Help

This help file includes help with spreadsheets, help with defining variables and help with equations necessary to answer questions associated with this exercise.

Help Index
Dosage Route | Dose | Weight | Total Dose | N Doses | Dose Interval | Dose Rate
PK Variables Clt | Vz | Ka | F
[Targets] Lower limit | Upper Limit |
Calculated PK λz | T1/2 |
Steady State Values Steady State | Tmax | Cmax | Cave | Cmin | AUC

General

The spreadsheets include a data calculator section (including user input and calculated value sections), and a graphing section. Click on the cell you want to change. You can either hit the enter key or click in another cell and the new value will change the calculations.

When you change values in the calculator section, the graphs will automatically change to reflect the new data.

Printing

If you wish to print spreadsheets, you may of course do so. Depending on your particular combination of device and printer, it may be necessary for you to manually adjust orientation (you'll usually want "landscape" I think) and scaling in order to both data and graphs on a single sheet of paper. Calculations and tables (usually hidden) are hidden on the spreadsheets but may cause your printer generate multiple blank pages.

Route of administration (toc)

The route of drug administration is set for each numbered simulation within each exercise. Calculations for simulations of intravenous administration do not include bioavailability or rate of absorption. The equations for all routes of administration that include the process of absorption are interchangeable (see Ka, F Help). Key for routes of administration:

Dose (toc)

For each simulation you can enter a single dose. The dose must be expressed in mg/kg. Depending on the simulation, this dose may be given once or repeated. If you set the dose to 0 no data will be graphed for that simulation.

Weight (toc)

Enter a reasonable weight, in kg, for any species. Weight is used to calculate the total dose administered, but does not enter into any other calculations. (All pharmacokinetic variables used in this simulation are expressed on a "per kilogram of body weight" basis).

Total Dose (toc)

Total dose is calculated from dose multiplied by body weight. This variable is calculated to give the user perspective on the total amount given to the animal. Total dose does not affect the other calculations.

Number of Doses (toc)

Number of Doses is the number of doses to be used in the calculations for this simulation. In multiple dose simulations, this variable is determined by the Dose Interval you enter.

Dose Interval(toc)

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.

Dose Rate(toc)

The dose rate is determined by dividing dose by the dose interval. The dose rate and total clearance determine the average plasma concentration of any therapeutic regime.

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 (toc)

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
Clt controls the average plasma concentration (Cave) for any DoseRate.
Cave = DoseRate X F / Clt
The EFFECTIVE Dose Rate may be reduced by the Fraction of the dose absorbed (F) for any route of administration other than IV.

Vz (toc)

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 (toc)

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 (toc)

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 (toc)

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 (toc)

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 (toc)

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 (toc)

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 (toc)

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 (toc)

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 (toc)

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 (toc)

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.)

Lower Limit (toc)

The lower concentration limit (setting) for most drugs is the minimum effective concentration (MEC). Used in these simulations to provide visual reference to some target concentration (effective or otherwise). Entering a value will determine where the MEC line will appear on the graphs. In certain exercises, MEC is replaced by minimum inhibitory concentration (MIC). The MIC represents the antibiotic concentration required to inhibit the growth of bacteria. In the case of aminoglycosides, the lower limit is the concentration that should be reached at the end of each dose interval in order to avoid intoxication.

Upper Limit (toc)

The upper concentration limit (setting) for most drugs is the minimum toxic concentration (MTC). If some target (toxic or otherwise) value is known, entering a value will determine where the MTC line will appear on the graphs. In certain exercises, MTC is replaced by, minimum bactericidal concentration (MBC). The MBC represents the antibiotic concentration required to kill bacteria.