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Towards artificial ossification for bone-inspired technical structures
Abstract
Since its first description in 1892, the adaptation of internal bone structure to changing loading conditions over time, known as Wolff 's Law, has inspired a wide range of research and imitation. This investigation presents a new bone-inspired algorithm, intended for the structural design of technical structures and capable of optimizing the shape and size of three-dimensional lattice structures. Unlike conventional structural optimization methods, it uses interacting artificial agents that closely follow the cellular behaviour of the biological blueprint. Agents iteratively move, alter cross-sections, and reposition axes in the latticework. The efficacy of the algorithm is tested and evaluated in two case studies. This agent-based approach lays the theoretical foundation for an implementation of adaptive structural building components and provides a tool for further research into the spatial aspects of natural ossification.
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The paper explores the possibilities of using Structural Optimization Tools (ESO) digital tools in an integrated structural and architectural design in response to the current needs geared towards sustainability, combining ecological and economic efficiency. The first part of the paper defines the Evolutionary Structural Optimization tools, which were developed specifically for engineering purposes using finite element analysis as a framework. The development of ESO has led to several incarnations, which are all briefly discussed (Additive ESO, Bi-directional ESO, Extended ESO). The second part presents result of using these tools in structural and architectural design. Actual building projects which involve optimization as a part of the original design process will be presented (Crematorium in Kakamigahara Gifu, Japan, 2006 SANAA"s Learning Centre, EPFL in Lausanne, Switzerland 2008 among others). The conclusion emphasizes that the structural engineering and architectural design mean directing attention to the solutions which are used by Nature, designing works optimally shaped and forming their own environments. Architectural forms never constitute the optimum shape derived through a form-finding process driven only by structural optimization, but rather embody and integrate a multitude of parameters. It might be assumed that there is a similarity between these processes in nature and the presented design methods. Contemporary digital methods make the simulation of such processes possible, and thus enable us to refer back to the empirical methods of previous generations.
▪ Abstract The term bone refers to a family of materials, all of which are built up of mineralized collagen fibrils. They have highly complex structures, described in terms of up to 7 hierarchical levels of organization. These materials have evolved to fulfill a variety of mechanical functions, for which the structures are presumably fine-tuned. Matching structure to function is a challenge. Here we review the structure-mechanical relations at each of the hierarchical levels of organization, highlighting wherever possible both underlying strategies and gaps in our knowledge. The insights gained from the study of these fascinating materials are not only important biologically, but may well provide novel ideas that can be applied to the design of synthetic materials.
We employ the variational theory of optimal control problems and evolutionary algorithms to investigate the form finding of min-imum compliance elastic structures. Mathematical properties of ground structure approaches are discussed with reference to ar-bitrary collections of structural elements. A numerical procedure based on a Breeder Genetic Algorithm is proposed for the shape op-timization of discrete structural models. Several numerical applica-tions are presented, showing the ability of the adopted search strat-egy in avoiding local optimal solutions. The proposed approach is validated against a parade of results available in the literature.
Automotive chassis design in view of car weight reduction is a challenging task due to the many performance targets that must be satisfied, in particular in terms of vehi- cle safety. In this paper a methodology for automotive chas- sis design in involving optimization techniques is presented. In particular, topology, topometry and size optimizations are coupled with F E M analyses and adopted in cascade for reaching an optimum chassis configuration. The methodol- ogy is applied to the design process of a rear-central engine high performance vehicle chassis. The objective of the op- timization process is the chassis weight reduction, yet in fulfilment of structural performance constraints as required by Ferrari standards. The results demonstrate the general ap- plicability of the methodology presented for obtaining the general trusses layout and thicknesses distribution of the structure. The numerical model at this stage shows a sig- nificant weight reduction when compared to the chassis of the Ferrari F458 Italia.
