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Robust Pore Size Analysis of Filamentous Networks from ThreeDimensional Confocal Microscopy
, 2008
"... We describe a robust method for determining morphological properties of filamentous biopolymer networks, such as collagen or other connective tissue matrices, from confocal microscopy image stacks. Morphological properties including pore size distributions and percolation thresholds are important f ..."
Abstract

Cited by 13 (1 self)
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We describe a robust method for determining morphological properties of filamentous biopolymer networks, such as collagen or other connective tissue matrices, from confocal microscopy image stacks. Morphological properties including pore size distributions and percolation thresholds are important for transport processes, e.g., particle diffusion or cell migration through the extracellular matrix. The method is applied to fluorescently labeled fiber networks prepared from rattail tendon and calfskin collagen, at concentrations of 1.2, 1.6, and 2.4 mg/ml. The collagen fibers form an entangled and branched network. The medial axes, or skeletons, representing the collagen fibers are extracted from the image stack by threshold intensity segmentation and distanceordered homotopic thinning. The size of the fluid pores as defined by the radii of largest spheres that fit into the cavities between the collagen fibers is derived from Euclidean distance maps and maximal covering radius transforms of the fluid phase. The size of the largest sphere that can traverse the fluid phase between the collagen fibers across the entire probe, called the percolation threshold, was computed for both horizontal and vertical directions. We demonstrate that by representing the fibers as the medial axis the derived morphological network properties are both robust against changes of the value of the segmentation threshold intensity and robust to problems associated with the pointspread function of the imaging system. We also provide empirical support for a recent claim that the percolation threshold of a fiber network is close to the fiber diameter for which the Euler index of the networks becomes zero.
Definition
"... A random closed subset of R d (or random graph) percolates if it has an unbounded component. Theorem Consider a Boolean model Z in R d (with d ≥ 2) where the typical grain is a deterministic ball with radius R0> 0. Then there exists a critical intensity λc> 0 such such Z percolates for λ> λ ..."
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A random closed subset of R d (or random graph) percolates if it has an unbounded component. Theorem Consider a Boolean model Z in R d (with d ≥ 2) where the typical grain is a deterministic ball with radius R0> 0. Then there exists a critical intensity λc> 0 such such Z percolates for λ> λc and does not percolate for λ < λc. Günter Last Lecture 5: Models of continuum percolationRemark Let Z be a Boolean model as above. The critical percolation threshold and the critical volume fraction pc: = 1 − e−λcκd Rd 0 are known “ from simulation: 0.6763475, if d = 2, pc ≈ 0.289573, if d = 3.