## The TDM of Vancomycin

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

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.

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.

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)

## Extended-Release Drug Products

Most conventional (immediate release) oral drug products, such as tablets and capsules, are  formulated to release the active drug immediately after oral administration. In the formulation of conventional drug products, no deliberate efforts is made to modify the drug release rate. Immediate-release products generally result in relatively rapid drug absorption and onset of accompanying pharmacodynamic effeccts. In the case of conventional oral products containing prodrug, the pharmacodynamic activity may be slow due to conversion to the active drug by hepatic or intestinal metabolism or by chemical hydrolysis. Alternatively, conventional oral products containing poorly soluble (lipophilic drugs), drug absorption may be gradual due to slow dissolution in or selective absorption across the GI tract, also resulting in a delayed onset time.

PS: Rate-limiting Steps in Drug Absorption

• Disintegration of the drug product and subsequent release of the drug (rate-limiting step)
• Dissolution of the drug in an aqueous environment (rate-limiting step)
• Absorption across the cell membranes into the systemic circulation (rate-limiting step)

The term modified-releae drug product is used to describe products that alter the timing and/or the rate of release of the drug substance. The pattern of drug release from modified-release (MR) dosage forms is deliberately changed from that of a conventional (immediate-release) dosage formulation to achieve a desired therapeutic objective or better patient compliance. Types of MR drug products include delayed release (e.g., enteric coated), extended release (ER), and orally disintegrating tablets (ODT). The modified-release drug products include:

• Extended-release drug products. A dosage form that allows at least a twofold reduction in dosage frequency as compared to that drug presented as an immediate-release (conventional) dosage form, including controlled-release, sustained-release, and long-acting drug products.
• Delayed-release drug products. A dosage form that releases a discrete portion or portions of drug at a time other than promptly after administration. An initial portion may be released promptly after administration. Enteric-coated dosage forms are common delayed-release products.
• Targeted-release drug products. A dosage form that releases drug at or near the intended physiologic site of action. Targetd-release dosage forms may have either immediate- or extended-release characteristics.
• Orally disintegrating tablets (ODT). ODT have been developed to disintegrate rapidly in the saliva after oral administration. ODT may be used without the addition of water. The drug is dispersed in saliva and swallowed with little or no water.

The Mission of MR Products

Modified-release drug product should produce a pharmacokinetic profile that provides the desired therapeutic efficacy and minimizes adverse events.

Ideally, the extended-release drug product should release the drug at a constant or zero-order rate. As the drug is released from the drug product, the drug is rapidly absorbed, and the drug absorption rate should follow zero-order kinetics similar to an intravenous drug infusion. The drug product is designed so that the rate of systemic drug absorption is limited by the rate of drug release from the drug delivery system. Unfortunately, most ER drug products that release a drug by zero-order kinetics in vitro do not demonstrate zero-order drug absorption, in vivo. The lack of zero-order drug absorption from these ER drug products after oral administration may be due to a number of unpredictable events happening in the gastrointestinal tract during drug absorption. For factors affecting oral drug absorption please visit the thread "Drug Absorption in Gastrointestinal Tract" at http://www.tomhsiung.com/wordpress/2016/04/drug-absorption-in-the-gastrointestinal-tract/.

ER drug products offer several important advantages over immediate-release dosage forms of the same drug. Extended release allows for sustained therapeutic blood levels of the drug; sustained blood levels provide for a prolonged and consistent clinical response in the patient. Moreover, if the drug input rate is constant, the blood levels should not fluctuate between a maximum and minimum compared to a multiple-dose regimen with an immediate-release drug product. Highly fluctuating blood concentrations of drug may produce unwanted side effects in the patient if the drug level is too high, or may fail to exert the proper therapeutic effect if the drug level is too low. Another advantage of extended release is patient convenience, which leads to better patient compliance. The third advantage is the possible benefit on econmic, that a single dose of an extended-release product may cost less than an equivalent drug dose given several times a day in rapid-release tablets. And the final benefit is that for patients under nursing care, the cost of nursing time required to administer medication is decreased if only one drug dose is given to the patient each day.

There are also a number of disadvantages in using extended-release medication. If the patient suffers from an adverse drug reaction or accidentally becomes intoxicated, the removal of drug from the system is more difficult with an extended-release drug product. Orally administered extended-release drug products may yield erratic or variable drug absorption as a result of various drug interactions with the contents of the GI tract and changes in GI motility. The formulation of extended-release drug products may not be practical for drugs that are usually given in large doses (e.g., 500 mg) in conventional dosage forms. Because the extended-release drug product may contain two or more times the dose given at more frequent intervals, the size of the extended-release drug product may have to be quite large, too large for the patient to swallow easily.

