Pharmacokinetics Lecture Notes (PhB-4122) PDF

Pharmacokinetics (PhB-4122) lecture-2 level-4 Rates and order of reactions 9/10/2023 Dr. Omnia Sarhan [email protected] Office : 319 Pharmacy Office Hours: Monday 11:00 am to 1:00 Text Books pm 1- Rowland and Tozer’s clinical pharmacokineti...

Pharmacokinetics (PhB-4122) lecture-2 level-4 Rates and order of reactions 9/10/2023 Dr. Omnia Sarhan [email protected] Office : 319 Pharmacy Office Hours: Monday 11:00 am to 1:00 Text Books pm 1- Rowland and Tozer’s clinical pharmacokinetics and pharmacodynamics: concepts and applications, 5th edition (2019). 2- Sara E. Rosenbaum basic Pharmacokinetics and Pharmacodynamics: An Integrated Textbook and Computer  Introduction Drug plasma level-time curve; After a single oral dose of a drug, a typical plasma drug concentration time curve is obtained. t max C max Absorption phase Ka Post absorption phase K Therapeutic range Elimination phase Dr/Omnia Sarhan 2  Introduction a. Pharmacokinetic parameters; 1- Peak plasma concentration ‘C max’ : The maximum plasma concentration, related to the dose, rate of absorption (ka), rate of elimination (k). 2 -Time of peak concentration ‘t max’ : The time to C max. 3 -Area under the curve ‘AUC’ : This equal to the total amount of drug absorbed after administration. b- Pharmacodynamics parameters; 1- Minimum effective concentration MEC: The minimum concentration of drug in plasma required to produce the desired therapeutic effect. The concentration below MEC is regarded the sub- therapeutic concentration. Dr/Omnia Sarhan 3 Introduction 2- Maximum safe concentration MSC It is also known as the minimum toxic concentration, the concentration of a drug in plasma beyond which side effects will results. Concentration above the MSC is regarded to be in the toxic level 3- Therapeutic range or therapeutic window The range of plasma concentration between MEC and MSC, As long as the drug level is maintained within the therapeutic window, the therapeutic effect of the drug is observed without side effect. 4- Onset of action The beginning of pharmacological response, it takes places when the plasma concentration just exceeds the required MEC. 5- Duration of action; The period of time for which the plasma concentration of the drug remain above the MEC level. Dr/Omnia Sarhan 4  Introduction 6- Fraction of drug absorbed F; The ratio of the amount of drug ultimately reaching the plasma stream to the total dose administered. The value of F will be the unity if the total dose of the drug reaches the plasma. Many dosage forms often show F values less than the unity because of the under mention factors *Slow release of drug from the dosage form and loss of the unabsorbed drug through faces. *Degradation of the drug in the GIT due to chemical or enzymatic processes. *Drugs undergo the first pass metabolism, the may be stable in the GIT and completely absorbed but extensively metabolized in the liver before reaching the blood. Kinetics The study dealing with the rate of chemical and physical reactions and the factors which influence the reaction rate. Dr/Omnia Sarhan 5  Introduction Rates and order of reactions Rates Is the velocity within which the reaction occurs. Consider the following reaction: Drug A drug B The amount of drug A is decreasing with respect to time So Rate = - dA / dt (forward reaction) Or since the amount of B increases with respect to time Rate = + dB / dt The order of a reaction Refers to the actual manner in which the concentration of the drug tends to influence the rate of reaction or process. If the drug A changed to B and the concentration of A is C, the rate of change of A to B as a function of time will expressed as Dr/Omnia Sarhan 6  Introduction dC / dt = - K Cn Where; dC / dt = the rate of reaction K = rate constant n = the order of the reaction or process. When n = zero, it is called zero order reaction, when n = 1, it is called first order reaction, and so on. 1- Zero order kinetics (constant rate process); Constant rate change and the change is independent on the concentration of the drug. It is not possible to increase the rate of process by increasing the concentration of the drug. An example is the elimination of alcohol. Drugs that show this type of elimination will show accumulation of plasma levels of the drug and hence nonlinear pharmacokinetics. Dr/Omnia Sarhan 7  Introduction The amount of the drug (A) is decreasing at a constant time interval (t) A = - Ko t + Ao Where Ao = the amount of the drug at time = zero A = the amount of the drug at time = t Dr/Omnia Sarhan 8  Introduction The half-life (t ½); Expresses the period of time required for the amount or concentration of a drug to decrease by one half. Or the time required for the plasma concentration to drop from its initial value to the half. i.e., when t = t ½ , A = Ao / 2. t ½ for zero order reaction; A = - Ko t + Ao When t = t ½, A = Ao / 2 t ½ = Ao / 2 Ko e.g., for zero order delivery 1. Sustained release 2. I.V infusion 3. Trans-dermal preparations Dr/Omnia Sarhan 9  C0 t1/ 2  10 2 k0 – Half life of zero order reaction is directly proportional to initial concentration. – Thus half life decrease as