A fully anisotropic hierarchical hybrid cellular automaton algorithm to simulate bone remodeling

Penninger, Charles L.; Patel, Neal M.; Niebur, Glen L.; Tovar, Andrés; Renaud, John E.

doi:10.1016/j.mechrescom.2007.10.007

Cited by 18 publications

(5 citation statements)

References 21 publications

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“…17 It is said that bone remodeling, a dynamic process, occurs in both cortical and trabecular (or cancellous) bone, allowing a rapid response to changes in circulating calcium levels. [18][19] Bone formation occurs when calcium is incorporated into the organic bone matrix secreted from osteoblasts.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of the stimulus response of hydroxyapatite/ calcium alginate composite gels

Obara

Yamauchi

Tsubokawa

2010

Polym J

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Stimuli-responsive gels have been actively studied and applied to a variety of devices such as drug carriers, artificial muscles and actuators. In this research study, calcium alginate gels containing hydroxyapatite were prepared in one step by adding a diammonium hydrogenphosphate-1% alginate solution to a calcium chloride solution and evaluated for pH dependence and electrochemical properties as stimuli-responsive gels. When the composite gel was immersed in a solution of pH 2-10 or subjected to an applied voltage, the composite gel with a high content of hydroxyapatite tended to maintain its volume. The composite gels immersed in a pH indicator solution changed color with an applied voltage. As a result, it was revealed that alteration of the pH of composite gels occurred by electro-osmosis and electrophoresis. Swelling and shrinking of the composite gels were controlled by the external stimuli of pH, voltage and the content of hydroxyapatite; therefore, it is proposed that composite gels would be good bone-filling material having the function of drug carriers.

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Section: Introductionmentioning

confidence: 99%

Evaluation of the stimulus response of hydroxyapatite/ calcium alginate composite gels

Obara

Yamauchi

Tsubokawa

2010

Polym J

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“…A design update scheme is therefore required to revise the suboptimal macroscale objective value close to the anticipated value: where J i is the objective evaluation of i th iteration, J 0 is objective of conceptual design and η is a small number. The following HCA (Penninger et al , 2008) principle is used to update elemental design variable x i or its Moore neighborhood N M based on local objective value: …”

Section: Multiscale Thermo-mechanical Topology Optimizationmentioning

confidence: 99%

“…In our study, by implementing a computationally efficient inverse homogenization method to maximize shear modulus of each unit cell, the whole structure is self-supporting and easy to manufacture. Furthermore, a hybrid cellular automata (HCA) (Penninger et al , 2008) updating scheme is used to guarantee the thermo-mechanical performance of the macroscale structure. Also, compared to our previous work (Wu et al , 2017), the method brings a manufacturing friendly design, and the design accuracy is improved, as each mesoscale unit cell is optimized.…”

Section: Introductionmentioning

confidence: 99%

Multiscale, thermomechanical topology optimization of self-supporting cellular structures for porous injection molds

Tovar

2019

RPJ

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Purpose This paper aims to establish a multiscale topology optimization method for the optimal design of non-periodic, self-supporting cellular structures subjected to thermo-mechanical loads. The result is a hierarchically complex design that is thermally efficient, mechanically stable and suitable for additive manufacturing (AM). Design/methodology/approach The proposed method seeks to maximize thermo-mechanical performance at the macroscale in a conceptual design while obtaining maximum shear modulus for each unit cell at the mesoscale. Then, the macroscale performance is re-estimated, and the mesoscale design is updated until the macroscale performance is satisfied. Findings A two-dimensional Messerschmitt Bolkow Bolhm (MBB) beam withstanding thermo-mechanical load is presented to illustrate the proposed design method. Furthermore, the method is implemented to optimize a three-dimensional injection mold, which is successfully prototyped using 420 stainless steel infiltrated with bronze. Originality/value By developing a computationally efficient and manufacturing friendly inverse homogenization approach, the novel multiscale design could generate porous molds which can save up to 30 per cent material compared to their solid counterpart without decreasing thermo-mechanical performance. Practical implications This study is a useful tool for the designer in molding industries to reduce the cost of the injection mold and take full advantage of AM.

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“…Early studies were focused on adaptation of the bone structure and density based on the prevailing loading conditions. Whereas first models were still ran in 2D [1], [2], [3], [4], [5], [6] and [7], later models would move to a 3D domain [8], [9], [10], [11], [12], [13] and [14] partially include experimental data from micro-computed tomography scans [15], [16], [17], [18] and [19].…”

Section: Introductionmentioning

confidence: 99%

Phase diagrams of bone remodeling using a 3D stochastic cellular automaton

Heller,

Valleriani,

Cipitria

2023

Preprint

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We propose a 3D stochastic cellular automaton model, governed by evolutionary game theory, to simulate bone remodeling dynamics. The model includes four voxel states:Formation, Quiescence, Resorption, andEnvironment. We simulate theResorptionandFormationprocesses on separate time scales to explore the parameter space and derive a phase diagram that illustrates the sensitivity of these processes to parameter changes. Combining these results, we simulate a full bone remodeling cycle. Furthermore, we show the importance of modeling small neighborhoods for studying local bone microenvironment controls. This model can guide experimental design and, in combination with other models, it could assist to further explore external impacts on bone remodeling. Consequently, this model contributes to an improved understanding of complex dynamics in bone remodeling dynamics and exploring alterations due to disease or drug treatment.Author summaryFunctional well-balanced bone remodeling is crucial for a healthy skeleton. Understanding the various causes for the disruption of this complex process requires models that combine behavior on micro- and macro-level. We propose a 3D stochastic cellular automaton model, where each voxel can take one of four different states representing phases of bone remodeling:Formation, Quiescence, ResorptionandEnvironment. With a qualitative analysis, we show how and when small changes in key interaction parameters can make the difference between healthy and pathological bone remodeling. We also highlight the importance of spatial modeling and the size of the neighborhood for investigating local mechanisms. Our proposed model opens the window to explore the complex interplay of factors essential for healthy bone remodeling and potential alterations due to disease or drug treatment. In the long term this could help with the development of new treatment options for bone diseases.

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A fully anisotropic hierarchical hybrid cellular automaton algorithm to simulate bone remodeling

Cited by 18 publications

References 21 publications

Evaluation of the stimulus response of hydroxyapatite/ calcium alginate composite gels

Evaluation of the stimulus response of hydroxyapatite/ calcium alginate composite gels

Multiscale, thermomechanical topology optimization of self-supporting cellular structures for porous injection molds

Phase diagrams of bone remodeling using a 3D stochastic cellular automaton

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