steady-state

[Clinical Art][Pharmacokinetics] Interpretation of Plasma Drug Concentrations (Steady-State)

November 11, 2016 Clinical Skills, Critical Care, Pharmacokinetics, Practice No comments , , , , , , , , , , , ,

Plasma drug concentration are measured in the clinical setting to determine whether a potentially therapeutic or toxic concentration has been produced by a given dosage regimen. This process is based on the assumption that plasma drug concentrations reflect drug concentrations at the receptor and, therefore, can be correlated with pharmacologic response. This assumption is not always valid. When plasma samples are obtained at inappropriate times or when other factors (such as delayed absorption or altered plasma binding) confound the usual pharmacokinetic behavior of a drug, the interpretation of serum drug concentrations can lead to erroneous pharmacokinetic and pharmacodynamic conclusions and utimately inappropriate patient care decisions. These facors are discussed below.

Confounding Factors

To properly interpret a plasma concentration, it is essential to know when a plasma sample was obtained in relation to the last dose administered and when the drug regimen was initiated.

  • If a plasma sample is obtained before distribution of the drug into tissue is complete, the plasma concentration will be higher than predicted on the basis of dose and response. (avoidance of distribution)
  • Peak plasma levels are helpful in evaluating the dose of antibiotics used to treat severe, life-threatening infections. Although serum concentrations for many drugs peak 1 to 2 hours after an oral dose is administered, factors such as slow or delayed absorption can significantly delay the time at which peak serum concentrations are attained. Large errors in the estimation of Css max can occur if the plasma sample is obtained at the wrong time. Therefore, with few exceptions, plasma samples should be drawn as trough or just before the next dose (Css min) when determining routine drug concentration in plasma. These trough levels are less likely to be influenced by absorption and distribution problems. (slow or delayed absorption)
  • When the full therapeutic response of a given drug dosage regimen is to be assessed, plasma samples should not be obtained until steady-state concentrations of the drug have been achieved. If drug doses are increased or decreased on the basis of drug concentrations that have been measured while the drug is still accumulating, disastrous consequences can occur. Nevertheless, in some clinical situations it is appropriate to measure drug levels before steady state has been achieved. If possible, plasma samples should be drawn after a minimum of two half-lives beause clearance values calculated from drug levels obtained less than one half-life after a regimen has been initiated are very sensitive to small differences in the volume of distribution and minor assay errors. (Whether steady-state attained)
  • The impact of drug plasma protein binding on the interpretation of plasma drug coencentration has been discussed in thread "The Plasma Protein Concentration and The Interpretation of TDM Report" before.

Revising Pharmacokinetic Parameters

The process of using a patient's plasma drug concentration and dosing history to determine patient-specific pharmacokinetic parameters can be complex and difficult. A single plasma sample obtained at the appropriate time can yield information to revise only one parameter, either the volume of distribution or clearance, but not both. Drug concentrations measured from poorly timed samples may prove to be useless in estimating a patient's V or Cl values. Thus, the goal is to obtain plasma samples at times that are likely to yield data that can be used with confidence to estimate pharmacokinetic parameters. In addition, it is important to evaluate available plasma concentration data to determine whether they can be used to estiamte, with some degree of confidence, V and/or Cl. The goal in pharmacokinetic revisions is not only to recognize which pharmacokinetic parameter can be revised, but also the accuracy or confidence one has in the revised or patient-specific pharmacokinetic parameter. In the clinical setting, based on the way drugs are dosed and the recommended time to sample, bioavailability is almost never revised, volume of distribution is sometimes revised, and most often clearance is the pharmacokientic parameter that can be revised to determine a patient-specific value.

Volume of Distribution

A plasma concentration that has been obtained soon after administration of an initial bolus is primarily determined by the dose administered and the volume of distribution. This assumes that both the absorption and distribution phases have been avoided.

