Clinical Pharmacokinetics and problem solving overview INTRODUCTION PHARMACOKINETICS

Clinical Pharmacokinetics and problem solving

overview • INTRODUCTION • PHARMACOKINETICS PARAMETERS – Linear/non-linear PK – Pharmacokinetics models – Clearance – Vd – Half-life – Bioavailability • DRUG DOSING IN – Renal & hepatic disease – Dialysis – Heart failure – Obesity - Time: …. min

Definition • Clinical pharmacokinetics is the application of pharmacokinetic principles to the safe and effective therapeutic management of drugs in an individual patient. • Enhancing efficacy and decreasing toxicity of a patient's drug therapy. • Plasma drug concentrations are affected by the rate at which drug is administered, the volume in which it distributes, and its clearance.

• When medications are given on a continuous basis(theophylline i. v 50 mg/hr, oral 300 mg/6 hr), serum concentrations increase until the rate of drug administration equals the elimination rate. • Steady-state serum or blood concentrations are used to assess patient response and compute new dosage regimens.

Linear/non-linear pharmacokinetics • When doses are increased for most drugs, steady-state concentrations increase in a proportional fashion leading to linear pharmacokinetics. • When steady-state concentrations change in a disproportionate fashion after the dose is altered, drug is said to follow nonlinear pharmacokinetics.

• Steady-state concentrations increase more than expected after a dosage increase, the most likely explanation is that the processes removing the drug from the body have become saturated. • When steady-state concentrations increase less than expected after a dosage increase, there are two typical explanations – Saturable plasma protein binding site- valproic acid & disopyramide – Carbamazepine increase their own rate of metabolism autoinduction • Drugs that exhibit nonlinear pharmacokinetics are oftentimes very difficult to dose correctly. • Drugs that follow linear pharmacokinetics is more straightforward and relatively easy

Problem no 1 • Two new antibiotics are marketed by a pharmaceutical manufacture. Reading the package insert, you find the following information CURACILLIN STEADY-STATE CONCENTRATIONS (mg/L) BETTERMYCIN STEADY-STATE CONCENTRATIONS (mg/L) 0 0 0 100 15 25 250 37. 5 62. 5 500 75 190 1000 150 510 Dose • What type of pharmacokinetics do each of these drugs follow?

Volume of distribution(Vd) • Fluid volume that would be required to contain all of the drug in the body at the same concentration measured in the blood or plasma: • Volume of distribution is an important pharmacokinetic parameter because it determines the loading dose=Css ⋅ V d. • How the drug binds in the blood or serum compared to the binding in tissues is also an important determinate of the Vd for a drug. • A drug's Vd therefore reflects the extent to which it is present in extra vascular tissues and not in the plasma, .

Problem no - 02 • If 3 g of a drug are added and distributed throughout a tank and the resulting concentration is 0. 15 g/L, calculate the volume of the tank. A. 10 L B. 20 L C. 30 L D. 200 L 3/0. 15= 20 L

Problem no - 03 • If 100 mg of drug X is administered intravenously and the plasma concentration is determined to be 5 mg/L just after the dose is given, calculate volume of distribution A B C D 20 L 25 L 500 L A 20 L

Problem no 4 • A physician wants to administer an anesthetic agent at a rate of 2 mg/hr by IV infusion. The elimination rate constant is 0. 1 hr– 1, and the volume of distribution (one compartment) is 10 L. What loading dose should be recommended if the drug level to reach 2 μg/m. L immediately?

Given, infusion rate =2 mg/hr elimination rate = 0. 1 hr– 1 volume of distribution =10 L Required concentration = 2 μg/m. L Loading dose = Vd X Css = 1000 m. L X 2 μg/m. L = 2000 μg = 20 mg Here we can calculate LD using infusion rate and elimination rate as well.

Pharmacokinetics models • A basic type of model used in pharmacokinetics is the compartmental model. • Compartmental models are categorized by the number of compartments needed to describe the drug's behavior in the body. • There are one- compartment, two-compartment, and multicompartment models. • The compartments do not represent a specific tissue or fluid but may represent a group of similar tissues or fluids. • These models can be used to predict the time course of drug concentrations in the body

¨ The one compartment model linear assumes that the drug in question is evenly distributed throughout the body into a single compartment. ¨ This model is only appropriate for drugs which rapidly and readily distribute between the plasma and other body tissues.

