Continuous Intravenous Infusion (One-Compartment Model) PDF

Continuous intravenous infusion (one-compartment model)  Introduction While a single intravenous bolus dose of a drug may produce the desired therapeutic concentration and, therefore, the desired pharmacological effect immediately This mode of administration is unsuitable when it is nec...

Continuous intravenous infusion (one-compartment model)  Introduction While a single intravenous bolus dose of a drug may produce the desired therapeutic concentration and, therefore, the desired pharmacological effect immediately This mode of administration is unsuitable when it is necessary to maintain plasma or tissue concentrations at a concentration that will prolong the duration of this effect We are interested in reaching the therapeutic range and then maintaining drug concentration within the therapeutic range for a longer duration  Introduction The main advantage for giving a drug by IV infusion is that it allows precise control of plasma drug concentrations to fit the individual needs of the patient For drugs with a narrow therapeutic window (eg, heparin), IV infusion maintains an effective constant plasma drug concentration by eliminating wide fluctuations between the peak (maximum) and trough (minimum) plasma drug concentration Moreover, the IV infusion of drugs, such as antibiotics, may be given with IV fluids that include electrolytes and nutrients. Furthermore, the duration of drug therapy may be maintained or terminated as needed using IV infusion.  Introduction It is common practice in the hospital setting to infuse a drug at a constant rate (constant rate input or zero-order input). This method permits precise and readily controlled drug administration. The infusion rate of a drug is controlled by: 1. flow rate (e.g., mL h-1) 2. concentration (µg mL-1, % w/v, etc.) of the drug in solution.  Model Assumptions : 1. The drug we are considering undergoes no metabolism (i.e., monitoring for unchanged parent drug in the blood). 2. The drug exhibits the characteristics of a one-compartment model (rapid distribution). 3. The elimination of the drug follows a first-order process and passive diffusion.  Theory of intravenous infusion 1. The drug is administered at a selected or calculated constant rate (Q) (i.e., dX / dt), units of this input rate (constant rate) will be those of mass per unit time (e.g., mg h-1). The constant rate (infusion rate) can be calculated from 1. the concentration of drug solution 2. the flow rate of this solution 2. The elimination of drug from the body follows a first-order process (i.e., – dX/dt = KX).  Theory of intravenous infusion For example, the concentration of drug solution is 1% (w/v) and the solution flow rate is 10 mL h-1 So 10 mL of solution will contain 0.1 g (100 mg) drug. Hence, the units of the infusion rate (constant rate) = solution flow rate (mL h-1) × concentration (µg mL-1), will be mass per unit time (µg h-1). In this example, the constant infusion rate will be 10 mL h-1 multiplied by 100 mg/10 mL, or 0.1 g h-1 (100 mg h-1).  Monitoring drug in the body or blood (plasma/serum) Drug is monitored in blood under two conditions: 1. during infusion (while the drug is being infused) 2. in the post-infusion period (following the cessation of infusion). scheme and set up for drug changes in the body or blood under constant infusion.  Monitoring drug in the body or blood (plasma/serum) X: amount of drug in the blood or body dX/dt: is the rate of change in the mass or amount of drug in the body (e.g., mg h-1); Q: is the zero-order input or constant infusion rate (e.g., mg h-1) K: is the first-order elimination rate constant KX: is the first-order elimination rate (e.g., mg h-1).  Monitoring drug in the body or blood (plasma/serum) Initially, the rate at which drug enters the body (infusion rate), though constant, is greater than the rate at which drug is eliminated (Q > K X) the rate of drug elimination (KX) from the body, being a first-order process, increases with time since there is a greater amount of drug in the body (X) as time increases  Monitoring drug in the body or blood (plasma/serum) consequently, the difference between the infusion rate and the elimination rate (i.e., Q – KX) becomes smaller as time increases, eventually reaching zero When the rate of elimination becomes equal to the rate of infusion (Q = KX ) and the difference between the two rates becomes zero, there will be no further change in the amount of drug in the blood or body with time. A graphical representation of drug administration at a constant rate and drug elimination at a changing rate (increasing until steady state) when a drug is administered as an infusion.  Monitoring drug in the body or blood (plasma/serum) Upon integration, The amount of drug in blood is influenced by 1. The chosen infusion rate the amount of drug in blood at a given time will be directly proportional to the chosen infusion rate 2. The elimination rate constant of the drug the elimination rate constant for a drug is constant for a given patient receiving a particular drug 3. The duration of infusion.  Monitoring drug in the body or blood (plasma/serum) Since drug concentration is measured Cp = X/V (or X = VCp), not the amount of drug, SO It should be apparent from equation, the plasma concentration of a drug is influenced by 1. the calculated infusion rate 2. the elimination rate constant 3. the apparent volume of distribution 4. the systemic clearance of a drug 5. the duration of the infusion.  