C1 = (S) (F) (Loading Dose) x e(-kt1) / V (IV Bolus Model)

When e(-kt1) approches 1 (i.e., when t1 is much less than t1/2), the plasma concentration (C1) is primarily a function of the administered dose and the apparent volume of distribution. At this point, very little drug has been eliminated from the body. As a clinical guideline, a patient's volume of distribution can usually be estimated if the absorption and distribution phase are avoided and t1, or the interval between the administration and sampling time, is less than or equal to one-third of the drug's half-life. As t1 exceeds one-third of a half-life, the measured concentration is increasingly infuenced by clearance. As more of the drug is eliminated (i.e., t1 increases), it is difficult to estimate the patient's V with any certainty. The specific application of this clinical guideline depends on the confidence with which one knows clearance. If clearance is extremely variable and uncertain, a time interval of less than one-third of a half-life would be necessary in order to revise volume of distribution. On the other hand, if a patient-specific value for clearance has already been determined, then t1 could exceed one-third of a half-life and a reasonably accurate estimate of volume of distribution could be obtained. It is important to recognize that the pharmacokinetic parameter that most influences the drug concentration is not determined by the model chosen to represent the drug level. For example, even if the dose is modeled as a short infusion, the volume of distribution can still be the important parameter controlling the plasma concentration. V is not clearly defined in the equation (see it below); nevertheless, it is incorporated into the elimination rate constant (K).

C2 =[(S) (F) (Dose/tin) / Cl]*(1-e-ktin)(e-kt2)

Although one would not usually select this equation to demonstrate that the drug concentration is primarily a function of volume of distribution, it is important to recognize that the relationship between the observed drug concentration and volume is not altered as long as the total elapsed time (tin + t2) does not exceed one-third of a half-life.

Our assumption in evaluating the volume of distribution is that although we have not sampled beyond one-third of a t1/2, we have waited until the drug absorption and distribution process is complete.

Clearance

A plasma drug concentration that has been obtained at steady state from a patient who is receiving a constant drug infusion is determined by clearance.

Css ave = (S) (F) (Dose / tau) / Cl

So, the average steady-state plasma concentration is not influenced by volume of distribution. Therefore, plasma concentrations that represent the average steady-state level can be used to estimate a patient's clearnace value, but they cannot be used to estimate a patient's volume of distribution. Generally, all steady-state plasma concentrations within a dosing interval that is short relative to a drug's half-life (tau =<1/3 t1/2) approximate the average concentration. Therefore, these concentrations are also primarily a function of clearance and only minimally influenced by V.

Also the below equation could be used,

Css 1 =[(S)(F)(Dose)/V]/(1-e-kτ)*(e-kt1)

the expected volume of distribution should be retained and the elimination rate constant adjusted such that Css1 at t1 equals the observed drug plasma concentration.

Sensitivity Analysis

Whether a measured drug concentration is a function of clearance or volume of distribution is not always apparent. When this is difficult to ascertain, one can examine the sensitivity or responsiveness of the predicted plasma concentration to a parameter by changing one parameter while holding the other constant. For example, for maintenance infusion, a plasma concentration (C1) at some time intervnal (t1) after a maintenance infusion has been started should be:

C1=[(S)(F)(Dose/τ)/Cl]*(1-e-kt1)

when the fraction of steady that has been reached (1-e-kt1) is small, large changes in clerance are frequently required to adjust a predicted plasma concentration to the appropriate value. If a large percentage change in the clearance value results in a disproportionately small change in the predicted drug level, then something other than clearance is controlling (responsible for) the drug concentration. In this case, the volume of distribution and the amount of drug administered are the primary determinants of the observed concentration. Also in cases where the drug concentration is very low, it might be assay error or sensitivity that is the predominant factor in determining the drug concentration making the ability to revise for any pharmacokinetic parameter limited if not impossible.

This type of sensitivity analysis is useful to reinforce the concept that the most reliable revisions in pharmacokinetic parameters are made when the predicted drug concentration changes by approximately the same percentage as the pharmacokinetic parameter undergoing revision.

When a predicted drug concentration changes in direct proportion, or inverse proportion to an alteration in only one of the pharmacokinetic parameters, it is likely that a measured drug concentration can be used to estimate that patient-specific parameter. But when both clearance and volume of distribution have a significant influence on th prediction of a measured drug concentration, revision of a patient's pharmacokinetic parameters will be less certain because there is an infinite number of combinations for clearance and volume of distribution values that could be used to predict the observed drug concentration. When this occurs, the patient's specific pharmacokinetic characteristics can be estimated by adjusting one or both of the pharmacokinetic parameters. Nevertheless, in most cases additional plasma level sampling will be needed to accurately predict the patient's clearance or volume of distribution so that subsequent dosing regimens can be adjusted.

