Latest researches predict the cosmic rays exposure during long space missions outside the Earth's geomagnetic sphere, as to the Moon and Mars, can double the cancer risk. The minimization of risk associated with radiation exposure in the Low Earth Orbit (LEO) is of great interest for astronauts of the International Space Station (ISS). This risk is due to radiation hazard and can be predicted by measurement of the dose equivalent produced by the radiation environment inside of the spacecraft. Since more than 15 years ago, the Centre For Medical Radiation Physics (CMRP), University of Wollongong, is developing silicon based microdosimeters as alternative solution to Tissue Equivalence Proportional Counters, for dose equivalent determination in the context of astronauts radiation protection. This work describes a Geant4-based study characterising the radiation environment encountered by astronauts inside the ISS. In particular, the energy spectra of different components of the cosmic radiation field, as Galactic Cosmic Rays (GCR), trapped protons and electrons and Solar Proton Event (SPE), has been simulated outside and inside the Columbus module where astronauts live. The simulated radiation environment inside of the ISS will be used to model the response of the 3D Mushroom Silicon On Insulator (SOI) microdosimeter recently developed at CMRP.