1. Given the following data, find the values of the listed variables.
Patient: Female human, 25 yrs old, 50 kg
Drug administered: Theophylline base, 4mg/kg, IV bolus, F per os = 0.96
Plasma Samples drawn at following times contained the listed concentrations of theophylline.
Time Concentration
(hr) (mg/L)
----------------- -----------------------
5 5.4
10 2.8
20 1.0
30 0.34
40 0.13
From Graph Paper:
Cp(0) = ____9______ mg/L
Cp(0) = Dose / Vd; Vd = Dose / Cp(0); 0.44 L/Kg = 4 mg/Kg / 9 mg/L
Vd(patient) = 0.44 L/Kg * 50 Kg/patient = 22.22 L
Vd(extrap) = ___22.22___ L ______0.44____L/kg
Elimination half-life = _____6.5____ hr
Ke = 0.693 / 6.5h; Ke = 0.1066/h
Ke = _____0.1066_________ / hr
Ke = CL / Vd; CL = Ke * Vd; 0.1066/h * 22.22L = 2.369 L/h
CL = _____2.369___ L/hr
Find dose of theophylline base required to produce initial concentration of 15 mg/ml (middle of therapeutic window). This is roughly equivalent to a loading dose.
Dose = desired conc * vol; mg = mg/L * L; 15 mg/L * 22.22 L = 333.3 mg
_____333_________ mg = dose of theophylline base
333 mg theophyline / [0.79 mg theophylline/mg hydrous aminophylline] = 422 mg hydrous aminoph
______422______ dose of "hydrous" aminophylline (0.79 g theoph/ 1g hydrous aminoph)
DR = CL * Desired Css; mg/h = L/h * mg/L; 2.369 L/h * 15 mg/L = 35.5 mg/h = 36
Infusion dose to produce Css of 15 mg/L = ___36_____ mg/hr of theophylline or __46__ mg/hr of the "hydrous" aminophylline
88% of Css @ 3 x 1 t1/2; 3 * 6.5h = 19.5 h; Therefore, convenient to take first sample
at 24 h after begin infusion. Could take it at 6.5 h and know that this is half of final value.
Assuming infusion started at 8:00 AM Day 1, when should one
sample plasma concentration?
__Day 2 8:00 AM_______Day
& hour
New DR = Old DR * ( Desired Css / Measured Css);
(15 mg/L / 30 mg/L) * 46 mg/h = 29 mg/h of "hydrous"
aminophylline
Assume concentration obtained was 30 mg/L, what new Dose Rate of "hydrous" aminophylline should be used? _23_____ mg/hr; of theophylline ___18______ mg/hr.
After the respiratory crisis has been controlled, what regimen of theophylline would be best for this patient? Assume that the new infusion Dose Rate produced a concentration of 15 mg/L.! How could you easily get an estimate of half-life specific to this patient? Assume plasma sample taken 4 hours after stopping the infusion contained 12 mg/L of theophylline.
Assume Cp(0) = 15 mg/L; Cp(4 h) = 12 mg/L
Cp(t) = Cp(0) * e-(Ke * t);
ln Cp(t) = ln Cp(0) - (Ke * t)
ln Cp(t) - ln Cp(0) = - (Ke * t)
-ln Cp(t) + ln Cp(0) = Ke * t
[ln Cp(0) - ln Cp(t)] / t = Ke; [2.708 - 2.484] / 4h = 0.0558 /h = Ke
0.694 / 0.0558/h = 12.4 h half-life
In following calculations will use Ke = 0.0558/h and Vd = 22.22 L
Maintenance Oral (PO) dose prediction and adjustment
Assume available Enteric Coated aminophylline tablets (0.79 mg theoph/mg Aminoph) include: 100 mg and 200 mg
Recommended Dose Rate (from adjusted level above): _____18________ mg/hr theoph; __23____mg/hr "hydrous" aminoph.
Dose/Interval:
12h * 23 mg/h = 276 mg/12h of "hydrous" aminophylline
8h * 23 mg/h = 184 mg/8h of "hydrous" aminophylline
Dose forms available: see above enteric coated ...
