## 3 Stimuli-Responsive Mechanisms: Avenues for 4D (Bio-)printing  
The main features that smart materials exhibit are self-adaptability, self-sensing, shape-memory, responsiveness, multifunctionality, and self-repair. These characteristics determine their after-printing properties in response to external stimuli, leveraging several promising applications [15; 40]. However, some reviews on stimuli-responsive materials have already been provided in other fields [5; 26; 41], it is now highly relevant to clarify their suitability for biomedical applications. Indeed, the functionality changes of a 4D bioconstruct critically depend on the given stimulus and material choice that are selected based on the desired application [42]. Polymers able to react to stimuli undergo changes in their properties, like size or shape, as well as permeability, mechanical, surface, optical, and electrical properties after applications of physical stimuli, such as temperature, light, electric, mechanic, and magnetic fields, and they will be described in the next sections. The possibility of 3D (bio-)printing smart materials seems to factually enable 4D (bio-)printing, even though future definitions in this field could better clarify any specific circumstances.  
As previously mentioned, stimuli-responsive hydrogels belong to the category of smart materials, as they can respond to various environmental factors [6]. Smart hydrogels are able to change their network structure, mechanical strength, permeability, and swelling behavior in response to stimuli. Interestingly, many stimuli-responsive hydrogels show a fully reversible change, being significantly attractive for the biomedical domains [43]. The major advantages of smart hydrogels are a high-water content that closely mimics the environment of the natural tissues and promotes a more efficient mass transport than those occurring in other materials. Furthermore, smart hydrogels have unique characteristics such as sol-gel transition, shape memory, or self-healing, which are highly relevant for bioprinting medical devices [29]. A successful bioprinted hydrogel construct should have the following properties: (i) printability, which is related to proper viscosity, short response, transition time, and a suitable sol-gel transition stimulus [44; 45]; (ii) biocompatibility, including biodegradability, ability to withstand cell-cell and cell-matrix connections and absence of toxicity; (iii) mechanical properties, identical to the target tissue regarding stiffness, elasticity, and strength, and (iv) shape and structure, as the print should exhibit high structural similarities to the natural tissue. Therefore, these hydrogels can be printed via different techniques [46]. For instance, extrusion usually requires high viscosity and shear-thinning property, while an inkjet-based technique requires low viscosity of the material with low sol-gel response and transition time [29; 45].  
Since hydrogel properties can be manipulated through chemistry and crosslinking [14], an additional aspect that researchers should consider is the effectiveness of computational modeling to predict the material responses without time-consuming experimental activities. Accordingly, theoretical and mathematical models have been developed, achieving an optimal association between the structure of the material, the desired final shape, the properties of the material, and the intended stimuli [26].