Phenotypic diversity in pancreatic ductal adenocarcinoma (PDAC) results in a variety of treatment responses. Rapid autopsy studies have revealed a subgroup of PDAC patients with a lower propensity to develop metastatic disease, challenging the common perception that all patients die of widely metastatic disease, but questions remain about root causes of this difference and the potential impact on treatment strategies. In this study, we addressed these questions through the development of a mathematical model of PDAC progression that incorporates the major alteration status of specific genes with predictive utility. The model successfully reproduced clinical outcomes regarding metastatic patterns and the genetic alteration status of patients from two independent cohorts from the United States and Japan. Using this model, we defined a candidate predictive signature in patients with low metastatic propensity. If a primary tumor contained a small fraction of cells with KRAS and additional alterations to CDKN2A, TP53, or SMAD4 genes, the patient was likely to exhibit low metastatic propensity. By using this predictive signature, we computationally simulated a set of clinical trials to model whether this subgroup would benefit from locally intensive therapies such as surgery or radiation therapy. The largest overall survival benefit resulted from complete resection, followed by adjuvant chemoradiation therapy and salvage therapies for isolated recurrence. While requiring prospective validation in a clinical trial, our results suggest a new tool to help personalize care in PDAC patients in seeking the most effective therapeutic modality for each individual. Cancer Res; 77(12); 3325–35. ©2017 AACR.

Major Findings
  • The mathematical model was feasible in analyzing major clinical features in two independent cohorts.

  • A patient is likely to exhibit low metastatic propensity if the primary tumor contains a small fraction of cells (<108 cells) with KRAS and an additional alteration of CDKN2A, TP53, and SMAD4 genes.

  • The largest overall survival benefit resulted in patients with low metastatic propensity who received: (i) complete resection; (ii) adjuvant chemoradiation therapy; and (iii) salvage therapies for isolated recurrence.

Quick Guide to Equations and Assumptions
Major Assumptions of the Model
  • We designed a stochastic model of PDAC progression, incorporating heterogeneous growth rates of the primary tumor cells according to the accumulation of specific genetic alterations—KRAS mutation, CDKN2A deletion/mutation, TP53 deletion/mutation, and SMAD4 deletion/mutation (Fig. 1B and C; Supplementary Fig. S1).

  • The model considers four cell types (Fig. 1C): ALTkras cells (blue) have KRAS mutations. They give rise to ALTtwo cells (yellow) when combined with their first additional alteration in CDKN2A, TP53, or SMAD4 genes at genetic alteration rate u. ALTtwo cells give rise to ALTmulti cells harboring the second additional alteration in CDKN2A, TP53, or SMAD4 genes at rate u (orange). ALTkras, ALTtwo, and ALTmulti cells exist in primary site. ALTtwo and ALTmulti cells have the potential to metastasize to other organs and generate MET cells (brown) at metastatic rate q. The growth and death rates of each cell type are a0 and b0 (ALTkras); a1 and b1 (ALTtwo); a2 and b2 (ALTmulti); and a3 and b3 (MET), respectively.

  • Parameter values used in the simulations are based on the estimates with clinical data in previous studies (Table 1).

  • Diagnostic and treatment criteria in the model follow the clinical practice guidelines of PDAC by the National Comprehensive Cancer Network.

Equations
Stochastic Tumor Progression Model

The stochastic simulation based on the model is performed by determining: (i) the probabilities of all possible events and (ii) the timing of each event. The total rate of all possible events during PDAC progression, Γ, is given by Γ = (a0+ b0)w+(a1+b1)x+(a2+b2)y+Σ(a3+b3)zi. Here, w, x, y, and Σzi are the cell numbers of ALTkras, ALTtwo, ALTmulti, and MET cells, respectively. zi represents the number of metastatic tumor cells at i-th metastatic sites. The probability that the number of ALTkras, ALTtwo, ALTmulti cells, and MET cells at the i-th metastasis increases by one, respectively, is given by:

formula

The probability that a metastatic site increases by one by exporting an ALTtwo or ALTmulti cell, respectively, is given by:

formula

The probability that the numbers of ALTkras, ALTtwo, ALTmulti, and MET cells decrease by one, respectively, is given by:

formula

The waiting time of each event is given by an exponential distribution with mean 1/Γ. Cancer starts from one ALTkras cell, w = 1, and no ALTtwo, ALTmulti, or MET cells, x = y = zi = 0 for all i. The total number of tumor cells within a body is given by w+x+yzi. This procedure of the stochastic simulations is based on standard Gillespie's algorithm (1).

Pancreatic ductal adenocarcinoma (PDAC) is one of the most commonly diagnosed cancers, in which the average annual percentage change predicts that it will become the second leading cause of cancer-related death in the United States by 2020 (2). It is among the deadliest of all solid malignancies with an overall 5-year survival rate no greater than 8% (3). Only up to 20% of patients undergo a potentially curative surgical resection, and even among this favorable subset of patients, results of surgery alone are poor, with an 80% or higher rate of recurrence. Patients with PDAC may receive surgery, chemotherapy (CTx), radiation therapy (RTx), and/or combined chemotherapy and radiation therapy (CRTx), but progression is common and it is difficult to reach a consensus-based clinical decision (4–8). One of the major difficulties underlying the complexity in clinical decision-making in PDAC is the lack of reliable factors to predict patterns of failure and treatment response. Therefore, oncologists are unable to identify which patients would benefit from each regimen.

