The Mathematical Institute, University of Oxford, Eprints Archive

Re-evaluating the use of voronoi tessellations in the assessment of oxygen supply from capillaries in muscle

Al-Shammari, A A and Gaffney, E. A. and Egginton, S (2012) Re-evaluating the use of voronoi tessellations in the assessment of oxygen supply from capillaries in muscle. Bulletin of Mathematical Biology, 74 (9). pp. 2204-2231.



The ability to characterise capillary supply plays a key role in developing effective therapeutic interventions for numerous pathological conditions, such as capillary loss in skeletal or cardiac muscle. However, quantifying capillary supply is fraught with difficulties. Averaged measures such as capillary density or mean inter-capillary distance cannot account for the local geometry of the underlying capillary distribution, and thus can only highlight a tissue wide, global hypoxia. Detailed tissue geometry, such as muscle fibre size, has been incorporated into indices of capillary supply by considering the distribution of Voronoi tessellations generated from capillary locations in a plane perpendicular to muscle fibre orientation, implicitly assuming that each Voronoi polygon represents the area of supply of its enclosed capillary. Using a modelling framework to assess the capillary supply capacity under maximal sustainable conditions in muscle, we theoretically demonstrate that Voronoi tessellations often provide an accurate representation of the regions supplied by each capillary. However, we highlight that this use of Voronoi tessellations is inappropriate and inaccurate in the presence of extensive capillary rarefaction and pathological variations in oxygen tension of different capillaries. In such cases, oxygen flux trapping regions are developed to provide a more general representation of the capillary supply regions, in particular incorporating the additional influences of heterogeneity that are absent in the consideration of Voronoi tessellations.

Item Type:Article
Uncontrolled Keywords:Oxygen transport – Capillary supply – Mathematical modelling – Voronoi tessellations – Flux trapping regions
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1610
Deposited By: Sara Jolliffe
Deposited On:26 Sep 2012 08:30
Last Modified:29 May 2015 19:18

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