The AAPS Journal

, Volume 15, Issue 3, pp 797–807 | Cite as

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

  • Zinnia P. Parra-Guillen
  • Pedro Berraondo
  • Emmanuel Grenier
  • Benjamin Ribba
  • Iñaki F. TroconizEmail author
Research Article


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.

Key words

cancer vaccine and mice immunotherapy mathematical modelling population approach 



ZPP-G was supported by FPU fellowship from the Spanish Ministerio de Educacion, Cultura y Deporte and a grant from INRIA. PB was supported by a Miguel Servet contract from Spanish Fondo de Investigacion Sanitaria. This work was supported by the Innovative Medicines Initiative Joint Undertaking under grant agreement no. 115156, resources of which are composed of financial contributions from the European Union’s Seventh Framework Programme (FP7/2007 –2013) and EFPIA companies’ in kind contribution. The DDMoRe project is also supported by financial contribution from Academic and SME partners. This work does not necessarily represent the view of all DDMoRe partners.

Supplementary material

12248_2013_9483_MOESM1_ESM.docx (31 kb)
ESM 1 (DOCX 31 kb)
12248_2013_9483_Fig7_ESM.jpg (121 kb)
Supplementary Figure 1

Additional individual mouse model predictions. Tumour size observations (points) and individual model predictions (solid lines) of five mice per CyaA-E7 dosing regimen are presented; 2 mm was considered as the limit of quantification (dashed line). (JPEG 121 kb)

12248_2013_9483_MOESM2_ESM.tif (1.1 mb)
High resolution image (TIFF 1143 kb)
12248_2013_9483_Fig8_ESM.jpg (2.1 mb)
Supplementary Figure 2

Visual and numerical predictive check to validate final model performance. Simulated tumour size measurements above the limit of quantification (upper panels) and percentage of data below the limit of quantification (lower panel) versus raw data (points) are plotted over time for two experiments not considered during the model building process. Grey areas in the upper panels represent the 90% prediction interval of the simulated median. Grey areas in the lower panels represent the 90% prediction interval of the simulated percentage of data below the limit of quantification. Solid and dashed black lines are the simulated and raw median respectively; 2 mm was considered as the limit of quantification (red dashed line). (JPEG 2104 kb)

12248_2013_9483_MOESM3_ESM.tif (1.2 mb)
High resolution image (TIFF 1202 kb)


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Copyright information

© American Association of Pharmaceutical Scientists 2013

Authors and Affiliations

  • Zinnia P. Parra-Guillen
    • 1
  • Pedro Berraondo
    • 2
  • Emmanuel Grenier
    • 3
  • Benjamin Ribba
    • 4
  • Iñaki F. Troconiz
    • 1
    Email author
  1. 1.Department of Pharmacy and Pharmaceutical Technology, School of PharmacyUniversity of NavarraPamplonaSpain
  2. 2.Division of Hepatology and Gene Therapy, Centre for Applied Medical ResearchUniversity of NavarraPamplonaSpain
  3. 3.INRIA Rhône-Alpes, Project-team NUMEDÉcole Normale Supérieure de LyonLyonFrance
  4. 4.INRIA Grenoble-Rhône-Alpes, Project-team NUMEDSaint-IsmierFrance

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