Modeling Cytostatic and Cytotoxic Responses to New Treatment Regimens for Ovarian Cancer

Though new targeted drugs are under study for ovarian cancer, first-line options are still based on a combination of the cytotoxic drugs with proven activity: platinum compounds, carboplatin and cisplatin (DDP), and paclitaxel (PTX). Conventional treatments are based on repeated 21-day cycles where carboplatin and PTX are both given once on day 1. A dose-dense schedule of PTX treatment has been proposed, splitting the PTX dose into three parts in each cycle (1). A debate is ongoing and clinical trials have demonstrated some superiority of the dose-dense scheme, some trials adopting a dose-dense scheme with equivalent total dose (2), others with a 50% higher dose (3) with respect to the conventional one. However, clinical studies aimed at optimizing the schedule are rare, the actual choices are often being empirically driven by practice. A further element of complexity was introduced with the inclusion of angiogenesis inhibitors such as bevacizumab (BEV) into the previous schemes, with the better timing of these drugs, which is still controversial (4). Although the addition of bevacizumab to chemotherapy showed benefits in term of progression-free survival (PFS; refs. 5, 6), leading to its incorporation in the primary treatment of ovarian cancer, the advantage of each of the different schedules and doses of chemotherapy in combination with bevacizumab was recently argued (7, 8).

Clinical studies rely on late outcomes, with no direct measure of the antitumor activities of a treatment, e.g., the fraction of tumor cells killed. The different schemes have not been compared yet for such parameters of activity, in either clinical or preclinical studies. Although the difficulties of comparing several schemes/doses in a single study are probably insurmountable in the clinical setting, this is not impossible in preclinical studies. The present study demonstrates its feasibility, directly comparing single versus double versus triple treatments with DDP, PTX and BEV, conventional or dose-dense PTX, and two dose-dense levels of PTX, on the basis of different parameters of antitumor activity obtained from analysis of the growth curves of individual tumors. This required a reconsideration of the methods currently used to evaluate growth curves, like the popular T/C ratio at an arbitrary time, which catches only a small piece of the information conveyed by the curves and depends strongly on the growth rate of untreated tumors. A tumor growth curve during and after treatment reflects—not in a trivial way—the underlying drug-induced phenomena, like cell-cycle arrest, cell killing, and changes in the tumor microenvironment (including extracellular matrix, tumor vasculature, and all kinds of host cells; ref. 9), which intertwine with drugs' dose and time dependence to determine the growth curve. It is clear therefore that evaluation of the response at a single time point—as in most preclinical studies—only very partially exploits the available data and may be misleading. This is particularly true with targeted drugs, such as the angiogenesis inhibitors, which mainly show a cytostatic-long-lasting, rather than a cytotoxic, effect (10, 11).

Integration of data with mathematical modeling of the relevant processes in principle would allow to extract the full information conveyed by each growth curve and to frame the comparisons between treatment groups on a common and objective ground. Moving in that direction, in the present study, we reproduced the growth curves of individual tumors, in a wide preclinical trial, in terms of a computer model rendering the proliferation process, exploiting methods previously developed in our laboratory (12–16) to extract a few parameters measuring separately the main drug effects. The approach provided a new insight into the response to single and combined treatments and allowed an in-depth comparison of the different treatment options, contributing to the controversial issues on the use of dose-dense versus conventional PTX treatment with the addition of an angiogenesis inhibitor.

Six- to 8-week-old female NCr-nu/nu mice were from Envigo Laboratories. Mice were maintained under specific pathogen-free conditions, housed in isolated vented cages, and handled using aseptic procedures. Procedures involving animals and their care were conducted in conformity with institutional guidelines that comply with national (DLgs. 26/2014) and international (EEC Council Directive 2010/63) laws and policies. Animals studies were approved by the Italian Ministry of Health (decree no. 84-2013).

The human tumor xenograft MNHOC18, derived from a primary ovarian tumor in a patient with high-grade serous ovarian carcinoma, was recovered from frozen stocks and used within 5 to 6 mouse passages after establishment from the patient. This xenograft, transplanted subcutaneously in female NCr-nu/nu mice, was molecularly, biologically, and pharmacologically characterized and found similar to the original patient tumor (17).

