Solution, Solutions

Okay; one of the first things you will learn about me as an instructor is that I often answer my own questions.  This is often true but not always.  Don't give me any grief if I don't occasionally provide the answers and you have to check with your classmates or the confirm your work with the texts.  I do answer questions in class at any time on any assignment.

Okay back to our problem.

There really are two solutions.  The first, as we often must do in medicine, we have to make some assumptions.  The assumption we are going to make is that the patients' compliance is linear.  This is seldom true but often true enough for the range of ventilating volumes and pressures we are using with most patients.  Like all assumptions you need to be cognoscente of making it and realize that it may not apply or alter your observations at the bedside.

Okay with that said, we now assume a constant lung compliance for the patient.  The present "C" (compliance) of the patient is 25ml/cmH2O.  Now we know the equation for calculating is; C= volume / pressure.  Using this equation we can solve for the change in pressures with the increased volume.  I like to set this up as a proportion;

present C 25 = Change in volume 800ml  /  unknown new pressure in lungs X

Cross multiply to solve for the unknown pressures X; so now

unknown pressure X = 800ml / 25 ml/cmH2O

X = 32 cmH2O

So this pressure, 32cmH2O is the expected increase in pressure that would result from increasing the lung volume from FRC (functional residual capacity) with an additional 800ml.  You can think of it as inflating a stiff balloon with 800ml of volume.

Now let us consider the second answer, what if the lung compliance is not linear?  How would this affect our estimation?  It is possibly a valid answer to say that the exact pressures could not be calculated without measuring the dynamic compliance of the lungs.  We will discuss and demonstrate this in class.  So if the actual lung compliance of the patient at the higher volume is lower, then our calculated pressure would be low.  The actual pressures in the patients' lungs would be higher than calculated.

If the actual patients' lung compliance is higher at the larger volume, and this can be true, then our calculated pressures would be high.  The actual lung pressures would be lower than our calculated value.

Comments or questions let me know below.

Added Later: Graph of idealized lung compliance, lower zone = low compliance with alveolar collapse, middle zone =best compliance with open lung, upper zone = low compliance due to alveoli over inflation.

Al