Malignant features of head and neck squamous cell carcinoma (HNSCC) may be derived from the presence of stem-like cells that are characterized by uniquely high tumorigenic potential. These cancer stem cells (CSC) function as putative drivers of tumor initiation, therapeutic evasion, metastasis, and recurrence. Although they are an appealing conceptual target, CSC-directed cancer therapies remain scarce. One promising CSC target is the IL6 pathway, which is strongly correlated with poor patient survival. In this study we created and validated a multiscale mathematical model to investigate the impact of cross-talk between tumor cell- and endothelial cell (EC)-secreted IL6 on HNSCC growth and the CSC fraction. We then predicted and analyzed the responses of HNSCC to tocilizumab (TCZ) and cisplatin combination therapy. The model was validated with in vivo experiments involving human ECs coimplanted with HNSCC cell line xenografts. Without artificial tuning to the laboratory data, the model showed excellent predictive agreement with the decrease in tumor volumes observed in TCZ-treated mice, as well as a decrease in the CSC fraction. This computational platform provides a framework for preclinical cisplatin and TCZ dose and frequency evaluation to be tested in future clinical studies.

Significance:

A mathematical model is used to rapidly evaluate dosing strategies for IL6 pathway modulation. These results may lead to nonintuitive dosing or timing treatment schedules to optimize synergism between drugs.

A critical need exists to decrease the number of negative clinical trials when evaluating new therapeutic strategies across the majority of cancer subtypes. Head and neck squamous cell carcinoma (HNSCC) has experienced slow therapeutic development with only a few FDA-approved drugs in the last 15 years. One successful strategy to improve delivery of therapeutic agents is using biologically-driven mathematical modeling frameworks. In this study we use a multiscale mathematical model of ordinary differential equations (ODE) that operates at the intracellular, molecular, and tissue levels to investigate the impacts of the cross-talk between tumor cells (TC) and endothelial cell (EC) secreted molecules during tumor growth. To study this model we have carefully designed in vivo experiments. We then predict and analyze the responses of HNSCC cells to combination therapy involving tocilizumab (an anti-IL6R antibody) and cisplatin. This computational platform provides a preclinical framework for cisplatin and tocilizumab dose and frequency evaluation to be tested in future clinical studies.

Head and neck cancer is the sixth most common type worldwide accounts for more than 600,000 new cases. Recurrence rates approach 50% and drug resistance remains a significant treatment challenge. The cancer stem cell (CSC) hypothesis posits that a minor fraction of cells within each HNSCC tumor, so-called CSCs, are responsible for tumor initiation, metastasis, resistance, and recurrence. CSCs do not obey the highly regulated processes of normal cell division and death, and can therefore mediate tumor initiation (1). According to the CSC hypothesis, tumors found in adult tissues arise from CSCs, exhibit the ability to self-renew, and give rise to differentiated carcinoma tissue cells (1–4). In addition, this hypothesis states that CSCs make up an often-argued minor subpopulation of cells and the bulk of the tumor tissue is composed of rapidly proliferating cells that lack longevity and have only limited long-term expansion. These, so-called, transit-amplifying cells do not contribute to tumor initiation (5–7). Heterogeneous populations of cancer cells composed of both CSCs and non-CSCs have also been identified in head and neck cancer (2).

Cisplatin is the most common chemotherapeutic agent for the treatment of HNSCC. It is proposed that CSCs evade cisplatin therapy (3, 8). Preclinical studies on the effects of cisplatin therapy on HNSCC TCs have shown that treatment with cisplatin enhances the fraction of CSCs in HNSCC and it has been shown that the combination of cisplatin with the high expression of IL6 in tumor niche leads to a dramatic increase in the fraction of CSCs (3). Furthermore, it has been reported that IL6 has roles in activation of key signaling pathways involved in the regulation of CSCs' self-renewal and survival (2, 9) and that IL6 also contributes to cisplatin-induced stemness (3). In addition, it has been shown that HNSCC CSCs reside in perivascular niches and depend on cross-talk with tumor-associated ECs for their survival and growth (2, 10). All together, these facts suggest that a combination therapy involving a platinum-based drug and IL6R inhibitor might be beneficial for improving the treatment for HNSCC tumors. Here we study the effects of combination therapy on head and neck tumors with tocilizumab (TCZ), a humanized anti-IL6R antibody, and cisplatin. TCZ inhibits both soluble and membrane-bound IL6R to prevent IL6 pathway activation.

Mathematical modeling is a useful framework to study cancer progression because they can integrate biological parameters and make predictions across different time and/or spatial scales. Mathematical models provide a tool to facilitate preclinical evaluation of efficacy, which cannot be easily understood by using conventional wet-lab experiments alone (11–13). Here we design a model to investigate the role of EC-secreted IL6 on bidirectional communications (i.e., cross-talk) between ECs and TCs that enhances key aspects of tumorigenesis. First, we propose a pretreatment model, which describes the cross-talk between ECs and TCs (EC–TC pretreatment model). Second, we extend the pretreatment model to include both single and combination therapy of HNSCC tumors. These models are used to describe tumor angiogenesis, vascular tumor growth, and response to treatment based on a mouse model described in ref. 14. To the authors' knowledge, this EC–TC cross-talk model is the first model of its kind. This model goes across the scales from intracellular signaling level to tissue level while incorporating the CSC hypothesis and the impacts of microenvironmental molecular factors (IL6, Bcl2, VEGF, and oxygen) on CSC-mediated tumor growth dynamics. This is a fully multiscale approach where the fractional occupancies of IL6R, VEGF receptors, VEGFR1 and VEGFR2, connect the cellular level (receptor-ligand binding) to both the tissue level (TC and EC growth) and the intracellular level (prosurvival protein, Bcl2 upregulation). Finally, we use this model to evaluate temporal treatment variations to propose nonintuitive clinical combinations. This approach could form the basis of an integrated preclinical evaluation program to optimize the effect these agents based on administration schedule.