When the dosing interval is much shorter than the drug's half-life, the changes in concentration within a dosing interval are relatively small, and any drug concentration obtained within a dosing interval can be used as an approximation of the average steady-state concentration. Even though Css max and Css min exist,

Css max =[(S)(F)(Dose)/V]/(1-e-kτ)

and

Css min =[(S)(F)(Dose)/V]/(1-e-kτ)*(e-kτ)

and could be used to predict peak and trough concentrations, a reasonable approximation could also be achieved by using the Css ave, that is

Css ave =(S)(F)(Dose/τ)/Cl

This suggests that even though Css max and Css min do not contain the parameter clearance per se, the elimination rate constant functions in such a way that the clearance derived from Css max or Css min and Css ave would all essentially be the same.

In the situation in which the dosing interval is greater than one-third of a half-life, the use of Css max and Css min are appropriate as not all drug concentrations within the dosing interval can be considered as the Css ave. However, as long as the dosing interval has not been extended beyond one half-life, clearance is still the primary pharmacokinetic parameter that is responsible for the drug concentrations within the dosing interval. Although the elimination rate constant and volume of distribution might be manipulated in Css max and Css min, it is only the product of those two numbers (i.e., clearance) that can be known with any certainty: Cl = (K) (V).

If a drug is administered at a dosing interval that is much longer than the apparent half-life, peak concentrations may be primarily a function of volume of distribution. Since most of the dose is eliminated within a dosing interval, each dose can be thought as something approaching a new loading dose. Of course for steady-state conditions, at some point within the dosing interval, the plasma concentration (Css ave) will be determined by clearance. Trough plasma concentrations in this situation are a function of both clearance and volume of distribution. Since clearance and volume of distribution are critical to the prediction of peak and trough concentrations when the dosing interval is much longer than the drug t1/2, a minimum of two plasma concentrations is needed to accurately establish patient-specific pharmacokinetic parameters and a dosing regimen that will achieve desired peak and trough concentrations.


Choosing A Model to Revise or Estimate A Patient's Clearance at Steady State

As previously discussed, a drug's half-life often determines the pharmacokinetic equation that should be used to make a revised or patient-specific estimate of a pharmacokinetic parameter. A common problem encountered clinically, however, is that the half-life observed in the patient often differs from the expected value. Since a change in either clearance or volume of distribution or both may account for this unexpected value, the pharmacokinetic model is often unclear. One way to approach this dilemma is to first calculate the expected change in plasma drug concentration assocaited with each dose:

delta C = (S) (F) (Dose) / V

where delta C is the change in concentration following the administration of each dose into the patient's volume of distribution. This change in concentration can then be compared to the steady-state trough concentration measured in the patient.

(S) (F) (Dose) / V versus Css min

or

delta C versus Css min

When the dosing interval (tau) is much less than the drug half-life, delta C will be small when compared to Css min. As the dosing interval increases relative to tau, delta C will increase relative to Css min. Therefore, a comparison of delta C or (S) (F) (Dose) / V to Css min can serve as a guide to estimating the drug t1/2 and the most appropriate pharmacokineitc model or technique to use for revision. With few exceptions, drugs that have plasma level monitoring are most often dosed at intervals less than or equal to their half-lives. Therefore, clearance is the pharmacokinetic parameter most often revised or calculated for the patient in question. The following guidelines can be used to select the pharmacokinetic model that is the least complex and therefore the most appropriate to estimate a patient-specific pharmacokientic parameter.

Condition 1

When, (S) (F) (Dose) / V =< 1/4 Css min

Then, tau =<1/3 t1/2

Under these conditions, Css min ≈ Css ave

And Cl can be estimated by Cl = (S) (F) (Dose / tau) / Css ave

Rules/Conditions: Must be at steady state.

