Reverse engineering of complex biological body parts by squared distance enabled non-uniform rational B-spline technique and layered manufacturing

In tissue engineering, the successful modeling of scaffold for the replacement of damaged body parts depends mainly on external geometry and internal architecture in order to avoid the adverse effects such as pain and lack of ability to transfer the load to the surrounding bone. Due to flexibility in controlling the parameters, layered manufacturing processes are widely used for the fabrication of bone tissue engineering scaffold with the given computer-aided design model. This article presents a squared distance minimization approach for weight optimization of non-uniform rational B-spline curve and surface to modify the geometry that exactly fits into the defect region automatically and thus to fabricate the scaffold specific to subject and site. The study showed that though the errors associated in the B-spline curve and surface were minimized by squared distance method than point distance method and tangent distance method, the errors could be minimized further in the rational B-spline curve and surface as the optimal weight could change the shape that desired for the defect site. In order to measure the efficacy of the present approach, the results were compared with point distance method and tangent distance method in optimizing the non-rational and rational B-spline curve and surface fitting for the defect site. The optimized geometry then allowed to construct the scaffold in fused deposition modeling system as an example. The result revealed that the squared distance–based weight optimization of the rational curve and surface in making the defect specific geometry best fits into the defect region than the other methods used.