A recent important clinical implication was the discovery of a subgroup of patients with a propensity to have a low burden of metastatic disease (Fig. 1A; ref. 9). These patients are defined as having “oligometastatic” disease and the cause of death is often due to destructive local progression or recurrence of disease (9). Several other studies have also supported this notion by demonstrating that 12% to 40% of patients showed a locally predominant progression pattern (10, 11). Such an observation defies conventional recognition that PDAC patients universally die as a result of widespread metastasis and sparked our interest in identifying patients with a local versus systemic profile of disease progression (12). We sought to explore the hypothesis that the subgroup destined to manifest oligometastatic disease may exhibit a more favorable response to intensive local therapy such as CRTx in the perioperative setting (4, 5). Likewise, surgical intervention or definitive/salvage RTx may benefit patients with established oligometastatic disease once it recurs (6, 7).

Figure 1.

Disease progression patterns and genetic features in PDAC, and a schematic of the mathematical model. A, Computed tomography images demonstrating representative spreading patterns at a terminal stage in PDAC. Nonmetastatic tumor (top left), large size of solitary metastasis (top right), medium size of several metastases (bottom left), and small size of multiple metastases (bottom right). B, Mutational frequency in PDAC. KRAS, CDKN2A, TP53, and SMAD4 genes are notably altered in PDAC. Other genes are altered at low frequencies. C, The mathematical framework of PDAC progression. See Major Assumptions of the Model and mathematical model of PDAC progression.

Figure 1.

Disease progression patterns and genetic features in PDAC, and a schematic of the mathematical model. A, Computed tomography images demonstrating representative spreading patterns at a terminal stage in PDAC. Nonmetastatic tumor (top left), large size of solitary metastasis (top right), medium size of several metastases (bottom left), and small size of multiple metastases (bottom right). B, Mutational frequency in PDAC. KRAS, CDKN2A, TP53, and SMAD4 genes are notably altered in PDAC. Other genes are altered at low frequencies. C, The mathematical framework of PDAC progression. See Major Assumptions of the Model and mathematical model of PDAC progression.

Close modal

The genetic features of PDAC genomes are well-defined by four frequently altered “driver” genes, namely KRAS, CDKN2A (p16), TP53, and SMAD4 (Fig. 1B). KRAS mutations occur at an early stage of carcinogenesis and are followed by genetic alterations in CDKN2A, TP53, and SMAD4 at late stages (12–14). Genetic alterations that deregulate core signaling pathways are also detected, albeit at low frequencies (15–17). Metastatic propensity of the alterations in the four genes has also been intensively explored; CDKN2A, TP53, and SMAD4 have been reported to drive metastasis in PDAC (Supplementary Table S1). On the basis of these evidence, experimental regimens based on the molecular profile of PDAC patients have been under investigation to achieve personalized care (18, 19). For example, the potential role of SMAD4 as a biomarker to stratify patients for intensive local therapy was being investigated in a clinical trial (RTOG 1201: http://www.rtog.org).

To address this issue, we hypothesized that mathematical modeling based on the genetic signatures of PDAC patients may predict treatment response and inform clinical decision-making. In recent decades, mathematical models have succeeded in identifying optimal treatments in colorectal, brain, breast, and prostate cancer (20–24). In PDAC, previous studies provided a fundamental method of predicting treatment progression with mathematical modeling; however, the study did not distinguish between the two distinct phenotypes of oligometastatic and widely metastatic diseases and, moreover, did not propose practical information for guiding management in each individual (9, 25). Herein, the objectives of this study were to identify favorable responders to intensive local treatments and to suggest personalized care that would lead to improved survival in this subgroup. By adopting parameters estimated in the previous study, we analyzed the dynamics of PDAC progression based on a mathematical model (25). The mathematical model was carefully validated with two independent clinical cohorts. By conducting computational clinical trials, our study results suggest that adjuvant CRTx and salvage therapies for an isolated recurrence would benefit a subset of patients destined to manifest oligometastatic disease. This study provides new insight into the complexity of clinical judgment and decision-making in this devastating disease.

