A microscopic pore in a clay brick collapses in response to an earthquake occurring in a region where there stands a building comprising a masonry wall containing the said clay brick. The causal dependence between the earthquake and masonry fracture is obvious. However, it is equally obvious that if we choose an instrument to measure how much the pore in the brick collapses, then that instrument cannot measure the magnitude of the seismic wave (and vice-versa).
This limitation is called the curse of resolution. It is inherent in problems where characteristics of a physical system have a cause–effect relationship but these characteristics are observable at vastly different space and/or time scales.
Such problems are known as multiscale problems, and these occur across a great diversity of engineering domains.
One such domain is biomechanics, which is our research interest. The various shots a professional tennis player makes over a tournament season cause a specific bone cell (located somewhere in one of the bones of the player’s arm) to deposit a specific amount of bone mineral during this period.
If we choose an instrument to measure how far the player’s arm travels during a single shot, then that instrument cannot measure the depth of the bone mineral layer deposited by the cell during this time (and vice-versa). So here too, we meet a multiscale problem.
Computational models are being increasingly employed to solve multiscale problems. Computational models are digital twins of a physical system (that may or may not possess multiscale characteristics). A computational model has the advantage that it can be analysed non-invasively to understand the physical system it represents.
In an earlier review paper, we considered some multiscale computational models that were applied to various biomechanics problems. In that paper, we categorised these models according to their motivation for credibility.
That review paper did not explore an important operational issue in multiscale modelling. The particular issue is that a vast majority of these multiscale models described the constituent “scales” of the problem with ambiguous references to the instrumentations used. In our view, this leaves open the possibility of misinterpreting scales, leading to poor model reproducibility, model use in inappropriate contexts, etc.
To correct this problem, the present study describes a novel approach to multiscale modelling. This approach systematically applies an instrumentation capability based definition of scale to all aspects of multiscale model development and model credibility assessment.
The application of this approach is illustrated by considering problems of significant interest to clinicians and drug developers in the area of bone health. The versatility of the approach is demonstrated by considering various combinations of available instruments for characterising the system at hand.
As the approach does not specify any mathematical form the equations must take, it could be applicable to a great variety of multiscale problems across engineering domains. The paper also discusses the complementarity of the present approach with some existing multiscale modelling approaches.
Article
A systematic approach to the scale separation problem in the development of multiscale models (PLOS One) P Bhattacharya, Q Li, D Lacroix, V Kadirkamanathan, M Viceconti.
