We extended our previous model for tumor growth and resistance to treatment with virotherapy and the resulting immune response46 to consider the impact of using dual VV ‘enhancer’ and VSV OV injection. In this scenario, the antitumor immune response is either upregulated or downregulated depending on the type of virus injected. We considered total vaccinia and vesicular stomatitis virions (VVV(t) and VVSV(t), respectively) and two corresponding infected cell populations Extra close brace or missing open brace and Missing \left or extra \right. Parameters from Cassidy and Craig46 relating to viral kinetics were taken here to be virus dependent (subscript notation for κ,δ,α and ω). Additionally, we included an immunomodulation term ρ∈[0,1] that modulates the production of immunostimulatory cytokines. The complete set of model equation is provided in the online supplemental technical information. A summary of the biological assumptions and model schematic is given in figure 1.

Briefly, the following biological interactions were added to the model described in Cassidy and Craig46:

All other interactions are as in Cassidy and Craig.46 For more information on the biological interactions and their model implementation see online supplemental technical information.

Parameters of the model were estimated via a hierarchical fitting algorithm in which subsets of the model were fit to different experiments using VV and VSV. Full details are provided in the online supplemental technical information. Briefly, we sequentially fit model parameters to the experimental measurements from HT29 and 4TI cell lines from Le Boeuf et al19 and Rausch et al51 (online supplemental figures TS1–TS3). Tumor growth parameters were obtained by fitting the rate quiescent cells enter the G1 phase (a1), the rate HT29 (human colorectal adenocarcinoma) and 4T1 (murine mammary carcinoma) cells leave G1 to enter the active phase (a2), and the rate cells undergo apoptosis in G1 phase (d2), in immunodeficient (ID) mice (ie, HT29/ID and 4T1/ID obtained by Le Boeuf et al19 and Rausch et al,51 respectively). We then fixed these parameter values and estimated the viral kinetic parameters κVSV,κVV,δVSV,δVV,αVSV and αVV from VSV, VV and VV+VSV treated HT29 tumor growth measurements in ID mice (ie, HT29/ID-VSV, HT29/ID-VV and HT29/ID-VV+VSV obtained by Le Boeuf et al19). Then, using IC mice experiments from Rausch et al,51 we estimated the immune cell-tumor cell contact rate kp, the immune cell digestion constant kq,s, the cytokine production half effect Ψ1/2 and the maximal immune cell production rate kcp. To account for the effects of humoral immune responses the viral-kinetic parameters ωVSV,ωVV,δVSV,δVV were then recalibrated to the presence of the immune system using 4T1 tumor growth measurements in IC mice under VSV, VV and VV+VSV (ie, 4T1/IC-VSV, 4T1/IC-VV and 4T1/IC-VV+VSV obtained by Le Boeuf et al.19).

To reflect interindividual variability and the heterogeneity in treatment outcomes, we generated a unique set of parameters to represent individual virtual patients (figure 2A, no human patients were involved in this study). For this, we sampled tumor and immune cell-related parameters a1,a2,d2,τ,kp,kq,ks,kcp (where τ is the expected tumor cell cycle duration) from a normal distribution with mean μ^ corresponding to the parameter value returned in the hierarchical fitting described above.

To avoid the inclusion of non-realistic virtual individuals, we verified that each parameter set resulted in a tumor growth within two SD of the experimental measurements and the mean prediction at each corresponding data time point (figure 2B). Using this approach, we created 200 patients with parameter values normally distributed about the mean empirical or fitted value (online supplemental figure S1, online supplemental information), rejecting 265 parameter sets for not meeting the inclusion criteria. Since the maximal immune cell production rate (kcp) changes when VSV is introduced, we assumed each individual patient’s parameter varied equivalently. To recapitulate heterogeneity in initial tumor size and immune populations, we simulated an initial seeding of 105 tumor cells, along with an initial cytokine concentration C0 and immune cell count P0 (day 0) for each in silico patient parameter set and fixed the initial conditions for treatment to be the tumor and immune populations on day 6 (online supplemental figure S2).

Kaplan-Meier survival curves for each cohort treated using the combination protocols were used to compare the effectiveness of the different trials. To determine a cull threshold for the survival of the virtual patients, we extrapolated the Kaplan-Meier curves in Le Boeuf et al19 by taking populations of 10 randomly sampled individuals and calibrating to their cumulative survival curve, giving a volume threshold (online supplemental technical information, online supplemental figure TS4). A local parameter sensitivity analysis of the mean empirical values showed that tumor growth was closely related to cell cycling rates and immune stimulation (online supplemental figure S3, online supplemental information).