Patients and tissue samples

We used two independent databases with a total number of 269 PDAC patients to validate whether our mathematical model reproduced PDAC progression including sequential accumulations of genetic alteration. The first database contained information on 106 PDAC patients who underwent potentially curative surgery between 2000 and 2011 at the Kagawa University Hospital and Social Insurance Ritsurin Hospital in Japan (Supplementary Table S2; ref. 26). The majority (99%) of patients had resectable disease. The alteration status of CDKN2A, TP53, and SMAD4 in each tumor was immunohistochemically tested (Supplementary Materials S1 and Supplementary Fig. S1) and clinical outcomes were collected. The concordance of immunohistochemistry and genetic sequencing in CDKN2A, TP53, and SMAD4 genes were shown in Supplementary Table S3. The data were approved by the Kagawa University Review Board. The second database from Johns Hopkins Hospital contained 163 PDAC patients who underwent surgery between 2008 and 2015 (Supplementary Table S2). These patients had borderline resectable (64%) or locally advanced, unresectable (36%) disease; therefore, patients received neoadjuvant therapy prior to surgery. The data were approved by the Johns Hopkins Institutional Review Board. The baseline characteristics of patients' ages, tumor sizes, and clinical stages were measured at a time before upfront surgery in patients with resectable disease and at a time before neoadjuvant therapies in patients with borderline resectable or locally advanced disease who received them. The study design is shown in Supplementary Fig. S2. Note that these cohorts were not used for any parameter estimations in our model. Instead, all parameter values including treatment efficacy were obtained from the independent cohorts, that is, cohorts from the previous autopsy program in PDAC or review of the literature (Table 1; refs. 25, 27–30).

Table 1.

Description and values of the mathematical model parameters

Biological processSymbolParameterReference
Growth rate of cancer cells a0, a1, a2, a3 0.11, 0.16, 0.24, 0.58 (25) 
Death rate of cancer cells b0, b1, b2, b3 Growth rate × 1/100 (25) 
Number of cancer cells at diagnosis M1 10N(9.47,0.59)a (25) 
Number of cancer cells at death M2 1011.2 (25) 
Alteration rate in specific genes u 6.31 × 10−5 (25) 
Metastatic rate q 6.31 × 10−7 (25) 
Resection rate by surgery ϵ 1.0 × 10−5 (25) 
Rate to reduce growth rate of cell by CTx γ 0.7 (25) 
Rate to reduce cells by RTx  e(ωD+ξD2) (29) 
Rate to increase growth rate of cell by immunosuppression α (28) 
Immunosuppresion duration  1 month (30) 
Biological processSymbolParameterReference
Growth rate of cancer cells a0, a1, a2, a3 0.11, 0.16, 0.24, 0.58 (25) 
Death rate of cancer cells b0, b1, b2, b3 Growth rate × 1/100 (25) 
Number of cancer cells at diagnosis M1 10N(9.47,0.59)a (25) 
Number of cancer cells at death M2 1011.2 (25) 
Alteration rate in specific genes u 6.31 × 10−5 (25) 
Metastatic rate q 6.31 × 10−7 (25) 
Resection rate by surgery ϵ 1.0 × 10−5 (25) 
Rate to reduce growth rate of cell by CTx γ 0.7 (25) 
Rate to reduce cells by RTx  e(ωD+ξD2) (29) 
Rate to increase growth rate of cell by immunosuppression α (28) 
Immunosuppresion duration  1 month (30) 

aThe exponent is normally distributed with mean 9.47 and variance 0.59.

Mathematical model of PDAC progression

We designed a mathematical model of PDAC progression in accordance with the alteration status of individuals (Fig. 1C). We considered heterogeneous growth rates of the primary pancreatic tumor cells according to the accumulation of specific genetic alterations to include KRAS mutation, CDKN2A deletion/mutation, TP53 deletion/mutation, and SMAD4 deletion/mutation. These four genes are known as the most frequent targets of genetic alterations in PDAC (Fig. 1B; refs. 15, 16, 31). In the model, three types of cells having different alteration status exist within the primary site. On the basis of the evidence that activating KRAS mutation is found in >96% of pancreatic intraepithelial neoplasms (PanIN; refs. 13, 14), the most common precursor to PDAC, we assume that tumor-initiating cells (ALTkras) in the model already had genetic alteration in KRAS (Fig. 1C). During clonal expansion, ALTkras cells give rise to a cell harboring the first additional alteration of CDKN2A, TP53, or SMAD4 genes (ALTtwo). Eventually, ALTtwo cells give rise to a cell harboring the second additional alteration of CDKN2A, TP53, or SMAD4 genes (ALTmulti). On the basis of the evidence in the Japan cohort, the preferential order of alteration in accumulating genetic alterations among the three genes was not considered (Supplementary Fig. S3). ALTtwo and ALTmulti cells have the potential to metastasize from the primary tumor to other organs such as lymph nodes, peritoneum, liver and lung, and generate MET cells (Supplementary Table S1). Patients are diagnosed and dead when the total number of cells reach M1 and M2, respectively (25). We expect that all of the four cell types contribute to M1 because cases with unknown primary disease may be diagnosed. Systemic symptoms in those patients may more reflect the sum of all cancer cells than the size of the largest tumor mass (32). All parameter values used in our model were obtained from the previous autopsy program in PDAC (Table 1; refs. 25, 27–30). See Quick Guide to Equations and Assumptions and Supplementary Materials S3 and S4 for details of the computational framework.

