About This Tool

The PK Parameter Estimator from Graph calculator performs a standard Non-Compartmental Analysis (NCA) on concentration-time data to derive fundamental pharmacokinetic (PK) parameters. This method allows for the characterization of a drug's disposition in the body without assuming a specific compartmental model (e.g., one- or two-compartment). It is a widely used approach in early drug development, bioequivalence studies, and preclinical research.

What This Calculator Does

This tool processes time-concentration data pairs to calculate a suite of essential PK parameters. After you provide the data—either by manual entry, file upload, or by digitizing a published graph—the calculator determines:

• Exposure Parameters: Cmax, Tmax, and Area Under the Curve (AUC).
• Elimination Parameters: The terminal elimination rate constant (λz), terminal elimination half-life (t½), and the quality of the regression fit (R²).
• Distribution and Clearance: Total body clearance (Cl) and the volume of distribution during the terminal phase (Vz), which require a dose input.
• Residence Time: Mean Residence Time (MRT) based on the Area Under the Moment Curve (AUMC).

When to Use It

NCA is a cornerstone of pharmacokinetic analysis and is appropriate in many contexts. This calculator is particularly useful for:

• Early Phase Clinical Trials: Analyzing data from First-in-Human (FIH) or single ascending dose (SAD) studies.
• Bioequivalence (BE) Studies: Comparing key exposure parameters (Cmax, AUC) between a test and reference formulation.
• Preclinical Studies: Evaluating the PK profile of a drug candidate in animal models.
• Academic Research: Quickly estimating PK parameters from published literature by using the graph digitizer function.
• Educational Purposes: Understanding the relationship between raw concentration data and the derived parameters that describe a drug's behavior.

Inputs Explained

To ensure accurate calculations, it's important to understand each input:

• Time and Concentration Data: The core of the analysis. Time is the independent variable (x-axis), and concentration is the dependent variable (y-axis). Ensure units are consistent (e.g., hours for time, ng/mL for concentration).
• Dose: The total amount of drug administered. This value is essential for calculating dose-dependent parameters like Clearance (Cl) and Volume of Distribution (Vz). Without a dose, these parameters cannot be determined.
• Dosing Interval (τ): The time between doses in a multiple-dosing regimen. While this tool focuses on single-dose analysis, this input is reserved for potential steady-state calculations.
• Infusion Duration (T): For intravenous (IV) infusions, this is the total time over which the drug was administered. For an IV bolus, this value is 0 or can be left blank.
• AUC Method: Determines how the area under the curve is calculated between two time points.
  • Linear Up / Log Down: The recommended and most common method. It uses the linear trapezoidal rule when concentrations are rising and the logarithmic trapezoidal rule when they are declining, which more accurately represents the exponential decay process.
  • Linear Trapezoidal: Uses the linear trapezoidal rule for all segments. It is simpler but can slightly overestimate AUC during the elimination phase.

Results Explained

The calculator provides the following standard NCA parameters:

Formula / Method

Terminal Phase Estimation

The terminal elimination rate constant (λz) is determined by user selection. On the semi-log plot, the user must select at least three points that form the final linear decay phase. The tool performs a linear regression on the natural logarithm (ln) of these concentrations versus time.

• Regression Equation: ln(C) = ln(C₀) - λz * t
• Half-life (t½): t½ = ln(2) / λz ≈ 0.693 / λz

Area Under the Curve (AUC) Calculation

AUC is calculated piece-wise using the trapezoidal rule. For a segment between time points t₁ and t₂ with concentrations C₁ and C₂, the area is:

• Linear Rule: AUC(t₁-t₂) = (C₁ + C₂) / 2 * (t₂ - t₁)
• Logarithmic Rule (used when C₂ < C₁): AUC(t₁-t₂) = (C₁ - C₂) / ln(C₁ / C₂) * (t₂ - t₁)

The total AUC up to the last time point (AUC₀-t) is the sum of these segments. The AUC is extrapolated to infinity using the last observed concentration (C_last) and λz:

• Extrapolation: AUC(t-∞) = C_last / λz
• Total AUC: AUC₀-∞ = AUC₀-t + AUC(t-∞)

Step-by-Step Example

Let's analyze a simple dataset for a drug administered as a 100 mg IV bolus.

