In this article we propose to investigate the analogy between early cortical folding process and cortical smoothing by mean curvature flow. First, we introduce a one-parameter model that is able to fit a developmental trajectory as represented in a Volume-Area plot and we propose an efficient optimization strategy for parameter estimation. Second, we validate the model on forty cortical surfaces of preterm newborns by comparing global geometrical indices and trajectories of central sulcus along developmental and simulation time.