Muon spin rotation/relaxation/resonance ( \(\mu \) SR) is an effective technique for studying fundamental processes and applications in biology, and theoretical approaches such as density functional theory (DFT) and Monte Carlo simulations play an essential role in supporting the interpretation of \(\mu \) SR results. In this work, we estimate the depth of maximum dose for muons (both \(\mu ^+\) and \(\mu ^-\) ) in brain tumors and soft-tissue tumors using Monte Carlo simulations. The muon energy required to place the maximum dose at the distal end of a brain tumor is estimated to be 28.92 MeV for both \(\mu ^+\) and \(\mu ^-\) . For soft-tissue tumors, the corresponding energies are 26.58 MeV and 26.55 MeV for \(\mu ^+\) and \(\mu ^-\) , respectively. Compared with normal tissue, a slightly higher incident muon energy is required in tumor tissue to achieve the maximum dose at the same depth. For \(\mu ^+\) and \(\mu ^-\) beams of identical energy, the deposited dose distributions in tissue are found to be essentially the same, despite their different interaction mechanisms in matter.
