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Goodpaster BH, Bertoldo A, Ng JM, Azuma K, Pencek RR, Kelley C, Price JC, Cobelli C, Kelley DE. Interactions among glucose delivery, transport, and phosphorylation that underlie skeletal muscle insulin resistance in obesity and type 2 Diabetes: studies with dynamic PET imaging. Diabetes 2014; 63:1058-68. [PMID: 24222345 PMCID: PMC3931396 DOI: 10.2337/db13-1249] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
Dynamic positron emission tomography (PET) imaging was performed using sequential tracer injections ([(15)O]H2O, [(11)C]3-O-methylglucose [3-OMG], and [(18)F]fluorodeoxyglucose [FDG]) to quantify, respectively, skeletal muscle tissue perfusion (glucose delivery), kinetics of bidirectional glucose transport, and glucose phosphorylation to interrogate the individual contribution and interaction among these steps in muscle insulin resistance (IR) in type 2 diabetes (T2D). PET imaging was performed in normal weight nondiabetic subjects (NW) (n = 5), obese nondiabetic subjects (OB) (n = 6), and obese subjects with T2D (n = 7) during fasting conditions and separately during a 6-h euglycemic insulin infusion at 40 mU · m(-2) · min(-1). Tissue tracer activities were derived specifically within the soleus muscle with PET images and magnetic resonance imaging. During fasting, NW, OB, and T2D subjects had similar [(11)C]3-OMG and [(18)F]FDG uptake despite group differences for tissue perfusion. During insulin-stimulated conditions, IR was clearly evident in T2D (P < 0.01), and [(18)F]FDG uptake by muscle was inversely correlated with systemic IR (P < 0.001). The increase in insulin-stimulated glucose transport was less (P < 0.01) in T2D (twofold) than in NW (sevenfold) or OB (sixfold) subjects. The fractional phosphorylation of [(18)F]FDG during insulin infusion was also significantly lower in T2D (P < 0.01). Dynamic triple-tracer PET imaging indicates that skeletal muscle IR in T2D involves a severe impairment of glucose transport and additional impairment in the efficiency of glucose phosphorylation.
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Affiliation(s)
- Bret H. Goodpaster
- Department of Medicine, University of Pittsburgh, Pittsburgh, PA
- Corresponding author: Bret H. Goodpaster,
| | | | - Jason M. Ng
- Department of Medicine, University of Pittsburgh, Pittsburgh, PA
| | - Koichiro Azuma
- Department of Medicine, University of Pittsburgh, Pittsburgh, PA
| | | | - Carol Kelley
- Department of Medicine, University of Pittsburgh, Pittsburgh, PA
| | - Julie C. Price
- Department of Radiology, University of Pittsburgh, Pittsburgh, PA
| | - Claudio Cobelli
- Department of Information Engineering, University of Padova, Padova, Italy
| | - David E. Kelley
- Department of Medicine, University of Pittsburgh, Pittsburgh, PA
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Huang HM, Ismail-Beigi F, Muzic RF. A new Michaelis-Menten-based kinetic model for transport and phosphorylation of glucose and its analogs in skeletal muscle. Med Phys 2011; 38:4587-99. [PMID: 21928632 DOI: 10.1118/1.3599034] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
Abstract
PURPOSE A new model is introduced that individually resolves the delivery, transport, and phosphorylation steps of metabolism of glucose and its analogs in skeletal muscle by interpreting dynamic positron emission tomography (PET) data. METHODS The model uniquely utilizes information obtained from the competition between glucose and its radiolabeled analogs. Importantly, the model avoids use of a lumped constant which may depend on physiological state. Four basic physiologic quantities constitute our model parameters, including the fraction of total tissue space occupied by interstitial space (f(IS)), a flow-extraction product and interstitial (IS(g)) and intracellular (IC(g)) glucose concentrations. Using the values of these parameters, cellular influx (CI) and efflux (CE) of glucose, glucose phosphorylation rate (PR), and maximal transport (V(G)) and phosphorylation capacities (V(H)) can all be determined. Herein, the theoretical derivation of our model is addressed and characterizes its properties via simulation. Specifically, the model performance is evaluated by simulation of basal and euglycemic hyperinsulinemic (EH) conditions. RESULTS In fitting the model-generated, synthetic data (including noise), mean estimates of all but IC(g) of the parameter values are within 5% of their values for both conditions. In addition, mean errors of CI, PR, and V(G) are less than 5% whereas those of VH and CE are not. CONCLUSIONS It is concluded that under the conditions tested, the novel model can provide accurate parameter estimates and physiological quantities, except IC(g) and two quantities that are dependent on IC(g), namely CE and VH. However, the ability to estimate IC(g) seems to improve with increases in intracellular glucose concentrations as evidenced by comparing IC(g) estimates under basal vs EH conditions.
