VACCINATION


Predicting Effect of Prostate Cancer Immunotherapy by Personalized Mathematical Models

Natalie Kronik,1 Yuri Kogan,1 Moran Elishmereni,1 Karin Halevi-Tobias,1 Stanimir Vuk Pavlović,2 Zvia Agur,1

1 Institute for Medical BioMathematics, Bene Ataroth, Israel;

2 College of Medicine, Mayo Clinic, Rochester, Minnesota, USA;

Background: Therapeutic vaccination against disseminated prostate cancer (PCa) is partially effective in some PCa patients. We hypothesized that the efficacy of treatment will be enhanced by individualized vaccination regimens tailored by simple mathematical models.

Methodology & Principal Findings:We developed a general mathematical model encompassing the basic interactions of a vaccine, immune system and PCa cells, and validated it by the results of a clinical trial testing an allogeneic PCa whole–cell vaccine (Figure 1).


Figure 1. Model of interactions among the cellular vaccine (V), immune system and prostate cancer cells (P). Dm, antigen-presenting dermal dendritic cells; DC, mature dendritic cells; DR, “exhausted” dendritic cells; R, regulatory/inhibitory cells; C, antigen–specific effector cells (e.g., cytotoxic T cells).

For model validation in the absence of any other pertinent marker, we used the clinically measured changes in prostate–specific antigen (PSA) levels as a correlate of tumor burden. Up to 26 PSA levels measured per patient were divided into each patient’s training set and his validation set. The training set, used for model personalization, contained the patient’s initial sequence of PSA levels; validation set, contained his subsequent PSA data points. Personalized models were simulated to predict changes in tumor burden and PSA levels and predictions were compared to the validation set. The model accurately predicted PSA levels over the entire measured period in each of 12 among the 15 vaccination–responsive patients (coefficient of determination R2=0.972 between the predicted and observed PSA values; figure 2).


Figure 2. Validation of individualized models for patients responding to vaccination. Patient–specific best–fit model parameters were derived by fitting the model to the respective pretreatment PSA values and the initial in–treatment PSA values. Subsequent PSA levels were predicted by the use of the obtained best–fit parameters. Achieving good predictive power required a different size of the training set for each patient.

The model could not account for the inconsistent changes in PSA levels in three of the 15 responsive patients at the end of treatment. Each validated personalized model was simulated under many hypothetical immunotherapy protocols to suggest alternative vaccination regimens. The personalized regimens predicted to enhance the effects of therapy differed among the patients (Figure 3).


Figure 3. Validation of individualized models for patients with non–monotonous PSA course.Best–fit model parameters for Patients 1, 9, and 10 were obtained by fitting the model to the training set (red dots). Solid lines indicate the predicted subsequent directions of the PSA level change. However, the measured PSA values indicate a drastic change in the behavior of PSA levels (blue circles).

Conclusions: Using a few initial measurements, we constructed robust patient–specific models of PCa immunotherapy, which were retrospectively validated by clinical trial results. Our results emphasize the potential value and feasibility of individualized model–suggested immunotherapy protocols. In further work we put forward a new algorithm for in-trial personalization and suggest it may have a significant impact on the structure of clinical trial and personalization of immunotherapy modalities.

The model could not account for the inconsistent changes in PSA levels in three of the 15 responsive patients at the end of treatment. Each validated personalized model was simulated under many hypothetical immunotherapy protocols to suggest alternative vaccination regimens. The personalized regimens predicted to enhance the effects of therapy differed among the patients (Figure 3).



  1. Kronik N., Kogan Y., Elishmereni M., Halevi-Tobias K., Vuk Pavlović S., Agur Z. Predicting Effect of Prostate Cancer Immunotherapy by Personalized Mathematical Models. PLoS one, 2011;6(9):e24225. Epub 2011 Sep 6.
  2. Agur, Z and Vuk Pavlović, S. Mathematical Modeling in Immunotherapy of Cancer: Personalizing Clinical Trials. J. Molecular Therapy, 20(1), 2012: 1-2.
  3. Yuri Kogan, Karin Halevi–Tobias, Moran Elishmereni, Stanimir Vuk Pavlović, and Zvia Agur. Reconsidering the Paradigm of Cancer Immunotherapy by Computationally Aided Real-Time Personalization. Cancer Res. 2012 May 1;72(9):2218-27.

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