Variability in regional flows is found in all organs. However this variation is NOT random, for there is considerable correlation between flows in neighboring regions. Fractals provide a measure of the variation AND the correlation, simultaneously. The key is self-similarity: the log of the apparent variation increases inversely with the log of the size of the tissue samples in which flow is measured. Two different fractal descriptions have been previously found adequate to describe the heterogeneity of regional flows within the heart and lung over a 200-fold range of voxel sizes; one was based on statistical self similarity, the other on a self-similar branching algorithm. The goals of this project are to carry out joint studies to yield needed data about the intraorgan flow distribution in the brain cortex in cooperation with Dr. Eke from the Semmelweis University of Medicine in Budapest. By his computerized videoimaging methodology, intraparenchymaldistribution of blood flow and its components, red cell and plasma microflow can be repetitively imaged in the feline and rat brain cortex resulting in microcirculatory parameter images of adequate spatial resolution (216 microflow data per image) for fractal analysis to be carried out. It will be based on statistical self similarity to be applied to determine the spatial fractal dimension of the observed microflow heterogeneity (Ds) within a 64-fold range of voxel sizes. We expect to gain a better understanding of how the fractal dimensions of red cell's and plasma's intraparenchymal distribution patterns relate to each other under physiological and pathological conditions. Because Dr. Eke's method allows for direct observation and overlaying of the pial vascular network on the microflow images, the grid method can be used to determine Ds of the observed pial vascular tree supplying and draining the mapped tissue area. Access to these two spatial fractal dimensions offers the unique possibility to develop a computer model of the observed pial and intraparenchymal circulation. By interaction between model and experiment, the model will be refined to the point when it will simulate microflow distributions at any level or section of the network and to provide simulated microflow images compiled from individual capillary data. We will use the model to extend our understanding of the topology of the internal structure of intraparenchymal microflow distributions relative to pial arterial inputs and venous outputs and depth from the pial surface.
| Bassingthwaighte, James B; Butterworth, Erik; Jardine, Bartholomew et al. (2012) Compartmental modeling in the analysis of biological systems. Methods Mol Biol 929:391-438 |
| Dash, Ranjan K; Bassingthwaighte, James B (2010) Erratum to: Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2, pH, 2,3-DPG and temperature levels. Ann Biomed Eng 38:1683-701 |
| Bassingthwaighte, James B; Raymond, Gary M; Butterworth, Erik et al. (2010) Multiscale modeling of metabolism, flows, and exchanges in heterogeneous organs. Ann N Y Acad Sci 1188:111-20 |
| Dash, Ranjan K; Bassingthwaighte, James B (2006) Simultaneous blood-tissue exchange of oxygen, carbon dioxide, bicarbonate, and hydrogen ion. Ann Biomed Eng 34:1129-48 |
| Dash, Ranjan K; Bassingthwaighte, James B (2004) Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2, pH, 2,3-DPG and temperature levels. Ann Biomed Eng 32:1676-93 |
| Kellen, Michael R; Bassingthwaighte, James B (2003) Transient transcapillary exchange of water driven by osmotic forces in the heart. Am J Physiol Heart Circ Physiol 285:H1317-31 |
| Kellen, Michael R; Bassingthwaighte, James B (2003) An integrative model of coupled water and solute exchange in the heart. Am J Physiol Heart Circ Physiol 285:H1303-16 |
| Wang, C Y; Bassingthwaighte, J B (2001) Capillary supply regions. Math Biosci 173:103-14 |
| Swanson, K R; True, L D; Lin, D W et al. (2001) A quantitative model for the dynamics of serum prostate-specific antigen as a marker for cancerous growth: an explanation for a medical anomaly. Am J Pathol 158:2195-9 |
| Swanson, K R; Alvord Jr, E C; Murray, J D (2000) A quantitative model for differential motility of gliomas in grey and white matter. Cell Prolif 33:317-29 |
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