MNHOC18 bearing mice were randomized at 100 to 300 mm³ tumor volume, 6 mice per group, in 12 treatment groups and 1 untreated group. PTX (Indena S.p.A.), dissolved in 50% Cremophor and 50% ethanol and diluted with saline, DDP (Sigma-Aldrich), and BEV (Avastin, Roche S.p.A.), dissolved in saline, were injected i.v. at different schedules and doses, as specified in Table 1. Measures of tumor volume were made twice a week with a Vernier caliper, and volume (V) was calculated as [length (mm) x width² (mm²)]/2, providing the growth curve relative to the volume at the start of treatment (V(t)/V(0)) for each individual tumor. The follow-up for tumor-free mice was 180 days, and the disappearance of the tumor observed macroscopically was then confirmed by histologic analysis of the residual tissue, if any. Each growth curve was then compared with the simulated growth curve obtained with the model described below.

In order to characterize the basal MNHOC18 proliferation, tumors from 6 untreated mice were collected, minced, and cells were suspended and fixed in 70% ethanol (18). Fixed cells were stained with propidium iodide for flow cytometric cell-cycle analysis (19) with a FACS Calibur (Becton Dickinson) and DNA histograms analyzed as described (20). DNA-PCNA analysis was made as previously described (21).

Statistical comparison between groups was made with one-way ANOVA with post hoc unpaired t test with Welch correction.

Proliferation of a cell population is the result of the contributions of cell cycling, quiescence, and cell loss. At any time, cells may be cycling, in G₁, S, G₂, or M phases, or quiescent. Each cell traverses the cell-cycle phases, with wide intercellular variability of cell-cycle times, and then divides and re-enters the cycle or become quiescent. At any time, some deaths naturally occur in a cell population. Our model (see Supplementary Methods A for a more detailed description; refs. 12, 16, 22) simulates these phenomena, on the basis of the theory of age-structured cell population models (23–25). The scheme of the model is shown in Fig. 1A: cells traverse the cell cycle (G₁, S, and G₂, or M phases) with variable cell-cycle times, divide, and some are assigned to a separate Q (G₀) compartment. The cell cycle is completely defined by the average and coefficient of variation of the three phase durations. pQ represents the probability that a newborn cell will eventually become quiescent, opposite to the cell propensity to stay cycling. Spontaneous cell death among quiescent cells is included in the model as parameter μ (loss rate). Simulation of the proliferation time course based on these parameters gives predictions of cell-cycle percentages, growth fraction (defined as the percentage of cycling cells), and the results of bromodeoxyuridine (BrdUrd) pulse-chase experiments that can be compared with actual flow cytometric or histology data from independent experiments of a specific cell line, providing a validated model of the proliferation of that line in the absence of treatment (basal proliferation model).

Following an anticancer treatment, a series of events strongly perturbs the normal equilibrium between cell-cycle flow, quiescence, and spontaneous death. Drug effects can be divided into cytostatic (causing cell-cycle arrest) and cytotoxic (leading to cell death). Proliferation after the start of treatment was modeled by introducing perturbative parameters into the basal model. We adapted the modular modeling framework developed for analysis of proliferation in vitro, maintaining the wide choice of options to simulate in detail different cytotoxic and cytostatic effects and their time courses (16). Several types of perturbations were preliminarily tested, eventually converging on a four-parameter model, trading between the need to provide separate information on the different phenomena in play while avoiding overparameterization. The four parameters of the final model were as follows: delay (Del), death rate (DR), dead cells' elimination rate (k), and quiescence probability (pQ).

The Del parameter is comprised between 0 (no effect) and 1, the latter indicating complete cell “freezing” of the cycle. Thus, Del measures the lengthening of the time to traverse the cell cycle (cytostatic effect), and was rated as: 0 = low [Del ≤ 0.25, corresponding to a minimal/null (≤25%) increase of cell-cycle time], 1 = mid (0.25 < Del < 0.75), 2 = high (Del ≥ 0.75, corresponding to a ≥330% increase of cell-cycle time). The time window of Del was limited to 3 days after each drug dose. Del acts in the short term (declining in the third day) after each dose, as cytostatic effects prevail over cytotoxic ones in the first days, after which the effects of cell killing became overwhelming and a simultaneous measure of delay would be unreliable.