EC–TC scaffold models: mouse treatment with antineoplastic therapies

To understand the therapeutic potential of targeting IL6 signaling in HNSCC along with chemotherapy, we use cell lines to conduct a series of combination therapy experiments with TCZ and cisplatin. Cell lines used (UM-SCC-1 and UM-SCC-22B) were kindly provided by Dr. Thomas Carey. The cell lines were genetically profiled and authenticated using STR profiling. Their origin and confirmation of identity is described in ref. 15. In two separate experiments designed specifically for this modeling study, 100,000 unsorted UM-SCC-1 and 100,000 UM-SCC-22B cell lines were seeded along with 900,000 ECs in biodegradable scaffolds and implanted bilaterally in SCID mice. The cells are negative for Mycoplasma, last tested in our lab in July 2018 using a Mycoplasma Detection Kit (Invitrogen). When tumors reached approximately 150 mm3, the mice were assigned into four groups: (i) treated with 5 mg/kg cisplatin combined with 5 mg/kg TCZ; (ii) treated with 5 mg/kg cisplatin; (iii) treated with 5 mg/kg TCZ and (iv) control. Cisplatin was administered weekly for 3 weeks and the tocilizumab was administered weekly for 9 weeks via i.p. injections. Treatment started on day 23 or 28 for the UM-SCC-1 cohort and on day 36 or 42 for the UM-SCC-22B cohort based on the tumor sizes at the treatment starting days. The tumor sizes were calculated as mm3 from length and width measurements via (long axis × short axis2)/2 and recorded over time (Fig. 1; Supplementary Fig. S1). Mice were euthanized and tumors were surgically retrieved according to our Institutional Animal Care and Use Committee–approved protocol. The protocols for animal care and human subject studies was reviewed and approved by the appropriate University of Michigan committees and institutional review boards.

Figure 1.

Effects of TCZ and/or cisplatin on tumor growth in the preclinical experimental setup of HNSCC model. HNSCC scaffold models treated with cisplatin and TCZ. The graphs show tumor volumes over time until the last day of study. Treatment starts at either day 23 or 28 for UM-SCC-1 cohort (A) or at either day 36 or 42 for UM-SCC-22B cohort (B).

Figure 1.

Effects of TCZ and/or cisplatin on tumor growth in the preclinical experimental setup of HNSCC model. HNSCC scaffold models treated with cisplatin and TCZ. The graphs show tumor volumes over time until the last day of study. Treatment starts at either day 23 or 28 for UM-SCC-1 cohort (A) or at either day 36 or 42 for UM-SCC-22B cohort (B).

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Furthermore, to determine whether significant differences exist between tumor growth trajectories in different treatment groups, regression modeling is performed using mixed effect linear regression [in R (3.5.1) using the NLME package] to account for repeated measures on each tumor. The tumor volume relative to implantation is log-transformed to assume exponential growth. Model fixed effects include time, cisplatin treatment by time, and tocilizumab treatment by time. Random effects include mouse and tumor within mouse. We assume an autoregressive correlation structure where more proximate time values have a higher degree of correlation (Supplementary Table S1).

Mathematical model for cross-talk between EC and TCs

On the basis of in vivo experimental model above, we develop a mathematical modeling framework for investigating IL6-mediated, CSC-driven tumor growth, and targeted treatment with TCZ alone and/or in combination with cisplatin. Our model includes the effects of both human TC and EC-secreted IL6 signaling on TC survival and proliferation, and also captures the effects of IL6 on the probability of self-renewal for CSCs. Specifically, it describes the temporal changes in CSC, progenitor cell and differentiated cell density, TC, and/or EC-secreted IL6 concentration, EC density, VEGF concentration, and Bcl2 mRNA expressed by both TC and ECs. The VEGF, Bcl2, and EC-TC cross-talk modules are the result of over a decade of modeling-experimental collaboration to isolate the parameters and calibrate those three subsystems. The CSC and IL6 subsystems were developed and analyzed as separate modules in ref. 16. In this paper, we integrate these subsystems into a larger framework for the first time. We also develop and incorporate novel modules describing the mechanism of action of TCZ and cisplatin treatment optimization subsystems. Figure 2A is a schematic diagram illustrating the proposed mechanism behind the pretreatment EC–TC cross-talk model. Under hypoxia TCs secrete VEGF. VEGF not only enhances EC proliferation and survival by upregulating Bcl2 expression through the CXCL8 pathway mediated by VEGFR2 dimerization, but also mediates TC proliferation and survival via pathways regulated by VEGFR1 (9, 17). The enhanced proliferation rate of ECs results in further secretion of IL6 and that leads to survival and proliferation of TCs, particularly CSCs. This bidirectional communication between ECs and TCs is centrally regulated by VEGF, which in turn, maintains this feedback loop (9, 17). We include a pretreatment model with the therapeutic administration of TCZ and cisplatin, to study the response of TCs to this targeted therapy along with chemotherapy (Fig. 2B). All the underlying assumptions, equations of the model, and the parameter estimation are described in Supplementary Materials and Methods (Supplementary Fig. S2; Supplementary Tables S2–S6).