Statistical analysis

Regarding the clinical cohorts, overall survival (OS) was defined as the time from the primary surgery to death attributed to any cause. Patients were censored on the date of the last follow-up visit. Regarding the computational trial cases, OS was calculated from the date of diagnosis and each case was followed until death or censored at 60 months. The survival rates were estimated using the Kaplan–Meier method. The log-rank test was performed to test the significance of survival differences between the groups. Cox proportional hazards model was used to calculate hazard ratios. The Mann–Whitney U test was used to test whether two samples were from the same distributions. An association between two categorical variables was tested by Pearson's chi-square test. All P values less than 0.05 were considered to be statistically significant. All statistical analyses were performed using R, version 3.3.0 (R Foundation for Statistical Computing, Vienna, Austria).

Computational clinical trial

To test whether patients destined to manifest oligometastatic disease obtain a greater survival benefit from locally intensive treatments, we designed computational clinical trials. We explored four scenarios: (i) adjuvant CRTx after surgery; (ii) neoadjuvant CRTx; (iii) surgical intervention; and (iv) salvage CRTx for the postoperative recurrent tumor. An advantage of this computational trial is the ability to evaluate and compare the effects of various treatments on the exact same case (patient). See Supplementary Material S5 for the study design of the computational clinical trials.

Validation of the model with clinical data

We tested whether the model recapitulated the PDAC progression by comparing the simulation outcomes from the model with the corresponding clinical outcomes from Japan and US cohorts (Fig. 2; ref. 26). The simulation cases in the model are denoted as Cohort A, and the clinical cohorts from Japan and United States as Cohorts B and C, respectively, in the following section.

Figure 2.

The predictions of the mathematical framework and the results of clinical data. A–F, Clinical outcomes and characteristics in three cohorts are shown. Simulation cohort (Cohort A), Japan cohort (Cohort B), and US cohort (Cohort C) are shown by red, blue, and green, respectively. Survival curves of all cases (A); with one (dashed line), two (dotted line), and more than two altered genes (line; B); with oligometastatic disease (PToligo; dashed line), and widely metastatic disease (PTwidely; line; C); and at T1 (dashed line) and T2-4 stages (line) per TNM classification (D) are shown. The distribution of the number of detectable metastatic sites at death (E) and those of primary tumor cells at diagnosis (F) are shown. Parameters used were a0 = 0.11, a1 = 0.16, a2 = 0.24, a3 = 0.58, b0 = 0.0011, b1 = 0.0016, b2 = 0.0024, b3 = 0.0058, M1 = 10N(9.47,0.59), M2 = 1011.2, u = 6.31 × 10−5, q = 6.31 × 10−7, ϵ = 10−5, γ = 0.7, α = 3.0. Here, N(9.47, 0.59) represents the normal distribution with mean 9.47 and variance 0.59. The number of simulation cases were 256 in Cohort A. Table shows P values between Cohort A and each of Cohorts B and C by log-rank test for panels A–D and by Mann–Whitney U test for E and K.

Figure 2.

The predictions of the mathematical framework and the results of clinical data. A–F, Clinical outcomes and characteristics in three cohorts are shown. Simulation cohort (Cohort A), Japan cohort (Cohort B), and US cohort (Cohort C) are shown by red, blue, and green, respectively. Survival curves of all cases (A); with one (dashed line), two (dotted line), and more than two altered genes (line; B); with oligometastatic disease (PToligo; dashed line), and widely metastatic disease (PTwidely; line; C); and at T1 (dashed line) and T2-4 stages (line) per TNM classification (D) are shown. The distribution of the number of detectable metastatic sites at death (E) and those of primary tumor cells at diagnosis (F) are shown. Parameters used were a0 = 0.11, a1 = 0.16, a2 = 0.24, a3 = 0.58, b0 = 0.0011, b1 = 0.0016, b2 = 0.0024, b3 = 0.0058, M1 = 10N(9.47,0.59), M2 = 1011.2, u = 6.31 × 10−5, q = 6.31 × 10−7, ϵ = 10−5, γ = 0.7, α = 3.0. Here, N(9.47, 0.59) represents the normal distribution with mean 9.47 and variance 0.59. The number of simulation cases were 256 in Cohort A. Table shows P values between Cohort A and each of Cohorts B and C by log-rank test for panels A–D and by Mann–Whitney U test for E and K.