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Affiliation(s)
- Hsuan-Ming Huang
- Department of Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio 44106, USA
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Wu Z, Chui CK, Hong GS, Chang S. Physiological analysis on oscillatory behavior of glucose–insulin regulation by model with delays. J Theor Biol 2011; 280:1-9. [DOI: 10.1016/j.jtbi.2011.03.032] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2010] [Revised: 03/24/2011] [Accepted: 03/24/2011] [Indexed: 10/18/2022]
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Ng JM, Kelley DE, Goodpaster BH. Mechanisms of insulin resistance assessed by dynamic in-vivo positron emission tomography imaging. Curr Opin Clin Nutr Metab Care 2009; 12:508-12. [PMID: 19550312 DOI: 10.1097/mco.0b013e32832eb59a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
PURPOSE OF REVIEW Skeletal muscle insulin resistance is a hallmark characteristic of type 2 diabetes, although the exact causes of insulin resistance are unknown. In-vivo methods to assess mechanisms that determine insulin resistance in humans are critical to improve our understanding of insulin resistance in obesity and type 2 diabetes. In this review, we examine recent studies utilizing dynamic in-vivo PET imaging in assessing insulin resistance in humans. RECENT FINDINGS PET imaging of glucose metabolism in vivo has revealed novel and important information about the regulation of glucose metabolism in skeletal muscle. Using dynamic PET imaging, studies have impairments in glucose metabolism at multiple sites, including delivery, phosphorylation, and transport within skeletal muscle. Impairments in glucose phosphorylation as well as glucose transport defects may play an important role in understanding the disorder of skeletal muscle insulin resistance. SUMMARY PET imaging has great potential to yield significant and promising insight into insulin resistance in skeletal muscle. Dynamic in-vivo PET imaging can provide valuable information regarding the mechanisms and specific loci of skeletal muscle insulin resistance in humans.
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Affiliation(s)
- Jason M Ng
- Department of Medicine, University of Pittsburgh, Montefiore Hospital, Pittsburgh, PA 15213, USA
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Perret P, Slimani L, Briat A, Villemain D, Halimi S, Demongeot J, Fagret D, Ghezzi C. Assessment of insulin resistance in fructose-fed rats with 125I-6-deoxy-6-iodo-D-glucose, a new tracer of glucose transport. Eur J Nucl Med Mol Imaging 2007; 34:734-744. [PMID: 17171359 PMCID: PMC2705461 DOI: 10.1007/s00259-006-0267-3] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2006] [Accepted: 08/08/2006] [Indexed: 12/28/2022]
Abstract
PURPOSE Insulin resistance, characterised by an insulin-stimulated glucose transport defect, is an important feature of the pre-diabetic state that has been observed in numerous pathological disorders. The purpose of this study was to assess variations in glucose transport in rats using (125)I-6-deoxy-6-iodo-D-glucose (6DIG), a new tracer of glucose transport proposed as an imaging tool to assess insulin resistance in vivo. METHODS Two protocols were performed, a hyperinsulinaemic-euglycaemic clamp and a normoinsulinaemic-normoglycaemic protocol, in awake control and insulin-resistant fructose-fed rats. The tracer was injected at steady state, and activity in 11 tissues and the blood was assessed ex vivo at several time points. A multicompartmental mathematical model was developed to obtain fractional transfer coefficients of 6DIG from the blood to the organs. RESULTS Insulin sensitivity of fructose-fed rats, estimated by the glucose infusion rate, was reduced by 40% compared with control rats. At steady state, 6DIG uptake was significantly stimulated by insulin in insulin-sensitive tissues of control rats (basal versus insulin: diaphragm, p < 0.01; muscle, p<0.05; heart, p<0.001), whereas insulin did not stimulate 6DIG uptake in insulin-resistant fructose-fed rats. Moreover, in these tissues, the fractional transfer coefficients of entrance were significantly increased with insulin in control rats (basal vs insulin: diaphragm, p<0.001; muscle, p<0.001; heart, p<0.01) whereas no significant changes were observed in fructose-fed rats. CONCLUSION This study sets the stage for the future use of 6DIG as a non-invasive means for the evaluation of insulin resistance by nuclear imaging.
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Affiliation(s)
- Pascale Perret
- INSERM, E340, 38000 Grenoble,, France.
