty ) will be twice these values .
a coverage factor of 2.0 corresponds to 95% confidence level . with 95% confidence level , the true value is in the  calculated value 
2u    calculated value + 2u  interval with the probability of 0.95 .
the input programs were run using a personal computer having 64-bit windows 7.0 operating system , 3.20 ghz intel ( r ) core i7 cpu , and 2.00 gb ram . with this computer ,
the running time for the air kerma strength , dose rate constant , radial dose function , anisotropy function , with the aforementioned numbers of particles histories , was 5.25 h , 24.75 h , 25.50 h , and 134.25 h , respectively . finally , the tg-43 dosimetric parameters of the hypothetical rh source were compared with the data for another hypothetical co source   and flexisource ir source .
in this project , the geometric structure of the hypothetical rh source was designed to be similar to the flexisource ir hdr source , just for the ease of the comparison of the dosimetric parameters between the two sources .
the active core of the source is a pure rh cylinder ( density of 12.41 g / cm ) with an active length of 3.5 mm and an active diameter of 0.6 mm .
the active core is covered by a 304 stainless steel capsule ( composition by weight  fe : 67.92% , cr : 19% , ni : 10% , mn : 2% ,
si : 1% and c : 0.08% ; density : 8.0 g / cm ) .
the outer dimensions of the source are 0.85 mm in diameter and 4.6 mm in total length .
the 304 stainless steel cable ( density of 8.0 g / cm ) has been considered as a cylinder with a length of 5 mm and a diameter of 0.5 mm .
the energy spectrum of the rh photons considered in this study is listed in table 1 , .
based on updated tg-43 formalism , dose rate at a point is calculated from the following formula:1d.(r,)=skg(r,)g(r0,0)g(r)f(r, ) 
  in the above formula , s 
 k ,  , g(r, ) , g(r ) and f(r, ) present air kerma strength , dose rate constant , geometry function , radial dose function , and 2d anisotropy function , respectively . the mcnpx monte carlo ( mc ) code ( version 2.4.0 )   was used for obtaining dosimetric parameters of the new source design . in the calculations , only photons emitted by the rh were defined in the source definition card .
it was assumed that the beta particles emitted by the source ( ranging 118.78 - 541 kev with the most probable energy of 215.77 ) are absorbed by the encapsulation of source , therefore they were ignored . for estimation of air kerma strength ,
a torus with a minor diameter of 0.5 mm and major radii of 20 cm was defined on the transverse plane of the hypothetical source .
f6 tally , which is a commonly used tally in mcnp simulations , was used for these calculations and the results were obtained in terms of kerma of the source in mev/(g.photon ) .
this torus is composed of air and the surrounding phantom material is composed of vacuum .
air kerma strength then was calculated from the air kerma strength formula presented in the updated tg-43 formalism using the kerma value and the corresponding units and other conversion factors ( such as ev to joule , grams to kilograms , photon yields , etc . ) . for determination of dose rate constant
, the hypothetical source was positioned at the center of a spherical water phantom with radius of 50 cm in the simulations .
a torus with 0.5 mm minor diameter and major radii of 1.0 cm was defined on the transverse plane and * f8 tally was calculated .
this torus was also composed of water . using * f8 tally ( in terms of mev ) in mcnp
therefore , dose rate is output of * f8 tally divided by the mass of the torus considering the units for conversion factors ( for example , ev to joule , grams to kilograms , yields , etc . ) .
dose rate constant then was obtained as the dose rate divided by the air kerma strength . as an example for conversion of the mc output ( for * f8 tally divided per mass in terms of : mev / g per photon ) to absorbed dose rate in units of cgy/(h.mci )
the following formula can be used:2dose rate(cgy / h)=mc output(mev / g per photon)106(ev / mev)1.60210 - 19(j / ev)103(g / kg)1.0mci10 - 3(ci / mci)3.71010(bq / ci)1(dis / s per bq)photon yield of101rh(photon
/ dis)100(cgy / gy)3600(s / h ) 
  with this regard , the value of photon yield of the rh radionuclide is equal to 2.37 photons / dis .
this value can be obtained from summation and normalization of the prevalences listed in table 1 .
the activity of rh source , used in this conversion was equal to 1.0 mci . in order to calculate radial dose function of the new source design , a spherical water phantom with 50 cm radius
torus voxels were considered at distances of 0.1 - 15.0 cm on the transverse plane of the source in the phantom .
the thicknesses of the tori were 0.4 mm at distances up to 1.0 cm , and 1.0 mm for other distances up to 15.0 cm .
the outputs of * f4 tally was used for calculation of dose rate at various radial distances . to have an acceptable level of uncertainty ,
this type of tally was used to speed up the calculations in the mcnp simulations .
finally , radial dose function was calculated from dose rate and geometry function values at various distances . for calculation of 2d anisotropy function ,
the same phantom ( i.e. spherical water phantom with 50 cm radius ) was defined as that described in calculation of radial dose function . for these simulations ,
the calculation points were located on a circular path around the source with the same radial distances , and different polar angles , ranging from 0 to 180 angles at 5 degrees intervals .