The extended-release dosage form contains the equivalent of two or more drug doses given in a conventional dosage form. Therefore, failure of the extended-release dosage form may lead to dose dumping. Dosing dumping is defined either as the release of more than the intended fraction of drug or as the release of drug at a greater rate than the customary amount of drug per dosage interval, such that potentially adverse plasma levels may be reached.

Kinetics of Extended-Release Dosage Form

The amount of drug required in an extended-release dosage form to provide a sustained drug level in the body is determined by the pharmacokinetics of the drug, the desired therapeutic level of the drug, and the intended duration of action. In general, the total dose required (Dtot) is the sum of the maintenance dose (Dm) and the initial dose (DI) released immediately to provide a therapeutic blood level.

Dtot = DI + Dm (Equation 17.1)

In practice, Dm (mg) is released over a period of time and is equal to the product of td (the duration of drug release) and the zero-order rate kr0td (mg/h). Therefore, Equation 17.1 can be expressed as

Dtot = DI + kr0td (Equation 17.2)

Ideally, the maintenance dose (Dm) is released after DI has produced a blood level equal to the therapeutic drug level (Cp). However, due to the limits of formulations, Dm actually starts to release at t = 0. Therefore, D1 may be reduced from the calculated amount to avoid "topping."

Dtot = DI – kr0tp + kr0td (Equation 17.3)

Equation 17.3 describes the total dose of drug needed, with tp representing the time needed to reach peak drug concentration after the initial dose.

For a drug that follows a one-compartment open model, the rate of elimination (R) needed to maintain the drug at a therapeutic level (Cp) is

R = CpClT (Equation 17.5)

where ClT is the clearance of the drug and kr0 must be equal to R (kr0 = R) in order to provide a stable blood level of the drug. So if we substitute R for kr0 we get the follow expression:

Dtot = DI + CpClT*tau (Equation 17.6)

For many sustained-release drug products, there is no built-in loading dose (i.e., DI = 0). The dose needed to maintain a therapeutic concentration for tau hours is

D0 = CpClT*tau (Equation 17.6)

(The End)

## Pharmacokinetics Series – Clearance and Maintenance Dose

Clearance and Maintenance Dose

Clearance can be thought of as the intrinsic ability of the body or its organs of elimination (usually the kidneys and the liver) to remove drug from the blood or plasma. Clearance is expressed as a volume per unit of time. It is important to emphasise that clearance is not an indicator of how much drug is being removed; it only represents the theoretical volume of blood or plasma which is completely cleared of drug in a given period. The amount of drug removed depends on the plasma concentration of drug and the clearance.

As steady state, the rate of drug administration (RA) and the rate of drug elimination (RE) must be equal, so that, RA = RE. Because RA can be described as (S)(F)(Dose/τ), and the RE equals to (Cl)(Css ave), we get the formula for Cl as Cl = (S)(F)(Dose/τ)/(Css ave) [Equation 1].

If an estimate for clearance is obtained from the literature, the clearance formula of [Equation 1] can be rearranged and used to calculate the rate of administration or maintenance dose that will produce a desired average plasma concentration of (Css ave) at steady state: Maintenance Dose = (Cl)(Css ave)(τ)/[(S)(F)] [Equation 2].

Attention must be paid that the units of all factors in these formulas must be consistent.

Factors Affecting Clearance

Body Surface Area/Weight

Most literature values for clearance are expressed as volume/kg/time or as volume/70 kg/time. There is some evidence, however, that drug clearance is best adjusted on the basis of BSA rather than weight. BSA can be calculated using BSA in m2 = (Patient’s Weight in kg/70 kg)0.7(1.73 m2) [Equation 3] or it can be obtained from various charts and nomograms. The value of a patient’s weight divided by 70 taken to the 0.7 power is an attempt to scale or size a patient as a fraction of the average 1.73 m2 or 70-kg individual. Weight divided by 70 taken to the 0.7 power has no units and should be thought of as the fraction of the average-size person.

As an example, a 7-kg patient has a weight ratio relative to 70 kg of 0.1 and, therefore, may be thought of as having a size and thus a metabolic and renal capacity that is one-tenth of the average 70-kg person (7 kg/70 kg = 0.1). If the same weight individual was compared to the 70-kg standard using weight to the 0.7 power, the ratio becomes 0.2 or 20%, (7 kg/70 kg)0.7 = 0.2. Therefore in these two examples, the difference between  0.1 and 0.2 is large. However, when patients do not differ significantly from 70 kg, the difference between using weight versus weight to the power 0.7 (BSA) becomes less significant.

