Optimization of 3D network topology for bioinspired design of stiff and lightweight bone-like structures.

A truly bioinspired approach to design optimization should follow the energetically favorable natural paradigm of "minimum inventory with maximum diversity". This study was inspired by constructive regression of trabecular bone - a natural process of network connectivity optimization occurring early in skeletal development. During trabecular network optimization, the original excessively connected network undergoes incremental pruning of redundant elements, resulting in a functional and adaptable structure operating at lowest metabolic cost. We have recapitulated this biological network topology optimization algorithm by first designing in silico an excessively connected network in which elements are dimension-independent linear connections among nodes. Based on bioinspired regression principles, least-loaded connections were iteratively pruned upon simulated loading. Evolved networks were produced along this optimization trajectory when pre-set convergence criteria were met. These biomimetic networks were compared to each other, and to the reference network derived from mature trabecular bone. Our results replicated the natural network optimization algorithm in uniaxial compressive loading. However, following triaxial loading, the optimization algorithm resulted in lattice networks that were more stretch-dominated than the reference network, and more capable of uniform load distribution. As assessed by 3D printing and mechanical testing, our heuristic network optimization procedure opens new possibilities for parametric design.

Analytical model of I-bar clasps for removable partial dentures.

OBJECTIVE: Clasps of removable partial dentures (RPDs) often suffer from fatigue stress that leads to plastic deformation, loss of retention, and RPD failure. Recently, computer-based technologies were proposed to optimize clasp geometry design. The objective of this study was to create an analytic model of I-bar clasps for computer-aided design (CAD)-RPD. METHODS: The analytical model based on mechanical laws was established to simulate I-bar clasp retention, and optimize its design. The model considered the lengths of the vertical (L1) and horizontal (L2) arms of the I-bar as well as the radius (r) of its half-round cross-section. The analytical model was validated with mechanical experiments evaluating the retention of cobalt-chromium (Co-Cr) clasps in vitro and compared with finite element analysis (FEA). RESULTS: The analytical model was in good agreement with the mechanical experiments and FEA, and showed that I-bar clasp design could provide optimal mechanical performance as long as the length of arms (L1 and L2) do not exceed 6 mm. Clasps with L1 > 8 mm and L2 > 9 mm presented stress values exceeding the fatigue limit of Co-Cr. The proposed solution was to increase the radius of I-bar to conserve the initial mechanical performance of Co-Cr. SIGNIFICANCE: Co-Cr I-bar clasps perform best on teeth with reduced mesiodistal dimensions (canine and premolar), and their designs could be optimized to prevent stress from reaching the yield strength and the fatigue failure limit.

Composition and characteristics of trabecular bone in osteoporosis and osteoarthritis.

BACKGROUND: Bone strength depends on multiple factors such as bone density, architecture and composition turnover. However, the role these factors play in osteoporotic fractures is not well understood. PURPOSE: The aim of this study was to analyze trabecular bone architecture, and its crystal and organic composition in humans, by comparing samples taken from patients who had a hip fracture (HF) and individuals with hip osteoarthritis (HOA). METHODS: The study included 31 HF patients and 42 cases of HOA who underwent joint replacement surgery between 1/1/2013 and 31/12/2013. Trabecular bone samples were collected from the femoral heads and analyzed using a dual-energy X-ray absorptiometry, micro-CT, and solid-state high-resolution magic-angle-spinning nuclear magnetic resonance (MAS-NMR) spectroscopy. RESULTS: No differences in proton or phosphorus concentration were found between the two groups using 1H single pulse, 31P single pulse, 31P single pulse with proton decoupling NMR spectroscopy, in hydroxyapatite (HA) c-axis or a-axis crystal length. Bone volume fraction (BV/TV), trabecular number (Tb.N), and bone mineral density (BMD) were higher in the HO group than in the HF group [28.6% ± 10.5 vs 20.3% ± 6.6 (p = 0.026); 2.58 mm-1 ± 1.57 vs 1.5 mm-1 ± 0.79 (p = 0.005); and 0.39 g/cm2 ± 0.10 vs. 0.28 g/cm2 ± 0.05 (p = 0.002), respectively]. The trabecular separation (Tp.Sp) was lower in the HO group 0.42 mm ± 0.23 compared with the HF group 0.58 mm ± 0.27 (p = 0.036). In the HO group, BMD was correlated with BV/TV (r = 0.704, p < 0.001), BMC (r = 0.853, p < 0.001), Tb.N (r = 0.653, p < 0.001), Tb.Sp (-0.561, p < 0.001) and 1H concentration (-0.580, p < 0.001) in the HO group. BMD was not correlated with BV/TV, Tb.Sp, Tb.Th, Tb.N, Tb.PF, 1H concentration or HA crystal size in the HF group. CONCLUSIONS: Patients with HO who did not sustain previous hip fractures had a higher femoral head BMD, BV/TV, and Tb.N than HF patients. In HO patients, BMD was positively correlated with the BV/TV and Tb.N and negatively correlated with the femoral head organic content and trabecular separation. Interestingly, these correlations were not found in HF patients with relatively lower bone densities. Therefore, osteoporotic patients with similar low bone densities could have significant microstructural differences. No differences were found between the two groups at a HA crystal level.

