A computer model simulating human glucose absorption and metabolism in health and metabolic disease states

Abstract

A computer model designed to simulate integrated glucose-dependent changes in splanchnic blood flow with small intestinal glucose absorption, hormonal and incretin circulation and hepatic and systemic metabolism in health and metabolic diseases e.g. non-alcoholic fatty liver disease, (NAFLD), non-alcoholic steatohepatitis, (NASH) and type 2 diabetes mellitus, (T2DM) demonstrates how when glucagon-like peptide-1, (GLP-1) is synchronously released into the splanchnic blood during intestinal glucose absorption, it stimulates superior mesenteric arterial (SMA) blood flow and by increasing passive intestinal glucose absorption, harmonizes absorption with its distribution and metabolism. GLP-1 also synergises insulin-dependent net hepatic glucose uptake (NHGU). When GLP-1 secretion is deficient post-prandial SMA blood flow is not increased and as NHGU is also reduced, hyperglycaemia follows. Portal venous glucose concentration is also raised, thereby retarding the passive component of intestinal glucose absorption. Increased pre-hepatic sinusoidal resistance combined with portal hypertension leading to opening of intrahepatic portosystemic collateral vessels are NASH-related mechanical defects that alter the balance between splanchnic and systemic distributions of glucose, hormones and incretins.The model reveals the latent contribution of portosystemic shunting in development of metabolic disease. This diverts splanchnic blood content away from the hepatic sinuses to the systemic circulation, particularly during the glucose absorptive phase of digestion, resulting in inappropriate increases in insulin-dependent systemic glucose metabolism. This hastens onset of hypoglycaemia and thence hyperglucagonaemia. The model reveals that low rates of GLP-1 secretion, frequently associated with T2DM and NASH, may be also be caused by splanchnic hypoglycaemia, rather than to intrinsic loss of incretin secretory capacity. These findings may have therapeutic implications on GLP-1 agonist or glucagon antagonist usage.

Keywords: GLP-1; Glucagon; Hyperglucagonaemia.; Hyperinsulinaemia; Insulin; Non-alcoholic steatohepatitis; Portosystemic shunting; Simulation of human intestinal glucose absorption; Superior mesenteric arterial blood flow; Type 2 diabetes.

Conflict of interest statement

Competing interests: No competing interests were disclosed.

Figures

Figure 1.. Diagram outlining splanchnic and systemic blood flows.

Figure 2.. Effects of varying the glucose sensitivity of GLP-1 secretion on splanchnic blood flows, volumes and pressure following 50 G glucose delivery by duodenal gavage at 100min.

All the graphs are contoured surface plots in which thex axis is the time coordinate, they axis is the GLP-1 sensitivity to glucose – this generates GLP-1at a rate proportional to the sensitivity and splanchnic blood glucose concentration, (Figure 1B GLP-1equations 1). With low GLP-1secretion the changes in glucose sensitive blood flow are reduced. Panel A The effects of GLP-1sensitivity and time on SMA flow. There GLP-1dependent increase in SMA flow response to glucose gavage peaks 3–6 min after glucose gavage and is sustained for 15–20min (K ½GLP-1 sens. = 12; maximal flow rate 1500 ml min -1; maximal flow rate 1500 ml min -1). Panel B Portal venous flow ml min -1 versus GLP-1sensitivity and time. The graph has a similar GLP-1sensitivity and time course to SMA in (Panel A). PV flow rises hyperbolically with GLP-1sensitivityK ½GLP-1 sens. = 12; maximal flow rate 1100 ml min -1. Panel C, the effects of GLP-1sensitivity and time after gavage on hepatic artery HA flow. The high GLP-1sensitivity is shown at front of they scale. HA flows fall simultaneously with the rise in PV flow. This is due to the decreased aortic pressure and volume (Panel D) resulting from the enlargement of the splanchnic volume (Panel E). Panel F Effects of glucose sensitivity GLP-1secretion on portal venous PV pressure changes after glucose gavage. The rise in pressure mirrors the changes in PV flow (Panel B) and SMA flow (Panel A), (peak PV pressure is approximately 8mm Hg; K ½GLP-1 sens. = 15).

