Clinical Pharmacokinetics (1)A fundamental hypothesis of clinical pharmacokinetics is that a relationship exists between effects of a drug and concentration of the drug in biological fluids.Clinical pharmacokinetics attempt to provide both a quantitative relationship between the dose and effect and a framework with which to interpret measurements of drug concentrations in biological fluids.The importance of pharmacokinetics in patient care rests on improvement in therapeutic efficacy that can be attained by attention to its principles when dosage regimens are chosen and modified.

Clinical Pharmacokinetics (2)It is a discipline that use mathematical models to describe and predict drug amounts and concentrations in various body fluids and the change in these quantities overtime.

Clinical Pharmacokinetics (3)Four most important pharmacokineticsparameters that dictate adjustment of dosage in individual patients:clearance (a measure of the bodys ability to eliminate drugs); volume distribution (a measure of the apparent space in the body available to contain the drug);elimination half-life ( a measure of rate of removal of drug from the body); and bioavailability (the fraction of drug absorbed as such into the systemic circulation).

Clearance (1)Is defined as that fraction of the apparent volume of distribution is removed in unit of time ml/min/kgIndicates the volume of biological fluid that would have to be completely freed of drug to account for eliminationThe total body clearance is usually subdivided into renal and non-renal (hepatic) clearances

The plasma clearance of cephalexin is 4.3 ml/min per kg with 90% of the drug excreted unchanged in the urine. For 60-kg man, the clearance from plasma would be 258/min, with renal clearance accounting for 90% of this elimination. Thus the kidney is able to excrete cephalexin at a rate such that the drug is completely removed (cleared) from approximately 232.2 ml of plasma per minute.

Clearance (2)Is the most important concept to be considered when a rational regimen for long-term drug administration is to be designed. We want to maintain steady-state concentrations of a drug within a known therapeutic range.The steady-state will be achieved when the rate of drug elimination equals the rate of drug administration:

Dosing rate = CL . Css (1-1)If the steady-state concentration of drug in blood is known, the rate of drug clearance by the patient will dictate the rate at which the drug should be administered.

Clearance (3) The clearance of a given drug is constant over the range of concentration encountered clinically, because the absolute rate of drug elimination is essentially a linear function of its plasma concentration.It means that the elimination of most drugs follows first order kinetics a constant fraction of drug is eliminated per unit of time.

First Order Kinetics (1)It is a type of kinetic behavior that apply to a large number of drugs.Drug distribution or elimination obeys this model.It means that the rate of change of drug concentrations overtime varies continuously in relation to the concentration itself.This concept can be presented in mathematical language: C/t = -kC k is a rate constant = a proportionality factor per unit of time.

First Order Kinetics (2)The equation indicates that when drug concentrations are high, the rate of decline of drug concentration is also high. At low concentration, the rate of decline is also low.When plotted on a graph, the concentration starts at an initial value at zero time, then declines in a curvilinear fashion.At high concentration, the rate of decline is rapid, at low levels the decline is slow.The graph shows that first-order kinetic governs an exponential fall in drug concentrations overtime: Ct = C0 e-kt

First-Order Kinetics (3)When plotted on semilogarithmic graphs, the first order process becomes straight line, from which it is easy to determine half-life and rate constant (k).Ct = C0 e-kt (e=2.7828) ln Ct = ln C0 kt log Ct = log C0 kt/2.303. (C0 is the intercept; k/2.303 is the slope of the straight-line; ).When Ct = 1/2 Co t1/2 (half-life) = 0.693/k

k = 0.693/t1/2

Clearance (4)Drug clearance is similar to creatinine clearance, where the rate of creatinine elimination in the urine is relative to its concentration in plasma. Clearance of a drug is its elimination by all routes normalized to the concentration of the drug in biological fluid where measurement can be made:

CL = Rate of elimination/C (1-2)

Clearance (5)For a single dose of a drug with complete bioavailability (F=100%) and first order kinetic elimination, total systemic clearance may be determined from a mass balance and the integration of equation (1-2) over time:

CL = F.Dose/AUC (1-3) AUC is the total area under the curve that describes the drug concentration in the systemic circulation as a function of time, from zero to infinity.

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Volume of distributionIs defined as the fluid volume that would be required to contain all the drug in the body at the same concentration as in the blood or plasma:

Vd = amount of drug in the body/C (1-4)The plasma volume is about 3 L, blood volume is 5.5 L, the extra cellular fluid is 12 L, and the volume of TBW is 42 L for a typical 70 kg man

Volume of distributionMany drugs exhibit Vd for an excess of those values. For example, if 500 ug of digoxin were in in the body of a 70 kg subject, a plasma conc. Of 0.75 ng would be observed.Vd = 500 ug/0.75 ng/ml = 700 L, a value 10 x greater than TBW of 70 kgDigoxin distributes preferentially to muscle, adipose tissue and its specific receptor, leaving a very small amount in the plasma.

