## Fluid mechanics in biological and technological systems

**Fluid mechanics in biological systems**

A recent field of research related to transport phenomena in fluid dynamics is the study of interactions between a turbulent fluid field and biological species. Turbulence acts both on the large and small scales of motion. As a consequence, a passive particulate tends to be transported and mixed by the carrying flow field. In the case of an active particulate however, the mixing and advection properties of the flow field can affect the biological production. On one hand, mixing can enhance biological productivity at small scales and, on the other hand, coherent structures, such as vortices and jets, may limit and localize the production processes.

In connection to this, the application of fluid mechanics to biological systems, in particular to the human cardiovascular system, is a rapidly emerging field that requires a deep knowledge of fluid mechanics as well as nonlinear solid mechanics, and specific technical methods for handling fluid-solid interacting systems. This field introduces important new theoretical issues to be addressed. It involves the interaction of fluid with biological systems as well as with technological devices. The study of flows in prosthetic elements, extra-corporeal flow systems, micro-devices involves a broad range of industrial fluid mechanics that is also part of the curriculum study.

Research projects include.

*a) Fluid dynamics in the human heart*** **

The function of the human heart is about creating blood motion. Cardiac fluid dynamics features the formation of vortices that influence the interaction between blood and tissue. Recent results demonstrated that the morphogenesis of the embryonic hearts is largely altered by changes in blood flow; similarly, dynamic properties of blood flow modulates the progression of cardiac diseases leading to heart failure.

We plan to use numerical methods, carefully integrated with medical imaging technology, to reproduce the details of cardiac fluid dynamics in either the left or the right ventricle of the human heart. The objectives of the research are the development of novel methods for predicting the evolution of pathologies in adults and in pediatric or fetal cardiology.

*b) Interaction between flow and tissues in the cardiovascular system*** **

The entire cardiovascular system is regulated by the interaction between the moving blood and the surrounding tissues. Cardiac valves as well as vascular valves are opened by the flow and prevent the backward motion. The fundamental phenomena associated with fluid-tissue interaction remain elusive and their analysis is methodological complex.

We plan to develop numerical and computational methods to properly evaluate the dynamics of fluid-tissue interactions in conditions of medical relevance. This approach, which is methodological challenging, presents an additional difficulty that mechanical properties of tissues cannot be measured “in vivo”. Applications are dedicated to optimization cardiac valve surgery.

*c) Methods based on of medical imaging for tissue deformation and blood flow *

The technology of medical imaging underwent enormous advances in the last decades and time-varying three-dimensional recording are routinely feasible in the clinical environments. However, the technological advancements require interpretative models capable to rearrange the large amounts of information into synthetic information.

We plan to develop techniques for image processing that move beyond regular image analysis and include the physical principles of the organ recorded in the images. Based on these the research is devoted to the development of mathematical models of tissue deformation and blood flow able to produce parameters that can be integrated in the diagnostic process.

**Fluid mechanics in industrial processes and technological systems**

New technological and industrial problems (single/ multiphase flows, complex geometry, local relaminarization and re-transition to turbulence, chemistry-fluid interaction) require development of new mathematical formulations and new accurate and robust numerical methods. This is particularly true when a new physical mechanism occurring in an applicative problem arising In an Industrial application, the physical process has to be fully understood. Within the present program, research activity related to study of technological problems is based on the development and application of novel, state-of-art methodology for the analysis of a specific problem that otherwise can hardly be undertaken using standard procedures.

The main problems mentioned above are typically studied using large-scale models with a resolution ranging from the order of hundreds of meters to kilometers. Thus horizontal and vertical small scale mixing cannot be directly resolved by the model itself. Local, or smaller-scale, phenomena, however have a strong impact on several environmental problems, including pollution. Such phenomena require a complete three-dimensional analysis of the fluid flow, to evaluate the dominant vortex structure arrangement of the resulting turbulent field.

These small scales are not present in the large scale models described above where they need to be parameterized. Similarly, three-dimensional turbulence in realistic systems still cannot resolve the entire flow field and parameterization of small-scales is a fundamental issue of any study involving turbulence. Indeed, the quality of the results from large-scale models depends on many features, among them a crucial aspect is the capability of the turbulence parameterization to correctly reproduce the small-scale mixing dynamics under complex-flow conditions, such as rotation, stratification and topographic effects.

The choice and, when needed, the improvement and the re-formulation of turbulence parameterization and closures to be used in conjunction with large-scale models require a deep knowledge of the underlying physics including the dynamics of turbulence. Hence, the study of small-scale processes per se, is essential to understand the physical mechanisms of mixing within the fluid, to identify the main drawbacks of the existing schemes, and to adapt or develop, whenever needed, new and more effective models.

An important role in the study of three-dimensional turbulence is played by transport/dispersion phenomena characterized by an interaction between different phases. The typical case is that of two-phase flows, where a diluted phase is transported within a carrying one (for instance water or air). Understanding and modeling transport phenomena is of great importance in may application of fluid dynamics, especially in the environment (dispersion of solid particulates, interaction between turbulence and biological species etc.). The mathematical and physical characterization of these phenomena is the basis for investigating applicative problems.

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