Modelling complex and partially identified engineering problems- Application to the individualised multiscale simulation of the musculoskeletal system

Traditionally, engineering design relies on scale separation. Virtually every physical process involves complex interactions across several space-time scales. For most engineering problems it is assumed that processes at different scales can be represented at the larger scale through some averaged property. However, when such assumptions of scale separation cannot be made, as in the modelling of biological systems where scales overlap, the inherent complexity of multi-scale interaction cannot be avoided. This proposal focuses on the establishment of a currently non-existent but essential computational platform for the treatment of musculoskeletal disorders. A multi-scale process in human physiology can be modelled as a collection of single scale models acting on a specific level of biological organisation coupled together across scales using appropriate scale bridging methods. Several unresolved challenges in the biomedical field have inhibited the development of predictive models needed in personalised medicine including (i) How to link mixed multiphysics models across several space-time scales. (ii) How to replace unobservable (possibly invasive and hence expensive) variables and states using proxy measurements (non invasive) reconstructed from the observable variables. (iii) How to use population data across patient classes or animal proxies to accommodate missing data. (iv) How to model uncertainty and the propagation of this across the simulations. (v) How to achieve these objectives within a framework that can be mapped to other engineering problems. This proposal will tackle each of these challenges with: - the development of a multi-scale model of the musculoskeletal system that describes the mechanobiological processes from the whole body (neuromuscular control and body dynamics) down to the cellular level (bone remodelling and mechanosensing); - the creation of a multi-scale model from a partially identified input obtained by fusing a generic atlas of the anatomy, physiology, biology, and biomechanics for each individual. This framework will be integrated in an efficient hypermodelling approach, numerically optimised at each scale level. Once fully realised, such a multi-scale framework will enable (i) deployment of specialised implementations as decision-support systems for diagnosis, prognosis, and treatment planning and monitoring for specific skeletal diseases such as lower back pain, osteoporosis, bone tumours and secondary metastases and osteoarthritis; (ii) implementation of in silico clinical trials for new orthopaedic and tissue engineering implants, modelling the variability of populations, providing a more accurate pre-clinical assessment for musculoskeletal devices and predicting the clinical outcome of these new devices; (iii) optimised interventions with respect to high socioeconomic impact conditions such as obesity, ageing population, disabilities, and chronic diseases in relation to physical activity, and assistive and rehabilitative technologies for neuromuscular deficits.