A compartmental model is presented to account for transient and steady-state changes in blood glucose concentration which result from transit through the forearm and hand in man. This model permits the inter-conversion of arterial and venous data and the derivation of arterial equivalent total body glucose models from venous data. Data were obtained from subjects in the basal state following a pulse injection of [1-14C]glucose tracer. An artery, an antecubital vein, and a dorsal vein of a heated hand (68 degrees C environment) were sampled. Blood transit time is shorter 0.3 vs. 1.0 min) and irreversible glucose loss is reduced (1.9 vs. 2.9%) in the heated hand preparation when compared to the antecubital vein preparation. Because of the smaller correction required and the smaller variation among individuals when heated hand rather than antecubital vein data are obtained, we suggest that for analysis of whole-body kinetics such data should be used along with the compartmental model correction when arterial data cannot be obtained.

A B S T R A C T 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.

Estrogen deficiency is a risk factor for osteoporosis and coronary artery disease. Osteoporosis can be evaluated by measuring bone mineral density (BMD). Coronary atherosclerotic burden can be evaluated by measuring coronary calcium using electron beam computed tomography (EBT) of the heart. We compared coronary calcium scores in 45 asymptomatic postmenopausal women with normal and low BMD. BMD of the lumbar spine and proximal femur was measured by dual X-ray absorptiometry (DXA), and coronary calcium was measured quantitatively by EBT. Women were divided into control, osteopenia, and osteoporosis groups based on the T score of the lumbar spine. Women were similar in age, years since menopause, height, weight, and body mass index (BMI). BMD +/- SD (g/cm2) of L1-L4 was 0.96 +/- 0.11, 0.83 +/- 0.03, and 0.73 +/- 0.05, in control, osteopenia, and osteoporosis group, respectively. The total coronary calcium score +/- SD (relative units) was 41.9 +/- 83.1, 115.1 +/- 181.9, and 221.7 +/- 355.4 for control, osteopenia, and osteoporosis group, respectively; the score was significantly higher in the osteoporosis than in the control group. This study provides initial data suggesting that women with osteoporosis may have a higher risk of developing coronary atherosclerosis.

A B S T R A C T The turnover of 125I-high density lipoprotein (HDL) was examined in a total of 14 studies in eight normal volunteers in an attempt to determiine 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 unider 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) anid ingesting the same isocaloric balanced diet. The dlecay of autologous 1251-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 Dr. Blum's current address is the Department of Medicine, College ofPhysicians & Surgeons, Columbia University, New York 10032. Dr. Eisenberg's current address is the Department of Medicine B, Hadassah Hospital, Jerusalem, Israel.Reprint requests should be addressed to Robert I. Levy, M.D., National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland, 20014. Receivedfor publication 7January 1977 given beginning 3 days before the injection of '25I-HDL, and ferrous sulfate, 300 mg, was given three times daily. The patients received no other medications. Informed consent was obtained.Collectiot of plasmrla. Blood was obtained in 0.1% EDTA, usually after an overnight fast (12-14 h), and the plasma was separated at 40C in a refrigerated centrifuge. In three instances during each turnover study, nonfastinig blood was obtained; these were at 6, 12, and 36 h after the 9:00 a.m. initiation of the studies.Isolation and labeling of HDL. Autologous HDL was isolated at 4°C over the density range 1.09-1.21 g/ml according to the method of Havel et al. (17). Successive ultracentrifugation was carried out in a Beckman 60 Ti rotor (Beckman Instruments, Inc., Fullerton, Calif.) at 59,000 rpm for 18 h at d 1.09 g/ml, and for 24 h at d 1.21 g/ml. The HDL thus obtained was resuspended in an NaCl-KBr solution of d 1.21 g/ml and washed by ultracentrifugation for 24 h at 64,000 rpm in a Beckman 65 rotor. KBr was then removed by at least four successive 30-min dialyses ...

A B S T R A C T Measurements oftransport oftriglycerides (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 ofhypertriglyceridemia seemed out of proportion to their transport rates. This finding and the fact that many patients have increased secretion ofVLDL-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 ratesThis work was presented, in part, at the 49th and 50th

A B S T R A C T Analyses of the control of glucose metabolism by insulin have been hampered by changes in blood 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 [1'C] During the glucose clamp experiments plasma insulin levels reached a plateau of 95±8 /U/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.

A new mathematical approach for the analysis of radioactive tracer experiments on compartmentalized systems in steady states is presented. The experimental measurements of the amounts of tracer in one or more compartments are approximated by a sum of exponential functions of time. The coefficients and exponential factors of these functions are shown to represent a set of invariants of the data. These are then related in a concise matrix equation to the compartmental model parameters, which are defined as the transition probabilities per unit time per unit quantity (turn-over rates) of molecules from one compartment (or state) into another. When measurements are incomplete, the freedom in choosing a model is expressed in turns of a minimum number of variables equal to the difference between the number of model parameters and the number of invariants found in the data. It is shown how other information regarding the model parameters or the amounts of material in steady state may be combined with the tracer data to reduce the degrees of freedom of a proposed model. Matrix transformations are worked out to allow the mapping of all mathematically consistent models in the configuration space of the minimum variables. The boundaries in this space corresponding to the limits for physically realizable models are found. Thus, a model is expressed by a set of coordinates and the values of all the parameters are obtained by substituting the values of the coordinates. Investigation of the range of variation of each parameter over the bounded region is also possible.

A B S T R A C T Plasma transport of free fatty acids (FFA) and triglyceride fatty acids (TGFA) was studied in seven subjects with normal lipid metabolism, one case of total lipodystrophy, and one case of familial hyperlipemia (Type V). Studies were carried out after intravenous injection of radioactive FFA, of lipoproteins previously labeled in vitro in the triglyceride moiety, or both.Computer techniques were used to evaluate a series of multicompartmental models, and a general model is proposed that yields optimum fitting of experimental data for both FFA and TGFA. The results show that as much as 20-30% of FFA leaving the plasma compartment in normal subjects is transported to an exchanging extravascular pool and quickly reenters the plasma pool as FFA. The rate of irreversible delivery of FFA from plasma to tissues averaged 358 AEq/min in normals. The lipodystrophy patient, despite the virtual absence of adipose tissue (confirmed at autopsy), had a plasma FFA concentration and a total FFA transport, both more than twice normal. Total TGFA transport ranged from 25 to 81 MLEq/min in four normal controls.The rate constant for TGFA turnover in the patient with Type V hyperlipemia was so small that total transport could not be quantified from the data available; the TGFA half-life was over 500 min.In two normal subjects given injections of autologous lipoproteins labeled in vitro with triolein-"C and simultaneously given oleic acid-8H, it was shown that the time course for the disappearance of the TGFA in the in vitro labeled samples conformed almost exactly to that of the physiologically labeled lipoprotein TGFA synDr. Eaton's present address is