Mathematical Model Approach to Describe Tumour Response in Mice After Vaccine Administration and its Applicability to Immune-Stimulatory Cytokine-Based Strategies

Abstract

Immunotherapy is a growing therapeutic strategy in oncology based on the stimulation of innate and adaptive immune systems to induce the death of tumour cells. In this paper, we have developed a population semi-mechanistic model able to characterize the mechanisms implied in tumour growth dynamic after the administration of CyaA-E7, a vaccine able to target antigen to dendritic cells, thus triggering a potent immune response. The mathematical model developed presented the following main components: (1) tumour progression in the animals without treatment was described with a linear model, (2) vaccine effects were modelled assuming that vaccine triggers a non-instantaneous immune response inducing cell death. Delayed response was described with a series of two transit compartments, (3) a resistance effect decreasing vaccine efficiency was also incorporated through a regulator compartment dependent upon tumour size, and (4) a mixture model at the level of the elimination of the induced signal vaccine (k 2) to model tumour relapse after treatment, observed in a small percentage of animals (15.6%). The proposed model structure was successfully applied to describe antitumor effect of IL-12, suggesting its applicability to different immune-stimulatory therapies. In addition, a simulation exercise to evaluate in silico the impact on tumour size of possible combination therapies has been shown. This type of mathematical approaches may be helpful to maximize the information obtained from experiments in mice, reducing the number of animals and the cost of developing new antitumor immunotherapies.

Modeling Tumor Response after Combined Administration of Different Immune-Stimulatory Agents

“…In this article, we have expanded a previous semimechanistic model (Parra-Guillen et al, 2013) developed to characterize tumor growth dynamics after administration of an antitumor vaccine (CyaA-E7). The model was expanded to account for the pharmacodynamic effects triggered by CpG and CTX, two commonly used coadjuvants in immunotherapeutic regimens.…”

“…The model included the following main aspects: 1) linear tumor growth, 2) kinetic-pharmacodynamic (K-PD) model (Jacqmin et al, 2007) describing vaccine (VAC) kinetics and vaccine effects through two transit compartment (TRAN VAC and SVAC), being effects over Ts controlled by SVAC, 3) a regulatory compartment (REG) controlled by the tumor and able to inhibit vaccine efficacy, and 4) finally, the existence of a subpopulation of mice able to trigger only a temporal tumor response to describe the relapse observed in a small size of the studied population. Figure 2 presents the schematic and mathematical representation of the vaccine model previously developed (yellow section), including a table with the parameter estimates for both CyaA-E7 and interleukin 12 (IL-12) agents (Parra-Guillen et al, 2013).…”

“…Internal model evaluation was graphically explored by simulating 1000 datasets with the same study design characteristics as the original one (Parra-Guillen et al, 2013). Simulated tumor size time-course, percentage of BQL over time, and probability of cure at the end of the study, including the 90% confidence interval, were plotted and compared with the raw data.…”

“…Tumor size data were simulated using the same model structure developed for CyaA-E7, but with the specific set of parameters previously estimated for IL-12 immunotherapy (summarized in Fig. 2) (Parra-Guillen et al, 2013), coupled with the CTX model here developed. Simulations were graphically inspected and compared versus raw data as described in model evaluation section.…”

“…A pharmacokinetic/pharmacodynamic (PK/PD) model to describe the antitumor response triggered by single immunotherapies has been previously developed and validated in our group (Parra-Guillen et al, 2013). The aim of the present work was to expand the mathematical modeling framework developed to incorporate the pharmacodynamic effects triggered by coadjuvants in immunotherapy, capturing the key biologic mechanisms implied in a simple but meaningful way.…”