Definition of a periodicaly distributed 'porosity gradient' in functionally graded materials to be used as bone scaffolds

A problem presented at the UK MMSG Strathclyde 2010.

Presented by:
Dr Carmen Torres-Sánchez (Mechanical Engineering, Heriot-Watt University)
A Bradley, LS Gallimore, NJ Mottram, Z Rong, C Torres-Sánchez, RJ Whittaker

Problem Description

One of the new exciting research fields is biomimetics, i.e. how we engineers can learn from the lessons that nature, the best engineer ever, can provide or inspire us with. In particular, the biomimetic design and manufacture of functionally engineered materials (e.g. porosity tailored foams that exhibit enhanced mechanical properties due to their heterogeneous architecture) is a main area of interest. Despite the recognised need for these biomimetic materials (i.e. porosity tailored artefacts that can be used, for example, as orthopaedic scaffolds), the research in manufacturing systems lags behind.

The definition of 'porosity gradient' for 3D volumes will be a major breakthrough for the optimized design and fabrication methodology of these functionally engineered materials. The breadth of this issue is large, therefore only a few focused, specific cases of this porosity gradient study will be addressed in this study group:

  1. How can asymmetry be quantified in a porosity gradation? i.e. when presented with non-linear (i.e. distributions that are not simply 'big to small', or radial) pore distribution, or not necessarily centred at the vertical axis, how can symmetry, or asymmetry, be quantified on these distributions?
  2. How can a periodically distributed 'porosity gradient' in a 3D volume be translated into a mathematical expression? In other words, how can porosity characteristics be coupled with location in a 3D volume without the need to individually define each single point or detail of a 'cloud'. (Note: this will be limited to periodic distributions)

This problem is not solely a medical problem that affects bioengineering, orthopaedics or tissue engineering. Solving this issue will also have an impact on numerous fields such as materials engineering, structural materials, geophysics, prospection and petroleum engineering, filtration and membranes in chemical engineering, food technology for functional foods, etc.

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Study Group Report

The study group first examined ways to clean the CT scan data, and then analysed the density gradients to find the major directions of the gradients. A simple density fitting routine was also considered. These techniques could be used to characterise and compare samples in order to aid the design of specific material properties.

The group also summarised a number of possible avenues of study for the modelling of the formation process of the porous material. The relative importance of these effects for the present situation needs to be investigated before a closed system of equations can be formulated, which will accurately model this process.

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Follow-Up Activities

The following funding for further work has been obtained to investigate aspects of this problem:

Mathematical Modelling of Wave Propagation in Heterogeneous Media
A Bradley, A Mulholland & S Webb
University of Strathclyde, PhD studentship, October 2010 to September 2013.