It is well known that the temperature profiles in a tokamak are self-consistent. This allows one to construct the heat conductivity equation in terms of so called "critical temperature gradients". In our previous work this critical gradient was expressed through the gradient of the canonical temperature profile. In this Report the self-consistency of pressure profiles is used to construct the extended model with particle diffusion equation. This new equation includes the "critical pressure gradient" expressed through the canonical pressure profile. The validation of the model is achieved in two ways. First, the concept of the "pressure gradient conservation" is pointed out and tested on some series of MAST Ohmic and NBI shots. Second, the full version of the canonical profiles transport model, which includes both heat and particle transport equations is used to simulate the experimental electron and ion temperatures and the density profiles in the series of MAST shots. For all MAST shots the linear deviations are less than 10-12%. The low deviation of the calculated data from the corresponding experimental ones confirms the principle of the pressure gradient conservation. To compare our model with other ones, we provide the simulation of the energy balance for two series of JET shots. This model uses the critical temperature gradients only. The model well describes the JET shots with high and moderate current, i.e. discharges with a good confinement. Only for very low current, I ~ 1MA, the deviations increase and reach the values of 30% for the ion temperature.