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

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Author Manuscript Published OnlineFirst on September 26, 2017; DOI: 10.1158/0008-5472.CAN-17-1099 Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited.

Modeling cytostatic and cytotoxic responses to new treatment regimens for ovarian cancer

Francesca Falcetta1, Francesca Bizzaro2, Elisa D’Agostini2, Maria Rosa Bani2,

Raffaella Giavazzi2* and Paolo Ubezio1*

1 Biophysics Unit, Laboratory of Anticancer Pharmacology and 2 Laboratory of Biology and

Treatment of Metastasis, Department of Oncology, IRCCS-Istituto di Ricerche

Farmacologiche Mario Negri, Milan, Italy.

* These authors share last authorship

Running title: Decoding tumor growth with different treatment schemes

Keywords: cell proliferation, paclitaxel, cisplatin, bevacizumab, drug scheduling, mathematical modeling

Financial support: This study was supported by grants from the Italian Association for

Cancer Research (AIRC IG2016 n. 18853) and by Nerina and Mario Mattioli Foundation

Correspondence to: Dr. Paolo Ubezio Istituto di Ricerche Farmacologiche "Mario Negri", Via La Masa 19, 20156 Milano, Italy Phone:+39-02-39014438; Fax:+39-02-3546277 E-mail: [email protected]

ABSTRACT

The margin for optimizing polychemotherapy is wide, but a quantitative comparison of current and new protocols is rare even in preclinical settings. In silico reconstruction of the proliferation process and the main perturbations induced by treatment provides insight into the complexity of drug response and grounds for a more objective rationale to treatment schemes.

We analysed a 12 treatment groups trial on an ovarian cancer xenograft, reproducing current therapeutic options for this cancer including one-, two- and three-drug schemes of cisplatin (DDP), bevacizumab (BEV) and paclitaxel (PTX) with conventional and two levels

(“equi” and “high”) of dose-dense schedules. All individual tumor growth curves were decoded via separate measurements of cell death and other antiproliferative effects, gaining fresh insight in the differences between treatment options.

Individual drug treatments were cytostatic, but only DDP and PTX were also cytotoxic.

After treatment, regrowth stabilized with increased propensity to quiescence, particularly with BEV. More cells were killed by PTX dose-dense-equi than with PTX conventional, but with the addition of DDP cytotoxicity was similar and considerably less than expected from that of individual drugs. In the DDP/PTX dose-dense-high scheme both cell death and regrowth impairment were intensified enough to achieve complete remission and addition of BEV increased cell death in all schemes.

The results support the option for dose-dense PTX chemotherapy with active single doses, showing the relative additional contribution of BEV, but also indicate negative drug interactions in concomitant DDP/PTX treatments, suggesting that sequential schedules could improve antitumor efficacy.

INTRODUCTION

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 of 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 total dose equivalent (2) others 50% higher (3) respect to the conventional one.

However, clinical studies aimed at optimizing the schedule are rare, the actual choices 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). While the addition of bevacizumab to chemotherapy showed benefits in term of progression-free survival (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 vs. double vs. 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 kill and changes in the tumor microenvironment (including extracellular matrix, tumor vasculature and all kinds of host cells (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 in-depth comparison of the different treatment options, contributing to the controversial issues on the use of dose-dense vs. conventional PTX treatment with the addition of an angiogenesis inhibitor.

MATERIALS AND METHODS Experimental procedures

Six- to eight-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 5-6 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 100-300 mm3 tumor volume, six mice per group, in 12 treatment groups and one 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 intravenously (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 histological 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 six untreated mice were collected, minced and cells 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, San Jose, CA) and DNA histograms analysed as described

(20). DNA-PCNA analysis was made as previously described (21).

Statistical comparison between groups were made with one-way ANOVA (ANalysis Of

VAriance) with post-hoc unpaired t test with Welch's correction.

