# Dissolution Profile Fitting

> Dissolution profile fitting in Pharmacy: Higuchi, Korsmeyer-Peppas n exponent, Weibull, f2 similarity factor, sink conditions and IVIVC levels.

- Canonical URL: https://prepelephant.com/topics/allied/pharmacy/dissolution-profile-fitting
- Exam / course: Allied Health · Subject: Pharmacy
- Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team
- First published: 2026-10-02
- Last updated: 2026-10-02
- How to cite: "Dissolution Profile Fitting", PrepElephant, https://prepelephant.com/topics/allied/pharmacy/dissolution-profile-fitting

## Direct answer

Dissolution profile fitting turns percent-dissolved-time curves into mechanism and comparability judgements. Mechanistic models include zero-order (amount linear in time), first-order (log of undissolved fraction linear in time), Higuchi's square-root law Q = kH·t^0.5 for diffusion from an inert matrix, Korsmeyer-Peppas Mt/M∞ = k·tⁿ whose exponent classifies release (cylinders: n up to 0.45 Fickian, 0.45-0.89 anomalous transport mixing diffusion with polymer relaxation, 0.89 and above near zero-order case-II), Hixson-Crowell's cube-root law for dissolving particles, and the empirical Weibull with shape parameter beta describing exponential, sigmoid or parabolic curves. Comparability is judged model-independently by the similarity factor f2 = 50·log{[1 + (1/n)Σ(R − T)²]^−0.5 × 100}, where 50-100 means similar (difference factor f1 within 0-15); by convention f2 is unnecessary when both products dissolve 85 per cent or more within 15 minutes. All rests on sink conditions — medium volume at least three times saturation — and at least 12 units per profile.

## What you must remember

- **Model equations:** zero-order Qt = Q0 + k0t; first-order log(Q∞ − Qt) versus t linear; Higuchi Q = kH√t; Korsmeyer-Peppas Mt/M∞ = k·tⁿ; Hixson-Crowell ∛W0 − ∛Wt = kt; Weibull F = 1 − exp[−(t/α)^β].
- **Korsmeyer thresholds (cylinders):** n ≤ 0.45 Fickian; 0.45-0.89 anomalous (diffusion plus chain relaxation); n ≥ 0.89 case-II, near zero-order — thresholds shift slightly for slabs and spheres.
- **Fitting window:** the Korsmeyer log-log plot uses only the early portion, conventionally Mt/M∞ below 0.6.
- **f2 arithmetic:** similarity factor 50-100 = similar; difference factor f1 between 0 and 15; a drop of a few points in f2 signals meaningful formulation change since f2 is logarithmic in squared differences.
- **The 85-per-cent rule:** when both products reach 85 per cent within 15 minutes, profiles are similar without f2 computation.
- **Sink condition:** medium dissolves at least three times the drug amount present (C well below Cs), otherwise dissolution is solubility-limited and meaningless as a formulation test.
- **Weibull beta reading:** β = 1 exponential, above 1 sigmoid with lag, below 1 initial-fast parabolic — descriptive power without mechanism.
- **Application map:** BCS biowaivers (Class I needs 85 per cent in 30 minutes), SUPAC-type post-approval change testing, and IVIVC levels A (point-to-point), B (statistical moments), C (single-point parameter).

## Choosing a model for a modified-release matrix

A hydroxypropyl methylcellulose matrix tablet gives 30, 55, 72 and 84 per cent at 1, 4, 8 and 12 hours. Plot against the square root of time and the points fall on a line — Higuchi behaviour, the signature of a diffusion-controlled matrix where drug percolates through a gel layer that thickens as t^0.5. Refine with Korsmeyer-Peppas using only early points below 0.6 fraction released: the log-log slope comes out near 0.6, anomalous transport, meaning diffusion and polymer relaxation both carry release — telling the formulator that raising HPMC viscosity or grade will slow release through both channels. A Hixson-Crowell fit instead would mark erosion-led release.

Now the comparability question: a proposed site change shifts the early points, 22 versus 30 per cent at 1 hour, converging later. Compute f2 across matched time points: the squared differences sum modestly, f2 lands around 55 — inside 50-100, similar. But if the curves cross, one faster early and slower late, f2 can read deceptively; that is when the Weibull fit earns its keep, comparing α (scale, the time to 63.2 per cent) and β (shape) separately to expose the crossing. And the ultimate purpose surfaces in IVIVC: with a level A correlation, dissolution becomes a surrogate for bioavailability, and the laboratory beaker inherits the authority of a clinical study — the reason regulators scrutinise the methods, media and sink discipline behind every fitted curve.

## Where students slip

The f1/f2 pair is remembered backwards: f2 is the similarity factor (higher is more similar, 50-100), f1 the difference factor (0-15) — writing "f2 below 15" is an instant marker error. Second, the Korsmeyer thresholds are quoted for cylinders but applied to any shape; slabs shift the Fickian boundary to 0.5 and spheres to 0.43, and stating the geometry alongside the number is what distinction answers do. Third, fitting the entire curve with Korsmeyer-Peppas: the model holds only below 0.6 Mt/M∞, and late points bend the log-log line meaninglessly. Fourth, model choice by best correlation coefficient alone — a Weibull will empirically fit almost anything, so pair statistical fit with mechanism (matrix diffusion, erosion, osmosis). Finally, forgetting sink conditions invalidates the entire discussion: a saturated medium measures solubility, not the dosage form.

## Frequently asked questions

### What does the Korsmeyer-Peppas exponent n indicate?

For cylindrical matrices, n ≤ 0.45 means Fickian diffusion, 0.45-0.89 anomalous transport combining diffusion with polymer relaxation, and n near or above 0.89 near zero-order case-II release.

### How is the similarity factor f2 calculated and interpreted?

f2 = 50·log{[1 + (1/n)Σ(R − T)²]^−0.5 × 100}; values 50-100 declare similarity, computed over matched points from at least 12 units.

### When is f2 calculation unnecessary?

When both formulations dissolve 85 per cent or more within 15 minutes, regulatory convention treats them as similar without modelling — very rapid dissolution makes comparison moot.

### What is the Higuchi model and its assumption?

Q = kH·t^0.5 describes Fickian diffusion from an inert, porous matrix, assuming little dimensional change and constant diffusivity.

### What does the Weibull shape parameter beta reveal?

β = 1 exponential, above 1 sigmoid with lag, below 1 fast-initial parabolic — descriptive flexibility where mechanism is unclear.