Takeru Higuchi
= Takeru Higuchi
{c}
= T. Higuchi
{c}
{synonym}
\b[Takeru Higuchi], credited as \b[T. Higuchi] in his 1963 paper, developed mathematical descriptions of <diffusion-controlled drug release> from solid matrices. The University of Kansas archive holds that exact paper among his personal papers, establishing the connection between the initial-only byline and the full name.<Takeru Higuchi papers in the University of Kansas archives>[Personal papers of Takeru Higuchi, PP359, Box10, Folder13; exact 1963 item title]{ref}
\Image[https://www.kansashistory.gov/real_people/graphics/higuchi_takeru.jpg]
{title=Takeru Higuchi, portrait identified by the Kansas Historical Society}
{description=External portrait linked from the Kansas Historical Society's named Kansapedia biography.}
The paper distinguished a uniform matrix serving as the diffusional medium from a granular matrix penetrated by a solvent. It considered planar and spherical geometries, rather than treating all sustained release as a single first-order process.<Mechanism of Sustained-Action Medication. Theoretical Analysis of Rate of Release of Solid Drugs Dispersed in Solid Matrices by T. Higuchi>[1963, publisher byline, affiliation and Abstract, pp.1145–1149]{ref} The resulting models connect formulation geometry and material properties with a measurable <drug release rate>.
A simplified planar derivation illustrates the <Higuchi equation>. Assume a stationary matrix with constant <diffusion coefficient> $D$, excess undissolved <drug>, a <perfect sink condition in drug release> at its exposed face, and a slowly moving depletion boundary at depth $h(t)$. Approximate the dissolved-drug <concentration> as linear from zero at the exposed face to its <solubility> $C_s$ at that boundary. If initial total loading per unit volume is $C_0$, the amount released per exposed area is
$$
Q=(C_0-C_s/2)h,
$$
because the depleted layer retains a triangular dissolved-drug profile. The outward <mass flux> is approximately $DC_s/h$, so mass conservation gives
$$
(C_0-C_s/2)\frac{\mathrm dh}{\mathrm dt}=\frac{DC_s}{h},
\qquad Q^2=DC_s(2C_0-C_s)t.
$$
Thus the cumulative released amount is proportional to $\sqrt t$ in this model, whereas its derivative decreases as $t^{-1/2}$. The high-loading approximation $C_0\gg C_s$ makes the slowly moving boundary assumption more plausible; the result is not a general solution for an arbitrary dissolving or swelling material.
For an original illustration, let $Q=k_H\sqrt t$ with $k_H=2\,\mathrm{mg\,cm^{-2}\,h^{-1/2}}$. The cumulative release is $2\,\mathrm{mg\,cm^{-2}}$ at one hour and $4\,\mathrm{mg\,cm^{-2}}$ at four hours, but the instantaneous rates per area are respectively $1$ and $0.5\,\mathrm{mg\,cm^{-2}\,h^{-1}}$. These are chosen model values. They show why sustained release need not be constant-rate release. Finite thickness, depletion of the solid phase, changing <solubility> or external transport resistance can end this regime. Measuring release tests the model's transport assumptions; a square-root fit alone does not uniquely identify them.