Problem Set 5 Renal

5.1 A back of the envelope calculation of GFR

  1. Estimate GFR using a back-of-the-envelope calculation. The calculation is

GFR = cardiac output X renal fraction X plasma fraction X filtration fraction

Look up reasonable values for the four variables to parameterize this equation. Do the computation in your Google Sheet. Insert the units of GFR in the adjacent cell.

5.2 Using renal clearance to measure GFR in an indivudal

\[\begin{equation} C_s = \frac{\dot{M}_s}{P_s} \end{equation}\]

where \(C_s\) is the clearance of solute \(s\), \(M_s\) (“m dot”) is the mass of \(s\) excreted in the urine per unit time, and \(P_s\) is the plasma concentration of \(s\).

  1. What are the units of \(C_s\)? These are the units of what kind of measure (for example Force per Area are the units of a pressure)?

  2. Remember that a dot over a variable is a first derivative; here we assume that this is constant and so \(\dot{M}_s = \frac{\Delta Mass}{\Delta Time}\). What are the units of \(\dot{M}_s\)? This kind of measure is “kinda like” the kind of measure in #2. Google around to see what we call \(\dot{M}_s\).

  3. The clearance of a solute is useful in pharmacology but we can also use the concept to measure the GFR in a person. This is done using a solute \(s\) that is filtered but no amount is either 1) secreted into the nephron, or 2) is not reabsorbed from the nephron). Inulin is an example. We could give a person some inulin and then measure the urine concentration of inulin (\(U_{in}\)), the volume of urine generated per time (\(\dot{V}\)), and the plasma concentration of inulin (\(P_{in}\)) to compute the GFR

\[\begin{equation} GFR = \frac{U_{in} \dot{V}}{P_{in}} \end{equation}\]

(Note that I use \(\dot{V}\) and not \(V\) to make it crystal clear that this is a measure of the volume of urine produced per time not simply a volume).

Using this information, compute the GFR for a person in which 1) inulin was given continuously to generate a constant plasma concentration of 1.0 mg/dL. 1.6 L of urine was collected over a 10 hour period. The urinary concentration of inulin was 462 mg/L.