these points were divided into two groups , those that were along the longitudinal axis of the source , and those that were off the longitudinal axis .
spherical voxels with 0.1 cm diameter were utilized to score the dose on the longitudinal axis of the source . for the other points , tori with minor diameter of 0.4 mm
the minor diamaters of these tori were 1 mm for larger distances ( larger than 1.0 cm , up to 15.0 cm ) .
the reason for different tally voxel sizes at various distances is due to the presence of steep dose gradient as a function of distance from the source , which is an inherent effect in brachytherapy .
therefore , using larger voxel size at shorter distances may introduce artifacts in the calculations by volume - averaging .
the outputs of * f4 was used for calculation of 2d anisotropy functions . from the selected tallies at various distances ,
the 2d anisotropy function values were calculated for distances ranging between 0.5 - 15.0 cm and for angles between 0 to 180 with 5.0 degrees intervals . in calculation of tg-43 parameters ,
an attempt was also made to use toroid cells not having large dimensions at various reference directions to avoid volume - averaging artifacts . as an example , for calculation of anisotropy function at 2.0 cm distance and 30 angle , a torus with minor diameter of 1 mm at horizontal and vertical directions was utilized .
it should be noticed that in these calculations , the source delivery cable is coincident on the angle of 180 degrees . in all calculations ,
for calculation of tg-43 dosimetric parameters , except for 2d anisotropy function , the input files were run for 2.5  10 particles .
for calculation of 2d anisotropy function , in order to reduce the calculation uncertainties at larger distances from the source , the input file was run for 10 photons .
the maximum type a errors or statistical uncertainties in monte carlo calculations for air kerma strength , dose rate constant and radial dose function over all the evaluated distances were 0.3% , 3.32% and 0.44% , respectively .
the reason for having larger uncertainty in dose rate constant than the other two parameters was due to the use of * f8 tally in this case compared to f6 or * f4 tallies for the others . for similar particle scoring numbers , using * f8 tally in mcnp normally incorporates to larger uncertainty compared to the other tallies . the maximum type a uncertainty in calculation of 2d anisotropy function was 4.42% .
it should be noted that these values are type a uncertainties , by having ignored type b uncertainties and with a coverage factor ( k ) of 2.0 , the expanded uncertainties ( u ; u = ku 
 c , in which u 
 c is the combined uncertainty ) will be twice these values .
, the true value is in the  calculated value  2u    calculated value + 2u  interval with the probability of 0.95 .
the input programs were run using a personal computer having 64-bit windows 7.0 operating system , 3.20 ghz intel ( r ) core i7 cpu , and 2.00 gb ram . with this computer ,
the running time for the air kerma strength , dose rate constant , radial dose function , anisotropy function , with the aforementioned numbers of particles histories , was 5.25 h , 24.75 h , 25.50 h , and 134.25 h , respectively .
finally , the tg-43 dosimetric parameters of the hypothetical rh source were compared with the data for another hypothetical co source   and flexisource ir source .
air kerma strength per activity and dose rate constant values for the hypothetical rh source were obtained , and found to be 1.09  0.01 u / mci and 1.18  0.08 cgy/(hu ) , respectively .
the errors in these values are reported with a coverage factor of 2. a comparison of other characteristics of these three sources is shown in table 2 .
these characteristics include specific activity , half - life , average photons energy , etc . it can be noticed that the specific activity was calculated theoretically from : s = ( n 
 a)/m .
radial dose function of the hypothetical rh source as a function of radial distance is shown in table 3 .
2d anisotropy function values of the hypothetical rh as a function of radial distance and polar angles were listed in table 4 .
radial dose function for rh hypothetical source 2d anisotropy function for rh hypothetical source a comparison of the radial dose function of the hypothetical rh source with the published data for the hypothetical co source , and flexisource ir source is shown in figure 2 .
moreover , figure 3 shows the comparison between the 2d anisotropy function of the hypothetical rh source and the values from hypothetical co source and flexisource ir source , at the distances of 0.5 , 1.0 , 5.0 , and 10.0 cm from the source .
the data presented in figures 2 and 3 for the hypothetical co source was obtained via personal communication .
the data for the flexisource ir source in these figures were extracted from the data reported by granero et al . .
a comparison of the radial dose function for the hypothetical rh source , hypothetical co source and flexisource ir source a comparison of the 2d anisotropy function for the hypothetical rh source , hypothetical co source and flexisource ir source at the distances of ( a ) : 0.5 cm ; ( b ) : 1.0 cm ; ( c ) : 5.0 cm ; ( d ) : 10.0 cm from the source
in the present study , tg-43 dosimetric parameters of a hypothetical rh source were calculated and compared with those of a hypothetical co and a commercially available flexisource ir sources .
based on the data in table 2 , air kerma strength per mci activity for the hypothetical rh source is higher ( factor of 2.37 ) than that of the hypothetical co source and less ( factor of 3.32 ) than that of ir source .
