Transport theory for HIV diffusion through in vivo distributions of topical microbicide gels

Abstract

Topical microbicide products are being developed for the prevention of sexually transmitted infections. These include vaginally-applied gels that deliver anti-HIV molecules. Gels may also provide partial barriers that slow virion diffusion from semen to vulnerable epithelium, increasing the time during which anti-HIV molecules can act. To explore the barrier function of microbicide gels, we developed a deterministic mathematical model for HIV diffusion through realistic gel distributions. We applied the model to experimental data for in vivo coating distributions of two vaginal gels in women. Time required for a threshold number of virions to reach the tissue surface was used as a metric for comparing different scenarios. Results delineated how time to threshold increased with increasing gel layer thickness and with decreasing diffusion coefficient. We note that for gel layers with average thickness > approximately 100 microm, the fractional area coated, rather than the gel layer thickness, was the primary determinant of time to threshold. For gel layers < approximately 100 microm, time to threshold was brief, regardless of fractional area coated. Application of the model to vaginal coating data showed little difference in time to threshold between the two gels tested. However, the protocol after gel application (i.e., with or without simulated coitus) had a much more significant effect. This study suggests that gel distribution in layers of thickness >100 microm and fractional area coated >0.8 is critical in determining the ability of the gel to serve as a barrier to HIV diffusion.

Figure 1

Schematic of female reproductive tract showing how microbicide gel and semen may be deployed after coitus. (Inset) Idealized scenario for mathematical modeling of a semen layer on top of a microbicide gel layer.

Figure 2

Schematic of mathematical model of HIV migration from semen layer, through microbicide gel layer, into tissue compartment.

Figure 3

Schematic showing how model is applied to in vivo deployment data. Thickness data taken from in vivo experiments are discretized into 12 bins, approximated by constant thickness. The fractional areas coated by each of these approximated thicknesses were also derived from experimental data. These, with the parameters defined in Table 1, were used to calculate the time required to reach the threshold number of virions in the tissue compartment, t_threshold.

Figure 4

Trade-offs between gel layer thickness and area coated when the volume of gel is conserved, such that $h_{\text{gel}}=V_{\text{gel}}/\varphi A_{\text{vagina}}$. As the fractional area coated increases, time to threshold increases.

Figure 5

Contour plot showing values of threshold time for different gel thicknesses and fractional areas coated. Note that fractional area coated is the more important factor for all but the thinnest gel layers.

Figure 6

Resulting threshold times for application of the mathematical model to experimental data obtained from deployment of vaginal gels in women. The numbers “1” and “2” represent data from two independent experiments for each gel/protocol. K, KY jelly; R, Replens; +, with simulated coitus; −, without simulated coitus. Three levels of viral hindrance were input (D_gel/D_semen = 0.1, 0.5, and 1).