Surface-weighted star volume: concept and estimation

The estimation of 'size' for an interconnected nonconvex phase is an ongoing problem in materials science and biomedicine. Examples of this type of phase include the pore space in a porous rock such as sandstone or the marrow space found in cancellous bone. A reasonable definition of size for this type of phase is provided by the mean volume-weighted star volume. This is defined as the average volume of the phase of interest seen unobscured from a typical point within the phase. One practical advantage of this definition of size is that it is easy to estimate stereologically. In this paper we extend the concept of star volume to consider the mean surface-weighted star volume. The mean surface-weighted star volume is the volume of a continuous phase seen unobscured from a typical point of the interface. We expect that this parameter could be useful in biological problems involving mass transfer across an interface. The stereological estimation of mean surface-weighted star volume is described and the method is illustrated on piglet lung tissue.