. 2024 Nov 29;25(23):12887. doi: 10.3390/ijms252312887

Table 9.

Data approximation using various mathematical models for the release of DNA adsorbed on CaPs.

Model	Equation *	Parameter	Coprecipitation	Sorption
Korsmeyer-Peppas	$\frac{M_{t}}{M_{\infty}} = K_{K P} \cdot t^{n}$	K	2.8 × 10⁻³	3 × 10⁻³
		n	0.88	0.52
		R²	0.97	0.99
Higuchi	$\frac{M_{t}}{M_{\infty}} = K_{H} \cdot t^{\frac{1}{2}}$	K	1.2 × 10⁻³	6 × 10⁻⁴
Higuchi	$\frac{M_{t}}{M_{\infty}} = K_{H} \cdot t^{\frac{1}{2}}$	R²	0.85	0.96
First order	$\ln (1 - \frac{M_{t}}{M_{\infty}}) = K_{1} \cdot t$	K	4.7 × 10⁻²	2.5 × 10⁻²
First order	$\ln (1 - \frac{M_{t}}{M_{\infty}}) = K_{1} \cdot t$	R²	0.55	0.86
Hixson-Crowell	${(1 - \frac{M_{t}}{M_{\infty}})}^{\frac{1}{3}} = 1 - K_{β} \cdot t$	K	6.8 × 10⁻⁵	3.7 × 10⁻⁵
Hixson-Crowell		R²	0.77	0.92

* Where M_t/M_∞ is a fraction of drug released at time t; K_KP is the Korsmeyer–Peppas release rate constant; n is the release exponent; K_H is the Higuchi release rate constant; K₁ is the first-order release rate constant; K_β is the Hixson–Crowell release rate constant.