# Korsmeyer-Peppas Drug Release Kinetic Model Fits experimental cumulative drug release data to the Korsmeyer-Peppas model using log10-transformed fraction released vs. log10-transformed time. The function automatically normalizes cumulative percent drug release to fraction (0-1) by default and removes t = 0. In addition, the function supports optional grouping variables (e.g., formulation, batch) and optional pH-dependent analysis. It generates publication-quality plots with experimental curves, fitted Korsmeyer-Peppas straight lines, mechanism table, and annotations for Korsmeyer-Peppas release constant (kKP), release exponent (n), intercept, coefficient of determination (R^2), and the time required for 50-percent drug release (t50). Users can toggle 'normalize = TRUE/FALSE' to use fraction (0-1) or raw percent drug release. Model: log10(Mt/MInf) = log10(k) + n * log10(t) The release exponent, n, indicates the drug release mechanism: - n = 0.5 : Fickian diffusion - 0.5 < n < 1 : Non-Fickian (anomalous) diffusion - n = 1 : Case II transport (zero-order release) - n > 1 : Super Case II transport ## Arguments - `data`: A data frame containing experimental cumulative percent drug release. - `time_col`: Character string specifying the column name for time (minutes). - `release_col`: Character string specifying the column name for cumulative percent drug release. - `group_col`: Optional character string specifying a grouping variable (e.g., formulation, batch). - `pH_col`: Optional character string specifying a column containing pH values. - `plot`: Logical; if TRUE, generates a plot with fitted Korsmeyer-Peppas lines. - `annotate`: Logical; if TRUE, annotates the plot with kKP, n, intercept, R^2, and t50 (only if <= 2 groups). - `normalize`: Logical; if TRUE (default), normalizes cumulative percent release to fraction (0-1). If FALSE, retains original percent values. ## Returns A list containing: - **`fitted_parameters`**: Data frame with kKP, n, intercept, R^2, and t50 for each group. - **`data`**: Processed data used for fitting and plotting. ## Examples ```r # Example I: Single formulation df1 <- data.frame( time = c(0, 15, 30, 45, 60, 90, 120, 150, 180), release = c(0, 11.4, 20.8, 30.8, 39.8, 57.8, 72, 84.8, 93.5) ) korsmeyer_peppas_model( data = df1, time_col = "time", release_col = "release", normalize = TRUE # default ) # Example II: Two formulations (grouped, not pH-dependent) df2 <- data.frame( time = rep(c(0, 30, 60, 90, 120, 150), 2), release = c( 0, 18, 35, 55, 72, 88, # Formulation A 0, 12, 26, 40, 58, 70 # Formulation B ), formulation = rep(c("Formulation A", "Formulation B"), each = 6) ) korsmeyer_peppas_model( data = df2, time_col = "time", release_col = "release", group_col = "formulation" ) # Example III: pH-dependent release df_pH <- data.frame( time = rep(c(0, 60, 120, 180), 2), release = c(0, 40, 75, 95, 0, 30, 60, 80), pH = rep(c(7.4, 4.5), each = 4) ) korsmeyer_peppas_model( data = df_pH, time_col = "time", release_col = "release", pH_col = "pH" ) # Example IV: Two formulations under two pH conditions df1 <- data.frame( time = rep(c(0, 20, 40, 60, 80, 100, 120, 140, 160, 180), 2), release = c( 0, 12, 25, 38, 50, 62, 73, 82, 89, 95, # pH 4.5 0, 15, 30, 45, 59, 70, 79, 86, 91, 97 # pH 7.6 ), pH = rep(c(4.5, 7.6), each = 10) ) df2 <- data.frame( time = rep(c(0, 15, 30, 45, 60, 75, 90, 105, 120, 135), 2), release = c( 0, 10, 22, 34, 46, 57, 67, 76, 84, 91, # pH 4.5 0, 13, 27, 41, 55, 67, 77, 85, 92, 98 # pH 7.6 ), pH = rep(c(4.5, 7.6), each = 10) ) df_all <- rbind( cbind(formulation = "Dataset 1", df1), cbind(formulation = "Dataset 2", df2) ) korsmeyer_peppas_model( data = df_all, time_col = "time", release_col = "release", group_col = "formulation", pH_col = "pH" ) ``` ## References Korsmeyer, R. W., Gurny, R., Doelker, E., Buri, P., & Peppas, N. A. (1983) Mechanisms of solute release from porous hydrophilic polymers. International Journal of Pharmaceutics, 15(1), 25–35. ## Author(s) Paul Angelo C. Manlapaz

korsmeyer_peppas_model function