Mones Berman

A Model of the Kinetics of Insulin in Man

The design of the present study of the kinetics of insulin in man combines experimental features which obviate two of the major problems in previous insulin studies. (a) The use of radioiodinated insulin as a tracer has been shown to be inappropriate since its metabolism differs markedly from that of the native hormone. Therefore porcine insulin was administered by procedures which raised insulin levels in arterial plasma into the upper physiologic range. Hypoglycemia was prevented by adjusting the rate of an intravenous infusion of glucose in order to control the blood glucose concentration (the glucose-clamp technique). (b) Estimation of a single biological half-time of insulin after pulse injection of the hormone has been shown to be inappropriate since plasma insulin disappearance curves are multiexponential. Therefore the SAAM 25 computer program was used in order to define the parameters of a three compartment insulin model. The combined insulin mass of the three compartments (expressed as plasma equivalent volume) is equal to inulin space (15.7% body wt). Compartment 1 is apparently the plasma space (4.5%). The other two compartments are extra-vascular; compartment 2 is small (1.7%) and equilibrates rapidly with plasma, and compartment 3 is large (9.5%) and equilibrates slowly with plasma. The SAAM 25 program can simulate the buildup and decay of insulin in compartments 2 and 3 which cannot be assayed directly. Insulin in compartment 3 was found to correlate remarkably with the time-course of the servo-controlled glucose infusion. Under conditions of a steady-state arterial glucose level, glucose infusion is a measure of glucose utilization. We conclude that compartment 3 insulin (rather than plasma insulin) is a more direct determinant of glucose utilization. We suggest that the combined use of glucose-clamp and kinetic-modeling techniques should aid in the delineation of pathophysiologic states affecting glucose and insulin metabolism.

High Density Lipoprotein Metabolism in Man

The turnover of (125)I-high density lipoprotein (HDL) was examined in a total of 14 studies in eight normal volunteers in an attempt to determine the metabolic relationship between apolipoproteins A-I (apoA-I) and A-II (apoA-II) of HDL and to define further some of the determinants of HDL metabolism. All subjects were first studied under conditions of an isocaloric balanced diet (40% fat, 40% carbohydrate). Four were then studied with an 80% carbohydrate diet, and two were studied while receiving nicotinic acid (1 g three times daily) and ingesting the same isocaloric balanced diet. The decay of autologous (125)I-HDL and the appearance of urinary radioactivity were followed for at least 2 wk in each study. ApoA-I and apoA-II were isolated by Sephadex G-200 chromatography from serial plasma samples in each study. The specific activities of these peptides were then measured directly. It was found that the decay of specific activity of apoA-I and apoA-II were parallel to one another in all studies. The mean half-life of the terminal portion of decay was 5.8 days during the studies with a balanced diet.Mathematical modeling of the decay of plasma radioactivity and appearance of urinary radioactivity was most consistent with a two-compartment model. One compartment is within the plasma and exchanges with a nonplasma component. Catabolism occurs from both of these compartments. With a balanced isocaloric diet, the mean synthetic rate for HDL protein was 8.51 mg/kg per day. HDL synthesis was not altered by the high carbohydrate diet and was only slightly decreased by nicotinic acid treatment. These perturbations had effects on HDL catabolic pathways that were reciprocal in many respects. With an 80% carbohydrate diet, the rate of catabolism from the plasma compartment rose by a mean of 39.1%; with nicotinic acid treatment, it fell by 42.2%. Changes in the rate of catabolism from the second compartment were generally opposite those in the rate of catabolism from the plasma compartment, suggesting that these two catabolic pathways may be reciprocally regulated.

Transport of Very Low Density Lipoprotein Triglycerides in Varying Degrees of Obesity and Hypertriglyceridemia

Measurements of transport of triglycerides (TG) in very low density lipoproteins (VLDL) were carried out in 59 patients by injection of radioactive glycerol, determinations of specific activities of VLDL-TG for 48 h thereafter, and treatment of the data by multicompartmental analysis. The patients were divided into three groups: normal weight (89-120% ideal weight), mildly obese (120-135% ideal weight), and markedly obese (135% ideal weight). They had varying levels of VLDL-TG ranging from normal to markedly elevated. In many subjects, there was a positive correlation between concentrations and transport of VLDL indicating that overproduction of VLDL-TG contributed to hypertriglyceridemia. In others, and particularly in several markedly obese subjects, transport rates were greatly increased without significant hypertriglyceridemia, suggesting that they had enhanced capacity to clear TG. In all groups, however, there were patients whose degree of hypertriglyceridemia seemed out of proportion to their transport rates. This finding and the fact that many patients have increased secretion of VLDL-TG without elevated plasma TG suggests that both overproduction of VLDL-TG and insufficient enhancement of clearance contributed to the development of hypertriglyceridemia.The data showed a poor correlation between transport rates determined by our multicompartment analysis and single-exponential analysis used previously by other investigators (r = 0.46); this comparison was not improved by segregating patients according to their degree of obesity. Although two conversion pathways (fast and slow synthetic paths) were required to fit the data, there was no correlation between transport rates and the ratio of the two pathways. Also, despite the known pathway of conversion of VLDL to low density lipoprotein, no correlation was found between VLDL-TG transport rates and estimated low density lipoprotein-cholesterol concentrations.