since all the three sources have the same geometrical structure , this effect is due to the differences in yield and specific activities , energy spectra of photons emitted from the radionuclides and self - absorptions inside the active cores .
higher air kerma strength per mci is an advantage for ir brachytherapy source over rh .
however , this source ( rh ) has more than twice air kerma strength per mci higher than that for co. air kerma strength per mci activity indicates the level of self - absorption inside a source , and depends on the energy spectrum of a radionuclide and source design . on the other hand ,
dose rate constant of the hypothetical rh source is approximately the same as than those for co and ir sources .
therefore , it can be concluded that per u of air kerma strength , these sources can release the same dose rates at the reference distance ( 1.0 cm ) from the source in water .
based on the data presented in figure 2 , radial dose function for the hypothetical rh source is larger than the values for ir source for distances greater than 1.0 cm .
this comparison indicates that there would be a larger dose delivered to the tissues located at larger distances from the hypothetical rh source than the ir source .
for example , at a distance of 8.0 cm , the radial dose functions of the rh and ir sources are 1.16 and 0.96 , respectively .
therefore , at this distance , rh delivers approximately 21% larger dose than ir source .
this is an excellent advantage for brachytherapy treatment of many different cancer patients , such as cervical or deep seated vaginal cancer .
moreover , the skin sparing characteristics of the rh source may become superior to the ir sources for some treatments such as the breast cancer with accuboost system .
interestingly , this graph indicates that the co source delivers larger dose than both rh and ir sources , which can be accounted as an advantage for this source . 

figure 3 shows that , except at very small angles ( < 20 degrees ) , the 2d anisotropy function data of rh very similar to the ir and co data for all distances .
2d anisotropy function explains the non - isotropic feature of dose distribution around the source due to self - absorption within the source and distribution of the activity with a linear pattern .
it should be clear that the present results of tg-43 parameters for the rh source are only valid for the geometry design that is defined in this study and they can not be used for the clinical purposes . therefore , the dose distribution and the tg-43 parameters will change by variation in the source design for the hypothetical rh sources .
in other words , the results of this work , especially anisotropy , depend on the structural details of the source design .
moreover , anisotropy can not be used as a criterion for advocating the use of a new radionuclide for brachytherapy .
there are cases , in which highly anisotropic sources can be used effectively , provided their anisotropy function is accurately known .
this leaves air kerma strength , dose rate constant , and radial dose function as tg-43 quantities meaningful for the evaluation of a candidate radionuclide for brachytherapy .
their appropriateness , however , should be assessed in the context of a specific application . as a sample ,
the study by lymperopoulou et al .   compares yb with ir for use as sources in prostate brachytherapy .
the same evaluations can be performed for the rh radionuclide for application in prostate brachytherapy . in the following text ,
some aspects of use of this source in interstitial rotating shield brachytherapy ( i - rsbt ) are described .
based on the data presented in table 2 , the energy of photons emitted by rh is on average lower than ir .
therefore , for medium energy photons emitted by rh , the required thickness of the shielding ( with half - value layer of 0.0331 mm lead ) is much lower than that needed for protection against ir brachytherapy source ( 2.97 mm lead ) .
it should be noticed that having compared only the average photon energies of these sources ( table 2 ) , the hvl differences are not justified .
the lower thickness for shielding requirement will reduce the costs of treatment room shielding for the rh source .
other advantages of rh are relatively long half - life of 3.3 years and high specific activity of 397 tbq / g .
these suitable characteristics made rh radionuclide interesting for application as a brachytherapy source . on the other hand ,
air kerma strength per mci activity of the rh source with the proposed geometry is lower than that of ir source . while this effect will depend on the geometries of these two sources with the assumed geometries
this is because that with the same and specific activities for these two sources , with ir the source strength will be higher and this is corresponded to a lower treatment time duration in a single treatment session . as listed in table 2 ,
dose rate constant of the rh is 1.18 cgy/(h.u ) , which is approximately 6% larger than the ir value of 1.114 .
therefore , the rh with the specified source design is able to deliver approximately 6% larger dose per air kerma strength than the ir source .
the significance of this difference should be evaluated by considering the radiobiology of the treatment site .
enger et al .   has reported a dose rate at 1.0 cm in water of 4.18  10 cgy / h for a varisource ir source with activity of 370 gbq ( i.e. equivalent to 10 ci ) .
based on our monte carlo calculations , this quantity for the rh hypothetical source with a flexisource design is equal to 35.29 cgy/(h.gbq ) .
while this variable for rh source is lower than that of ir source , the source designs should be taken into account , since varisource ir source has an active length of 10.0 mm but flexisource design have a 3.5 mm one .
this comparison was performed roughly for these two sources and a precise comparison should be performed with sources with the same geometries because self - absorption inside a source and encapsulation geometry and composition will affect the dose rate at 1.0 cm distance inside a water phantom .
generally , a lower dose rate per activity at 1.0 cm will need to higher activity or higher treatment time for a standard prescribed dose regime , and , therefore , for having a reasonable treatment time a multiple - source choice may be relevant . for having a higher activity , the production costs will be higher due to longer irradiation time needed for the target in a cyclotron or nuclear reactor . with this regard ,
a comparison more consistent with tg-43 formalism can be performed with comparison of dose rate constants of the sources . since in dose rate constant ,
dose rate is normalized to air kerma strength ( instead of activity in mci ) and having mci to u conversion factors for the ir and rh sources is necessary to have a conversion from dose rate at 1.0 cm per activity to dose rate constant . in a study by lymperopoulou et al .
