Introduction to Veterinary Pharmacokinetics: 
Route of administration
 IV = intravenous
 IM = intramuscular
 Oral = per os
 SC = subcutaneous
Dose
Number of Doses
Dose Interval
Enter the dose interval, which is the number of hours between given doses. For simulations of a single dose, the interval determines the length of time that concentration data will be displayed. Dose interval also affects the calculation of steadystate values (C_{max}, C_{min}, C_{ave}). Dose Interval can only be set to 6, 8, 12, or 24.
DoseRate = Dose ÷ (Dose Interval)

The dose rate is calculated by dividing the dose given by the dose interval. (units are mg/kg/hr in this simulation). This is equivalent to the infusion rate for constant intravenous administration. 
C_{lt}
Because clinically relevant changes in pharmacokinetics affect total clearance (C_{lt}) it is a user entered value. C_{lt} is controlled by the animal's physiologic and metabolic capabilities and physicalchemical properties of the drug. C_{lt} is a measure of drug removal (from plasma water) by the liver, the lungs and the kidney.
C_{lt} = Σ_{(all routes)}(Q X E)

Organ clearance is calculated from organ blood flow (Q) and extraction efficiency (E). C_{lt} in the present model is the sum of all individual organ clearances. C_{lt}, therefore, is the volume of plasma water cleared completely of the drug during any unit time period. 
C_{lt} = V_{z} X λ_{z}

Used during an assessment of a pharmacokinetic experiment to determine C_{lt} following single IV doses of the drug. 
C_{ave} = DoseRate ÷ C_{lt}

This equation calculates average concentration for an intravenous dose. C_{lt} controls the average plasma concentration (C_{ave}) for any DoseRate. 
C_{ave} = (DoseRate X F) ÷ C_{lt}

This equation calculates average concentration for a nonintravenous dose. The EFFECTIVE Dose Rate may be reduced by the Fraction of the dose absorbed (F) for any route of administration other than IV. 
V_{z}
V_{z} stands for volume of distribution. The volume of distribution determines the plasma concentration of drug for a given amount of drug in the body. The volume of distribution of a drug is determined from a following administration of a single intravenous dose.
V_{z} = Dose ÷ C_{p}0

V_{z} is determined from the Intravenous Dose and the Yaxis intercept (C_{p}0). 
A_{b}t = C_{p}t X V_{z}

The amount of drug in the body at any given time (A_{b}t) can be calculated from the plasma concentration (C_{p}t). 
λ_{z} = C_{lt} ÷ V_{z}

V_{z}controls the relationship between C_{lt} and λz. 
K_{a}
K_{a} is the absorption rate constant. K_{a} describes rate that the drug moves from the dose at the site of absorption (injection site, gi tract etc.) into the systemic circulation. It is applicable to all routes of administration other than intravenous.
C_{p}t = (K_{a} x F x Dose) ÷ (V_{z} (K_{a}λ_{z})) x ((e^{λzt}) (e^{Kat}))

In this simulation, K_{a} is used to generate data for all nonintravenous routes of administration. 
F
F is the fraction of the dose absorbed. Essentially, F is synonymous with the term bioavailability. It is applicable to all routes of administration other than intravenous.
C_{p}t = (k_{a} x F x Dose) ÷ (V_{z} (k_{a}λ_{z})) x ((e^{λzt})(e^{kat}))

In this simulation, F is used to generate data for all nonintravenous routes of administration. 
F = (AUC_{oral} ÷ AUC_{iv}) x (Dose_{iv} ÷ Dose_{oral})

F is determined by comparing areas under plasma concentration versus time profiles between single intravenous and single nonintravenous administration. 
λ_{z}
λ_{z} is the rate constant of elimination and is, in fact, the slope of a natural log plot of plasma concentration versus time.
λ_{z} = C_{lt} ÷ V_{z}

Although λ_{z} is determined from the slope of a single intravenous dose of the drug, it is PRODUCED by the interaction between clearance and the volume of distribution. 
C_{p}t = C_{p}0 x e^{λzt}