We also quantified the growth rate r of the control tumors by approximating the growth curves with an exponential growth function from day 12 to 18, that is, r=(ln⁡(T18-ln⁡(T12)/6, to obtain an estimate of later tumor growth. This measurement period was chosen to account for the discernable differences between cell lines after day 12 and the experimental end point at day 18.19 The implicit parameter r describes the aggressivity of the tumors, with high r corresponding to aggressively growing tumors and low r corresponding to slowly growing tumors. Ordering patients by their tumor growth rate showed a gradual increase in r values across the cohort (figure 2C). Numerical simulations, the creation of the virtual cohort, all statistical analyses and figure generation were performed using Matlab R2019b.

The effect of the multiplicity of VV enhancer injections on the success of therapy is largely unknown, especially for a cohort with varying underlying tumor growth rates. To assess the impact of the number of enhancer administrations, we simulated our virtual cohort after multiple daily enhancer infections followed by a VSV injection given 7 days after the last enhancer (figure 3A). The total number of VV injections (NE) ranged from 1 to 7 and the dosage sizes were fixed to those used in the Le Boeuf et al19 (online supplemental technical information).

To assess the performance of different enhancer schedules, we quantified the number of tumor cells 15 days after VSV administration (VSV +15 days; figure 3B). In particular, we found that the number of VV enhancers (NE) did not significantly impact the average tumor size at VSV+15, and that the distribution of tumor sizes between sequential enhancer multiplicities, that is, one enhancer and two enhancers, two enhancers and three enhancers etc., was not significantly different. There was, however, a difference in the distribution of tumor sizes between one enhancer and all other enhancer multiplicities from three enhancers onwards (as confirmed by a Kolmogrov-Smirnov test, p=0.0475, see online supplemental figure S4A for significant pairings). We also determined that the mean number of tumor cells was only significantly different between one and six enhancers, and one and seven enhancers (pairwise t-test, p=0.034 and p=3.8×10-4, respectively; online supplemental figure S4B, online supplemental information). This suggests that the duration of treatment and tumor aggressivity could be the principle drivers of the distribution in tumor sizes at 20 days, irrespective of the number of enhancers.

Nonetheless, we were able to distinguish low and high responders by their tumor growth at VSV +15 days after 7 vs 1 enhancer (figure 3C; results for all multiplicities of enhancer injections in online supplemental figure S5A). Though the mean dynamics of the number of tumor cells are qualitatively similar after one or seven enhancers, there is a statistically significant difference in the mean number of tumor cells at VSV +15 days for one enhancer compared with seven enhancers. The difference in variance of cohort responses can be explained by the fact that the last enhancer is administered on day 1 for the one enhancer protocol vs day 6 under the seven enhancer schedule, implying that tumors have ultimately been growing for a longer period of time under the seven enhancer protocol, supporting the conclusion that therapeutic success is largely driven by intrinsic aggressivity (ie, higher growth rates). Log-rank tests of the cohort’s Kaplan-Meier survival curves also showed that the one enhancer protocol was significantly different from all others (figure 3D and online supplemental figure S5B in the online supplemental information).

An increase in the variability of responses was observed with a corresponding increase in the number of enhancers (figure 3B). To investigate whether there was a link between a patient’s intrinsic tumor growth rate r and the optimal number of enhancers, we established each patient’s optimal number of enhancers through numerically simulating all possible treatment protocols and finding the one that minimized tumor burden at VSV +15. We found that the optimal number of enhancers grew with decreases in intrinsic tumor growth rates (figure 4A). Further, our results show that individuals with high growth rates consistently had worse outcomes, even during ‘optimal’ treatment with two enhancers. To discern patterns of responses in less aggressive tumors and higher growth rates, we ordered the number of enhancers from best protocol to worst protocol for each patient, based on the tumor size 15 days after the VSV injection (figure 4B). Patients with low tumor growth rates were found to perform best under treatment with seven enhancers and worst under treatment with a single enhancer, whereas patients with high tumor growth rates performed best with two enhancers and worst under seven enhancers. These results suggest that there is a significant difference in the efficacy of protocols given a patient’s intrinsic tumor growth rate.

Thus far, enhancer multiplicity was investigated with VSV administered 7 days after the last enhancer. However, the number of days between the final enhancer and the VSV administration can also influence the priming of the immune response and the efficacy of the treatment. To measure the impact of the VSV lag (DB days), we simulated a single administration of VSV 1–15 days after the final enhancer, with dosages fixed as in Le Boeuf et al19 (figure 5A). The number of enhancers was set to either 1 or 7, based on the enhancer multiplicity results described previously. As before, therapeutic response was assessed by the number of tumor cells (ie, tumor size) at VSV +15 days (figure 5B).

Similar to what was observed with the enhancer multiplicity, increasing the VSV lag increased the variance of the cohort’s response (figure 5B). A VSV lag of 1 day, irrespective of the number of enhancers, produced the smallest average tumor size, with a very small distribution of responses at VSV +15 days. In comparison, we observed more dispersion in overall responses for VSV lags of 7 days or more, with some individuals achieving lower tumor sizes than for shorter VSV lags (see online supplemental information, online supplemental figure S6A).

