## 5 Lattice Structures in Medical Devices and Applications
### Stochastic Cellular Structures  
Stochastic, open cellular structures apply biomimetic principles to create random pore shapes, sizes, and distributions without a clear, repetitive pattern [115]. These structures aim to mimic the natural variability found in biological tissues, particularly in trabecular bone, which has an irregular and anisotropic architecture [116; 117]. The randomness in pore geometry allows for stochastic designs to exhibit anisotropic mechanical responses, meaning their strength and stiffness can vary depending on the direction of the applied load. This characteristic is beneficial for mimicking the load-bearing behavior of trabecular bone, which naturally adapts to directional stresses in the body [115]. Despite these advantages, there are significant challenges associated with the design and manufacturing of stochastic scaffolds, which limit their practical application in orthopedic implants. The complexity of producing these irregular structures, particularly through AM or the traditional fabrication techniques, can lead to inconsistencies in the mechanical properties of the final product. Since the pores and struts of a stochastic structure vary randomly, the scaffold's mechanical performance can be heterogeneous, with areas of varying strength and stiffness [116; 118]. This lack of uniformity can compromise the structural integrity of the implant, making it difficult to predict how it will perform under the physiological loads encountered in spinal or other orthopedic applications. Moreover, the inherent heterogeneity of stochastic structures means that certain regions may be more prone to failure than others, particularly under repeated stress or in load-bearing environments. This limitation has hindered the widespread adoption of stochastic designs in orthopedic implants, as their mechanical performance must be reliably consistent to ensure long-term success in clinical applications [115; 116].  
To address these challenges, other researchers have proposed improving stochastic designs by introducing a hierarchical order into the structure. A hierarchical approach would involve organizing the random pores into multiple levels of scale, like how natural bone is structured at both the micro and macro levels [119]. This could improve the overall mechanical properties of the scaffold by providing additional layers of support and load distribution, while still retaining the benefits of a biomimetic, anisotropic design. By organizing pores in a controlled, yet random manner along different scales, the scaffold could achieve greater strength and durability, making it more suitable for spinal implants and other orthopedic devices [119]. Hierarchical stochastic designs may also allow for more precise control over critical parameters, such as pore size, distribution, and interconnectivity, which are essential for promoting tissue ingrowth, vascularization, and nutrient flow [119; 120]. With these improvements, stochastic cellular structures could overcome their current limitations, providing a more effective solution for mimicking natural bone properties and enhancing the mechanical performance of orthopedic implants.