reaction proceed with time (when C0 is reduced by a factor of 2, the half- life is also decreased by a factor of 2 (in fact each successive half-life is half the preceding one) 10 min 5 min 2.5 min 100% 50% 25% 12.5% A A A A Dr/Omnia Sarhan  Zero-Order Reaction Graphically on cartesian paper: C0 Ct Ct  CC00  kk0t0t Slope=-k0 Ct Time Dr/Omnia Sarhan 11  – Equation of straight 12 line: – y = ax + b y – (a: slope, b: intercept) Slope = a Ct C0  kt Intercept =b x Dr/Omnia Sarhan  Example 1 A drug product has an initial concentration of 125 mg/ml 13 decays by zero order kinetics, (k=0.5 mg/ml/hr). What is the concentration of the intact drug remaining after 3 days? When the drug reaches zero concentration? Answer: C = Co – Kt C = 125 - 0.5 * (3 x 24) C = 89 mg / ml C = Co – Kt 0 = 125 – 0.5*t t = 250 hour Dr/Omnia Sarhan  Example 2 The decomposition of multi-sulfa compound was found to 14 follow zero order kinetics. If its concentration was 0.47 mole/liter, when freshly prepared, and after 473 days its concentration reached 0.225 mole/liter, calculate the degradation rate constant and t1/2. Answer: Ct C0  kt Co  Ct k t 0.47- 0.225 k  .00052mole/ liter.days 1 473 Co 0.47 t 1/ 2    452days 15 months 2K 2 0.00052 Dr/Omnia Sarhan  Introduction 2- First order kinetics (linear kinetics) The rate of reaction is directly proportional to the concentration. i.e., the change depends on the concentration. ln A – ln Ao = - k t ln (A/Ao) = - k t A /Ao = e-Kt………….. (1) Where e is the natural logarithm, the equation has one exponent and called monoexponential rate process. Since ln = 2.303 log, equation 1 can be written as; Log A = log Ao – k t / 2.303............ (2) A plot of log A versus time, a straight line is obtained whose slope = k / 2.303 Dr/Omnia Sarhan intercept = log Ao 15 Introduction T½ for first order reaction t ½ =0.693/ k Dr/Omnia Sarhan 16  17 Graphically on semilog paper Co log y2  log y1 slope  t 2  t1 Dr/Omnia Sarhan  100 18 Conc. Time 10 100 1 Log scale 90 2 14 3 1 9 4 4.2 5 0.08 6 o.1 v Ordinary scale Dr/Omnia Sarhan 1 2 3 4 5 6 o.o1  19 C0 % Remaining Slope = -k/2.303 = (log y2 – log y1) / (x2 – x1) No zero on y axis Dr/Omnia Sarhan Time  kt log Ct log C0  2.303 20 kt1/ 2 log 1 / 2C0 log C0  2.303 kt1/ 2 log C0  log 1 / 2C0 2.303 kt1/ 2 C0 log 2.303 1 / 2C0 2.303 C0 t1 / 2  log k 1 C0 2 2.303 t1/ 2  log 2 Half life t1/2 is k t1/ 2  0.693 constant & Dr/Omnia Sarhan k doesn’t depend  10 10 10 100%A 50% 25% 12.5% min min min 21 A A A Half life t1/2 is constant & doesn’t depend on concentration. Dr/Omnia Sarhan  Example 1 22 An ophthalmic solution dispensed at 5 mg/ml conc. exhibits a first order reaction, with a rate constant of 0.0005 day-1. How much drug remaining after 120 days? & how long will it take for the drug to degrade to 90% of its initial concentration? Answer: A first order reaction  ln c ln co  kt Don’t forget to check the ln C ln 5  0.0005 120  units of the problem ln C 1.549 shift ln  C 4.71 mg / ml 0.105 0.105 t 90%   210 days Dr/Omnia Sarhan k 0.0005  23 Example 2 The original concentration of one sample was 50 mg/ml. When assayed 20 months later the concentration was found to be 40 mg/ml, assuming that the decomposition is first order, What is the half-life of this product? Ans.: Co= 50mg/mL Ct= 40mg/mL t= 20 mon. log Ct= log Co- Kt/2.303 log 40= log 50- 20K/2.303 K= 0.0111mon-1.T1/2= 0.693/K= 0.693/ 0.0111= 62.43 mon Dr/Omnia Sarhan  Example 3 At 25 °C, the half-life period for the decomposition 24 of N205 is 5.7 hours and is independent of the initial pressure of N205, calculate: a- The time for the completion of the reaction. b- The specific rate constant for the reaction. Answer: t1/2 is independent on the initial conc. So, it is 1st order, hence the reaction never goes to an end and the life time (time for completion of the reaction) is infinity. 0.693 0.693 k   0.1215 hr-1 t 1/ 2 5.7 Dr/Omnia Sarhan  Interce Slope (x- (y-axis) Half-life Integrated Orde pt axis) eqn. rate eqn. r Co -Ko t C t1/2 = Co Co – C = kt 0 2k Log Co -K kt t LogC t1/2 = 1 log C t log C0  2.3032.303 0.693 k Dr/Omnia Sarhan  Problems *The linear relationship that describes the change in the drug amount (A) in mg, as a function of time (t) in h, can be described by the following equation: A = 120 mg − 2 (mg/h) t. a. Calculate the amount of the drug remaining after 10 h. b. What is the time required for the drug amount to decrease to zero? Dr/Omnia Sarhan 26  Problem 1 Degradation of a suspension of triamcinolone acetonide, 50 mg/mL, was followed over a year at 40oC and the following results were obtained: 27 a. Plot the data and prove that the degradation follows zero order. b. Determine the constant of degradation. Time (months) Concentration remaining (mg/ml) 0 50 4 44.1 8 36.4 12 30.2 16 25.3 20 18.1 24 12.6 Dr/Omnia Sarhan  Problem 2 The following are the concentrations of sulphadiazine remaining at various times during the thermal decomposition at 40 C Using the above data determine: 1.the order of the decomposition reaction. 2.The rate constant of the reaction. 3.The shelf life of the product. Time Conc. (months) 0 100 4 81.4 8 68.8 12 56.4 16 44.6 20 36.2 24 31.2 Dr/Omnia Sarhan Dr/Omnia Sarhan 29