Condition 2

When, (S) (F) (Dose) / V =< Css min

Then, tau =< t1/2

Under these conditions, Css min + (1/2) (S) (F) (Dose) / V ≈ Css ave

And Cl can be estimated by Cl = (S) (F) (Dose / tau) / Css ave

Rules/Conditions: Must be at steady state; C is Css min; Bolus model for absorption is acceptable (dosage form is not sustained release; short infusion model is not required, that is, tin =<1/6t1/2)

Conditon 3

When, (S) (F) (Dose) / V > Css min

Then, tau > t1/2

Under these conditions: Css min + (S) (F) (Dose) / V = Css max

where V is an assumed value from the literature.

K is revised (Krevised):

Krevised = ln {[(Css min + (S) (F) (Dose / V)] / Css min} / tau = ln (Css max / Css min) / tau

Rules/Conditions: Must be at steady state; C is Css min; Bolus model for absorption is acceptable (dosage form is not sustained release; short infusion model is not required, that is, tin =< 1/6 t1/2)

Note that the approaches used become more complex as the dosing interval increases relative to the drug half-life. If a drug is administered at a dosing interval less than or equal to one-third of its half-life and the technique in Condition 3 is used to revise clearance, the revised clearance would be correct. The calculation is not wrong, just unnecessarily complex. However, if a drug is administered at a dosing interval that exceeds one half-life and the technique in Condition 1 is used to revise clearance, the revised clearance value would be inaccurate because Css min cannot be assumed to be approximately equal to Css ave. While it could be argued that the technique used in Condition 3 would suffice for all the previous conditions, it is more cumbersome and tends to focus on the intermediate parameters, K and V rather than Cl. One should also be ware that as the dosing interval increases, relative to the drug's half-life, the confidence in a revised clearance diminishes because the volume of distribution, which is an assumed value from the literature, begins to influence the revised clearance to a greater degree. As a general rule, the confidence in Cl is usually good when the dosing interval is < t1/2, steady state has been achieved, and drug concentrations are obtained properly.

The TDM of Vancomycin

August 16, 2016 Critical Care, Infectious Diseases, Pharmacokinetics No comments , , , , ,

Question #1. B.C., a 65-year old, 45-kg man with a serum creatinine concentration of 2.2 mg/dL, is being treated for a presumed hospital-acquired, MRSA infection. Design a dosing regimen that will produce peak concentration less than 40 to 50 mg/L and through concentrations of 5 to 15 mg/L.

Target Plasma Concentration

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Clearance and Volume of Distribution

The first step in calculating an appropriate dosing regimen for B.C. is to estimate his pharmacokinetic parameters (i.e., volume of distribution, clearance, elimination rate constant, and half-life).

The volume of distribution for B.C. can be calculated by using Equation 13.1.

V (L) = 0.17 (age in years) + 0.22 (TBW in kg) + 15

So, B.C.'s expected volume of distribution would be: V (L) = 0.17 (65 yrs) + 0.22 (45 kg) + 15 = 36.0 L [Equation 13.1]

Using Equation 13.2 and Equation 13.4 to calculated B.C.'s expected creatinine clearance and vancomycin clearance.

Clcr for males (mL/min) = (140 – Age)(Weight in kg) / [(72)(SCrss)] [Equation 13.2]

Vancomycin Cl ≈ Clcr [Equation 13.4]

For B.C. the vancomycin Cl ≈ (140 – 65 yrs)(45 kg) / [(72)(2.2 mg/dL)] = 21.3 mL/min = 1.28 L/hr

The calculated vancomycin clearance of 1.28 L/hr and the volume of distribution of 36.0 L then can be used to estimate the elimination rate constant of 0.036 hr-1. And the corresponding vancomycin half-life can be calculated, which equals (0.693)(V) / Cl = 19.5 hr.

Loading Dose

In clinical practice, loading doses of vancomycin are seldom administered. This is probably because most clinicians prescribe about 15 mg/kg as their maintenance dose.

C0 = (S)(F)(Loading Dose) / V = (1)(1)(15 mg/kg x 45 kg) / 36 L = 18.8 mg/L ≈ 20 mg/L (Equation 13.8)

If you want to administer a loading dose, the loading dose = (V)(C) / [(S)(F)] = (36.0 L)(30 mg/L) / [(1)(1)] = 1080 mg or ≈ 1000 mg.