The underlying assumption in using weight or surface area to adjust clearance is that the patient’s liver and kidney size (and hopefully function) vary in proportion to these physical measurements (weight or BSA). However, this may not always be the case; therefore, clearance values derived from the patient population having a similar age and size should be used whenever possible. When a patient’s size is substantially greater or less than the standard 70 kg, or 1.73 m2, a careful assessment should be made to determine if the patient’s body stature is normal, obese, or emaciated. In obese and emaciated patients, neither weight nor surface area is likely to be helpful in predicting clearance, since the patient’s body size will not reflect the size or function of the liver and kidney.

Plasma Protein Binding

For highly protein-bound drugs, diminished plasma protein binding is associated with a decrease in reported steady-state plasma drug concentrations (total of unbound plus free drug) for any given dose that is administered. According to Equation 1, a decrease in the denominator, (Css ave), increases the calculated clearance. This actually would be misleading, however, to assume that because the calculated clearance is increased, the amount eliminated of drug per unit of time has increased. Equation 1 assumes that when (Css ave) changes, the free drug concentration, which is available for metabolism and renal elimination, changes proportionately. In actuality the free or unbound fraction of drug in the plasma generally increases with diminished plasma protein binding. As a result, the amount of free drug eliminated per unit of time remains unchanged. This should be apparent if one considers that at steady state, the amount of drug administered per unit of time (RA) must equal the amount eliminated per unit of time (RE). If RA has not changed, RE must remain the same.

In summary, when the same daily dose of a drug is given in the presence of diminished protein binding, an amount equal to that dose will be eliminated from the body each day at steady state despite a diminished steady-state plasma concentration (Css ave) and an increase in the calculated clearance (Cl). This lower plasma concentration (C bound + C free) is associated with a decreased C bound, no change in C free, and as a result there is an increase in the fraction of unbound drug (fu). Therefore, the pharmacologic effect achieved will be similar to that produced by the higher serum concentration observed, under normal protein binding conditions. This example re-emphasizes the principle that clearance alone is not a good indicator of the amount of drug eliminated per unit of time (RE).

Extraction Ratio

The direct proportionality between calculated clearance and fraction unbound (fu) does not apply to drugs that are so efficiently metabolised or excreted that some (perhaps all) of the drug bound to plasma protein is removed as it passes through the elimination organ. In this situation the plasma protein acts as a “transport system” for the drug, carrying it to the eliminating organs, and clearance becomes dependent on the blood or plasma flow to the eliminating organ. To determine whether the clearance for a drug with significant plasma binding will be influenced primarily by blood flow or plasma protein binding, its extraction ratio is estimated and compared to its (fu) value.

The extraction ratio is the fraction of the drug presented to the eliminating organ that is cleared after a single pass through that organ. It can be estimated by dividing the blood or plasma clearance of a drug by the blood or plasma flow to the eliminating organ. If the extraction ratio exceeds the (fu), then the plasma proteins are acting as a transport system and clearance will not change in proportion to (fu). If, however, the extraction ratio is less than (fu), clearance is likely to increase by the same proportion that (fu) changes. This approach does not take into account other factors that may affect clearance such as red blood cell binding, elimination from red blood cells, or changes in metabolic function.

Renal and Hepatic Function

Drugs can be eliminated or cleared as unchanged drug through the kidney and by metabolism in liver. These two routes of clearance are assumed to be independent of one another and additive. A decrease in the function of an organ of elimination is most significant when that organ serves as the primary route of drug elimination. However, as the major elimination pathway becomes increasingly compromised, the “minor” pathway becomes more significant because it assumes a greater proportion of the total clearance. For example, a drug that is usually 67% eliminated by the renal route and 33% by the metabolic route will be 100% metabolised in the event of complete renal failure; the total clearance, however, will only be one-third of the normal value.

Cardiac Output

Cardiac output also affects drug metabolism. Hepatic or metabolic clearances for some drugs can be decreased by 25% to 50% in patients with CHD. For example, the metabolic clearances of theophylline and digoxin are reduced by approximately one-half in patients with CHD. Since the metabolic clearance for both of these drugs is much lower than the hepatic blood or plasma flow (low extraction ratio), it would not have been predicted that their clearances would have been influenced by cardiac output. The decreased cardiac output and resultant hepatic congestion must, in some way, decrease the intrinsic metabolic capacity of the liver.