12518 Development Of A Four-compartment, Dynamic (In Vivo) Model For Insulin Disposition In Healthy Humans: Use Of Fick’s Law To Model Plasma-interstitial Insulin Flux
Authors: Dorin Richard I , Qualls Clifford R 
Published: October 2024

Abstract
Disclosure: R.I. Dorin: None. C.R. Qualls: None.
Introduction: Metabolic elimination of insulin (I) in vivo includes pathways mediated by high-affinity and potentially saturable insulin receptor binding; endogenous insulin secreted into the portal vein is subject to first pass elimination. The rate of insulin flux between vascular (Vp) and interstitial (Vi) compartments is often modeled by first order rate constants; here we analyzed an alternative approach using Fick’s law. Methods: The four-compartment, insulin (I) model is expressed by four differential equations that represent I flow (mass/time) in 4 volumes (V) (or compartments) having 3 corresponding elimination rate functions (α): (i) vascular plasma (Vp), (ii) interstitial (Vi, αi), (iii) hepatic (Vh, αh), and (iv) kidney (Vk, αk). Fick’s law was used to model diffusion of insulin between Vp and Vi; Michaelis-Menten like functions were used for saturable elimination functions (αh and αi); rates of hepatic (HPF) and renal (KPF) plasma flow were from literature. Realistic bounds for solved parameters (insulin permeability constant [k, L/min] and αi [min-[1]]) were developed by test bed analysis of published plasma (Ip) and interstitial (Ii) insulin concentration data. The inverse problem (estimating parameters) used Ip data from insulin-modified, frequently sampled iv glucose tolerance (IM-FSIVGT) studies performed in 40 healthy, non-diabetic women (1). Parameter solutions for individual subjects were obtained by iterative least squares method minimizing differences between model-predicted and measured Ip. Results: For infusion of exogenous I (ZI) at a constant rate (e.g., insulin clamp), reported steady state Ii/Ip data suggest that interstitial insulin elimination (αi) is conditionally saturable. Together with non-steady state data for Ip and Ii, initial estimates of k and αi were obtained. Steady state solutions give rise to four algebraic equations: (1) Ii/Ip = a, where a &lt; 1 is consistent with experimental data, (2) Ih is a reduced version of a linear combination of Ip and endogenous insulin secretion (Zβ), where the factor of reduction (b) is &lt;1, (3) Ik/Ip = d, where d&lt;1, and (4) Ip is a linear combination of (i) ZI and (ii) the reduced (by factor b) Zβ. For Ip, this linear combination of ZI and reduced Zβ is also normalized by factor c (weighted sum of k, HPF, and KPF). Conclusions: (i) The proposed insulin flow model using Fick’s law was advantageous in providing realistic parameters and solutions that are tractable to physiologic interpretation, (ii) a simplified version of this model is generalizable to C-peptide, and (iii) since measurement of Ii is impractical in the clinical setting, the proposed prediction model may provide useful modeling adjunct to personalize pharmacokinetic and pharmacodynamic strategies for insulin administered by subcutaneous, iv, and hybrid closed-loop insulin pump routes. 1. Gower et al. Nutrition & Metabolism (2016) 13:2
Presentation: 6/1/2024