Biomechanical System Optimization (BSO)

Bones mainly serve as supporting columns which transfer body weight and levers which permit various motions of the body. In daily activities, bones are subject to a variety of axial, bending, and torsional loads which cause mechanical stresses. Julius Wolff (1892) stated that the functional adaptation of bones reorients the trabeculae, so that they align with altered principal stress trajectories when the environmental loads are changed by trauma or a life pattern. He also suggested that the bone obtains the “maximum” mechanical efficiency with the "minimum" mass; this is well known as Wolff’s law. Based on this observation, a bone structure is referred as an "optimal" structure.

Osteoporosis is a metabolic bone disease which degrades a bone microstructure and therefore increases bone fragility. Osteoporotic fractures result in decreased quality of life as well as excessive financial costs. If the morphological changes of a bone structure can be estimated and diagnosed, osteoporosis can be properly managed with clinical treatments. 

This research develops a topology optimization-based bone remodeling simulation which can reflect the morphological changes in a bone structure over time. Note that topology optimization is mathematically matched well with phenomenological bone remodeling simulation. Topology optimization determines the optimal bone structure under a given loading condition by iteratively redistributing mass in a design domain. The proposed method can contribute to the development of early diagnosis for osteoporosis and patient-specific models for various clinical purposes.


* Y. H. Lee, Y. Kim, J. J. Kim, I. G. Jang, "Homeostasis-based aging model for trabecular changes and its correlation with age-matched bone mineral densities and radiographs," European Journal of Radiology, vol. 84, no. 11, pp. 2261-2268, 2015. 

* I. G. Jang, I. Y. Kim, “Computational simulation of trabecular adaptation progress in human proximal femur during growth,” Journal of Biomechanics, vol. 42, no. 5, pp. 573-580, 2009. 

* I. G. Jang, I. Y. Kim, B. M. Kwak, “Analogy of strain energy density based bone-remodeling algorithm and structural topology optimization,” Journal of Biomechanical Engineering, vol. 131, no. 1, pp. 011012-1-7, 2009.

* I. G. Jang, I. Y. Kim, “Computational study of Wolff’s law with trabecular architecture in the human proximal femur using topology optimization,” Journal of Biomechanics, vol. 41, no. 11, pp. 2353-2361, 2008.

To consider dynamic loads in bone remodeling simulation, various dynamic activities of seconds needed to be simulated in the bone remodeling phenomenon of months. However, this direct approach leads to an extreme computational burden, which is one of the challenging issues in the field. Based on two-scale homogenization approach, we proposed a novel method that can determine the representative static loads (RSLs) to efficiently consider the effects of cyclic dynamic loads on the bone remodeling simulation. The proposed method successfully reflects the subject-specific gait cycle of its own period and phase length during bone remodeling simulation through the coordinate transformation of the time scale.


* B. J. Chun, I. G. Jang, "Framework of sampling the subject-specific static loads from the gait cycle of interindividual variation," Computer Methods and Programs in Biomedicine, vol. 225, 2022.

* B. J. Chun, I. G. Jang, "Determination of the representative static loads for cyclically repeated dynamic loads: a case study of bone remodeling simulation with gait loads," Computer Methods and Programs in Biomedicine, vol. 200, 2021.

Clinical high-resolution (HR) skeletal images which can represent a bone microstructure are essential for accurate bone strength assessment. However, they are still unavailable because the current in vivo HR imaging modalities have a limited resolution due to high radiation doses, low signal-to-noise ratios, and/or long scan times. 

In this study, a HR skeletal image can be reconstructed from a clinical low-resolution (LR) image by applying topology optimization. The proposed method conducts mesh refinement for resolution upscaling and then performs topology optimization with a constraint for the bone mineral density deviation to preserve the subject-specific bone distribution data.


* J. J. Kim, J. Nam, I. G. Jang, "Computational study of estimating 3D trabecular bone microstructure for volume of interest from CT scan data," International Journal for Numerical Methods in Biomedical Engineering, vol. 34, no. 4, pp. 2950, 2018.

* J. J. Kim, I. G. Jang, "Image resolution enhancement for healthy weight-bearing bones based on topology optimization," Journal of Biomechanics, vol. 49, no. 13, pp. 3035-3040, 2016.

Although the topology optimization-based method shows the potential to reconstruct the bone microstructure from LR skeletal images, excessive computing time due to iterative large-scale FE analyses makes it impractical to be further implemented in the clinical field. Conventional deep-learning methods also have difficulties: 1) limited upscaling ratio due to a complex structure, 2) the lack of HR trabecular scan data for training, and 3) the necessity for large computing resources to train a network.

To overcome the above obstacles, we propose a patchwise bone microstructure reconstruction scheme. HR skeletal images, which are difficult to obtain in clinical practice, can be replaced with the results from topology optimization-based bone remodeling. Then, an artificial neural network is trained with 1) the LR image patch and corresponding structural behavior as input, and 2) the HR image patch as output. The reconstructed HR image patches are assembled into a whole trabecular structure in the VOI.

By integrating the RSLs and bone microstructure reconstruction, patient-specific bone health assessment would be available. The proposed framework can be utilized as a breakthrough technique for the quantitative bone strength assessment, thereby contributing to personalized, predictive, and preventive medicine in the clinical field.