Figure 2.

Schematic representation of different scales of the EC–TC cross-talk model and the treatment setup. A, A model for cross-talk between EC and TCs. TC-secreted VEGF binds to its receptors to induce Bcl2 expression. Bcl2 signaling is sufficient to induce IL6 secretion by ECs. IL6 enhances proliferation and survival of tumor cells. B, Conceptual effects of TCZ and/or cisplatin therapy on tumor growth and CSC%. i, Tumor growth in control group (without treatment); ii, cisplatin therapy increases the percentage of CSCs; iii, TCZ therapy shrinks tumor volume and decreases the percentage of CSCs; iv, combination therapy with TCZ and cisplatin significantly decreases tumor size and controls the increase in the percentage of CSCs.

Figure 2.

Schematic representation of different scales of the EC–TC cross-talk model and the treatment setup. A, A model for cross-talk between EC and TCs. TC-secreted VEGF binds to its receptors to induce Bcl2 expression. Bcl2 signaling is sufficient to induce IL6 secretion by ECs. IL6 enhances proliferation and survival of tumor cells. B, Conceptual effects of TCZ and/or cisplatin therapy on tumor growth and CSC%. i, Tumor growth in control group (without treatment); ii, cisplatin therapy increases the percentage of CSCs; iii, TCZ therapy shrinks tumor volume and decreases the percentage of CSCs; iv, combination therapy with TCZ and cisplatin significantly decreases tumor size and controls the increase in the percentage of CSCs.

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Treatment I: chemotherapy with cisplatin

We extend the pretreatment EC–TC model to include cisplatin therapy of HNSCC tumors. We then use the experimental data described above to validate the predictions of the proposed model. Once validated, this model is used and extended to study the tumor cell responses to combination therapy with TCZ and cisplatin. To modify our model to include treatment, we need to estimate the pharmacokinetic parameters of cisplatin. See Supplementary Materials and Methods for the details of parameter estimation and for the development of the full therapy model (Supplementary Fig. S3; Supplementary Tables S7–S9).

Treatment II: Treatment of HNSCC cell lines with tocilizumab

TCZ, an anti-IL6R antibody binds to IL6R on tumor cells and inhibits formation of IL6–IL6R complex molecules. Soon after drug administration, TCZ reaches the tumor environment and binds to IL6R on tumor cells and dissociates at experimentally determined rates. In our model, we keep track of the association and dissociation of TCZ to IL6 cell-bound receptors on tumor cells. All the underlying assumptions and the full TCZ therapy model equations are given in Supplementary Materials and Methods. This model is used to predict and also to compare the behavior of tumor growth dynamics with the TCZ therapy data. Once we confirm that our proposed model can successfully capture the tumor responses to the TCZ therapy, we combine it with the cisplatin therapy model to design a model for combination therapy with TCZ and cisplatin.

Tumor growth rates

The results from the regression modeling show that in the SCC1 model, time, cisplatin, and tocilizumab all significantly influence tumor size changes. In the SCC22B model, time and tocilizumab treatment significantly influence tumor size changes, but cisplatin does not. In models that additionally included the interaction effect of time, cisplatin, and tocilizumab, the interaction term is not statistically significant (Supplementary Table S1).

Our mathematical model for CSC-driven tumor growth is designed to quantify the influence of IL6 signaling on tumor growth, cellular composition, and targeted therapy. To calibrate and test the abilities of the EC–TC pretreatment model, we first fit it to the control data for both UM-SCC-1 and UM-SCC-22B cohorts. The black dots in Figs. 3A to 3D and 4A to 4D show the average tumor volume generated in six mice in the control group (i.e., with no treatment) whereas the black solid line passing through the black dots shows the best fit of the model to the control data over time for UM-SCC-1 and UM-SCC-22B groups, respectively. Moreover, the percentage of CSCs, predicted by the model, is shown along with tumor growth dynamics in the right panels of Figs. 3A to 3C and 4A to 4C.

Figure 3.

The EC–TC model achieves good prediction accuracy for IL6 pathway and combination therapy for UM-SCC-1 cohort. At day 23 and 28 after tumor implantation, treatment models were used to predict the tumor volume growth dynamics and the results were compared with the treatment data related to UM-SCC-1 cohort. Model predictions along with treatment and control data for UM SCC-1 tumor growth are plotted. A, Cisplatin therapy. B, TCZ therapy. C, Co-therapy. D, All the tumor volumes were normalized and the relative tumor growth dynamics are shown and compared with the model predictions (solid/dashed lines).

Figure 3.

The EC–TC model achieves good prediction accuracy for IL6 pathway and combination therapy for UM-SCC-1 cohort. At day 23 and 28 after tumor implantation, treatment models were used to predict the tumor volume growth dynamics and the results were compared with the treatment data related to UM-SCC-1 cohort. Model predictions along with treatment and control data for UM SCC-1 tumor growth are plotted. A, Cisplatin therapy. B, TCZ therapy. C, Co-therapy. D, All the tumor volumes were normalized and the relative tumor growth dynamics are shown and compared with the model predictions (solid/dashed lines).

