Biodegradable Implant Drug Elution

Implant & Drug Parameters

Diffusion coefficient D₀ 0.030

Hydrolysis rate k_h (day⁻¹) 0.060

Erosion–diffusivity coupling β 3.0

Drug loading (particles) 900

Live State

Cumulative release

0.0%

Simulated time

0.0 d

D_eff (matrix)

0.030

Polymer M_w remaining

100.0%

Cumulative release fraction vs. time

How it works

Drug trapped in a biodegradable polymer matrix (e.g. PLGA) escapes by two coupled processes: random-walk (Fickian) diffusion through the polymer, and a slow rise in that diffusivity as the polymer backbone hydrolyses and the matrix becomes more porous.

Diffusion step (per axis, each Δt):  Δx = √(2·D_eff·Δt) · N(0,1)

Bulk hydrolysis (first-order, Siepmann-type):
  M_w(t) = M_w0 · exp(−k_h·t)

Erosion-coupled diffusivity:
  D_eff(t) = D_0 · exp(β·(1 − M_w(t)/M_w0))

A drug particle is "released" once its random walk carries it
past the implant's outer radius R.

D₀ — the intrinsic diffusion coefficient through the intact (undegraded) polymer. Higher D₀ gives faster early (burst-phase) release.
k_h — the hydrolysis rate constant governing how fast the polymer's average molecular weight M_w decays. Faster hydrolysis opens pores sooner.
β — how strongly diffusivity ramps up as the polymer degrades. At β = 0 release is pure diffusion-controlled (roughly √t, Higuchi-like); larger β adds an erosion-triggered acceleration phase, the classic biphasic (burst → lag → erosion-driven) PLGA release profile.
Drug loading — number of drug particles seeded uniformly through the implant; only changes sampling resolution of the release curve, not the underlying kinetics.

This is the qualitative mechanism behind clinically used biodegradable drug-eluting implants and microspheres (PLGA/PLA depots, drug-eluting sutures, some coronary stent coatings): the release rate is not constant, because the material carrying the drug is itself dissolving.

Drug particle (in matrix) Released (eluted)

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