Abstract
The flow of epithelial cells over villi of mouse small intestine is calculated from equations of cell number balance and irrotational flow. The influence of both villus geometry and crypt distribution about the villus base are studied. Specific, experimentally verifiable predictions are made.
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References
Al-Nafussi, A. I., Wright, N. A.: Circadian rhythm in the rate of cellular proliferation and in the size of the functional compartment of mouse jejunal epithelium. Virchows Arch. (Cell Pathol.) 40, 71–79 (1982).
Bjerknes, M., Cheng, H.: Mucous cells and cell migration in the mouse duodenal epithelium. Anat. Rec. 212, 69–73 (1985).
Cheng, H., Bjerknes, M.: Cell production in mouse intestinal epithelium measured by stathmokinetic flow cytometry and Coulter particle counting. Anat. Rec. 207, 427–434 (1983).
Cheng, H., Bjerknes, M.: Whole population cell kinetics and postnatal development of the mouse intestinal epithelium. Anat. Rec. 211, 420–426 (1985).
Leblond, C. P., Stevens, C. E.: The constant renewal of the intestinal epithelium in the albino rat. Anat. Rec. 100, 357–377 (1948).
O'Connor, T. M.: Cell dynamics in the intestine of the mouse from late fetal life to maturity. Am. J. Anat. 118, 525–536 (1966).
Rice, J. R., Boisvert, R. F.: Solving elliptic problems using ELLPACK. New York Heidelberg Berlin: Springer 1985.
Sokolnikoff, I. S.: Tensor analysis. New York: Wiley 1967.
Spain, B.: Tensor calculus, 3rd edn. Edinburgh: Oliver & Boyd 1965.
Stevenson, N. R., Day, S. E., Sitren, H.: Circadian rhythmicity in rat intestinal villus length and cell number. Int. J. Chronobiol. 6, 1–12 (1979).
Totafurno, J., Bjerknes, M., Cheng, H.: The crypt cycle: crypt and villus production in the adult intestinal epithelium. Biophys. J 52, 279–294 (1987).
Totafurno, J., Bjerknes, M., Cheng, H.: Variation in crypt size and its influence on the analysis of epithelial cell proliferation in the intestinal crypt. Biophys. J. 54, 845–858 (1988).
Tsubouchi, S.: Theoretical implications for cell migration through the crypt and the villus of labelling studies conducted at each position within the crypt. Cell Tissue Kinet. 16, 441–456 (1983).
Weinberg, S.: Gravitation and cosmology: principles and applications of the general theory of relativity. New York: Wiley 1972.
Wright, N., Alison, M.: The biology of epithelial cell populations, vol. 2. Oxford: Clarendon Press 1984.
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Totafurno, J., Bjerknes, M., Allen, M.J. et al. Theoretical analysis of the flow of cells over villi of the small intestine. J. Math. Biol. 28, 567–584 (1990). https://doi.org/10.1007/BF00164163
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DOI: https://doi.org/10.1007/BF00164163