PK PD Analysis Services

In linear pharmacokinetics, systemic concentration over time data fits a one-compartment model. Typically, the concentration data may be matched to a single or multi-compartment PK model to help interpret pharmacokinetic equations and make therapeutic decisions. Most pharmacokinetics of drugs are performed without specifying the applicable mathematical model (non-compartmental analysis). One primary characteristic of linear models is that the change in concentration over time is constant. Thus, the compound’s half-life is constant and area under curve (AUC) pharmacokinetics increases linearly with dosage regardless of the body’s drug level. Therefore, doubling the dose will result in doubling the AUC, or administering half the dose twice per day will result in the same AUC as administering the total dose once per day. Contrastingly, non-linear pharmacokinetic models result from saturable behavior in the absorption, distribution, metabolism, or excretion of the compound. Here, saturable metabolism or excretion results in higher than dose-proportional increases in AUC pharmacokinetics with dosage, and saturable absorption results in lower than dose-proportional increases in AUC pharmacokinetics with dosage. In either case, the validity of PK parameters depends on the data’s quality entered into the model. Thus, dosing and sample collection must be precisely timed, and analytical methods must be sensitive and specific. Pharmacokinetics of drugs must be weighted appropriately to avoid bias due to the increased probability of errors at drug concentrations near the assay’s detection limit. Results obtained using a specific pharmacokinetic model should be compared to those using noncompartmental methods.

Area under curve (AUC) is calculated for the concentration vs. time curve by totaling trapezoidal areas between each measured time point. We can use various mathematical rules for these calculations based on linear or logarithmic transformations. One simple AUC pharmacokinetics calculation uses the linear trapezoidal rule with the equation Atrap = ((c1 + c2) / 2) / (t2 – t1). Here, Atrap is the trapezoidal area, and c1 and c2 are the measured concentrations at time points t1 and t2. AUC is the integration or summation of all such areas throughout the measured time points. We can extrapolate AUC in pharmacokinetics to infinity by adding the final triangle area created by the terminal extrapolation of the elimination phase to the time axis. Our scientists calculate and interpret your drug’s AUC figures to understand total exposure following any pharmacokinetic modeling.

Systemic Clearance (CL or CLs)in pharmacokinetics represents the rate at which a drug gets removed from the bloodstream. Clearance is determined from non-compartmental analysis following IV dosing. It represents total additive clearance from all potential clearing organs (e.g., liver, kidneys, etc.). We measure clearance values in units of volume/time and think of it as a proportionality constant between drug concentration and elimination rate. The non-compartmental pharmacokinetic equation for clearance is CL = Dose/AUC.

Tmax in pharmacokinetics represents the time after dosing when a compound reaches its maximum concentration in the bloodstream following extravascular dosing. Usually, the lower rates of absorption result in extended Tmax values.

Cmax in pharmacokinetics is the maximum observed concentration during a PK study. There is no mathematical calculation for the determination of Cmax. Therefore, we must design PK studies appropriately to capture Cmax and Tmax accurately.

Following repeated drug administrations, the systemic concentrations in the body reach an equilibrium where the rate of drug intake equals the rate of excretion. This equilibrium is described as steady-state. Typically, it takes administrations over approximately five half-lives of the drug to reach steady-state independent of dose level and dosing interval. We can calculate steady-state concentration (Css) by dividing the total exposure over the dosing interval (AUClast) by the interval time (Tlast).

Steady state is attained with repeated dosing and increasing drug concentrations in the body until saturation. At this point, the amount of drug administered is equivalent to the amount of drug leaving the body between each dose (rate in = rate out). Here, drug concentrations rise and fall according to a repeating wave pattern as long as the same dose level gets administered with the same time interval between doses. This repeated dosing interval is often abbreviated using the Greek letter tau (τ) in pharmacokinetics. Generally, drug accumulation and attainment of steady state are possible using any route of administration for dosing.

T1/2 in pharmacokinetics, i.e., elimination half-life, represents the time it takes to clear half of the compound’s concentration from systemic circulation during the log-linear elimination phase. Even as elimination half-life can be calculated for any dose route, it is best represented for a compound following an IV dose given the absorption component is bypassed with direct systemic administration. IV bolus curves for most drugs are biphasic, including a steep early phase representative of compound distribution to tissues, metabolism, and excretion. Once tissue distribution is equilibrated, the second phase of the curve represents metabolism and excretion. Points in this log-linear elimination phase are selected and used to determine the curve slope (m). The elimination rate constant (λz, k, or kel) is calculated from the slope as λz = 2.303 x m. Then, we calculate elimination half-life (t½) as 0.693 / λz. For reliability, the half-life calculation should be performed with a minimum of three terminal points in the λz range and have a determination coefficient (R2) of at least 0.85.

Cp in pharmacokinetics is a common abbreviation used to indicate blood plasma concentration. Usually, the first step following sample bioanalysis for performing PK calculations is to plot the measured blood plasma or serum concentrations versus time.

In a standard non-compartmental model, the elimination rate constant can be represented by several abbreviations including λz, k, kel, β, λn, λlast), and represents the log-linear elimination phase following compound absorption and distribution to tissues. For a mathematical pharmacokinetic model, compound flow through each compartment can be characterized by rates in and out, typically expressed as kin, kout, ka, kb, k1, k2, etc.. Here, an increasing number of constants are needed for an increased number of compartments used in the modeling. These constants vary depending upon the complexity of the mathematical model used.

Volume of Distribution in pharmacokinetics is typically abbreviated Vd, Vz, or Varea. Vd in pharmacokinetics reflects the reversible uptake of drugs by tissues from the blood. It is thought of as a fictitious volume that a drug occupies in the body as a uniform sack relative to the drug concentration in blood. Large Volumes of Distribution indicates more significant levels of the drug, reaching tissues relative to measured plasma concentrations and can show the compound’s potential for achieving the desired target. We calculate Vd in pharmacokinetics by dividing the measured Clearance (CL) with the elimination rate constant (λz). Volumes of distribution can be calculated following IV doses. Similarly, the apparent Volume of Distribution (Vd/F) may be determined for extravascular doses and includes a bioavailability correction factor to account for the compound’s absorption. Volume of distribution at steady-state (Vss) is another useful PK parameter for predicting tissue distribution and is calculated as mean residence time (MRT) times clearance (CL) following IV dosing.