Models of subcutaneous insulin kinetics. A critical review

Abstract

Subcutaneous insulin kinetics is a complex process whose quantitation is needed for a reliable glycemic control in the conventional therapy of insulin-dependent diabetes. The major difficulties in modeling include accounting for the distribution in the subcutaneous depot and transport to plasma. A single model describing in detail the various processes for all the commercially available insulin preparations is not available. Several models however have been proposed which vary in the degree of complexity. Virtually all of them handle the regular insulin preparation while a few handle the intermediate acting and the novel insulin analogues. In this paper we critically review these models.

Introduction

The recent diabetes clinical trials [1], [2] have clearly shown the need for an intensive subcutaneous insulin treatment in order to delay/reduce the diabetes complications in type 1 (insulin-dependent) diabetes (IDDM). However these studies have also demonstrated the necessity of a close control of an intensive insulin treatment, since it may lead to an increased risk of hypoglycemic events. Decision support systems can thus play an important role in optimizing the conventional subcutaneous (sc) insulin injection therapy of IDDM patients [3], [4]. Essential ingredients of a type 1 diabetes support system are the data analysis technique and the control strategy and these heavily depend on a poor vs. rich data environment, e.g. glucose concentration may only be available 4–7 times a day in a conventional therapeutic regimen or virtually at continuous time if a subcutaneous glucose sensor is working. Within this context simulation models are almost a necessity [5], [6], [7], [8], [9], e.g. they can help in the development and evaluation of sensors, data analysis techniques, control strategies and the overall quality of a decision support system.

An important component of a simulation model of an IDDM patient in a conventional therapeutic regimen is the description of how insulin is absorbed and enters plasma after a sc injection. Since the landmark work of Binder [10], it is a well accepted notion that sc insulin absorption is a complex process influenced by many factors including the associated state of insulin, i.e. hexameric and dimeric in soluble insulin and monomeric in insulin analogues, concentration, injected volume, injection site/depth and tissue blood flow [11], [12], [13], [14], [15], [16]. In particular, the absorption rate of subcutaneously injected insulin decreases with increasing insulin concentrations as well as with increasing volumes, and this explains the well-known inverse relation between the rate of absorption and the size of injected dose. The quantitative description of insulin absorption is thus a difficult task.

A single model describing in detail the various processes of subcutaneous absorption for all the commercially available insulin preparations is not available, but several more macroscopic models of sc insulin absorption have been proposed which handle one or more preparations [17], [18], [19], [20], [21], [22], [23]. Most of them [17], [18], [19], [20] are of compartmental nature, while in [21] an empirical description of subcutaneous insulin absorption based on published data is utilized and in [22], [23] a physico–chemical distributed parameter model has been proposed. All the models handle soluble (regular) insulin while monomer insulin is only analyzed in [20], [23] and intermediate acting insulin (NPH or lente) is only considered in [21].

The scope of this paper is to critically review the available models. While motivation here was an evaluation of available sc insulin absorption models in view of a possible incorporation into an IDDM simulation model, we believe that this exercise has a value per se, i.e. the availability of a reliable quantitative description of sc insulin absorption is an important tool to help controlling glycemia in an IDDM patient.