Fig. 1.

Schematic for Sellier's backward displacement method, see Algorithm 3 in Appendix A. A forward inflation problem ϕ (blue curve) is solved in the first iteration (it₁), where a measured in vivo pressure p_ed is applied to an interim reference configuration with coordinates X⁰ = x^dat. This generates an updated configuration with coordinates x⁰. Subsequently, the per node displacement vector between the updated deformed configuration and the target in vivo configuration (R⁰) is computed. Finally, the reference configuration is updated by subtracting this per node displacement vector (blue dashed line). This iterative procedure is repeated until a given error tolerance ∈ between the computed reference configuration and the given in vivo configuration is reached. Here, the algorithm converges to the unloaded reference configuration X* after four iterations. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)