1. Enter Data: Input the following time (hr) and concentration (ng/mL) pairs into the manual entry table.

   Time (hr)	Concentration (ng/mL)
   0.5	82.1
   1	70.3
   2	51.5
   4	28.9
   8	10.1
   12	3.5

2. Enter Dose: In the "Model Parameters" section, enter 100 into the "Dose" field.
3. Switch to Semi-Log Plot: Click the "Semi-Log" pill above the plot to view the data on a logarithmic Y-axis. You should see the later points forming a straight line.
4. Select Terminal Phase: Click on the last three data points on the plot (at t=4, 8, and 12 hr). They will be highlighted, and a regression line will appear through them.
5. Review Results: The "PK Parameters" panel will automatically update. You will see values for Cmax (82.1), Tmax (0.5), and calculated values for t½, AUC₀-∞, Cl, and Vz based on your selected terminal phase. The R² value will indicate how well the line fits the selected points.

Tips + Common Errors

• Tip - Terminal Phase Selection: The choice of points for the terminal phase is critical. Choose at least 3-4 points that clearly form a straight line on the semi-log plot. Starting the terminal phase too early (including distribution phase points) will result in an artificially short half-life.
• Tip - Consistent Units: Ensure all your inputs use a consistent set of units (e.g., mg for dose, hours for time, mg/L for concentration). The output units will be derived from your inputs (e.g., Clearance will be in L/hr).
• Error - Missing Dose: If the Dose field is empty, the calculator cannot determine Clearance (Cl) or Volume of Distribution (Vz). These fields will remain blank in the results.
• Error - Poor R² Value: An R² value significantly below 0.95 suggests that the selected points do not form a good linear fit. This could mean there is high variability in the data, or you have selected an inappropriate set of points for the terminal phase. Try selecting a different range of points.
• Error - Zero or Negative Concentrations: Zero concentrations cannot be displayed on a logarithmic scale and are ignored for terminal phase regression. Negative concentrations are invalid and should be treated as zero or below the limit of quantification (BLQ).

Frequently Asked Questions (FAQs)

What is Non-Compartmental Analysis (NCA)?

NCA is a method used to determine pharmacokinetic parameters without making assumptions about the underlying physiological model (i.e., how many "compartments" the drug distributes into). It relies on algebraic equations and the application of the trapezoidal rule to the observed data.

What's the difference between the "Linear" and "Linear Up / Log Down" AUC methods?

The "Linear" method approximates the area between two points with a straight line (a trapezoid). The "Linear Up / Log Down" method does the same when concentrations are rising but uses a logarithmic formula when concentrations are falling, which better models the first-order elimination process and is generally considered more accurate.

How many points should I select for the terminal phase?

A minimum of three points is required for a regression. It is best practice to use 3-5 points that provide a high R² value (typically >0.95) and visually form a straight line on the semi-log plot.

Why is my R² value low?

A low R² can be caused by high data variability, assay noise near the limit of quantification, or selecting points that are not all part of the true terminal elimination phase. Try re-evaluating your point selection.

Why are Clearance (Cl) and Volume (Vz) not calculated?

These are dose-dependent parameters. You must enter a numerical value for "Dose" for the calculator to compute them. They also depend on a valid calculation of AUC₀-∞, which requires a valid terminal phase selection.

Can I use this tool for oral (extravascular) administration data?

Yes, NCA is suitable for any route of administration. For oral data, the calculated clearance is technically Apparent Clearance (Cl/F) and volume is Apparent Volume (Vz/F), where F is the unknown bioavailability.

What does "exclude" a point (Shift-click) mean?

Excluding a point removes it from all calculations (Cmax, Tmax, AUC, and terminal phase regression). This is useful for removing an obvious outlier without deleting the data row entirely.

Does this tool handle multiple-dose data?

The tool is primarily designed for single-dose data. While you can analyze data from a single dosing interval (τ) at steady-state, it does not calculate steady-state specific parameters like accumulation ratio or average concentration (Cav).

What are AUMC and MRT?

AUMC is the Area Under the Moment Curve, calculated as ∫(t*C)dt. MRT, or Mean Residence Time, is the average time a drug molecule resides in the body before being eliminated. It's calculated as AUMC₀-∞ / AUC₀-∞ and provides insight into the overall persistence of a drug.

References

1. Gibaldi M, Perrier D. Pharmacokinetics. 2nd ed. New York: Marcel Dekker; 1982. (A foundational text on pharmacokinetic principles).
2. FDA, Center for Drug Evaluation and Research (CDER). Guidance for Industry: Bioavailability and Bioequivalence Studies for Orally Administered Drug Products — General Considerations. 2003. View PDF
3. European Medicines Agency (EMA). Guideline on the investigation of bioequivalence. 2010. View PDF
4. Tóth K, Csorba M, Lévai G, et al. Non-compartmental analysis of pharmacokinetic data: a comparison of two standard software packages. Acta Pharm Hung. 2014;84(3):111-9.