¨ Drugs which exhibit a slow equilibration with peripheral tissues, are best described with a two compartment model.

• The solid line shows the serum concentration/time graph for a drug that follows one-compartment model pharmacokinetics. • The dashed line represents the serum concentration/time plot for a drug that follows two- compartment model pharmacokinetics after an intravenous bolus is given.

Plasma concentration-time curve fallowing i. v administration of a drug (500 mg) to a 70 kg p • V= dose/Cp = 500/16= 31. 3 L • Cl=k. V= 90 m. L/mim • V= dose/Cp =500/31= 16. 1 L • Cl=k. V= 84 m. L/mim

Importance of two-compartment models • For many drugs, multicompartment kinetics may be observed for significant periods of time. • Failure to consider the distribution phase can lead to significant errors in estimates of clearance and in predictions of the appropriate dosage. • Also, the difference between the "central" distribution volume is important in deciding a loading dose strategy.

Clearance • The definition of clearance is the volume of serum or blood completely cleared of the drug per unit time. • Clearance is the most important pharmacokinetic parameter because it determines the maintenance dose=Cl. Css. • Theophylline clearance for a patient, 3 L/h and the desired steady-state theophylline serum concentration, 10 µg/m. L, theophylline maintenance dose to achieve this concentration would be 30 mg/h. • The liver is most often the organ responsible for drug metabolism while kidney is responsible for drug elimination.

Clearance(2) • The drug clearance for an organ is equal to the product of the blood flow to the organ and the extraction ratio of the drug. • extraction ratio (ER) : The ability of an organ to remove or extract the drug from the blood or serum ER = (Cin − Cout)/Cin • How the pharmacokinetics of a drug will change during a drug interaction or if a patient develops hepatic, renal, or cardiac failure.

Clearance(3) Hepatic clearance • hepatic clearance (Cl. H) for a drug is product of liver blood flow and the hepatic extraction ratio (ERH). Cl. H = LBF ⋅ Cl′int • ERH- intrinsic ability of the enzyme to metabolize a drug (intrinsic clearance) • hepatic clearance is very sensitive to changes in liver blood flow due to congestive heart failure or liver disease

Hepatic clearance • high hepatic extraction ratios(ER>70%) – Capacity to metabolize drug is very large, hepatic clearance is mainly a function of liver blood flow. – Cl. H, does not change much when protein binding displacement or enzyme induction or inhibition occurs due to drug interactions. – lidocaine, morphine, and most TCA. • low hepatic extraction ratio (ER<30%) – Cl. H does not change much when liver blood flow decreases secondary to liver or cardiac disease. – valproic acid, Phenytoin, and warfarin.

Clearance(4) Renal clearance • The physiological determinants of renal clearance are glomerular filtration rate (GFR), the free fraction of drug in the blood or serum (f. B), renal tubular secretion (Clsec), and the fraction of drug reabsorbed in the kidney (FR) • If the renal clearance of a drug is greater than glomerular filtration rate, it is likely that the drug was eliminated, in part, by active tubular secretion.

Problem no - 5 • Verapamil has a hepatic extraction ratio of 90% (ERH = 0. 90) For patients with normal liver blood flow (LBF = 1. 5 L/min) calculate hepatic clearance.

• Cl. H = LBF ⋅ ERH, Cl. H = 1. 5 L/min x 0. 90 = 1. 35 L/min; • hepatic clearance would be 1. 35 L/min

Half-life • The time that it takes for serum concentrations to decrease by 1/2 in the elimination phase is a constant and is called the half-life (t 1/2). • t 1/2 = 0. 693/ ke, • Ke, elimination rate constant = -(ln C 1 − ln C 2)/(t 1 − t 2)

The half-life, determines the time to steady state concentration and the dosage interval. The half-life is dependent parameters because their values depend on the clearance (Cl) and volume of distribution (Vd)

Problem no - 6 • After the first dose of gentamicin is given to a patient with renal failure, the following serum concentrations are obtained: TIME AFTER DOSAGE ADMINISTRATION (HOUR) CONCENTRATION (µg/m. L) 1 7. 7 24 5. 6 48 4. 0 • Compute the half-life and the elimination rate constant for this patient.

