Capillary Spatial Pattern and Muscle Fiber Geometry in Three Hamster Striated Muscles
The maintenance of an adequate tissue oxygen tension is a principal function of the respiratory and circulatory systems. In 1919, Krogh presented a mathematical model that described the diffusion of oxygen from capillaries to the surrounding tissue (Krogh, 1919). This was the first model to relate oxygen diffusion and capillary spacing within muscles and the first to quantify the relationship between the rate of delivery of the oxygen to various sites in the tissue to the rate of consumption of oxygen at those sites. Determinants of tissue oxygen tension include the PO2 of blood, blood flow, red blood cell spacing, diameter of microvessels, hemoglobin oxygen saturation, as well as the spatial pattern of capillaries within the tissue. Krogh’s model assumes homogeneity in the composition of blood and muscle tissue, uniform consumption of oxygen at every point in the tissue, and a uniform and radial movement of oxygen outward from the center of a capillary into the surrounding tissue independent of oxygen diffusion from all other capillaries within the tissue. Since the model neglects the intrinsic heterogeneities of capillary spacing and shape of the muscle fibers, it fails to characterize completely the movement of oxygen from the hemoglobin in the red blood cells to the sites of oxygen utilization in muscle tissue.
KeywordsFiber Type Soleus Muscle Poisson Point Process Complete Spatial Randomness Retractor Muscle
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- Bartels, C.P.A. and R.H. Ketellapper, eds. Exploratory and explanatory statistical analysis of spatial data. Boston: Martinus Nijhoff Publishing, 1979.Google Scholar
- Cliff, A.D. and J.K. Ord. Spatial Processes Models & Applications. London: Pion Limited, 1981, pp. 86–117.Google Scholar
- Cox, D.R. and P.A.W. Lewis. The Statistical Analysis of Series of Events. London: Methuen, 1966.Google Scholar
- Diggle, P.J. Preliminary testing for mapped patterns. In Statistical Analysis of Spatial Point Patterns, London: Academic Press, 1983b, pp. 10–30.Google Scholar
- Diggle, P.J. Introduction. In Statistical Analysis of Spatial Point Patterns, London: Academic Press, 1983c, pp. 1–9.Google Scholar
- Getis, A. and B. Boots. Models of Spatial Processes: An approach to the study of point, line and area patterns. Cambridge: Cambridge University Press, 1978, pp. 1–85.Google Scholar
- Guarascio, M., C.J. Huijbregts and M. David. Advanced Geostatistics. Dordrecht: Reidel, 1976.Google Scholar
- Journel, A.G. and C.J. Huijbregts. Mining Geostatistics. London: Academic Press, 1978.Google Scholar
- Skellam, J.G. Studies in statistical ecology. I. Spatial pattern. Biometrika 39, 1952, 346–362.Google Scholar