In the past, Type-1 diabetes patients had to inject

Chapter 3, Problem 22

(choose chapter or problem)

In the past, Type-1 diabetes patients had to inject themselves with insulin three to four times a day. New delayed-action insulin analogues such as insulin Glargine require a single daily dose. A similar procedure to the one described in the Pharmaceutical Drug Absorption case study of this chapter is used to find a model for the concentration-time evolution of plasma for insulin Glargine. For a specific patient, state-space model matrices are given by (Tarín, 2007)

\(\begin{aligned} & \mathbf{A}=\left[\begin{array}{ccc} -0.435 & 0.209 & 0.02 \\ 0.268 & -0.394 & 0 \\ 0.227 & 0 & -0.02 \end{array}\right] ; \quad \mathbf{B}=\left[\begin{array}{l} 1 \\ 0 \\ 0 \end{array}\right] ; \\ & \mathbf{C}=\left[\begin{array}{lll} 0.0003 & 0 & 0 \end{array}\right] ; \quad \mathbf{D}=0 \end{aligned}\)

where the state vector is given by

\(\mathbf{x}=\left[\begin{array}{l} x_1 \\ x_2 \\ x_3 \end{array}\right]\) .

The state variables are

\(x_1=\) insulin amount in plasma compartment

\(x_2=\) insulin amount in liver compartment

\(x_3=\) insulin amount in interstitial (in body tissue) compartment

The system’s input is u= external insulin flow.

The system’s output is y= plasma insulin concentration.

(a) Find the system’s transfer function.

(b) Verify your result using MATLAB.