The package REGULARIZATION TOOLS consists of 54 Matlab routines for analysis and solution of discrete ill-posed problems, i.e., systems of linear equations whose coefficient matrix has the properties that its condition number is very large, and its singular values decay gradually to zero. Such problems typically arise in connection with discretization of Fredholm integral equations of the first kind, and similar ill-posed problems. Some form of regularization is always required in order to compute a stabilized solution to discrete ill-posed problems. The purpose of REGULARIZATION TOOLS is to provide the user with easy-to-use routines, based on numerical robust and efficient algorithms, for doing experiments with regularization of discrete ill-posed problems. By means of this package, the user can experiment with different regularization strategies, compare them, and draw conclusions from these experiments that would otherwise require a major programming effert. For discrete ill-posed problems, which are indeed difficult to treat numerically, such an approach is certainly superior to a single black-box routine. This paper describes the underlying theory gives an overview of the package; a complete manual is also available.

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REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems

Loss of Insulin Signaling in Hepatocytes Leads to Severe Insulin Resistance and Progressive Hepatic Dysfunction

Glucose tolerance depends on a complex interaction among insulin secretion from the beta-cells, clearance of the hormone, and the actions of insulin to accelerate glucose disappearance and inhibit endogenous glucose production. An additional factor, less well recognized, is the ability of glucose per se, independent of changes in insulin, to increase glucose uptake and suppress endogenous output (glucose effectiveness). These factors can be measured in the intact organism with physiologically based minimal models of glucose utilization and insulin kinetics. With the glucose minimal model, insulin sensitivity (SI) and glucose effectiveness (SG) are measured by computer analysis of the frequently sampled intravenous glucose tolerance test. The test involves intravenous injection of glucose followed by tolbutamide or insulin and frequent blood sampling. SI varied from a high of 7.6 x 10(-4) min-1.microU-1.ml-1 in young Whites to 2.3 x 10(-4) min-1.microU-1.ml-1 in obese nondiabetic subjects; in all of the nondiabetic subjects, SG was normal. In subjects with non-insulin-dependent diabetes mellitus (NIDDM), not only was SI reduced 90% below normal (0.61 +/- 0.16 x 10(-4) min-1.microU-1.ml-1), but in this group alone, SG was reduced (from 0.026 +/- 0.008 to 0.014 +/- 0.002 min-1); thus, defects in SI and SG are synergistic in causing glucose intolerance in NIDDM. One assumption of the minimal model is that the time delay in insulin action on glucose utilization in vivo is due to sluggish insulin transport across the capillary endothelium. This was tested by comparing insulin concentrations in plasma with those in lymph (representing interstitial fluid) during euglycemic-hyperinsulinemic glucose clamps. Lymph insulin was lower than plasma insulin at basal (12 vs. 18 microU/ml) and at steady state, indicating significant loss of insulin from the interstitial space, presumably due to cellular uptake of the insulin-receptor complex. Additionally, during clamps, lymph insulin changed more slowly than plasma insulin, but the rate of glucose utilization followed a time course identical with that of lymph (r = .96) rather than plasma (r = .71). Thus, lymph insulin, which may be reflective of interstitial fluid, is the signal to which insulin-sensitive tissues are responding. These studies support the concept that, at physiological insulin levels, the time for insulin to cross the capillary endothelium is the process that determines the rate of insulin action in vivo.(ABSTRACT TRUNCATED AT 400 WORDS)

Lilly lecture 1989. Toward physiological understanding of glucose tolerance. Minimal-model approach.

Insulin secretion rates can be accurately estimated from plasma C-peptide levels with a two-compartment model for C-peptide distribution and degradation. In previous studies, the kinetic parameters of C-peptide clearance were derived in each subject from the decay curve observed after bolus intravenous injection of biosynthetic human C-peptide. To determine whether standard parameters for C-peptide clearance could be defined and used to calculate insulin secretion without obtaining a decay curve in each subject, we analyzed 200 decay curves of biosynthetic human C-peptide obtained in normal, obese, and non-insulindependent diabetes mellitus subjects studied in ourlaboratory. This analysis showed that the volume of distribution and kinetic parameters of C-peptide distribution and metabolism vary by

Estimation of Insulin Secretion Rates from C-Peptide Levels: Comparison of Individual and Standard Kinetic Parameters for C-Peptide Clearance

Integrated insulin secretion rates calculated from peripheral venous C-peptide measurements by two-compartment kinetic analysis were measured in six young normal subjects after increasing oral glucose loads of 25, 50, and 100 g and respective isoglycemic glucose infusions. The differences in B-cell secretory responses between oral and iv glucose challenges were attributed to factors other than glycemia itself (incretin effect). Both insulin and C-peptide concentrations as well as calculated integrated insulin secretion rates increased with increasing oral glucose loads. Due to the similarity in the glucose profiles after all oral loads, almost identical amounts of iv glucose (approximately 20 g) were infused in all "isoglycemic" infusion experiments, with resulting similar hormone profiles and insulin secretion rates. The percent contribution of incretin factors to total immunoreactive insulin responses after 25, 50, and 100 g glucose (85.6%, 74.9%, and 93.0%; response to oral load, 100%) was significantly higher than their contribution to integrated C-peptide responses (27.6-62.9%) or calculated integrated insulin secretion rates (19.2-61.0%). These findings indicate that the degree of incretin stimulation of insulin secretion depends on the amount of glucose ingested. A discrepancy between the estimates of the incretin effect derived from peripheral venous insulin responses, on the one hand, and C-peptide responses or calculated insulin secretion rates, on the other hand, exists. Inasmuch as peripheral insulin values reflect both insulin secretion and hepatic insulin removal, this discrepancy suggests that elimination kinetics of insulin differ between oral and iv glucose administration. This difference can be related to a significantly reduced fractional hepatic insulin extraction after oral (46.9-54.6%) compared to iv (63.4-76.5%) glucose administration when calculated by a three-compartment kinetic model. This reduction in fractional hepatic insulin extraction could be caused by gastrointestinal factors (hormones or nerves) stimulated in the course of glucose ingestion.

