The behaviour of spins at a classical level in the presence of an external magnetic field is completely described by
the Bloch equation. This is the main equation governing the magnetic resonance imaging (MRI) system, and as
such the Bloch equation is extensively used for design purposes. Here we have transferred the Bloch equation to
the spherical coordinate system that, to the best of our knowledge, has not previously been applied in this field.
The mathematical framework and the simulation results show that this fresh view of the Bloch equation provides
better insight into the magnetic resonance (MR) phenomenon. In this mathematical framework, without using
spinor space, the order of the Bloch equation is reduced in a much simpler way and can therefore provides a novel
insight to the slice selection problem. Simulation results are presented for a variety of slice selective pulses, with
and without post excitation rephasing gradients. In this paper nonlinear gradient is tried as well which shows
an improvement in uniformity of the selected slice. It is feasible to find an analytic approximate solution to the
Bloch equation in spherical coordinate system by adopting averaging techniques over spatial variables available
available in nonlinear dynamical systems. We anticipate that our new description of the MR phenomenon will
allow researchers to revisit the excitation pattern design question to achieve better slice selectivity or to find an
optimal excitation pattern from a theoretical basis. This has the potential to result in practical improvements
affecting all forms of MR imaging.