DR is the fraction of cycling cells killed by a single dose in a given interval. A direct cytotoxic effect on quiescent cells was considered negligible. In the absence of experimental information on the timing of cell death, in the final model, DR was applied irrespective of the cell-cycle phase on the third day after each drug dose. Thus, DR measures the overall cell killing of a single dose as if all death events occurred after the period dominated by cytostatic effects, and any time dependence of the cell loss phenomenon is included in the subsequent elimination-rate parameter. For a proper comparison of the treatment groups, the fraction of cells spared by the whole treatment (three doses in conventional and seven in dose-dense schemes) was calculated as

(1 – DR)ⁿ, where “n” is the number of repeated doses.

The death process may last days, and dead cells are not immediately lost from the tumor site. Thus, the consequent decrease in tumor volume is detectable some days after the drug challenge. The lag between cell commitment to death and shrinkage was modeled with a parameter (k), representing the first-order rate of passage of a cell through three dying compartments before definitive loss (15, 26). In other words, k measures the rate of dissolution of dead cells. The average time lag between cell death and volume decrease (Lag(k), days) is directly computed from the value of k and was shown in place of k.

The pQ parameter, determining the balance between cycling and quiescent statuses, may be altered by the treatment, so its posttreatment value can differ from the basal value in the untreated tumor, as regrowth may occur in different environmental conditions. In the final model, the posttreatment pQ value was gradually reached a week after the end of treatment, to avoid overlap with the window dominated by cell killing, where the effects of repopulation would be undetectable. pQ = 0.5 would produce zero growth, and higher values would lead to shrinkage and eventually disappearance of the tumor.

In double and triple treatments, we did not separate the contributions of the single drugs, and the model parameters refer to the overall effect of DDP/PTX or BEV/DDP/PTX treatment, as for the single drugs. Preliminary attempts to model the effect of individual drugs, introducing specific parameters for each drug, led to overparameterization with multiple indistinguishable solutions and were abandoned.

The growth of untreated MNHOC18 xenografts was characterized by steady exponential growth and was modeled with the kinetic parameters shown in Fig. 1B, such us cell-cycle times, pQ, and spontaneous loss rate μ (Supplementary Methods A). The values of the parameters of the MNHOC18 basal in silico model were optimized to fit contemporaneously the measured tumor growth curve with its doubling time and other experimental data obtained ex vivo with different techniques: %PCNA-positive cells (giving the growth fraction as percentage of cycling cells), the percentages of cells in the phases of the cell cycle (%G1, %S, %G₂–M; Fig. 1B), and percentages of labeled cells obtained from a published BrdUrd pulse-chase experiment (Supplementary Fig. S1).

The time course of the whole proliferation process of each individual tumor in the treatment groups was reconstructed in silico on the basis of the basal (untreated) MNHOC18 model and four parameters (Del, DR, k, and pQ; Fig. 1C), miming cytostatic effect, cell killing, and quiescence-cycling interplay, as explained in Materials and Methods and Supplementary Methods B. This produces a simulated tumor growth curve as function of the values of the treatment parameters. The simulation was coupled to a standard optimization routine to fit the experimental growth curves and to obtain the parameters' values explaining the observed growth curve (Supplementary Methods C).

Figure 1D shows an example of fitting, where the experimental data (dots) are plotted with the reconstructed growth curve (continuous line) obtained with the values reported in the inset. The growth curve includes dying/dead cells not yet swept out of the tumor mass. As reference, the plot also shows the growth curve with only cells surviving after each drug dose (dashed line).

The experiment included 1 untreated and 12 treatment groups with 6 mice per group. Three PTX schemes were considered: PTX conventional (20 mg/kg Q6 × 3), PTX dose-dense-equi (8 mg/kg Q2 × 7) with similar total dose, PTX dose-dense-high (12 mg/kg Q2 × 7) with 50% higher dose; DDP and BEV were always given Q6 × 3 (Table 1).

Tumor volumes were measured longitudinally for up to 6 months. The tumor growth curves of individual mice, with the respective best fit, are shown in Fig. 2 (DDP, BEV, and BEV/DDP treatments), Fig. 3 (conventional and dose-dense single-drug PTX), Fig. 4 (DDP/PTX schemes), and Fig. 5 (three-drug BEV/DDP/PTX treatments), described in detail in the respective subchapters below. As a whole, the consistency of the fits demonstrates that the model was suitable and provided enough flexibility to fit properly all time courses measured.

