Skip to main content
Log in

Application of multivariate autoregressive modelling for analysing chloride/potassium/bicarbonate relationship in the body

  • Modelling
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

The authors repeatedly analysed course data of acid-base disturbances accompanying hypochloraemia and/or hypokalaemia by means of multivariate autoregressive modelling. It was found that the regulatory relationship between chloride and bicarbonate is inverse between the following two hypochloraemic hyperbicarbonataemic states: the one induced by chloride depletion and the other induced by CO2 retention. Also, the study revealed an independent role of potassium deficiency in the development of metabolic alkalosis, especially in cases with mineralocorticoid-induced alkalosis. The present approach enabled the authors to solve a long-standing problem, i.e. to differentiate between the roles of chloride and potassium in the development of metabolic alkalosis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • ADLER, S. and FRALEY, D. S. (1977) Potassium and intracellular pH. Kidney Int., 11, 433–440.

  • AKAIKE, H. (1967) Some problems in the application of the cross spectral methods. In Spectral analysis of time series. HARRIS, B, (Ed.) John Wiley, New York, 81–107.

  • AKAIKE, H. (1968) On the use of a linear model for the identification of feedback systems. Ann. Inst. Statist. Math., 20, 425–439.

  • AKAIKE, H. (1973) Information theory and an extension of the maximum likelihood principle. In Proceedings of 2nd International Symposium on Information Theory (PETROV, I. N. and CSAKI, F. (Eds.) Akademiai Kiado, Budapest, 267–281.

  • AKAIKE, H., OZAKI, T., ISHIGURO, M., OGATA, Y., KITAGAWA, G., TAMVRA, Y. H., ARAHATA, E., KATSURA, K. and TAMURA, Y. (1985) Computer science monographs. Institute of Stational Mathematics, Tokyo, 23, TIMSAC-84 Part 2, 1–168.

  • ATKINS, E. L. and SCHWARTZ, W. B. (1962) Factors governing correction of the alkalosis associated with potassium deficiency; the critical role of chloride in the recovery process. J. Clin. Invest., 41, 218–229.

  • BURG, M. B. (1986) Renal handling of sodium chloride, water, and glucose. In The kidney, Third ed. BRENNER, B. M. and RECTOR, F. C. Jr. (Eds.) WB Saunders, Philadelphia, 145–175.

  • COOAN, M. G., MADDOX, D. A. and RECTOR, F. C. Jr. (1979) Control of proximal bicarbonate reabsorption in normal and acidotic rats. J. Clin. lnvest., 64; 1168–1180.

  • COOAN, M. G. and LIT;, F. Y. (1983) Metabolic alkalosis in the rat: Evidence that reduced glomerular filtration rather than enhanced tubular bicarbonate reabsorption is responsible for maintaining the alkalotic state. Ibid., 71, 1141–1160.

  • CRONIN, R. E. and KNOCHEL, J. P. (1978) The consequences of potassium deficiency. In Acid base and potassium homeostasis, contemporary issues in nephrology. Vol. 2. BRENNER, I. M. and STERN, J. H. (Eds.) Churchill Livingstone, New York, 205–231.

  • GALLA, J. H., BONDURIS, D. N. and LUKE, R. G. (1983) Correction of acute chloride depletion alkalosis in the rat without volume expansion in the rat. Am. 3". Physiol., 244, F217–221.

  • GENNARI, F. J. (1990) Hypokalemia in metabolic alkalosis: a new look at an old controversy. In Nephrology: Proceedings of Xlth International Congress of Nephrology. HATANO, M. (Ed.) Springer-Verlag, Tokyo, Berlin, Heidelberg, New York, London, Paris, Hong Kong, Barcelona, 262–269.

  • GULLYASSY, P. F., YPERSELE DE STRIHOU, C. and SCHWARTZ, W. B. (1962) On the mechanism of nitrate-induced alkalosis. The possible role of selective chloride depletion in acid-base regulation. J. Clin. Invest., 41, 1850–1862.

  • KASSIRER, J. P., BERKMAN, P. M., LAWRENZ, D. R. and SCHWARTZ, W. B. (1965) The critical role of chloride in correction of hypokalemic alkalosis in man. Am. J. Med., 38, 172–180.

  • KASSIRER, J. P. and SCHWARTZ, W. B. (1966a) The response of normal man to selective depletion of hydrochloric acid. Ibid., 40, 10–18.

  • KASSIRER, J. P. and SCHWARTZ, W. B. (1966b) Correction of metabolic alkalosis in man without repair of potassium deficiency. A reevaluation of the role of potassium. Ibid., 40, 19–26.

