In Silico Oncology: Quantification of the In Vivo Antitumor Efficacy of Cisplatin-Based Doublet Therapy in Non-Small Cell Lung Cancer (NSCLC) through a Multiscale Mechanistic Model

The 5-year survival of non-small cell lung cancer patients can be as low as 1% in advanced stages. For patients with resectable disease, the successful choice of preoperative chemotherapy is critical to eliminate micrometastasis and improve operability. In silico experimentations can suggest the optimal treatment protocol for each patient based on their own multiscale data. A determinant for reliable predictions is the a priori estimation of the drugs’ cytotoxic efficacy on cancer cells for a given treatment. In the present work a mechanistic model of cancer response to treatment is applied for the estimation of a plausible value range of the cell killing efficacy of various cisplatin-based doublet regimens. Among others, the model incorporates the cancer related mechanism of uncontrolled proliferation, population heterogeneity, hypoxia and treatment resistance. The methodology is based on the provision of tumor volumetric data at two time points, before and after or during treatment. It takes into account the effect of tumor microenvironment and cell repopulation on treatment outcome. A thorough sensitivity analysis based on one-factor-at-a-time and latin hypercube sampling/partial rank correlation coefficient approaches has established the volume growth rate and the growth fraction at diagnosis as key features for more accurate estimates. The methodology is applied on the retrospective data of thirteen patients with non-small cell lung cancer who received cisplatin in combination with gemcitabine, vinorelbine or docetaxel in the neoadjuvant context. The selection of model input values has been guided by a comprehensive literature survey on cancer-specific proliferation kinetics. The latin hypercube sampling has been recruited to compensate for patient-specific uncertainties. Concluding, the present work provides a quantitative framework for the estimation of the in-vivo cell-killing ability of various chemotherapies. Correlation studies of such estimates with the molecular profile of patients could serve as a basis for reliable personalized predictions.


Method
The range sensitivity measures (SM) defined here are similar to the local sensitivity measures of the main manuscript; however the inputs are now varied over the anticipated value range [1,2], instead of assuming a small perturbation around the baseline values. Each input parameter takes its minimum and maximum value and the corresponding change in the calculated CKR, expressed as a percentage of the reference value, is recorded. The rest of the model parameters are kept at their baseline values. All percentage changes in the output are then expressed in relation to ±1% variation of the input, by dividing with the percentage change of the input, according to the formulas: where pi,base: the baseline value of the i-th parameter, pi,max: the maximum value of the i-th parameter, pi,min: the minimum value of the i-th parameter, CKRbase: the calculated CKR with all parameters set at their baseline values, CKRmax: the calculated CKR with the i-th parameter, only, set at its maximum value, CKRmin: the calculated CKR with the i-th parameter, only, set at its minimum value. The value range of input parameters (Table A) has been derived after taking into consideration the literature (Table 4 of main manuscript), while certain cell proliferation constraints should be satisfied (e.g. positive growth rate, volume doubling time higher than 26 days, percentage of stem cells not exceeding 1%). It should be noted that between the adenocarcinoma (ADC) and squamous cell carcinoma (SCC) different value ranges for some of the parameters are observed (Table A). These boundaries have been derived after applying the aforementioned constraints, and their values depend on the baseline values of the remaining model parameters [3, S2 Text].

Results
The range sensitivity measures consider a larger increment compared with their local counterparts and, therefore, are expected to give a different value for parameters having a nonlinear effect on the output. In our case, a small deviation from linearity exists for the majority of the input parameters (Fig 3 of manuscript). As a result, a very small divergence between the values of the local and range sensitivity measures is noted (Table B). Looking at the overall sensitivity (two last columns of Table B), the most remarkable differences are observed for the following parameters: -TC, TC,stem, TC,LIMP: A considerable deviation between the results of the local and the range methods is observed for the SCC case, with the latter method indicating a higher overall sensitivity. For the ADC case a noteworthy deviation exists only when the cell cycle duration of both stem and LIMP cells are varied at once, i.e. for TC. -RADiff: The range method gives a higher overall sensitivity for the ADC case. However a low sensitivity is still indicated by both methods. -NLIMP: The range method gives a slightly higher overall sensitivity especially for the SCC case. However, a low sensitivity is still indicated by both methods. -PG0toG1, PG0toG1,stem: The range method gives a fairly lower overall sensitivity especially for the ADC case. However, a relatively high sensitivity is indicated by all methods.
Both methods identify the same parameters having a trivial effect on output (overall sensitivity measure <0.1% in Table C). The only noteworthy deviation concerns the parameter RADiff, as stated above. The local method ranks the parameter as non-sensitive for both the ADC and SCC cases, whereas the range method indicates a low sensitivity for ADC only (Table B).
For the rest of the parameters, having a low to high impact on output (overall sensitivity measure >0.1% in Table C), the local method results almost in the same ranking as the range one. Both methods identify the same parameters as the two most sensitive. Differences observed in the overall ranking order are due to the underestimation of the sensitivity for TC compared to PG0toG1 and PG0toG1,stem by the local method, resulting in a lower rank in respect to the range method.
In summary, the sensitivity results of the local sensitivity measures are rather consistent with the range ones, even though the latter method encompasses the effect of non-linearity.