Define the logarithmic mean c of the input and output

Question

Question

Consider the steady-state solution to the liver model

(i) Define the logarithmic mean c' of the input and output substrate concentrations c_i and c_o as

Show that the total rate of removal of substrate V satisfies the Michaelis-Menton reaction rate law corresponding to a substrate concentration c' i.e. show that

(ii) Suppose the enzyme distribution is constant along the length of each sinusoid. Show that the concentration profile c(x) is a decreasing, concave upward function of the distance x from the beginning of the sinusoid.

In your answer you may quote without proof any equation from the notes, but please state the equation number.