Drug Administration & Dosing Calculations PDF

DRUG ADMINISTRATION & DOSING CALCULATIONS Readings: Ch 12, 13 in Pharmacology Revealed © Dr. E. Cates, Fall2021 3 AGENDA • Review from Last Week • Volume of Distribution • Drug Administration • Drug Dosing Calculations • Plasma Clearance Calculations © Dr. E. Cates, Fall2021 4 LAST TIME, ON...

DRUG ADMINISTRATION & DOSING CALCULATIONS Readings: Ch 12, 13 in Pharmacology Revealed © Dr. E. Cates, Fall2021 3 AGENDA • Review from Last Week • Volume of Distribution • Drug Administration • Drug Dosing Calculations • Plasma Clearance Calculations © Dr. E. Cates, Fall2021 4 LAST TIME, ON PHARMACOTHERAPY… • Routes of drug administration • Drug Absorption • Movement of drug from its site of application to the circulation • • • • Lipid Solubility Membrane Characteristics Drug size Affinity of drug for other molecules • Drug Distribution • Water solubility • Concentration gradient • Tissue Perfusion • Tissue Barriers • Blood Brain Barrier • Placental Barrier • Drugs in Human Milk © Dr. E. Cates, Fall2021 5 DISTRIBUTION • The movement of a drug from its site of administration to its site of action • Mostly dependent on the movement of blood, which carries the drug around the body Image courtesy of Dr. C. Beites © Dr. E. Cates, Fall2021 6 DRUG DOSING & ADMINISTRATION • When a drug is being given – we need to know how much drug to give, so that it is distributed to the target in an appropriate amount to have a therapeutic effect. • How much we need to give depends on the drug’s pharmacokinetic profile • absorption, distribution, metabolism, & elimination • How do we figure out how much to give?! © Dr. E. Cates, Fall2021 7 VOLUME OF DISTRIBUTION • To figure out doses, we want to know how much drug will end up in the plasma portion of the blood • Really, we’d like to know how much drug ended up in the target tissue of interest • This is difficult to measure, so we settle for the amount of drug found in plasma • Doses of drugs are based on calculations of amounts of drug in plasma © Dr. E. Cates, Fall2021 8 VOLUME OF DISTRIBUTION A few different definitions: • “An expression of the proportion of the drug in plasma compared to the rest of the body” • “The apparent volume into which drug is distributed to provide the same concentration as it currently is in blood plasma” • “…relates the amount of drug in the body to the concentration of drug in plasma.” • “The fluid volume that is required to contain the entire drug in the body at the same concentration measured in plasma” • “A scavenger hunt” https://www.sciencedirect.com/topics/pharmacology-toxicology-and-pharmaceutical-science/volume-of-distribution © Dr. E. Cates, Fall2021 9 VOLUME OF DISTRIBUTION • Mathematically, it is expressed as Vd • Drugs with a high Vd tend to leave the plasma and enter the tissue • Vd has no physiologic or physical basis – but is mathematically useful • Why do we need this weird, abstract concept?? • Need to be able to estimate plasma concentrations • Because drugs do not stay in the plasma, they go all sorts of places… © Dr. E. Cates, Fall2021 10 VOLUME OF DISTRIBUTION If you are 70 kg and 60% fluid, then you have a total body water of about 42 L • Drugs tend to go to all of the 3 distinct compartments of body water – The first compartment is all the water inside your body cells, this is called the intracellular water – The second and third compartments consist of extracellular water • The first extracellular compartment is the plasma (4 L) • The second extracellular water compartment is the interstitial volume which is the water which is not in the cells or in the plasma (10 L) Intracellular Water (28 L) Total Body Water (42 L) Extracellular Water (14 L) Serum Volume (4 L) Interstitial Volume (10 L) Slide modified from Dr. B. Wainman © Dr. E. Cates, Fall2021 11 VOLUME OF DISTRIBUTION Intracellular Water (28 L) Total Body Water (42 L) Extracellular Water (14 L) • Only 4 L of that 42 L are plasma • If a drug were given and it all stayed in the plasma, then the Vd would be exactly the volume of plasma or about 4 L • Virtually no drugs have a Vd of 4 L because they all tend to leave the plasma to some degree • So Vd tells us where the drug will go Serum Volume (4 L) Interstitial Volume (10 L) Slide modified from Dr. B. Wainman © Dr. E. Cates, Fall2021 12 DRUG WITH A VERY LOW Vd Intracellular Water © Dr. E. Cates, Fall2021 Extracellular Water (plasma above and interstitial water below) The drug ends up with a Vd of the plasma volume (about 4 L in a 70 kg person) Slide modified from Dr. B. Wainman 13 DRUG WITH A LOW Vd Intracellular Water Extracellular Water (plasma above and interstitial water below) © Dr. E. Cates, Fall2021 The drug ends up with a Vd of the plasma volume plus the volume of interstitial water. This would be about 14 L in a 70 kg person Slide modified from Dr. B. Wainman 14 DRUG WITH A HIGH Vd Intracellular Water Extracellular Water (plasma above and interstitial water below) © Dr. E. Cates, Fall2021 The drug ends up with a Vd of the total body water. This would be about 42 L in a 70 kg person Slide modified from Dr. B. Wainman 15 DRUGS WITH AN EXTREMELY LARGE Vd • Some drugs have a Vd more than total body water (e.g., diazepam (VALIUM) has a Vd of 168 L and digoxin has Vd of 490 • These drugs either bind to tissues very tightly (like digoxin) and thus do not show up in the plasma or are highly lipophilic (like diazepam) • The drugs that have really high Vd will end up crossing the placenta easily and accumulating in the fetus! • In many ways the fetus can be thought of as another compartment where drugs can enter and distribute  if drugs can cross the placenta, this increases Vd Slide modified from Dr. B. Wainman © Dr. E. Cates, Fall2021 16 PRACTICE QUESTIONS Would the Vd be high or low for: A. A lipophilic drug? B. A drug that binds significantly to plasma proteins? C. A hydrophilic drug? © Dr. E. Cates, Fall2021 17 CALCULATING Vd • What we need to calculate the Vd is: • Amount of drug added (the dose), D = dose (mg) • Concentration in the plasma before the drug begins to get broken down which is called C0 • This hypothetical concentration is called C0, and it is estimated from a graph. It is measured in mg/L of plasma Vd = Amount of drug in the body Plasma concentration at time zero Slide modified from Dr. B. Wainman © Dr. E. Cates, Fall2021 18 CALCULATING Vd Vd = D / C0 • Units: Vd in L D in mg C0 in mg/L Logic it through! Tell me why… • If the drug has a high volume of distribution, then it is mostly in the tissue not in the plasma even with a high dose (D) the amount in the blood (C0) will be low • If the drug has a low Vd then it is mostly in the plasma © Dr. E. Cates, Fall2021 19 SAMPLE PROBLEM! Vd (L) = D (mg) / C0(mg/L) • Given: D = 500mg C0 = 12mg/L • Find: Vd Vd = D / C0 Vd = 500mg / 12mg/L Vd = 41.6L © Dr. E. Cates, Fall2021 20 LOADING DOSE • A single, large dose designed to bring the concentration of a drug up to therapeutic levels in the bloodstream • Common examples: • loperimide (IMMODIUM) Image derived from: Amazon.ca • 2 capsules (4mg) • Followed by 1 capsule (2mg) after each unformed stool • azithromycin (ZITHROMAX) • 500mg as a single dose on the first day • Followed by 250mg per day on each subsequent day • What is a common example from midwifery practice? © Dr. E. Cates, Fall2021 21 CALCULATING LOADING DOSE USING Vd • It can only be calculated if you know where the drug is going to go (Vd) • Using the formula Vd = D / C0 we can rewrite the formula to give us the formula for dose (D) • D = Vd x C0 • Q: What is the dose of drug