Estimate extracellular fluid volume
For the indicator-dilution method described in Lab 2 Inulin is often used to estimate extracellular fluid volume (VECFVECF). Inulin is not metabolized in the body but inulin is excreted by the kidney at a rate of kI(t) where k is the rate of inulin loss [L/min] and I(t) is the concentration of inulin [mg/L]. The system dynamic equation from a material balance on inulin results in: dI(t)dt+kVECFI(t)=QI(t)VECFdI(t)dt+kVECFI(t)=QI(t)VECF Assume that the injection of inulin into the system can be modeled by an impulse: QI(t)=Mδ(t)QI(t)=Mδ(t) where M is the mass of inulin injected and δ(t)δ(t) is the unit impulse function. Also assume instantaneous mixing. a) Draw out a Simulink model to solve for I(t). Label the important signals in the model. b) What is the solution for I(t) with the initial condition I(0)=0? c) Sketch the solution for I(t). If you measure I(t) continuously during the experiment and know M the mass of inulin injected (but you do not know k) how can you determine the volume of extracellular fluid (VECFVECF)? Requirements: send right away ‘
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