Altered topological blueprint of trabecular bone associates with skeletal pathology in humans.

Bone is a hierarchically organized biological material, and its strength is usually attributed to overt factors such as mass, density, and composition. Here we investigate a covert factor - the topological blueprint, or the network organization pattern of trabecular bone. This generally conserved metric of an edge-and-node simplified presentation of trabecular bone relates to the average coordination/valence of nodes and the equiangular 3D offset of trabeculae emanating from these nodes. We compare the topological blueprint of trabecular bone in presumably normal, fractured osteoporotic, and osteoarthritic samples (all from human femoral head, cross-sectional study). We show that bone topology is altered similarly in both fragility fracture and in joint degeneration. Decoupled from the morphological descriptors, the topological blueprint subjected to simulated loading associates with an abnormal distribution of strain, local stress concentrations and lower resistance to the standardized load in pathological samples, in comparison with normal samples. These topological effects show no correlation with classic morphological descriptors of trabecular bone. The negative effect of the altered topological blueprint may, or may not, be partly compensated for by the morphological parameters. Thus, naturally occurring optimization of trabecular topology, or a lack thereof in skeletal disease, might be an additional, previously unaccounted for, contributor to the biomechanical performance of bone, and might be considered as a factor in the life-long pathophysiological trajectory of common bone ailments.

High strength brushite bioceramics obtained by selective regulation of crystal growth with chiral biomolecules.

Chirality seems to play a key role in mineralization. Indeed, in biominerals, the biomolecules that guide the formation and organization of inorganic crystals and help construct materials with exceptional mechanical properties, are homochiral. Here, we show that addition of homochiral l-(+)-tartaric acid improved the mechanical properties of brushite bioceramics by decreasing their crystal size, following the classic Hall-Petch strengthening effect; d-(-)-tartaric acid had the opposite effect. Adding l-(+)-Tar increased both the compressive strength (26 MPa) and the fracture toughness (0.3 MPa m1/2) of brushite bioceramics, by 33% and 62%, respectively, compared to brushite bioceramics without additives. In addition, l-(+)-tartaric acid enabled the fabrication of cements with high powder-to-liquid ratios, reaching a compressive strength and fracture toughness as high as 32.2 MPa and 0.6 MPa m1/2, respectively, approximately 62% and 268% higher than that of brushite bioceramics prepared without additives, respectively. Characterization of brushite crystals from the macro- to the atomic-level revealed that this regulation is attributable to a stereochemical matching between l-(+)-tartaric acid and the chiral steps of brushite crystals, which results in inhibition of brushite crystallization. These findings provide insight into understanding the role of chirality in mineralization, and how to control the crystallographic structure of bioceramics to achieve high-performance mechanical properties. STATEMENT OF SIGNIFICANCE: Calcium-phosphate cements are promising bone repair materials. However, their suboptimal mechanical properties limit their clinical use. Natural biominerals have remarkable mechanical properties that are the result of controlled size, shape and organization of their inorganic crystals. This is achieved by biomineralization proteins that are homochiral, composed of l- amino acids. Despite the importance of chiral l-biomolecules in biominerals, using homochiral molecules to fabricate bone cements has not been studied yet. In this study, we showed that homochiral l-(+)-tartaric acid can regulate the crystal structure and improve the mechanical properties of a calcium-phosphate cement. Hence, these findings open the door for a new way of designing strong bone cement and highlight the importance of chirality in bioceramics.