Insulin Control of Glucose Metabolism in Man: A New Kinetic Analysis

Analyses of the control of glucose metabolism by insulin have been hampered by changes in bloog glucose concentration induced by insulin administration with resultant activation of hypoglycemic counterregulatory mechanisms. To eliminate such mechanisms, we have employed the glucose clamp technique which allows maintenance of fasting blood glucose concentration during and after the administration of insulin. Analyses of six studies performed in young healthy men in the postabsorptive state utilizing the concurrent administration of [14C]glucose and 1 mU/kg per min (40 mU/m2 per min) porcine insulin led to the development of kinetic models for insulin and for glucose. These models account quantitatively for the control of insulin on glucose utilization and on endogenous glucose production during nonsteady states. The glucose model, a parallel three-compartment model, has a central compartment (mass = 68 +/- 7 mg/kg; space of distribution = blood water volume) in rapid equilibrium with a smaller compartment (50 +/- 17 mg/kg) and in slow equilibrium with a larger compartment (96 +/-21 mg/kg). The total plasma equivalent space for the glucose system averaged 15.8 liters or 20.3% body weight. Two modes of glucose loss are introduced in the model. One is a zero-order loss (insulin and glucose independent) from blood to the central nervous system; its magnitude was estimated from published data. The other is an insulin-dependent loss, occurring from the rapidly equilibrating compartment and, in the basal period, is smaller than the insulin-independent loss. Endogenous glucose production averaged 1.74 mg/kg per min in the basal state and enters the central compartment directly. During the glucose clamp experiments plasma insulin levels reached a plateau of 95 +/-8 microU/ml. Over the entire range of insulin levels studied, glucose losses were best correlated with levels of insulin in a slowly equilibrating insulin compartment of a three-compartment insulin model. A proportional control by this compartment on glucose utilization was adequate to satisfy the observed data. Insulin also rapidly decreased the endogenous glucose production to 33% of its basal level (0.58 mg/kg per min), this suppression being maintained for at least 40 min after exogenous insulin infusion was terminated and after plasma insulin concentrations had returned to basal levels. The change in glucose utilization per unit change in insulin in the slowly equilibrating insulin compartment is proposed as a new measure for insulin sensitivity. This defines insulin effects more precisely than previously used measures, such as plasma glucose/plasma insulin concentration ratios. Glucose clamp studies and the modeling of the coupled kinetics of glucose and insulin offers a new and potentially valuable tool to the study of altered states of carbohydrate metabolism.

Multicompartmental Analysis of Cholesterol Metabolism in Man: CHARACTERIZATION OF THE HEPATIC BILE ACID AND BILIARY CHOLESTEROL PRECURSOR SITES

