A revised Sorensen model: Simulating glycemic and insulinemic response to oral and intra-venous glucose load

Abstract

In 1978, Thomas J. Sorensen defended a thesis in chemical engineering at the University of California, Berkeley, where he proposed an extensive model of glucose-insulin control, model which was thereafter widely employed for virtual patient simulation. The original model, and even more so its subsequent implementations by other Authors, presented however a few imprecisions in reporting the correct model equations and parameter values. The goal of the present work is to revise the original Sorensen’s model, to clearly summarize its defining equations, to supplement it with a missing gastrio-intestinal glucose absorption and to make an implementation of the revised model available on-line to the scientific community.

SPINA Carb: a simple mathematical model supporting fast in-vivo estimation of insulin sensitivity and beta cell function

“…In this project, we have developed a novel mathematical model of insulin-glucose homeostasis that is founded in basic physiological and biochemical properties of the involved control motifs. Compared with the relatively more complex theories, e. g. the approaches by Sorensen, Misgeld et al or Panunzi et al 14 , 15 , 41 , it is a relatively simple model that synopses from several details and special interactions. On the other hand, key functional relationships including receptor binding and pharmacokinetic properties are described based on physiological evidence.…”

A comparison among three maximal mathematical models of the glucose-insulin system

“…The models analysed are the Hovorka model [ 17 – 19 ], the Sorensen model [ 20 , 21 ] and the UVAPadova model [ 22 – 27 ]. The Sorensen model is the most complex; it has been extensively described in the Author’s PhD thesis and has been thoroughly analyzed in a previous work [ 28 ], correcting some errors which were present in the original description by the Author. An extended version of the model, including a representation of the gastrointestinal tract, was also presented in [ 28 ], and is used in the present work to simulate experiments where glucose is orally administered.…”

“…The Sorensen model is the most complex; it has been extensively described in the Author’s PhD thesis and has been thoroughly analyzed in a previous work [ 28 ], correcting some errors which were present in the original description by the Author. An extended version of the model, including a representation of the gastrointestinal tract, was also presented in [ 28 ], and is used in the present work to simulate experiments where glucose is orally administered. Sorensen’s model consists of three sub-models (one for glucose, one for insulin and one for glucagon) that describe the time-course of the variable concentrations in the brain, liver, heart and lungs, periphery (tissue and muscles), gut and kidney.…”

“…This obviously represents a simplification, because in the treatment of patients with T1DM insulin is administered subcutaneously, via bolus or continuous infusion. To make the three models comparable, two subcutaneous compartments were therefore added to the revised Sorensen model (which already includes the gastro-intestinal compartment [ 28 ]). The model of the subcutaneous compartments used is equivalent to that present in the Hovorka model.…”

“…The implemented version of the Sorensen model derives from the equations presented in his original PhD thesis [ 20 ], with the corrections introduced in [ 28 ] and modified to account for both (possible) subcutaneous administration of insulin and for the reduced insulin-sensitivity, which would be expected in a diabetic patient with respect to a normal individual [ 1 ]. The three models present different levels of complexity and a comparison among them gives the opportunity to understand to which extent increasing complexity translates into richer and more correct physiological behaviour.…”