Methods for Optimization of Bone Scaffold

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1		Yongtao Lu	--	1881	2023-02-12 03:34:14	\|
2	There is no change.	Yongtao Lu	+ 652 word(s)	2533	2023-02-13 03:44:41	\| \|
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This entry is adapted from the peer-reviewed paper 10.3390/ma16030974

As the application of bone scaffolds becomes more and more widespread, the requirements for the high performance of bone scaffolds are also increasing. The stiffness and porosity of porous structures can be adjusted as needed, making them good candidates for repairing damaged bone tissues. However, the development of porous bone structures is limited by traditional manufacturing methods. Today, the development of additive manufacturing technology has made it very convenient to manufacture bionic porous bone structures as needed. In the present text, the current state-of-the-art optimization techniques for designing the scaffolds and the settings of different optimization methods are introduced. Additionally, various design methods for bone scaffolds are reviewed. Furthermore, the challenges in designing high performance bone scaffolds and the future developments of bone scaffolds are also presented.

bone scaffolds bio-porous structures mechanical properties numerical techniques optimized design

1. Introduction

Bone defects are one of the major challenges in orthopedics, with approximately 2.2 million bone graft procedures performed worldwide each year and the annual cost of these procedures approaching $2.5 billion ^[1]^[2]. Tissue transplants have been used in humans for tissue repair since at least 1660 ^[3]. Allogeneic bone grafting is considered an effective option for bone repair, but the problem of allograft immune rejection seriously affects its use in clinical practice. However, the widely used artificial bone substitutes sometimes produce foreign body reactions due to the mismatch in biocompatibility and mechanical properties and the inability to participate in normal metabolic activities ^[4]. For this reason, new methods and techniques are explored to solve the challenges of bone defect treatment.

Tissue engineering is a new discipline that has emerged in recent years with the development of modern biomaterials technology and cellular biotechnology and other emerging technologies to develop biological substitutes for repairing and maintaining or promoting functional and morphological recovery of tissues or organs after injury. Tissue engineering research consists of four main elements: signaling molecules, target cells that respond to the regulation of the signaling molecules, scaffold materials, and recipient beds with good blood supplies ^[5]. Bone tissue scaffolds not only provide a three-dimensional environment for cell growth and metabolism but also play a supporting role. Thus, how to construct a scaffold that meets the requirements is one of the priorities of bone tissue scaffold research. The ideal bone scaffold should have properties such as bioactivity, biodegradability, biocompatibility, mechanical support, good porosity, and the ability to deliver material, and the scaffold gradually degrades as new bone tissue proliferates and grows until it completely replaces the scaffold and grows into new bone ^[6]^[7]^[8]^[9]^[10]. However, the traditional methods for producing bone tissue scaffolds, such as particle elution, electrostatic spinning, phase separation/freeze-drying, and gas forming, cannot precisely control the size of the scaffold pores, and the connectivity of the pores cannot be guaranteed, which cannot simulate the anisotropy of natural bone ^[11]. The structural shape also cannot match the anatomical morphology of the bone defect site, and the preparation of personalized bone tissue scaffolds cannot be realized ^[12]^[13].

Bone tissue engineering has benefited from the development of additive manufacturing technologies in the past few years. Scaffold geometric parameters such as porosity, pore size, shape, and interconnectivity can be precisely controlled by additive manufacturing techniques. Tissue scaffold structures can be fabricated to meet functional requirements. The additive manufacturing techniques that can produce tissue scaffolds include selective laser sintering (SLS), selective laser melting (SLM), electron beam melting (EBM), and binder jetting (BJ) ^[14].

With the increasing maturity of additive manufacturing technology and computer-aided design (CAD) technology, it has become possible to achieve the design and fabrication of complex controllable porous scaffolds. To better mimic the function of natural bone structures, various methods have been proposed for the design of bone tissue scaffolds.