Close modal

We investigated survival outcomes in each of three cohorts and confirmed there were no statistical differences between Cohort A and either of Cohorts B and C (Fig. 2A). The median overall survival (mOS) of Cohort A was 22.1 months, whereas those of Cohorts B and C were 22.1 and 18.1 months (Fig. 2A), respectively. We then classified Cohort A into three categories based on the identified alterations in the four genes at surgery: one altered gene (KRAS only, number: n = 4), two altered genes (n = 71), and three or four altered genes (n = 184; Fig. 2B). Cohort B was also classified into three groups: one altered gene (n = 4), two altered genes (n = 18), and three or four altered genes (n = 84; Fig. 2B). There were no differences in OS with two and three or four altered genes between Cohort A and either of the two clinical cohorts (Fig. 2B). We also classified Cohort A into two groups: cases destined to have oligometastatic disease (PToligo) and those destined to have widely metastatic disease (PTwidely), according to the extent of metastatic burden at death (Fig. 2C). PToligo was defined as cases with a limited number (i.e., 0–10) of metastases (Fig. 1A) as defined in the previous article (9). We performed the same analysis using Cohorts B and C and confirmed there were no differences in OS between Cohort A and either of the two clinical cohorts (Fig. 2C). Moreover, we classified Cohort A into two groups: group diagnosed as T1 versus T2-4 stages per TNM classification. Again, there were no differences in OS between Cohort A and either of the two clinical cohorts (Fig. 2D). Next, we investigated the frequency of the number of metastases at the time of patients' death (Fig. 2E). There were no differences in the number distributions between Cohort A and either of two clinical cohorts; our simulation outcome reproduced the tendency that approximately 40% of patients are PToligo (Fig. 2E). We further investigated the size distribution of the primary tumor at diagnosis and again confirmed there were no differences between Cohort A and either of two clinical cohorts (Fig. 2F). Collectively, the simulation outcomes from the model reproduced PDAC progression of two entirely distinct clinical cohorts in terms of its genetic alteration status, disease progression patterns, and metastatic features. Note that the two clinical cohorts were only used for the validation and the parameter values used in the simulations were obtained from the previous study (Table 1; refs. 25, 27–30).

Beneficial effect of complete resection on survival outcome in PToligo

To investigate the clinical significance of complete resection (R0 resection), we investigated how different resection rates of the primary tumor influenced patients' survival by the mathematical model (Fig. 3). Our model suggested that PToligo obtained a statistically significant survival benefit as resection rate increased; mOS was 23.5, 36.9, 38.2, and 39.1 months when the remaining tumor fractions by resection were ϵ = 0.9, ϵ = 0.1, ϵ = 10−5, and ϵ = 10−10, respectively (Fig. 3B). By contrast, survival outcome was comparable as resection rate increased in the analysis of all cases; mOS was 25.7, 25.9, 24.2, and 22.5 months, respectively (Fig. 3A). The result was consistent with the meta-analysis of randomized control trials (33). We did not observe significant effect of complete resection on survival duration among groups subdivided by other clinicopathological or alteration status (Supplementary Figs. S4–S8).

Figure 3.

Improvement of OS among PToligo by complete resection. Panels show OS of all cases (A) and PToligo (B), when different rates of surgical resection were delivered. The remaining tumor fractions by resection were (a) ϵ = 0.9, (b) ϵ = 0.1, (c) ϵ = 10−5, and (d) ϵ = 10−10. The number of simulation cases is 100 for each of eight panels. Hazard ratio (HR) describes the relative risk in cases with different resection rates compared with that in cases with a resection rate of ϵ = 0.9. Other parameter values used for the panels were the same as those described in Fig. 2.

Figure 3.

Improvement of OS among PToligo by complete resection. Panels show OS of all cases (A) and PToligo (B), when different rates of surgical resection were delivered. The remaining tumor fractions by resection were (a) ϵ = 0.9, (b) ϵ = 0.1, (c) ϵ = 10−5, and (d) ϵ = 10−10. The number of simulation cases is 100 for each of eight panels. Hazard ratio (HR) describes the relative risk in cases with different resection rates compared with that in cases with a resection rate of ϵ = 0.9. Other parameter values used for the panels were the same as those described in Fig. 2.

Close modal

Small volume of cells with two altered genes at diagnosis as a predictive factor of PToligo

To select potential responders to complete resection, we next identified a valid factor that predicts PToligo. We investigated the distribution of the number of each cell type in both primary and metastatic sites at diagnosis (Fig. 4; Supplementary Fig. S9). Interestingly, patients who became PToligo had smaller number of ALTtwo cells compared with those became PTwidely (Fig. 4A). On the other hand, the number of other types of cells including MET cells did not predict future progression patterns (Fig. 4B; Supplementary Fig. S9). These findings imply that the number of ALTtwo cells can be used as a predictive factor identifying PToligo. Herein, the threshold of ALTtwo cells, 108 cells, was determined by the condition that the threshold split the two distinct subpopulations of PToligo and PTwidely throughout a range of size at diagnosis (Fig. 4; Supplementary Fig. S10).

Figure 4.

Prediction of PToligo or PTwidely by the volume of cells with two gene alterations (ALTtwo cells). Panels show a box plot of the number of ALTtwo (A) or MET (B) cells at diagnosis in PToligo and PTwidely in a logarithmic scale with base 10. The median, the first quartile, and third quartile in A are 7.03, 6.53, and 7.43 (column PToligo), and 8.17, 7.79, and 8.51 (column PTwidely), respectively. These values in B are 3.80, 1.06, and 7.94 (column PToligo), and 7.09, 5.59, and 8.07 (column PTwidely), respectively. Parameter values used for the panels were the same as those described in Fig. 2.

