(A) At each trial, a random particle beam enters at a random point on

*xy*-plane and propagates along the +

*z*-direction. The neuron is bounded by the volume

*Cyl* _{Neuron} and embedded on a larger scoring volume

*Cyl* _{Score}.

*L* _{Score} is the height of the

*Cyl* _{Score} and randomly selected 20 μm tracks from the irradiation library are lined up to create a particle beam equal or larger than

*L* _{Score}. The constant distances between the cylinders

*L* _{Forward},

*L* _{Backward} and

*R* _{Gap} contribute to the electronic equilibrium in

*Cyl* _{Neuron}.

*L* _{Neuron} is the maximum extension of the neuron along the

*z*-axis and changes at each trial with random orientation of the neuron. Particle fluence is calculated as 1/

*A* _{Score} where

. If there are one or more coincidence events, then the trial is recorded as a ‘hit’. For clarity, only one out of twenty voxels are shown for a

^{56}Fe beam at 600 MeV/u in (A) and 20 nm

^{3} voxels are shown much larger than their actual size on the panels. (B) A close up view of

^{12}C at 300 MeV/u which is grazing the dendritic branches.

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