The present report has presented the first clear evidence in man for the existence of specific hepatic cholesterol precursor sites associated with the formation and secretion of bile acids and biliary cholesterol. These hepatic compartments derive virtually all their cholesterol from newly synthesized and lipoprotein free cholesterol. The model which is presented was formulated on current concepts of cholesterol metabolism in man and is concerned, at this initial stage, with the elucidation of the bile acid and biliary cholesterol compartments. The complexity of cholesterol metabolism in man necessitated an initial approach that would minimize the number of inputs of cholesterol into the system, allow for the sampling of several cholesterol compartments, and permit the simultaneous labeling of newly synthesized cholesterol and preformed cholesterol. To achieve these objectives, we studied the patient with a total bile fistula. Six patients were administered simultaneously pulse injections of labeled mevalonic acid and [(14)C]cholesterol. The qualitative features of the specific activity time course curves after labeled mevalonic acid revealed no precursor-product relationship between bile acid, biliary cholesterol, and plasma free cholesterol. The peak specific activity of the bile acids was reached in approximately 100 min and was higher than the biliary cholesterol, which was higher than the plasma free cholesterol. The plasma free cholesterol specific activity became higher than the other lipids after 12 h and remained higher throughout the period of study. Similar related observations were made with [(14)C]cholesterol. The data were then subjected to simulation analysis and modeling using the SAAM-27 computer program. Computer least-square fits of the data were obtained after the model was evolved. During the model development, the least number of compartments and transport pathways were introduced consistent with a good fit of the data. Of particular importance was the constraint that the model fit the data obtained from both [(14)C]cholesterol and labeled mevalonic acid. The same parameter values were used to fit the data from both tracers. The fluxes arrived at in the model indicate that 31% and 20%, respectively, of the cholesterol input into the bile acid and biliary cholesterol precursor sites were derived directly from the newly synthesized hepatic cholesterol. The remainder had its origin predominantly from lipoprotein free cholesterol. Plasma esterified cholesterol (as free) made a small contribution (11%) to the bile acid compartment. Similarly, 10% of the biliary cholesterol arose from an unknown hepatic site. The present report has provided the basis for a new procedure for studying in vivo cholesterol metabolism in man. Examination of the derived cholesterol flux rates between the compartments suggests the presence of an important mechanism regulating the partitioning of lipoprotein free cholesterol between the bile acid and biliary cholesterol precursor sites. Aberrations in the proportioning of precursor cholesterol between these sites could be a causative factor precipitating the excessive secretion of biliary cholesterol and the production of lithogenic bile.

Very low density lipoprotein triglyceride transport in type IV hyperlipoproteinemia and the effects of carbohydrate-rich diets

Transport of plasma-free fatty acids (FFA) and of fatty acids in triglycerides of plasma very low density lipoproteins (VLDL-TGFA) was studied in two normal subjects, five patients with type IV hyperlipoproteinemia, and two patients with type I hyperlipoproteinemia. After intravenous pulse-labeling with albumin-bound 1-palmitate-(14)C, specific radioactivity of plasma FFA and VLDL-TGFA were determined at intervals up to 24 hr. The results were analyzed using several different multicompartmental models each compatible with the experimental data. Fractional transport of VLDL-TGFA was distinctly lower (no overlap) in the type IV patients than in the control subjects, both on a usual balanced diet (40% of calories from carbohydrate) and on a high-carbohydrate diet (80% of calories). However, net or total transport of VLDL-TGFA in the type IV patients was not clearly distinguishable from that in the control subjects, there being considerable overlap on either diet. The results suggest that in this group of type IV patients the underlying defect leading to the increased pool size of VLDL-TGFA is not overproduction but a relative defect in mechanisms for removal of VLDL-TGFA. Since some of these type IV patients had only a moderate degree of hypertriglyceridemia at the time they were studied, and since it is not established that patients with the type IV phenotype constitute a biochemically homogeneous population, the present results should not be generalized. Four studies were done (in two control subjects and two type IV patients) in which the kinetic parameters in the same individual were determined on the balanced diet and on the high-carbohydrate diet. All subjects showed an increase in VLDL-TGFA pool size. Using two of the models for analysis, all showed an increase in net transport of VLDL-TGFA; using the third model, three of the four studies showed an increase in VLDL-TGFA transport. The results are compatible with the interpretation that the carbohydrate-induced increase in VLDL-TGFA, both in controls and type IV patients, is at least in part due to an increased rate of production of VLDL-TGFA. The magnitude of the increase was approximately the same in controls and patients. Thus, metabolic adjustment to a high-carbohydrate regimen in these type IV patients may not be basically different from that in normal controls; the higher levels of VLDL-TGFA reached may simply be another reflection of a defective removal mechanism. An alternative interpretation, compatible with the data, would involve both a carbohydrate-induced increase in fractional rate of release of VLDL-TGFA from liver to plasma and a decrease in fractional removal of VLDL-TGFA from plasma without increase in net production rate. The simpler hypothesis of a single primary effect on net VLDL-TGFA production from FFA seems more likely.

Multicompartmental Analysis of Calcium Kinetics in Normal Adult Males

This report describes studies of calcium kinetics in ten normal young men. Serum, urinary, and fecal radioactivity was measured from 1 minute to 20 days after intravenous tracer (47)Ca injection, and these results were analyzed jointly with data obtained from a simultaneous metabolic balance study, using digital computer techniques. Surface radioactivity measurements were also obtained to gain further insight into the anatomic correlates of the tracer distribution. The data were satisfied by a model with four exchanging compartments. Series, branching, and mammillary models were analyzed. Several parameters of physiologic interest were independent of the model, but two were dependent on the duration of the study. Individual and mean values for these kinetic analyses are presented with their statistical uncertainties. These studies present detailed analyses in a healthy, normal population and provide a reference for future studies of skeletal metabolism and serum calcium homeostasis.