2. Current Methods in the Optimization of Bone Scaffold

Bone is a three-dimensional non-homogeneous structure with complex characteristics ranging from macroscopic to the nanoscale. A sound design approach is needed that combines structural stiffness with fluid permeability so that the scaffold is both permeable enough to transport nutrients and rigid enough to resist physical loading. Completely solid metals are not compatible because they are impermeable, and the Young’s modulus of solid metals is much higher than the bone modulus of the human body. Because of the mismatch in stiffness, a stress shielding phenomenon will occur, resulting in scaffold failure. Recently, porous structures have been introduced into orthopedic surgery to replace damaged bone tissues. If the structure of porous metals can be digitally designed and fabricated with advanced manufacturing techniques, they can be designed to replicate the properties of bones ^[15].

It is almost impossible to analyze quantitatively the properties of conventional porous scaffolds because they are composed of a large number of randomly shaped pores. In order to obtain a simplified model, researchers assume that the scaffold is composed of periodically repeating unit cells. CAD, image-based design, and implied surfaces are the conventional design strategies for typical cyclical scaffolds. The CAD-based approach is the most commonly used method in scaffold design, mainly using various CAD tools such as Unigraphics NX (UG), Computer Aided Tri-Dimensional Interface Application (CATIA), and Pro/ENGINEER (Pro/E) ^[16]^[17]. To simplify the design process based on CAD, several specialized design software packages have been developed containing libraries of widely used construction units. Based on the scaffolding libraries, the Computer Aided System for Organizing Scaffolds (CASTS) was developed. The aim was to achieve effective automation of the entire design process for the desired topology ^[18]^[19]. Shape functions are used to construct porous supports with implicit functional surfaces or irregular polygon models in mathematical modeling, breaking through the geometric limitations of conventional porous units. Although scaffolds with ideal stiffnesses and permeability can be obtained using these methods, these methods require extensive experiments to achieve the desired performance. Moreover, the final results obtained may not be optimal ^[20].

2.1. Solid Isotropic Material with Penalization (SIMP) Method

Currently, there are numerous types of topology optimization methods. In the case of the SIMP method, it is a material interpolation model that allows for the existence of intermediate relative densities (between 0 and 1), penalizes the material density, and filters low-density cells to obtain accurate topological results. This method, which is of great power, can design complex structures with multiscale features ^[21].

The SIMP method was used to design the porous structure using the customized morphology and mechanical properties of trabecular bone to design a three-dimensional structure with gradient porosity similar to the pore structure ^[22]. In order to obtain the desired porosity and elastic properties, a homogenization-based algorithm was used to design a three-dimensional bone scaffold ^[23]. The authors also demonstrated that the method can produce a porous structure that matches the anisotropic stiffness of human trabecular bone using recognized biomaterials. Porous structures with maximum permeability have been designed by this method ^[24]. Researchers also optimally designed multifunctional porous material microstructures for two competing properties, namely, stiffness and fluid permeability ^[25]. The topological optimization technique was used to minimize the difference between the effective elastic tensor of the optimized scaffold and the elastic tensor of natural bone. By comparison, it was concluded that bone remodeling was optimal when the elastic tensor of the bone scaffold was slightly higher than that of natural bone ^[26]. Despite the advantages of the SIMP method, the resulting optimized structures generally suffer from numerical instabilities such as tessellation, grid dependence, and grayscale cells. Moreover, there is no way for pore connectivity to be ensured by the material model in the microstructure design, and additional non-physical constraints are needed during the optimizations ^[27].

2.2. The Voronoi Method

Voronoi tessellation method (VTM) is a way of modeling irregular open-hole structures that can be used to delineate spatial regions ^[28].

In previous studies, a method that allows for the design of interconnected porous lattices was proposed, which can mimic specific tissue characteristics to achieve bone regeneration scaffolds ^[29]. The method combined the anatomical shape of the defect by controlling the porosity and pore size of the scaffold. The advantage of this method is to provide geometrical heterogeneity, thus resulting in a very biomimetic shape.