Selective Crystal Growth Regulation by Chiral α-Hydroxycarboxylic Acids Improves the Strength and Toughness of Calcium Sulfate Cements.

Natural biominerals, such as bones and teeth, use acidic matrix biomolecules to control growth, morphology, and organization of the brittle hydroxyapatite crystals. This interplay provides biominerals with outstanding mechanical properties. Recently, we reported that the l-enantiomer of chiral tartaric acid has a potent regulatory effect on the crystal structure and mechanical performance of brushite cement, a mineral with a monoclinic crystal system. We hypothesized that this strategy could be applied using various chiral α-hydroxycarboxylic acids to enhance the mechanical performance of calcium sulfate dihydrate cements, another mineral belonging to the monoclinic crystal system. Calcium sulfate cements are widely used in dentistry, medicine, and construction, but these cements have low mechanical properties. In this work, we first determined the impact of different chiral α-hydroxycarboxylic acids on the properties of calcium sulfate cements. After that, we focused on identifying the regulation effect of chiral tartaric acid on gypsum crystals precipitated in a supersaturated solution. Here, we show that the selective effect of α-hydroxycarboxylic acid l-enantiomers on calcium sulfate crystals improved the mechanical performance of gypsum cements, while d-enantiomer had a weak impact. Compare to the calcium sulfate cements prepared without additives, the presence of l-enantiomer enhanced the compressive strength and the fracture toughness of gypsum cements by 40 and 70%, respectively. Thus, these results prove the generalizability of this approach and help us to fabricate high-strength cements.

Determining the retention of removable partial dentures.

STATEMENT OF PROBLEM: Removable partial dentures (RPDs) provide a cost-effective treatment for millions of partially edentulous patients worldwide. However, they often fail because of loss of retention. One reason for this problem is lack of precise guidelines for designing retentive RPDs. PURPOSE: The purpose of this in vitro study was to determine the forces produced by food and clasps during mastication to develop an algorithm for predicting RPD retention and to help determine the optimal number of clasps. MATERIAL AND METHODS: The forces that food exerts on acrylic resin teeth during simulated mastication and the retention forces provided by clasps (wrought wire, circumferential, and I-bar) engaging on teeth were measured using a universal testing machine. A statistical analysis was performed with a 1-way ANOVA and repeated-measures ANOVA while the developed algorithm was evaluated by using sensitivity and specificity analysis. RESULTS: The force exerted by food mastication on each individual tooth ranged between 1.7 and 12.2 N, depending on the type of tooth, tooth anatomy, occlusion, and food. The retention force of the clasps after cyclic testing ranged between 2.9 and 14.5 N, depending on the type of tooth abutment and clasp. Using these measurements, an algorithm was developed to predict RPD retention. The algorithm was confirmed experimentally on 36 RPDs, showing a sensitivity of 96%, specificity of 100%, and an accuracy of 97%. CONCLUSIONS: The forces generated by food mastication on teeth varied according to the type of tooth, occlusion, and food. The retention force of RPD clasps varied according to the type of tooth and clasp. An algorithm for predicting RPD retention and determining the optimal number of clasps was developed and validated experimentally.

Bio-inspired and optimized interlocking features for strengthening metal/polymer interfaces in additively manufactured prostheses.