Volume of distributionVd may vary widely depending on pKa, degree of binding to plasma protein, the partition coefficient of the drug in fat, the degree of binding to other tissues, and so forthVd for a given drug can vary according to patients age, gender, disease, and the body composition

Volume of DistributionThe Vd in equation (1-4) considers the body as single compartment. In this one-compartment model, all drug administration occurs directly into the central compartment and distribution of drug is instantaneous throughout volume (V).Clearance of drug from this compartment occurs in a first order kinetic; that is, the amount of drug eliminated per unit time depends on the amount (concentration) of drug in the body compartment.

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Volume of distributionThe decline of plasma concentration with time for a drug introduced into one-compartment model : Ct = (Dose/Vd) . exp(-kt) (1-5) Ct = C0 . exp(-kt) k = 0.693/t1/2 (1-6)k = the rate constant for elimination that reflects the fraction of drug removed from the compartment per unit of time.The one-compartment model is sufficient to apply to most clinical situation for most drugs

024681012Time (Hours)2481632Plasma Drug Concentration g/ml t CoVd = Dose/CoThe semi-logarithmic plot of plasma concentration vs. time

Half-Life (t1/2)It is the time it takes for the plasma concentration as the amount of drug in the body to be reduced by 50%.It is a derived parameter that changes as a function of both clearance and Vd.Relationship between t1/2, clearance, and Vd at steady state is given by:

t1/2 = 0.693. Vss/CL (1-7)

Half-life (t1/2)CL is the measure of bodys ability to eliminate a drug; as CL decreases due to a disease process, t1/2 would be expected to increase. This reciprocal relation is valid only when the disease does not change Vd.T1/2 of diazepam increases with aging; it is not CL that change as a function of age, but the volume of distribution.

Half-Life (t1/2)Changes in drug protein binding may affect its CL as well as its Vd, leading to an unpredictable changes in t1/2.Although it can be a poor index of drug elimination, t1/2 provides a good indication of time required to reach steady state after a dosage regimen is initiated. It is required four half-lives to reach approximately 94% of a steady-state drug concentration in the body.It is also and indication of the time for a drug to be removed from the body, and a means to estimate the appropriate dosing interval.

Steady-State Drug ConcentrationA steady-state concentration will be achieved when a drug is administered at a constant rate. At this state, drug elimination (the product of clearance and concentration; see equation 1-2) will equal the rate of drug availability.This concept also extend to intermittent dosage. During each interdose interval, the concentration of drug rises and falls. Equation 1-1 still applies, but it describes the average drug concentration.Average concentration when the steady-state is attained:

Css = F. Dose / (CL . T) (1-8)

BioavailabilityIs defined as the amount of administered drugs which reaches the systemic intactIt is determined from the relationship between AUC after equivalent IV and PO doses

F (absolute) = AUC after oral dose/AUC after IV doseF (relative) = AUC after an oral dose of me-too product AUC after an oral dose of original product

Nonlinear Pharmacokinetics Due to Saturable Protein BindingAs protein binding become saturated, the unbound fraction eventually has to increase.For a drug of low hepatic extraction ratio, saturation of protein binding will cause both Vd and CL to increase as drug conc. increase; t1/2 may remain constant. For such a drug, Css will not increase linearly as the rate of drug administration is increased ( see equation 1-8). For a drug of high hepatic extraction ratio, saturation of protein binding will not change hepatic CL, but the increase in Vd would increase the t1/2; Css can remain linearly proportional to the rate of drug administration. Most drugs fall between two extremes.

Nonlinear Kinetics Due to Saturable MetabolismThe Michaelis-Menten equation describes the nonlinearity of saturable metabolism:

CLp = Vm.Cp / (Km+Cp) (1-9) CLp = total plasma clearance; Vm = the maximal rate of elimination; Km = the plasma concentration at which half of the maximal rate of elimination is reached; Cp = plasma drug concentration.All active processes will become saturable, but they appear to be linear if values of drug concentrations are much less than Km. When they exceed Km, nonlinear kinetics are observed.

Nonlinear Kinetics Due to Saturable MetabolismThe major consequences of saturation of metabolism are the opposite of those saturation of protein binding.Saturation of protein binding will lead to increased CL because CL increases as drug conc. Increases, whereas saturation of metabolism may decrease CL.When both conditions are present simultaneously, they may cancel each others effects, and surprisingly linear kinetics may result.Saturable metabolism causes first-pass metabolism to be less, Css increases greater than increase in the rate of drug administration.

Nonlinear Kinetics Due to Saturable First-Pass Metabolism It causes oral first-pass metabolism to be less than expected ( higher bioavailability, F ), there is a greater fractional increase in Css:

dosing rate. Km Css = --------------------- Vm dosing rate

Optimization of Dosage RegimensIn drug therapy usually it is asked: What degree of effect is desired and achievable?Some effect of the drug is easily measured (e.g., blood pressure), so it can be used to guide dosage, and a trial-and-error approach to optimal dosage is both practical and sensible. For some drugs, the effects are difficult to measure, toxicity and lack of efficacy are both potential danger, or the therapeutic window is narrow. In these circumstances doses must be titrated to achieve a target level.

