RENAL CLEARANCE PROBLEMS

Dr. Harley Schmedlap, Jr., noted physiologist and former 422 student, has returned to the lab to brush up on his renal physiology.  While at the surgical table, he has taken the following data from his long time associate, Ralphie the rat.

A.     After injecting Ralphie (i.v.) with 10 mg of a very high molecular weight (>500,000) dextran, Harley has drawn venous blood samples and measured the following plasma concentrations at the times indicated:

             at 1 minute:           2.0 mg/ml of plasma
             at 2 minutes:         1.0 mg/ml of plasma
             at 5 minutes:         0.2 mg/ml of plasma               Hematocrit = .50
             at 10 minutes:       0.2 mg/ml of plasma
             at 30 minutes:       0.2 mg/ml of plasma

B.     After then injecting Ralphie with substance Pz and inulin, Harley obtained the following measurements:

Substance           [renal vein plasma]          [arterial plasma]                [Urine]
                         (mg/100 mls plasma)         (mg/100 mls plasma)         (mg/ml)

 Pz                               0.2                                      0.5                            0.45

 Inulin                         0.015                                0.025                          0.015
 

Rate of Urine formation = 0.1 ml/min

Plasma osmotic pressure = 400 mOsm/l

Urine pH = 4.5                                        Urine [glucose] = 0.001 mg/ml

Respiratory Rate = 15 breaths/min                      Tidal volume = 12 mls/breath

Respiratory dead space (due to tracheal cannula & conductive airways) = 2 mls

Plasma pH = 7.30                            Plasma HCO3 = 30 mmoles/l

1.     Ralphie's Blood volume (Not plasma volume!) =      __________________
 

2.     Ralphie's alveolar ventilation =                               __________________
 

3.     Ralphie's renal blood (not plasma) flow =               __________________
 

4.     Ralphie's GFR =                                                  __________________
 

5.     The Filtration Fraction =                                       __________________
 

6.     How much inulin is filtered/min?                             __________________
 

7.     How much water are the kidneys reabsorbing/min?__________________
 

8.     What is happening to substance Pz in the kidneys? __________________
 

9.     Prove this (#8) two ways:    ____________________________________
 

                                                  ____________________________________                             
 

10. How much of Pz is reabsorbed or secreted/min?     __________________
 

11. After reviewing the data, what can you conclude about Ralphie's respiration at the time the data was taken?  Is it normal?  Explain the nature of the problem, if any.
 
 
 
 

ANSWERS
 

1.     Ralphie's BLOOD volume: first, you must use the data for high MW dextran so that it stays in the circulation.  Note that after injection, it takes some time for the dextran to distribute evenly throughout the circulatory system.  Thus,
 10mg/0.2mg/ml = 50ml of plasma.  Corrected for hematocrit = 50ml x 1/(1-0.50) = 100 mls of blood.

2.     Alveolar ventilation = (TV-dead space) x rate = (12 - 2 mls) x 15/min = 150 mls/min.

3.     To calculate renal blood flow, use substance with highest E, i.e., substance Pz.
First, E of Pz = (0.5 mg/100 ml - 0.2 mg/100) / 0.5 mg/100) = 0.6 (NO units!)
Then CPz = 0.45 mg/ml x 0.1 ml/min / 0.5 mg /100 ml = 9 ml / min (UNITS, please).  Next, RPF = C/E, so 9 ml/min / 0.6 = 15 ml /min and RBF = 15 ml/min x 1/(1-hematocrit) = 30 ml/min.  (Units are required at every step!)

4.     GFR = C of inulin (since inulin is only filtered!). C of inulin = 0.015 mg/ml x 0.1 ml/min / 0.025 mg/100 mls = 6 ml/min.  OR, since FF or Einulin = GFR/RPF, then 0.4 = GFR/ 15 ml/min, and GFR = 6 ml/min.

