From Homogeneous to Fractal Normal and Tumorous Microvascular Networks in the Brain

Abstract

We studied normal and tumorous three-dimensional (3D) microvascular networks in primate and rat brain. Tissues were prepared following a new preparation technique intended for high-resolution synchrotron tomography of microvascular networks. The resulting 3D images with a spatial resolution of less than the minimum capillary diameter permit a complete description of the entire vascular network for volumes as large as tens of cubic millimeters. The structural properties of the vascular networks were investigated by several multiscale methods such as fractal and powerspectrum analysis. These investigations gave a new coherent picture of normal and pathological complex vascular structures. They showed that normal cortical vascular networks have scaleinvariant fractal properties on a small scale from 1.4 lm up to 40 to 65 lm. Above this threshold, vascular networks can be considered as homogeneous. Tumor vascular networks show similar characteristics, but the validity range of the fractal regime extend to much larger spatial dimensions. These 3D results shed new light on previous two dimensional analyses giving for the first time a direct measurement of vascular modules associated with vessel-tissue surface exchange.

Cerebral Blood Flow Modeling in Primate Cortex

“…A hysteresis thresholding method was used for the binarization step. Some morphological mathematical opening/ closure procedures were then used to finalize this step, so as to remove black islands inside white vessels (Risser et al, 2007). The vessel's density, volume, and length, which is obtained after this procedure, has been recently found consistent with other reported measures in primate and rodents (Risser et al, 2009;Tsai et al, 2009).…”

“…To our knowledge, this issue has not been clearly discussed in earlier studies (Reichold et al, 2009). In the case of brain vessels, earlier investigations have shown that a representative elementary volume can be identified in primate cortex (Risser et al, 2007). The length scale associated with statistical decorrelation of the spatial distribution of the brain's microvascular networks has been found to be within 50 to 80 mm.…”

“…We first briefly summarize the main methodological techniques that we have developed for the preparation of marmoset monkey (Callithrix jacchus) tissue, image acquisition (Plouraboué et al, 2004), image segmentation (Risser et al, 2007), vessel skeletonization and vectorization (Risser et al, 2008), and postprocessing (Risser et al, 2009). Next, we emphasize the important new steps needed for the computation of blood flow in microvascular beds associated with the topological postprocessing of the networks, implementation of boundary conditions, and blood flow modeling.…”

“…This is an important improvement over other recent works (Reichold et al, 2009) where rectilinear, single diameter tubes with homogeneous plasma flows were used to model CBF in rat cortex. Our method is applied to primate cortical brain microvascular networks whose structure has been exhaustively analyzed (Risser et al, 2007(Risser et al, , 2009. Moreover, the present work aims at determining how the network topology and geometry influence the pressure, hematocrit, and flow distributions in the cerebral microvascular circulation, as what has been shown in mesentery (Pries et al, 1995(Pries et al, , 1996.…”

Scaling rules for diffusive drug delivery in tumor and normal tissues

“…3C). These statistics can be readily compiled and many have been published (13). We note that nðδÞ for normal tissues rises to a peak and then drops quickly as the maximum distance from a vessel is approached.…”