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Figure 4.

The EC-TC model achieves good prediction accuracy for IL6 pathway and combination therapy for UM-SCC-22B cohort. At day 36 and 42 after tumor implantation, treatment models were used to predict the tumor volume growth dynamics and the results are compared with the treatment data related to UM-SCC-22B cohort. Model predictions along with treatment and control data for UM SCC-22B tumor growth are plotted. A, CIS-therapy. B, TCZ therapy. C, Co-therapy. D, All the tumor volumes were normalized and the relative tumor growth dynamics are shown and compared with the model predictions (solid/dashed lines).

Figure 4.

The EC-TC model achieves good prediction accuracy for IL6 pathway and combination therapy for UM-SCC-22B cohort. At day 36 and 42 after tumor implantation, treatment models were used to predict the tumor volume growth dynamics and the results are compared with the treatment data related to UM-SCC-22B cohort. Model predictions along with treatment and control data for UM SCC-22B tumor growth are plotted. A, CIS-therapy. B, TCZ therapy. C, Co-therapy. D, All the tumor volumes were normalized and the relative tumor growth dynamics are shown and compared with the model predictions (solid/dashed lines).

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Chemotherapy with cisplatin increases the CSC fraction

Within our experimental setup, we observe a significant decrease in tumor growth of one cell line (UM-SCC-1) and minimal change of other (UM-SCC-22B) after cisplatin treatment. Figures 3Ai and 4Ai illustrate the average tumor volumes treated with cisplatin (n = 6) versus the average tumor volumes in the control group (n = 6) for UM-SCC-1 and UM-SCC-22B, respectively. The empty (filled) red diamonds show the average tumor volumes treated with 5 mg/kg cisplatin for three weeks starting at day 23 (28) for UM-SCC-1 and day 36 (42) for UM-SCC-22B cohort after implantation. We use cisplatin treatment data starting at day 23 (for UM-SCC-1 cohort) and day 36 (for UM-SCC-22B cohort) to estimate the unknown parameter values of cisplatin therapy model (Supplementary Table S9). Then, we use the cisplatin therapy model to predict (no additional parameter fitting) responses of the tumors treated with cisplatin at treatment starting days 28 and 42 after implantation in UM-SCC-1 and UM-SCC-22B cohort, respectively. We also study the relative tumor volume variation by normalizing the data in the both cisplatin and control groups by dividing it by the average tumor volume at the first day of treatment (Figs. 3D and 4D). This allows us to compare the corresponding normalized values in the cisplatin group (red solid and dashed lines) and the control group (the black solid and dashed lines) and shows that the rate of growth in tumors treated with cisplatin and in the control group do not differ by much.

Figures 3Aii and 4Aii show the CSC percentage changes over time predicted by the model for both control and cisplatin treatment groups. We observe that the increase in the CSC percentage during treatment period in UM-SCC-1 cohort is higher than the increase in UM-SCC-22B group (Figs. 3Aiii and 4Aiii). In other words, we observe that where there is a small or insignificant decrease in tumor growth rate, a small increase in the CSC percentage during/after cisplatin chemotherapy is expected. Collectively, our model can capture the chemotherapeutic effects of cisplatin therapy and further predicts that although cisplatin may cause a significant decrease in tumor volumes, it increases the CSC percentage in the tumor. Notably, the model predictions are consistent with the experimental data and published results in ref. 3.

IL6R targeted therapy with TCZ decreases both tumor volume and CSC fraction

We observe that treatment with TCZ can cause a considerable decrease in the tumor growth rate in UM-SCC-1 cohort while treating UM-SCC-22B cell lines with TCZ can only partially reduce tumor volumes when compared with the control group. Figures 3Bi and 4Bi illustrate the average tumor volume in TCZ-treatment group (n = 6) versus the average tumor volumes in the control group (n = 6) for UM-SCC-1 and UM-SCC-22B, respectively. The empty (filled) squares show the average tumor volumes treated weekly with 5 mg/kg TCZ to the end of the experiment starting at day 23 (28) in UM-SCC-1 and day 36 (42) in UM-SCC-22B cohort after implantation. We use the TCZ therapy model to predict tumor response to administration of TCZ as a single agent to understand the mechanism behind the role of IL6 on tumor growth behavior. Importantly, by incorporating no additional parameter fitting and only by directly comparing the model predictions and the TCZ therapy data we can validate the treatment model. We use the best fit parameter values obtained from fitting the EC–TC model to the control data for both UM-SCC-1 and UM-SCC-22B cell lines and predict the tumor growth dynamics post TCZ therapy. Figures 3Bi and 4Bi show the model predictions as compared with experimental data for UM-SCC-1 and UM-SCC-22B cohorts, respectively.

Furthermore, we use the TCZ therapy model to predict the CSC% dynamics over time. As shown in Figs. 3Bii and 4Bii, the model outcomes suggest that also the sooner the TCZ-treatment starts the more TCZ-induced CSC% reduction we see. Overall, the model suggests a significant dependence between time since treatment and TCZ-mediated CSC reduction.