, monte carlo simulation was utilized and yb was compared to ir for breast hdr brachytherapy with multiple catheter implants .
the results using dose volume histogram indicated that yb could be at least as effective as ir in delivering the same dose to the lung and with slightly less dose to the skin on breast .
the finding implied that for the sources with intermediate photon energy such as yb , there is a need for the modification of calculation algorithms used in clinical treatment planning applied in particular brachytherapy practices .
.   assumed a hypothetical yb source in evaluation of the use of this radionuclide for prostate hdr brachytherapy .
yb proved to be at least equivalent to ir , independent to the prostate volume in the situation that the radiation scattering be overcompensated for absorption in intermediate energies and distances in prostate hdr brachytherapy .
having reviewed the methods used in the aforementioned studies , and the point that the rh source was evaluated only from tg-43 and general dosimetric specifications , it is recommended that this radionuclide be evaluated further in comparison with ir in brachytherapy applications for various cancers .
one may need to consider two other aspects of the rh source in application of this source in brachytherapy .
it is mentioned in the introduction section that rh is produced by deuteron irradiation of isotopes of ru . theoretically , there are also other possible reactions for rh production .
some examples are : rh(n , 3n)rh ; pd(n , np)rh and pd(n , d)rh .
these reactions can be achieved by neutron irradiation of the target in a nuclear reactor .
it should be noticed that these reactions require fast neutrons and are not accounted as fission reactions .
the cross sections of these deuteron or neutron reactions are of importance when having enough activity of the rh product is aimed .
recently , a study was performed and it was disclosed that with 100 h cyclotron run time having 1 a beam current , about 900 mbq of rh can be produced . in other words ,
a maximum beam current of 1 a could be achieved in the experiments with bonn cyclotron .
rh decays to rh with a half - life of 4.34 days , and due to the short half - life of rh and long half - life of rh , production of rh with a cyclotron can be an alternative for achievement of rh . as another pathway for production of rh , it was also reported that irradiation of y by c can be proposed as a pathway to produce rh .
an issue , which could be considered with this process is the contamination of rh by other radionuclides and its influence on the tg-43 parameters .
the cross section of rh as compared to those of ir is relevant in these considerations .
ir is produced as a fission product in a nuclear reactor by irradiation of the target by thermal neutrons .
production of a radioisotope in a nuclear reactor result to lower production costs compared to a cyclotron .
although , due to lower energy photons emitted by rh relative to ir , the construction costs of shielding for treatment room may be lower , the production costs for rh source may be more than that of ir source .
i - rsbt method was evaluated for gd radioisotope in a study by adams et al . .
in that study a novel needle , catheter and source system was presented for ( i - rsbt ) application in brachytherapy of prostate .
their justification for application of a shielded source and catheter system was their aim to reduce the dose received by urethra , rectum , and bladder .
the reason for use of gd source instead of i and ir sources was that i sources has normally rapid dose fall - off in soft tissue and the thickness for shielding of ir sources would be large and can not be fitted in catheters , which are normally used in prostate brachytherapy .
however , rh emits a number of relatively high energy photons albeit with lower prevalence ( table 1 ) .
the average photon energy and half - value layer ( hvl ) in lead for rh is much lower than that of ir .
a comparison between the hvl for gd and rh may be interesting for use in i - rsbt .
the hvl ( in mm pb ) for gd and rh are 0.0783 and 0.0331 , respectively .
it is evident that with rh a lower thickness of shielding is required in this method .
however , a quantitative evaluation of shielding requirements for application in i - rsbt as a subject of further research in this field and will be interesting . the evaluations on the rh radionuclide could be accomplished simply using point source approximation that is time efficient but still meaningful with the purpose of only indication of an effect .
a number of previous studies have used this approximation in their evaluations . in a report on dose calculation in brachytherapy , it was proposed as a consideration for high energy photon emitting brachytherapy sources that modeling of sources using point source approximation is facilitated by averaging dose anisotropy over all angles .
this method of calculation can be used in permanent prostate brachytherapy dose calculation , in which seed orientation is not distinguishable for clinical non - stranded application due to the large number of seed orientations .
utilizing a point source could be easier and faster to perform but we preferred to execute a precise evaluation on this source similar to other articles on hypothetical sources by simulation of the source in its complete geometry [ 1012 ] .
based on the aapm and estro report on high - energy sources , spherical phantom radius of 40 cm was recommended .
the size of the spherical phantom used in this study is 50 cm and therefore the full scatter condition is obtained .