A parametric design method for lattice porous structures was proposed based on the design characteristics of Voronoi structures ^[30]. Deviations in model porosity and surface area are ensured because the uniform distribution of seed points has a high stability in the lattice cells. By this method, not only lattice structures with uniformly fractionated or graded distribution of porosity can be generated, but also lattice structures with customized porosity according to each cell can be generated. A VTM-based structural design method was proposed in order that the dominant elastic modulus of the scaffold could be controlled, and the stress shielding between the scaffold and the bone could be reduced ^[31]. A gradient scaffold suitable for the natural bone modulus can be obtained by this method, which also improves the stress shielding. It was found that the stochastic structure can be defined independently by nodal connectivity Z, strut density d, and strut thickness t during the design phase. The relative density, stiffness, and ultimate strength of the structure can also be predicted based on the parameters ^[32]. The advantage of the stochastic structure is that the single integrated model can define the structure to achieve a broad range of design requirements, even as a gradient of properties within the same component.

The relationship between porosity or apparent elastic modulus and compressive strength of irregular porous structures cannot be simply generalized, as an increase in one parameter leads to a decrease in the other parameter. A more complex relationship may exist based on the complex irregular porous structure of VTM and needs to be further investigated ^[33].

2.3. The Machine Learning Method

Machine learning (ML) has proven to be a valuable method for research in various fields. It is used to discern patterns from complex data sets and is a branch of artificial intelligence. ML algorithms are used in areas such as image and speech recognition, spam detection, and drug discovery ^[34]. The properties of materials or structures can already be predicted by machine learning models, and new materials with the desired properties can also be designed.

Machine learning techniques (MLTs) were combined with parametric finite element analysis (FEA) to further optimize the geometry of the short-stemmed hip scaffold to reduce proximal femoral stress shielding ^[35]. The minimization algorithm was used to obtain the optimal geometry, which allows unseen values of selected parameters of the hip brace geometry to be explored. The combination of FEA, MLT, and search pattern optimization algorithms can significantly reduce the computational cost ^[35]. An efficient method for the design optimization of scaffolds in biological tissues was proposed, which reduced computational time ^[36]. The optimization problem for the design of the geometry of titanium scaffolds was formulated by introducing a probabilistic model of mesoscale cortical bone. With this advanced algorithm, this very difficult constrained nonconvex optimization problem can be solved in the presence of uncertainty in biomechanics. A new method for designing layered materials using machine learning was proposed ^[37]. A database of hundreds of thousands of structures from FEA was used for training, along with a self-learning algorithm for discovering high-performance materials in which inferior designs are eliminated to obtain superior candidates. It further demonstrated that coarse graining can be replaced by machine learning, which means that materials can be analyzed and designed without the use of complete microstructural data. New material designs can be discovered and fabricated by this new paradigm for intelligent additive manufacturing with several orders of magnitude improvement in computational efficiency over conventional methods. A Generative Adversarial Network (GAN) model was proposed to learn the Inverse Homogenization (IH) mapping from attributes to cell shapes that can be used to optimize functionally graded cell structures ^[38]. Machine learning algorithms were used to predict the most suitable polymer/blend for cartilage replacement, using as input a range of tensile modulus, elongation at break, and tensile strength of natural cartilage ^[39].

However, as the number of parameters increases, the time required for MLT increases exponentially. As a data-driven model, IH-GAN cannot generate the shape and properties of cells outside of a given training data distribution. This may limit the performance of the optimized cell structure ^[38].

