The nanoparticle carries its drug payload behind a polymer shell. The shell releases molecules by first-order kinetics — a good approximation of Fickian diffusion through a swollen polymer matrix — where the release rate is proportional to how much drug still remains inside:
M(t) = M₀·e^(−k·t) released fraction = 1 − e^(−k·t)
dC/dt = k·(M₀−M) − k_e·C (plasma build-up minus elimination)
The rate constant k depends on the shell chemistry and the surrounding pH. A pH-sensitive shell is built from a polymer that protonates and swells in acid — it stays nearly closed at normal blood pH (7.4) and releases quickly only once it reaches the acidic microenvironment typical of solid tumors (pH ≈ 6.5). That mismatch is the physical basis of real targeted delivery: the same particle circulates safely through healthy tissue and dumps its payload selectively where it is needed. A slow-diffusion shell releases at a low, steady rate regardless of pH — smooth and sustained but not site-selective. A fast-release shell offers little barrier at all and empties quickly in either environment.
- Shell type — sets the base release-rate constant and, for the pH-sensitive shell, how strongly pH modulates it.
- Environment pH — normal blood (7.4) vs. acidic tumor interstitium (6.5); only the pH-sensitive shell responds strongly to this.
- Blood flow speed — how fast the carrier and released molecules are swept downstream; faster flow dilutes and clears released drug sooner.
The chart compares this controlled-release curve against a conventional instant-release tablet: the tablet dumps its whole dose almost immediately, producing a sharp concentration spike (that may cross into toxicity) followed by a fast decline below the effective dose — while the nanoparticle keeps concentration inside the therapeutic window for far longer.