Figure 3.. Effects of varying glucose sensitivity of GLP-1secretion on glucose flows and metabolism following 50 G glucose duodenal gavage at 100min.

Panel A The rise and fall of PV glucose flow following gavage, (peak flow rate 18 mmole min -1 at 2–5 min after gavage, K ½GLP-1 sens. = 12). Panel B, HA glucose flow does not fully reciprocate PV glucose flow since raised GLP-1only reduces HA glucose to a small extent (14.3 to 7–8 mmole min -1 between 4–6 min after gavage). Panel C, HV glucose flow is the sum of PV and HA flows shown in (Panels A andB). Panel D The rise off unidirectional intestinal glucose permeability following gavage. Intestinal glucose permeability varies transiently with the transluminal glucose concentration gradient. This rises with the increase in luminal glucose concentration and falls from the peak when glucose gavage ceases and luminal glucose concentration falls and splanchnic capillary glucose concentration rises due to glucose absorption (see Figure 4Panel G) Raising GLP-1glucose sensitivity increases the peak glucose permeability by 20%. GLP-1increases peak flow glucose permeability from the baseline at the start of gavage compared with maximal glucose gradients by five-fold. Panels Ei,Eii Mirror views of the effects of GLP-1on hepatic glucose metabolism following gavage. Negative values signify negative net glucose uptake NHGU i.e. positive glucose outflow resulting from glucagon stimulation and suppression of GLP-1and insulin signalling to liver. High GLP-11 sensitivities increase NHGU during times of peak PV glucose flow, however later times, high GLP-1sensitivities leads indirectly to very high rates of glucagon-dependent gluconeogenesisK ½GLP-1 sens. = 18. Panel F Peripheral glucose metabolism increases only slightly with raised systemic glucose concentration following glucose absorption and falls when high rates of glucose sensitive GLP-1secretion drive metabolism to induce hypoglycaemia. Panel G Insulin-dependent glucose metabolism is extremely sensitive to glucose sensitive GLP-1secretion. The maximal rate is > 100-fold higher than fasting rates. With low GLP-1 net hepatic glucose output is reduced and hepatic uptake reduced during the absorption phase 100–145 min. Low GLP-11 secretion reduces peripheral insulin sensitive glucose uptake.

Figure 4.. Effects of varying the GLP-1glucose sensitivity of secretion on systemic and splanchnic glucose, hormone and GLP-1concentrations post duodenal glucose gavage.

Panel A–D systemic concentrations of glucagon, insulin, glucose and GLP-1.Panels E–H splanchnic concentrations of glucagon, insulin, glucose and GLP-1respectively. Note that the splanchnic concentrations are generally nearly twice those in the systemic circulation. Peak SM capillary glucose concentration decreases as GLP-1 secretion rate increases, (GLP-1glucose sensitivity range 0–50 K ½GLP-1=7.2 required to give half maximal splanchnic glucose concentration maximum splanchnic glucose ranging from 45 to 22 mM as GLP-1is increased). After the glucose absorptive phase glucagon levels rapidly recover with high rates of GLP-1secretion in both splanchnic blood (K ½ GLP-1sec = 10) and in systemic blood (K ½ GLP-1sec = 5). With high rates of GLP-1-1 secretion glucagon remains high in both splanchnic and systemic blood until fasting is relieved. Panel B andF Insulin concentration in SM-cap is 2.5-fold higher than in systemic blood. Splanchnic insulin is nearly 10x higher with low GLP-1 than with high rates of GLP-1secretion. Panels C andG Splanchnic glucose exceeds systemic glucose by 1-5-2 fold during glucose absorption but falls below that of systemic glucose particularly with high rates of GLP-1secretion during fasting and in the later post absorptive phases of digestion.Fasting glucose in systemic blood with high GLP-1 glucose 5.6 mM; with low GLP-1, glucose 9.6mM; splanchnic blood glucose with high GLP-14.4 mM and with low GLP-1 -1 glucose 3.6 mM. In contrast during the absorptive phage splanchnic glucose with low rates of GLP-1secretion glucose 47.5 mM exceeds systemic glucose 19.5 mM this is caused by the lower rates of SMA flow than with higher rates of GLP-1secretion. Panels D and H Splanchnic GLP-1always exceeds systemic glucose however with high rates of GLP-1secretion due to high glucose sensitivity,the peak splanchnic GLP-126 pM observed during glucose absorption is similar to systemic 19.7 pm whereas during fasting systemic GLP-12–3pm and splanchnic GLP-1 20–22 pM.

