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As use of Particulate Filters (PFs) is growing not only for diesel but also for gasoline powered vehicles, the need for better understanding of deposit structure, growth dynamics and evolution arises. In the present paper we address a number of deposit growth and restructuring phenomena within particulate filters with the aim to improve particulate filter soot load estimation. To this end we investigate the dynamic factors that quantify the amount of particles that are stored within the wall and the restructuring of soot deposits. We demonstrate that particle accumulation inside the porous wall is dynamically controlled by the dimensionless Peclet number and provide a procedure for the estimation of parameters of interest such as the loaded filter wall permeability, the wall-stored soot mass at the onset of cake filtration.