Explanation of transfer function from electrical design

Question

I am a bio-engineer student so not that profound with electric cirquits. But I understand how transfer function works. My problem is the following: I have found a source from literature that derives a transfer function from a given electrical circuit. The electrical circuit is the one I've attached as an image. It is actually a biological circuit based on a model of the mechanics in the lungs.

Now the transfer function from the paper is given by:

It is possible that the above transfer function is incorrect (Rst does appear in the transfer function and not in the diagram, which is weird). User rioaxe pointed out that the transfer function above is actually the impedance of the circuit, that is Pressure (P) / Flow (F) = Vin / Iin, which is very logical because the equation relating pressure to flow is: P = Raw * F, with Raw the airway resistance. Equivalent to Vin = R * Iin in electrical circuits.

The problem that I face now is how to derive the transfer function Vin / Iin from what rioaxe has given as answer. I never worked with electrical circuits like that before (in series + parallel).

If someone can help me derive the TF this will be very kind. And thanks for who already tried to help. Cheers

Here is a second picture of the (viscoelastic) model:

Answer 1

In the model, it is not Flow in on the left side and Pressure out on the right side. But rather:

^{simulate this circuit – Schematic created using CircuitLab}

$$ Transfer\ Function = \frac{Pressure}{Flow} = \frac{Vin}{Iin} = impedance\ of\ the\ circuit $$

To analyze the circuit in Laplace s domain, substitute impedance of capacitor with 1/sC (impedance of resistor is simply R).