On the Use of Bone Remodelling Models to Estimate the Density Distribution of Bones. Uniqueness of the Solution.
On the Use of Bone Remodelling Models to Estimate the Density Distribution of Bones. Uniqueness of the Solution.
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DOI：
10.1371/journal.pone.0148603
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发表时间：
2016
期刊：
影响因子：
3.7
通讯作者：
Mayo J
中科院分区：
文献类型：
--
作者：
Martínez-Reina J;Ojeda J;Mayo J
骨重建模型以现象学的方式被广泛地用于从骨每天受到的载荷中数值地估计骨中的表观密度分布。这些模拟从一个任意的初始分布开始，通常是均匀的，密度局部变化，直到达到骨重建平衡。骨对机械刺激的反应传统上是用数学关系来表示的，该数学关系考虑了一系列刺激的存在，称为死区或惰性区，对于这些刺激，没有净骨量变化发生。实现这样的关系会导致不同的解决方案，这取决于起始密度。本文采用两种不同的骨重建模型：一种是各向同性模型，另一种是各向异性模型，证明了该解的非唯一性。研究还表明，非唯一性问题只能通过消除死区来缓解，但除非骨形成和骨吸收率限制在某些最大值，否则它并不能完全解决。
Bone remodelling models are widely used in a phenomenological manner to estimate numerically the distribution of apparent density in bones from the loads they are daily subjected to. These simulations start from an arbitrary initial distribution, usually homogeneous, and the density changes locally until a bone remodelling equilibrium is achieved. The bone response to mechanical stimulus is traditionally formulated with a mathematical relation that considers the existence of a range of stimulus, called dead or lazy zone, for which no net bone mass change occurs. Implementing a relation like that leads to different solutions depending on the starting density. The non-uniqueness of the solution has been shown in this paper using two different bone remodelling models: one isotropic and another anisotropic. It has also been shown that the problem of non-uniqueness is only mitigated by removing the dead zone, but it is not completely solved unless the bone formation and bone resorption rates are limited to certain maximum values.