5.     FF = GFR / RPF, so FF = 6 ml/min / 15 ml/min = 0.4 (no units!)

6.     Inulin filtered per min = Pinulin x GFR = 0.025 mg/100ml x 6 ml/min = 0.0015 mg/min.  (note units!)

7.     Water reabsorption = GFR (rate of filtrate formed) - V (rate of urine production).  Thus, 6 ml/min - 0.1 ml/min = 5.9 ml of water reabsorbed per min.
 

8.     Since Cinulin < CPz, and Einulin or FF < EPz, and  UPz x V (amount of Pz in urine per minute) > PPz x GFR (amount of Pz filtered per minute), Pz must be secreted.

9.     see # 8 for all three ways

10.     Pz secreted/min = amount in urine/min - amount filtered/min (the difference must have been added by secretion).  Thus (U x V) - (P x GFR) or (0.45 mg/ml x 0.1 ml/min) - (0.5 mg/100 ml x 6 ml/min) = 0.015 mg/min is secreted.

11.     Looking at the data, we see that plasma pH is down (pH = 7.3) while plasma bicarbonate is elevated from a normal of 23 to 30 mmoles/l.  This means the subject is not blowing off normal amounts of carbon dioxide (thus elevated bicarb and lower pH), so respiration must be depressed.
 
 

MORE RENAL CLEARANCE PROBLEMS

1.     Once again the notorious Dr. Harley Schmedlap Sr., returns to work this time measuring the renal capabilities of the bull rhinoceros during the mating season.  Dr. Schmedlap made the following measurements shortly before his untimely (and rather gruesome) demise.

     - Arterial Plasma concentration of X = 10 mg/100 mls of plasma
     - Renal vein concentration of X = 5 mg/100 mls of plasma
     - U  = 5 mg/mls
     - Vx  = 10 mls of urine/minute
     - C inulin = 200 mls/min

     As Dr. Schmedlap's trusted assistant, you will calculate the following values for publication in the Journal of Irreproducible Results.  Note:  you must show all work and units.

a)  Clearance of X
b)  Filtration fraction?
c)  Amount of X put into the urine?
d)  Is X reabsorbed or secreted?  Prove it?
 

2. Schmedlap Strikes Again!!

 Dr. Harley Schmedlap, Jr., noted physiologist and part time aluminum siding salesman, has just taken the following measurements from South African warthog in heat.
 
 
 

Arterial B.P.  140/70 mm Hg
Filtration Fraction = 0.30
Osmotic pressure of the plasma = 310 mosm
Osmotic pressure of the urine = 600 mosm
Hematocrit = 0.50
Urine output = 0.2 mls/min
 

After Schmedlap recovers, he wants to publish the results in the Journal of Warthog Physiology.  As his trusty lab assistant, you will perform the necessary calculations and show all work and units!!

A)     Calculate E of X, Y & Z.
B)     Calculate GFR
C)     Calculate RBF
D)     Which substance is filtered and secreted?  Prove it.  How much is filtered?  How much is secreted?
E)     How much is only filtered?
F)     How much is only filtered & reabsorbed?
 

3.     From Dr. Harley Schmedlap's data (below) collected from the East Glockomoran ring-tailed tree squab, calculate the following quantities.  You must show all work and all units.
   
 
 

________________________________________________________________________

-  Filtration fraction =  volume of filtrate formed per min  =  .25
                                          renal plasma flow

-  Rate of urine formation = 10 mls/min
-  B.P. = 00/50 mm Hg
-  Hematocrit = 50%

a)      Clearance of Z
b)      E of X
c)      GFR
d)      RPF
e)      RBF
f)       How much of Z is filtered/min.
g)      How much water is reabsorbed/min.
 