Figure 5.. Effects of varying paracellular glucose permeability P gl (0–0.15 μm s -1) on blood flow and metabolism.

All the panels show 3D surface plots of the effects of two variables GLP-1glucose sensitivity (2–50) that controls GLP-1secretion rate with changes in splanchnic glucose concentration (GLP-1equations 1) and intestinal paracellular glucose permeability, P gl (0–0.15 μm s -1). The interaction between these variables is shown as the coefficientc. All the panels show paired effects contrasting the interactions at peak splanchnic glucose flow (feed) with those during when splanchnic glucose is at a minimal value (fastpanels D andE, the feeding and fasting values are determined at maximal and minimal systemic glucose concentrations. Panel 5A SMA flow after feeding increases as a linear function of GLP-1and as a hyperbolic function of P gl; K ½max = 0.02 μm s -1 and the interaction coefficientc for = 4.1, indicating a strong positive interaction between P gl and GLP-1secretion, as can be seen from the upward elevation of the surface towards higher values of both independent variables. Panel 5B During fasting, in contrast to effects seen with feeding inpanel 5A there is no effect of altering P gl although SMA increases with GLP-1secretion, (coefficient c = 0) when intestinal glucose absorption is absent. Panel 5C There is a synergistic response of portal blood flow and glucose flow as a result of the interaction between P gl and GLP-1secretion which leads to both increased splanchnic blood flow and glucose concentrationsc= 2.74. With P gl intestinal paracellular permeability = zero, increased SMA in response to raised GLP-1is almost without effect on portal glucose flow rates. Increasing P gl from 0 to 0.16 μm s -1 with a constant rate of GLP-1secretion (= 50) and low pre-sinusoidal resistance (0.005 mm Hg.s ml -1), results in a hyperbolic increase in portal venous glucose flow from a base of 2.45 mmole min -1 to a maximal flow of 22.3± 1.37 mmole min -1, the P gl giving half maximal increase in glucose flow is 0.024± 0.007 µm s -1. Panels F andG As with SMA flow seePanels A andB portal vein flows increase synergistically with increases in GLP-1and P gl during when glucose is present in the splanchnic circulation c= 4.15, but during fasting Pgl effects are absentc= 0. Figure 5H There is a relatively high degree of negative interaction between the rate of GLP-1secretion and P gl on splanchnic capillary glucose concentration, c= -4.58 due to both dilution of the intestinal glucose absorbate by the higher capillary blood flow rate, however as already shown glucose flow rate there is a positive interaction between P gl with GLP-1-1 on PV glucose flow rates c = 1.21. When glucose paracellular permeability is high there the glucose uptake from intestine to the splanchnic blood is increased by high rates of capillary flow induced by GLP-1secretion. This due to the raised glucose gradient between the intestinal lumen and the submucosal capillaries.

Figure 6.. Effects of varying paracellular glucose permeability and GLP-1secretion on metabolism.

Panel A, Unidirectional intestinal permeability decreases as SM capillary glucose concentrations increase ( Figure 3D). Unidirectional glucose permeability increases as a hyperbolic function of increasing paracellular permeability P gl (K ½ = 0.045 μm s -1 and GLP-1glucose sensitivity K ½ = 5.5, c = 1.69). The positive interaction between paracellular permeability and glucose sensitive SMA flow indicates that raising capillary flow increases unidirectional permeability only when the paracellular leakage is fast enough to increase splanchnic capillary glucose concentration enough to retard permeability substantially if not cleared by splanchnic blood flow. (Panels 6B, 6C and6D). During feeding increased rates of GLP-1secretion and intestinal glucose permeability P gl synergistically increase NHGU (c = 6.08), and peripheral glucose metabolism (c =14.6). (Figure 6D), Insulin-independent metabolism (c= -13.55) decreases from the more intense competition for systemic glucose from insulin dependent tissues. (Panel 6E) Systemic insulin and (Panel 6H) GLP-1concentrations also increase with increasing P gl (K ½ ≈ 0.03 µm s -1).