Steady-State

During the steady-state, Css max = Css min + [(S)(F)(Dose) / V] (Equation 13.5). This equation is based on several conditions including: 1) Steady state has been achieved; 2) the measured plasma concentration is a trough concentration; and 3) the bolus dose is an acceptable model (infusion time <1/6 half-life).

In the clinical setting, trough concentrations are often obtained slightly before the true trough. Because vancomycin has a realtive long half-life, most plasma concentrations obtained within 1 hour of the true trough can be assumed to have met condition 2 above.

Since vancomycin follows a multicompartmental model, it is difficult to avoid the distribution phase when obtaining peak plamsa concentrations. If peak levels are to be measured, samples should be obtained at least 1 or possibly 2 hours after the end of the infusion period. It is difficult to evaluate the appropriateness of a dosing regimen that is based on plasma samples obtained before steady state. Additional plasma concentrations are required to more accurately estimate a paient's apparent clearance and half-life, and to ensure that any dosing adjustments based on a non-steady-state trough concentration actually achieve the targeted steady-state concentrations.

Maintenance Dose

The maintenance dose can be calculated by a number of methods. One approach might be to first approximate the hourly infusion rate required to maintain the desired average concentration. Then, the hourly infusion rate can be multiplied by an appropriate dosing interval to calculate a reasonable dose to be given on an intermittent basis. For example, if an average concentraion of 20 mg/L is selected (approximately halfway between the desired peak concentration of ≈ 30 mg/L and trough concentration of ≈ 10 mg/L), the hourly administration rate would be 25.6 mg/hr.

Maintenance Dose = (Cl)(Css ave)(tau) / [(S)(F)] 

For this patient the 24 hour dose should be (1.28 L/hr)(20 mg/L)(24 hr) / [(1)(1)] = 614 mg ≈ 600 mg

– or –

Maintenance delivery rate = Dose/tau = (Cl)(Css ave) / [(S)(F)]

For this patient the maintenance deliver rate = (1.28 L/hr)(20 mg/L) / [(1)(1)] = 25.6 mg/hr

The second approach that can be used to calculate the maintenance dose is to select a desired peak and trough concentration that is consistent with the therapeutic range and B.C.'s vancomcin half-life. For example, it steady-state peak concentrations of 30 mg/L are desired, it would take approximately two half-lives for that peak level to fall to 7.5 mg/L. Since the vancomycin half-life in B.C. is approximately 1 day, the dosing interval would be 48 hours. The dose to be administered every 48 hours can be calculated as follows using Equation 13.5:

Dose = (V)(Css max – Css min) / [(S)(F)] = (36.0 L)(30 mg/L – 7.5 mg/L) / [(1)(1)] = 810 mg ≈ 800 mg

The peak and trough concentrations that are expected using this dosing regimen can be calcualted by using Equations 13.12 and 13.14, respectively.

Css max = (S)(F)(Dose) / {V x [1- e(-k*tau)]} = 27.0 mg/L (Equation 13.12)

Note that although 27 mg/L is an acceptable peak, the actual clinical peak would normally be obtained approximately 1 hour after the end of a 1-hour infusion, or 2 hours after this calculated peak concentration, and would be about 25 mg/L, as calculated by Equation 13.13.

C2 = C1[e(-k*t)] = 25.1 mg/L (Equation 13.13)

The calculated trough concentration would be about 5 mg/L.

Css min = (S)(F)(Dose / V)[e(-k*tau)] / [1 – e(-k*tau)] = (Css max)[e(-k*tau)] = 4.8 mg/L (Equation 13.14 and 13.15)

This process of checking the expected peak and trough concentrations is most appropriate when the dose or the dosing interval has been changed from a calculated value (e.g., twice the half-life) to a practical value (e.g., 8, 12, 18, 24, 36, or 48 hours). Many institutions generally prefer not to use dosing intervals of 18 or 36 hours because the time of day whent the next dose is to be given changes, potentially resulting in dosing errors. If different plasma vancomycin concentrations are desired, Equations 13.12 and 13.14 can be used target specific vancomycin concentrations by adjusting the dose and/or the dosing interval.

A third alternative is to rearrange Equation 13.14, such that the dose can be calculated:

Dose = (Css min)(V)[1 – e(-k*tau)] / {(S)(F)[e(-k*tau)]} (Equation 13.16)