Incretin effects of increasing glucose loads in man calculated from venous insulin and C-peptide responses

The prehepatic production of insulin in normal man was evaluated by kinetic analysis of connecting peptide (C-peptide) behavior in the plasma in men and women. Studies were performed during suppression of endogenous insulin secretion (induced by both fasting and exogenous insulin injection) as well as during stimulation of secretion (induced by oral glucose ingestion) and iv glucose injection. Least squares spline fitting of the C-peptide data by interactive computer analysis permitted evaluation of the precursor production of insulin using a two-compartment model for C-peptide removal. Basal prehepatic insulin production averaged 15-4 mU/70 kg.min in 20 subjects and was reduced to 0.9 +/- 2.2 mU/70 kg.min after 84 h of fasting. The injection of exogenous iv insulin resulted in suppression of endogenous production to 0 +/- 2.5 mU/70 kg.min. Maximum prehepatic insulin production induced by a 100-g oral glucose tolerance test was 91 +/- 1.2 mU/70 kg.min, with a cumulative hormone secretion of 11.4 +/- 2.0 U over the 5 h of observation. After the acute iv injection of 25 g glucose, production rose to 465 +/- 108 mU/70 kg.min at 2 min post injection and rapidly returned toward basal. Levels of insulin in the portal vein calculated from this analysis were markedly elevated relative to simultaneous peripheral venous levels. These results quantitate prehepatic insulin production and portal venous insulin concentration from an analysis of the behavior of C-peptide within the plasma in both the steady state and the nonsteady state in man.

Prehepatic Insulin Production in Man: Kinetic Analysis Using Peripheral Connecting Peptide Behavior*

The hepatic extraction of insulin in normal man was evaluated by kinetic analysis of peripheral insulin behavior in the plasma following stimulation of endogenous insulin secretion. Prehepatic insulin production was determined by deconvolution of plasma connecting peptide behavior (C-peptide) and hepatic extraction of the secreted insulin determined with a three-compartment model for hepatic, vascular, and extravascular plasma spaces. Three dosages of oral glucose (10, 25, and 100 g) administered to normal volunteers resulted in 1.8 +/- 0.5, 2.7 +/- 1.1, and 7.2 +/- 1.6 U endogenous insulin secretion, respectively. Total hepatic exposure to insulin exceeded the endogenous secretion due to recycling to the liver from the systemic circulation. Decreasing insulin extraction by the liver (67-53-42%) in the presence of increasing insulin exposure (2.6-4.4-13.2 U) was observed during the dose-response to glucose. The rates of hepatic insulin extraction observed with arginine (58 +/- 9% with 3.2 U), and a normal meal (50 +/- 9% with 7.6 U) were intermediate between the extremes seen with the 10- and 100-g glucose challenge. These results quantitate hepatic exposure of insulin in man during differing stimuli of endogenous insulin secretion, and demonstrate reduced fractional hepatic extraction with increasing insulin exposure.

Hepatic removal of insulin in normal man: dose response to endogenous insulin secretion.

To evaluate the in vivo participation of insulin receptors in both hepatic and extrahepatic removal of insulin, compartmental kinetic analysis of insulin behavior was performed in a patient with blocked receptors due to endogenous antiinsulin receptor antibodies. Using the standard three-compartment simulation of insulin behavior, the responses to both a 5-U injection of exogenous insulin and a 4.2-U secretion of endogenous insulin subsequent to tolbutamide injection were examined. In response to both exogenous and endogenous insulin, hepatic removal of insulin was reduced to less than 18% of the insulin exposure (normal, 40-60%). The metabolic clearance of insulin was reduced from the normal level of 520 ml/min to less than 120 ml/min, consistent with a reduction in receptor-mediated removal of insulin from the blood. These studies propose quantitative parameters for insulin receptor function in hepatic and extrahepatic removal of insulin in man.

Insulin removal in man: in vivo evidence for a receptor-mediated process.

An invariant imbedding algorithm for the solution of inhomogeneous linear two-point boundary value problems

Overproduction of a kinetic subclass of VLDL-apoB, and direct catabolism of VLDL-apoB in human endogenous hypertriglyceridemia: an analytical model solution of tracer data.

R.C Allen

Papers

Prehepatic Insulin Production in Man: Kinetic Analysis Using Peripheral Connecting Peptide Behavior*

Hepatic removal of insulin in normal man: dose response to endogenous insulin secretion.

Insulin removal in man: in vivo evidence for a receptor-mediated process.

An invariant imbedding algorithm for the solution of inhomogeneous linear two-point boundary value problems

Overproduction of a kinetic subclass of VLDL-apoB, and direct catabolism of VLDL-apoB in human endogenous hypertriglyceridemia: an analytical model solution of tracer data.