Homework Assignment

The following Assignment is due Tuesday, October 13th:

1.  Problem 5.7.
2.  Do the calculations shown in Example 5.7 (page 151) using Matlab. Compute the impulse, step, and frequency domain response of the system.  The model equations are given on pages 86-87, and assume the following parameter values:

• V_1 = 0.07 L/kg (blood volume)
• V_2 = 0.40 L/kg (intracellular fluid volume)
• q_0 = q = 0.0015 L/min/kg (outflow)
• c_0 = 1.0 (normalized input concentration)

3.  For the system in problem 2, compute the steady state value of u necessary to obtain C_2 = 1 for the second compartment.
4.  Suppose you can apply an initial impulse and a step function input the system of Example 5.7. These correspond to an initial dose followed by a steady state input to the compartment model. What should be the maximum size of these inputs so that the final value of C_2 is 1.0, and the concentration never goes over 2.0?