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Table 4 Other assumed parameters

From: A mathematical model of brain glucose homeostasis

Symbol Description Assumed value
k 1 Positive parameter concerning contribution of hepatic glucose state to hepatic glucose production in Equation 10 1.0
k 2 Positive parameter concerning contribution of hepatic insulin state to hepatic glucose production in Equation 10 0.005
k 3 Positive parameter concerning contribution of hepatic glucagon state to hepatic glucose production in Equation 10 0.25
k 4 Positive parameter concerning contribution of local glucose state to glucose utilization by peripheral tissue in Equation 11 0.001
k 5 Positive parameter concerning contribution of local insulin state to glucose utilization by peripheral tissue in Equation 11 0.001
k 6 Positive parameter concerning contribution of local glucose state to insulin secretion within the pancreatic mass compartment in Equation 18 1.0
k 7 Positive parameter concerning contribution of local glucagon state to insulin secretion within the pancreatic mass compartment in Equation 18 0.01
k 8 Positive parameter concerning contribution of local insulin state to insulin removal from insulin-sensitive tissue in Equation 19 0.03
k 9 Positive parameter concerning contribution of local glucose state to glucagon secretion within the pancreatic mass compartment in Equation 27 0.01
k 10 Positive parameter concerning contribution of local insulin state to glucagon secretion within the pancreatic mass compartment in Equation 27 0.1
Maximum value of glucose concentration in the brain blood compartment at the steady state in equations 4 and 21 1.0
Minimum value of glucose concentration in the brain blood compartment at the steady state in equations 4 and 21 0.8
κ G Gain in Equation 5 0.3
κ I Gain in Equation 22 0.1
τ G Time constant in Equation 5 1200
τ I Time constant in Equation 22 1200
a cg Positive parameter concerning contribution of central glucose state to the controlled error in Equation 30 4.0
a ci Positive parameter concerning contribution of central insulin state to the controlled error in Equation 30 0.004
a pg Positive parameter concerning contribution of peripheral glucose state to the controlled error in Equation 30 0.02
k γ Positive parameter concerning signal regulating hepatic glucose production in Equation 31 0.0001
k β Negative parameter concerning signal regulating insulin secretion in Equation 31 -0.1
k α Positive parameter concerning signal regulating glucagon secretion in Equation 31 100.0