2.4. The Genetic Algorithm (GA)

Genetic algorithms are widely used in many structural optimization designs due to their high efficiency ^[40]. Therefore, in many current research works, genetic algorithms are used to obtain the optimal bracket structures. For example, a new computer method was developed that combines FEA and GA to design the scaffold by selecting the scaffold fiber diameter and inter-fiber spacing to show the required stiffness for each degradation stage ^[41]. The Kriging (KRG) method was used for multi-objective optimization using the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) to obtain the optimal design of hierarchical three-dimensional porous (H3DP) structure with the best crush resistance ^[42]. Based on the structure of the multi-constrained knapsack problem modeled as an ellipsoid, the inverse model of the porous structure was solved by a hybrid genetic algorithm. The bionic bone scaffold generated had good bioactivity, better mechanical properties, and a uniform degradation rate ^[43]. A numerical method for metamaterial reverse engineering was proposed that combines an asymptotic homogenization scheme with a genetic algorithm that can determine the optimal internal material pattern using the complete set of parameters contained in the target compliance tensor ^[44]. By integrating finite element analysis and multi-objective GA, a novel multi-objective custom shape optimization scheme was developed for cementless femoral scaffolds ^[45]. An optimization framework was proposed for generating readily available preoperative planning solutions in a fully automated manner ^[46]. It was based on a genetic algorithm capable of solving multi-objective optimization problems with nonlinear constraints. A GA-based search was carried out to optimize the scaffolds by minimizing the back-propagation neural network (BPNN) predicted micromotion. The best MMGs obtained based on the GA search provided better primary stability compared to the initial design ^[47].

Although the genetic algorithm is a very powerful tool, the need to evaluate the constraint and fitness functions for each generation in the process of scaffold optimization by the genetic algorithm is time-consuming, especially in the calculation of scaffolds with complex structures.

2.5. Other Methods

A comparison of the advantages and disadvantages of the above-mentioned four methods is shown in Table 1. In addition to this, there are other ways to optimize the bone scaffold. The level set algorithm is centered on tracking phase boundaries, thus effectively describing smooth boundaries to control topological variations ^[48]. A more systematic and comprehensive study of topology optimization based on level sets was conducted ^[49]. In order to obtain materials with maximum magnetic permeability, a variable level set technique was developed for the periodic material design problem controlled by the Navier–Stokes and Maxwell’s set of equations ^[50]. The Bi-directional Evolutionary Structure Optimization (BESO) method allows for the simultaneous addition and removal of materials during the optimization process ^[51]. In the present text, only some of the optimization methods regarding bone scaffolds were reviewed, but not all of them were presented. The mechanical analysis and optimization of equations for bone and bone implants were also not mentioned.

Table 1. Comparison of different optimization methods.

	Advantages	Disadvantages	References
The Voronoi method	Excellent structure, good distribution of voids	Complex structure, complex relationship between parameters	^[29]^[30]^[31]^[33]
The Machine learning method	Low calculation cost	High demand for training data	^[36]^[38]^[39]
Genetic algorithm	Good scalability, simple process, fast convergence	Complex programming, high experience requirement for parameter selection, slow speed	^[41]^[42]^[45]^[46]
The SIMP method	Good mechanical properties	High calculation cost, complex programming, slow calculation speed	^[22]^[23]^[24]^[25]