Combination therapy improves the therapeutic effects of monotherapy with TCZ or cisplatin

We combine the TCZ and cisplatin therapy models to include the effects of combination therapy on tumor growth dynamics. Our experimental results show that UM-SCC-1 cell lines positively respond to combination treatment and have a slower growth rate compared with the control group, whereas the tumors initiated from UM-SCC-22B cell lines have a mixed reaction to the treatment. Figures 3Ci and 4Ci show the average tumor volumes responding to cotreatment with cisplatin and TCZ (n = 6) versus the average tumor volumes in the control group (n = 6) for UM-SCC-1 and UM-SCC-22B, respectively. The empty (filled) squares show the average tumor volumes cotreated weekly with 5 mg/kg cisplatin and 5 mg/kg TCZ for 3 weeks followed by TCZ therapy only to the end of the experiment starting at day 23 (28) for UM-SCC-1 and day 36 (42) for UM-SCC-22B cohort after implantation. Comparing the corresponding normalized tumor volumes in the combination therapy and control groups shows that the treated tumors are growing relatively slower than the tumors in the control group (Fig. 4D).

Finally, the predicted CSC% suggests that TCZ therapy compensates for the observed increased in the CSC% induced by cisplatin in tumors in both cohorts (Figs. 3Cii and 4Cii). In addition, the model predictions along with experimental data suggest that the reduction in both tumor volumes and CSC% is, on average, greater if the treatment starts earlier.

Treatment schedule optimization

This model can then be used to predict the effects of combination therapy and can be deployed to find the most optimal dosing schedule within our experimental setup. To determine the most favorable combinations and to investigate the potential synergism between TCZ and cisplatin, we simulate a number of dose-scheduling regimens by using the baseline parameter values for UM-SCC-1 cohort (Table 1). The ultimate goal is to determine the optimal dosing strategy that minimizes both tumor growth and CSC%, while also minimizing the amount of drug administered. In these simulations, TCZ is administered weekly for 3, 4, or 5 weeks, starting at day 0 of week 0 of treatment, which corresponds to day 28 after implantation in our experiment. Tumors are pre-, co-, or post-treated with 5 mg/kg cisplatin weekly for either 2 or 3 weeks. For each treatment strategy we compute the IC70, which corresponds to the amount of TCZ required for 70% reduction (compared with control) in tumor volume after 6 and 8 weeks, called “reference weeks” (RWs), from the start of cotreatment day. Using the IC70, we compute a metric (defined in ref. 18) that we refer to as the dose scheduling index (SI) to indicate the level of synergism between the two drugs. SI is defined as a ratio of the predicted IC70 for each dose scheduling strategy with the IC70 for the baseline case, wherein the tumor is cotreated with cisplatin and TCZ weekly for 3/2 weeks followed by treatment with only TCZ for the remainder of the therapeutic time window (highlighted rows 3, 8, 13, 18, 23, and 28). The SI values help us to quantify the therapeutic efficacy of the different dose scheduling strategies. An SI value greater than one represents suboptimal dosing; whereas, a value less than one indicates some level of synergism between the two drugs (18, 19). Moreover, considering the important role of CSCs in the tumor growth dynamics, we are also interested in maximizing the decrease in the CSC percentage. Therefore, to find an optimal schedule, we need to minimize the amount of TCZ required for a fixed amount of the total injected cisplatin (10 or 15 mg/kg) by changing timing/ordering of administering the two drugs with respect to each other while maximizing the percentage of induced CSC reduction (ICR).

Table 1.

Multiobjective optimization for combination treatment schedules.

Multiobjective optimization for combination treatment schedules.
Multiobjective optimization for combination treatment schedules.

The distinctive half-life values of TCZ and cisplatin impact the predicted optimal strategy(ies) for combination-therapy

Once administered, TCZ remains within the tumor environment for a few weeks due to its slow clearance rate, and as a result, blockade of IL6 signaling by TCZ has a long-lasting inhibitory effect on HNSCC CSCs. In contrast, half-life value of cisplatin is short (3). The potential impacts of the distinctive pharmacokinetics patterns of cisplatin and TCZ are evaluated in different time windows. We look at the residual impacts of cisplatin via simulating cases wherein tumors are pretreated with 5 mg/kg of cisplatin either 1 day before, 2 days before, …, 7 days before cotreatment day 0 (corresponds to day 28 in the experiment) and also post-treated 1 day after, 2 days after, …, 7 days after day 0 with different initial CSC% (2, 6, 10, 14, and 18). Then, for each case, we measure the reduction in tumor volume and CSC% at day 7 (Fig. 5A and B). The simulations suggest that the maximum tumor volume reduction occurs at 5 to 7 days after cisplatin injection. However, CSC% drops quickly right after cisplatin administration. Therefore, to avoid the potential biased results induced by cisplatin's relatively short cytotoxic time window, we measure both the SI and ICR values at 6 and 8 weeks after treatment starting day.

Figure 5.

Residual impacts of cisplatin on combination therapy and effects of tumor composition and treatment starting day on tumor growth and CSC% dynamics. A, Tumor volume reduction in response to combination therapy with cisplatin and TCZ. B, CSC% reduction in response to combination therapy with cisplatin and TCZ. C and D, Effects of various initial CSC% on tumor growth and CSC% dynamics. E and F, Effects of treatment starting day on tumor growth and CSC% dynamics.

Figure 5.

