Indian Journal of Nuclear Medicine

: 2013  |  Volume : 28  |  Issue : 1  |  Page : 17--22

Bremsstrahlung dose of therapeutic beta nuclides in bone and muscle

HC Manjunatha 
 Department of Physics, Government College for Women, Kolar, Karnataka, India

Correspondence Address:
H C Manjunatha
Department of Physics, Government College for Women, Kolar - 563 101, Karnataka


In the nuclear medicine, beta nuclides are released during the treatment. This beta interacts with bone and muscle and produces external Bremsstrahlung (EB) radiation. Present work formulated a new method to evaluate the EB spectrum and hence the Bremsstrahlung dose of therapeutic beta nuclides (Lu-177, Sr-90, Sm-153, I-153, Cs-137, Au-201, Dy-165, Mo-99, Sr-89, Fe-59, P-32, Ho-166, Sr-92, Re-188, Y-90, Pr-147, Co-60, K-42) in bone and muscle. The Bremsstrahlung yields of these beta nuclides are also estimated. Bremsstrahlung production is higher in bone than that of muscle. Presented data provides a quick and convenient reference for radiation protection and it can be quickly employed to give a first pass dose estimate prior to a more detailed experimental study.

How to cite this article:
Manjunatha H C. Bremsstrahlung dose of therapeutic beta nuclides in bone and muscle.Indian J Nucl Med 2013;28:17-22

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Manjunatha H C. Bremsstrahlung dose of therapeutic beta nuclides in bone and muscle. Indian J Nucl Med [serial online] 2013 [cited 2023 Mar 24 ];28:17-22
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In the therapeutic nuclear medicine, application of incorporated beta emitting radionuclides finds extremely high potential in the treatment of both malignant and non-malignant conditions. The beta emitting nuclides are also used for therapy of non-malignant conditions like radiosynovectomy. This includes the treatment of painful conditions associated with disease of joints such as rheumatoid arthritis or villonodular synovitis. [1] After careful evaluation and diagnosis, a small amount of radioisotope is injected into the joint. These radioisotopes emit beta rays, which penetrate only from fraction of a millimeter to a few millimeters and destroy the inflammatory tissue and thus reduce swelling and pain. Beta emitting nuclides such as Y-90, P-32, Dy-265, etc., offers clinically proven and cost-effective alternative to surgical synovictomy. [2] Uchiyama et al. [3] reported that Sr-89 chloride is being widely used as a palliative treatment for patients with bone pain caused by bone metastases. The radio nuclides such as Sr-89 and P-32 have also been successfully and effectively utilized to provide palliative therapy to patients with multifocal skeletal metastatic lesions in cases of breast and prostatic cancers. Furthermore, Y-90 appears to be a potential beta emitting radionuclide, which has been shown to offer attractive considerations for being used in radioimmunotherapy. [4] In radioimmunotherapy, beta nuclide delivers lethal dose of radiation directly to cancerous tumor cells there by reducing the radiation exposure to surrounding tissues. Beta emitting radionuclide like P-32 also finds application in infusional brachytherapy. [5] The incorporated therapeutic beta emitting nuclides produces Bremsstrahlung radiation and could have different energies and intensities. The Bremsstrahlung component of beta emitters has been traditionally ignored in internal dosimetry calculations. This may be due to a lack of available methods for including this component in the calculations or to the belief that the contribution of this component is negligible compared to that of other emissions. The resulting hazard of Bremsstrahlung radiation released during beta therapy may therefore be of some concern, at least theoretically and should be systematically evaluated. In the present investigation, it has been estimated that the Bremsstrahlung spectrum and dose of therapeutic nuclides (Lu-177, Sr-90, Sm-153, I-153, Cs-137, Au-201, Dy-165, Mo-99, Sr-89, Fe-59, P-32, Ho-166, Sr-92, Re-188, Y-90, Pr-147, Co-60, K-42) in bone and muscle.

 Present Work

Estimation of external Bremsstrahlung (EB) cross-section

Markowicz and VanGriken [6] proposed an equation (1) to take into account the self-absorption of Bremsstrahlung and electron back scattering and to obtain the accurate description of the Bremsstrahlung process


A i , W i and Z i are mass number, weight fraction and atomic number of the i th element respectively, f is a function of E 0 , Eγ and composition. The modified atomic number Z mod defined for compound is more accurate [7] one than Z mean . The six elements whose atomic numbers adjacent to that of bone (Z mod = 10.2509) chosen are N, O, F, Ne, Na and Mg and their Z values are 7, 8, 9, 10, 11 and 12 respectively. Z mod is evaluated using equation (2) and their composition. [8] The EB cross-section is evaluated using Lagrange's interpolation technique, Seltzer-Berger [9] theoretical EB cross-section data given for elements using the following equation


where, lower case z is the atomic number of the element of known EB cross-section σz adjacent to Z mod of the compound whose EB cross-section σZmod is desired and upper case Z are atomic numbers of other elements of known EB cross-section adjacent to Z mod . Similarly, we have evaluated cross-section for muscle.