Figure 7.. Effects of varying portosystemic shunt resistance on blood flow and glucose flow.

Panel 7A Hepatic shunt blood flow increases as PSS resistance diminishes giving half maximal portal venous glucose flow, (coefficients V = 600 ml min -1; K ½= 0.025 mm Hg.s ml -1 is maximum 3–4 min after gavage). A slower but more prolonged rise occurs 20–30 min after gavage. Panel 7B Portosystemic glucose flow 3–4 min after glucose gavage. Glucose flow increases with decreasing PSS resistance (K ½ = 0.05 mm Hg.s ml -1). Panel 7C PV flow decreases from its peak at a slower rate t ½ ≈ 7.5 min to reach a plateau phase. During this plateau phase PV flow also decreases as a hyperbolic function of PSS resistance (K ½ = 0.028 Hg.s ml -1) Panel 7D With zero PSS flow PV glucose flow has peak of approximately 20 mmole min -1 PV glucose flow decreases (t ½ = 1.2 min, with zero shunt flow and t ½ = 0.45 min with high shunt flows). Panels 7E and7F PSS resistance change has negligible effects on either SM arterial blood flow or HA blood flow. Panel 7G Increasing PSS decreases peak portal venous pressure(K ½ = 0.05 Hg.s ml -1 occurs at 5-5 min after the beginning of gavage, the t ½ = 5–6 min of peak portal pressure decline). Panel 7H HV flow is maximal during peak glucose absorption 1500–1800 ml min -1 5 min after the start of gavage. HV flow decreases as a hyperbolic function of PSS resistance(K ½ = 0.03 Hg.s ml -1). Panel 7I There is a strong interaction between PSS and presinusoidal resistance on hepatic shunt flow(c = 2425); when GLP-1secretion rates are high reducing the PSS resistance below 0.027 Hg.s ml -1 reduces peak PV pressure by 50%.

Figure 8.. Portosystemic shunting effects on insulin, glucagon and GLP-1shunt flows and metabolism.

Panel 8A GLP-1flow increase as hyperbolic function of PSS (the shunt resistance giving half maximal GLP-1flow is 0.027 Hg. s ml -1, Peak flow 3 mins after the start of duodenal glucose gavage and decreases very rapidly (t ½ ≈ 3 min). Panel 8B Insulin flow via the PSS peaks 2.5–3 min following the start of glucose gavage.The shunt resistance giving half maximal peak insulin flow (K ½ = 0.063 Hg.s ml -1). A second wave of insulin flow via the shunt is seen with low shunt resistance (K ½ = 0.03 Hg.s ml -1). Panel 8C When shunt resistance is ≤ 0.015 Hg.s ml -1 glucagon flows via the PSS in two waves, The first wave peaks (1–2 min after gavage, flow rate of 20 fmoles min -1 and t ½ = 1.5 min decrease). The second glucagon wave (peaks at 38 fmoles min -1, 8–10 min after gavage shunt resistance is K ½ ≈ 0.055 Hg.s ml -1 (decay t ½ = 10–15min). Panel 8D Opening the PSS resistance < 0.05 Hg.s ml -1 curtails the effect of GLP-1on hepatic glucose metabolism. With high shunt flows of glucose gavage net hepatic glucose uptake, NHGU, switches 6 minutes after the start glucagon-activated gluconeogenesis. Panel 8E Both hepatic (panel 8D) and peripheral insulin-dependent (Panel 8F) glucose consumption peaks are reduced at high rates of GLP-1secretion and a large PSS (K ½ = 0.02 Hg.s.ml -1). The peaks occur earlier and end sooner. Panel 8F Insulin independent metabolic rate is stable over a wide range of PSS but is decreased with open PSS resistance < 0.02 Hg.s ml -1 simultaneously with the decrease in peripheral glucose concentration. Panel 8G Unidirectional intestinal glucose permeability increase after gavage as the glucose gradient between intestinal lumen and splanchnic capillaries increases with luminal glucose concentration, it also increases slightly 19% with increased PSS due to decreased splanchnic glucose concentration, ( Figure 10A).