Study of calcium absorption in man: a kinetic analysis and physiologic model

A physical model of calcium absorption was developed from analysis of data obtained on 23 subjects, including 13 patients having a variety of abnormalities of calcium metabolism. The model was tested and found consistent in all subjects studied. This technique provides a quantitative description of the rate of entry of oral dose of (47)Ca into the circulation as a function of time by analysis of serum or forearm radioactivity in response to intravenous and oral administration of (47)Ca. The kinetics of the absorption process as proposed by the model are characterized by an initial delay phase of 15-20 min, by a maximal rate of absorption at 40-60 min after ingestion, and by 95% completion of the absorption within 2(1/2) hr. Partial identification of the physiological counterparts of the model was possible by introduction of the isotope at various levels of the gut. Although the region of the duodenum was found to have the greatest rate of absorption per unit length in normal subjects, it was least responsive to stimulation by parathyroid hormone and suppression by calcium loading. Furthermore, the response of the gut to parathyroid hormone was delayed, whereas the suppression of absorption by intravenous or oral calcium loading was rapid and dramatic. The implications of these observations are discussed.

Kinetic model for production and metabolism of very low density lipoprotein triglycerides. Evidence for a slow production pathway and results for normolipidemic subjects.

A model for the synthesis and degradation of very low density lipoprotein triglyceride (VLDL-TG) in man is proposed to explain plasma VLDL-TG radioactivity data from studies conducted over a 48-h interval after injection of glycerol labeled with 14C, 3H, or both. The curve describing the radioactivity of plasma VLDL triglycerides reaches a maximum at about 2 h, after which the decay is biphasic in all cases; the late curvature becoming evident only after 8--12 h. To fit the complex curve, it was necessary to postulate two pathways for the incorporation of plasma glycerol into VLDL-TG, one much slower than the other. A process of stepwise delipidation of VLDL in the plasma compartment, previously proposed for VLDL apoprotein models, was also necessary. Predicted VLDL-TG synthesis rates calculated with this model can differ significantly from those based on experiments of shorter duration in which the slow VLDL-TG component is not apparent. The results of these studies strongly support the interpretation that the late, slow component of the VLDL-TG activity curve is predominantly due to the slowly turning-over precursor compartment in the conversion pathway and is not due either to a slow compartment in the labeled precursor, plasma free glycerol, or to an exchange of plasma VLDL-TG with an extravascular compartment. It also cannot, in these studies, be attributed to a slowly turning-over VLDL-TG moiety in the plasma. The model was tested with data from 59 studies including normal subjects and patients with obesity and(or) various forms of hyperlipoproteinemia. Good fits were obtained in all cases, and the estimated parameter values and their uncertainties for 13 normolipemic nonobese subjects are presented. Sensitivty testing was carried out to determine how critical various parameter estimations are to the assumptions introduced in the modeling.

The formulation and testing of models.

The term “model” is used in both a physical and mathematical sense to represent any set of equations or functions that describe the response of a system to a stimulus. In a mathematical model, functions or differential equations are employed without regard to any mechanistic aspects of the system. On the other hand a physical model implies certain mechanisms or entities that have physiological, biochemical, or physical significance. The parameters of a model are the arbitrary constants of the functions or equations and apply to both physical and mathematical models. Procedures for the formulation of models to interpret kinetic data involve a number of quantitative and qualitative phases. It is the purpose of this paper to discuss from a single point of view some of these phases and the way they may fit into a formalism for the formulation and testing of models. It is first necessary to choose the type or class of models applicable. Frequently a choice can be based on theoretical considerations of the system studied. For example, linear compartmental analysis is often justifiable for tracer kinetics. Other types of models may be chosen for their conceptual simplicity, for the relative ease with which they can be treated mathematically, or for their simplicity in predicting the experimental data. To choose a model from a given type or class of models it is necessary to consider its complexity. Two aspects contribute to this: (1) the “order” of the wodel, namely, the number of independent functions or equations necessary to describe its response, and (2) the number of parameters for a given order. In the case of linear compartmental models, the order is equivalent to the number of compartments (or the number of exponential components), and the number of parameters is equivalent to the number of interconnections or transition paths between compartments. It is not possible to derive the order of a model on the basis of the data alone because any model that is compatible with the data can always be interpreted as a degenerate case for one of higher order. One can, however, derive a minimal order below which, based on some criterion, the data cannot be predicted satisfactorily, and this is usually the order chosen for a model. For compartmental models, this means that a model with the smallest number of compartments compatible with the data is usually chosen, unless other criteria are introduced. Given the number of compartments, it is necessary next to determine