Bariatric surgery and T2DM improvement mechanisms: a mathematical model

Abstract

Background: Consensus exists that several bariatric surgery procedures produce a rapid improvement of glucose homeostasis in obese diabetic patients, improvement apparently uncorrelated with the degree of eventual weight loss after surgery. Several hypotheses have been suggested to account for these results: among these, the anti-incretin, the ghrelin and the lower-intestinal dumping hypotheses have been discussed in the literature. Since no clear-cut experimental results are so far available to confirm or disprove any of these hypotheses, in the present work a mathematical model of the glucose-insulin-incretin system has been built, capable of expressing these three postulated mechanisms. The model has been populated with critically evaluated parameter values from the literature, and simulations under the three scenarios have been compared.

Results: The modeling results seem to indicate that the suppression of ghrelin release is unlikely to determine major changes in short-term glucose control. The possible existence of an anti-incretin hormone would be supported if an experimental increase of GIP concentrations were evident post-surgery. Given that, on the contrary, collected evidence suggests that GIP concentrations decrease post-surgery, the lower-intestinal dumping hypothesis would seem to describe the mechanism most likely to produce the observed normalization of Type 2 Diabetes Mellitus (T2DM) after bariatric surgery.

Conclusions: The proposed model can help discriminate among competing hypotheses in a context where definitive data are not available and mechanisms are still not clear.

Figure 1

Model block diagram. State variables are represented with circles, solid arrows represent mass transfers, while dashed arrows indicate stimulations. The model is here schematically represented: the path of ingested glucose (M_i) from the stomach (S) through duodenum (D) and ileum (L), and absorption in the plasmatic compartment (G) is along the central set of compartments (bottom-down). The insulin compartment (I) is on the bottom right of the figure, while the incretins (W and U) and DPP4 (P) are represented in between glucose compartments and insulin. Finally, on the left side, anti-incretin (A) and ghrelin (H) are represented. All the compartments are linked with dashed arrows, indicating stimulation of the entry rates or of the elimination rates, showing the relationship between state variables.

Figure 2

Model simulation. Thick gray line: pre-surgery case; solid line: lower-intestinal hypothesis (LIH); dash-dot line: anti-incretin hypothesis (AIH); dashed line: ghrelin hypothesis (GH). 2.1 Stomach glucose content is unchanged in all the hypotheses. 2.2 Glucose content in the duodenum is zero in the LIH, while is unchanged in the other scenarios. 2.3 Ileum glucose content is higher and the peak is earlier, compared to the pre-surgery scenario, for the LIH. In the other hypotheses the dynamics is the same. 2.4 Plasma glucose concentration is lower in the AIH and the LIH (more markedly in the latter). The curve in the GH is unchanged compared to the pre-surgery case. 2.5 Plasma insulin concentration is higher in the AIH and the LIH (more markedly in the latter). GH is unchanged compared to the pre-surgery case. 2.6 GLP-1 concentration is markedly higher in the LIH, while is slightly higher in the AIH and unchanged in the GH. 2.7 GIP concentration increases in the AIH, decreases in the LIH, is unchanged in the GH. 2.8 Anti-incretin concentration is constant at the basal value in the LIH, zero in the AIH, unchanged in the GH 2.9 Ghrelin concentration dynamics is slightly lower in the LIH and the AIH, while for the GH ghrelin concentration is zero.