**Preface to "Numerical Simulation in Biomechanics and Biomedical Engineering"**

In the last decades, the improvement of the computational technology has allowed the introduction of advanced numerical models and high-performance simulations in several fields of engineering. In particular, biomedical engineering, which can be a bridge discipline between medicine and engineering, and combines the knowledge of several aspects of both fields, has received great attention from the scientific community for its direct relation to human health. In a more general meaning, biomedical engineering also includes the study of the processes related to nature and animals. Specific applications can be found in the understanding of human pathologies and diseases; in the advancement of the medical health care; and in the improvement of the diagnosis, therapies, medical devices, and clinical outcomes, among other aspects. However, biomedical engineering should theoretically also help to reduce the number of tests in animals, and should also contribute to the improvement of their health care. More recent applications can be found in the analysis of biological problems, such as the cells' culture and motility, and the microfluidic and diffusion processes.

Numerical methods and computer simulation have been widely used to help the biomedical engineering for providing computational models able to reproduce many aspects associated to the human medicine and to the biology. Considerable research has been obtained with the improvement of the computer performances that allows for the increase of more and more complexity in such in silico modeling. Despite the extensive investigation in this field and the large improvement in computer technology, the complex mechanism of different biological problems and related pathologies has been not fully understood. This is partially due to the difficulties to reproduce, with the necessary accuracy, the complexity of certain phenomena and the overall limitations of the computational and experimental modeling.

This e-book presents a collection of several examples of application of the numerical modeling to complex problems in the field of biomechanics and biomedical engineering. Some of the fields included in the book are tissue engineering, computational biofluid dynamics, structural analysis of muscle skeletal system and bone tissue, design and analysis of medical devices, 3D printing technique for the biomedical engineering, analytical and numerical solution of blood flow, and analysis of topological data.

The Editor thanks the contribution, effort, and dedication of the authors to describe and show by means of their papers some of the application of the mathematics by means of the numerical models to the biomedical engineering. Their recognized expertise in the mentioned fields of the biomechanics and biomedical engineering have contributed to the scientific quality of this book that will certainly be appreciated by the readers.

> **Mauro Malv`e** *Editor*
