Non-Compartmental Analysis

Non-Compartmental Analysis (NCA) is a method used to describe the pharmacokinetics of a drug by focusing on the observed plasma concentration-time curve. Unlike compartmental modelling, which treats the body as a series of linked containers, NCA treats the body as a 'black box' and relies on empirical data with minimal assumptions.

When is it used?

NCA is the workhorse of the pharmaceutical industry, specifically during:

  1. Bioequivalence Studies: Comparing a generic drug to a brand-name drug.
  2. Dose Escalation: Seeing how exposure increases as the dose goes up.
  3. Toxicokinetics: Assessing safety margins in early clinical trials.

NCA vs. Compartmental Modelling

NCA treats the body as a 'Black Box'. It doesn't care about specific organs or tissues; it only cares about the drug concentration in the blood (C) and the time (t). It uses the trapezoidal rule to calculate the area under the curve (AUC).

Compartmental Modelling treats the body as one or more interconnected tanks (compartments). The central compartment usually represents highly perfused organs like the heart, liver, and kidneys. The peripheral comparments represent tissues where the drug distributes more slowly, like fat or muscle. It uses differential equations to describe the rate of drug transfer between these tanks.

Key Parameter List

Area Under the Curve (AUC): The Core Concept

The fundamental principle of NCA is the Trapezoidal Rule. Since drug concentration is measured at specific intervals, NCA calculates the area of the trapezoids formed between these data points to estimate total drug exposure. This provides a robust summary of the drug's behaviour without needing to define a specific physiological model.

Linear Trapezoidal method

AUC∣t1t2=Δt×(C1+C2)2AUC\rvert_{t_1}^{t_2} = \frac{\Delta t \times \left(C_1 + C_2\right)}{2}

Logarithmic Trapezoidal method

AUC∣t1t2=Δt×(C2−C1)ln⁡(C2C1)AUC\rvert_{t_1}^{t_2} = \frac{\Delta t \times \left(C_2 - C_1\right)}{\ln\left(\frac{C_2}{C_1}\right)}

The two most common AUC calculation methods are listed below:

  1. Linear Trapezoidal: Assumes a straight line between points. This is accurate during the absorption phase (when concentrations are increasing) but tends to overestimate the area during the elimination phase (where the decay is naturally exponential).
  2. Linear-up/Log-down: A hybrid approach. It uses the Linear rule when concentrations are rising up to Cmax and the Log-Linear rule when concentrations are falling. This is considered the industry standard for most PK profiles.

Cmax

Maximum concentration from dose time (first observation) or dose time + τ (if τ > 0)

Where:

τ: The dosing interval (the time between doses, such as 8, 12, or 24 hours).

Clast

Last concentration from dose time (first observation) or dose time + τ (if τ > 0)

Area under the Moment Curve (AUMC)

While the standard AUC (Area Under the Curve) measures the total drug exposure over time, AUMC is the area under the curve of the product of time and concentration (Time x Concentration) versus time. It is a mathematical 'moment' of the concentration-time curve.

Linear trapezoidal rule:

The area of a partial segment (AUMCn) between t1 and t2 is given as :

AUMC∣t1t2=Δt×(t1×C1+t2×C2)2AUMC\rvert_{t_1}^{t_2} = \frac{\Delta t \times \left(t_1 \times C_1 + t_2 \times C_2\right)}{2}

Logarithmic trapezoidal rule:

AUMC∣t1t2=Δt×(t2×C2−t1×C1)ln⁡(C2C1)−Δt2×(C2−C1)[ln⁡(C2C1)]2AUMC\rvert_{t_1}^{t_2} = \frac{\Delta t \times \left(t_2 \times C_2 - t_1 \times C_1\right)}{\ln\left(\frac{C_2}{C_1}\right)} - \frac{\Delta t^2 \times \left(C_2 - C_1\right)}{\left[\ln\left(\frac{C_2}{C_1}\right)\right]^2}

Cavg

In pharmacokinetics, the average concentration (Cavg) represents the constant concentration that would result in the same total drug exposure (AUC) as the actual fluctuating concentrations observed over a specific dosing interval.

Cavg=AUCττC_{avg} = \frac{AUC_{\tau}}{\tau}

Where:

AUCτ: The area under the concentration-time curve during one dosing interval (e.g., from 0 to 12 hours).

τ: The dosing interval (the time between doses, such as 8, 12, or 24 hours).

Terminal Elimination Rate Constant

In pharmacokinetics, Kel (often denoted as λz in NCA) is the terminal elimination rate constant. It represents the fraction of a drug that is removed from the body per unit of time.

