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Define the logarithmic mean c of the input and output

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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

721_Define the logarithmic mean.png

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

1955_Define the logarithmic mean1.png

(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.

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