Glucose Insuline Regulation

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● ● Glucose-Insuline Regulation There is a physiological control system in charge of the regulation of glucose concentration in the plasmatic compartment, to keep glicemia levels within the normal range and avoid ipoglicemia or iperglicemia. The amount of glucose in inside the body ( x ) is regulated by 3 main mechanisms: the RENAL LOSS, which is active only when the glucose level is above a certain value (theta) the TISSUE UTILIZATION, which is divided in two rates one insulin ( y ) dependent (depending also on the cell’s response to insulin, v) ● and one independent from it On the other hand, the insuline production depends on the glucose concentration and it is produced at a certain rate, but in the meantime is also destructed proportionally to its amount (alpha), furthermore it is active only when glucose exceeds a certain threshold: GLUCOSE- INSULINEDYNAMICMODEL ⊥= plasmaticoglncosecapacitance Cadj= Ut)- ti- vxy ✗<e CI= plasmaticiinsulinacapacitava{Ult)- Ix- vxy- µ(x-0)×>0 ✗= plasmatiglncoseconcentrazioni Y= plasmatiinsulinaconcentratori ✗<0Gdi= { - ✗y dt _ ay+plx- ¢)×>0 thatMealsthatthelevelofglncose 1. EQUILIBRIUM@Constant/NpviUlt)= Q, → {×")>× isalonetheminimumthresholdforinsulina✗(t)-Y Production,soit isenouglehighto produceinsulina,butnottotheextent 0= Ql- Xx- VXY ✗to thattheRENALlossisactivated ]soif ✗€(¢;f)0= Qe- ax- vxy- µ(x-0) ×>e 0= - xy ✗E { Q= IX+VXY (o. . ,.gg, ×,, y, qq.gg a. LINEARIZATIONAROUNDtheWORKINGPOINT(X,Y) assuming✗c-(0,0) Ult)= Q,+SUA) }ma Cadè= Qi- XIX+Sx)- v(✗+Sx)(Y+Sy)+SUA) { ✗A)= ✗+Sx Ylt)= Y+Sy CIOÈ= - ✗(Ytdy)+p(✗+Sx-0) 1 a.E:/= - a-VI E-'È!;" ⊥Silt)= asxlt)+Bsylt)+Csult) (☒it) {G.Sjlt)= Dsyit)+Esxct) ←È!- "☒ F-- ¥-1, +p [= 1 p3.TRANSFERFUNCTIONS@WP (g.s. SXCS)= - (✗+VY)SXCS)- VX (gg, +a)S✗(s)+SUIS) )⊥" °" """= ' ""+"")""' "×" """+&""…