you want to give if you want have a circulating drug level of 25 mg /L? The Vd of the drug is 5 L. • A: Given that D = Vd x C0 and: Vd = 5 L C0 = 25 mg / L then: D = 5 L x 25 mg/L (the liters cancel) D = 125 mg • A dose of 125 mg will immediately bring the blood levels of drug into the therapeutic range of 25 mg / L Slide modified from Dr. B. Wainman © Dr. E. Cates, Fall2021 22 Vd AND PREGNANCY • Many things can change Vd including the amount of plasma protein, the level of hydration and body weight • All of these things can occur in pregnancy so Vd will often change • Less plasma albumin (a protein) usually leads to an increased volume of distribution for drugs that are protein bound like most NSAIDS and salicylates • In general, an increase in Vd will occur for water soluble drugs simply because there is an increase of about 40% or so in body water • Examples: • Vd of ampicillin is 36 L at 10 weeks but 68 L at 40 weeks • In general, there will be an increase in Vd for lipophilic drugs like caffeine, thiopental and diazepam (VALIUM) because of an increase in body fat during pregnancy • Examples: • Caffeine’s Vd goes from 2 L at 10 weeks to 32 L at 40 weeks • This means the drug is found in the fat to a great degree at term Slide modified from Dr. B. Wainman © Dr. E. Cates, Fall2021 23 DRUG DOSING • The purpose of drug dosing is to keep drug concentration at a therapeutic level • Most drugs have standard doses: • • • • E.g., 5 to 10 IU of oxytocin are given for postpartum hemorrhage There are not calculations to be done, which prevents a miscalculation Unlikely a major accidental overdose/under dose will ever occur But a standard dose will yield higher serum concentration of drug in smaller people than larger • E.g., DEMEROL (meperidine) is given at a dose of 50 to 100 mg IM or SC depending on the severity of the pain and the practitioner’s preference • Someone who is 50 kg gets exactly twice the bioavailable DEMEROL per kg of someone who is 100 kg • Kidney or liver dysfunction can lead to inappropriate drug levels • Want to try to avoid overdose (and side effects) and under dose (and lack of drug effect) • Number of parameters to think about… • Size/body weight • Plasma clearance rate (factors that may influence clearance rate) • Volume of distribution (specific to each drug) © Dr. E. Cates, Fall2021 25 DRUG CLEARANCE AND ELIMINATION • Clearance (Clp): measure of body’s efficiency at removing a drug from circulation; expressed as L/h • Clearance of drugs depends on plasma cleared per hour which is constant for each drug • The amount of drug cleared depends on concentration, which changes.. • The more drug there is, the faster the body works to clear it. So, as amount of drug decreases over time, the amount cleared decreases too • Elimination: measure of time taken for clearance; expressed as half life (t½) in hours (time taken to decrease drug concentration by half) • The half life is constant • Only drugs eliminated by first-order kinetics have a half life © Dr. E. Cates, Fall2021 26 FIRST-ORDER DRUG KINETICS Concentration of Drug (mg/L) Distribution Phase Elimination or Clearance Phase 12 10 The distribution phase is very quick with IV drugs 8 During the clearance phase the amount of drug decreases very rapidly at first and then slows down 6 4 2 0 2 4 6 8 10 12 14 16 18 20 Time (min) IV drug injection © Dr. E. Cates, Fall2021 27 CLEARANCE KINETICS AND STEADY-STATE CONCENTRATION (CSS) • If drugs administered continuously (by IV), an equilibrium forms between amount of drug administered and amount of drug cleared • This is steady-state concentration (Css):  drug concentration in blood maintained after 4-5 half lives with infusion • Factors affecting clearance rate: • Hydration status • Kidney function • Liver function © Dr. E. Cates, Fall2021 