  An approach, recently proposed to calculate the nucleon generalized parton
distributions (GPDs) in a constituent quark model (CQM) scenario, in which the
constituent quarks are taken as complex systems, is used to obtain
helicity-dependent GPDs. They are obtained from the wave functions of the non
relativistic CQM of Isgur and Karl, convoluted with the helicity-dependent GPDs
of the constituent quarks themselves. The latter are modelled by using the
polarized structure functions of the constituent quark, the double distribution
representation of GPDs, and a phenomenological constituent quark form factor.
The present approach permits to access a kinematical range corresponding to
both the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi and the
Efremov-Radyushkin-Brodsky-Lepage regions, for small values of the momentum
transfer and of the skewedness parameter. In this kinematical region, the
present calculation represents a prerequisite for the evaluation of cross
sections relevant to deeply virtual Compton scattering. In particular, we have
calculated the leading twist helicity-dependent GPD \tilde H and, from our
expressions, its general relations with the non relativistic definition of the
axial form factor and with the leading twist polarized quark density are
consistently recovered.