DDP tended to delay tumor growth during the first week of treatment and hampered tumor growth up to 2 weeks after the end of treatment (Fig. 2A, left). All tumors regrew, although at a slower rate than untreated tumors. Modeling (Fig. 2B) indicated a variable delay, with low, intermediate, and high scores equally represented. A single DDP dose killed 58% of the cells on average, resulting in 8% of cells surviving the whole treatment. Regrowth occurred with increased pQ.

The response to BEV (Fig. 2A, middle) was more varied. Tumor growth was slow in the first 2 weeks, and then, when treatment stopped, tumor grew with a rate similar to untreated ones, subsequently the growth rate dropped in 4 of 6.

Best fits indicated an intermediate/high delay but no cell killing (Fig. 2B). The model fitted the time course of the four BEV-treated tumors with growth rate drop, assigning pQ values near the critical 0.5 point. In this situation, even small variations of pQ would radically affect the outcome from arrest to expansion and vice versa during the tumor time course, explaining the heterogeneity of the resulting growth curves.

During the first week of the combined BEV/DDP treatment, the tumor mass grew slowly, similarly to DDP alone, but after the second dose, the tumor growth was inhibited (Fig. 2A, right). Growth restarted shortly after the end of treatment, but none were definitely arrested. Modeling (Fig. 2B) indicated a delay similar to single DDP or BEV and 48% cell kill (DR), lower than with DDP (58%). pQ was higher than in the DDP group but somewhat lower than with BEV alone. All these observations suggest that with the combination BEV/DDP both the short-term effects of DDP and the-long term ones of BEV were present but were reduced by the other drug.

PTX reduced the tumor mass from the second week up to 1 week after the end of treatment, more steeply with dose-dense regimens (Fig. 3A).

The models of PTX response (Fig. 3B) indicated that initial delay was prevalently mild with PTX conventional, low with PTX dose-dense-equi, and high with PTX dose-dense-high.

A single dose killed 59% cells in PTX conventional (20 mg/kg) and 40% to 43% in the dose-dense schemes (8 mg/kg in PTX-equi or 12 mg/kg in PTX-high); the whole treatment left 8% of the surviving cells in PTX conventional and 3% in PTX dose-dense regimens.

PTX-induced cell killing occurred with a time lag to definitive cell loss of 8 days (Fig. 3B, Lag(k) panel), much faster than DDP (3 weeks: Fig. 2B). This suggests an effect of PTX in the tumor environment, resulting in a shorter time to eliminate dead cells, regardless of PTX schedule. pQ was 0.43 to 0.45, indicating a less fit environment for regrowth, although not approaching the critical 0.5 point.

In the DDP/PTX groups, the tumor showed shrinkage from the second week, and this continued after the end of treatment in all groups, reaching the nadir in the fourth week (Fig. 4A). Mice were cured only in the DDP/PTX dose-dense-high group, with 4 of 6 undetectable tumors at the end of the 6-month observation period.

The model indicated that the cytostatic effects (Fig. 4B, left) only slightly outperformed the single-drug treatments (Fig. 3B), with the highest effect observed in the DDP/PTX dose-dense-high group.

Concerning cytotoxic effects, cell killing was only slightly higher than that with single PTX in DDP/PTX conventional and DDP/PTX dose-dense-equi, whereas a higher increase was observed in DDP/PTX dose-dense-high. Cell killing of the complete course of treatment was similar in DDP/PTX dose-dense-equi and DDP/PTX conventional (3% surviving cells) and statistically higher in the DDP/PTX dose-dense-high group (less than 1%), despite a probable underestimation of the killing in the cured mice (see Supplementary Methods C).

pQ was similar in DDP/PTX conventional and DDP/PTX dose-dense-equi (Fig. 4B), not higher than with single PTX (Fig. 3B), whereas in the DDP/PTX dose-dense-high group, it was 0.46 and 0.48 in the two regrowing tumors.

Thus, the regrowth impairment in the DDP/PTX dose-dense-high group, adding to cell killing, gave a contribution decisive to the cure, with pQ values approaching 0.5 and possibly higher in the cured mice.