Figure 4.

Prediction of PToligo or PTwidely by the volume of cells with two gene alterations (ALTtwo cells). Panels show a box plot of the number of ALTtwo (A) or MET (B) cells at diagnosis in PToligo and PTwidely in a logarithmic scale with base 10. The median, the first quartile, and third quartile in A are 7.03, 6.53, and 7.43 (column PToligo), and 8.17, 7.79, and 8.51 (column PTwidely), respectively. These values in B are 3.80, 1.06, and 7.94 (column PToligo), and 7.09, 5.59, and 8.07 (column PTwidely), respectively. Parameter values used for the panels were the same as those described in Fig. 2.

Close modal

Beneficial effect of adjuvant CRTx on survival outcomes in PToligo

To test whether PToligo obtain a greater survival benefit from adjuvant CRTx, we designed a computational clinical trial (Fig. 5A). After surgical resection, cases were stratified into two groups; cases with less than 108 ALTtwo cells (ALTtwo cases) and cases with over 108 ALTtwo cells (ALT+two cases) at diagnosis. Both ALT+two and ALTtwo cases received two treatment arms: adjuvant CRTx or adjuvant CTx (Fig. 5A). See Supplementary Material S5 for details of the simulations.

Figure 5.

Beneficial effect of adjuvant CRTx on survival outcomes in ALTtwo. A, Schema of a computational clinical trial comparing adjuvant CTx with CRTx. B, Survival curves comparing adjuvant CTx (gray curves) with CRTx (black curves) in ALTtwo [n = 190; (a)] and ALT+two [n = 190; (b)]. ALT+two and ALTtwo denoted cases with over or less than 108 ALTtwo cells at diagnosis, respectively. Parameter values used for the panels were the same as those described in Fig. 2. In the treatment of CRTx, the surviving fraction of irradiated cells is given by e(ωD+ξD2), in which ω and ξ are constants, and D is dose. In simulations, CRTx was delivered for 30 fractions. ω = 10, and ξ and D were 0.02 and 1.8 Gy, respectively.

Figure 5.

Beneficial effect of adjuvant CRTx on survival outcomes in ALTtwo. A, Schema of a computational clinical trial comparing adjuvant CTx with CRTx. B, Survival curves comparing adjuvant CTx (gray curves) with CRTx (black curves) in ALTtwo [n = 190; (a)] and ALT+two [n = 190; (b)]. ALT+two and ALTtwo denoted cases with over or less than 108 ALTtwo cells at diagnosis, respectively. Parameter values used for the panels were the same as those described in Fig. 2. In the treatment of CRTx, the surviving fraction of irradiated cells is given by e(ωD+ξD2), in which ω and ξ are constants, and D is dose. In simulations, CRTx was delivered for 30 fractions. ω = 10, and ξ and D were 0.02 and 1.8 Gy, respectively.

Close modal

Our results indicated that adjuvant CRTx was significantly beneficial to ALTtwo cases (P = 0.003, Fig. 5B), whereas it did not impact survival outcome in ALT+two cases (Fig. 5B). Interestingly, ALTtwo cases identified potential responders throughout various primary tumor sizes at diagnosis (Supplementary Figs. S11 and S12). We also investigated the role of neoadjuvant CRTx in PToligo, and found that the improvement in survival was observed in both ALT+two and ALTtwo cases (Supplementary Fig. S13).

Beneficial effect of curative surgical intervention or salvage CRTx on survival outcomes in PToligo with isolated recurrence

To test whether PToligo obtain a survival benefit from salvage intervention to the initial recurrence, we designed a computational clinical trial (Fig. 6A). Again, resectable cases were stratified into two groups (ALT+two and ALTtwo cases) based on the numbers of ALTtwo cells at diagnosis. Once the initial isolated metastatic recurrence was detected, both ALT+two and ALTtwo cases received two arms: intensive local control to the recurrent site by surgical intervention or CRTx administration, or CTx alone (Fig. 6A). See Supplementary Material S5 for details of the simulations.

Figure 6.

Beneficial effect of salvage therapies to isolated recurrence on survival outcomes in ALTtwo. A, Schema of a computational clinical trial comparing adjuvant CTx with salvage therapies to an isolated recurrence with concurrent CTx. B, Survival curves comparing adjuvant CTx (gray curves) with surgical intervention (black curves) in ALTtwo [n = 190; (a)] and ALT+two [n = 190; (b)]. C, Survival curves comparing adjuvant CTx (gray curves) with salvage CRTx (black curves) in ALTtwo [n = 190; (a)] and ALT+two [n = 190; (b)]. Parameter values used for the panels were the same as those described in Fig. 5.

Figure 6.