• ke =−(ln C 1 − ln C 2)/(t 1 − t 2) = −(ln 7. 7 − ln 4)/(1 h − 48 h) = 0. 0139 per hr. • The elimination rate constant can be used to calculate the half-life for the patient: t 1/2 = 0. 693/ke, = 0. 693/0. 0139 h− 1 = 50 h

Problem no - 7 • PZ is a 35 -year-old, 60 -kg female with a Staphylococcus aureus wound infection. While receiving vancomycin 1 g every 12 hours (infused over one hour), the steady- state peak concentration (obtained one-half hour after the end of infusion) was 35 mg/L, and the steady-state trough concentration (obtained immediately predose) was 15 mg/L. so calculate elimination rate and half-life

• Css after one-half hr is 35 mg/L & Css obtained immediately predose is 15 mg/L • Elimination rate , ke =− (ln C 1 − ln C 2)/(t 1 − t 2) =− [35 mg/L − 5 mg/L] / (1. 5 h − 12 h) = 0. 081 per hr • t 1/2 = 0. 693/ ke = 0. 693/0. 081 = 8. 6 hr

Bioavailability • The fraction of the administered dose that is delivered to the systemic circulation is known as the bioavailability for the drug. • The loss of drug before entering the systemic vascular system is known as presystemic metabolism or the first-pass effect.

Problem no - 8 • A new immunosuppresant, is being studied in the renal transplant clinic. Based on previous studies, the following area under the serum concentration/time curves (AUC) were measured after single doses of 10 mg in renal transplant patients: intravenous bolus AUC = 1530 mg ⋅ h/L, oral capsule AUC = 1220 mg ⋅ h/L, oral liquid AUC = 1420 mg ⋅ h/L. What is the bioavailability of the oral capsule and oral liquid? What is the relative bioavailability of the oral capsule compared to the oral liquid?

• The bioavailability for the capsule and liquid are: F = AUCPO/AUCIV for capsule, F = (1220 mg ⋅ h/L)/(1530 mg ⋅ h/L) = 0. 80 or 80%; for liquid, F = (1420 mg ⋅ h/L)/(1530 mg ⋅ h/L) = 0. 93 or 93%. • The relative bioavailability is: Frelative = AUCCAPSULE/ AUCLIQUID; = (1220 mg ⋅ h/L)/(1420 mg ⋅ h/L) = 0. 86 or 86%

Problem no - 9 • A patient with liver failure need to be treated with a new antiarrhythmic drug. You find a research study that contains the following information in patients similar to the ones you need to treat: normal subjects: clearance = 45 L/h, volume of distribution = 175 L; liver failure: clearance = 15 L/h, volume of distribution = 300 L. calculate recommend intravenous loading dose (LD) and continuous intravenous infusion maintenance dose (MD) to achieve a steady-state concentration of 10 mg/L.

Given information Cl = 15 L/h, Vd = 300 L, Css= 10 mg/L • LD = Vd ⋅ Css LD = (300 L)(10 mg/L) = 3000 mg intravenous bolus. • Loading dose dimension is mg • MD = Cl ⋅ Css MD = (15 L/h) (10 mg/L) = 150 mg/h intravenous infusion. • Maintenance dose dimension is mg/h

Problem no - 10 • A patient with heart failure need to be treated with a new antiarrhythmic drug. normal subjects: clearance = 45 L/h, volume of distribution = 175 L; heart failure: clearance = 30 L/h, volume of distribution = 100 L. Recommend an intravenous loading dose (LD) and continuous intra- venous infusion maintenance dose (MD) to achieve a steady-state concentration of 10 µg/m. L for patients based on this data and estimate the time it will take to achieve steady-state conditions.