All mice were cured except two in the BEV/DDP/PTX conventional scheme (Fig. 5A).

Modeling indicated a high short-term cytostatic effect in all groups (Fig. 5B), stronger than that in the double treatment. Cell killing was also greater in all groups than the respective double DDP/PTX treatment. The cells surviving the whole treatment were 2% in the conventional and <0.1% in the dose-dense schemes. pQ reached values close to the 0.5 threshold in the two regrowing tumors.

Figure 6 shows simulations of the proliferation with the average of the best fit parameter values obtained in each experimental group and thus representative of the typical features of the response to each treatment regimen. BEV treatment was characterized by initial growth delay, no cell killing, and long-term maintenance of a slow growth rate, with pQ near the critical 0.5 point. DDP was cytotoxic, with slow cell death and elimination [Lag(k): 23 days] that prevented shrinkage, and a moderate long-term effect, with regrowth slower than untreated tumors. The combination of BEV and DDP led to a reduction of cytostatic effects, compared with either BEV or DDP, somewhat lower cell killing than with DDP, and lower quiescence probability than with BEV alone.

PTX was cytotoxic, with relatively fast dead cell elimination, leading to tumor shrinkage, progressively greater with PTX conventional, PTX dose-dense-equi, and PTX dose-dense-high. The regrowth of surviving cells between subsequent drug administrations (dotted line) was important in the conventional and negligible in the dose-dense schemes. This resulted in a lower nadir in the dose-dense scheme, with fewer surviving cells, which may mean a higher chance to cure. However, the absence of regrowth during the treatment per se would not have been enough to guarantee a long-term advantage, as suggested by the simulations shown in Supplementary Fig. S2.

With combined DDP/PTX treatments (Fig. 6, second row), the cytotoxic effect was higher than that with the single drugs. However, the performance of the combination was much lower than expected when applying the single drug killing rates of DDP and PTX together and independently, at least in the PTX conventional and PTX dose-dense-equi schemes (Supplementary Fig. S3). In the DDP/PTX dose-dense-high scheme, the concurrent potentiation of all effects in play resulted in the disappearance of the tumor, with DR high enough to reach a nadir well below the detection limit, and preventing regrowth of the few surviving tumor cells.

BEV/DDP/PTX treatment was superior to DDP/PTX, and all effects were potentiated compared with BEV/DDP or PTX alone, leading to cure with all schemes. The addition of BEV also led to an important increase of pQ. Long-term environmental change, particularly when the residual tumor burden is very low, is expected to play an important role in preventing relapse, possibly even more than the residual number of surviving cells.

Current clinical protocols for first-line treatment of advanced ovarian cancer are based on platinum compounds and PTX. Though novel combination chemotherapy regimens or dosing-schedule provide a more durable front-line response for ovarian cancer, the advantage of a weekly dose-dense regimen over the standard 3-week dosing schedule is still debated (1–4). Even more tricky is to appreciate the advantage of adding BEV to the different regimens (1, 4, 7). However, studies addressing the question of optimizing the combination of these drugs are difficult in a clinical setting. With this aim in mind, we made a deep comparative analysis of the clinical schedules in use, reproduced in a patient-derived ovarian cancer xenograft model, including additional arms for the study of single-drug treatments, an option obviously unavailable in clinic. Clinical trials considering PFS as end point have indicated that dose-dense PTX has similar efficacy to conventional schedule when the same cumulative dose is administered (2). Dose-dense provides 4 to 10 months of PFS advantage when the PTX cumulative dose was increased by 50% (1); this difference tends to disappear when BEV is included in the therapy regimen (4, 7). Our experimental data with the MNHOC18 xenograft go in the same direction, thus representing a prototype for studying the protocols in depth.

