## 1 Introduction  
So-called \"tissue engineering science\" refers to the practice of combining cells, biomaterials, and suitable biochemical and physicochemical factors to assemble a biological functional tissue. Tissue engineering science is emerging as a promising technique to build functional constructs that restore, maintain, or improve damaged tissues [1]. The physical and structural properties of the tissue, along with biological and biochemical environments, play key roles in achieving cell differentiation, maturation, and organogenesis [2]. Hence, the field of tissue engineering relies on the search for a three-dimensional (3D) scaffold representing a template for tissue formation that can be used in vivo, where it can act as a guidance for cellular regeneration, or can be seeded in vitro with cells and growth factors or subjected to biophysical/mechanical/chemical stimuli that promote tissue growth [3]. A crucial step in building a 3D tissue lies in its thickness, because the exceeding of a certain size (from 100 to 200 \(\upmu\)m) prevents the oxygen, nutrients, and metabolic exchange among cell layers, irreparably leading to tissue necrosis [4]. To overcome this issue, current strategies rely on in vitro settings that increase the diffusion/perfusion of the tissue, such as a dynamic culture, while in vivo the colonization of the tissue by host vessels after grafting is promoted. Nevertheless, as happens in natural tissues, the fabrication of a network of microvessels that can be integrated with the host vasculature, could increase the survival of cells more sensitive to reduction of supply of nutrients and oxygen [5]. In recent research activities, 3D bioprinting, wherein both the layer-by-layer precise positioning of biological materials, biochemicals, and living cells, and the spatial control of the placement of functional components has been adopted, allowed for the fabrication of 3D structures exploiting bio-mimicry, autonomous self-assembly, and mini-tissue building blocks [6]. These goals can be pursued with the help of different deposition and shaping techniques, such as inkjet, microextrusion, and laser assisted printing, although these innovative technologies require expensive instrumentation. Bioprinters and bioplotters typically adopt piezoelectric or pneumatic devices for depositing cells, even dispersed into a proper liquid solution [7], and have the benefit of the flexibility of customizable patterning design, but have several drawbacks, such as the relatively large amount of time necessary to correctly achieve the spatial location of cells within the hydrogel, and limitations with respect to the density and viscosity of the liquid solution in which the cells need to be dispersed [8]. The main challenge remains the reproduction of the complex microarchitecture of extracellular matrix components with sufficient resolution, in which multiple cell types interact and exert their biological functions [9]. As an alternative, several strategies for cell trapping have been proposed and exploited in the literature. The most straightforward is hydrodynamic cell trapping, where a (series of) microchannel(s) of sufficiently small size in order to trap cells by suction is fabricated within microsystems [10]. Microbioreactors allowing direct-perfusion of culture medium through tissue-engineered constructs may overcome diffusion limitations associated with static culturing and may provide flow-mediated mechanical stimuli. The hydrodynamic stress imposed on cells within scaffolds is directly dependent on scaffold microstructure and on bioreactor configuration [11]. Microfluidic systems based on acoustic waves generated through the piezoelectric effect have recently received a great deal of attention in biological and medical fields for mixing, sorting, separation, counting, and positioning of particles and cells, mostly relying on the nodes and antinodes generated by standing waves [12].