• • Cl = 30 L/h, V = 100 L, Css=10µg/ml LD = V ⋅ Css, Css= 10µg/m. L=10 mg/L LD = (100 L)(10 mg/L) = 1000 mg intravenous bolus; MD = Cl ⋅ Css, MD = (30 L/h) (10 mg/L) = 300 mg/h intravenous infusion. • The half-life would be estimated using the clearance and volume of distribution • t 1/2 = (0. 693 V)/Cl, t 1/2 = [(0. 693)(100 L)]/ (30 L/h) = 2. 3 h. • Steady state would be achieved in 3– 5 t 1/2 equal to 7– 12 hours.

Problem no -11 • An antibiotic has a volume of distribution of 10 L and a k of 0. 2 hr– 1. A steady-state plasma concentration of 10 μg/m. L is desired. Calculate the infusion rate needed to maintain this concentration. If patient developed uremic condition and the elimination rate constant has decreased to 0. 1 hr– 1. calculate infusion rate.

Infusion rate= Css x Vd x k = 10 μg/m. L x 1000 ml x 0. 2 = 20 mg/hr Uremic condition, K reduced to 0. 1 hr– 1 =10 μg/m. L x 1000 ml x 0. 1 = 10 mg/hr When the elimination rate constant decreases, the infusion rate must decrease proportionately to maintain the same Css. However, because the elimination rate constant is smaller (ie, the elimination t 1/2 is longer), the time to reach C SS will be longer

Problem no – 12* • An antibiotic has an elimination half-life of 3– 6 hours in the general population. A patient was given an IV infusion of an antibiotic at an infusion rate of 15 mg/hr. Blood samples were taken at 8 and at 24 hours and plasma drug concentrations were 5. 5 and 6. 5 mg/L, respectively, If the desired therapeutic plasma concentration is 8 mg/L for the above patient (), what is a suitable infusion rate for the patient?

• Because the second plasma sample was taken at 24 hours, or 24/6 = 4 half-lives after infusion, the plasma drug concentration in this sample is approaching 95%, (Css) We know MD= Css x Cl Cl= MD/Css = 15/6. 5 =2. 31 L/hr The new infusion rate should be MD= Css X Cl = 8 X 2. 31 =18. 48 mg/hr

Saturable pharmacokinetics • This is the type of non- linear pharmacokinetics that occurs when the number of drug molecules saturates the enzyme’s ability to metabolize the drug. • Clearance of a drug is not a constant & it is concentration dependent. As the dose or concentration increases, the clearance rate (Cl) decreases and half-life becomes longer for the drug. • This situation is also known as zero-order pharmacokinetic • Drugs that exhibit nonlinear pharmacokinetics are very difficult to dose correctly.

Drug dosing in special populations Renal disease Hepatic disease Dialysis Heart failure Obesity

Renal disease(1) • In patients with renal disease, there is a functional loss of nephrons. • The method recommended by FDA to estimate renal function for the purposes of drug dosing is to measure creatinine clearance. • The most widely used method to estimate creatinine clearance , is by Cockcroft and Gault formula. • FDA, required pharmacokinetic studies & package insert for initial dosage guidelines to be done before receiving agency approval.

Problem no - 13 • A 52 -year-old, 65 -kg, 5 -ft 3 -in tall female patient with a methicillin-resistant Staphylococcus aureus (MRSA) infection needs to have an initial vancomycin dose computed. In order to do this, an estimated creatinine clearance needs to be calculated. The patient has a serum creatinine value equal to 1. 8 mg/d. L. Calculate this patient’s estimated creatinine clearance and estimated vancomycin clearance [assume vancomycin clearance is Cl (in m. L/min/kg) = 0. 695 (Cr. Cl in m. L/min/kg) + 0. 05].