- Univ Grenoble, 38000 Grenoble,, France.
| | - Lotfi Slimani
- INSERM, E340, 38000 Grenoble,, France
- Univ Grenoble, 38000 Grenoble,, France
| | - Arnaud Briat
- INSERM, E340, 38000 Grenoble,, France
- Univ Grenoble, 38000 Grenoble,, France
| | - Danièle Villemain
- INSERM, E340, 38000 Grenoble,, France
- Univ Grenoble, 38000 Grenoble,, France
| | - Serge Halimi
- CHRU Grenoble, Hôpital Michallon, Service de Diabétologie, , 38000 Grenoble,, France
| | - Jacques Demongeot
- Univ Grenoble, 38000 Grenoble,, France
- CNRS, UMR 5525, 38000 Grenoble, , France
| | - Daniel Fagret
- INSERM, E340, 38000 Grenoble,, France
- Univ Grenoble, 38000 Grenoble,, France
| | - Catherine Ghezzi
- INSERM, E340, 38000 Grenoble,, France
- Univ Grenoble, 38000 Grenoble,, France
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Bertoldo A, Pencek RR, Azuma K, Price JC, Kelley C, Cobelli C, Kelley DE. Interactions between delivery, transport, and phosphorylation of glucose in governing uptake into human skeletal muscle. Diabetes 2006; 55:3028-37. [PMID: 17065339 DOI: 10.2337/db06-0762] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Abstract
Skeletal muscle accounts for a large proportion of insulin-stimulated glucose utilization. It is generally regarded that much of the control over rates of uptake is posited within the proximal steps of delivery, transport, and phosphorylation of glucose, with glucose transport as the main locus of control. Whether insulin modulates the distribution of control across these steps and in what manner remains uncertain. The current study addressed this in vivo using dynamic positron emission tomography (PET) imaging of human muscle with sequential injections of three tracers ([(15)O]H(2)O, [(11)C]3-O-methyl glucose [3-OMG], and [(18)F]fluoro-deoxy glucose [FDG]) that enabled quantitative determinations of glucose delivery, transport, and its phosphorylation, respectively. Lean, healthy, research volunteers were studied during fasting conditions (n = 8) or during a euglycemic insulin infusion at 30 mU/min per m(2) (n = 8). PET images were coregistered with magnetic resonance imaging to contrast glucose kinetics in soleus, a highly oxidative muscle, with tibialis anterior, a less oxidative muscle. During fasting conditions, uptake of [(11)C]3-OMG was similar in soleus and tibialis anterior muscles, despite higher delivery to soleus (by 35%; P < 0.01). Uptake of [(18)F]FDG was also similar between muscle during fasting, and glucose transport was found to be the dominant locus of control (90%) for glucose uptake under this condition. Insulin increased uptake of [(11)C]3-OMG substantially and strongly stimulated the kinetics of bidirectional glucose transport. Uptake of [(11)C]3-OMG was higher in soleus than tibialis anterior muscle (by 22%; P < 0.01), a difference partially due to higher delivery, which was again found to be 35% higher to soleus (P < 0.01). The uptake of [(18)F]FDG was 65% greater in soleus compared with tibialis anterior muscle, a larger difference than for [(11)C]3-OMG (P < 0.01), indicating an added importance of glucose phosphorylation in defining insulin sensitivity. Analysis of the distribution of control during insulin-stimulated conditions revealed that most of the control was posited at delivery and transport and was equally divided between these steps. Thus, insulin evokes a broader distribution of control than during fasting conditions in governing glucose uptake into skeletal muscle. This redistribution of control is triggered by the robust stimulation of glucose transport, which in turn unmasks a greater dependence upon delivery and glucose phosphorylation.
