Biomechanics and Modeling in Mechanobiology

, Volume 11, Issue 6, pp 869–882 | Cite as

A remodelling metric for angular fibre distributions and its application to diseased carotid bifurcations

  • Arthur Creane
  • Eoghan Maher
  • Sherif Sultan
  • Niamh Hynes
  • Daniel J. Kelly
  • Caitríona Lally
Original Paper


Many soft biological tissues contain collagen fibres, which act as major load bearing constituents. The orientation and the dispersion of these fibres influence the macroscopic mechanical properties of the tissue and are therefore of importance in several areas of research including constitutive model development, tissue engineering and mechanobiology. Qualitative comparisons between these fibre architectures can be made using vector plots of mean orientations and contour plots of fibre dispersion but quantitative comparison cannot be achieved using these methods. We propose a ‘remodelling metric’ between two angular fibre distributions, which represents the mean rotational effort required to transform one into the other. It is an adaptation of the earth mover’s distance, a similarity measure between two histograms/signatures used in image analysis, which represents the minimal cost of transforming one distribution into the other by moving distribution mass around. In this paper, its utility is demonstrated by considering the change in fibre architecture during a period of plaque growth in finite element models of the carotid bifurcation. The fibre architecture is predicted using a strain-based remodelling algorithm. We investigate the remodelling metric’s potential as a clinical indicator of plaque vulnerability by comparing results between symptomatic and asymptomatic carotid bifurcations. Fibre remodelling was found to occur at regions of plaque burden. As plaque thickness increased, so did the remodelling metric. A measure of the total predicted fibre remodelling during plaque growth, TRM, was found to be higher in the symptomatic group than in the asymptomatic group. Furthermore, a measure of the total fibre remodelling per plaque size, TRM/TPB, was found to be significantly higher in the symptomatic vessels. The remodelling metric may prove to be a useful tool in other soft tissues and engineered scaffolds where fibre adaptation is also present.


Biomechanics Carotid bifurcation Fibre remodelling Remodelling metric Earth mover’s distance Patient-specific models 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Arthur Creane
    • 1
  • Eoghan Maher
    • 2
  • Sherif Sultan
    • 3
    • 4
  • Niamh Hynes
    • 3
    • 4
  • Daniel J. Kelly
    • 2
  • Caitríona Lally
    • 1
    • 2
  1. 1.School of Mechanical and Manufacturing EngineeringDublin City UniversityDublin 9Ireland
  2. 2.Trinity Centre for Bioengineering, School of EngineeringTrinity CollegeDublin 2Ireland
  3. 3.Department of Vascular & Endovascular Surgery, Western Vascular InstituteUniversity College Hospital GalwayGalwayIreland
  4. 4.Department of Vascular & Endovascular SurgeryGalway ClinicGalwayIreland

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