The inverse square law: A basic principle in brachytherapy

The purpose of this article is to remind the importance of the inverse square law in radiotherapy and especially in brachytherapy. Indeed, beyond the impact in radiation therapy with high energy beam, there is the use of radionuclides and low energy photons with short FSD where it is still more important. Comparisons between Iridium Brachytherapy and low energy X-rays brachytherapy show equivalent dose distributions in the first few centimeters. If the inverse square law is not the only element influencing the dose distributions calculations, it must not be forgotten. And it is playing a major role in brachytherapy with short FSD (<6cm).

Accuracy evaluation of distance inverse square law in determining virtual electron source location in Siemens Primus linac

Aim

The aim of this study is to evaluate the accuracy of the inverse square law (ISL) method for determining location of virtual electron source (S_Vir) in Siemens Primus linac.

Background

So far, different experimental methods have presented for determining virtual and effective electron source location such as Full Width at Half Maximum (FWHM), Multiple Coulomb Scattering (MCS), and Multi Pinhole Camera (MPC) and Inverse Square Law (ISL) methods. Among these methods, Inverse Square Law is the most common used method.

Materials and methods

Firstly, Siemens Primus linac was simulated using MCNPX Monte Carlo code. Then, by using dose profiles obtained from the Monte Carlo simulations, the location of S_Vir was calculated for 5, 7, 8, 10, 12 and 14 MeV electron energies and 10 cm × 10 cm, 15 cm × 15 cm, 20 cm × 20 cm and 25 cm × 25 cm field sizes. Additionally, the location of S_Vir was obtained by the ISL method for the mentioned electron energies and field sizes. Finally, the values obtained by the ISL method were compared to the values resulted from Monte Carlo simulation.

Results

The findings indicate that the calculated S_Vir values depend on beam energy and field size. For a specific energy, with increase of field size, the distance of S_Vir increases for most cases. Furthermore, for a special applicator, with increase of electron energy, the distance of S_Vir increases for most cases. The variation of S_Vir values versus change of field size in a certain energy is more than the variation of S_Vir values versus change of electron energy in a certain field size.

Conclusion

According to the results, it is concluded that the ISL method can be considered as a good method for calculation of S_Vir location in higher electron energies (14 MeV).

No actual measurement … was required: Maxwell and Cavendish's null method for the inverse square law of electrostatics

In 1877 James Clerk Maxwell and his student Donald MacAlister refined Henry Cavendish's 1773 null experiment demonstrating the absence of electricity inside a charged conductor. This null result was a mathematical prediction of the inverse square law of electrostatics, and both Cavendish and Maxwell took the experiment as verifying the law. However, Maxwell had already expressed absolute conviction in the law, based on results of Michael Faraday's. So, what was the value to him of repeating Cavendish's experiment? After assessing whether the law was as secure as he claimed, this paper explores its central importance to the electrical programme that Maxwell was pursuing. It traces the historical and conceptual re-orderings through which Maxwell established the law by constructing a tradition of null tests and asserting the superior accuracy of the method. Maxwell drew on his developing 'doctrine of method' to identify Cavendish's experiment as a member of a wider class of null methods. By doing so, he appealed to the null practices of telegraph engineers, diverted attention from the flawed logic of the method, and sought to localise issues around the mapping of numbers onto instrumental indications, on the grounds that 'no actual measurement … was required'.