Monitoring drug in the body or blood (plasma/serum) Since the elimination rate constant, the apparent volume of distribution, and the systemic clearance for a drug are constant for a given patient receiving a particular drug, the plasma concentration of a drug will be influenced by the chosen infusion rate and the duration of infusion, the plasma concentration of a drug at a specific time will always be directly proportional to the chosen infusion rate.  Monitoring drug in the body or blood (plasma/serum) If two different drugs are administered at an identical infusion rate to a subject, the plasma concentration of each drug at a given time will be influenced by the ratio of the infusion rate to the systemic clearance of each drug (i.e., Q / VK).  True steady state and steady-state plasma concentration (Cp)ss True steady-state condition refers to the condition when the rate of elimination and the rate of infusion become equal (Q = KX) and it occurs, theoretically, only when time is equal to infinity. when t = ∞, Cp = (Cp)ss. When e–kt∞ = zero  True steady state and steady-state plasma concentration (Cp)ss Unit for concentration (Cp)ss is mass per volume,e.g., mg mL-1. Unit for clearance will be volume per unit time,e.g., mL h-1. Q will be mg mL-1 × mL h-1, or mg h-1 the infusion rate (Q) required to attain and then maintain the desired steady-state plasma concentration is determined by the desired plasma concentration the systemic clearance of a drug. In addition, the systemic clearance of a drug being a constant, there is a directly proportional relationship between the desired steady-state plasma concentration and the infusion rate required for attaining this concentration.  True steady state and steady-state plasma concentration (Cp)ss Elimination follow first order kinetics so, K = 0.693/t1/2 Since the apparent volume of distribution, elimination rate constant, and elimination half life (t1/2) are constants for a given drug administered to a particular patient, the absolute value of steady-state plasma concentration is determined only by the rate of infusion.  True steady state and steady-state plasma concentration (Cp)ss 1. For instance, if the rate of infusion is increased by a factor of 2, the steady- state plasma concentration will also increase by a factor of 2 2. it is important to recognize that the time at which this steady state is attained is independent of the rate of infusion. In other words, doubling the infusion rate will not allow the steady-state condition to be achieved faster.  Practical steady-state concentration 1. Practical steady-state concentration has been reached when the plasma concentration of a drug in the blood represents 95% or greater of the true steady-state plasma concentration. 2. The time required to reach “practical” steady-state condition (95%) is always equal to 4.32t1/2 of that drug. 3. The time required to reach the steady-state drug concentration in the plasma is dependent on the elimination rate constant Practical steady-state concentration For example, let us assume we wish to attain a plasma concentration of 10 µg mL-1 at true steady state. the chosen infusion rate yields a true steady-state plasma concentration of 10 µg mL-1. Therefore, 10 µg mL-1 × 0.95 = 9.5 µg mL-1 is the “practical” steady-state concentration and it will occur at 4.32t1/2.  Practical steady-state concentration 1. Let us assume that the desired true steady-state plasma concentration of the same drug is 20 µg mL-1 2. the chosen infusion rate (twice the infusion rate of the first example) yields a true steady-state plasma concentration of 20 µg mL-1. 3. Therefore, 20 µg mL-1 × 0.95 = 19.0 µg mL-1 is the “practical” steady-state concentration and it will occur at the same time (i.e., 4.32t1/2) since the same drug is being infused. 4. If the elimination half life of the drug is 2 h, it will take 2 × 4.32 = 8.64 h to attain the “practical” steady-state condition. Practical steady-state concentration  Practical steady-state concentration The number of elimination half lives required to attain a fraction (in this example, 0.95) of true steady state will remain unaffected by the infusion rate, the drug chosen, and the subject. the number of elimination half lives required to attain the “practical” steady-state condition will always be same for every drug and in every patient, normal as well as renally impaired.  Practical steady-state concentration The time required to attain a fraction of steady state (Nt1/2) will be different for each drug and in normal and renally impaired subjects since the elimination half life for each drug may be different and the elimination half life of the same drug will be different in normal and in renally impaired subjects. if a drug has a short elimination half life (30 min to 2 h), it is possible to attain and then maintain the desired plasma concentration in approximately 2–8 h so we can use this approach.  Practical steady-state concentration if a drug has a long half life (for example, the elimination half life of digoxin is approximately is 40–50 h and for phenobarbital is approximately 90–110 h) and such a drug is administered to a patient using the single infusion approach, it may take a long time (approximately 7 and 15 days for digoxin and phenobarbital, respectively) before drug concentration is at a level that produces the desired effect; consequently, this may not be a suitable approach if the intention is to attain and then maintain the desired plasma concentration rapidly.  