this report also announced recommendations on maximum voxel sizes , which are being used for scoring the dosimetric variables to minimize the volume - averaging artifacts : ( 0.1 mm ) voxels for r  1 cm ; 0.5  0.5  0.5 mm voxels for 1 cm < r  5 cm ; 1  1  1 mm voxels for 5 cm < r  10 cm and 2  2  2 mm voxels for 10 cm < r  20 cm . in the present study , voxels are not cubic and are in the form of toroidal cells with 0.4 mm in thickness for r < 1 cm and with 1 mm thickness for the other distances .
there are minor differences between our methodology for the thickness of the tally cells and those recommended by the aapm and estro report at close distances from the source , and this point should be noticed in the further methodologies .
the spectral data of rh radionuclide used in the simulations in this study ( table 1 ) were extracted from a database presented by lund university . on the other hand , a joint report by american association of physicists in medicine ( aapm ) , and european society for therapeutic radiology and oncology ( estro )  
recommends that national nuclear data center ( nndc ) data be used in application of brachytherapy sources , which are clinically related .
nndc includes three datasets for energy spectra of the rh radionuclide . in a study by rivard et al .
, the influence of the choice of energy spectrum on kerma and dose distributions of three brachytherapy sources was evaluated .
it was observed that there were water - kerma differences of about 2% , 2% , and 0.7% with various spectrum choices for ir , i , and pd sources , respectively .
furthermore , the influence of photon spectrum on the dose rate constant and the radial dose function ranged from 0.1 - 2% . as a rough evaluation , the photon yields from the spectrum used in this study ( table 1 ) and the dataset no .
3 of nndc   for rh are 2.3705 photons / dis . and 2.3670 photons / dis .
the details are not presented herein but the spectrum used in the present study for the rh has more detailed energies than that announced by nndc .
while it is predicted that relatively the same results will be obtained with various choices of reference spectra for the hypothetical rh source , it is recommended that the spectrum from the nndc website be used in the future studies on this source .
treatment planning in brachytherapy has advancements starting from simple look - up tables up to computerized dose calculation algorithms .
the current algorithms are based on the tg-43 formalism with recent advances in calculation of dose distributions for single sources . however , this formalism has limitations for calculation of patient dose .
various dose calculation algorithms are being developed based on : monte carlo methods , collapsed cone , etc .
the scopes of current advancements in brachytherapy include : improved dose calculation tools , planning systems to account for heterogeneities , scattering conditions , radiobiology , and image guidance brachytherapy .
following literature reports announcing the deficiencies involved in the approximations of conventional brachytherapy dosimetry , model - based dosimetry algorithms were incorporated in commercial brachytherapy treatment planning systems .
the primary calculations of these algorithms are defined , having criteria established by the developers with the purpose of optimization of computation speed and accuracy . on the other hand ,
a basic realization of the limitations of these algorithms in commissioning step and their further evaluations compared to the conventional ones is necessary .
186 provided guidance for early adopters of model - based dose calculation algorithms for brachytherapy users .
dose calculation accuracy in brachytherapy highly depends on the scatter conditions and photoelectric cross - sections relative to water . in some situations
, differences between the tg-43 and model - based algorithms can lead to dose differences exceeding a factor of 10 .
model - based dose calculation algorithms raise the major aspects , which are not addressed by current guidelines : dose sensitivity to the dose specification medium , dose calculation for the local medium in heterogeneous medium , and the dose in a small volume of water in heterogeneous medium .
was evaluated from only general and tg-43 dosimetric parameters , further evaluation of this source from the view of model - based dose calculation algorithms can be a subject of more complementary studies .
in the present study , tg-43 dosimetric parameters of a hypothetical rh source were calculated and compared with those of a hypothetical co and a commercially available flexisource ir sources .
based on the data in table 2 , air kerma strength per mci activity for the hypothetical rh source is higher ( factor of 2.37 ) than that of the hypothetical co source and less ( factor of 3.32 ) than that of ir source .
since all the three sources have the same geometrical structure , this effect is due to the differences in yield and specific activities , energy spectra of photons emitted from the radionuclides and self - absorptions inside the active cores .
higher air kerma strength per mci is an advantage for ir brachytherapy source over rh .
however , this source ( rh ) has more than twice air kerma strength per mci higher than that for co. air kerma strength per mci activity indicates the level of self - absorption inside a source , and depends on the energy spectrum of a radionuclide and source design . on the other hand ,
dose rate constant of the hypothetical rh source is approximately the same as than those for co and ir sources .
therefore , it can be concluded that per u of air kerma strength , these sources can release the same dose rates at the reference distance ( 1.0 cm ) from the source in water .
based on the data presented in figure 2 , radial dose function for the hypothetical rh source is larger than the values for ir source for distances greater than 1.0 cm .
this comparison indicates that there would be a larger dose delivered to the tissues located at larger distances from the hypothetical rh source than the ir source .
for example , at a distance of 8.0 cm , the radial dose functions of the rh and ir sources are 1.16 and 0.96 , respectively .
therefore , at this distance , rh delivers approximately 21% larger dose than ir source .
this is an excellent advantage for brachytherapy treatment of many different cancer patients , such as cervical or deep seated vaginal cancer .
moreover , the skin sparing characteristics of the rh source may become superior to the ir sources for some treatments such as the breast cancer with accuboost system .
interestingly , this graph indicates that the co source delivers larger dose than both rh and ir sources , which can be accounted as an advantage for this source . 

