ANSWER SHEET:
Problems related to Vd & LD

  Problem 01. A drug has a volume of distribution of 300 L in a 500 Kg horse.

1. What is its Vd in L/Kg?
   
   
   if ("01" == prob_num){
   ans= "Problem "+prob_num+"<br><OL>";
   ans+= "<LI>Vd in L/Kg = 300 L/500 Kg = 0.6 L/Kg";
   ans+="</OL>";
   break;}

Problem 02. A drug has a volume of distribution of 0.3 L/Kg.

1. What is the total Vd in a 15 Kg Beagle?
2. What is the total Vd in a 40 pound Beagle?
   
   
   if ("02" == prob_num){
   ans= "Problem "+prob_num+"<br><OL>";
   ans+= "<LI>Vd = 15 Kg * 0.3 L/Kg = 4.5 L<BR>";
   ans+= "<LI>Vd = 40 lb * 0.45 Kg/lb * 0.3 L/Kg = 5.4 L"
   ans+="</OL>";
   break;}
   

Problem 03. A drug was given IV to a 70 Kg calf at a dose of 2.5 mg/Kg. Concentrations of drug in plasma were found to be the as follows (mg/L): 2 hr = 7.07; 4 hr = 5.00; 6 hr = 3.54; 8 hr = 2.50.

1. What is the total dose?
2. What is the Cp(0)?
3. What is the Vd/Kg?
4. What is the whole animal Vd?
   
   
   if ("03" == prob_num){
   ans= "Problem "+prob_num+"<br><OL>";
   ans+= "<LI>D = 70 Kg * 2.5 mg/Kg = 175 mg<BR>";
   ans += "<LI>By extrapolation of the data, One obtains Cp(0) of 10 mg/L<BR>"
   ans += "<LI>0.25 L/Kg<BR>";
   ans += "Cp(0) = 10 mg/L and D = 2.5 mg/Kg; 2.5 mg/Kg / 10 mg/L = 0.25 L/Kg<BR>";
   ans += "Cp0 = DF/Vd; Vd = DF/Cp0<BR>";
   ans += "<LI>0.25 * 70<BR>";
   ans += "Vd = Vd/Kg * Kg; 0.25 L/Kg * 70 Kg = 17.5 L";
   ans+="</OL>";
   break;}

 Problem 04. A drug was given IV to a 3 Kg cat at a dose of 5 mg/Kg. The resulting Cp(0) was 20 mg/L. The same dose of drug was given to the cat 1 month later by mouth and the animal had no significant change in weight or hydration status. The resulting Cp(0) was 17 mg/L. Assume both of these values were "correct."

1. What is the approximate F?
2. What formula did you use to calculate F?
3. How does it compare to the approach described in class?
   
   
   if ("04" == prob_num){
   ans= "Problem "+prob_num+"<br><OL>";
   ans+= "<LI>F = 17/20<br>";
   ans += "<LI>Cp(0) = FD/Vd; F = Cp(0) * Vd/D<br>";
   ans += "Assume Dose and Vd stayed constant. IV dose F = 1. <br>";
   ans += "Therefore, 17/20 = new F<br>";
   ans += "<LI>Less accurate, but conceptually possible.";
   ans+="</OL>";
   break;}

Problem 05. A drug was given IV to an animal that had an estimated Vd of 0.9 L/Kg. The dose was 4 mg/Kg.

1. What is the estimated Cp(0)?
2. What is the estimate of F?
3. How does this Cp(0) correspond to the "A" in the one-compartment pharmacokinetic model?
   
   
   if ("05" == prob_num){
   ans= "Problem "+prob_num+"<br><OL>";
   ans+="<LI>Cp(0) = FD/Vd; therefore, Cp(0)= 1 * 4 mg/Kg /0.9 L/Kg = 4.44 mg/L<br>"
   ans+="<LI>IV??? It has to be 1 by definition!<br>"
   ans +="<LI>Cp(0) is a calculated estimate of A at zero time<br>"
   ans+="</OL>"; break; }
   

Problem 06. A drug was given PO to an animal that had an estimated Vd of 0.6 L/Kg. The dose was 3 mg/Kg and the literature states the F for this drug give PO is 0.8.

• What is the highest possible value for Cp(0) in this case?
• Is the actual value going to be higher or lower that this?
  (Remember Cp(0) in this case would be the extrapolated value.)
  
  
  if ("06" == prob_num){
  ans= "Problem "+prob_num+"<br><OL>";
  ans+="<LI>Cp(0) = F*D/Vd; Cp(0) = 0.8 * 3 mg/Kg / 0.6 L/Kg = 4 mg/L"
  ans+="<LI>Actual value will be lower because Ka << Ke is NOT true"
  ans+="</OL>";
  break;}
  

Problem 07. You are treating a 25 pound terrier with a drug that has a Vd of 0.4 L/Kg and you want the concentration to be in the range of 15 mg/L.

• How much drug should you give IV for the initial dose (LD)?
  
  
  if("07" == prob_num){
  ans= "Problem "+prob_num+"<br><OL>";
  ans+="<LI>25 lb * .45 kg/lb * .4 L/Kg * 15 mg/L = 67.5 mg<br>";
  ans+="<LI>Cp0 = DF/Vd; D = Cp0 * Vd / F";
  ans+="</OL>";
  break;}

Problem 08. You are treating a 15 Kg dog with a drug that has a Vd of 0.3 L/Kg, a PO F=0.6, and you want a Cp(0) of 10 mg/L.

• How much drug should you give PO to this dog?
  
  
  if ("08" == prob_num){
  ans= "Problem "+prob_num+"<br><OL>";
  ans+="<LI>D = Cp0 * Weight * Vd/F = 10 * 15 * 0.3 / 0.6 = 75 mg / dog";
  ans+="</OL>";
  break;}