Residual impacts of cisplatin on combination therapy and effects of tumor composition and treatment starting day on tumor growth and CSC% dynamics. A, Tumor volume reduction in response to combination therapy with cisplatin and TCZ. B, CSC% reduction in response to combination therapy with cisplatin and TCZ. C and D, Effects of various initial CSC% on tumor growth and CSC% dynamics. E and F, Effects of treatment starting day on tumor growth and CSC% dynamics.

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Because the ICR values at week 6 posttherapy (i.e., at day 70 after implantation) are very close for the different schedules investigated here, we choose the most optimal time/dosing strategy(ies) based on the minimum total amount of TCZ. IC70 values along with SI values suggest that, in general, cotreatment (SI = 1) with cisplatin is preferred over posttreatment and pretreatment (highlighted baseline rows). Among those with SI = 1, administrating 3 mg/kg (2.5 mg/kg) TCZ for only 3 (4) weeks (a total of 9 or 10 mg/kg TCZ) offers the lowest total amount of TCZ in comparison to other schedules that can cause 70% reduction in tumor volume six weeks posttreatment (rows 3 and 13). To the contrary, measuring SI and ICR values at a longer time-interval after treatment starts, at week 8, we observe that much smaller values of TCZ is required to cause 70% tumor volume reduction. However, there will be a lower decrease in CSC% when compared with the results at week 6 posttherapy [columns ICR (RD 6) and ICR (RD 8)]. Moreover, we observe that, pre- and posttherapy has almost the same level of influence as co-therapy on tumor shrinkage and CSC% reduction. Collectively, although small amount of TCZ is enough to decrease tumor growth rate, it is less successful at decreasing the fraction of CSCs over a long-term period.

The sizable difference between the half-life values of cisplatin and TCZ suggest nonintuitive treatment scheduling

The overall results from Table 1 show that these two drugs cannot achieve optimal synergistic activity with conventional treatment scheduling regimens. Alternatively, the long-lasting influences of TCZ on tumor growth versus the short cytotoxic time interval of cisplatin leads us to investigate impacts of the same amount of cisplatin administered in a larger time intervals. For instance, we administer cisplatin every 2 weeks instead of every week (Table 2). Cisplatin is co-, pre-, and post-treated with TCZ biweekly for a total of 3 weeks where TCZ is administered weekly for a total of 3/4 weeks. The results are compared with the original baseline schedule from Table 1 (Table 2, rows 1 and 8). At week 6 posttreatment, comparing SI values with the baseline value, biweekly administration of cisplatin posttreated with TCZ for a total of 3 weeks (row 4) suggests the lowest total amount of TCZ, however, there is much less decrease in CSC% reduction when compared with the baseline ICR value (approximately 67% smaller). As an alternative, biweekly administration of cisplatin cotreated with TCZ for a total of 3 weeks (row 3) decreases the total amount of TCZ from 9 to 7.5 mg/kg when compared with the baseline SI while the decrease in ICR is not as significant (approximately 33% smaller).

Table 2.

Optimizing combination therapy using nonintuitive dosing schedules.

Optimizing combination therapy using nonintuitive dosing schedules.
Optimizing combination therapy using nonintuitive dosing schedules.

Furthermore, we investigate the biweekly injections for both of the drugs under two scenarios: (i) cisplatin and TCZ are administered with 1 week difference (rows 10–13), and (ii) TCZ and cisplatin are simultaneously administered (rows 14–16). Row 9 represents the baseline values of SI and ICR. The results suggest that starting treatment 1 week earlier with 5 mg/kg cisplatin coinjected with only 1.5 mg/kg TCZ and repeating the treatment after 2 weeks and then after another 2 weeks (total of 3 weeks of co-therapy; row 14) can significantly decrease the total value of TCZ in comparison to any other regimen presented in Table 2. Importantly, the ICR value is fairly comparable to the baseline ICR value (approximately 35% smaller). On the contrary, starting TCZ injection with 1 week delay, on week 1, results in a very high amount of TCZ for causing 70% decrease in tumor volume at week 6 (row 11 and 16). All together, these results suggest that among all the treatment schedules starting at week 0, biweekly administration of cisplatin with weekly administration of TCZ reduce the frequency of chemotherapy while improving the synergism between the two drugs. Taking this schedule (row 3 of Table 2) as the optimal regimen, we simulate the optimal dosing schedule where the tumor is cotreated with biweekly administration of 5 mg/kg cisplatin for a total of 3 weeks and 3 weeks of 5 mg/kg TCZ and compare the results to the ones obtained from the experiment (Supplementary Fig. S4). The simulations show that the predicted optimal dosing schedule is better than either therapy alone and is also more effective than the cotreatment strategy used experimentally.

Initial tumor composition and timing of treatment

To simulate distinctive, personal tumor characteristics, we evaluate the potential effects of both “timing of treatment initiation” and “initial CSC% at the day of implantation.” Therefore, first, we simulate tumor volume and CSC% growth dynamics for tumors with a range of initial CSC% (2, 6, 10, 12, and 18). We observe that higher initial CSC% results in a higher rate of tumor growth (Fig. 5C). On the contrary, CSC% in tumors with a higher initial CSC% drops to the equilibrium level at a faster rate (Fig. 5D). Next, we use one of the optimal regimens suggested above on tumors with different initial CSC% starting at day 21 and day 28. We cotreat tumors (with different initial CSC%) with 5 mg/kg of cisplatin biweekly and 5 mg/kg TCZ weekly for a total of 3 weeks and compare the results at day 51 (the same end day as our in vivo experiment) for the two treatment starting days. We observe that an earlier timing of treatment initiation (which corresponds to a higher CSC% at the day of treatment initiation) leads to a higher decrease in both tumor volume and CSC% post treatment (Fig. 5E and F).

