What is the Higuchi release equation and when does it apply?

• A. Mt/M∞ = kH t
• B. Mt/M∞ = kH t^2
• C. Mt/M∞ = kH√t
• D. Mt/M∞ = kH / t

Answer: (C)

The key idea is diffusion-controlled release from a solid matrix, which gives a square-root–time relationship. The Higuchi model states that the fraction released, Mt/M∞, equals kH times the square root of time: Mt/M∞ = kH √t. This form arises when the drug is uniformly dispersed in a non-swelling, non-eroding matrix, release is driven mainly by Fickian diffusion, the external medium is a sink, and the surface area stays essentially constant (planar geometry so diffusion is effectively one-dimensional). As time passes, the diffusion distance grows, the concentration gradient driving release decreases, and the rate slows in proportion to t^−1/2, which is captured by the square-root time dependence. For other geometries or release mechanisms, the exact constant changes, but the square-root form is the hallmark of the Higuchi model. The other forms (linear in time, quadratic in time, or inverse time) do not reflect diffusion-controlled release from a solid matrix.