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Introduction: I N D I A

Introduction: I N D I A. Bangalore 2008 – Insulin/Glucose modelling. India, diabetes capital of the world (before China and US as No. of cases; data: WHO). India: 2000:32 mill 2020: 81 mill. Zimmet, Nature 2001. Type 2 DM: global epidemic. Prevalence depends on: Age

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Introduction: I N D I A

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  1. Introduction:I N D I A Bangalore 2008 – Insulin/Glucose modelling

  2. India, diabetes capital of the world(before China and US as No. of cases; data: WHO) India: 2000:32 mill 2020: 81 mill Zimmet, Nature 2001

  3. Type 2 DM: global epidemic Prevalence depends on: • Age • Residence(urban/rural) • Obesity • Physical activity • Ethnicity

  4. Rising Prevalence of Obesity in Urban India BMI >27 kg/m2 Gupta et al, IHJ 2002

  5. Obese people develop Diabetes • RR risk of DM in females (ref. BMI < 22) • 22-23: 3.0 • 24-25: 5.0 • > 31:40 (Colditz & al, Ann Int Med, 1995, 122; 481-6)

  6. Rising prevalence of diabetes in Southern India Ramchandran et al: Diab Care 92, Diabetol 97, Diabetol 2001

  7. so what?

  8. Diabetes and CAD risk7 year incidence of CV events (%) Haffner SM et al. N Engl J Med 1998;339:229-234.

  9. Pathophysiology of the glucose/insulin system Andrea De Gaetano CNR IASI BioMatLab – Rome Italy Bangalore 2008

  10. CNR • Consiglio Nazionale delle Ricerche (Italian National Research Council): the research organization of the Italian Government, 6000+ researchers distributed over 100+ Institutes in the Country. • Research ranging from humanities to genomics, linguistics, aerospace engineering, pure mathematics, …

  11. CNR IASI • IASI, Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti” (Institute for Systems Analysis and Informatics) in Rome: 30+ researchers, 20 administrative/technical personnel. • seven research areas • Systems and Control Theory • Mathematical Programming in Operations Research • Mathematical Modeling in Biology and Medicine • Algorithms, data structures and networks • Language and Programming theory • Information Systems and Knowledge Bases • Pathophysiology of Metabolism and Immunology

  12. CNR IASI BioMatLab • BioMathematics Lab, within the Catholic University School of Medicine (2000 bed hospital), Rome • 5 full-time lab researchers (1 biomathematician, 1 statistician, 3 engineers), clerical personnel, part-time associates. • ODE, DDE, SDE models: analytical study of behavior of solutions, numerical integration, statistical parameter estimation www.biomatematica.it

  13. Hypoglicemia • Brain works on sugar • Little sugar: hunger, irritability, confusion, hyperactivity, cold sweat, tremor (adrenergic response) • No sugar: brain death. • COUNTERREGULATION: Adrenalin (fight-or-flight), glucagon, cortisol, Growth Hormone all INCREASE blood glucose levels. • Food......

  14. …but, Hyperglycemia • Acute above renal threshold: sweet, abundant urine (Diabetes Mellitus), dehydration. • Chronic: microvascular damage in retina (blindness), kidneys (renal insufficiency), extremities; peripheral neuropathy.

  15. Insulin resistance   lack of secretion Diabetes type 1 and 2 Insulin dependent Glucose utilization (muscle) Insulin independent Glucose utilization (brain) Endogenous Glucose production (liver, kidney) insulinemia glycemia Exhogenous glucose administration pancreatic b-cell Insulin secretion Modified from A.Mari 2001

  16. Insulin • Proinsulin (86 AA) = C-Peptide (35 AA) + Insulin(51=A+B chain) • Secreted from pancreatic beta-cells (Langerhans islets) in response to: GLUCOSE, AA, neurotransmitters (AC, like after a meal), hormones (glucagon);FFA? • Increases Glycogen synthesis, inhibits Gluconeogenesis, inhibits lipases and increases FFA deposition in Adipose tissue

  17. Portal circulation

  18. Insulin resistance: operational definition Insulin resistance may be defined as inappropriately high glycemia for the insulinemia, or again as inappropriately high insulinemia for the glycemia

  19. Increasing Glycemia Disposition Index Insulin secretion Insulin sensitivity

  20. An overview of energy metabolism following diagrams ...

  21. Glycolysis

  22. glycolysis protein breakdown lipid b-oxidation DA oxidation Krebs’ Cycle

  23. Randle’s Cycle • 1963, Sir Philip Randle: cardiac and skeletal muscle shifts back and forth between CHOand fat oxidation depending onthe availability of FFA. • In vivo infusion of lipid increases fat oxidation and decreases glucose oxidation

  24. Inhibition of Lipases Fat storage Hyperinsulinemia Insulin resistance Insulin secretion Glucose Uptake Hyperglycemia (Randle) FFA TG How McDonald & KFC make you diabetic!