Figure 9.. Effects of GLP-1secretion on the time course of insulin secretion.

Panel 9A. Insulin secretion rates are increased during the glucose absorptive phase of metabolism. This increase is stimulated directly be systemic glucose concentration and by the glucose sensitivity of GLP-1secretion. During fasting insulin secretion rates are directly proportional to GLP-1glucose sensitivity however during peak glucose absorption insulin secretion rates vary to a much lesser extent as with low rates of GLP-1systemic glucose is raised and therefore compensates for lack of glucose sensitivity of GLP-1secretion. 1 (K ½GLP-1gluc sens = 0.80, V max= 0.41 nmol s -1) Panel 9B Insulin secretion rates with PSS (K ½GLP-1gluc sens = 0.72, Vmax0.375 nmol s -1) Panel 9C GLP-1secretion is very similar to insulin, GLP-1secretion increases rapidly during the glucose absorptive phase of metabolism and tails of splanchnic glucose is diminishes during the course of metabolism. During fasting GLP-1secretion is hyperbolically dependent on glucose as glucose sensitivity of GLP-1K ½ = 4.4 Vmax 12.3 12 pmol s -1) secreting cells in splanchnic blood is concentrations are lower with high rates of GLP-1secretion ( Figure 4G). Panel 9DGLP-1secretion with PSS glucose sensitivity of GLP-1K ½ = 4.6 Vmax10.3 pmol s -1 Shunting reduces insulin secretion by approximately 20%. Panel 9FShunting increases glucagon secretion rates. The increase is a hyperbolic function of GLP-1 glucose sensitivity(K ½ = 6.7 Vmax = 0.12 nmol s -1). During glucose absorption glucagon secretion rates decrease as systemic glucose increases. The decrease is negligible with low rates of GLP-1secretion due to the slow rise in systemic glucose.

Figure 10.

Panels 10A and 10E Portosystemic shunting has a relatively small effect on systemic and splanchnic GLP-1concentrations. Figure 10 Panels 10A and10E Portosystemic shunting has a relatively small effect on systemic and splanchnic GLP-1concentrations. Panel 10B and10F Peak systemic glucose decreases as PSS increases (PSS resistance K ½= 0.05 Hg.s.ml -1). Panels 10C and10G, Splanchnic insulin is decreased by shunting 2–7 min after duodenal gavage(PSS resistance K ½= 0.145 Hg.s.ml -1). The decrease in splanchnic insulin coincides with a shunting-dependent increase in systemic and splanchnic glucagon (Panels 10D,10H). Portosystemic shunts increase fasting systemic insulin concentrationsPSS resistance K ½= 0.06 Hg.s.ml -1). Panels 10D and10H. Systemic and splanchnic glucagon concentrations have the relatively the largest responses to portosystemic shunt opening. As well as an early peak at 10 min after gavage(PSS resistance K ½= 0.06 Hg.s.ml -1), a second later sustained rise in both systemic and splanchnic glucagon(PSS resistance K ½= 0.075 Hg.s.ml -1). Panel 10F Fasting glucagon secretion rates with shunting increase hyperbolically with GLP-1glucose sensitivityK ½ = 9.5 Vmax 0.19 nmol s -1).

Figure 11.. Effects of shunting on normalized systemic insulin/GLP-1-dependent metabolism/glucose ratios.

