Chromatography Theory Calibration

Chromatography Theory - Calibrations

Topic - Chromatography Theory Calibration Chromatography calibration is how you turn peak responses into reliable amounts. In this chapter-style guide, we walk through the theory behind calibration curves, how to choose and fit them, and the practical decisions (weighting, origin handling, troubleshooting) that make the difference between “works on paper” and robust, audit-ready results in Chromperfect.

What is chromatography calibration and Chromatography Theory Calibration?

Chromatography calibration relates measured detector response to true amount. You build a curve from data points (amount, response), then use the curve’s formula to compute unknowns. We assume peak detection, integration, and identification are sound, so areas/heights are trustworthy.

Units and consistency

• The calibration file’s “units” field labels amounts on reports; it doesn’t alter calculations.

• Use any consistent basis—mass (ng, µg), concentration (µmol/L), or fraction—so long as all components are coherent.

External standard calibration (overview)

Prepare a standard (often a stock solution diluted to several levels), inject, integrate, and update calibration levels. Each level provides a response for each component; amounts stay as defined by you.

Single-point linear calibration

• Assumes strict proportionality (line through the origin).

• Response factor (RF) = response / amount. One good point can suffice, but it ignores day-to-day and low-level effects.

Replicate-point linear calibration

• Inject the same level multiple times to capture variability.

• The fitted line passes through the mean of the replicates—better precision and a visible audit trail for outliers.

Multi-level linear calibration

• Uses ≥2 distinct amounts; the best-fit line need not pass through the origin.

• Non-zero intercepts matter at low levels: small positive intercepts can reflect baseline noise; negative intercepts can force small negative amounts. Evaluate and manage (see Origin Treatments).

Measuring calibration precision

Coefficient of determination (R²)

• 0 to 1 scale of fit quality; great for multi-level curves, unhelpful for pure replicate single-level sets (often 0).

Average error (%)

• Mean absolute vertical deviation (%) of each point from the curve at its amount—an intuitive “typical % error.”

Average calibration factor (CF) & %RSD (ASTM style)

• Treats proportionality explicitly (line through origin).

• Report CF (mean slope to points from origin) and %RSD of CFs as an alternative quality view.

Weighting: when low-levels matter most

Errors may scale with signal. If low-level accuracy is critical:

• Equal weighting (instrumental noise dominates).

• 1/Y or 1/Y² (or 1/X, 1/X²) to emphasize low responses.

• Expect R² to fall with heavier weighting; average error may rise or fall. Choose by validation goals, not aesthetics.

Origin treatments: ignore, extrapolate, or force

• Ignore: ordinary regression; may yield non-zero intercepts.

• Extrapolate: use the fitted line above the lowest level; below it, connect a straight segment from origin to the curve—better low-level behavior, but with a slope discontinuity.

• Force: constrain the fit through (0,0). Smooth, but it can worsen % errors and R² if the true behavior isn’t strictly proportional.

Non-linear calibration curves

Real detectors often deviate from linearity. Chromperfect supports:

• Quadratic (parabolic): Degree-2; one “bend.” Beware a critical point (apex) beyond which amounts can’t be computed (over-range).

• Cubic: Degree-3; up to two bends. Can fit wider behavior but may turn over outside the data range depending on point placement.

• Power-fit (y = a·xᵇ): Always through origin, no critical point, curvature typically decreases with amount; excellent general choice. Slope near the origin becomes steep (theoretical), but practical error on small peaks is usually minor.

Rule of thumb: prefer the simplest curve that passes validation across your working range. Validate especially near the lower limit, where fit choices and origin handling bite hardest.

Point-to-point (segment) calibration

Connects origin to each (possibly averaged) level with straight segments and extends beyond the last point. Useful when you want a piecewise definition; weighting/origin settings don’t apply.

Troubleshooting calibration curve fitting

1. Sanity-check data: positive, sensibly spaced amounts; responses roughly proportional.

2. Are all points present/active? Expand the plot; reactivate any accidentally inactivated or frozen points, then re-update levels.

3. Peak mapping & baselines: verify the correct peak was used; re-check integration for suspect levels.

4. Curve settings: fit type, weighting, origin treatment.

5. Non-linear warnings: For quadratics, ensure the critical amount is well above your top level; for cubics, watch for turn-overs. Adjust degree/forcing or add levels.

Internal standard calibration (overview)

Add a stable, non-overlapping compound to every standard and sample. Quantify using response ratios (analyte vs. IS), plotted against amount ratios.

• Minimizes injection volume effects.

• Everything above (fits, weighting, origin logic) applies, just on ratios.

• You may define IS amounts in practical units (e.g., “1 IS unit” per mL), especially when using multiple IS compounds.

Best-practice checklist

• Cover the full working range with enough levels (and some replicates).

• Choose fit and weighting to minimize % error where it matters (often the low end).

• Validate origin behavior: ignore/extrapolate/force only after seeing the unconstrained fit’s low-level performance.

• Monitor R², average % error, CF %RSD, and residuals.

• Lock your curve once validated, and re-verify after method or hardware changes.