Modelizado y optimización de problemas biomecánicos mediante la combinación del método de los elementos finitos (mef) y técnicas avanzadas de optimización

Abstract

Usually, biomechanical problems present non-linear behaviours produced by mechanical contacts, large deformations, large displacements, hyperelasticity, etc. This type of nonlinear behaviour is difficult to model and optimise by widely used methods such as the Finite Element Method (FEM). First, there is a very high computational cost when only FEM is applied to model and optimise biomechanical problems. In addition, solving this type of biomechanical problems experimentally (through trial-error tests) is nowadays unfeasible for ethical reasons. This thesis presents a methodology that combines FEM with advanced data analysis techniques, such as the Multiple Response Surface Method (MRS) or Machine Learning (ML) algorithms, to model and optimise the biomechanical problems that are present in humans and animals. The application of the proposed methodology in this thesis is carried out in three main phases. The first phase focuses on the creation of FE models, while the second phase is devoted to the generation of prediction models by means of regression techniques, decision trees, neural networks, etc. Finally, in the third phase, an optimisation is performed using either the MRS or genetic algorithms. The proposed methodology can be applied to any biomechanical problem. In this thesis, it has been validated through its implementation in four actual problems that are found in humans and animals. In animals, it is applied to model the biomechanical behaviour of a canine pelvis with two different types of fixation plates (ventral and DPO), used for the treatment of canine pelvic osteotomy. In this case, the FEM is solely applied to analyse and compare the stiffness difference between ventral and DPO fixation plates. In this manner, the experimental cost is reduced and the ethical problem is avoided. In the case of human problems, the methodology that combines the FEM and the MRS with desirability functions is applied for the modelling and optimisation of the biomechanical behaviour of intervertebral discs (DIV) in lumbar functional spinal units (FSU), with the aim of obtaining the most appropriate parameters that define the biomechanical behaviour of the FE models. The advantage of the combined use of FEM and MRS, as proposed in this thesis, is that it allows adjusting and optimising the parameters that define the biomechanical behavior of FE models of complex structures in a more efficient way. Thus, avoiding the arduous adjustment of the parameters to obtain the optimal FE model through the trial-error method. Finally, the proposed methodology is applied to the design of an artificial disc or lumbar prosthesis by combining FEM and ML techniques. In this case, the regression models generated are based on neural networks and regression trees, while the optimisation of the geometry of the artificial disc is carried out through the application of genetic algorithms. This way, it is also possible to obtain, the parameters that best define the geometry proposed for the artificial lumbar disc for different patient’s weights and statures in an efficient manner. Therefore, this methodology is considered to provide an important tool for the design and optimisation of artificial disc prostheses (custom-made prostheses). In short, it has been proven that the methodology proposed in this thesis, which combines several techniques (FEM, MSR MRS and ML) to generate mathematical models or metamodels, is very useful to efficiently model and optimise complex biomechanical problems. The main advantages of the methodology are the following: • It significantly reduces the experimental cost and eliminates the ethical problem associated with the use of cadavers. • It allows to obtain prediction models that are accurate enough, easy to interpret and much more computationally efficient than the models obtained through the FEM to model biomechanical problems. • It allows to optimise complex biomechanical problems, in a more efficient way. That is, it substantially reduces the computational cost as compared to the solely use of the FEM by applying the trial-error method.