pkpd.Release (version 0.1.0)

hixson_crowell_model: Hixson-Crowell Drug Release Kinetic Model

Description

Fits experimental cumulative drug release data to the Hixson-Crowell cube-root model, which describes drug release from systems where dissolution occurs with a change in surface area and particle diameter over time. The model is based on a linear regression of \((W_0^{1/3} - W_t^{1/3})\) versus time.

The function assumes that the initial drug amount (\(W_0\)) is known and that the remaining drug amount (\(W_t\)) can be calculated from cumulative percent drug remaining data. It supports optional grouping variables (e.g., formulation, batch) and optional pH-dependent analysis. The function generates publication-quality plots with experimental data points, fitted Hixson-Crowell straight lines, and annotations for the Hixson-Crowell rate constant (kHC), intercept, coefficient of determination (R^2), and the time required for 50-percent drug release (t50).

Model: $$W_0^{1/3} - W_t^{1/3} = k_{HC} * t$$

where: - \(W_0\) is the initial amount of drug - \(W_t\) is the remaining amount of drug at time \(t\) - \(k_{HC}\) is the Hixson-Crowell dissolution rate constant

The Hixson-Crowell model is applicable to dosage forms where drug release is governed by erosion or dissolution with a decreasing surface area (e.g., tablets, pellets).

Value

A list containing:

fitted_parameters

Data frame with Hixson-Crowell parameters (kHC, intercept), coefficient of determination (R^2), and t50 for each group.

data

Processed data used for model fitting and plotting.

Arguments

data

A data frame containing experimental drug release data.

time_col

Character string specifying the column name for time (minutes).

remain_col

Character string specifying the column name for cumulative percent drug remaining.

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 Hixson-Crowell lines.

annotate

Logical; if TRUE, annotates the plot with kHC, intercept, R^2, and t50 (only if <= 2 groups).

Author

Paul Angelo C. Manlapaz

References

Hixson, A. W., & Crowell, J. H. (1931) <doi:10.1021/ie50260a018> Dependence of reaction velocity upon surface and agitation. Industrial & Engineering Chemistry, 23(8), 923–931.

Examples

# Example I: Single formulation
df <- data.frame(
  time = c(0, 15, 30, 45, 60, 90, 120, 150, 180),
  remain = c(100, 88.6, 79.2, 69.2, 60.2, 42.2, 28.0, 15.2, 6.5)
)
hixson_crowell_model(
  data = df,
  time_col = "time",
  remain_col = "remain"
)

# Example II: Two formulations (grouped, not pH-dependent)
df2 <- data.frame(
  time = rep(c(0, 20, 40, 60, 80, 100, 120, 140, 160, 180), 2),
  remain = c(
    100, 90, 81, 72, 63, 54, 45, 36, 27, 18,  # Formulation A
    100, 92, 84, 76, 68, 60, 52, 44, 36, 28   # Formulation B
  ),
  formulation = rep(c("Formulation A", "Formulation B"), each = 10)
)
hixson_crowell_model(
  data = df2,
  time_col = "time",
  remain_col = "remain",
  group_col = "formulation"
)

# Example III: pH-dependent release
df_pH <- data.frame(
  time = rep(c(0, 20, 40, 60, 80, 100, 120, 140, 160, 180), 2),
  remain = c(
    100, 90, 80, 70, 60, 50, 40, 30, 20, 10,  # pH 7.4
    100, 92, 84, 76, 68, 60, 52, 44, 36, 28   # pH 4.5
  ),
  pH = rep(c(7.4, 4.5), each = 10)
)
hixson_crowell_model(
  data = df_pH,
  time_col = "time",
  remain_col = "remain",
  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),
  remain = c(
    100, 88, 75, 62, 50, 38, 28, 18, 10, 5,   # pH 4.5
    100, 90, 78, 65, 52, 40, 30, 20, 12, 6    # 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),
  remain = c(
    100, 90, 78, 66, 54, 44, 34, 25, 16, 8,   # pH 4.5
    100, 92, 80, 68, 56, 44, 34, 24, 15, 7    # 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)
)
hixson_crowell_model(
  data = df_all,
  time_col = "time",
  remain_col = "remain",
  group_col = "formulation",
  pH_col = "pH"
)