• Calculate estimated creatinine clearance: • Cr. Clest = [0. 85(140 − age)BW]/ (72 ⋅ SCr) = [0. 85(140 − 52 y)65 kg]/ (72 ⋅ 1. 8 mg/d. L) = 37 m. L/min Cr. Clest= (37 m. L/min)/65 kg = 0. 569 m. L/min/kg • Calculate estimated vancomycin clearance: Cl (in m. L/min/kg) = 0. 695 (Cr. Cl in m. L/min/kg) + 0. 05 = 0. 695(0. 569 m. L/min/kg) + 0. 05 = 0. 446 m. L/min/kg(65 kg) = 29 m. L/min

Problem no - 14 • A 70 -year-old, 80 -kg, 5 -ft 11 -in tall male with a Pseudomonas aeruginosa infection needs to have an initial tobramycin dose computed. In order to do this, an estimated creatinine clearance must be calculated. The patient’s current serum creatinine equals 2. 5 mg/d. L and is stable. Compute this patient’s estimated creatinine clearance and estimated tobramycin elimination rate constant and half-life [assume tobramycin elimination rate constant is ke (in h− 1) = 0. 00293 (Cr. Cl in m. L/min) + 0. 014].

• Calculate estimated creatinine clearance: Cr. Clest = [(140 – age)BW]/(72 ⋅ SCr) = [(140 − 70 y)80 kg]/(72 ⋅ 2. 5 mg/d. L) = 31 m. L/min Calculate estimated tobramycin elimination rate constant and half-life: • ke(in h− 1) = 0. 00293(Cr. Cl in m. L/min) + 0. 014 = 0. 00293(31 m. L/min) + 0. 014 = 0. 105 /hr • t 1/2 = 0. 693/ke = 0. 693/0. 105 /hr = 6. 6 h

Renal disease(4) • Modify doses for patients with renal impairment – Decrease the drug dose and retain the usual dosage interval, – Retain the usual dose and increase the dosage interval, or – Simultaneously decrease the dosage and prolong the dosage interval

Dialysis(1) • In a renal failure patient & receiving dialysis, clearance is from nonrenal routes and dialysis (Cl = Cl. NR + Cl. D) • It is important to understand when drug dosing needs to be modified in renal failure patients undergoing dialysis.

Dialysis(2) • Drug Characteristics that Effect Dialysis Removal 1. Molecular size : - Molecular size relative to pore size in the semipermeable membrane, low-flux/high-flux artificial kidneys 2. Water/lipid solubility 3. Plasma protein binding : - Only unbound drug molecules are able to pass through the pores in the semipermeable membrane 4. Volume of distribution Ø Ø Ø V = VB + (f. B/f. T)VT Agents with large volumes of distribution are not easily removed from the body Compounds with small volumes of distribution (aminoglycoside, theophylline) usually high dialysis clearance rates

• Concentration/time graph for tobramycin in a hemodialysis patient

Problem no - 15 • A patient receiving hemodialysis has the following concentrations obtained during a hemodialysis run: concentration into artificial kidney = 75 mg/L, concentration leaving artificial kidney = 25 mg/L. Blood flow through the artificial kidney is 400 m. L/min. Compute the hemodialysis extraction ratio and clearance.

• ERHD = (Cpredialysis – Cpostdialysis)/Cpredialysis = (75 mg/L − 25 mg/L)/75 mg/L = 0. 67 or 67% • Cl. HD = HDBF ⋅ ERHD = (400 m. L/min)(0. 67) = 268 m. L/min

Problem no - 16 • A 47 -year-old, 75 -kg, male hemodialysis patient with chronic renal failure has a serious gram-negative infection being treated with a new antibiotic. The following concentrations were obtained: Monday, 1200 H (post-hemodialysis) = 15 mg/L, Monday, 1205 H (post-IV bolus 1000 mg dose) = 65 mg/L, Wednesday, 0800 H (pre-hemodialysis) = 32 mg/L, Wednesday, 1200 H (post-hemodialysis for 4 hours) = 8 mg/L. Compute volume of distribution, elimination rate constant, and half-life for the interdialysis period, and the hemodialysis extraction ratio. What post-hemodialysis dose on Wednesday would achieve a postdose concentration of 100 mg/L?