Computer simulation of proliferation and drug effects

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, then divides and re-enters the cycle or become quiescent. At any time some deaths naturally occur in a cell population. Our model (12,16,22) (see Supplementary Methods A for a more detailed description) 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

Figure 1a: cells traverse the cell cycle (G1, S and G2M 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 (BrdU) 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

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 over-parametrization. The four parameters of the final model were: Delay (Del), Death rate (DR), Dead cells elimination rate (k) and Quiescence probability (pQ).

Delay (Del, cytostatic effect)

The Delay 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 three days after each drug dose. Del acts in the short term (declining in the third day) after each dose, cytostatic prevailing over cytotoxic effects in the first days, after which the effects of cell killing became overwhelming and a simultaneous measure of delay would be unreliable.

Death rate (DR, cytotoxic effect)

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

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(three doses in conventional and seven in dose-dense schemes) was calculated as

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

Dead-cells elimination rate (k)

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.

Quiescence probability (pQ, long term effects)

The pQ parameter, determining the balance between cycling and quiescent statuses, may be altered by the treatment, so its post-treatment value can differ from the basal value in the untreated tumor, as regrowth may occur in different environmental conditions. In the final model the post-treatment 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

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RESULTS

Proliferation of MNHOC18 xenograft

The growth of untreated MNHOC18 xenografts was characterized by steady exponential growth and was modeled with the kinetic parameters shown in Figure 1b, such us cell cycle times, quiescence probability (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, %G2M) (Figure 1b) and percentages of labeled cells obtained from a published BrdU pulse-chase experiment (Supplementary

Figure S1).

Measuring the response to treatment

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)

MNHOC-18 model and four parameters (Del, DR, k, pQ) (Figure 1c) miming cytostatic effect, cell kill 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 one untreated and twelve treatment groups with six mice per group. Three PTX schemes were considered: PTX conventional (20 mg/kg Q6x3), PTX dose-dense-equi (8 mg/kg Q2x7) with similar total dose, PTX dose-dense-high (12 mg/kg

Q2x7) with 50% higher dose; DDP and BEV were always given Q6x3 (Table 1).

Tumor volumes were measured longitudinally for up to six months. The tumor growth curves of individual mice, with the respective best fit, are shown in Figure 2 (DDP, BEV and BEV/DDP treatments), Figure 3 (conventional and dose-dense single-drug PTX),

Figure 4 (DDP/PTX schemes) and Figure 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, BEV and BEV/DDP treatments

DDP tended to delay tumor growth during the first week of treatment and hampered tumor growth up to two weeks after the end of treatment (Figure 2a, left panels). All tumors regrew, although at a slower rate than untreated tumors. Modeling (Figure 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 (Figure 2a, middle panels) was more varied. Tumor growth was slow in the first two weeks, then, when treatment stopped, tumor grew with a rate similar to untreated ones, subsequently the growth rate dropped in 4/6.

Best fits indicated an intermediate/high delay but no cell killing (Figure 2b). The model fitted the time course of the four BEV-treated mice mentioned 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 (Figure

2a, right panels). Growth restarted shortly after the end of treatment, but none were definitely arrested. Modeling (Figure 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 single-drug treatment

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

The models of PTX response (Figure 3b) indicated that initial delay was prevalently mid with PTX conventional, low with PTX dose-dense-equi, high with PTX dose-dense-high.

A single dose killed 59% cells in PTX conventional (20 mg/kg) and 40%-43% in the dose- dense schemes (8 mg/kg in PTX -equi or 12 mg/kg in PTX-high); the whole treatment leaving 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 eight days (Figure

3b, Lag(k) panel), much faster than DDP (three weeks: Figure 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 0.43-0.45, indicating a less fit environment for regrowth, although not approaching the critical 0.5 point.

DDP/PTX combined treatments

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

(Figure 4a). Mice were cured only in the DDP/PTX dose-dense-high group, with 4/6 undetectable tumors at the end of the six-month observation period.

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

As concerns cytotoxic effects, cell kill was only slightly higher than with single PTX in

DDP/PTX conventional and DDP/PTX dose-dense-equi, while a higher increase was observed in DDP/PTX dose-dense-high. Cell kill 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 underestimate of the kill in the cured mice (see Supplementary Methods C). pQ was similar in DDP/PTX conventional and DDP/PTX dose-dense-equi (Figure 4b), no higher than with single PTX (Figure 3b), while 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 kill, gave a contribution decisive to the cure, with pQ values approaching 0.5 and possibly higher in the cured mice.