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Bertoldo A, Price J, Mathis C, Mason S, Holt D, Kelley C, Cobelli C, Kelley DE. Quantitative assessment of glucose transport in human skeletal muscle: dynamic positron emission tomography imaging of [O-methyl-11C]3-O-methyl-D-glucose. J Clin Endocrinol Metab 2005; 90:1752-9. [PMID: 15613423 DOI: 10.1210/jc.2004-1092] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
Insulin-stimulated glucose transport in skeletal muscle is regarded as a key determinant of insulin sensitivity, yet isolation of this step for quantification in human studies is a methodological challenge. One notable approach is physiological modeling of dynamic positron emission tomography (PET) imaging using 2-[18-fluoro]2-deoxyglucose ([(18)F]FDG); however, this has a potential limitation in that deoxyglucose undergoes phosphorylation subsequent to transport, complicating separate estimations of these steps. In the current study we explored the use of dynamic PET imaging of [(11)C]3-O-methylglucose ([(11)C]3-OMG), a glucose analog that is limited to bidirectional glucose transport. Seventeen lean healthy volunteers with normal insulin sensitivity participated; eight had imaging during basal conditions, and nine had imaging during euglycemic insulin infusion at 30 mU/min.m(2). Dynamic PET imaging of calf muscles was conducted for 90 min after the injection of [(11)C]3-OMG. Spectral analysis of tissue activity indicated that a model configuration of two reversible compartments gave the strongest statistical fit to the kinetic pattern. Accordingly, and consistent with the structure of a model previously used for [(18)F]FDG, a two-compartment model was applied. Consistent with prior [(18)F]FDG findings, insulin was found to have minimal effect on the rate constant for movement of [(11)C]3-OMG from plasma to tissue interstitium. However, during insulin infusion, a robust and highly significant increase was observed in the kinetics of inward glucose transport; this and the estimated tissue distribution volume for [(11)C]3-OMG increased 6-fold compared with basal conditions. We conclude that dynamic PET imaging of [(11)C]3-OMG offers a novel quantitative approach that is both chemically specific and tissue specific for in vivo assessment of glucose transport in human skeletal muscle.
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Hovorka R, Shojaee-Moradie F, Carroll PV, Chassin LJ, Gowrie IJ, Jackson NC, Tudor RS, Umpleby AM, Jones RH. Partitioning glucose distribution/transport, disposal, and endogenous production during IVGTT. Am J Physiol Endocrinol Metab 2002; 282:E992-1007. [PMID: 11934663 DOI: 10.1152/ajpendo.00304.2001] [Citation(s) in RCA: 150] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
We have separated the effect of insulin on glucose distribution/transport, glucose disposal, and endogenous production (EGP) during an intravenous glucose tolerance test (IVGTT) by use of a dual-tracer dilution methodology. Six healthy lean male subjects (age 33 +/- 3 yr, body mass index 22.7 +/- 0.6 kg/m(2)) underwent a 4-h IVGTT (0.3 g/kg glucose enriched with 3-6% D-[U-(13)C]glucose and 5-10% 3-O-methyl-D-glucose) preceded by a 2-h investigation under basal conditions (5 mg/kg of D-[U-(13)C]glucose and 8 mg/kg of 3-O-methyl-D-glucose). A new model described the kinetics of the two glucose tracers and native glucose with the use of a two-compartment structure for glucose and a one-compartment structure for insulin effects. Insulin sensitivities of distribution/transport, disposal, and EGP were similar (11.5 +/- 3.8 vs. 10.4 +/- 3.9 vs. 11.1 +/- 2.7 x 10(-2) ml small middle dot kg(-1) small middle dot min(-1) per mU/l; P = nonsignificant, ANOVA). When expressed in terms of ability to lower glucose concentration, stimulation of disposal and stimulation of distribution/transport accounted each independently for 25 and 30%, respectively, of the overall effect. Suppression of EGP was more effective (P < 0.01, ANOVA) and accounted for 50% of the overall effect. EGP was suppressed by 70% (52-82%) (95% confidence interval relative to basal) within 60 min of the IVGTT; glucose distribution/transport was least responsive to insulin and was maximally activated by 62% (34-96%) above basal at 80 min compared with maximum 279% (116-565%) activation of glucose disposal at 20 min. The deactivation of glucose distribution/transport was slower than that of glucose disposal and EGP (P < 0.02) with half-times of 207 (84-510), 12 (7-22), and 29 (16-54) min, respectively. The minimal-model insulin sensitivity was tightly correlated with and linearly related to sensitivity of EGP (r = 0.96, P < 0.005) and correlated positively but nonsignificantly with distribution/transport sensitivity (r = 0.73, P = 0.10) and disposal sensitivity (r = 0.55, P = 0.26). We conclude that, in healthy subjects during an IVGTT, the two peripheral insulin effects account jointly for approximately one-half of the overall insulin-stimulated glucose lowering, each effect contributing equally. Suppression of EGP matches the effect in the periphery.
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Affiliation(s)
- Roman Hovorka
- Centre for Measurement and Information in Medicine, City University, London EC1V 0HB.