Cisplatin is the most common conventional chemotherapeutic drug used in multimodality HNSCC treatment. However, there is unacceptably high recurrence rate potentially mediated by CSCs, indicating the need for novel approaches for HNSCC treatment. One of the options is therapeutic inhibition of IL6–IL6R signaling pathway, which promotes CSCs' self-renewal and survival in combination with cisplatin. In this work, we use a mathematical model to investigate tumor responses to a combination of cisplatin and IL6-targeted therapy and to suggest the timing/dosing schedules that optimize the synergism between the two agents to control HNSCC tumor growth.

We developed a pretreatment mathematical model based on experimental studies of human head and neck primary tumor xenografts generated from a small population of HNSCC CSCs in mice. Our model successfully captured the tumor growth dynamics observed in experimental data. Then, based on both our experimental data and biological knowledge of cisplatin and TCZ, we extended our model to include treatment to evaluate the impact of EC-secreted IL6 on tumorigenic potentials of HNSCC CSCs and targeted therapy with TCZ alone and/or in combination with cisplatin. Moreover, these models are calibrated using the data from multiple xenograft cell lines, and are further validated by directly comparing (i.e., no additional parameter fitting) the experimental data and the model predictions to the therapies.

The simulations of cisplatin therapy model showed that the antitherapeutic effects of cisplatin on tumor growth is directly correlated with the increase in CSC percentages during/after treatment. These lead us to hypothesize that as cisplatin-chemotherapy shrinks tumor volume, it induces an increase in CSC%, which in turn can enhance tumor growth dynamics. This result is in line with the experimental results observed by Nor and colleagues (3). Similarly, the TCZ therapy model captures the tumor growth dynamics observed in experiments for both cell line cohorts. In addition, the results reflected the TCZ therapy-induced reduction in CSC% as expected. Interestingly, we see that the earlier the TCZ therapy starts, the larger the impact of TCZ on antitumor growth. In both cohorts, TCZ administration compensates for the cisplatin-induced increase in CSC%.

In an attempt to find the most optimal outcome of the combinations of the two drugs, we use the baseline parameter values for UM-SCC-1 cohort and simulate various dose-scheduling regimens of cisplatin and TCZ. The results suggest that to find the optimal timing/dosing schedule(s), it may be important to consider the difference between the half-life of each drug. Therefore, to avoid the effects of relatively short half-life of cisplatin on the combinational therapy in a short-term period, we chose two different reference weeks to calculate our therapeutic metrics (i.e., IC70, SI, and ICR). Looking at the tumor responses to the combination therapy 1 week after the last injection shows that, in general, cotreatment with TCZ and cisplatin is preferred over posttreatment and pretreatment whereas the scheduling itself is less influential if we look at the results 3 weeks after the last drug administration. In fact, further analysis shows that due to the fact that TCZ has a considerably longer half-life than cisplatin, the continuation of TCZ therapy at low doses is more effective than high doses at a short period of time. More importantly, our results suggest biweekly administration of cisplatin with weekly administration of TCZ to reduce the number of chemotherapy while controlling the CSC percentage. In summary, studying the behavioral differences of cisplatin and TCZ guided us to propose that biweekly injections of cisplatin along with continuous weekly administration of low amounts of TCZ optimizes the synergism between the two drugs while controls the cisplatin-induced increase of CSCs within tumor. We note that a full practical identifiability analysis would be a valuable addition to our work, we plan to provide this as a separate publication in the future.

Finally, given the fact that UM-SCC-22B cell lines are established from the metastatic lymph node and also observing the poor responses to the treatment in comparison to the UM-SCC-1 cell lines, our simulations suggest that tumor intrinsic factors such as CSC% are important for choosing and testing the treatment regimens in the pretrial experiments. Using a computational model with biologically plausible inputs is a framework for future clinical cotreatment personalization.

A.T. Pearson has provided expert testimony for Smith Haughey Rice & Roegge. No potential conflicts of interest were disclosed for the other authors.

Conception and design: F. Nazari, A.E. Oklejas, A.T. Pearson, T.L. Jackson

Development of methodology: F. Nazari, A.E. Oklejas, A.T. Pearson, T.L. Jackson

Acquisition of data (provided animals, acquired and managed patients, provided facilities, etc.): A.E. Oklejas, J.E. Nör, A.T. Pearson

Analysis and interpretation of data (e.g., statistical analysis, biostatistics, computational analysis): F. Nazari, A.E. Oklejas, A.T. Pearson

Writing, review, and/or revision of the manuscript: F. Nazari, A.E. Oklejas, J.E. Nör, A.T. Pearson, T.L. Jackson

Administrative, technical, or material support (i.e., reporting or organizing data, constructing databases): F. Nazari, A.T. Pearson

Study supervision: T.L. Jackson

This work was supported by Simon's Foundation Collaboration Grant No. 312622 (to T.L. Jackson); Institutional Research Grant No. #IRG-16-222-56 (to A.T. Pearson) from the American Cancer Society; University of Michigan Head and Neck SPORE P50-CA97248 from the NIH/NCI; grants K08-DE026500 (to A.T. Pearson), R01-DE23220 (to J.E. Nör), and R01-DE21139 (to J.E. Nör) from the NIH/NIDCR.