28 IV INFUSION AND STEADYSTATE CONCENTRATION (CSS) Concentration of Drug (mg/L) Distribution Phase 12 Css for a drug infused at a moderate rate 10 Css for a drug infused at a low rate 8 6 High rate of drug infusion 4 Moderate rate of drug infusion 2 Low rate of drug infusion 0 2 4 Begin IV drug infusion © Dr. E. Cates, Fall2021 Css for a drug infused at a high rate 6 8 10 12 14 16 18 20 © B Wainman Time (min) Note that the time to reach steady state is the same regardless of infusion rate. 29 IV INFUSION AND STEADYSTATE CONCENTRATION (CSS) • In the previous slide the higher the rate of drug infusion then the higher the steady state drug concentration, Css • Drug clearance increases with increased infusion rate until input and elimination reach equilibrium • Clearance is related to dose: greater the dose, greater the clearance • This is based on first-order kinetics (concentration-dependent) • This is not true with zero-order kinetics… © Dr. E. Cates, Fall2021 30 FIRST VS. ZERO ORDER KINETICS Concentration of Drug (mg/L) Concentration Dependent Time Dependent Distribution Phase Distribution Phase Metabolism Elimination or Clearance Phase 10 8 6 4 2 0 2 4 6 8 10 12 14 16 18 20 Time (min) Concentration of Drug (mg/L) 12 Phase 12 10 8 6 4 2 0 2 4 6 8 10 12 14 16 18 20 Time (min) IV drug injection IV drug injection ©© Dr. Dr. E. E. Cates, Cates, Fall2021 Fall 2023 31 Concentration of Drug (mg/L) IV INFUSION AND STEADYSTATE CONCENTRATION (CSS) Because this drug will never reach a steady state, sooner or later this rate of infusion will lead to overdose 12 10 8 6 Zero-Order Kinetics (theoretically) OR… 4 Really high rate of infusion! 2 0 High rate of drug infusion 2 4 Begin IV drug infusion 6 8 10 12 14 16 18 20 Time (min) Modified from B Wainman ©© Dr. Dr. E. E. Cates, Cates, Fall2021 Fall 2023 32 Concentration of Drug (mg/L) t1/2 AND STEADY-STATE CONCENTRATION (CSS) 12 10 Css for a drug with a short half-life 8 6 Css for a drug with a long half-life 4 2 0 2 4 Begin IV drug infusion 6 8 10 12 14 16 18 20 © B Wainman Time (min) The steady-state concentration nears its equilibrium in 4 to 5 half lives of the drug. The time required to reach steady state concentration depends only on a drug’s half life. So, drugs with shorter half lives reach steady state concentration quickly. See pg. 89. © Dr. E. Cates, Fall2021 33 CALCULATING THE MAINTENANCE DOSE • Maintenance dose: dose regime that keeps blood levels of a drug in the therapeutic range; input in balance with elimination Ro mg h   Css  mg L  x Clp  L h  Ro = Maintenance dose of infused drug CSS = Constant level of drug that is desired Clp = Clearance rate • Notice that a high infusion rate will be required if drugs have high plasma clearance rates, or if you want to achieve a steady, high target concentration • Regardless of the rate of infusion, it takes about 4 half-lives of the drug to establish the steady state • E.g., If you want a steady state concentration of 0.5mg/L and the plasma clearance is 0.5L/h then the infusion rate = 0.5mg/L x 0.5L/h = 0.25mg/h © Dr. E. Cates, Fall2021 34 CALCULATING THE STEADY STATE CONCENTRATION • You can calculate the steady state drug concentration (Css) from the infusion rate (Ro) and plasma clearance rate (Clp) R o mg  h Css  mg L   Clp  L h  • E.g., Drug infused at 50 mg/h and the plasma clearance rate is 3 L/h then the steady state drug concentration will be 50 mg/h / 3 L/h = 16.7 mg/L • You can also calculate how much actual drug was lost since loss equals input = 50 mg/h • Drugs are seldom given as infusions rather they are given in discrete doses at a fixed time interval © Dr. E. Cates, Fall2021 35 CALCULATING PLASMA CLEARANCE RATE • You can calculate the plasma clearance rate (Clp) from the half-life and the volume of distribution (Vd). The