figure 3 shows that , except at very small angles ( < 20 degrees ) , the 2d anisotropy function data of rh very similar to the ir and co data for all distances .
2d anisotropy function explains the non - isotropic feature of dose distribution around the source due to self - absorption within the source and distribution of the activity with a linear pattern .
it should be clear that the present results of tg-43 parameters for the rh source are only valid for the geometry design that is defined in this study and they can not be used for the clinical purposes . therefore , the dose distribution and the tg-43 parameters will change by variation in the source design for the hypothetical rh sources .
in other words , the results of this work , especially anisotropy , depend on the structural details of the source design .
moreover , anisotropy can not be used as a criterion for advocating the use of a new radionuclide for brachytherapy .
there are cases , in which highly anisotropic sources can be used effectively , provided their anisotropy function is accurately known .
this leaves air kerma strength , dose rate constant , and radial dose function as tg-43 quantities meaningful for the evaluation of a candidate radionuclide for brachytherapy .
their appropriateness , however , should be assessed in the context of a specific application . as a sample ,
the study by lymperopoulou et al .   compares yb with ir for use as sources in prostate brachytherapy .
the same evaluations can be performed for the rh radionuclide for application in prostate brachytherapy . in the following text ,
some aspects of use of this source in interstitial rotating shield brachytherapy ( i - rsbt ) are described .
based on the data presented in table 2 , the energy of photons emitted by rh is on average lower than ir .
therefore , for medium energy photons emitted by rh , the required thickness of the shielding ( with half - value layer of 0.0331 mm lead ) is much lower than that needed for protection against ir brachytherapy source ( 2.97 mm lead ) .
it should be noticed that having compared only the average photon energies of these sources ( table 2 ) , the hvl differences are not justified .
the lower thickness for shielding requirement will reduce the costs of treatment room shielding for the rh source .
other advantages of rh are relatively long half - life of 3.3 years and high specific activity of 397 tbq / g .
these suitable characteristics made rh radionuclide interesting for application as a brachytherapy source . on the other hand ,
air kerma strength per mci activity of the rh source with the proposed geometry is lower than that of ir source . while this effect will depend on the geometries of these two sources with the assumed geometries
this is because that with the same and specific activities for these two sources , with ir the source strength will be higher and this is corresponded to a lower treatment time duration in a single treatment session . as listed in table 2 ,
dose rate constant of the rh is 1.18 cgy/(h.u ) , which is approximately 6% larger than the ir value of 1.114 .
therefore , the rh with the specified source design is able to deliver approximately 6% larger dose per air kerma strength than the ir source .
the significance of this difference should be evaluated by considering the radiobiology of the treatment site .
enger et al .   has reported a dose rate at 1.0 cm in water of 4.18  10 cgy / h for a varisource ir source with activity of 370 gbq ( i.e. equivalent to 10 ci ) .
based on our monte carlo calculations , this quantity for the rh hypothetical source with a flexisource design is equal to 35.29 cgy/(h.gbq ) .
while this variable for rh source is lower than that of ir source , the source designs should be taken into account , since varisource ir source has an active length of 10.0 mm but flexisource design have a 3.5 mm one .
this comparison was performed roughly for these two sources and a precise comparison should be performed with sources with the same geometries because self - absorption inside a source and encapsulation geometry and composition will affect the dose rate at 1.0 cm distance inside a water phantom .
generally , a lower dose rate per activity at 1.0 cm will need to higher activity or higher treatment time for a standard prescribed dose regime , and , therefore , for having a reasonable treatment time a multiple - source choice may be relevant . for having a higher activity , the production costs will be higher due to longer irradiation time needed for the target in a cyclotron or nuclear reactor . with this regard ,
a comparison more consistent with tg-43 formalism can be performed with comparison of dose rate constants of the sources . since in dose rate constant ,
dose rate is normalized to air kerma strength ( instead of activity in mci ) and having mci to u conversion factors for the ir and rh sources is necessary to have a conversion from dose rate at 1.0 cm per activity to dose rate constant . in a study by lymperopoulou et al .
, monte carlo simulation was utilized and yb was compared to ir for breast hdr brachytherapy with multiple catheter implants .
the results using dose volume histogram indicated that yb could be at least as effective as ir in delivering the same dose to the lung and with slightly less dose to the skin on breast .
the finding implied that for the sources with intermediate photon energy such as yb , there is a need for the modification of calculation algorithms used in clinical treatment planning applied in particular brachytherapy practices .
