An off-centre ignition model has been used to study the ignition conditions for laser targets related to the fast ignition scheme. A 2-D hydrodynamic code has been used, including alpha particle heating. The main goal of the study is the possibility of obtaining a high gain ICF target with fast ignition. In order to determine the ignition conditions, samples with various compressed core densities having different spark density-radius product (i.e. areal density) values were selected. The study was carried out in the presence of an external heating source, with a constant heating rate. A dependence of the ignition conditions on the heating rate of the external pulse is demonstrated. For a given set of ignition conditions, our simulation showed that an 11 ps pulse with 17 kJ of injected energy into the spark area was required to achieve ignition for a compressed core with a density of 200 g/cm3 and 0.5 g/cm2 spark areal density. It is shown that the ignition conditions are highly dependent on the heating rate of the external pulse.