The hyperbolic law?a 25-year perspective

Abstract

In people with normal glucose tolerance, a decrease in insulin action is accompanied by up-regulation of insulin secretion, and vice versa. This is interpreted as a compensatory increase of insulin secretion, which maintains normoglycaemia despite decreased insulin sensitivity. In this issue of Diabetologia [1], Dr Hockaday deplores the fact that a landmark paper by the late Robert Turner and colleagues (himself included), which dates back to 1979, is rarely cited when this quasi-hyperbolic relationship is under discussion [2]. And Dr Hockaday is right, because the “hyperbola” in Fig. 7 of that paper, after two algebraic transformations (the insulin resistance factor being equivalent to 1/[insulin sensitivity] plus switching axes, the fraction of functioning beta cells being equivalent to beta cell function with opposite orientation), becomes the hyperbola now commonly used with acute insulin response (AIR) as a function of insulin sensitivity (Fig. 1a and b). In their abstract the authors already claim that “the height of basal plasma insulin is a function of the degree of insulin resistance.” Hence, Dr Hockaday appropriately claims that the concept was already shaped in their paper, which was published 25 years ago, 2 years before the classical paper of Bergman and co-workers [3]. However, it is not surprising that this paper went somewhat unnoticed by the “hyperbola aficionados,” because its main focus, and that of Fig. 7 in particular, was on factors involved in the pathogenesis of hyperglycaemia. In contrast, the concept of the hyperbola is now used to illustrate the fact that in a healthy individual any decrease in insulin sensitivity is compensated by up-regulation of beta cell function, and vice versa [4, 5]. The concept is self-sufficient at this level, and does not necessarily explain the development of hyperglycaemia. Its fundamental importance remains, however, because measurements of beta cell function can only be interpreted appropriately when a (more or less) simultaneous measure of insulin sensitivity is available [6]. These ideas were not fully developed in the 1979 paper. The beauty of Bergman’s simplification lies in the introduction of the so-called disposition index as the mathematical product of insulin action and beta cell function [7]. The disposition index is a way of measuring the ability of the beta cells to compensate for insulin resistance. This compensation is thought to be perfect when the disposition index remains constant in the face of decreasing insulin action; only when glucose tolerance becomes impaired, does the disposition index actually fall. Turner and co-workers used “HOMA factors” for insulin resistance and per cent beta cell function, which, in essence, are the product and ratio respectively of basal insulin and glucose concentrations. This is to some extent a self-fulfilling construct, because the product and ratio of any set of numbers will inevitably produce a hyperbola. The intrinsic dependence of the two HOMA factors thus limits the validity of any conclusions drawn from the data they provide. The “modern” hyperbola is clearly more informative, because it arose from variables that are not only independent but also employ stimulated measures of insulin secretion (or beta cell function) and insulin sensitivity such as the IVGTT and the euglycaemic clamp. It leads to the remarkable conclusion that the stimulated beta cell somehow knows whether the organism it belongs to can dispose of more or less glucose during the hyperinsulinaemic–euglycaemic clamp, i.e. whether it is in an insulin-sensitive or in an insulin-resistant person. The burning question relates to the nature of the signal that alerts the beta cell to the presence of insulin resistance. This latter point is addressed with acuity by Dr Hockaday in his next paragraph: “The disturbance brought about, for instance, by a decrease in insulin sensitivity is most unlikely to be completely compensated, for if so, the compensating M. Stumvoll (*) 3rd Medical Department, University of Leipzig, Philipp-Rosenthal-Str. 27, 04301 Leipzig, Germany e-mail: michael.stumvoll@medizin.uni-leipzig.de Tel.: +49-341-9713380 Fax: +49-341-9713389