| Section 2 - Applied Pharmacokinetics |
Introduction
With this freedom comes responsibility. The goal of this tutorial is to help you better understand one-compartment modeling and population kinetics, so that you can create your own drug models and exploit the flexibility that these tools give you.
The one compartment linear model
The second criteria for utilizing a one-compartment linear model is that the drug is eliminated from the body in a first-order fashion. That is, the rate of elimination is proportional to the amount of drug in the body. The proportionality constant which relates the rate and amount is the first order elimination rate constant, Kel, which has units of reciprocal time (usually 1/hours). In this model, the Kel is a constant, it does not change when different doses or multiple doses are given.
Volume of distribution (Vd)
If we know the dose and we can measure the serum level, then we can calculate the Vd by rearranging the above equation.
Population model
If we calculate Vd for a group of patients, we can then derive an average Vd for
our patient group. A population average Vd is usually expressed in Liters per kilogram (L/kg).
Elimination rate constant (Kel)
Population model
If we calculate Kel for a group of patients, we can then derive an average for
our patient group. If the drug is largely excreted unchanged in the urine, it is
customary in the literature to list average Half-Life for those patients with normal
renal function, and average Half-Life for those with ESRD (End Stage Renal Disease). In order
to extrapolate these two points to all patients, we assume a linear relationship between
CrCl and half-life:
Because of this assumption, we can set up a simple proportion equation to derive the components of our Kel equation:
The values from Equation 4 can then be plugged into the following equation to estimate Kel for any patient with a known CrCl:
Prospective dosing
Introduction
"Where can I find model parameters for a drug", is one of our most frequently asked questions. Unfortunately, this information is not easily found in one reference. Furthermore, what little pk data you may find is often either incomplete or impractical.
Finding pk data in Bennet's tables
Here is their data on Cefepime:
Drug | Percent excreted unchanged | Half-life (Normal/ESRD) | Plasma Protein Binding | Volume of Distribution | Dose for Normal Renal Function |
---|---|---|---|---|---|
% | hrs | % | L/kg | ||
Cefepime | 85 | 2.2 / 18 | 16 | 0.3 | 250-2000 mg q8h |
Finding pk data in the Package insert
Pharmacokinetics:
The average plasma concentrations of cefepime observed in healthy adult male
volunteers (n=9) at various times following single 30-minute infusions (IV)
of cefepime 500 mg, 1 g, and 2 g are summarized in Table 1. Elimination of
cefepime is principally via renal excretion with an average (± SD)
half-life of 2.0 (±0.3) hours and total body clearance of 120.0 (±
8.0) mL/min in healthy volunteers. Cefepime pharmacokinetics are linear over
the range 250 mg to 2 g. There is no evidence of accumulation in healthy
adult male volunteers (n=7) receiving clinically relevant doses for a period
of 9 days.
Absorption: The average plasma concentrations of cefepime and its derived pharmacokinetic parameters after intravenous administration are portrayed in Table 1. | ||||||||||||||||||||||||||||||||||||||||||||
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Distribution:
The average steady state volume of distribution of cefepime is 18.0 (±
2.0)L. The serum protein binding of cefepime is approximately 20% and is
independent of its concentration in serum.
Renal Insufficiency: Cefepime pharmacokinetics have been investigated in patients with various degrees of renal insufficiency (n=30). The average half-life in patients requiring hemodialysis was 13.5 (± 2.7) hours and in patients requiring continuous peritoneal dialysis was 19.0 (± 2.0) hours. Cefepime total body clearance decreased proportionally with creatinine clearance in patients with abnormal renal function, which serves as the basis for dosage adjustment recommendations in this group of patients. |
Reconciling the literature with the FreeKin Modeler
Although there are some discrepancies between the two sources, they are close.
Bennett's tables | Package insert | |
---|---|---|
Half-life (Normal/ESRD) | 2.2 / 18 | 2 / 19 |
Volume of distribution | 0.3 L/kg | 0.26 L/kg |
A huge problem occurs though when we try to plug these literature values into a model. What looks good on paper does not translate to a practical dose. If we were to use these numbers in our dose prediction equations, Equation 6 and Equation 7, we get results which are 2 or 3 times the recommended dose!
Because of this difficulty in translating literature data into a practical dosing model, I created the FreeKin Modeler program.
The basic parameters you will need from the literature are:
The parameters that are created by the modeler are:
Below is a screen shot of FreeKin. The program breaks down the process of creating a model into 3 steps: Kel, Vd, and target levels. After you have created your model, you can then test it with various creatinine clearances. The assumption made in testing is that you are dosing the average 70kg patient.
Finishing up our Cefepime example using the FreeKin Modeler, our inputs are:
The resulting parameters for Cefepime are:
The dosage recommendations from this model compare favorably with the published guidelines for dosage adjustment in renal failure. Notice that the parameter which differed most from that cited in the literature is the Volume of distribution. You can double check the results of FreeKin for yourself using Equation 2 for a rough estimate of Vd:
The package insert states that the average steady-state Vd is 18 liters, and multiplying out Bennett's 0.3 L/kg gives us 21 liters for the average 70 kg patient. If you plug either of these Vd's into Equation 7, you will get an ideal dose which is 2 or 3 times the recommended dose. Of course, this makes absolutely no sense. And this leads to one of the problems you will run into when creating a practical model. Some misguided colleague will tell you just how wrong your Vd value is by quoting some figure from the literature. Just remember this one important, irrefutable fact:
Conclusion
The RxKinetics family of pk programs are tools. And just like any other tool, you need to understand how they work before you use them. It is my hope that this tutorial has given you some insight and practical information about our pk tools that will allow you to provide better care for your patients.
| Section 2 - Applied Pharmacokinetics |
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