We analyzed the experimental growth curves of individual tumors with mathematical rendering of the proliferation process. The antiproliferative response to a treatment is complex, including cytostatic effects (i.e., delays in cell-cycle progression or arrest at checkpoints), the kinetics of recovery of drug-induced damage and re-entry in cycle, the induction of apoptosis or other death mechanisms, and interactions with the environment. Thorough studies of the antiproliferative effects of several drugs, including PTX and DDP, on ovarian cancer cells in vitro have been previously published by us (see ref. 14 and references therein). Those studies use complete time-course measures of absolute cell count and flow cytometric cell-cycle distributions after short treatments with a range of drug concentrations, integrated and interpreted by in silico dynamic models of the proliferation of the cell population. Moving to in vivo studies, the amount of information available is necessarily limited, and such detailed reconstruction of the response cannot be achieved. Nevertheless, DNA and BrdUrd measures are feasible in vivo, and in principle, similar investigations could be done, but are limited by the number of animals required and by the workload.

Here, we retrieved additional flow cytometric measures only in the untreated tumors, with the minimal experimental design needed for reconstruction of the proliferation process (basal model). Then, we set up a simplified model of drug effect looking for a trade-off between maintaining the distinction of the main mechanisms in play, the need for introducing schemes of repeated and combined treatments, the flexibility required to fit very different time-course profiles, and the need to avoid overparameterization. Because different effects may predominate in different time ranges, suitable time limitations were introduced, so that cytostatic effects act mainly for a short time after drug administrations, then cell death can occur, followed by dead cell removal, whereas the environmental effects act later, changing the interplay between cycling and quiescence. In the model adopted, the effects of treatment were described by a combination of four parameters miming the main mechanisms in the way they affect the basal proliferation model. This in silico model univocally fitted all time-course profiles of MNHOC18 with different schemes of treatment.

This analysis provided a number of new details, which were not derivable from a conventional growth curve analysis. First, a strong cytotoxic effect was induced by all PTX monotherapy schemes. Complete courses of treatment caused >90% cell killing with all schemes, but the dose-dense scheme was superior to the conventional one even at the equivalent total dose, leading to a lower nadir. This was due not only to the absence of growth between the closely repeated treatments but also to a higher overall cell killing. Reducing the interval between drug doses per se did not necessarily give a better long-term outcome than more widely spaced treatments, as suggested by in silico experiments (Supplementary Fig. S2). However, if there is a threshold of surviving cells, below which the tumor is unable to regrow, the dose-dense treatment had a higher chance to reach that limit and achieve a cure.

On the other hand, the relatively low single dose in the PTX dose-dense-equi scheme had a lower cytostatic effect than with PTX conventional. This points to the possibility that a low single dose in the dose-dense scheme might have a higher risk of ineffectiveness, particularly in less responding tumors. That is why a higher dose, like in the PTX dose-dense-high scheme considered here as well as in current clinical trials of dose-dense polychemotherapy after JGOG3016 (1), may be important or even crucial. In fact, PTX dose-dense-high was superior to the other schemes in both its cytotoxic and cytostatic effects in the MNHOC18 model.

Besides those direct effects, environmental changes are expected to play an important role to sustain lasting tumor shrinkage and eventually cure. In the MNHOC18 xenograft, the regrowth of tumor after treatment was slower than in untreated tumors, similar in PTX conventional and PTX dose-dense-equi and even slower with PTX dose-dense-high. This was caught in our in silico model by a higher pQ, the probability of entering a quiescent status. In principle, an increase of pQ can be interpreted in two ways: it might be due to selection of a slow-growing cell subset or to environmental changes hampering cell growth. In our opinion, the former hypothesis is less probable in this case, because the new selected cell population should have emerged in a relatively short time, similarly in all PTX schemes, also without extensive cell killing of the main fast-growing population. Instead, the effects of PTX on the microenvironment, (e.g., antiangiogenic and reduction of interstitial pressure or mobilization of myeloid cells; refs. 27–30) might make it less fit for proliferation and thus change the cycling-quiescence interplay.