Unlike clearance (CL), which measures volume, Kel measures speed. For example, if a drug has a Kel of 0.1 h-1, it means approximately 10% of the drug remaining in the body is eliminated every hour.

Most drugs follow first-order kinetics, meaning the rate of elimination is proportional to the concentration. On a standard linear graph, this looks like a downward curve. However, if you transform the concentration to a natural logarithmic (ln) scale, the elimination phase becomes a straight line.

How is it calculated?

It is calculated using Linear Regression on the terminal (end) portion of the log-transformed plasma concentration-time curve.

The relationship between concentration (C) and time (t) during the elimination phase is:

ln⁡(C)=ln⁡(C0)−Kel×t\ln\left(C\right) = \ln\left(C_0\right) - K_{el} \times t

So,

Kel=−ln⁡(C2)−ln⁡(C1)t2−t1K_{el} = -\frac{\ln\left(C_2\right) - \ln\left(C_1\right)}{t_2 - t_1}

Elimination Half-Life (t1/2)

The elimination half-life (t1/2) is the time required for the concentration of a drug in the plasma to decrease by exactly 50%.

t1/2=ln⁡(2)Kel≈0.693Kelt_{1/2} = \frac{\ln\left(2\right)}{K_{el}} \approx \frac{0.693}{K_{el}}

Mean Residence Time (MRT)

Mean Residence Time (MRT) represents the average amount of time a single molecule of drug stays in the body before it is eliminated.

While t1/2 tells you how long it takes for the concentration to drop by 50%, MRT gives you a more holistic 'average' life expectancy for the drug molecules within the system.

MRT=AUMCAUCMRT = \frac{AUMC}{AUC}

Clearance (CLlast)

Clearance last (CLlast) is a specific measurement of how efficiently the body removes a drug, calculated using the total exposure observed up until the very last measurable data point.

While 'Total Clearance' (CL) usually refers to the body's ability to clear a drug over an infinite amount of time, CLlast is a more conservative estimate based strictly on the experimental data you have actually collected.

CLlast=DoseAUClastCL_{last} = \frac{Dose}{AUC_{last}}

AUCinf

AUCinf (Area Under the Curve from time zero to infinity) is the most complete measure of total drug exposure. While AUClast only accounts for the drug measured in blood samples during a study, AUCinf estimates the total amount of drug that will ever reach the systemic circulation, including the 'tail' of the curve that remains after the last sample is taken.

AUC∞=AUClast+ClastλzAUC_{\infty} = AUC_{last} + \frac{C_{last}}{\lambda_z}

Why extrapolate to infinity?

Realistically, we cannot keep a patient in a clinic until every single molecule of a drug has left their body—that could take weeks for some medications. However, we need to know the total exposure to calculate Total Clearance (CL) and Volume of distribution (Vz)

Clearance to infinity (CLinf)

CLinf (Total Body Clearance extrapolated to infinity) represents the body's overall ability to remove a drug from the systemic circulation. It is the most comprehensive measure of drug elimination because it accounts for the entire time the drug is present in the body, from the moment of dosing until every single molecule is gone.

In NCA, it is considered the 'true' clearance of the drug.

CLinf=DoseAUC∞CL_{inf} = \frac{Dose}{AUC_{\infty}}

Volume of distribution (Vz,inf)

Volume of Distribution to infinity (often denoted as Vz or V z/F for extravascular doses) represents the apparent volume in which the drug is distributed during the terminal (elimination) phase.

It is called 'to infinity' because it relies on the terminal elimination rate constant (λz) which is calculated as the drug is being cleared from the body over time.

Vz is not a real physiological volume (like the volume of your blood or water). Instead, it is a mathematical value that relates the amount of drug in the body to the concentration measured in the plasma.

  • Small Vz: The drug is mostly staying in the blood (e.g., Warfarin).
  • Large Vz: The drug has left the blood and is 'hiding' or distributed deep in tissues, fat, or muscle (e.g., Digoxin or Chloroquine).
Vz=DoseAUC∞×λzV_z = \frac{Dose}{AUC_{\infty} \times \lambda_z}

Or, expressed through clearance:

Vz=CLλzV_z = \frac{CL}{\lambda_z}

Acknowledgement

  1. Arnautov, V. (2025). PharmCat/MetidaNCA.jl: v0.7.1 (v0.7.1). Zenodo. Last Accessed: 11/03/2026. https://doi.org/10.5281/zenodo.15793887
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