Volume of Distribution
and Loading Dose

Calculating an Initial Dose

• Assume you decide to treat 5 expensive fish in a 50 L tank with miraclemycin and that the desired final concentration is 10 mg/L. 
  • How much drug (in mg) should be added?
  Enter (mg)>
  
  

• How much drug should be given to a patient that weighs 75 kg and has a body water content of 50 L (assume uniform distribution of drug). Desired concentrationis 10 mg/L.
  • How much drug (in mg) should be added?
  Enter (mg)>
  
  

• Can you see the similarity in these examples? You have a known volume of fluid in which you want to have a specific concentration of drug.

• In this case,
  • Amount of drug = dose
  • Desired concentration = target concentration (mean or average) in sampled fluid
  • Volume = the volume of sampled fluid in which the drug is distributed
  • These cases assume that no drug has left the tank or body, i.e.,they are values taken at the instant drug was administered. This time is called zero-time.
  • They further assume that no drug was lost during that instant
• How REALISTIC are these assumptions? We will see that at the first level of approximation and given a few qualifiers that you are to know, they are not bad.

Loading Dose

• Loading Dose (DL) = a dose of drug sufficient to produce a plasma conentration that would fall within the therapeutic window after only one or very few doses over a very short interval. It is larger than the dose rate needed to maintain the concentration within the window and would produce toxic concentrations if given in repeated doses.
  
• Maintenance Dose (DM) = The dose needed to maintain the concentration within the therapeutic window when given repeatedly at a constant interval
  

Information needed to calculate a DL

• Volume of "tank" (Volume of distribution, usually in L or L/Kg)
  • from literature
• Desired concentration
  • from literature
• Knowledge of assumptions
  • absorption very rapid relative to elimination
  • volume of tank is in terms of the sampled fluid (i.e., plasma or serum) because this is the only concentration you know by direct measurement.
  • one must use the same terms throughout calculations
    • mg / L; mcg/L; mcg/mL, etc.
      Note that mg/L and mcg/mL are the same!
    • total drug vs unbound drug
      Usually use total drug concentration due to cost-effectiveness

Finding Vd

• Look it up!

• Simple experiments

  • Conceptual approach given here. Actual determinations are much more complex and by different methods to get more accurate values
    

• Vd Experiment #1 (closed system)

  • MEASURE DILUTION!
  • Add 500 mg of drug to ____ L of water in a beaker
  • Measured drug concentration after mixing is 5 mg/L
  • What is the volume of distribution?
  Enter (L)>

• Vd Experiment #1 (open [real] system)

  • 70 kg patient given dose of 2,800 mg of miraclemycin
  • Plasma drug concentrations --

  Times (hrs)	2	4	6	8
  Conc (mg/L)	10	5	2.5	1.25

  • Plot the data on arithmetic graph paper with labels
    • X- axis = 0 hours to 20 hours
    • Y-axis = 0 mg/L to 25 mg/L
    • What is the shape of the plot?
    • Draw light horizontal lines from each data point to the 0 h axis (parallel to bottom of graph paper!)
    • Is the vertical distance between each of the horizontal lines constant? Why or why not?
    • Can you make a meaningful extrapolation of the data to "zero hours"?
    • See Excel Spreadsheet [plot]

    ---

  • Plot the data on semi-logarithmic graph paper with labels
    (Keep this graph for later use!)
    • Note that on a 2 or 3-cycle sheet of paper, each "1' could represent 0.1, 1.0, 10.0, and 100.0! For this experiment, make the top-most "1" = 100 mg/L.
    • Plot the data and connect the data points.
    • Draw light horizontal lines to each data point as you did previously
    • What difference do you note? The vertical distances between each of the data points are now the same!
    • Semi-log paper represents a "geometric progression" where each multiple is distributed evenly, i.e., 1, 2, 4, 8, 16, 32, 64, 128, ..., n*2 are distributed evenly. OR 1, 10, 100, 1,000, ..., n*10 are distributed evenly on one of the axes.
    • By the same token, if we start with 100 ug/ml and cut the concentration by half to 50 and then again to 25, the vertical distances are the same. Each FRACTIONAL change of 0.5 gets the same vertical distance.
    • Can you make a meaningful extrapolation of these data to "zero hours"? YES! [Excel plot]
    • What is the concentration at the "zero hours" intercept?
  Enter (mg/L)>

  • What is the volume into which the drug APPEARS to have distributed? That is, how much plasma-equivalent is required to explain the dilution?

  Enter (L)>

  • How does this compare to the weight of the patient?

  • If body water is approximately 70% of body weight, how can a drug appear to have distributed into 2 L/Kg of body weight?
  • Hint: Think about what fluid we are measuring and our assumption of uniform distribution? Are these data consistent with the notion that miraclemycin distributes in such a way that the concentration outside the plasma is higher than that in the plasma?
  • How can one use an estimate of Vd to calculate a loading dose?
  • What is the "pharmacokinetic usefulness" of the Vd term?

Summarizing statements for Vd

• Definition: volume of plasma/serum (Vd) required to explain the plasma/serum concentration (C) when there is a known amount (A) of drug in the body. The amount (A) is equivalent to the dose (D) at zero time after administration of a single dose. For many of our purposes, this would equate to an initial dose, or a loading dose (DL)
• Note the dimensions of the terms below. Vd can be in L or in L/Kg. The former would be the Vd for the entire patient, whereas the term "L/Kg" is a way of normalizing the Vd to account for differences in body mass.

  Vd = D / Measured Conc {L = mg / (mg/L)}

• One can rearrange the formula for various uses. To find a loading dose (DL),

  DL = Vd * Desired Conc {mg = L * (mg/L)}

• A frequent use is in formulae to replace the "initial concentration" (C0),

  Predicted Conc = DL /Vd { mg/L = mg / L }

• The easiest way to remember these is to use the most obvious form of the equation, the one above where (mg/L) = (mg) / (L), and then do simple rearrangements as needed. ALWAYS CHECK the TERMS to be sure you are correct.
• The Vd is not a specific anatomic space
• Vd changes in various conditions, e.g., with age, pregnancy, disease, levels of protein binding of drug, fat content of the animal, etc.
• The simplest conceptual way to determine Vd is to administer a dose of drug, measure concentration over time and extrapolate the concentrations to "zero-time" to find the initial concentration. Then use the known dose (DL) and concentration (C0) to calculate Vd.
  [full] [icon] Figure: Example of using a simple plot to determine Vd