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. 2022 Dec 1:402:115484.
Epub 2022 Aug 17.

Optimizing combination therapy in a murine model of HER2+ breast cancer

Ernesto A B F Lima  1   2 , Reid A F Wyde  1 , Anna G Sorace  3   4   5 , Thomas E Yankeelov  1   6   7   8   9   10
Affiliations

Optimizing combination therapy in a murine model of HER2+ breast cancer

Ernesto A B F Lima et al. Comput Methods Appl Mech Eng. .

Abstract

Human epidermal growth factor receptor 2 positive (HER2+) breast cancer is frequently treated with drugs that target the HER2 receptor, such as trastuzumab, in combination with chemotherapy, such as doxorubicin. However, an open problem in treatment design is to determine the therapeutic regimen that optimally combines these two treatments to yield optimal tumor control. Working with data quantifying temporal changes in tumor volume due to different trastuzumab and doxorubicin treatment protocols in a murine model of human HER2+ breast cancer, we propose a complete framework for model development, calibration, selection, and treatment optimization to find the optimal treatment protocol. Through different assumptions for the drug-tumor interactions, we propose ten different models to characterize the dynamic relationship between tumor volume and drug availability, as well as the drug-drug interaction. Using a Bayesian framework, each of these models are calibrated to the dataset and the model with the highest Bayesian information criterion weight is selected to represent the biological system. The selected model captures the inhibition of trastuzumab due to pre-treatment with doxorubicin, as well as the increase in doxorubicin efficacy due to pre-treatment with trastuzumab. We then apply optimal control theory (OCT) to this model to identify two optimal treatment protocols. In the first optimized protocol, we fix the maximum dosage for doxorubicin and trastuzumab to be the same as the maximum dose delivered experimentally, while trying to minimize tumor burden. Within this constraint, optimal control theory indicates the optimal regimen is to first deliver two doses of trastuzumab on days 35 and 36, followed by two doses of doxorubicin on days 37 and 38. This protocol predicts an additional 45% reduction in tumor burden compared to that achieved with the experimentally delivered regimen. In the second optimized protocol we fix the tumor control to be the same as that obtained experimentally, and attempt to reduce the doxorubicin dose. Within this constraint, the optimal regimen is the same as the first optimized protocol but uses only 43% of the doxorubicin dose used experimentally. This protocol predicts tumor control equivalent to that achieved experimentally. These results strongly suggest the utility of mathematical modeling and optimal control theory for identifying therapeutic regimens maximizing efficacy and minimizing toxicity.

Keywords: Chemotherapy model; Model calibration; Model selection; Optimal control theory; Tumor growth model; Uncertainty quantification.

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Conflict of interest statement

Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Figures

Fig. 1.
Fig. 1.
Model calibration and selection framework. We start with a set of possible models M. Every model Mi is calibrated using the experimental data, and the Bayesian information criterion (BIC) is calculated for each calibration. The model with the highest BIC model weight is selected, and if the average mean percent error is considered acceptable (i.e., lower than a defined threshold), the model is approved to be used in the optimal control step.
Fig. 2.
Fig. 2.
Distributions of the 3CLM0 parameters. Each scatter plot represents the correlation between two model parameters, and the top figure in each row shows the histogram of the parameter distribution. The strongest correlations are: a negative correlation between the tumor growth and carrying capacity (i.e., r and K, respectively), and a positive correlation between the trastuzumab decay rate and the death rate due by trastuzumab (i.e., λt and τt, respectively). The red line represents the median of each parameter distribution.
Fig. 3.
Fig. 3.
Temporal evolution of the experimentally measured tumor volume (black; error bars represent the standard deviation) and the 3CLM0 (magenta) in the following scenarios: (a) control (b) doxorubicin (c) trastuzumab (d) doxorubicin 24 h prior to trastuzumab (e) trastuzumab 24 h prior to doxorubicin (f) trastuzumab + doxorubicin. The mean absolute percent error is 22.77 ± 11.84%. The vertical lines indicate the day each drug was delivered; doxorubicin in blue, trastuzumab in red, and doxorubicin + trastuzumab in green.
Fig. 4.
Fig. 4.
Temporal evolution of doxorubicin (blue) and trastuzumab (red) availabilities for model 3CLM0 in the following scenarios: (a) doxorubicin (b) trastuzumab (c) doxorubicin 24 h prior to trastuzumab (d) trastuzumab 24 h prior to doxorubicin (e) trastuzumab + doxorubicin. The effects of trastuzumab delivery inhibition by doxorubicin, modeled by the parameter λdi, can be observed in (c), and for the second trastuzumab dose in (e). In these scenarios, the current doxorubicin availability blocks the increase of trastuzumab availability as in panel (c), where there is no trastuzumab availability, and in panel (e) where the effects of the second trastuzumab dose is blocked.
Fig. 5.
Fig. 5.
Temporal evolution of the 3CLM0 model using the best experimental protocol (magenta), the 3CLM0 model using the optimal computationally designed protocol with same total drug dose (blue), and the 3CLM0 model using the optimal computationally designed protocol with a 42.81% reduction in total doxorubicin dose (green). The results of the different treatment protocols are compared for (a) the tumor volume dynamics, (b) doxorubicin availability, and (c) trastuzumab availability. In panel (a), the red line indicates the tumor volume at the first day of treatment (day 35), the black line indicates a 30% reduction in tumor volume, and the orange line indicates a 50% reduction in treatment volume. The optimized protocol (blue) reaches the 30% reduction time point 0.6 days earlier than the best experimental protocol (magenta), the 50% reduction time point 2.25 days earlier, and the 100% reduction time point on day 59 (note that the best experimental protocol does not ever achieve a 100% reduction in tumor size). The green line demonstrates that the optimized treatment protocol is able to achieve the same tumor control as the best experimental protocol, but using only 42.81% of the doxorubicin dose employed in the experiment. In panel (c), the blue line overlaps with the green line, as we kept the same trastuzumab protocol. Note also how the best experimental treatment protocol yields approximately half of the trastuzumab availability as compared to the computationally optimized protocol.
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