Over longer time, the separation in the tumor size under a 1-day vs 15-day VSV lag becomes clearer (figure 5C). On average, 15-day VSV injection-lags performed the worst of all tested scenarios, especially at longer time points (65 days past VSV). This further solidifies that, as opposed to enhancer multiplicity, the time to VSV administration is the key determinant of tumor size. Since the immune cell population is essentially stabilized by VSV +15 days (figure 5E), and cytokine concentrations are saturated (figure 5D), the dynamics that occur immediately after the VSV injection must lead to the divergence of long-term tumor behavior.

As we hypothesized that interindividual variability would significantly impact treatment responses, we next investigated the optimal VSV lag for each individual after either one or seven enhancers. For the one enhancer protocol, the optimal VSV lag was a single day for all but three individuals with particularly slow growing tumors, for whom a 5-day VSV lag was best (figure 6A). However, we expect this response to be not particularly significant, as the difference in tumor cell numbers between the optimal and the second most optimal protocol for these three individuals was negligible compared with the rest of the cohort (results not shown).

Tumor responses to treatment were increasingly stratified for optimal schedules after seven enhancer administrations (figure 6B), likely related to the increased interindividual variability observed in this case. We found that optimal schedules for virtual patients with the slowest intrinsic growth rates required a 15-day VSV lag vs 1 day for those with slow growing tumors. Indeed, there was a clear delineation between aggressively growing tumors that required as short of a lag as possible for maximal therapeutic effect and slower growing tumors that responded best with as long of a VSV lag as possible (figure 6C and online supplemental figure S7 in the online supplemental information). Crucially, individuals with the slowest tumor growth were predicted to have the most meaningful responses, completely recovering in some cases. This again underlines that patient stratification and schedule tailoring is crucial for ensuring the most meaningful clinical response.

To further delineate vaccination scheduling in distinct subcohorts, we tailored VV enhancer multiplicity (between 1 and 7) and VSV lag (between 1 and 15 days) for each virtual individual according to intrinsic tumor characteristics (figure 7A). The individual optimal protocol was determined by simulating all scheduling possibilities and minimizing tumor size at VSV +15 days.

As before, we found clear stratification between optimal protocols for slowly growing (seven enhancers followed by a 14 or 15 days VSV lag) and fast growing (one enhancer followed by a 1-day VSV lag) tumors (figure 7A). Interestingly, for a range of low intrinsic growth rates r, optimal schedules resulted in near complete tumor removal, whereas we found a jump in the number of tumor cells, followed by a linear dependence on the intrinsic growth rate after a critical value around r≈0.03 1/day. Clinically, an r value of 0.03 corresponds to a tumor doubling time of 23 days, which was above the original cohort average of 15 days (figure 2C). Overall, these results underline that tumor aggressivity is the determining factor for combination OV scheduling and the outcome of enhancer-VSV therapy.

To confirm that outcomes are improved by employing therapeutic strategies based on tumor aggressivity and investigate the robustness of our stratification strategy, we generated two new cohorts comprised of 50 virtual individuals with slow growing tumors (0.0196§amp;lt;r§amp;lt;0.0260) and 50 with aggressively growing tumors (0.0629§amp;lt;r§amp;lt;0.0657). These ranges for r where chosen to correspond to the top and bottom 10% of the initial cohort’s r value (figures 2C and 7B). We next simulated the tumor growth of these cohorts under the previously determined optimal protocols, that is, 7 enhancers and a 15-day VSV lag for slow growing tumors, and one enhancer and a 1-day VSV lag for aggressive tumors (figure 7C). Additionally, we simulated each cohort under the alternate optimal protocol, that is, aggressively growing tumors with the slow tumor growth protocol and vice versa.

Overall, in terms of survival and irrespective of protocol, the aggressive tumor growth cohort performed markedly worse than the slow tumor growth cohort (figure 7D). As these represent the 10% most aggressive tumors of the original cohort, it is not surprising that the efficacy of therapy is minimal. In contrast, survival in the slow growing cohort was markedly different under the two protocols: when treated with their optimized protocol, all individuals survived, and while survival declined when treated with the aggressive tumor growth protocol, it remained overall stronger than in the aggressive tumor cohort treated with its matched optimal treatment strategy. Nonetheless, both strategies perform better than the no treatment case (results not shown). To further confirm the optimality of the aggressive and slow tumor growth protocols, we also determined each virtual patient’s optimized combination schedule for the new cohorts (figure 7E). Unsurprisingly, the optimal protocols were the same as in the larger original cohort, implying there is a robust link between tumor aggressivity and the optimal combination OV-therapy protocol. Interestingly, for patients with extremely slow growing tumors (r close to 0.0196, doubling time of roughly 35 days) the optimal VSV lag was slightly shorter (DB=13 days) than the rest of the slow growing tumor cohort. Thus, we posit that a combined OV therapeutic vaccination approach with VV +VSV will be most effective for slow growing tumors.