DDP had cytostatic and cytotoxic effects of similar intensity to those of PTX conventional in MNHOC18, but pQ was modified less by the treatment, and the cell killing process up to final elimination of dead cells was slow, suggesting less impact on the environment than PTX. With DDP/PTX, both the cytostatic potency and cytotoxic potency of the two drugs were not fully exploited, and efficacy was much lower than expected (Supplementary Fig. S3), with little advantage over PTX alone. DDP/PTX conventional performed even worse than PTX dose-dense-high monotherapy. These findings are consistent with previous studies (31–33), which indicated that giving DDP and PTX at the same time is not advisable and suggested at least a 48-hour interval between the two drugs, with PTX first. Dose-dense schemes partially go in that direction, because the majority of PTX administrations are not in the same day with DDP. The addition of DDP to PTX dose-dense-high (but not to PTX dose-dense-equi) increased all effects enough to reach cure in the majority of mice, overcoming the small gap between the high efficacy of PTX dose-dense-high alone and the level where the tumor was not able to regrow and the mice were cured. In other words, the addition of DDP increased and consolidated the probability of cure in a situation where the efficacy was already quite high. In this MNHOC18 model, the DDP/PTX dose-dense-high treatment increased the overall killing to more than 99% and brought pQ near the critical 0.5 point, above which tumor expansion becomes impossible.

BEV monotherapy was not cytotoxic but caused a prolonged delay of cell cycling and an important increase of pQ. Although we cannot exclude that the effect of bevacizumab is underestimated due to its relative affinity to human VEGF and missing mouse-host derived VEGF, its profile of activity reflected the antiangiogenic action of the drug (34). BEV was poorly effective in hampering tumor expansion in the short term, but in two instances, tumor growth stopped or regressed at longer times, well after the end of treatment. In these cases, the model suggested that pQ reached and overcame the critical point, and cell divisions were not enough to counteract spontaneous deaths, causing continuous tumor shrinkage.

Although the simple combination BEV/DDP does not seem optimal, BEV provided a frank superiority to the BEV/DDP/PTX compared with the DDP/PTX scheme, leading to a cure also in the conventional group. In this case, BEV appears to play a role not only by hampering regrowth capacity, but also by acting on the cytotoxic effects of DDP and PTX, which were fully exploited in the triple treatment. The DDP/PTX dose-dense-high scheme already caused long-term inhibition of regrowth, making the contribution of BEV irrelevant, whereas DDP/PTX dose-dense-equi was not sufficient to inhibit regrowth, which was achieved by the addition of BEV. It is also possible that the antivascular effects of PTX and BEV synergize (35), an effect that is fostered by metronomic chemotherapy (36).

In conclusion, this study demonstrates the feasibility and utility of detailed analysis of the responses for studying treatment schemes. We describe how the different protocols affect tumor expansion, showing up significant differences and how and to what extent the addition of a second and third drug modifies the response to single-drug treatments.

Given the recent interest on evaluating dose-dense strategies of chemotherapy with the addition or not of antiangiogenic drugs, our study can help to get insight into mechanisms of drug interactions at the basis of recent clinical trials on ovarian cancer (1, 2, 4). As in clinic, we found that the PTX dose-dense was superior to the conventional scheme, but a fairly high individual dose was required to fully exploit the cell killing and regrowth inhibition induced by PTX. DDP contributed little to the efficacy in the DDP/PTX scheme, when the two drugs were given in the same day, suggesting the utility of shifting the DDP administration at the end of each cycle or exploring sequential treatments. In principle, DDP cytotoxicity could be fully exploited starting with two/three cycles of PTX dose-dense high, followed by cycles with DDP hitting cells surviving the PTX exposure, with a further advantage from the environmental changes induced by the PTX.

BEV was confirmed as providing a further advantage in both conventional and equivalent dose-dense schemes, strengthening regrowth inhibition, though this ceases to be profitable if it was already achieved with the dose-dense-high scheme.

No potential conflicts of interest were disclosed.

Conception and design: R. Giavazzi, P. Ubezio

Development of methodology: F. Falcetta, P. Ubezio

Acquisition of data (provided animals, acquired and managed patients, provided facilities, etc.): F. Bizzaro, E. D'Agostini

Analysis and interpretation of data (e.g., statistical analysis, biostatistics, computational analysis): F. Falcetta, F. Bizzaro, M.R. Bani, P. Ubezio

Writing, review, and/or revision of the manuscript: M.R. Bani, R. Giavazzi, P. Ubezio

Administrative, technical, or material support (i.e., reporting or organizing data, constructing databases): F. Falcetta, F. Bizzaro

Study supervision: R. Giavazzi, P. Ubezio

We thank Judith Baggott for editing this article.

This study was supported by grants from the Italian Association for Cancer Research (AIRC IG2016 n. 18853) and by Nerina and Mario Mattioli Foundation.

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.