new variable, k, is the elimination rate constant for the drug Clp  L h   k h 1 Vd L  • k is directly related to half-life: k 0.693 t 1 h  2 • So, this formula tells you one thing: drugs with short half-lives have fast elimination • The big formula tells you that drugs with short half-lives and large volumes of distribution have high plasma clearance rates © Dr. E. Cates, Fall2021 36 Clp  L h   k h 1 Vd L  and 0.693 k t 1 h  2   0.693    L    Clp  h     V L d  t 1 h    2  Drugs with short half-lives and large volumes of distribution have high plasma clearance rates Q. Why do drugs which have large volumes of distribution have high clearance rates? A. Drugs which have large volumes of distribution are going to be in the tissues which is to say that the drugs are hardly in the blood. This does not mean that the half life is short it simply means that large volumes of plasma with only a small amount of drug are cleared when the Vd is high. Q. Why do drugs with short half-lives have high clearance rates? A. By definition, drugs which have short half-lives are easily metabolized or cleared. The volume of plasma cleared of the drug over time will normally be high. © Dr. E. Cates, Fall2021 37 Concentration of Drug (mg/L) DISCRETE MULTIPLE DOSING AND THE AVERAGE CSS 12 10 8 The average concentration steady state C ss 6 Notice that the steady state is reached in about 4 half lives just like with infusion (t1/2 ≈ 4h) 4 2 0 2 4 6 8 10 12 14 16 18 Time (h) First Drug Dose © Dr. E. Cates, Fall2021 2nd Drug Dose 3rd Drug Dose 4th Drug Dose 5th Drug Dose 20 © B Wainman 6th Drug Dose 7th Drug Dose 38 Concentration of Drug (mg/L) DISCRETE MULTIPLE DOSING AND THE AVERAGE CSS 12 10 8 6 Notice that the steady state is reached in about 4 half lives just like with infusion and it is not dose dependent (t1/2 ≈ 4h) 4 2 0 First Drug Dose © Dr. E. Cates, Fall2021 The average concentration steady state C ss 2 4 6 2nd Drug Dose 8 10 12 Time (h) 3rd Drug Dose 14 16 18 20 © B Wainman 4th Drug Dose 39 12 Therapeutic Range 10 8 6 4 2 0 First Drug Dose © Dr. E. Cates, Fall2021 Increasing chance of drug toxicity Concentration of Drug (mg/L) CONSEQUENCES OF INFREQUENT DOSING 2 4 6 10 8 Time (h) 12 2nd Drug Dose 14 16 18 20 © B Wainman 40 MULTIPLE DOSING AND THE CSS • Usually, drugs are given in tablets or by discrete injections not by infusion • Because a true CSS cannot be reached, the average CSS is written D  mg   C ss  mg L  x Clp  L h  T  h Q: What is the dose regime necessary to maintain an average steady-state of a drug at 40 mg/L if the drug clearance is 5 L/h. The calculation is: 40 mg/L x 5 L/h = 200 mg/h A: This drug must be given at a rate which provides 200 mg every hour so the drug regime might be: i) 800 mg every 4 hours (q4hrs) or ii) 1600 mg every 8 hours (q8hrs) or iii) 4800 mg (1 dose) once a day © Dr. E. Cates, Fall2021 41 DOSE CALCULATION • Initial dosages of drugs are usually based on some measure of size • The most common measure of size is weight: • The dose is calculated on the basis of person’s weight, e.g., if the person weighs 50 kg and the dose is 1mg/kg then 50 mg are given • In children, doses are usually altered for body weight • E.g., DEMEROL (meperidine) is given to children orally at 1.1 to 1.8 mg/kg q3h (every three hours) or q4h (every four hours) • But we want to know is how well they are metabolizing and excreting the drug • Surface area can also be used for drug dose calculation • Surface area is well correlated with cardiac output, glomerular filtration and rates of biotransformation and a better measure of how a dose of drug will be reflected in circulating drug levels • Body surface area is estimated using a nomogram (see Fig 12-4) which uses height (cm) and weight (kg) to find body surface area © Dr. E. Cates, Fall2021 42