  The Interstellar Boundary Explorer (IBEX) has been measuring fluxes of the
Energetic Neutral Atoms (ENAs) using the IBEX-Hi (0.3 -- 6 keV) instrument
since 2008. We have developed a numerical time-depended code to calculate
globally distributed flux (GDF) of hydrogen ENAs employing both 1) 3D
kinetic-MHD model of the global heliosphere and 2) reconstruction of atom
trajectories from 1 au, where they are observed by IBEX, to the point of their
origin in the inner heliosheath (IHS). The key factor in the simulation is a
detailed kinetic consideration of the pickup ions (PUIs), the supra-thermal
component of protons in the heliosphere, which is "parental" to the ENAs and
originates in the region of the supersonic solar wind being picked by the
heliospheric magnetic field. As a result of our study, we have concluded that
(1) the developed model is able to reproduce the geometry of the multi-lobe
structure seen in the IBEX-Hi GDF maps, (2) the GDF is extremely sensitive to
the form of the velocity distribution function of PUIs in the IHS, and the
accounting for the existence of an additional energetic population of PUIs is
essential to explain the data, (3) despite a relatively good agreement, there
are some quantitative differences between the model calculations and IBEX-Hi
data. Possible reasons for these differences are discussed.
