Analytical investigation of the practical range and deflection of megavoltage electron beam in the water phantom with the presence of magnetic field

Introduction: Integrated radiation therapy - MRI systems are capable of delivering high doses to the target tissues near sensitive organs and achieve better therapeutic results; however, the Applied magnetic fields for imaging, can influence the charged path, change the penetration depth and deflect the particles, laterally, leading to dose distribution variations. Therefore, investigating the effects of magnetic field on charged particles is important in treatment planning. Therefore, this study aimed to calculate the effects of magnetic field on the range and lateral deflection electrons to determine analytic relations for treatment planning of electron therapy integrated with MRI-systems. Also, these relations will be used to active condensing of charged particle dose in target volume. Materials and methods: An analytical survey based on electron practical range and energy, was done. The penetration depth and lateral deflection of electrons with therapeutic energy ranges in the presence of uniform magnetic field were calculated, analytically. Calculations were done with Mathematica software version 7.0 and MATLAB 7.0 was applied to plot curves and curve fittings. Results: A cubic polynomial with linear coefficients and a power model with constant power model were applied to illustrate lateral deflection and practical range of electrons as a function of initial energy and magnetic field intensity. Electrons go to spiral path with increasing magnetic field intensity about 1.25 Tesla. Conclusion: The proposed analytical approach can calculate the lateral deflection and penetration depth of electrons in the water phantom in the presence of magnetic field of any intensities fast and accurately. This method can be used to calculate dose variations in integrated radiation therapy- MRI imaging systems for treatment planning and research proposes. Due to fast calculations of the presented analytical method in comparison with Monte Carlo based approaches, the calculations time in treatment systems will be decreased.