  25. Bariatric Surgery

  26. BPD and insulin resistance • Insulin resistance after BPD drops dramatically, well before body weight does:Using EHC, whole body glucose uptake increased from 18.18.6 to 35.5 9.9 moles/min/kgbw after an average weight loss of only 11 kg reached 3 months after BPD. A marked reduction of both plasma FFA and TG was observed together with the therapeutic lipid malabsorption (Mingrone, Castagneto et al. Diabetologia 1997). • Also in normal weight subjects with a genetic defect of LPL activity, insulin resistance and frank diabetes mellitus were reversed by lowering plasma TG through lipid malabsorption induced by BPD (Mingrone, Castagneto et al. Diabetes 1999).

  27. Models of the glucose-insulin system

  28. Why modelling the G/I system? To identify the components of insulin resistance and measure its level: • Diabetologist approach (lots of data, make a diagnosis) • Standard modeling approach (less data, try to figure out the whole system )

  29. Models • Tracer “hot” vs. “cold” models • Why cold? Our perspective is the clinical application. • TRACERS: Steele 1956 traced glucose constant infusion with approx computation of SteadyState cold inflow.

  30. eqs/hr

  31. Bolie 1961 • First attempt to understand actual time-concentration points in plasma. • Introduces plasma insulin and LGE • Problems?

  32. - p1 G- p2 I+ p3 I2 I1 Insulinemia G1 G2 Glycemia

  33. qualitative analysis reveals ... • the actual model functional form, which allows negative solutions to appear, must have something in it which goes against the physiology as we think we know it • Bolie: no matter how little glucose there is in blood, by increasing insulin we would be able to make the tissues extract as much more as we wanted, linearly with insulin levels. • Mechanism seems wrong. Better to change model.

  34. IVGTT • three days of standard composition diet (55% carbohydrate, 30% fat, 15% protein) ad libitum with at least 250g carbohydrates per day • Overnight fast, at 8:00 AM 0.33 g/kgBW IV Glucose • Contralateral IV samples at -30, -15, 0, 2, 4, 6, 8, 10, 12, 15, 20, 25, 30, 35, 40, 50, 60, 80, 100, 120, 140, 160, 180 minutes (23 pts.) • On each blood sample determine Glucose, Insulin (C-peptide).

  35. Plasma Glucose Plasma Insulin 0 10 20 30 40 50 minutes 0 10 20 30 40 50 minutes IVGTT The K+ channel opens causing depolarization Glucose increases the ATP/ADP ratio - Glycogenolysis Gluconeogenesis Ca2+ b cell Depolarization cause Ca2+ influx

  36. Bergman, Cobelli 1979/1981

  37. Sample run (IVGTT+MM)

  38. SI : derivation

  39. SI : derivation Solving Eq.2 MM for X

  40. SI • For infinite time, SI = b3/b2 • in one third to one half of studies on obese subjects SI cannot be estimated, due to insufficient variation of glucose decrement with insulin. • An IVGTT obvious for insulin resistance (high constant insulin levels) yields no estimable SI.

  41. Applications of MM • Physicians want a single test returning a single measure of insulin resistance, like M/I or SI • MM applied to diabetes, aging, hyperthyroidism, hyperparathyroidism, myotonic dystrophy, pregnancy and gynecological conditions, obesity, hypertension, cirrhosis, ethnical subpopulations, in siblings of diabetic patients, during pharmacological tests

  42. Minimal model • Whole body, cold • Can compute SI … • …de-facto standard

  43. Minimal problems • Models only IVGTT (nonautonomous) • Fitting: piecewise? • SI strictly valid at infinite time, MM “valid” for 3 hrs. • SI not estimable in many interesting cases.

  44. Structural problems Suppose Gb > b5, Then In other words, for any value b5 < Gb the system does not admit an equilibrium.

  45. Estimation problems • Two-step procedure advocated by Authors • Each step fits one arm of feedback cycle • Interpolated observed concentrations used as forcing function G I

  46. We would like: • single model, single fit of both feedback arms • positiveness, boundedness of solutions • stability WRT parameters & initial conditions • good fit, identifiability • direct physiological meaning

  47. The SDM ,

  48. The SDM insulin sensitivity index

  49. SDM characteristics • Single locally attractive equilibrium at baseline • Positive, limited solutions • Global stability guaranteed under conditions on parameters* • Physiologically limited pancreatic secretion ability • Single pass GLS estimation *Giang, Lenbury, Palumbo, Panunzi, De Gaetano, 2006-2007

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