Evaluation of Bremsstrahlung spectrum

The number n (T, k) of EB photons of energy k when all of the incident electron energy T completely absorbed in thick target is given by Bethe and Heitler [10] is


where, σ (E, k) is EB cross-section at photon energy k and electron energy E, N is the number of atoms per unit volume of target and E is the energy of an electron available for an interaction with nucleus of the thick target after it undergoes a loss of energy per unit length (−dE/dx). For a beta emitter with end point energy T max , spectral distribution of EB photons (S [k]) is given by


where P (T) is the beta spectrum. Evaluated results of σ (E, k) of equation (3) and tabulated values of (−dE/dx) of Seltzer-Berger data are used to get S (k) for the target compounds.

Evaluation of Bremsstrahlung yield

The number of EB photons produced by electrons or beta particle while passing through a thick target enough to absorb them can be defined as photon yield (N) of the target. Energy yield (I) is the total Bremsstrahlung energy radiated per incident beta particle. EB photon yield (N) and energy yield (I) are evaluated from S (k) from the following equations


where k is the photon energy, k min and k max are the minimum and maximum energy of the measured photon spectrum.

Evaluation of Bremsstrahlung dose

We have used the following equation [11] for the calculation of specific absorbed fraction of energy at distance x from the point source monoenergetic photon emitter


Here, μ en is linear absorption coefficient of photons of given energy, μ is linear attenuation coefficient of photons of given energy, B en is energy absorption build up factor; ϱ is density of the medium. The energy absorption build up factors has been computed using Geometric progression fitting method.[12] The values of μ en and μ of photons have been taken from Hubbel. [13] The specific absorbed fraction for a given beta source was estimated by integrating over the entire Bremsstrahlung spectrum using the following equation (8).


where T max is the maximum energy of beta. Estimation of the value of Φ allows calculation of the absorbed dose at fixed distances from the point source in the infinite, homogeneous medium


where D (x) is the absorbed dose at distance × per unit initial activity (Gy/MBq); τ is the residence time of activity; and Δ is the mean energy emitted per unit cumulated activity and it is numerically equal to (2.13 n iEi ), where ni is the frequency of occurrence of emissions with energy E i ; the quantities n and E are provided by the calculated Bremsstrahlung spectrum using equation (5).

 Results and Discussion

The estimated σZmod (barn/MeV) for bone and muscle are shown in [Figure 1] and [Figure 2] respectively. In the [Figure 1] and [Figure 2], k and T are outgoing photon and incident electron energies respectively. The Bremsstrahlung cross-section values decreases with the increase in the electron energy. The maximum energy, Bremsstrahlung energy, Bremsstrahlung number and energy yield of the beta isotopes used in the present study are given in the [Table 1]. The evaluated Bremsstrahlung spectra employed in the dose calculations are shown in [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7] and [Figure 8]. These figures show that shapes of Bremsstrahlung spectra, which indicates the maximum and minimum Bremsstrahlung yield corresponds to their energy. Hence, the presented data provides a quick and convenient reference for radiation protection. Bremsstrahlung production is higher in bone than that of muscle. The shape of the Bremsstrahlung spectrum depends on the corresponding beta spectrum. Calculated values of absorbed dose (in Gy/MBq) due to Bremsstrahlung radiation for bone and muscle shown in [Table 2], [Table 3], [Table 4], [Table 5], [Table 6] and [Table 7]. These tables show that absorbed dose of Bremsstrahlung of bone and muscle decreases with the distance in the target medium. For example, injection of I-131 induce Bremsstrahlung dose 138.5 Gy/Bq at 1 mm from injected place [From [Table 2], which is not negligible. Similarly, we can analyze Bremsstrahlung dose for other nuclides also. Hence, the results showed that Bremsstrahlung dose may not always be negligible with in few mm of the target thickness and in such cases Bremsstrahlung component should be included in the dosimetric calculations of beta therapy.{Figure 1}{Figure 2}{Figure 3}{Figure 4}{Figure 5}{Figure 6}{Figure 7}{Figure 8}{Table 1}{Table 2}{Table 3}{Table 4}{Table 5}{Table 6}{Table 7}


The author thank Vision Group on Science and Technology (VGST), Govt. of Karnataka, India, for providing financial grants in the scheme ''SEED MONEY TO YOUNG SCIENTIST RESEARCH''.


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