Introduction to Veterinary Pharmacokinetics:

Route of administration

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 steady-state values (Cmax, Cmin, Cave). 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.

Clt

Because clinically relevant changes in pharmacokinetics affect total clearance (Clt) it is a user entered value. Clt is controlled by the animal's physiologic and metabolic capabilities and physical-chemical properties of the drug. Clt is a measure of drug removal (from plasma water) by the liver, the lungs and the kidney.

Clt = Σ(all routes)(Q X E)
Organ clearance is calculated from organ blood flow (Q) and extraction efficiency (E). Clt in the present model is the sum of all individual organ clearances. Clt, therefore, is the volume of plasma water cleared completely of the drug during any unit time period.
Clt = Vz X λz
Used during an assessment of a pharmacokinetic experiment to determine Clt following single IV doses of the drug.
Cave = DoseRate ÷ Clt
This equation calculates average concentration for an intravenous dose. Clt controls the average plasma concentration (Cave) for any DoseRate.
Cave = (DoseRate X F) ÷ Clt
This equation calculates average concentration for a non-intravenous dose. The EFFECTIVE Dose Rate may be reduced by the Fraction of the dose absorbed (F) for any route of administration other than IV.

Vz

Vz 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.

Vz = Dose ÷ Cp0
Vz is determined from the Intravenous Dose and the Y-axis intercept (Cp0).
Abt = Cpt X Vz
The amount of drug in the body at any given time (Abt) can be calculated from the plasma concentration (Cpt).
λz = Clt ÷ Vz
Vzcontrols the relationship between Clt and λz.

Ka

Ka is the absorption rate constant. Ka 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.

Cpt =  (Ka x F x Dose) ÷ (Vz (Kaz)) x ((ezt)- (e-Kat))
In this simulation, Ka is used to generate data for all non-intravenous 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.

Cpt =  (ka x F x Dose) ÷ (Vz (kaz)) x ((ezt)-(e-kat))
In this simulation, F is used to generate data for all non-intravenous routes of administration.
F = (AUCoral ÷ AUCiv) x (Doseiv ÷ Doseoral)
F is determined by comparing areas under plasma concentration versus time profiles between single intravenous and single non-intravenous administration.  

λz

λz is the rate constant of elimination and is, in fact, the slope of a natural log plot of plasma concentration versus time.

λz = Clt ÷ Vz
Although λz 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. 
Cpt = Cp0 x ezt
λz can be used with the time-zero y-axis intercept (Cp0) to calculate the plasma concentration at any time (t) following a single intravenous dose of drug.

T1/2

T1/2 stands for half-life. By definition, it is the time required for elimination of one-half of ANY amount of drug in the body. (During this time the plasma concentration will drop by a corresponding 1/2).

T1/2 = 0.693 ÷ λz
λz can be used with the time-zero y-axis intercept (Cp0) to calculate the plasma concentration at any time (t) following a single intravenous dose of drug. 

Tmax

Tmax is the time at which the plasma concentration is maximum for each dose interval. For IV injections it would be 0. For non-intravenous routes, it is controlled by the relationship between the absorption rate constant (ka) and the elimination rate constant (λz).

Tmax = ln (ka ÷ λz) x 1 ÷ (ka - λz)
Notice that the only pharmacokinetic constants in the equation are the rate constants of absorption (ka) and elimination (λz).

Steady-State

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 (Cmax) and all trough concentrations are the same (Cmin). The TIME to steady state is controlled by half-life (see T1/2 help above). The magnitude of Cmax and Cmin are also affected by dose, dose interval, ka (if applicable), and Clt.

Time to 97% Steady State = 5 x T1/2
The TIME required to reach steady state is determined solely by the half-life of elimination of the drug.  The actual concentrations (Cmax, Cmin, Cave) are also controlled by dose, interval, absorption rate, fraction absorbed, and Vz.
Acc = 1 ÷ (1 - ezT)
The proportional increase in the peak concentration following the first dose, compared to the peak concentration (Cmax) 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 Cmax and Cmin concentrations. 

Cmax

Cmax is the maximum plasma concentration for every dose given at steady state. The first step in the calculation of Cmax is to determine the y-axis intercept (or in the case of non-IV routes, a pseudo-intercept) of a single dose. Then the Accumulation Constant (calculated under Steady-State Help above) is applied along with absorption and elimination rate Constants.

Intercept = Dose ÷ Vz
The IV y-axis intercept. 
Pseudointercept =  (ka x F x Dose) ÷ Vz x (kaz)
The non-IV y-axis "pseudo-intercept". 
Cmax = Intercept x Acc
The IV Cmax
Cmax = Acc x Pseudointercept x ((ezTmax)-(e-ka Tmax))
The non-IV Cmax.

Cave

Cave is the average plasma concentration. Only dose, dose interval, fraction of the dose absorbed, and clearance are necessary to calculate Cave

Cave = DoseRate ÷ Clt
The IV Cave.
Cave = F x DoseRate ÷ Clt
The non-IV Cave.

Cmin

Cmin is the minimum (or trough) plasma concentration for every dose given at steady state. The first step in the calculation of Cmin is to determine the y-axis intercept (or in the case of non-IV routes, a pseudo-intercept) of a single dose. (see calculations in Cmax Help above) Then the Acc Constant (calculated under Steady-State Help above) is applied along with absorption and elimination rate Constants.

Cmin = Acc x Dose ÷ Vz x ezT
The IV Cmin. T is the dose interval
Cmin = Acc x Intercept x ((ezT)- (e-kaT))
The non-IV Cmin. T is the dose interval

AUC

AUC is used to calculate the fraction absorbed for a non-IV dose. (See F Help above).

F = (AUCoral ÷ AUCiv ) x (Doseiv ÷ Doseoral)
F is calculated from IV and non-IV AUCs.