Panel 11A Opening the PSS resistance from 40 to 0.005 mm Hg.s ml -1, increases the normalized systemic insulin: glucose ratio to 2.1 in the fasting state(K ½ = 0.03 mm Hg.s ml -1) The normalized systemic insulin: glucose ratio increases as a hyperbolic function to maximum of 5.4 as shunt resistance falls (K ½ = 0.03–0.04 mm Hg.s ml -1). Two peaks in the systemic insulin: glucose ratio (Figure 11A) The second smaller, longer lasting rise in the insulin/glucose ratio coincides with the second wave in hepatic gluconeogenesis/glucose ratio ( Figure 12E) (K ½ = 0.06 mm Hg.s ml -1) and peripheral insulin-dependent metabolism (K ½ = 0.015 mm Hg.s ml -1) (Figure 11D). Panel 11B Opening the PSS increases GLP-1/glucose ratio as a hyperbolic function of shunt opening (K ½ = 0.015 mm Hg.s ml -1) the ratio peaks 5 min after gavage, and thereafter decreases (t½ =2.5–3 min from the peak maximum). Panel 11C Opening the PSS increases glucagon/glucose ratio as a hyperbolic function of shunt opening (K ½ = 0.015 mm Hg.s ml -1) the ratio peaks 5.5 min after gavage, and thereafter decreases (t½ =3 min after the peak maximum). With a wide open shunt the glucagon/glucose ratio increases continuously during fasting owing to glucagon stimulated gluconeogenesis. Panel 11D, GLP-1 and insulin interactively stimulate systemic glucose metabolism in insulin-sensitive tissues. Plots of the product of the normalized GLP-1. Insulin product/glucose peak 4.5 min after gavage. Shunting raises the GLP-1.insulin product 30-fold increase above that without shunting. The enhancement remains during the later digestive periods. Panel 11E The normalized product of GLP-1*insulin in systemic blood increases as a hyperbolic function of PSS resistance. (K ½ = 0.01 mm Hg.s ml -1to amaximum 30-fold above the level with without shunting 7 min after gavage; t ½ = 2.5–3 min from the peak maximum a residual increase remains throughout the later digestive phase. (K ½= 0.08 mm Hg.s ml -1).

Figure 12.. Effects of shunting on normalized splanchnic insulin/GLP-1-dependent metabolism/glucose ratios.

Panel 12A Opening the PSS resistance from 40 to 0.005 mm Hg.s ml -1, increases the normalized splanchnic insulin: glucose ratio in the fasting state to 2.1(K ½ = 0.03 mm Hg.s ml -1) Two peaks in the splanchnic insulin/glucose ratio (Figure 12panel A). The second smaller, longer lasting rise in the insulin/glucose ratio coincides with the second wave in hepatic gluconeogenesis/glucose ratio (Figure 12panel E) (K ½ = 0.06 mm Hg.s ml -1) and peripheral insulin-dependent metabolism (K ½ = 0.015 mm Hg.s ml -1) ( Figure 11 panel D). Panel 12B Opening the PSS increases splanchnic glucagon/glucose ratio as a steep hyperbolic function of shunt opening (K ½ = 0.01 mm Hg.s ml -1) the ratio peaks 8 min after gavage, and thereafter decreases (t½ =2.5 min after the peak maximum). Panel 12C Opening the PSS increases splanchnic GLP-1/glucose ratio as a hyperbolic function of shunt opening (K ½ = 0.015 mm Hg.s ml -1) the ratio peaks 6 min after gavage, and thereafter decreases (t½ =2.5–3 min from the peak maximum). Panel 12D The normalized product of GLP-1*insulin in splanchnic blood increases as a hyperbolic function of PSS resistance. (K ½ = 0.05 mm Hg.s ml -1,peak maximum is 7 min after gavage; t ½ = 2.5–3 min from the peak maximum) The shunting dependent increase in splanchnic blood peaks approximately 5× higher and a residual increase remains throughout the later digestive phase. (K ½= 0.08 mm Hg.s ml -1). Panel 12E The ratio of hepatic metabolism/splanchnic glucose decreases falls dramatically during the early phase of glucose absorption when the PSS is opened (K ½ = 0.015 mm Hg.s ml -1) peaking 10 min after starting gavage.

Figure 13.

Panels 1–D The time courses of normalized shunt flow of glucose, insulin, glucagon, GLP-1 and peripheral insulin sensitive metabolism, hepatic metabolism. Panel C normalized shunt/control insulin, GLP-1 and glucagon secretion rates. Panel E Shunt/control ratio of glucose, insulin, GLP-1 and glucagon in splanchnic blood and hepatic gluconeogenesis rates (positive).

Figure 14.. Ratios of insulin/glucose; GLP-1/glucose; glucagon/glucose disease/control (primary data from (Junker et al. 2016).

Panel A Normalized ratios of systemic insulin/glucose; glucagon/glucose and GLP-1/glucose in patients with NAFLD. Panel B Normalized ratios insulin/glucose, glucagon/glucose and GLP-1/glucose in patients with T2DM having no liver disease/control data.