Instantaneous and continuous steady state Life-threatening situations in the hospital setting will often demand that the desired plasma concentration of the drug (of course, always within its therapeutic range) is attained instantaneously and then is maintained for a long duration. This may be accomplished by administering a loading intravenous bolus dose (DL) concomitant with the commencement of the infusion rate. The loading dose is an intravenous bolus dose. However, in this instance, unlike the case of a single, isolated intravenous bolus dose, the loading dose is immediately followed by the commencement of an intravenous infusion at constant rate.  Instantaneous and continuous steady state The intravenous bolus dose permits us to attain the desired plasma concentration at time 0 and the concomitant constant infusion allows us to maintain this concentration. This represents the mass of drug in the This represents the mass of drug in the body at a time (t) from the infusion alone body at any time from the intravenous bolus. If an intravenous bolus of drug is administered at the time an intravenous infusion of the drug is started, then X0 is the loading dose (DL) (X)t is the total amount (or mass) of drug in the body at any time from both bolus and infusion.  Instantaneous and continuous steady state The equation can be modified in terms of concentration: will yield the contribution to the total will yield the contribution to the plasma concentration at time t owing to total plasma concentration at the infusion administered at time t owing to the intravenous rate Q bolus loading dose, DL.  Instantaneous and continuous steady state (Cp)ss = Q / VK So The total plasma drug concentration from bolus and infusion at time infinity should be equal to the total plasma drug concentration from bolus and infusion at time zero (Cp)ss is the desired plasma concentration of a drug at steady state (e.g., mg mL-1) DL is the intravenous bolus loading dose (e.g., mg or mg kg-1) V is the apparent volume of distribution of the drug (e.g., mL or mL kg-1).  Instantaneous and continuous steady state (Cp)ss = Q / V K DL = V (Cp)ss So DL = Q / K DL: is the loading dose K: is the elimination rate constant Q: is the infusion rate. Since K = 0.693 / t1/2 DL = Q t1/2 / 0.693  Instantaneous and continuous steady state For a one-compartment drug, if the DL and infusion rate are calculated such that C 0 and (Cp)ss are the same and both DL and infusion are started concurrently, then steady state and (Cp)ss will be achieved immediately after the loading dose is administered. Similarly, curve b shows the blood level after a single loading dose of Q/k plus infusion from which the concentration desired at steady state is obtained.  Instantaneous and continuous steady state If the DL is not equal to Q/k, then steady state will not occur immediately. If the loading dose given is larger than Q/k, the plasma drug concentration takes longer to decline to the concentration desired at steady state (curve a). If the loading dose is lower than Q/k, the plasma drug concentrations will increase slowly to desired drug levels (curve c), but more quickly than without any loading dose.  Sampling blood following cessation of infusion (t-): is the time following the cessation of infusion (the time in the post- infusion period) (t – T). (T): is the time at which the infusion was stopped (Xt-): is the mass or amount of drug in the blood at time t–, in the post- infusion period; (X)T is the mass or amount of drug in the body at the time of cessation of infusion; (K): is the first-order elimination rate constant  Sampling blood following cessation of infusion  Use of post-infusion plasma concentration data to obtain half life, elimination rate constant and the apparent volume of distribution the intercept is (Cp)T = (X)T / V ; this approach, however, is not a practical way to determine apparent volume of distribution (V) since we do not know the value of (X)T. The absolute values of (Cp)T and (X)T, and, therefore, the value of the rate of elimination are time dependent. In general, if there is no loading dose: However, when T approaches infinity,  Use of post-infusion plasma concentration data to obtain half life, elimination rate constant and the apparent volume of distribution Typical profiles of the plasma concentration (Cp) against time following the administration of a drug by an intravenous infusion when the infusion is stopped at two different times: rectilinear plot  Use of post-infusion plasma concentration data to obtain half life, elimination rate constant and the apparent volume of distribution Typical profiles of the plasma concentration (Cp) against time following the administration of a drug by an intravenous infusion when the infusion is stopped at two different times: semilogarithmic plot.  Use of post-infusion plasma concentration data to obtain half life, elimination rate constant and the apparent volume of distribution Plasma concentration (Cp) versus time profile following the cessation of infusion (i.e. post infusion).  Method for obtaining the volume of distribution when T = ∞, (Cp)T = (Cp)ss then T=t  EXAMPLES 1) An antibiotic has a volume of distribution of 10 L and a k of 0.2 h-1. A steady-state plasma concentration of 10 μg/mL is desired. The infusion rate needed to maintain this concentration will be 20 mg/h Assume the patient has a uremic condition and the elimination rate constant has decreased to 0.1 h-1. To maintain the steady state concentration of 10 μg/mL, we must determine a new rate of infusion 10 mg/h because the elimination rate constant is smaller (ie, the elimination t1/2 is longer), the time to reach (Cp)ss will be longer  EXAMPLES 2) A patient was given an antibiotic (t1/2 = 6 hours) by constant IV infusion at a rate of 2 mg/h. At the end of 2 days, the serum drug concentration was 10 mg/L. Calculate the total body clearance ClT for this antibiotic. 200 mL/h