Adaptive Gradient Elasticity and Mechanical Stimulation in Bone Remodelling

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.

Research in the area of numerical analysis of non-invasive vibrational therapy of bone diseases is extremely timely and has potentially a significant impact.
Although research in vibrational therapy has already been approached experimentally there exists no general and flexible tool that can be quickly made patient specific. The novelty, benefits and impact of the proposed research is in the development of a numerical, generic at the same time, easily personalised framework to describe, analyse and optimise the vibration therapy for the particular patient's needs.

The timeliness and the impact of this research should also to be acknowledged as fitting within the remit of two EPSRC Priority Research Areas: "Towards next-generation healthcare" and "Ageing - lifelong health wellbeing".

Three types of potential beneficiaries from this project can be identified:

1. Stakeholders in academia. The world-wide academic community will benefit through publication of results in internationally leading research journals together with the presentation of results in international conferences and seminars. Both experimental and numerical communities will benefit from the research. A complex but accessible numerical tool will be presented for the numerical community where the elegant but sophisticated multi-scale model that is taking into account the underlying anisotropic, evolving with time, micro-structure will be offered. On the other hand the presence of the numerical technique will highly benefit the experimental community by indicating, for example, the optimal and crucial vibration parameters for their experiments.

2. The general public. They will benefit from the research in vibrational therapy of bone diseases, through improving the quality of life in the ageing population. There is also a cost reduction due to
- in the short term offering simple and generic numerical models with patient-specific parameters, that can be used easily by clinicians and that are cheap alternatives to the elaborate and expensive experiments for each particular patient;
- in the intermediate term interchanging expensive pharmacological treatment by significantly cheaper mechanical stimulation, which can be performed in common gyms. The added benefit here is the social welfare aspect: the patients who, due to bone disease were confined to home, would now be able to do the light gym vibration exercises in a communal area while communicating and sharing the experience with fellow patients;
- in the longer term potentially reducing the cost of osteoporosis-related fractures which, according to [1] from 2000 to 2010 was more than 20 billion pounds and would only grow in an ageing population.

3. Healthcare practitioners community will also benefit from the proposed research as the patient specific accessible tool will be developed that will be able to predict the outcomes of particular treatments scenarios.

[1] Burge, Worley, A.Johansen, Bhattacharyya, Bose, Journal of Medical Economics 4 (2001) 51-62.