.   assumed a hypothetical yb source in evaluation of the use of this radionuclide for prostate hdr brachytherapy .
yb proved to be at least equivalent to ir , independent to the prostate volume in the situation that the radiation scattering be overcompensated for absorption in intermediate energies and distances in prostate hdr brachytherapy .
having reviewed the methods used in the aforementioned studies , and the point that the rh source was evaluated only from tg-43 and general dosimetric specifications , it is recommended that this radionuclide be evaluated further in comparison with ir in brachytherapy applications for various cancers .
one may need to consider two other aspects of the rh source in application of this source in brachytherapy .
it is mentioned in the introduction section that rh is produced by deuteron irradiation of isotopes of ru . theoretically , there are also other possible reactions for rh production .
some examples are : rh(n , 3n)rh ; pd(n , np)rh and pd(n , d)rh .
these reactions can be achieved by neutron irradiation of the target in a nuclear reactor .
it should be noticed that these reactions require fast neutrons and are not accounted as fission reactions .
the cross sections of these deuteron or neutron reactions are of importance when having enough activity of the rh product is aimed .
recently , a study was performed and it was disclosed that with 100 h cyclotron run time having 1 a beam current , about 900 mbq of rh can be produced . in other words ,
a maximum beam current of 1 a could be achieved in the experiments with bonn cyclotron .
rh decays to rh with a half - life of 4.34 days , and due to the short half - life of rh and long half - life of rh , production of rh with a cyclotron can be an alternative for achievement of rh . as another pathway for production of rh , it was also reported that irradiation of y by c can be proposed as a pathway to produce rh .
an issue , which could be considered with this process is the contamination of rh by other radionuclides and its influence on the tg-43 parameters .
the cross section of rh as compared to those of ir is relevant in these considerations .
ir is produced as a fission product in a nuclear reactor by irradiation of the target by thermal neutrons .
production of a radioisotope in a nuclear reactor result to lower production costs compared to a cyclotron .
although , due to lower energy photons emitted by rh relative to ir , the construction costs of shielding for treatment room may be lower , the production costs for rh source may be more than that of ir source .
i - rsbt method was evaluated for gd radioisotope in a study by adams et al . .
in that study a novel needle , catheter and source system was presented for ( i - rsbt ) application in brachytherapy of prostate .
their justification for application of a shielded source and catheter system was their aim to reduce the dose received by urethra , rectum , and bladder .
the reason for use of gd source instead of i and ir sources was that i sources has normally rapid dose fall - off in soft tissue and the thickness for shielding of ir sources would be large and can not be fitted in catheters , which are normally used in prostate brachytherapy .
however , rh emits a number of relatively high energy photons albeit with lower prevalence ( table 1 ) .
the average photon energy and half - value layer ( hvl ) in lead for rh is much lower than that of ir .
a comparison between the hvl for gd and rh may be interesting for use in i - rsbt .
the hvl ( in mm pb ) for gd and rh are 0.0783 and 0.0331 , respectively .
it is evident that with rh a lower thickness of shielding is required in this method .
however , a quantitative evaluation of shielding requirements for application in i - rsbt as a subject of further research in this field and will be interesting .
the evaluations on the rh radionuclide could be accomplished simply using point source approximation that is time efficient but still meaningful with the purpose of only indication of an effect .
a number of previous studies have used this approximation in their evaluations . in a report on dose calculation in brachytherapy , it was proposed as a consideration for high energy photon emitting brachytherapy sources that modeling of sources using point source approximation is facilitated by averaging dose anisotropy over all angles .
this method of calculation can be used in permanent prostate brachytherapy dose calculation , in which seed orientation is not distinguishable for clinical non - stranded application due to the large number of seed orientations .
utilizing a point source could be easier and faster to perform but we preferred to execute a precise evaluation on this source similar to other articles on hypothetical sources by simulation of the source in its complete geometry [ 1012 ] .
based on the aapm and estro report on high - energy sources , spherical phantom radius of 40 cm was recommended .
the size of the spherical phantom used in this study is 50 cm and therefore the full scatter condition is obtained .
this report also announced recommendations on maximum voxel sizes , which are being used for scoring the dosimetric variables to minimize the volume - averaging artifacts : ( 0.1 mm ) voxels for r  1 cm ; 0.5  0.5  0.5 mm voxels for 1 cm < r  5 cm ; 1  1  1 mm voxels for 5 cm < r  10 cm and 2  2  2 mm voxels for 10 cm < r  20 cm . in the present study ,
voxels are not cubic and are in the form of toroidal cells with 0.4 mm in thickness for r < 1 cm and with 1 mm thickness for the other distances .
there are minor differences between our methodology for the thickness of the tally cells and those recommended by the aapm and estro report at close distances from the source , and this point should be noticed in the further methodologies .
the spectral data of rh radionuclide used in the simulations in this study ( table 1 ) were extracted from a database presented by lund university . on the other hand , a joint report by american association of physicists in medicine ( aapm ) , and european society for therapeutic radiology and oncology ( estro )  
recommends that national nuclear data center ( nndc ) data be used in application of brachytherapy sources , which are clinically related .
nndc includes three datasets for energy spectra of the rh radionuclide . in a study by rivard et al .
