Diffusion‐limited binding explains binary dose response for local arterial and tumour drug delivery

Abstract

Background Local drug delivery has transformed medicine, yet it remains unclear how drug efficacy depends on physicochemical properties and delivery kinetics. Most therapies seek to prolong release, yet, recent studies demonstrate sustained clinical benefit following local bolus endovascular delivery. Objectives The purpose of the current study was to examine the interplay between drug dose, diffusion and binding in determining tissue penetration and effect. Methods We introduce a quantitative framework that balances dose, saturable binding and diffusion and measured the specific binding parameters of drugs to target tissues. Results Model reduction techniques augmented by numerical simulations revealed that the impact of saturable binding on drug transport and retention is determined by the magnitude of a binding potential, Bp, the ratio of the binding capacity to the product of the equilibrium dissociation constant and accessible tissue volume fraction. At low Bp (<1) drugs are predominantly free and transport scales linearly with concentration. At high Bp (>40) drug transport exhibits a threshold dependence on applied surface concentration. Conclusions In this paradigm, drugs and antibodies with large Bp penetrate faster and deeper into tissues when presented at high concentrations. A threshold dependence of tissue transport on the applied surface concentration of paclitaxel and rapamycin may explain the threshold dose dependence of the in vivo biological efficacy of these drugs.

A Mathematical Model for the Release of Peptide-Binding Drugs from Affinity Hydrogels

“…In this section, we display numerical solutions to the initial boundary value problem (21). The purpose here is to illustrate the wide range of release behaviours the system is capable of exhibiting, and to numerically confirm the analytical predictions of the previous section.…”

“…An explicit finite difference scheme was used to numerically integrate (21). Forward differences were used to approximate the time derivatives, centred differences for the second order spatial derivatives, and the boundary condition on x = 0 was handled by introducing a fictitious line in the usual way.…”

“…Forward differences were used to approximate the time derivatives, centred differences for the second order spatial derivatives, and the boundary condition on x = 0 was handled by introducing a fictitious line in the usual way. The values for c T G and c T P were updated in time using (21), and the updates for the remaining quantities were then calculated using (20). The scheme was coded using the mathematical software package MATLAB.…”

“…In Figure 6, numerical solutions to (21) are displayed for η P/G = 2 and various values of r, and with K bP = 1000 in (a), and K bP = 100 in (b). In Figure 6 (a), we see as expected that a fraction (1 − r) of the drug is lost in the first few days, but that release thereafter is slow.…”

“…The results of this analysis are very briefly summarized here. For related studies, see [21] and [23]. Taking the limit K bP → ∞ in (24) with c…”