## 1 Introduction  
Ceramic materials demonstrate excellent mechanical performance, high dimensional stability, high wear and corrosion resistance, and exceptional chemical stability. Current advances in 3D printing can potentially solve the problem of efficient production of custom made complex ceramic parts of arbitrary geometry [1; 2; 3; 4]. Today, 3D printing is used to manufacture complex shaped ceramic parts for various applications, such as integrated ceramic casting models [5; 6], cutting tools [7], sensors [8; 9; 10], structural parts [11; 12; 13], photonic crystals [14; 15], and dental components [16; 17]. Besides, 3D printing is used to manufacture ceramic implants for various applications [18; 19; 20; 21; 22; 23], mostly for the replacement of lost bones or restoration of damaged bone tissues [24]. Various porous structures (scaffolds) can be used to ensure successful proliferation of cells, demonstrating good biocompatibility and adhesion of live cultures. Scaffolds can have an irregular [25] or regular structure formed by way of 3D printing processes [26]. 3D printing allows the fabrication of scaffold structures with dimensions varying from several nanometers to several meters [27]. As was already shown in the previous studies, synthetic scaffolds can be designed based on various unit cell models, such as cube, gyroid, diamond, disberoid, and others [26]. These models make it possible to obtain materials with different mechanical properties and biological activity. Such scaffolds can be used to splice both bone [28] and soft tissues [29] such as nerves. Pores in such scaffolds should have a certain size to ensure effective splicing of tissues. The effect of the pore size on bone tissue splicing efficiency is studied in [30], using 3D printed scaffolds with various pore sizes, fabricated from Al2O3-based materials. The optimal pore size for bone tissue proliferation was shown to constitute 390 to 590 \(\upmu\)m.  
Alumina-based ceramics are biologically inert and resistant materials [31]. High compression strength and wear resistance make these materials an ideal choice for use in stomatology and hip joint surgery. Ceramic parts are produced by sintering at high temperatures (1600-1700 \({}^{\circ}\)C) and have residual porosity of about 1-3%. The size of the pores depends on thermal treatment conditions and on the micromorphology of feedstock powders, and usually does not exceed dozens of microns [32], which impedes the growth of tissues, blood vessels, and other nutrient ducts. Alumina-based ceramics can perform a supporting function in the defected bone or in joining two broken bone parts, but they cannot be used for full bone remodeling during treatment. A macroporous architecture is suggested to stimulate bone tissue ingrowth in the region of implant placement. There are several methods of producing highly porous ceramic materials, allowing a trade-off between ceramics porosity and the strength of implants. These are, in particular, the use of foaming [33] and burnt-out additives, and the method of replicas [34]. However, these methods are difficult to control. 3D printing allows the fabrication of parts of any shape [35], implementing a personalized approach to patients' treatment [36] that involves the use of computerized tomography, while controlling porosity and the size of pores (from 400 \(\upmu\)m and higher) [37], necessary for better implant acceptance within the damaged area. Considering this, the design and fabrication of 3D printed ceramic implants with complex tailored porous structure becomes an urgent issue. In this work, we use a promising stereolithographic (SLA) method of 3D printing of ceramic parts, based on the layer-by-layer polymerization of photocurable ceramic suspension or paste [38], consisting of photocurable multicomponent binder and ceramic powder. Each layer (slice) of a 3D model is solidified by laser hatching in a working area and then, a new layer of paste is applied by spreading blades. Figure 1 shows an illustration of the stereolithographic printing process.