Vertebrates come with a skeleton of bones whose inner structure combines two contradicting properties in a fascinating way: On the one hand, bones are stable and robust against mechanical stress, and on the other hand they are lightweight to minimise the energy necessary for motion of the organism. By means of a biological process called ossification, the inner structure of bones becomes permanently optimised during organism’s lifetime which implies a high adaptability to varying environmental and behavioural needs. An appropriate computational model of ossification provides a promising bionics tool with widespread applicability for instance in architecture for construction of technical structures. To this end, we introduce the framework of osteogenetic P systems able to generate and to manage the spatial inner structure of bones in a dynamical manner during ossification. Starting from an initial porous network of interwoven filaments surrounded by vesicles, a variety of osteoblasts and osteoclasts is placed alongside the filaments throughout the whole network. External forces, freely configurable in their intensity and effective direction, affect the outer nodes of the network inducing a spatial distribution of mechanical stress in its inner filamentary structure. Now, the osteoblasts move towards heavily loaded positions and strengthen the corresponding filaments while osteoclasts eliminate filamentary material wherever dispensible. Over time, the inner network structure adapts to its demands by strong filaments along the main force lines. Complementing our framework of osteogenetic P systems, we demonstrate its practicability using two case studies: The first one describes generation of a dice-shaped cage resistant against weights on top. The second study addresses construction of an arched bridge with two opposite bearings.
Bone formation, for example during bone remodelling or fracture repair, requires mature osteoblasts to deposit bone with remarkable spatial precision. As osteoblast precursors derive either from circulation or resident stem cell pools, they and their progeny are required to migrate within the three-dimensional bone space and to navigate to their destination, i.e. to the site of bone formation. An understanding of this process is emerging based on in vitro and in vivo studies of several vertebrate species. Receptors on the osteoblast surface mediate cell adhesion and polarization, which induces osteoblast migration. Osteoblast migration is then facilitated along gradients of chemoattractants. The latter are secreted or released proteolytically by several cell types interacting with osteoblasts, including osteoclasts and vascular endothelial cells. The positions of these cellular sources of chemoattractants in relation to the position of the osteoblasts provide the migrating osteoblasts with tracks to their destination, and osteoblasts possess the means to follow a track marked by multiple chemoattractant gradients. In addition to chemotactic cues, osteoblasts sense other classes of signals and utilize them as landmarks for navigation. The composition of the osseous surface guides adhesion and hence migration efficiency and can also provide steering through haptotaxis. Further, it is likely that signals received from surface interactions modulate chemotaxis. Besides the nature of the surface, mechanical signals such as fluid flow may also serve as navigation signals for osteoblasts. Alterations in osteoblast migration and navigation might play a role in metabolic bone diseases such as osteoporosis.
The Karamba plug-in developed by Clemens Preisinger in collaboration with Bollinger + Grohmann Engineers has been developed to predict the behaviour of structures under external loads. Intended to be used by architects rather than being solely confined to an engineering setting, it enables a seamless flow of data between structural and geometric models. Preisinger here describes the program's evolution and application.
A new method is presented for structure optimization in view of lightweight design. The optimization algorithm simulates adaptive bone mineralization by varying the Young's modulus according to a calculated stress distribution. Several examples demonstrate the efficiency of this procedure, which can be done with any commercial finite element code. A combination with the shape optimization method CAO is a complete layout procedure to design mechanical components after the rules of nature.
The objective of this paper is to investigate the efficiency of various evolutionary algorithms (EA), such as genetic algorithms and evolution strategies, when applied to large-scale structural sizing optimization problems. Both type of algorithms imitate biological evolution in nature and combine the concept of artificial survival of the fittest with evolutionary operators to form a robust search mechanism. In this paper modified versions of the basic EA are implemented to improve the performance of the optimization procedure. The modified versions of both genetic algorithms and evolution strategies combined with a mathematical programming method to form hybrid methodologies are also tested and compared and proved particularly promising. The numerical tests presented demonstrate the computational advantages of the discussed methods, which become more pronounced in large-scale optimization problems.