  • KASSIRER, J. P., APPLETON, F. M., CHAZAN, J. A. and SCHWARTZ, W. B. (1967) Aldosterone in metabolic alkalosis. J. Clin. Invest., 46, 1558–1571.

  • JACOBSON, H. R. and SELDIN, D. W. (1983) On the generation, maintenance and correction of metabolic alkalosis. Am. J. Physiol., 245, F425–432.

  • MATSUO, N. and WADA, T. (1987) Spectral analysis in studying the mechanism of SIADH. In Recent advances in pediatric nephrology. MURARAr~I, K. et al. (Eds.) Excerpta Medica, New York, 595–598.

  • NAKAMURA, H. and AKAIKE, H. (1991) Statistical identification for optimal control of thermal power plants. Automatica, 17, 143–155.

  • NEEDLE, M. A., KALOYANIDES, J. and SCHWARTZ, W. B. (1964) The effects of selective depletion of hydrochloric acid on acid-base and electroylte equilibrium. J. Clin. Invest., 43, 1836–1846.

  • OTOMO, T., NAKAGAWA, K. and ARMKE, H. (1972) Statistical approach to computer control of cement rotary kilns. Automatica, 8, 35–48.

  • OTSV, K., HORIGOME, M. and KITAGAWA, G. (1979) A new ship's auto pilot design through a stochastic model. Ibid., 15, 255–268.

  • POLAR, A., HAVNIE, G. D., HAYS, R. M. and SCHWARTZ, W. B. (1961) Effects of chronic hypercapnea on electrolyte and acid-base equilibrium. I. Adaptation. J. Clin. Invest., 40, 1223–1237.

  • SCHWARTZ, W. B., HAYS, R. M., POLAK, A. and HAYNIE, G. D. (1961) Effects of chronic hypercapnea on electrolyte and acid-base equilibrium. II. Recovery, with special reference to the influence of chloride intake. Ibid., 40, 1238–1249.

  • SCHWARTZ, W. B., BRACKETT, N. C. and COHEN, J. J. (1965) The response of extracellular hydrogen ion concentration to graded degrees of chronic hypercapnea: The physiologi c limits of the defense of pH. Ibid., 44, 291–302.

  • SCHWARTZ, W. B., VAN YPERSELE DE STRIJOU, C. and KASSIRER, J. P. (1968) Role of anions in metabolic alkalosis and potassium deficiency. New Eng. J. Med., 279, 630–639.

  • SEBASTIAN, A,, HULTER, H. N. and RECTOR, F. C. Jr. (1978) Metabolic alkalosis. In Acid-base and potassium homeostasis. Contemporary issues in nephrology Vol. 2. BRENNER, B. M. and STEIN, H. H. (Eds.) Churchill Livingstone, New York, 101–136.

  • VELAZQUEZ, H., WRIGHT, F. S. and GOOD, D. W. (1982) Luminal influences on potassium secretion: chloride replacement with sulfate. Am, J. Physiol., 11, F46-F55.

  • WADA, T., AKAIKE, H. and KATO, E. (1986a) Autoregressive models provide stochastic descriptions of homeostatic processes in the body. Jpn. J. Nephrol., 28, 263–268.

  • WADA, T., AKAIKE, H., SUDO, S. and KATO, E. (1986b) Frequency dependency of causal factors for hypertension in hemodialysis patients. Ibid., 28, 1237–1243.

  • WADA, T. (1988) Application of autoregressive modeling for the analysis of clinical and other biological data. Ann. Inst. Statist. Math., 40, 211–227.

  • WADA, T., KOJIMA, F., AOYAGI, T. and UMEZAWA, H. (1988a) Feedback analysis of renin-angiotensin system under the effect of angiotensin converting enzyme inhibitors. Biotech. Appl. Biochem., 10, 435–446.

  • WADA, T., AKAIKE, H., YAMADA, H. and UDAGAWA, E. (1988b) Application of multivariate autore~ressive modeling for analysis of immunologic networks in man. Comput. Math. Applic., 15, 713–722.

  • WADA, T., YAMADA, H., INOUE, H., ISO, T., UDAGAWA,E. and KURODA, S. (1990) Clinical usefulness of multivariate autoregressive modeling as a tool for analyzing T-lymphocyte subset fluctuations. Math. Comput. Model, 14, 610–613.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wada, T., Sato, S. & Matsuo, N. Application of multivariate autoregressive modelling for analysing chloride/potassium/bicarbonate relationship in the body. Med. Biol. Eng. Comput. 31 (Suppl 1), S99–S107 (1993). https://doi.org/10.1007/BF02446657

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02446657

Keywords

Navigation