BEV/DDP/PTX three-drug treatments

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

Modeling indicated a high short-term cytostatic effect in all groups (Figure 5b), stronger than in the double treatment. Cell kill 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.

Representative models of treatment and alternative schedules

Figure 6 shows simulations of the proliferation with the average of the best fit parameter values obtained in each experimental group, 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 to 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 after each drug administration (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 Figure S2.

With combined DDP/PTX treatments (Figure 6, second row), the cytotoxic effect was higher than with the single drugs. However, the performance of the combination was much lower than expected 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 Figure 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 to 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.

DISCUSSION

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 three-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 progression-free survival (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 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 (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

Downloaded from cancerres.aacrjournals.org on September 25, 2021. © 2017 American Association for Cancer Research. Author Manuscript Published OnlineFirst on September 26, 2017; DOI: 10.1158/0008-5472.CAN-17-1099 Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. 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 BrdU 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 over-parameterization. Because different effects may predominate in different time ranges, suitable time limitations were introduced, so that cytostatic effects act mainly for short time after drug administration, then cell death occurs, followed by dead cell removal, while 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 kill 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 Figure 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.

Beside 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 (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 and cytotoxic potency of the two drugs was not fully exploited, and efficacy was much lower than expected (Supplementary Figure 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 suggesting at least a 48h 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 kill 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 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.

While the simple combination BEV/DDP does not seem optimal, BEV provided a frank superiority to the BEV/DDP/PTX compared to the DDP/PTX scheme, leading to cure also in the conventional group. In this case, BEV appears to play a role not only by hampering

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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 treatment schemes. We describe how the different protocols impact on 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.

Acknowledgments

We thank Judith Baggott for editing the manuscript.

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Table 1. Treatment schedule.

Nr. Nr. Day°: 1 2 3 4 5 6 7 8 9 10 11 12 13 mice cured^ Untreated control 6 0

DDP (3mg/kg) X X X 6 0

BEV (5mg/kg) X X X 6 0

PTXconv (20mg/kg) X X X 6 0

PTXequi (8mg/kg) X X X X X X X 6 0

PTXhigh (12mg/kg) X X X X X X X 6 1

BEV/DDP X X X 6 0

DDP/PTXconv X X X 6 0

DDP/PTXequi X P P X P P X 5* 0

DDP/PTXhigh X P P X P P X 6 4

BEV/DDP/PTXconv X X X 6 4

BEV/DDP/PTXequi X P P X P P X 6 6

BEV/DDP/PTXhigh X P P X P P X 6 6

°Time from randomization. X: all drugs of the scheme. P: PTX only, in dose-dense schedules of combined treatment. ^ Cured: mice surviving at the end of six months follow up without detectable tumor at necroscopy. * One of the six mice in this group died for causes unrelated to treatment and was skipped from the analysis.

Legends to Figures

Figure 1. Scheme of the proliferation model and data fitting. a: Scheme of the basal proliferation model for untreated cells with the associated model parameters: averages (T̅ G1, T̅ S, T̅ G2M ) and coefficient of variation (CVG1/S/G2M, not shown) of phase durations, quiescence probability (pQ) and loss rate (μ). b: Parameter values of the MNHOC18 basal in silico model predicting experimental measures (mean ± SE, n=6) of the tumor growth curve, doubling time, growth fraction (%PCNA positive cells), cell cycle percentages (by DNA flow cytometry). The basal MNHOC18 in silico model was also consistent (Supplementary Figure S1) with the results of a pulse-chase experiment previously reported by our group (18). c: Scheme of the time course of the main perturbations induced by treatments and of the four associated model parameters: Del measures the lengthening of the time to traverse the cell cycle (cytostatic effect); DR is the fraction of cells killed by a single dose; k measures the rate of dissolution of dead cells, which were slowly removed from the tumor mass; pQ is the fraction of cells entering quiescence, possibly changed in the regrowing tumor after treatment respect to the basal value. d: Example of fitting of the volume of a treated tumor (given seven doses of PTX in the dose-dense-high scheme) and best-fit parameters. k was translated in terms of the average time dead cells remained in the tumor mass (Lag(k), in days). Dots: experimental data (tumor volume measured with calipter); continuous line: fitted time course of the number of cells in the tumor (in relation to the start of treatment); dashed line: time course of the cells surviving the treatment.

