Term
First Order Overall Elimination Rate Constant 

Definition
K = k_{e} + k_{m} + k_{n} or K = k_{e} + k_{m}_{} 


Term
Total Amount of Free Drug in the compartment at time t, A_{t} 

Definition


Term
The overall rate of elimination from the compartment 

Definition


Term
dA/dt =  KA can be integrated to yield the following equations based on the amount of free drug in the compartment: 

Definition
ln A = ln A°  Kt log A = log A°  Kt/2.303 A = A° e^{Kt} Where, A is the amount of free drug in the body at time t and A° is the initial amount or dose at time zero.



Term
The dA/dt =  KA integrations may also be written in terms of plasma or serum concentration of free drug: 

Definition
ln Cp = ln Cp°  Kt log Cp = log Cp°  Kt/2.303 Cp = Cp° e^{Kt} Cp and Cp° are the plasma concentrations of free drug at time t and initial concentration (t = 0), respectively. 


Term
Halflife of Elimination: A useful pharmacokinetic constant of the model is the halflife of elimination. It is the time required for 50% of drug at any initial level to be eliminated from the compartment, i.e. At t = T_{1/2}, Cp_{2} = 1/2 Cp_{1}, or A_{2} = 1/2 A_{1} 

Definition
Therefore T_{1/2 }= 0.693/K, or T_{1/2} = ln2/K, or T_{1/2}^{ }= 2.303log 2/K 


Term
halflife of elimination of a drug that follows linear pharmacokinetics is of amount or concentration and to the overall elimination rate constant. 

Definition
Independent; Inversely proportional 


Term
Time Constant: Occasionally it is more convenient to use time constant rather than the halflife. The time constant is the reciprocal of the firstorder rate constant. The relationship between the time constant and the halflife is as follows: 

Definition
Time Constant = 1/K 1/K = 1/(0.693/T_{1/2}) = 1.44 T_{1/2} 


Term
The time constant is also known as turnover time and in noncompartmental analysis of i.v. bolus, 1/K is referred to as Mean Residence Time (MRT). The noncompartmental analysis will be discussed later on in the course. The time constant or MRT represents the time for 63% of an i.v. bolus dose to be eliminated from the body. The relationship between MRT and T_{1/2 }is as follows: 

Definition
MRTi.v. = 1/K = T_{1/2}/0.693 T_{1/2 }= 0.693( MRT)_{i.v. bolus} 


Term
Apparent Volume of Distribution: A large volume of distribution indicates that the concentration of free drug in plasma is low and the drug is localized and associated with regions that are not easily accessible or being a part of the sampling compartment. The equation for V_{d} is..... 

Definition
Vd = A_{t}/Cp_{t}_{ } Since the amount of free drug is only known at time zero, a more practical equation would be: Vd = Dose/Cp° 


Term
Total Body Clearance: The total body clearance (Cl_{t}), as it was discussed in chapter five, is the rate of elimination of drug from the body per unit of concentration, i.e. 

Definition
Cl_{t} = K x Vd Therefore, the total body clearance is the product of apparent volume of distribution and the firstorder overall elimination rate constant and according to the following equations it is also the sum of metabolic and renal clearances. Cl_{t} = Vd ´ K = Vd (k_{e} + k_{m}) = Cl_{r} + Cl_{m} 


Term
Duration of Action: The duration of action is the time that plasma concentration remains within the therapeutic range of a drug. Duration of action may be estimated as follows.....


Definition


Term
Fraction of dose remaining in the body at time t : If equation Cp = Cp° e^{Kt} is normalized with respect to Cp°^{ }(i.e., dividing both sides of the equation by Cp°) the following equations that represent the fraction of dose in the body (f_{b}) at time t will be obtained: 

Definition


Term
Fraction of dose eliminated by all routes of elimination at time t: At time zero the fraction of dose in the body is equal to one. As the fraction of dose in the body declines with time, the fraction of dose eliminated by all routes of elimination increases. Therefore the sum of fraction in the body and fraction eliminated at any time will be equal to 1. Based on this concept of mass balance the following equations define the fraction of dose eliminated (f_{el}) from the body by all routes of elimination time t: 

Definition


Term
Area Under Plasma ConcentrationTime Curve after I.V. Bolus: The area under plasma concentration of free drug versus time (AUC) is a useful parameter in determining the extent of availability of a drug in the body after any route of administration. 

Definition
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AUC is directly proportional to initial plasma concentration or dose and inversely proportional to the overall elimination rate constant and clearance. This means that if we double the dose the area under the curve will be doubled.
Also, AUC can be calculated by
AUC = Cp_{0}/K 


Term
Total amount of drug in the body after administration of a second dose 

Definition
A_{12 noon} = 2^{nd} Dose + (Cp_{12 noon of 1st dose }x Vd) *Notes: 12 noon is just a random time put in to the equation. If we want to know the concentration when a SECOND dose is given (12 noon), then we have to know what the concentration is in the body BEFORE that second dose is given at 12 noon. 


Term
The regression equation of logCp versus time is:
LogCp = 0.602 –0.401 t
What makes up each number? 

Definition
LogCp = 0.602 –0.401 t 0.602 = Cp_{0} 0.401 = K/2.303 So....Log Cp = Cp_{0}  Kt 2.303 


Term
Relationship between slope and K 

Definition


Term
Rate of Elimination at time "t" 

Definition
(Rate)t = Cl_{t} x Cp_{t} 

