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

<div><p>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. <i>In silico</i> 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 <i>in-vivo</i> 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.</p></div

Summary of clinical data.

<p>Summary of clinical data.</p

Main mechanism of action of cisplatin, gemcitabine, vinorelbine and docetaxel.

<p>Main mechanism of action of cisplatin, gemcitabine, vinorelbine and docetaxel.</p

Baseline Values of Model Parameters Used in OFAT Sensitivity Analysis.

<p>Baseline Values of Model Parameters Used in OFAT Sensitivity Analysis.</p

Simulated time course of selected cancer cell populations.

<p>(A) Various tumor cell populations as a function of time in the case of free tumor growth. A homogeneous spherical tumor of 10mm diameter is considered. The values of code input parameters that regulate tumor growth kinetics are given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005093#pcbi.1005093.t005" target="_blank">Table 5</a> (Squamous Cell Carcinoma—SCC representative case). (B) Various tumor cell populations as a function of time in the case of treatment response. A homogeneous spherical tumor of 10mm diameter is considered. A cell cycle specific (gemcitabine) and a cell cycle non-specific (cisplatin) drug are administered as a three-week cycle. Gemcitabine is given on days 7, 14, 28, 35, 49, 56. Cisplatin is administered on days 7, 28 and 49. After each chemotherapeutic session a drop in the various tumor cell populations is observed, followed by tumor repopulation. The values of code input parameters are given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005093#pcbi.1005093.t005" target="_blank">Table 5</a> (Squamous Cell Carcinoma—SCC representative case). Abbreviations: DIFF: terminally DIFFerentiated tumor cell, G0: dormant, resting phase.</p

Generic cell kinetic model for tumor response to chemotherapy.

<p>(A) Transition diagram between the five main cancer cell categories. (B) Cell cycle of cancer cells with proliferative capacity, either stem or LIMP (C) Cell cycle of cancer cells with proliferative capacity that are lethally hit by chemotherapy. Cells enter a rudimentary cell cycle that leads to apoptotic death from the phase dictated by the mechanism of action of the chemotherapeutic drug. In the schema, lethally hit cells are assumed to die at the end of S phase. Parameter symbols are explained in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005093#pcbi.1005093.t004" target="_blank">Table 4</a>. Abbreviations: LIMP: LImited Mitotic Potential tumor cell (also called committed or restricted progenitor cell), DIFF: terminally DIFFerentiated tumor cell, G1: Gap 1 cell cycle phase, S: DNA synthesis phase, G2: Gap 2 phase. M: Mitosis phase, G0: dormant, resting phase.</p

PRCC results.

<p>PRCC results.</p

Scatterplots of the cell kill rate estimates vs. indicative model parameters and tumor proliferation features for the clinical cases 3 (Squamous Cell Carcinoma—SCC) and 12 (Adenocarcinoma—ADC).

<p>All model parameters are varied simultaneously. The ordinate represents the sum of cisplatin and gemcitabine cell kill rates for case #3 (panels (A)-(I)) and cisplatin and vinorelbine cell kill rates for case #12 (panels (J)-(R)). The samples have a size of 146 and 175 for the SCC (#3) and ADC (#12) cases, respectively. They originate from two Latin Hypercube Sampling runs of 2000 combinations of parameter values after excluding the ones with negative cell proliferation kinetics or cell proliferation kinetics that fall beyond the reference values for non-small cell lung cancer in general and SCC and ADC representative cases specifically (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005093#sec017" target="_blank">Results</a> section). The scatterplots are displayed for the following model parameters and proliferation features: (A) and (J) duration of cell cycle, when considered equal for both stem and LIMP cells, (B) and (K) removal rate of DIFF cells defined as the number of cells that enter the apoptotic or necrotic pathway per hour, (C) and (L) fraction of stem cells that undergo symmetric division, (D) and (M) fraction of newborn cells that enter a quiescent state following mitosis, (E) and (N) fraction of cells that re-enter cell cycle from a quiescent state, when considered equal for both stem and LIMP cells, (F) and (O) number of mitoses performed by LIMP cells before becoming terminally differentiated, (G) and (P) resistance of stem cells to chemotherapy, expressed as the ratio of the stem cell kill rate to the estimated drug cell kill rate, (H) and (Q) the proportion of living tumor cells that are in a quiescent state, (I) and (R) the proportion of living tumor cells that are terminally differentiated. Abbreviations: ADC: Adenocarcinoma, SCC: Squamous cell carcinoma, LIMP: LImited Mitotic Potential tumor cell (also called committed or restricted progenitor cell), DIFF: terminally DIFFerentiated tumor cell. G0: dormant, resting phase.</p

Results of the local sensitivity analysis.

<p>Each input parameter has been varied by ±10%, with the exception of <i>P</i>_<i>sym</i> and <i>P</i>_<i>sleep</i> that have been varied by ±5%. Following, the corresponding percentage change in the estimated sum of cisplatin and gemcitabine cell kill rates is recorded. The rest of the model parameters are kept at their baseline value (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005093#pcbi.1005093.t005" target="_blank">Table 5</a>). Two sets of baseline values have been considered (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005093#pcbi.1005093.t005" target="_blank">Table 5</a>), corresponding to a Squamous Cell Carcinoma (SCC) and an Adenocarcinoma (ADC) representative case. (A) Sensitivity measures for each input parameter defined as the % change in estimated sum of cell kill rates per +1% or -1% change in the input parameter, for ADC and SCC cases respectively. (B) Overall sensitivity score for each input parameter defined as the average of the sensitivity measures for ADC and SCC cases respectively, weighted by a normalized measure of input variability (the latter being the value range divided by the mean) (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005093#pcbi.1005093.e003" target="_blank">Eq (3)</a>). The value ranges considered are reported in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005093#pcbi.1005093.s004" target="_blank">S4 Text</a>. Parameter symbols are explained in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005093#pcbi.1005093.t004" target="_blank">Table 4</a>.</p

Model Parameters Related to Tumor Free Growth and Therapy.

<p>Model Parameters Related to Tumor Free Growth and Therapy.</p