, the influence of the choice of energy spectrum on kerma and dose distributions of three brachytherapy sources was evaluated .
it was observed that there were water - kerma differences of about 2% , 2% , and 0.7% with various spectrum choices for ir , i , and pd sources , respectively .
furthermore , the influence of photon spectrum on the dose rate constant and the radial dose function ranged from 0.1 - 2% . as a rough evaluation , the photon yields from the spectrum used in this study ( table 1 ) and the dataset no .
3 of nndc   for rh are 2.3705 photons / dis . and 2.3670 photons / dis . , respectively .
the details are not presented herein but the spectrum used in the present study for the rh has more detailed energies than that announced by nndc .
while it is predicted that relatively the same results will be obtained with various choices of reference spectra for the hypothetical rh source , it is recommended that the spectrum from the nndc website be used in the future studies on this source .
treatment planning in brachytherapy has advancements starting from simple look - up tables up to computerized dose calculation algorithms .
the current algorithms are based on the tg-43 formalism with recent advances in calculation of dose distributions for single sources . however , this formalism has limitations for calculation of patient dose .
various dose calculation algorithms are being developed based on : monte carlo methods , collapsed cone , etc .
the scopes of current advancements in brachytherapy include : improved dose calculation tools , planning systems to account for heterogeneities , scattering conditions , radiobiology , and image guidance brachytherapy .
following literature reports announcing the deficiencies involved in the approximations of conventional brachytherapy dosimetry , model - based dosimetry algorithms were incorporated in commercial brachytherapy treatment planning systems .
the primary calculations of these algorithms are defined , having criteria established by the developers with the purpose of optimization of computation speed and accuracy . on the other hand ,
a basic realization of the limitations of these algorithms in commissioning step and their further evaluations compared to the conventional ones is necessary .
186 provided guidance for early adopters of model - based dose calculation algorithms for brachytherapy users .
dose calculation accuracy in brachytherapy highly depends on the scatter conditions and photoelectric cross - sections relative to water . in some situations
, differences between the tg-43 and model - based algorithms can lead to dose differences exceeding a factor of 10 .
model - based dose calculation algorithms raise the major aspects , which are not addressed by current guidelines : dose sensitivity to the dose specification medium , dose calculation for the local medium in heterogeneous medium , and the dose in a small volume of water in heterogeneous medium .
was evaluated from only general and tg-43 dosimetric parameters , further evaluation of this source from the view of model - based dose calculation algorithms can be a subject of more complementary studies .
advantages of rh to ir are having relatively longer half - life ( 3.3 years versus 74 days ) , higher specific activity ( 397 tbq / g versus 341 tbq / g)k , and very low half - value layer ( 0.0331 mm in lead versus 2.97 mm of lead ) .
air kerma strength per activity for hypothetical rh source is about twice than that of hypothetical co source and it has a dose rate constant comparable to hypothetical co and ir sources .
radial dose function for the rh hypothetical source is greater than that of ir source for distances greater than 1.0 cm .
the 2d anisotropy function of rh is very similar to that of ir , which can be taken into account as another advantage of this new proposed source . with these suitable physical properties ,
 purposerecently a number of hypothetical sources have been proposed and evaluated for use in brachytherapy . in the present study , a hypothetical 101rh source with mean 
 photon energy of 121.5 kev and half - life of 3.3 years , has been evaluated as an alternative to the existing high - dose - rate ( hdr ) sources . 
 dosimetric characteristics of this source model have been determined following the recommendation of the task group 43 ( tg-43 ) of the american association of the physicist in medicine ( aapm ) , and the results are compared with the published data for 57co source and flexisource 192ir sources with similar geometries.material and methodsmcnpx monte carlo code was used for simulation of the 101rh hypothetical hdr source design . 
 geometric design of this hypothetical source was considered to be similar to that of flexisource 192ir source . 
 task group no . 
 43 dosimetric parameters , including air kerma strength per mci , dose rate constant , radial dose function , and two dimensional ( 2d ) anisotropy functions were calculated for the 101rh source through simulations.resultsair kerma strength per activity and dose rate constant for the hypothetical 101rh source were 1.09  0.01 u / mci and 1.18  0.08 cgy/(h.u ) , respectively . at distances beyond 1.0 cm in phantom , radial dose function for the hypothetical 101rh source is higher than that of 192ir . 
 it has also similar 2d anisotropy functions to the flexisource 192ir source.conclusions101rh is proposed as an alternative to the existing hdr sources for use in brachytherapy . 
 this source provides medium energy photons , relatively long half - life , higher dose rate constant and radial dose function , and similar 2d anisotropy function to the flexisource 192ir hdr source design . 
 the longer half - life of the source reduces the frequency of the source exchange for the clinical environment . 
Purpose
Material and methods
Design for the hypothetical 
Calculation of TG-43 dosimetric parameters
Results
Discussion
Dosimetric comparison with other radionuclides
Production of 
Use of 
Limitations and suggestions for further research
Conclusions
Disclosure