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Improved understanding and compact descriptions of the pressure drop evolution of Particulate Filters (both for diesel and gasoline powered vehicles) are always in demand for intelligent implementations of exhaust emission system monitoring and control. In the present paper we revisit the loading process of a particulate filter focusing on a parametric description of the deep bed-to-cake transition in the light of recent progress in the understanding of soot deposit structure, growth dynamics and evolution. Combining experimental data, simulation models and information theoretic concepts we provide a closed-form representation of the entire evolution of pressure drop (from the initial clean state up to the evolving linear cake growth regime) parameterized in terms of the physical parameters of the system (filter and particle structure/geometry and flow properties).