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Mandarino LJ, Bonadonna RC, Mcguinness OP, Halseth AE, Wasserman DH. Regulation of Muscle Glucose Uptake In Vivo. Compr Physiol 2001. [DOI: 10.1002/cphy.cp070227] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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Bertoldo A, Peltoniemi P, Oikonen V, Knuuti J, Nuutila P, Cobelli C. Kinetic modeling of [(18)F]FDG in skeletal muscle by PET: a four-compartment five-rate-constant model. Am J Physiol Endocrinol Metab 2001; 281:E524-36. [PMID: 11500308 DOI: 10.1152/ajpendo.2001.281.3.e524] [Citation(s) in RCA: 61] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Various modeling strategies have been developed to convert regional [(18)F]fluorodeoxyglucose ([(18)F]FDG) concentration measured by positron emission tomography (PET) to a measurement of physiological parameters. However, all the proposed models have been developed and tested mostly for brain studies. The purpose of the present study is to select the most accurate model for describing [(18)F]FDG kinetics in human skeletal muscle. The database consists of basal and hyperinsulinemic-euglycemic studies performed in normal subjects. PET data were first analyzed by an input-output modeling technique (often called spectral analysis). These results provided guidelines for developing a compartmental model. A new model with four compartments and five rate constants (5K model) emerged as the best. By accounting for plasma and extracellular and intracellular kinetics, this model allows, for the first time, PET assessment of the individual steps of [(18)F]FDG kinetics in human skeletal muscle, from plasma to extracellular space to transmembrane transport into the cell to intracellular phosphorylation. Insulin is shown to affect transport and phosphorylation but not extracellular kinetics, with the transport step becoming the main site of control. The 5K model also allows definition of the domain of validity of the classic three-compartment three- or four-rate-constant models. These models are candidates for an investigative tool to quantitatively assess insulin control on individual metabolic steps in human muscle in normal and physiopathological states.
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Affiliation(s)
- A Bertoldo
- Department of Electronics and Informatics, University of Padova, Via Gradenigo 6/A, Padua 35131, Italy
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Abstract
Understanding the in vivo functioning of endocrine-metabolic systems requires the quantitative knowledge of system parameters like production/utilization of substrales, secretion/degradation of hormones, and substrate-hormone signaling. Unfortunately, these system parameters are not directly accessible and an indirect measurement approach is needed based on a model of the system. We review first the principals of the model of system methodology focusing on compartmental and input-output modeling. Then, the model of system methodology is applied to the measurement of nonaccessible parameters/variables of the glucose system like glucose fluxes, insulin fluxes, and glucose-insulin signaling.
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Affiliation(s)
- C Cobelli
- Department of Electronics and Informatics, University of Padova, Italy
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Saccomani MP, Bonadonna RC, Bier DM, DeFronzo RA, Cobelli C. A model to measure insulin effects on glucose transport and phosphorylation in muscle: a three-tracer study. THE AMERICAN JOURNAL OF PHYSIOLOGY 1996; 270:E170-85. [PMID: 8772490 DOI: 10.1152/ajpendo.1996.270.1.e170] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
We studied five healthy subjects with perfused forearm and euglycemic clamp techniques in combination with a three-tracer (D-[12C]mannitol, not transportable; 3-O-[14C]methyl-D-glucose, transportable but not metabolizable; D-[3-3H]glucose, transportable and metabolizable) intra-arterial pulse injection to assess transmembrane transport and intracellular phosphorylation of glucose in vivo in human muscle. The washout curves of the three tracers were analyzed with a multicompartmental model. A priori identifiability analysis of the tracer model shows that the rate constants of glucose transport into and out of the cells and of glucose phosphorylation are uniquely identifiable. Tracer model parameters were estimated by a nonlinear least-squares parameter estimation technique. We then solved for the tracee model and estimated bidirectional transmembrane transport glucose fluxes, glucose intracellular phosphorylation, extracellular and intracellular volumes of glucose distribution, and extracellular and intracellular glucose concentrations. Physiological hyperinsulinemia (473 +/- 22 pM) caused 2.7-fold (63.1 +/- 7.2 vs. 23.4 +/- 6.1 mumol.min-1.kg-1, P < 0.01) and 5.1-fold (42.5 +/- 5.8 vs. 8.4 +/- 2.2 mumol.min-1.kg-1, P < 0.01) increases in transmembrane influx and intracellular phosphorylation of glucose, respectively. Extracellular distribution volume and concentration of glucose were unchanged, whereas intracellular distribution volume of glucose was increased (approximately 2-fold) and intracellular glucose concentration was almost halved by hyperinsulinemia. In summary, 1) a multicompartment model of three-tracer kinetic data can quantify transmembrane glucose fluxes and intracellular glucose phosphorylation in human muscle; and 2) physiological hyperinsulinemia stimulates both transport and phosphorylation of glucose and, in doing so, amplifies the role of glucose transport as a rate-determining step of muscle glucose uptake.
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Affiliation(s)
- M P Saccomani
- Department of Electronics and Informatics, University of Padua, Italy
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