From primary HPV infection to carcinoma in situ: a mathematical approach of cervical intraepithelial neoplasia

TL;DR

This study develops a nonlinear PDE framework to model the progression from HPV infection to CIN/CIS on a layered cervical epithelium, coupling epithelial ($u$), HPV particles ($v$), dysplastic cells ($c$), and immune cells ($w$). The integrated reaction-diffusion-advection model incorporates basement membrane geometry via a random surface $f(x,y)$, weighted cell motility, virus–host interactions, immune influx, and boundary conditions to enable 3D numerical experiments. By varying basement membrane shape, immune flux, and viral exposure frequency, the authors show that geometry can determine dysplasia establishment, that reduced immune flux facilitates progression, and that repeated viral exposures accelerate or enable lesion development. The findings provide mechanistic insights into CIS risk factors and offer a computational platform for exploring thresholds and intervention strategies with potential clinical relevance.

Abstract

Cervical intraepithelial neoplasia (CIN) is the development of abnormal cells on the surface of the cervix, caused by a human papillomavirus (HPV) infection. Although in most of the cases it is resolved by the immune system, a small percentage of people might develop a more serious CIN which, if left untreated, can develop into cervical cancer. Cervical cancer is the fourth most common cancer in women globally, for which the World Health Organization (WHO) recently adopted the Global Strategy for cervical cancer elimination by 2030. With this research topic being more imperative than ever, in this paper, we develop a nonlinear mathematical model describing the CIN progression. The model consists of partial differential equations describing the dynamics of epithelial, dysplastic and immune cells, as well as the dynamics of viral particles. We use our model to explore numerically three important factors of dysplasia progression, namely the geometry of the cervix, the strength of the immune response and the frequency of viral exposure.

Figures (9)

• Figure 1: Cervical precancerous lesions classification based on the CIN (cervical intraepithelial neoplasia) staging. These lesions are initiated with HPV infection. HPV viral particles traverse the epithelium, infecting the cells of the basal layer.
• Figure 2: The graph of $f$ for random samples of $\ell$ and $\phi$, with (a) different values of $\beta$, and (b) the same value of $\beta$. The different colors represent different pairs of $\ell$ and $\phi$. Additionally, we have that $N=M=10$.
• Figure 3: Vertical illustration of the geometry of the basal layer.
• Figure 4: The domain, $\Omega$, of the proposed model.
• Figure 5: Dysplastic cells after 3600 days. The geometry of the basement membrane varies between each simulation, while keeping the rest of the parameters fixed. We observe that this factor alone shapes the outcome of the infection. Namely, in simulations (a) and (d-f) the dysplastic cells tend to vanish, while in (b) and (c) they are established.