Modeling $\mathrm{CD4}^{+}$ T cells dynamics in HIV-infected patients receiving repeated cycles of exogenous Interleukin 7

Abstract

Combination antiretroviral therapy successfully controls viral replication in most HIV infected patients. This is normally followed by a reconstitution of the $\mathrm{CD4}^{+}$ T cells pool, but not for all patients. For these patients, an immunotherapy based on injections of Interleukin 7 (IL-7) has been recently proposed in the hope of obtaining long-term reconstitution of the T cells pool. Several questions arise as to the long-term efficiency of this treatment and the best protocol to apply. Mathematical and statistical models can help answer these questions.

We developed a model based on a system of ordinary differential equations and a statistical model of variability and measurement. We can estimate key parameters of this model using the data from the main studies for this treatment, the INSPIRE, INSPIRE 2, and INSPIRE 3 trials. In all three studies, cycles of three injections have been administered; in the last two studies, for the first time, repeated cycles of IL-7 have been administered. Repeated measures of total $\mathrm{CD4}^{+}$ T cells count in 128 patients, as well as $\mathrm{CD4}^{+}\mbox{Ki67}^{+}$ T cells count (the number of cells expressing the proliferation marker Ki67) in some of them, were available. Our aim was to estimate the possibly different effects of successive injections in a cycle, to estimate the effect of repeated cycles and to assess different protocols.

The use of dynamical models together with our complex statistical approach allow us to analyze major biological questions. We found a strong effect of IL-7 injections on the proliferation rate; however, the effect of the third injection of the cycle appears to be much weaker than the first ones. Also, despite a slightly weaker effect of repeated cycles with respect to the initial one, our simulations show the ability of this treatment of maintaining adequate $\mathrm{CD4}^{+}$ T cells count for years. We also compared different protocols, showing that cycles of two injections should be sufficient in most cases.