Beneficial effect of salvage therapies to isolated recurrence on survival outcomes in ALTtwo. A, Schema of a computational clinical trial comparing adjuvant CTx with salvage therapies to an isolated recurrence with concurrent CTx. B, Survival curves comparing adjuvant CTx (gray curves) with surgical intervention (black curves) in ALTtwo [n = 190; (a)] and ALT+two [n = 190; (b)]. C, Survival curves comparing adjuvant CTx (gray curves) with salvage CRTx (black curves) in ALTtwo [n = 190; (a)] and ALT+two [n = 190; (b)]. Parameter values used for the panels were the same as those described in Fig. 5.

Close modal

Surgical intervention significantly improved OS in ALTtwo cases (Fig. 6B), whereas it did not impact OS in ALT+two cases (Fig. 6B). Similar favorable effects were observed when salvage CRTx was delivered (Fig. 6C). Moreover, ALTtwo cases again identified potential responders in various sizes of primary tumors at diagnosis (Supplementary Figs. S14 and S15). For validation of the feasibility of our model of salvage CRTx in PDAC patients, we compared the survival outcome in simulation cases with that of clinical patients for whom CRTx was administered for isolated recurrence (Supplementary Fig. S16; ref. 7). We observed good agreement between the two (Supplementary Fig. S16B). Similarly, the impact of surgical intervention (although it often is not feasible clinically) on survival outcome was validated by literatures (Supplementary Fig. S16A; refs. 6, 34, 35).

The identification of PDAC patients destined to fail with loco-regional or oligometastatic disease has provoked the hypothesis that intensive local treatment such as RTx or surgery may be beneficial to a subset of patients. In this study, we adopted a combined clinical and theoretical approach with the goal of identifying factors that can be used to select potential responders to intensive local treatments and described personalized management that could lead to improved survival. This translational approach was achieved by establishing a mathematical framework in which both the growth and metastatic dynamics in PDAC are considered. The framework was adequately validated with two independent clinical cohorts from the United States and Japan in the contexts of: (i) the diversity of disease progression in individual patients; (ii) the genetic alteration status within PDAC; (iii) the existence of both phenotypes of oligometastatic and widely metastatic diseases; and (iv) the survival outcome of patients after medical interventions such as surgery and CTx following a standard guideline (Fig. 2; ref. 36).

The diversity of disease phenotypes in PDAC results in a variety of treatment responses among patients, thus making it difficult to reach a consensus-based, standardized clinical decision. Several clinical questions remain: (i) is there any survival difference between complete resection and incomplete resection (33, 37, 38); (ii) is the routine use of adjuvant CRTx recommended (4, 39); and (iii) is surgical intervention or salvage CRTx recommended for patients with an isolated local recurrence (6, 7)? In this study, we clearly demonstrated that (i) complete resection, (ii) adjuvant CRTx, and (iii) surgical resection when possible or salvage CRTx administration to an isolated recurrent site would best treat patients destined to have an oligometastatic disease profile (PToligo; Figs. 3B, 5B, and 6B and C). In contrast, these regimens were not always effective for those destined to have widely metastatic disease profile (PTwidely), for whom CTx alone may be more appropriate (Figs. 3A, 5B, and 6B and C). These findings emphasize the importance of personalization of care in PDAC. Knowledge of the patient profile of oligometastatic versus widely metastatic could be instrumental in helping oncologists determine the optimal treatment regimens for specific patients.

To select potential responders to the various treatments, we identified the small number of ALTtwo cells at diagnosis as a predictive factor (Fig. 4; Supplementary Fig. S9). This factor is feasible because it is obtained by analyzing common genetic alterations presented in a greater proportion of patients (Fig. 1B) and predicts favorable responders to the personalized treatments throughout the range of primary tumor sizes at detection (Figs. 5 and 6; Supplementary Figs. S11, S12, S14, and S15). We also investigated how the results of computational clinical trials are affected by using different cutoff values, 107 or 109. When the cutoff value is 107 ALTtwo cells, beneficial effects of adjuvant CRTx and salvage interventions to the initial recurrent site were observed in both ALT+two and ALTtwo cases (Supplementary Figs. S17–S19); whereas no survival differences were observed when the cutoff value is 109 ALTtwo cells (Supplementary Figs. S17–S19). Therefore, the threshold of 108 ALTtwo cells better identifies patients with favorable response to intensive local control therapies by distinguishing the two disease phenotypes in PDAC. To estimate the number of ALTtwo cells, we may be able to employ single-cell analysis such as the sequence from individual cells or STAR-FISH (specific-to allele PCR-FISH), albeit their use in the present study have not been developed. STAR-FISH aims to detect single-nucleotide mutations in combination with genomic copy-number variation at a single-cell level (40). These analyses may allow us to quantify the true extent of genetic alterations in each cell in one sample. It should be noted that single samples from a tumor would have a bias in the estimation of the number of ALTtwo cells, due to intratumor heterogeneity. In principle, a whole primary tumor is required to measure the true number of ALTtwo cells; however, a whole primary tumor may not always be available in clinics (33). To overcome these limitations, multiple-region samplings of a tumor may help in improving the accuracy to infer the number of ALTtwo cells. Collectively, we consider that a methodological development based on combination of the single cell analysis and multiple-region sampling approach will help in estimation of the number of ALTtwo cells and making our theoretical prediction clinically testable in the future.