Target-Level Strategy of Dosage RegimensA desired (target) steady-state concentration of the drug in plasma is chosen, and a dosage is computed that is expected to achieve this value. Drug concentrations are subsequently measured, and the dosage is adjusted if necessary to approximate the target more closely.To apply the target-level strategy, the therapeutic objectives must be defined in a range called therapeutic range. For many drugs, the lower limit of therapeutic range appears to be equal to the concentration that produces half of the greatest possible effect. The upper limit of the range is fixed by toxicity (5% to 10% of patients will have a toxic effect).

Maintenance Dose of Dosage RegimensDrugs are administered in a series of repetitive dose as a continuous infusion in order to maintain a steady-state concentration in plasma within a given therapeutic range. Thus, calculation of the appropriate maintenance dosage is a primary goal.To maintain the target concentration, the rate of drug administration is adjusted such that the rate of input equals the rate of loss:

Dosing rate = target Cp . CL/F (1-10)

An Example of Maintenance Dose CalculationA steady-state plasma concentration of theophylline of 15 mg/l is desired to relieve acute bronchiale asthma in a 68-kg patient. If the patient does not smoke and is otherwise normal except for asthmatic condition, one can use a mean theophylline clearance of 0.65 ml/min/kg. F = 1 because the drug is to be given intravenously.Dosing rate = Target . CL/F = 15 ug/ml x 0.65 ml/min/kg = 9.75 ug/min/kg = 40 mg/h for a 68-kg patient.

Dosing Interval for Intermittent Dosage (1)Marked fluctuations in drug concentrations between doses are not beneficial.If absorption and distribution were instantaneous, fluctuation of drug concentrations between doses would be governed entirely by the drugs elimination half-life. If the dosing interval (T) was chosen to be equal to the half-life, then the total fluctuation would be twofold.For some drugs with a narrow therapeutic range, it may be important to estimate the maximal and minimal concentrations that will occur for a particular dosing interval.

Dosing Interval for Intermittent DosageCss,min can be determined by the use of equation:

f.Dose/Vss Css,min = --------------------- . Exp(-kT) (1-11) 1-exp(-kT)One may easily predict Css,max by omitting the exp(-kT) in the numerator of equation (1-11).

f.Dose/Vss Css,max = -------------------- (1-12) 1-exp(-kT)

Examples of Css,max and Css,min Calculation The clinician wants to maintain plasma concentration of theophyllin at 15mg/l with oral dose of 960 mg/day. What is the appropriate dosage regimen for this patient?For a 12-hour dosing interval (T) the maximal and minimal concentration would be:

480mg/34 liters Css,max= -------------------------- = 21.7 mg/l 0.65 ml/min/kg Css,min= (21.7mg/liter . (0.35) = 7.6 mg/l

For T=6, Css,max=17mg/l; Css,min=10mg/l

Loading DoseA loading dose is one of a series of doses that may be given at the onset of therapy with the aim of achieving the target concentration rapidly:

Loading dose=Target concentration.Vss/F

Therapeutic Drug Concentration Monitoring (1)The major use of measured drug concentrations at steady-state is to refine the estimate of CL/F for the patient being treated:

CL/F (patient) = dosing rate/Css (measured)

The calculated CL/f can be used to adjust the new maintenance dose to achieve the desired target concentration:

Adjusted dosing rate=target concentration.CL/F

Therapeutic Drug Concentration MonitoringIf a drug follows first-order kinetics, the average, minimum, and maximum concentrations at steady-state are linearly related to dose and dosing rate. Therefore, the ratio between the measured and the desired concentration can be used to adjust the dose:

Css(measured) Dose(previous) ----------------- = ------------------ Css(desired) Dose(new)

If the measured steady-state concentration (Css) is found to be 1.65 ng/ml rather than a desired level of 1.3 ng/ml, what is the appropriate dose for a patient receiving digoxin 0.375 mg/day?

Css (measured) New dose = -------------------- X previous dose Css (desired) = 1.3 / 1.5 X 0.375 = 0.25 mg/day.

Pharmacokinetic data available for designing and optimizing dosage regimensAvailability (%)Urinary excretion (%)Bound in plasma (%)Clearance (ml/min/kg/BW)Volume of distribution (L/kg BW)Half-life (hours)Effective concentration (g/ml)Toxic concentration (g/ml)

Examples of pharmacokinetic calculationThe Vd and clearance of theophylline is 35 L and 3 L/h respectively in a 70 kg person. If the target concentration is 10 ugr/ml, then the loading dose is :Loading dose = Target Cp . Vss/F = 10 g/ml . 35 L = 350 mg

Examples of pharmacokinetic calculationMaintenance dose rate = clearance . concentration = 3 l/h . 10 mg/l = 30 mg/h = 720 mg/dayHalf-life = 0.693 . Vd/CL = 0.693 . 35 L/ 31/h = 8 hoursThe expected time to achieve 90 % Css is about 4 half-lives or 32 hours