Multifractal properties of pore-size distribution in apple tissue using X-ray imaging

Abstract

The pore-size distribution (PSD) has an important influence on the complex gas transport phenomena (O 2 and CO 2) that occur in apple tissue during storage under controlled atmosphere conditions. It defines the apple tissue microstructure that is correlated to many other apple properties. In this article multifractal analysis (MFA) has been used to study the multiscale structure of the PSD using generalized dimensions in three varieties of apples ( Jonagold, Greenstar, and Kanzi) based on X-ray imaging technology (8.5 μm resolution). Tomographic images of apple samples were taken at two positions within the parenchyma tissue: close to the peel and near to the core. The images showed suitable scaling properties. The generalized dimensions were determined with an R 2 greater than 0.98 in the range of moment orders between −1 and +10. The variation of D q with respect to q and the shape of the multifractal generalized spectrum revealed that the PSD structure of apple tissue has properties close to multifractal self-similarity measures. Comparisons among cultivars showed that, in spite of the complexity and variability of the pore space of these apple samples, the extracted generalized dimensions from PSD were significantly different ( p < 0.05). The generalized dimensions D 0, D 1, D 2, and the quantity D 0– D 2 could be used to discriminate tissue samples from different positions or cultivars. Also, high correlations were found between these parameters and the porosity ( R 2 ⩾ 0.935). These results demonstrate that MFA is an appropriate tool for characterizing the internal pore-size distribution of apple tissue and thus may be used as a quantitative measure to understand how tissue microstructure affects important physical properties of apple.