Optimization of the cut configuration for skin grafts

TL;DR

This paper investigates optimizing skin graft cut configurations using a linear elasticity model, employing gradient and genetic algorithms to improve procedure efficiency and address complex stretching scenarios.

Contribution

It introduces a combined genetic and gradient descent approach for optimizing skin graft cuts, enhancing results in complex stretching conditions.

Findings

Gradient descent performs well under uniaxial stretching.

Genetic algorithm improves optimization in multidirectional stretching.

Solutions exist for the optimization problems, though uniqueness is not guaranteed.

Abstract

The subject of this work is the problem of optimizing the configuration of cuts for skin grafting in order to improve the efficiency of the procedure. We consider the optimization problem in the framework of a linear elasticity model. We choose three mechanical measures that define optimality via related objective functionals: the compliance, the \(L^p\)-norm of the von Mises stress, and the area of the stretched skin. We provide a proof of the existence of solutions for each problem, but we cannot claim uniqueness. We compute the gradient of the objectives with respect to the cut configuration using shape calculus concepts. To solve the problem numerically, we use the gradient descent method, which performs well under uniaxial stretching. However, in more complex cases, such as multidirectional stretching, its effectiveness is limited due to low sensitivity of the functionals. To avoid this difficulty, we use a combination of the genetic algorithm and the gradient descent method, which leads to a significant improvement in the results.