1、Blood Glucose Regulation,BIOE 4200,Glucose Regulation Revisited,input: desired blood glucose output: actual blood glucose error: desired minus measured blood glucose disturbance: eating, fasting, etc.,controller: a and b cells actuator: glucose storing or releasing tissues plant: glucose metabolism
2、sensor: a and b cells (again),glucose tissues,a & b cells,desired glucose,actual glucose,a & b cells,glucose metabol.,eating, fasting,Insulin/Glucagon Secretion,Complex chemical reaction Not all details have been worked out Need to simplify our analysis Suppose error 0 (actual desired), then insulin
3、 will be secreted,a & b cells,error signal = desired actual (mg/dl),insulin (mg/sec),glucagon (mg/sec),Insulin/Glucagon Secretion,Attempt to model process empirically from experimental data Data shows how hormone secretion rate changes when constant glucose concentration is applied,insulin (mg/sec),
4、100 sec,actual,glucagon (mg/sec),100 sec,error,Insulin/Glucagon Secretion,Rate of insulin secretion decreases with error (increases with actual blood glucose) Rate of insulin secretion decreases as more insulin is released (chemical equilibrium drives reaction back)Rate of glucagon secretion increas
5、es with error (decreases with actual blood glucose) Rate of glucagon secretion decreases as more glucagon is released (chemical equilibrium again),Insulin/Glucagon Secretion,Can now formulate state equations x1 = insulin (mg/sec) x2 = glucagon (mg/sec) u = error (mg/dl) Note dx1/dt and dx2/dt repres
6、ent the change in hormone secretion rate Output equations are written to get states y1 = insulin (mg/sec) y2 = glucagon (mg/sec),Parameters kr and kf have units 1/sec Adjust kr and kf to get hormone secretion rate observed in laboratory,Insulin/Glucagon Diffusion,We have modeled the rate of insulin
7、and glucagon secretion at the pancreas How does this translate to insulin and glucagon concentration at target tissues? First calculate concentration of insulin and glucagon in pancreas given hormone secretion rates Then use diffusion equation to estimate hormone concentration in target tissues,horm
8、one diffusion,insulin (mg/dl),glucagon (mg/dl),insulin (mg/sec),glucagon (mg/sec),Insulin/Glucagon Diffusion,Hormone is added to the bloodstream at a rate of dm/dt (mg/sec) Blood is flowing through the body at a rate of dQ/dt (dl/sec) The concentration of hormone (mg/dl) isThis assumes that the horm
9、ones are uniformly and rapidly mixed within the entire blood supply as it passes through,Insulin/Glucagon Diffusion,This is a simple gain process (no states) Input u1 = insulin secretion rate (mg/sec) Input u2 = glucagon secretion rate (mg/sec) Output y1 = insulin concentration in pancreatic blood (
10、mg/dl) Output y2 = glucagon concentration in pancreatic blood (mg/dl),Parameter kv is inverse of blood flow (sec/dl) Obtain kv from known values Blood flow is 8 10 l/min in normal adults,Insulin/Glucagon Diffusion,Model spread of hormones between pancreas and target tissues with diffusion equationAs
11、sumes diffusion is uniform across entire volume of blood between pancreas and target tissues Assumes all target tissues in same location This models diffusion across static volume and neglects spread due to blood flow The diffusion coefficient can be increased to partially account for effects of blo
12、od flow,Insulin/Glucagon Diffusion,Input u1 = insulin concentration in pancreatic blood (mg/dl) Input u2 = glucagon concentration in pancreatic blood (mg/dl) State x1 and output y1 = insulin concentration in target tissues (mg/dl) State x2 and output y2 = glucagon concentration in target tissues (mg
13、/dl),kd = diffusion coefficient (1/sec) Determine value of kd from laboratory or clinic,Glucose Uptake/Release,Target tissues include kidney, liver, adipose tissue Can model this as separate processes in parallel Each process has two inputs - insulin and glucagon concentration in mg/dl Each process
14、has single output for glucose release rate (mg/sec) Negative output value indicates glucose uptake or excretion,target tissues,glucose (mg/sec),insulin (mg/dl),glucagon (mg/dl),Glucose Uptake/Release,Liver and adipose tissues incorporate glucose into larger molecules (glycogen and fat) as storage Ki
15、dney controls flow of glucose between blood and urine Consider liver and adipose tissues together Consider kidney separately,Liver and Adipose,glucose (mg/sec),insulin (mg/dl),glucagon (mg/dl),Kidneys,insulin (mg/dl),glucagon (mg/dl),Glucose Uptake/Release,Similar to model for secretion of insulin a
16、nd glucagon driven by glucose Complex chemical reaction that we will simplify Rate of glucose secretion decreases with insulin Rate of glucose secretion increases with glucagon Rate of glucose secretion decreases as more glucose is released (chemical equilibrium drives reaction back),Glucose Uptake/
17、Release,Input u1 = insulin concentration at target tissues (mg/dl) Input u2 = glucagon concentration at target tissues (mg/dl) State x and output y = glucose release rate (mg/sec) Note dx/dt represents the change in glucose secretion rate,Parameter kb has units 1/sec Parameter kh has units dl/sec Se
18、t parameters to match time course of glucose release,Glucose Uptake/Release,Model kidney function as a simple gain process (no states) Assumes response of glucose uptake or excretion rate changes rapidly Uptake increases with glucagon, excretion increases with insulin Output y = glucose release rate
19、 (mg/sec),Input u1 = insulin concentration at target tissues (mg/dl) Input u2 = glucagon concentration at target tissues (mg/dl) Parameter kn has units of dl/sec,Glucose Diffusion,Must translate glucose release/uptake from target tissues into blood glucose concentration Blood glucose concentration w
20、ill be measured at pancreas, so this will serve as convenient output Like we did earlier, calculate concentration of glucose at target tissues given glucose secretion rates Then use diffusion equation to estimate blood glucose concentration at pancreas,glucose diffusion,glucose (mg/dl),glucose (mg/s
21、ec),Glucose Diffusion,First convert from glucose release rate to concentration at target tissues Input u = glucose secretion rate (mg/sec) Output y = glucose concentration in blood around target tissues (mg/dl),Parameter kv is inverse of blood flow (sec/dl) Obtain kv from known values Blood flow is
22、8 10 l/min in normal adults,Glucose Diffusion,Then use diffusion equation to model spread of glucose from target tissues back to pancreas Input u = glucose concentration in target tissues (mg/dl) State x and output y = glucose concentration in pancreas (mg/dl),ke = diffusion coefficient (1/sec) Do n
23、ot assume same value for hormone diffusion Smaller molecule and different direction,Final Notes,We are now ready to assemble the individual processes and simulate the system in MATLAB Desired blood glucose is system input (constant) Disturbance input is glucose intake and metabolism Disturbance inpu
24、t will generally be negative to indicate basal glucose metabolism with positive periods to indicate glucose intake Model feedback as unity gain process Assumes measured glucose equals glucose concentration in pancreas,Model Summary,desired blood glucose,actual blood glucose,hormone secretion (6, 9, 11),glucose diffusion (18, 19),glucose intake and metabolism (20),liver and adipose (15),kidneys (16),Slide numbers with relevant state equations are indicated for each process,