Another important finding was that neoadjuvant CRTx may improve survival in both PToligo and PTwidely (Supplementary Fig. S13). One possible reason for this is that the restaging after neoadjuvant CRTx could efficiently exclude patients with a PTwidely profile from even going to surgery. Another possible reason is that neoadjuvant CRTx efficiently reduced cancer cells in advance, which otherwise might have aggressively grown during postoperative immunosuppression. There has been a growing interest in neoadjuvant CTx followed by CRTx or stereotactic body radiotherapy, and most retrospective studies have reported the feasibility and promising efficacy in resectable, borderline resectable, and possibly even unresectable PDAC (5, 41–44). Our results theoretically suggest that neoadjuvant CTx and RTx is effective in patients with any disease phenotype, and advocate the need to explore neoadjuvant therapy in randomized trials.

The strongest point in this study is that we succeeded in reproducing the clinical outcomes from the entirely distinct US and Japan cohorts by using our mathematical framework whose parameter values were established in the independent previous rapid autopsy program (25). This implies our PDAC progression model is applicable in a range of clinical cohorts with heterogeneous populations under different clinical stages as well as treatment regimens. Nonetheless, we admit there are also several assumptions in this study. Although investigation of the earliest-stage of PDAC showed only 6.0% to 36.4% of patients had (epi)genetic alterations in CDKN2A gene (14), a high frequency of CDKN2A gene deletion, mutations, and hypermethylation in the promoter have been reported in advanced PDAC (45). Therefore, there is a possibility that alterations in CDKN2A are earlier events in tumorigenesis in some patients. Physicians obtain information on patients' disease progression phenotype by surgical samples in our framework; therefore, they know whether complete resection is recommended to the patient only after they perform surgery. Ideally, the identification of disease phenotype before surgery could help physicians to determine surgical procedure. In this regard, the use of endoscopic ultrasound fine needle aspiration biopsy, which aims for confirming malignancy before the initiation of treatment by collecting specimens in multiple locations, might shed light on improving the applicability of our model in the future (46). Among all carcinomas, PDAC displays one of the most prominent desmoplastic stromal reactions. We considered the malignant cells to consist of 20% of the tumor volume (47). Regardless of the use of the neoadjuvant therapy, we uniformly used the date of surgery as a baseline for the analyses of clinical outcomes for consistency, because all patients underwent curative-intent surgery as the backbone in treatment strategies. Because this study aimed to identify the optimal intervention for patients with resectable disease, treatment effects for non-resectable disease, such as CTx effects in initially unresectable disease or effects of resection in borderline resectable disease, are beyond the scope of the purpose of the framework. These options should be addressed in future studies.

PDAC is an ideal tumor type for studies of cancer progression by using a simple theoretical model. The genetic progression during carcinogenesis has been well-investigated. In addition, the heterogeneity in terms of driver genes is minimal compared with other cancer types. On the basis of a firmly established model, we have demonstrated the possibility of personalized treatments for these patients, which may translate into clinical benefit. Whether the personalized management should be applied to clinical settings requires validation in clinical studies.

J.M. Herman has received speakers bureau honoraria from Btg and Abbvie. No potential conflicts of interest were disclosed by the other authors.

Conception and design: K.N. Yamamoto, S. Yachida, A. Nakamura, J.M. Herman, C.A. Iacobuzio-Donahue

Development of methodology: K.N. Yamamoto, A. Nakamura, L.M. Rosati, J.M. Herman, H. Haeno

Acquisition of data (provided animals, acquired and managed patients, provided facilities, etc.): K.N. Yamamoto, S. Yachida, A. Nakamura, M. Oshima, L.M. Rosati, J.M. Herman

Analysis and interpretation of data (e.g., statistical analysis, biostatistics, computational analysis): K.N. Yamamoto, A. Nakamura, A. Niida, S. De, L.M. Rosati, J.M. Herman

Writing, review, and/or revision of the manuscript: K.N. Yamamoto, S. Yachida, A. Nakamura, S. De, L.M. Rosati, J.M. Herman, C.A. Iacobuzio-Donahue, H. Haeno

Administrative, technical, or material support (i.e., reporting or organizing data, constructing databases): K.N. Yamamoto, A. Nakamura, L.M. Rosati, J.M. Herman, C.A. Iacobuzio-Donahue

Study supervision: A. Nakamura, C.A. Iacobuzio-Donahue, H. Haeno

We thank Michor F, Liu LL, Janiszewska M, Altrock PM, Wu HJ, Shi J, and all other Michor laboratory members for their helpful discussion.

The study was supported by Japan Society for the Promotion of Science (JSPS), 16K10584 to K.N. Yamamoto; Japan Society for the Promotion of Science (JSPS), 15H05707 to K. Aihara; and Ministry of Education, Culture, Sports, Science, and Technology (MEXT), 26115006 to H. Haeno.

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.

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Supplementary data