The notions of bounded expansion and nowhere denseness capture uniform sparseness of graph classes and render various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter tractable over such graph classes. With the aim of generalizing such results to dense graphs, we introduce structurally bounded expansion and structurally nowhere dense graph classes, dfined as first-order interpretations of bounded expansion and nowhere dense graph classes. As a first step towards their algorithmic treatment, we provide a characterization of structurally bounded expansion classes via low shrubdepth decompositions, a dense analogue of low treedepth decompositions. We prove that structurally nowhere dense graph classes are vc-minimal.