Construction of the model.

<p>(<b>A</b>) Naive branching geometry. The epithelium (black) is undergoing branching. <i>Fgf10</i> expression is restricted to the sub-mesothelial mesenchyme. In the model, only the most distal cells are source of FGF10 (blue). (<b>B</b>) Resolution of Laplace’s equation for FGF10 concentration <i>c</i> in the same geometry using finite elements methods. Near the mesothelium the concentration is maximum (red), while it is minimum on the epithelium (blue). (<b>C</b>) Calculation of the gradient norm of FGF10 concentration in the same geometry. Blue stands for weak gradients while red stands for high gradients. Gradient focuses on distal tips.