Adaptive Gradient Elasticity and Mechanical Stimulation in Bone Remodelling

在人口老龄化的今天，与骨质流失有关的问题越来越多。因此，提供一种能够逆转骨退化的策略对公众健康和总体福祉至关重要。需要计算建模策略来补充和增强最近开发的骨退化治疗，即使用低幅度的机械振动来触发骨再生。计算机模型随后将用于优化个体患者的治疗。该项目是工程学（“机械振动”）和生物医学科学（“骨骼再生”）之间的跨学科项目，它需要强大的数学模型输入，以补充现有的实验性生物医学计划。骨退化是一种普遍的现象，通常伴随有骨折。骨退化有多种原因，其中最突出的是骨质疏松症、骨癌和常见的衰老。某些人群特别容易出现骨质退化，比如绝经后的妇女。逆转骨退化已被世界各地的顶尖医学专家公认为对公众健康和福祉至关重要。药物治疗可刺激骨再生；然而，它们的长期影响仍不明确，可能有不希望的副作用。最近，研究人员致力于通过机械刺激来触发骨骼再生。特别是动态负荷（相对于静态负荷）有利于刺激骨骼生长，即通过使患者反复暴露（例如每天20分钟，持续一年）于站立等日常活动强度的紧张中。不幸的是，实验项目很昂贵，需要大量的组织和研究工作。通常还需要获得相关专业机构或道德委员会的批准。正如在许多工程领域一样，计算机建模可以用来补充和/或部分取代昂贵的实验程序。在目前的研究中，建议使用计算机建模技术来模拟由于振动机械刺激引起的骨重塑，从而通过多尺度方法考虑到骨材料的微观结构，这被认为是合适的。建议使用升级技术，将这些微观结构响应转化为宏观水平上的有效特性。由此产生的模型使用起来相对简单，比相关的微观结构模型更“透明”；因此，受益人使用它们应该更加直接。在本研究中，将开发一种特殊的多尺度技术，即自适应梯度弹性模型，以供后续应用。最后，将分析骨刺激对机械振动各方面的依赖性，如频率、振幅和持续时间。对这些方面的部分敏感性可以被量化，并随后用于操纵机械振动的细节，以优化骨骼生长并使患者治疗合理化。

In nowadays ageing population, the problems related to bone loss are on the rise. As such it is of crucial importance to the public health and well-being in general to offer a strategy that can reverse bone degradation.Computational modelling strategies are needed to complement and enhance a recently developed treatment for bone degradation, namely using mechanical vibrations of low magnitude to trigger bone regrowth. The computer modelling will subsequently be used to optimise this treatment for individual patients. The project is interdisciplinary between Engineering ("mechanical vibrations") and Biomedical Sciences ("bone regrowth") and it requires strong mathematical modelling input to complement the existing experimental biomedical programme.The degradation of bone is a widespread phenomenon that is often followed by fracture. Bone degradation has various causes, most prominent of which are osteoporosis, bone cancer and common ageing. Certain groups of individuals are particularly prone to bone degradation, such as post-menopausal women. Reversing bone degradation has been recognised by leading medical specialists around the world to be of crucial importance to public health and public well-being. Bone regrowth can be stimulated by pharmaceutical measures; however, their long-term effects remain unspecified and there may be undesired side effects. More recently, research efforts have been directed towards triggering bone regrowth through mechanical stimulation. Especially dynamic loading (as opposed to static loading) is advantageous to stimulate bone growth namely through exposing the patient repeatedly (say 20 minutes per day for the duration of a year) to straining of the intensity of everyday activities such as standing.Unfortunately, the experimental programmes are expensive and require a lot of organisation and research efforts. It is also often necessary to acquire approval of the relevant Professional Institutions or Ethical Committees. As in many areas of engineering, computer modelling can be used to complement and/or partially replace the expensive experimental programmes. It is thought to be opportune to suggest in the present research computer modelling techniques that can be used to simulate bone remodelling due to vibrationary mechanical stimulation, thereby taking into account the microstructure of the bone material via a multi-scale approach. It is suggested to use upscaling techniques and translate these microstructural responses into effective properties on the macro-scopic level. The resulting models would be relatively simple to use and much more "transparent" than the associated microstructural models; thus, their use by the beneficiaries should be much more straightforward. In this research, a particular type of multi-scale techniques, adaptive gradient elasticity model, will be developed for the benefit of subsequent applications.Finally the dependence of bone stimulation on the various aspects of the mechanical vibration, such as frequency, amplitude and duration will be analysed. The partial sensitivities to these aspects can be quantified and subsequently used to manipulate the details of the mechanical vibrations in order to optimise bone growth and rationalising patient treatment.