Figure 2. DDP, BEV and BEV/DDP treatments: time courses of tumor volumes and best fit parameters. a: Time courses of individual tumor volumes measured over time with a Venier caliper

(circles) in the DDP (D), BEV (B) and BEV/DDP (B/D) groups, with best fit tumor growth

Downloaded from cancerres.aacrjournals.org on September 25, 2021. © 2017 American Association for Cancer Research. Author Manuscript Published OnlineFirst on September 26, 2017; DOI: 10.1158/0008-5472.CAN-17-1099 Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. curves (continuous lines, with their coefficient of determination R2) and the relative number of cells surviving treatment (dotted line). b: Measures of cytostatic, cytotoxic and long-term effects in the three treatment groups. Cytostatic effect (left panel) was quantified in terms of the frequency of the Del score, cytotoxic effect (middle panels) was quantified

(mean ± SE) in terms of i) the percent of killed cells for a single dose (DR), ii) the percent of cells surviving the whole treatment, and iii) Lag(k); long-term effect (right panel) was quantified in terms of pQ, (mean ± SE) of late-regrowing tumors, with the bold and dashed horizontal lines indicating pQ (mean ± SE) in untreated tumors.

* p <0.05, ** p <0.01, *** p <0.001.

Figure 3. Single drug PTX treatments: time courses of tumor volumes and best fit parameters. a: Time courses of the measured individual tumor volumes (circles), in the single drug PTX groups: PTX conventional (Pc), PTX dose-dense-equi (Pe) and PTX dose-dense-high

(Ph), with best fit tumor growth curves (continuous lines) and the relative number of cells surviving treatment (dotted lines). b: Measures of cytostatic, cytotoxic and long-term effects in the three treatment groups. See legend of Figure 2 for details.

Figure 4. DDP/PTX treatments: time courses of tumor volumes and best fit parameters. a: Time courses of the measured individual tumor volumes (circles), in the DDP/PTX groups: DDP/PTX conventional (D/Pc), DDP/PTX dose-dense-equi (D/Pe) and DDP/PTX dose-dense-high (D/Ph), with best fit tumor growth curves (continuous lines) and the relative number of cells surviving treatment (dotted lines). b: Measures of cytostatic, cytotoxic and long-term effects in the three treatment groups. See legend of Figure 2 for details.

Figure 5. BEV/DDP/PTX treatments: time courses of tumor volumes and best fit parameters.

Time courses of the measured individual tumor volumes (circles), in the BEV/DDP/PTX groups: BEV/DDP/PTX conventional (B/D/Pc), BEV/DDP/PTX dose-dense-equi (B/D/Pe) and BEV/DDP/PTX dose-dense-high (B/D/Ph), with best fit tumor growth curves

(continuous lines) and the relative number of cells surviving treatment (dotted lines). b:

Measures of cytostatic, cytotoxic and long-term effects in the three treatment groups. See legend of Figure 2 for details.

Figure 6. Comparative overview of the response to all treatments.

Typical growth curves (continuous lines) in each treatment group, obtained with the average parameter values (indicated in the insets) given by the best fits of the measured volumes of individual tumor. Dotted lines represent the relative number of cells surviving treatment.

Modeling cytostatic and cytotoxic responses to new treatment regimens for ovarian cancer

Francesca Falcetta, Francesca Bizzaro, Elisa D'Agostini, et al.

Cancer Res Published OnlineFirst September 26, 2017.

Updated version Access the most recent version of this article at: doi:10.1158/0008-5472.CAN-17-1099

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