Biomedical and dental prostheses combining polymers with metals often suffer failure at the interface. The weak chemical bond between these two dissimilar materials can cause debonding and mechanical failure. This manuscript introduces a new mechanical interlocking technique to strengthen metal/polymer interfaces through optimized additively manufactured features on the metal surface. To reach an optimized design of interlocking features, we started with the bio-mimetic stress-induced material transformation (SMT) optimization method. The considered polymer and metal materials were cold-cured Poly(methyl methacrylate) (PMMA) and laser-sintered Cobalt-Chromium (Co-Cr), respectively. Optimal dimensions of the bio-inspired interlocking features were then determined by mesh adaptive direct search (MADS) algorithm combined with finite element analysis (FEA) and tensile experiments such that they provide the maximum interfacial tensile strength and stiffness while minimizing the stress in PMMA and the displacement of PMMA at the Co-Cr/PMMA interface. The SMT optimization process suggested a Y-shape as a more favorable design, which was similar to mangrove tree roots. Experiments confirmed that our optimized interlocking features increased the strength of the Co-Cr/PMMA interface from 2.3 MPa (flat interface) to 34.4 ±â€¯1 MPa, which constitutes 85% of the tensile failure strength of PMMA (40.2 ±â€¯1 MPa). STATEMENT OF SIGNIFICANCE: The objective of this study was to improve metal/polymer interfacial strength in dental and orthopedic prostheses. This was achieved by additive manufacturing of optimized interlocking features on metallic surfaces using laser-sintering. The interlocking design of the features, which was a Y-shape similar to the roots of mangrove trees, was inspired by a bio-memetic optimization algorithm. This interlocking design lowered the PMMA displacement at the Co-Cr/PMMA interface by 70%, enhanced the interfacial strength by more than 12%, and increased the stiffness by 18% compared with a conventional bead design, meanwhile no significant difference was found in the toughness of both designs.

An analytical model to design circumferential clasps for laser-sintered removable partial dentures.

OBJECTIVE: Clasps of removable partial dentures (RPDs) often suffer from plastic deformation and failure by fatigue; a common complication of RPDs. A new technology for processing metal frameworks for dental prostheses based on laser-sintering, which allows for precise fabrication of clasp geometry, has been recently developed. This study sought to propose a novel method for designing circumferential clasps for laser-sintered RPDs to avoid plastic deformation or fatigue failure. METHODS: An analytical model for designing clasps with semicircular cross-sections was derived based on mechanics. The Euler-Bernoulli elastic curved beam theory and Castigliano's energy method were used to relate the stress and undercut with the clasp length, cross-sectional radius, alloy properties, tooth type, and retention force. Finite element analysis (FEA) was conducted on a case study and the resultant tensile stress and undercut were compared with the analytical model predictions. Pull-out experiments were conducted on laser-sintered cobalt-chromium (Co-Cr) dental prostheses to validate the analytical model results. RESULTS: The proposed circumferential clasp design model yields results in good agreement with FEA and experiments. The results indicate that Co-Cr circumferential clasps in molars that are 13mm long engaging undercuts of 0.25mm should have a cross-section radius of 1.2mm to provide a retention of 10N and to avoid plastic deformation or fatigue failure. However, shorter circumferential clasps such as those in premolars present high stresses and cannot avoid plastic deformation or fatigue failure. SIGNIFICANCE: Laser-sintered Co-Cr circumferential clasps in molars are safe, whereas they are susceptible to failure in premolars.

Removable partial denture alloys processed by laser-sintering technique.

Removable partial dentures (RPDs) are traditionally made using a casting technique. New additive manufacturing processes based on laser sintering has been developed for quick fabrication of RPDs metal frameworks at low cost. The objective of this study was to characterize the mechanical, physical, and biocompatibility properties of RPD cobalt-chromium (Co-Cr) alloys produced by two laser-sintering systems and compare them to those prepared using traditional casting methods. The laser-sintered Co-Cr alloys were processed by the selective laser-sintering method (SLS) and the direct metal laser-sintering (DMLS) method using the Phenix system (L-1) and EOS system (L-2), respectively. L-1 and L-2 techniques were 8 and 3.5 times more precise than the casting (CC) technique (p < 0.05). Co-Cr alloys processed by L-1 and L-2 showed higher (p < 0.05) hardness (14-19%), yield strength (10-13%), and fatigue resistance (71-72%) compared to CC alloys. This was probably due to their smaller grain size and higher microstructural homogeneity. All Co-Cr alloys exhibited low porosity (2.1-3.3%); however, pore distribution was more homogenous in L-1 and L-2 alloys when compared to CC alloys. Both laser-sintered and cast alloys were biocompatible. In conclusion, laser-sintered alloys are more precise and present better mechanical and fatigue properties than cast alloys for RPDs. © 2017 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 106B: 1174-1185, 2018.