65 mg/L 32 mg/L 8 mg/L 15 mg/L

• Compute pharmacokinetic parameters: • Vd = D/(Cpostdose − Cpredose) = 1000 mg/(65 mg/L − 15 mg/L) = 20 L ke = (ln C 1 − ln C 2)/∆t = (ln 65 mg/L − ln 32 mg/L)/44 h = 0. 0161 /hr t 1/2 = 0. 693/ke = 0. 693 /0. 0161 /hr = 43 h • Calculation hemodialysis extraction ratio: • ERHD = (Cpredialysis – Cpostdialysis)/Cpredialysis = (32 mg/L − 8 mg/L)/32 mg/L = 0. 75 or 75% • Compute postdialysis dose for Wednesday: D = V(Cpostdose − Cpredose) = (20 L) ⋅ (100 mg/L − 8 mg/L) = 1840 mg

Peritoneal dialysis(pd) • Compared to hemodialysis, pd removes drug much less efficiently. • less likely require replacement drug doses. • Drug dosages need to be increased while patients receive chr. Pd • T 1/2 aminoglycoside – end-stage renal disease~50 hours. – During haemodialysis ~4 hours, – during pd ~36 hours

Hepatic disease Hepatocyte damage/permanent loss of functional hepatocytes, Liver blood flow decreases, increase in free fraction of drugs( ~increase Vd) Reduces the hepatic clearance of the drug A simultaneous decrease in liver first-pass effect results in extremely large increases in steady-state concentrations for orally administered drugs.

Hepatic disease(2) • Child-Pugh Scores • The Child-Pugh score consists of five laboratory tests or clinical symptoms. The five areas are serum albumin, total bilirubin, prothrombin time, ascites, and hepatic encephalopathy. • A Child-Pugh score equal to 8– 9 - decrease (~25%) in initial daily drug dose • A score of 10 or greater indicates that a significant decrease in initial daily dose (~ 50%) is required for drugs that are mostly liver metabolized

Hepatic disease(3) • for a drug with a low hepatic extraction ratio • For a drug with a high hepatic extraction ratio

Effect of physiologic, pharmacokinetic, and drug effect parameters when low hepatic extraction ratio drug is given to a patient as a continuous intravenous infusion, acute hepatitis

a high hepatic extraction ratio drug if liver blood flow decreases

Obesity • The presence of excessive adipose tissue can alter the pharmacokinetics of drugs by changing the volume of distribution. • High lipid solubility drugs tend to partition into adipose tissue, & Vd is dramatically larger than in norma. (diazepam, carbamazepine, and trazodone) • If the Vd for a hydrophilic drug is small, the additional extracellular fluid contained in adipose tissue may significantly alter the distribution of the agent. aminoglycoside • obese individuals, increased GFR. thus increase the renal clearance.

• Half-life = (0. 693 ⋅ V)/Cl. • Aminoglycoside antibiotics, CL & Vd increases of same magnitude in obese patients, so half-life does not change. • If the Vd increases with obesity, but Cl is unaffected, half-life can increase dramatically as with carbamazepine. • Finally, if Cl changes and Vd remains constant, obesity may also cause a change in the half-life of a drug as is the case for methylprednisolone

Drug interactions Pharmacokinetic drug interactions occur between drugs when one agent changes the Cl or Vd of another medication. Enzyme inhibition decreases intrinsic clearance, and enzyme induction increases intrinsic clearance. Two drugs eliminated by the same active renal tubular secretion mechanism can compete for the pathway and decrease the renal clearance of one or both agents Changes in plasma protein binding also cause alterations in volume of distribution.

Plasma Protein Binding Displacement • Drug with a low hepatic extraction ratio – plasma protein binding displacing compound will increase clearance (↑Cl =↑f. BCl′int) and volume of distribution [↑V = VB + (↑f. B/f. T)VT] – The pharmacologic effect of the drug does not change because the free concentration of drug in the blood is unchanged. • For drugs with high hepatic extraction ratios – clearance does not change. However, both Vd and half-life [↑t 1/2 = (0. 693 ⋅↑V)/ Cl] will increase because of plasma protein binding displacement of the drug – pharmacologic effect (↑effect ∝↑Cssu) of the drug will both increase

Alteration in Organ Blood Flow β-blockers can decrease heart rate and cardiac output which decreases liver blood flow Decrease clearance for high hepatic extraction ratio drugs (lidocaine). Vd remains unaltered, the half-life increase, total steady-state drug concentrations will increase

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