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Three-dimensional topology optimization model to simulate the external shapes of bone.

ABSTRACT: Elucidation of the mechanism by which the shape of bones is formed is essential for understanding vertebrate development. Bones support the body of vertebrates by withstanding external loads, such as those imposed by gravity and muscle tension. Many studies have reported that bone formation varies in response to external loads. An increased external load induces bone synthesis, whereas a decreased external load induces bone resorption. This relationship led to the hypothesis that bone shape adapts to external load. In fact, by simulating this relationship through topology optimization, the internal trabecular structure of bones can be successfully reproduced, thereby facilitating the study of bone diseases. In contrast, there have been few attempts to simulate the external structure of bones, which determines vertebrate morphology. However, the external shape of bones may be reproduced through topology optimization because cells of the same type form both the internal and external structures of bones. Here, we constructed a three-dimensional topology optimization model to attempt the reproduction of the external shape of teleost vertebrae. In teleosts, the internal structure of the vertebral bodies is invariable, exhibiting an hourglass shape, whereas the lateral structure supporting the internal structure differs among species. Based on the anatomical observations, we applied different external loads to the hourglass-shaped part. The simulations produced a variety of three-dimensional structures, some of which exhibited several structural features similar to those of actual teleost vertebrae. In addition, by adjusting the geometric parameters, such as the width of the hourglass shape, we reproduced the variation in the teleost vertebrae shapes. These results suggest that a simulation using topology optimization can successfully reproduce the external shapes of teleost vertebrae. By applying our topology optimization model to various bones of vertebrates, we can understand how the external shape of bones adapts to external loads.

SUBMITTER: Sakashita M

PROVIDER: S-EPMC8208580 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:During therapeutic beam irradiation, an unvisualized three-dimensional (3D) target position should be estimated using an external surrogate with an estimation model. Training periods for the developed model with no additional imaging during beam irradiation were optimized using clinical data.Dual-source 4D-CBCT projection data for 20 lung cancer patients were used for validation. Each patient underwent one to three scans. The actual target positions of each scan were equally divided into two equal parts: one for the modeling and the other for the validating session. A quadratic target position estimation equation was constructed during the modeling session. Various training periods for the session-i.e., modeling periods (TM)-were employed: TM???{5,10,15,25,35} [s]. First, the equation was used to estimate target positions in the validating session of the same scan (intra-scan estimations). Second, the equation was then used to estimate target positions in the validating session of another temporally different scan (inter-scan estimations). The baseline drift of the surrogate and target between scans was corrected. Various training periods for the baseline drift correction-i.e., correction periods (TCs)-were employed: TC???{5,10,15;?TC???TM} [s]. Evaluations were conducted with and without the correction. The difference between the actual and estimated target positions was evaluated by the root-mean-square error (RMSE).The range of mean respiratory period and 3D motion amplitude of the target was 2.4-13.0 s and 2.8-34.2 mm, respectively. On intra-scan estimation, the median 3D RMSE was within 1.5-2.1 mm, supported by previous studies. On inter-scan estimation, median elapsed time between scans was 10.1 min. All TMs exhibited 75th percentile 3D RMSEs of 5.0-6.4 mm due to baseline drift of the surrogate and the target. After the correction, those for each TMs fell by 1.4-2.3 mm. The median 3D RMSE for both the 10-s TM and the TC period was 2.4 mm, which plateaued when the two training periods exceeded 10 s.A widely-applicable estimation model for the 3D target positions during beam irradiation was developed. The optimal TM and TC for the model were both 10 s, to allow for more than one respiratory cycle.UMIN000014825 . Registered: 11 August 2014.

Project description:Dynamic bone histomorphometry is the standard method for measuring bone remodeling at the level of individual events. Although dynamic bone histomorphometry is an invaluable tool for understanding osteoporosis and other metabolic bone diseases, the technique's two-dimensional nature requires the use of stereology and prevents measures of individual remodeling event number and size. Here, we used a novel three-dimensional fluorescence imaging technique to achieve measures of individual resorption cavities and formation events. We performed this three-dimensional histomorphometry approach using a common model of postmenopausal osteoporosis, the ovariectomized rat. The three-dimensional images demonstrated the spatial relationship between resorption cavities and formation events consistent with the hemiosteonal model of cancellous bone remodeling. Established ovariectomy was associated with significant increases in the number of resorption cavities per unit bone surface (2.38 ± 0.24 mm⁻² sham surgery versus 3.86 ± 0.35 mm⁻² bilateral ovariectomy [OVX], mean ± SD, p < 0.05) and total volume occupied by cavities per unit bone volume (0.38% ± 0.06% sham versus 1.12% ± 0.18% OVX, p < 0.001), but there was no difference in surface area per resorption cavity, maximum cavity depth, or cavity volume. In addition, we found that established ovariectomy is associated with increased size of bone formation events because of the merging of formation events (23,700 ± 6,890 µm² sham verusus 33,300 ± 7,950 µm² OVX). No differences in mineral apposition rate (determined in 3D) were associated with established ovariectomy. That established estrogen depletion is associated with increased number of remodeling events with only subtle changes in remodeling event size suggests that circulating estrogens may have their primary effect on the origination of new basic multicellular units with relatively little effect on the progression and termination of active remodeling events.

Project description:BACKGROUND: The quaternary structure of eukaryotic NADH:ubiquinone oxidoreductase (complex I), the largest complex of the oxidative phosphorylation, is still mostly unresolved. Furthermore, it is unknown where transiently bound assembly factors interact with complex I. We therefore asked whether the evolution of complex I contains information about its 3D topology and the binding positions of its assembly factors. We approached these questions by correlating the evolutionary rates of eukaryotic complex I subunits using the mirror-tree method and mapping the results into a 3D representation by multidimensional scaling. RESULTS: More than 60% of the evolutionary correlation among the conserved seven subunits of the complex I matrix arm can be explained by the physical distance between the subunits. The three-dimensional evolutionary model of the eukaryotic conserved matrix arm has a striking similarity to the matrix arm quaternary structure in the bacterium Thermus thermophilus (rmsd=19 Å) and supports the previous finding that in eukaryotes the N-module is turned relative to the Q-module when compared to bacteria. By contrast, the evolutionary rates contained little information about the structure of the membrane arm. A large evolutionary model of 45 subunits and assembly factors allows to predict subunit positions and interactions (rmsd=52.6 Å). The model supports an interaction of NDUFAF3, C8orf38 and C2orf56 during the assembly of the proximal matrix arm and the membrane arm. The model further suggests a tight relationship between the assembly factor NUBPL and NDUFA2, which both have been linked to iron-sulfur cluster assembly, as well as between NDUFA12 and its paralog, the assembly factor NDUFAF2. CONCLUSIONS: The physical distance between subunits of complex I is a major correlate of the rate of protein evolution in the complex I matrix arm and is sufficient to infer parts of the complex's structure with high accuracy. The resulting evolutionary model predicts the positions of a number of subunits and assembly factors.

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Three-dimensional topology optimization model to simulate the external shapes of bone.

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