The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

1.
Jackson
T
,
Komarova
N
,
Swanson
K
. 
Mathematical oncology: using mathematics to enable cancer discoveries
.
Am Math Month
2014
;
121
:
840
56
.
2.
Krishnamurthy
S
,
Warner
KA
,
Dong
Z
,
Imai
A
,
Nör
C
,
Ward
BB
, et al
Endothelial interleukin-6 defines the tumorigenic potential of primary human cancer stem cells
.
Stem Cells
2014
;
32
:
2845
57
.
3.
Nor
C
,
Zhang
Z
,
Warner
KA
,
Bernardi
L
,
Visioli
F
,
Helman
JI
, et al
Cisplatin induces Bmi-1 and enhances the stem cell fraction in head and neck cancer
.
Neoplasia
2014
;
16
:
137
46
.
4.
Zhu
Y
,
Luo
M
,
Brooks
M
,
Clouthier
SG
,
Wicha
MS
. 
Biological and clinical significance of cancer stem cell plasticity
.
Clin Transl Med
2014
;
3
:
32
.
5.
Prince
ME
,
Ailles
LE
. 
Cancer stem cells in head and neck squamous cell cancer
.
J Clin Oncol
2008
;
26
:
2871
5
.
6.
Reya
T
,
Morrison
SJ
,
Clarke
MF
,
Weissman
IL
. 
Stem cells, cancer, and cancer stem cells
.
Nature
2001
;
414
:
105
11
.
7.
Weekes
SL
,
Barker
B
,
Bober
S
,
Cisneros
K
,
Cline
J
,
Thompson
A
, et al
A multicompartment mathematical model of cancer stem cell-driven tumor growth dynamics
.
Bull Math Biol
2014
;
76
:
1762
82
.
8.
Krishnamurthy
S
,
Nör
J
. 
Head and neck cancer stem cells
.
J Dent Res
2012
;
91
:
334
40
.
9.
Neiva
KG
,
Zhang
Z
,
Miyazawa
M
,
Warner
KA
,
Karl
E
,
Nör
JE
. 
Cross talk initiated by endothelial cells enhances migration and inhibits anoikis of squamous cell carcinoma cells through STAT3/Akt/ERK signaling
.
Neoplasia
2009
:
11
:
583
93
.
10.
Krishnamurthy
S
,
Dong
Z
,
Vodopyanov
D
,
Imai
A
,
Helman
JI
,
Prince
ME
, et al
Endothelial cell-initiated signaling promotes the survival and self-renewal of cancer stem cells
.
Cancer Res
2010
;
70
:
9969
78
.
11.
Olsen
MM
,
Siegelmann
HT
. 
Multiscale agent-based model of tumor angiogenesis. Multiscale agent-based model of tumor angiogenesis
.
Procedia Comput Sci
2013
;
18
:
1016
25
.
12.
Tang
L
,
van de Ven
AL
,
Guo
D
,
Andasari
V
,
Cristini
V
,
Li
KC
, et al
Computational modeling of 3D tumor growth and angiogenesis for chemotherapy evaluation
.
PLoS One
2014
;
9
:
e83962
.
13.
Wang
Z
,
Butner
JD
,
Kerketta
R
,
Cristini
V
,
Deisboeck
TS
. 
Simulating cancer growth with multiscale agent-based modeling
.
Semin Cancer Biol
2015
;
30
:
70
8
.
14.
Nör
JE
,
Peters
MC
,
Christensen
JB
,
Sutorik
MM
,
Linn
S
,
Khan
MK
, et al
Engineering and characterization of functional human microvessels in immunodeficient mice
.
Lab Invest
2001
;
81
:
453
.
15.
Chad
BJ
,
Graham
MP
,
Kumar
B
,
Saunders
LM
,
Kupfer
R
,
Lyons
RH
, et al
Genotyping of 73 UMSCC head and neck squamous cell carcinoma cell lines
.
Head Neck
2010
;
32
:
417
26
.
16.
Nazari
F
,
Pearson
AT
,
Nör
JE
,
Jackson
TL
. 
A mathematical model for IL-6-mediated, stem cell driven tumor growth and targeted treatment
.
PLoS Comput Biol
2018
;
14
:
e1005920
.
17.
Kaneko
T
,
Zhang
Z
,
Mantellini
MG
,
Karl
E
,
Zeitlin
B
,
Verhaegen
M
, et al
Bc-l2 orchestrates a cross-talk between endothelial and tumor cells that promotes tumor growth
.
Cancer Res
2007
;
67
:
9685
93
.
18.
Jain
HV
,
Meyer-Hermann
M
. 
The molecular basis of synergism between carboplatin and ABT-737 therapy targeting ovarian carcinomas
.
Cancer Res
2011
;
71
:
705
15
.
19.
Cook
AB
,
Ziazadeh
DR
,
Lu
J
,
Jackson
TL
. 
An integrated cellular and sub-cellular model of cancer chemotherapy and therapies that target cell survival
.
Math Biosci Eng
2015
;
12
:
1219
35
.