References

Gómez, S.; Vlad, M.D.; López, J.; Fernández, E. Design and Properties of 3D Scaffolds for Bone Tissue Engineering. Acta Biomater. 2016, 42, 341–350.
Giannoudis, P.V.; Dinopoulos, H.; Tsiridis, E. Bone Substitutes: An Update. Injury 2005, 36, S20–S27.
Sanan, A.; Haines, S.J. Repairing Holes in the Head: A History of Cranioplasty. Neurosurgery 1997, 40, 588–603.
Korzinskas, T.; Jung, O.; Smeets, R.; Stojanovic, S.; Najman, S.; Glenske, K.; Hahn, M.; Wenisch, S.; Schnettler, R.; Barbeck, M. In Vivo Analysis of the Biocompatibility and Macrophage Response of a Non-Resorbable PTFE Membrane for Guided Bone Regeneration. Int. J. Mol. Sci. 2018, 19, 2952.
Croteau, S.; Rauch, F.; Silvestri, A.; Hamdy, R.C. Bone Morphogenetic Proteins in Orthopedics: From Basic Science to Clinical Practice. Orthop. (Thorofare N.J.) 1999, 22, 686–695.
Jones, J.R.; Ehrenfried, L.M.; Hench, L.L. Optimising Bioactive Glass Scaffolds for Bone Tissue Engineering. Biomaterials 2006, 27, 964–973.
Lee, S.-H.; Shin, H. Matrices and Scaffolds for Delivery of Bioactive Molecules in Bone and Cartilage Tissue Engineering. Adv. Drug Deliv. Rev. 2007, 59, 339–359.
Leong, K.F.; Cheah, C.M.; Chua, C.K. Solid Freeform Fabrication of Three-Dimensional Scaffolds for Engineering Replacement Tissues and Organs. Biomaterials 2003, 24, 2363–2378.
Li, W.-J.; Laurencin, C.T.; Caterson, E.J.; Tuan, R.S.; Ko, F.K. Electrospun Nanofibrous Structure: A Novel Scaffold for Tissue Engineering. J. Biomed. Mater. Res. 2002, 60, 613–621.
Yang, S.; Leong, K.F.; Du, Z.; Chua, C.K. The Design of Scaffolds for Use in Tissue Engineering. Part I. Traditional Factors. Tissue Eng. 2001, 7, 679–689.
Shen, S.; Chen, M.; Guo, W.; Li, H.; Li, X.; Huang, S.; Luo, X.; Wang, Z.; Wen, Y.; Yuan, Z.; et al. Three Dimensional Printing-Based Strategies for Functional Cartilage Regeneration. Tissue Eng. Part B Rev. 2019, 25, 187–201.
Frazier, W.E. Metal Additive Manufacturing: A Review. J. Mater. Eng. Perform. 2014, 23, 1917–1928.
Gao, W.; Zhang, Y.; Ramanujan, D.; Ramani, K.; Chen, Y.; Williams, C.B.; Wang, C.C.; Shin, Y.C.; Zhang, S.; Zavattieri, P.D. The Status, Challenges, and Future of Additive Manufacturing in Engineering. Comput. Aided Des. 2015, 69, 65–89.
Huo, Y.; Lu, Y.; Meng, L.; Wu, J.; Gong, T.; Zou, J.; Bosiakov, S.; Cheng, L. A Critical Review on the Design, Manufacturing and Assessment of the Bone Scaffold for Large Bone Defects. Front. Bioeng. Biotechnol. 2021, 9, 753715.
Lv, Y.; Wang, B.; Liu, G.; Tang, Y.; Lu, E.; Xie, K.; Lan, C.; Liu, J.; Qin, Z.; Wang, L. Metal Material, Properties and Design Methods of Porous Biomedical Scaffolds for Additive Manufacturing: A Review. Front. Bioeng. Biotechnol. 2021, 9, 641130.
Ovsianikov, A.; Deiwick, A.; Van Vlierberghe, S.; Dubruel, P.; Möller, L.; Dräger, G.; Chichkov, B. Laser Fabrication of Three-Dimensional CAD Scaffolds from Photosensitive Gelatin for Applications in Tissue Engineering. Biomacromolecules 2011, 12, 851–858.
Naing, M.W.; Chua, C.K.; Leong, K.F.; Wang, Y. Fabrication of Customised Scaffolds Using Computer-aided Design and Rapid Prototyping Techniques. Rapid Prototyp. J. 2005, 11, 249–259.