λ_{z} can be used with the timezero yaxis intercept (C_{p}0) to calculate the plasma concentration at any time (t) following a single intravenous dose of drug. 
T_{1/2}
T_{1/2} stands for halflife. By definition, it is the time required for elimination of onehalf of ANY amount of drug in the body. (During this time the plasma concentration will drop by a corresponding 1/2).
T_{1/2} = 0.693 ÷ λ_{z}

λ_{z} can be used with the timezero yaxis intercept (C_{p}0) to calculate the plasma concentration at any time (t) following a single intravenous dose of drug. 
T_{max}
T_{max} is the time at which the plasma concentration is maximum for each dose interval. For IV injections it would be 0. For nonintravenous routes, it is controlled by the relationship between the absorption rate constant (k_{a}) and the elimination rate constant (λ_{z}).
T_{max} = ln (k_{a} ÷ λ_{z}) x 1 ÷ (k_{a}  λ_{z})

Notice that the only pharmacokinetic constants in the equation are the rate constants of absorption (k_{a}) and elimination (λ_{z}). 
SteadyState
At the end of each dose interval, some drug remains in the body. With repeated dosing, drug will accumulate based on this remaining fraction of the dose. (Peak and trough concentrations are higher with successive doses). Steady state is said to exist when the amount of drug eliminated during each dose interval equals the effective dose. At this time, all peak concentrations are the same (C_{max}) and all trough concentrations are the same (C_{min}). The TIME to steady state is controlled by halflife (see T_{1/2} help above). The magnitude of C_{max} and C_{min} are also affected by dose, dose interval, k_{a} (if applicable), and C_{lt}.
Time to 97% Steady State = 5 x T_{1/2}

The TIME required to reach steady state is determined solely by the halflife of elimination of the drug. The actual concentrations (C_{max}, C_{min}, C_{ave}) are also controlled by dose, interval, absorption rate, fraction absorbed, and V_{z}. 
Acc = 1 ÷ (1  e^{λzT})

The proportional increase in the peak concentration following the first dose, compared to the peak concentration (C_{max}) following a dose at steady state is calculated as an Accululation Constant (Acc) where T = dose interval. The Accumulation constant is used to calculate the C_{max} and C_{min} concentrations. 
C_{max}
C_{max} is the maximum plasma concentration for every dose given at steady state. The first step in the calculation of C_{max} is to determine the yaxis intercept (or in the case of nonIV routes, a pseudointercept) of a single dose. Then the Accumulation Constant (calculated under SteadyState Help above) is applied along with absorption and elimination rate Constants.
Intercept = Dose ÷ V_{z}

The IV yaxis intercept. 
Pseudointercept = (k_{a} x F x Dose) ÷ V_{z} x (k_{a}λ_{z})

The nonIV yaxis "pseudointercept". 
C_{max} = Intercept x Acc

The IV C_{max}. 
C_{max} = Acc x Pseudointercept x ((e^{λzTmax})(e^{ka Tmax}))

The nonIV C_{max}. 
C_{ave}
C_{ave} is the average plasma concentration. Only dose, dose interval, fraction of the dose absorbed, and clearance are necessary to calculate C_{ave}.
C_{ave} = DoseRate ÷ C_{lt}

The IV C_{ave}. 
C_{ave} = F x DoseRate ÷ C_{lt}

The nonIV C_{ave}. 
C_{min}
C_{min} is the minimum (or trough) plasma concentration for every dose given at steady state. The first step in the calculation of C_{min} is to determine the yaxis intercept (or in the case of nonIV routes, a pseudointercept) of a single dose. (see calculations in C_{max} Help above) Then the Acc Constant (calculated under SteadyState Help above) is applied along with absorption and elimination rate Constants.
C_{min} = Acc x Dose ÷ V_{z} x e^{λzT}

The IV C_{min}. T is the dose interval 
C_{min} = Acc x Intercept x ((e^{λzT}) (e^{kaT}))

The nonIV Cmin. T is the dose interval 
AUC
AUC is used to calculate the fraction absorbed for a nonIV dose. (See F Help above).
F = (AUC_{oral} ÷ AUC_{iv} ) x (Dose_{iv} ÷ Dose_{oral})

F is calculated from IV and nonIV AUCs. 