To get 276 mg / 12 h can use (1 x 100 mg tab) + (1 x 200 mg tab) for total of 300 mg
(2 x 200 mg tab) for a total of 400 mg
To get 184 mg / 8 h can use (1 x 200 mg tab) for total of 200 mg
Find Css(max)
Css(max) = F x D/Vd * 1 / [1 - e-(Ke * T)]; Css(max) = Cp(0) * accumulation factor
For 12 h interval accumulation factor = 2.049
For 8 h interval accumulation factor = 2.777
Find Cp(0) estimates:
Find value of (F/Vd) * 079 mg theoph/mg "hydrous" aminoph and use as a constant
(0.96 / 22.22) * 0.79 = 0.0341/L
200 mg * 0.0341/L = 6.82 mg/L
300 mg * 0.0341/L = 10.23 mg/L
400 mg * 0.0341/L = 13.64 mg/L
Css(max)
Dose Cp(0) Css(max) for 8 h interval Css(min) for 12 h interval
("hydrous") (theoph) (Cp(0) * 2.777) (Cp(0) * 2.049)
( mg ) (mg/L) ( mg/L ) ( mg/L )
-------------- ----------- ------------------ --------------------
200 06.82 18.94 14.00
300 10.23 28.41 20.96
400 13.64 37.88 27.95
Css(min) = Css(max) * e-(Ke * T) ; Cp(0) * Frcn remaining
Frcn remaining at 8 hr = 0.6399; at 12 hr = 0.5119
Css(min)
Dose Trough for 8 hr interval Trough for 12 h interval
200 12.12 7.17
300 18.17 10.72
400 ? 14.31
Dose Peak Trough
mg "hydrous" mg theoph/L mg theoph/L
12-h
200 14.0 7.17
300 20.96 10.72
400 27.95 14.31
8 h
200 18.94 12.12
300 28.41 18.17
Given a therapeutic window of 10 to 20 mg/L, dosage regimens of 200 mg "hydrous" aminophylline q8h and 300 mg "hydrous" aminophylline" q12h are probably reasonable first guesses. The q12h regimen appears to produce a Css(max) slightly above the recommended range, but this assumes instantaneous absorption. When given orally, this is unlikely so the true peak will be somewhat less than estimated using these formulae.
Recommended PO dose __See above________ mg and Dose Interval: ____See above_________ hr
Number __See above_____ and size __See above_____ of tablets to produce this dose rate
Predicted peak (css(max)) with this regimen: ___See above___ mg/L; Css(min) __See above_____mg/L
Is this within the therapetic window? ___See above____
Assume desire to have initial peak at 15 mg/L; Given a Vd of 22.22 L, then need 15 mg/L * 22.22 L = 333 mg of theophylline or 422 mg "hydrous" aminophylline. This can be obtained by giving 2 x 200 mg tabs of the enteric coated dose form. The fact that this is slightly less than needed provides a reasonable safety factor for the initial dose.
Assume a loading dose was required -- what would it be? ____________ mg
2. An elimination half-life of 5 hours corresponds to what Ke? ___ 0.139_____/hr
Ke = 0.693/half-life; 0.693 / 5h = 0.139/h
3. What assumptions are made when we apply one compartment model kinetic analysis to drug disposition? Why are we able to rationally use this model when some of the assumptions are obviously not strictly valid?
We assume instantaneous mixing throughout the body. We can use the model despite its obvious limitation because for many drugs, mixing is rapid relative to the rate of elimination and our need for accuracy. We do not try to predict concentrations earlier than one hour with 1-COM model data.
We also assume first order kinetics. and that input and output are from the one compartment. (obviously!)
4. How do we find the values A and 'alpha', B and 'beta' when we analyze a plot for a 2-compartment model?
By finding the slowest process and extrapolating it back to zero-time. This slope is -beta and the intercept is "B". Then subtract all points on the "beta" slope from the corresponding time points on the observed concentration versus time curve. Plot the residuals. The slope of this line is -alpha. The intercept is "A".
5. What are the relationships among extraction ratio, clearance, Vd, and Ke?
Extraction ratio is the fraction of drug removed by an organ of elimination in one pass of the blood thought it. By multiplying this fraction times the volume of blood passing through the organ per "unit" of time, one obtains the clearance/"unit" of time.
CL (L/h) = Fraction * Flow (L/h)
Ke (frcn/h) = CL (L/h) / Vd (L), i.e., the Ke can be conceived of as the fraction of the Vd that is completely freed of drug per unit of time, in this case per hour. It must be remembered that this is a "virtual" volume.
6. What is meant by the idea that an elimination process is "extraction-limited" versus "flow-limited"?
Extraction-limited indicates that the eliminating organ's ability to biotransform or excrete the drug is the limiting factor in determining elimination. In this case, changes in organ function related to disease can be of great importance and changes in blood flow will be less important except at the extremes.
Flow-limited elimination indicates that the capacity of the organ of elimination to biotransform or excrete the drug is great relative to the amount presented to it by the circulatory system. In this case, there can be some diminution in organ function without significant decrease in the rate of elimination.
7. What is the real use of Vd?
Vd is used as a constant in pharmacokinetic calculations to use with concentration to find the amount of drug in the body. It is also used in loading dose calculations. It has no anatomic correlates.
8. How does one determine bioavailability?
Answers to some of these questions/problems will be posted outside Dr. Coppoc's office.
These are some samples of the kind of questions that might be asked on an exam. Some multiple-choice questions will be included as well.
[pkprb01a.doc 9/95]
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Last modified: 8/18/96 glc