The law of bone remodeling, commonly referred to as Wolff's Law, asserts that the internal trabecular bone adapts to external loadings, reorienting with the principal stress trajectories to maximize mechanical efficiency creating a naturally optimum structure. The goal of the current study was to utilize an advanced structural optimization algorithm, called design space optimization (DSO), to perform a micro-level three-dimensional finite element bone remodeling simulation on the human proximal femur and analyse the results to determine the validity of Wolff's hypothesis. DSO optimizes the layout of material by iteratively distributing it into the areas of highest loading, while simultaneously changing the design domain to increase computational efficiency. The result is a "fully stressed" structure with minimized compliance and increased stiffness. The large-scale computational simulation utilized a 175 μm mesh resolution and the routine daily loading activities of walking and stair climbing. The resulting anisotropic trabecular architecture was compared to both Wolff's trajectory hypothesis and natural femur samples from literature using a variety of visualization techniques, including radiography and computed tomography (CT). The results qualitatively revealed several anisotropic trabecular regions, that were comparable to the natural human femurs. Quantitatively, the various regional bone volume fractions from the computational results were consistent with quantitative CT analyses. The global strain energy proceeded to become more uniform during optimization; implying increased mechanical efficiency was achieved. The realistic simulated trabecular geometry suggests that the DSO method can accurately predict bone adaptation due to mechanical loading and that the proximal femur is an optimum structure as the Wolff hypothesized.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, 2009. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Includes bibliographical references (p. 145-153). This dissertation presents Thrust Network Analysis, a new methodology for generating compression-only vaulted surfaces and networks. The method finds possible funicular solutions under gravitational loading within a defined envelope. Using projective geometry, duality theory and linear optimization, it provides a graphical and intuitive method, adopting the same advantages of techniques such as graphic statics, but offering a viable extension to fully three-dimensional problems. The proposed method is applicable for the analysis of vaulted historical structures, specifically in unreinforced masonry, as well as the design of new vaulted structures. This dissertation introduces the method and shows examples of applications in both fields. Thrust Network Analysis, masonry, historic structures, compression-only structures, limit analysis, equilibrium analysis, funicular design, form-finding, structural optimization, Gothic vaults, reciprocal diagrams. by Philippe Block. Ph.D.
In the field of bone adaptation, it is believed that the morphology of bone is affected by its mechanical loads, and bone has self-optimizing capability; this phenomenon is well known as Wolff's law of the transformation of bone. In this paper, we simulated trabecular bone adaptation in the human proximal femur using topology optimization and quantitatively investigated the validity of Wolff's law. Topology optimization iteratively distributes material in a design domain producing optimal layout or configuration, and it has been widely and successfully used in many engineering fields. We used a two-dimensional micro-FE model with 50 microm pixel resolution to represent the full trabecular architecture in the proximal femur, and performed topology optimization to study the trabecular morphological changes under three loading cases in daily activities. The simulation results were compared to the actual trabecular architecture in previous experimental studies. We discovered that there are strong similarities in trabecular patterns between the computational results and observed data in the literature. The results showed that the strain energy distribution of the trabecular architecture became more uniform during the optimization; from the viewpoint of structural topology optimization, this bone morphology may be considered as an optimal structure. We also showed that the non-orthogonal intersections were constructed to support daily activity loadings in the sense of optimization, as opposed to Wolff's drawing.
Direct assessment of bone competence in vivo is not possible, hence, it is inevitable to predict it using appropriate simulation techniques. Although accurate estimates of bone competence can be obtained from micro-finite element models (muFE), it is at the expense of large computer efforts. In this study, we investigated the application of structural idealizations to represent individual trabeculae by single elements. The objective was to implement and validate this technique. We scanned 42 human vertebral bone samples (10 mm height, 8 mm diameter) with micro-computed tomography using a 20 microm resolution. After scanning, direct mechanical testing was performed. Topological classification and dilation-based algorithms were used to identify individual rods and plates. Two FE models were created for each specimen. In the first one, each rod-like trabecula was modeled with one thickness-matched beam; each plate-like trabecula was modeled with several beams. From a simulated compression test, assuming one isotropic tissue modulus for all elements, the apparent stiffness was calculated. After reducing the voxel size to 40 microm, a second FE model was created using a standard voxel conversion technique. Again, one tissue modulus was assumed for all elements in all models, and a compression test was simulated. Bone volume fraction ranged from 3.7% to 19.5%; Young's moduli from 43 MPa to 649 MPa. Both models predicted measured apparent moduli equally well (R2 = 0.85), and were in excellent agreement with each other (R2 = 0.97). Tissue modulus was estimated at 9.0 GPa and 10.7 GPa for the beam FE and voxel FE models, respectively. On average, the beam models were solved in 219 s, reducing CPU usage up to 1150-fold as compared to 40 microm voxel FE models. Relative to 20 microm voxel models 10,000-fold reductions can be expected. The presented beam FE model is an abstraction of the intricate real trabecular structure using simple cylindrical beam elements. Nevertheless, it enabled an accurate prediction of global mechanical properties of microstructural bone. The strong reduction in CPU time provides the means to increase throughput, to analyze multiple loading configuration and to increase sample size, without increasing computational costs. With upcoming in vivo high-resolution imaging systems, this model has the potential to become a standard for mechanical characterization of bone.
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