Cheah, C.-M.; Chua, C.-K.; Leong, K.-F.; Cheong, C.-H.; Naing, M.-W. Automatic Algorithm for Generating Complex Polyhedral Scaffold Structures for Tissue Engineering. Tissue Eng. 2004, 10, 595–610.
Sudarmadji, N.; Tan, J.Y.; Leong, K.F.; Chua, C.K.; Loh, Y.T. Investigation of the Mechanical Properties and Porosity Relationships in Selective Laser-Sintered Polyhedral for Functionally Graded Scaffolds. Acta Biomater. 2011, 7, 530–537.
Liu, X.; Zhao, K.; Gong, T.; Song, J.; Bao, C.; Luo, E.; Weng, J.; Zhou, S. Delivery of Growth Factors Using a Smart Porous Nanocomposite Scaffold to Repair a Mandibular Bone Defect. Biomacromolecules 2014, 15, 1019–1030.
Chen, W.; Huang, X. Topological Design of 3D Chiral Metamaterials Based on Couple-Stress Homogenization. J. Mech. Phys. Solids 2019, 131, 372–386.
Liu, R.; Chen, Y.; Liu, Y.; Yan, Z.; Wang, Y.-X. Topological Design of a Trabecular Bone Structure With Morphology and Mechanics Control for Additive Manufacturing. IEEE Access 2021, 9, 11123–11133.
Lin, C.Y.; Kikuchi, N.; Hollister, S.J. A Novel Method for Biomaterial Scaffold Internal Architecture Design to Match Bone Elastic Properties with Desired Porosity. J. Biomech. 2004, 37, 623–636.
Guest, J.K.; Prévost, J.H. Design of Maximum Permeability Material Structures. Comput. Methods Appl. Mech. Eng. 2007, 196, 1006–1017.
Guest, J.K.; Prévost, J.H. Optimizing Multifunctional Materials: Design of Microstructures for Maximized Stiffness and Fluid Permeability. Int. J. Solids Struct. 2006, 43, 7028–7047.
Sturm, S.; Zhou, S.; Mai, Y.-W.; Li, Q. On Stiffness of Scaffolds for Bone Tissue Engineering—A Numerical Study. J. Biomech. 2010, 43, 1738–1744.
Wang, H.; Cheng, W.; Du, R.; Wang, S.; Wang, Y. Improved Proportional Topology Optimization Algorithm for Solving Minimum Compliance Problem. Struct. Multidiscip. Optim. 2020, 62, 475–493.
Xiao, F.; Yin, X. Geometry Models of Porous Media Based on Voronoi Tessellations and Their Porosity–Permeability Relations. Comput. Math. Appl. (1987) 2016, 72, 328–348.
Fantini, M.; Curto, M.; De Crescenzio, F. A Method to Design Biomimetic Scaffolds for Bone Tissue Engineering Based on Voronoi Lattices. Virtual Phys. Prototyp. 2016, 11, 77–90.
Lei, H.-Y.; Li, J.-R.; Xu, Z.-J.; Wang, Q.-H. Parametric Design of Voronoi-Based Lattice Porous Structures. Mater. Des. 2020, 191, 108607.
Zhao, H.; Han, Y.; Pan, C.; Yang, D.; Wang, H.; Wang, T.; Zeng, X.; Su, P. Design and Mechanical Properties Verification of Gradient Voronoi Scaffold for Bone Tissue Engineering. Micromachines 2021, 12, 664.
Kechagias, S.; Oosterbeek, R.N.; Munford, M.J.; Ghouse, S.; Jeffers, J.R.T. Controlling the Mechanical Behaviour of Stochastic Lattice Structures: The Key Role of Nodal Connectivity. Addit. Manuf. 2022, 54, 102730.
Du, Y.; Liang, H.; Xie, D.; Mao, N.; Zhao, J.; Tian, Z.; Wang, C.; Shen, L. Design and Statistical Analysis of Irregular Porous Scaffolds for Orthopedic Reconstruction Based on Voronoi Tessellation and Fabricated via Selective Laser Melting (SLM). Mater. Chem. Phys. 2020, 239, 121968.
Michalski, R.S.; Carbonell, J.G.; Mitchell, T.M. Machine Learning: An Artificial Intelligence Approach; Artificial Intelligence; Springer: Berlin/Heidelberg, Germany, 1984; ISBN 978-3-662-12407-9.