 
4. From the following calculate the clearance of X, ERPF, Extraction ratio of X, and R Blood flow:

         Urine conc. of X                             =  14 mg/ml
         Urine Volume                                 =  54 ml/hr
         Arterial Plasma conc. of X              =    0.02 mg/ml
         Renal Arterial plasma conc. of X     =    0.02 mg/ml
         Renal Vein conc. of X                     =    0.002 mg/ml
         Hematocrit                                     =  47%
 

5.     Inulin conc. in Urine                         =  29 mg/ml
        Urine volume                                  =    1.1 ml/min
        Arterial Plasma Inulin Conc.            =    0.25 mg/ml
        Renal Vein conc. of inulin                =    0.05 mg/ml
        Hematocrit                                     =  45%

 Calculate GFR, CInulin, EInulin, BF, ERPF
 

6. From the following data, calculate renal blood flow and glomerular filtration rate:
 
 

 Hematocrit         =  0.50 Urine Osmotic Pressure = 1100 mosm
 Blood pressure   =  120/80 Plasma Osmotic Pressure = 300 mosm
 Heart rate          =  72/min

 A.   Renal Blood Flow

 B.   G.F.R.
 

ANSWERS

1.      a. 500 mls
         b. 0.2
         c. 50 mg/min
         d. E>FF and UV>GFR x PA

2.      a. EX = 0.1
             EY = 0.6
             EZ = 0.3
         b. 1.2 ml/min
         c. 8.0 ml/min
         d. Y E>FF 0.06 mg secreted/min
         e. Z only filtered 0.06 filtered/min E = FF
         f. X

3.     a. 50 ml/min
        b. EX = 0.2
        c. GFR = 25 ml/min
        d. 100 ml/min
        e. 200 ml/min
        f. 5.0 mg/min
        g. 15 ml/min

4.    a. 630 ml/min = CX
       b. ERPF = 700 ml/min
       c. EX = 0.9
       d. 1321 ml/min = RBF

5.   GFR = 127.6 ml/min
      CInulin = 127.6 ml/min
      EInulin = 0.80
      RPF = 159.5 ml/min
      RBF = 290 ml/min

6. You're on your own!

And one more!

#1.
Dr. Harley Schmedlap, Jr., that noted physiologist and former 440 student, has taken the following measurements from your experimental animal during one of his frequent visits to the 422 lab.  He doesn't have time to complete the calculations, so he leaves the task to you, his trusty lab partner.

Arterial plasma concentration of Substance D = 0.04 mg/100mls
Renal vein plasma concentration of Substance D = 0.01 mg/100mls
Urine concentration of Substance D = 0.06 mg/ml
GFR = 0.5 ml/min    Rate of urine formation = 0.01 ml/min
Hematocrit = 0.45
Respiratory Rate = 18 breaths/min  Respiratory tidal volume = 15ml/breath
Expiratory Reserve Volume = 10 ml  Inspiratory Reserve Volume = 15 ml
Residual Lung Volume = 5 ml  Respiratory dead space = 3 mls
Plasma osmotic pressure = 310 mOsm
Heart Rate = 120 beats/min   Stroke volume = 2 ml/beat
Diastolic Pressure = 80 mm Hg    Systolic Pressure = 120 mm Hg

     Schmedlap has injected 1mg of inulin and 1 mg of a high molecular weight dextran (MW > 500,000) into the animal's circulation.  After reaching equilibrium in the appropriate body fluids, plasma [inulin] = 0.015mg/ml and [dextran] = 0.035 mg/ml.

     Please do all calculations on a separate page and place only your final answers with the correct units in the spaces provided below.

a. What is the cardiac output of this beast?   ________________________
 

b. What is the rate of alveolar ventilation?   ________________________
 

c. What is the blood volume of the animal?   ________________________
 

d. What is the volume of extracellular body fluids?  ________________________
 

e. What is the renal filtration fraction?    ________________________
 

f. How much of Substance D is filtered/min?   ________________________
 

g. Substance D is filtered and secreted.  Prove it 2 ways using data (numbers) to support your statements:
 

  1.________________________________________________
 

  2._________________________________________________
 

h. How much of Substance D is filtered/min?   ________________________
 

i. How much Substance D appears in the urine/min?  ________________________
 

j. What is the renal plasma flow?    ________________________
 

k. What is the renal blood flow?     ________________________
 

l. How much water is reabsorbed/min?    ________________________
 

m. What is animal's vital lung capacity?    ________________________
 

n. How much renal filtrate is made/min?   ________________________