Cilla, M.; Borgiani, E.; Martínez, J.; Duda, G.N.; Checa, S. Machine Learning Techniques for the Optimization of Joint Replacements: Application to a Short-Stem Hip Implant. PLoS ONE 2017, 12, e0183755.
Soize, C. Design Optimization under Uncertainties of a Mesoscale Implant in Biological Tissues Using a Probabilistic Learning Algorithm. Comput. Mech. 2017, 62, 477–497.
Gu, G.X.; Chen, C.-T.; Richmond, D.J.; Buehler, M.J. Bioinspired Hierarchical Composite Design Using Machine Learning: Simulation, Additive Manufacturing, and Experiment. Mater. Horiz. 2018, 5, 939–945.
Wang, J.; Chen, W.; Da, D.; Fuge, M.; Rai, R. IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures. Comput. Methods Appl. Mech. Eng. 2022, 396, 115060.
Mairpady, A.; Mourad, A.-H.I.; Mozumder, M.S. Accelerated Discovery of the Polymer Blends for Cartilage Repair through Data-Mining Tools and Machine-Learning Algorithm. Polymers 2022, 14, 1802.
Atherton, M.A.; Bates, R.A. Robust Optimization of Cardiovascular Stents: A Comparison of Methods. Eng. Optim. 2004, 36, 207–217.
Heljak, M.K.; Kurzydlowski, K.J.; Swieszkowski, W. Computer Aided Design of Architecture of Degradable Tissue Engineering Scaffolds. Comput. Methods Biomech. Biomed. Eng. 2017, 20, 1623–1632.
Yin, H.; Zheng, X.; Wen, G.; Zhang, C.; Wu, Z. Design Optimization of a Novel Bio-Inspired 3D Porous Structure for Crashworthiness. Compos. Struct. 2021, 255, 112897.
You, F.; Yao, Y.; Hu, Q. Generation and Evaluation of Porous Structure of Bionic Bone Scaffold. Ji Xie Gong Cheng Xue Bao 2011, 47, 138–144.
Dos Reis, F.; Karathanasopoulos, N. Inverse Metamaterial Design Combining Genetic Algorithms with Asymptotic Homogenization Schemes. Int. J. Solids Struct. 2022, 250, 111702.
Chanda, S.; Gupta, S.; Kumar Pratihar, D. A Genetic Algorithm Based Multi-Objective Shape Optimization Scheme for Cementless Femoral Implant. J. Biomech. Eng. 2015, 137, 34502.
Carrillo, F.; Roner, S.; von Atzigen, M.; Schweizer, A.; Nagy, L.; Vlachopoulos, L.; Snedeker, J.G.; Fürnstahl, P. An Automatic Genetic Algorithm Framework for the Optimization of Three-Dimensional Surgical Plans of Forearm Corrective Osteotomies. Med. Image Anal. 2020, 60, 101598.
Chanda, S.; Gupta, S.; Pratihar, D.K. A Combined Neural Network and Genetic Algorithm Based Approach for Optimally Designed Femoral Implant Having Improved Primary Stability. Appl. Soft Comput. 2016, 38, 296–307.
Osher, S.; Sethian, J.A. Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations. J. Comput. Phys. 1988, 79, 12–49.
Wang, M.Y.; Wang, X.; Guo, D. A Level Set Method for Structural Topology Optimization. Comput. Methods Appl. Mech. Eng. 2003, 192, 227–246.
Zhou, S.; Li, Q. A Variational Level Set Method for the Topology Optimization of Steady-State Navier–Stokes Flow. J. Comput. Phys. 2008, 227, 10178–10195.
Wang, X.; Xu, S.; Zhou, S.; Xu, W.; Leary, M.; Choong, P.; Qian, M.; Brandt, M.; Xie, Y.M. Topological Design and Additive Manufacturing of Porous Metals for Bone Scaffolds and Orthopaedic Implants: A Review. Biomaterials 2016, 83, 127–141.

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