Edited by: Maria Rodriguez Martinez, IBM Research–Zurich, Switzerland
Reviewed by: Jeffrey West, Moffitt Cancer Center, United States; Kevin Leder, University of Minnesota Twin Cities, United States
*Correspondence: Hiroshi Haeno,
This article was submitted to Cancer Genetics, a section of the journal Frontiers in Oncology
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Locoregional recurrence after surgery is a major unresolved issue in cancer treatment. Premalignant lesions are considered a cause of cancer recurrence. A study showed that premalignant lesions surrounding the primary tumor drove a high local cancer recurrence rate after surgery in head and neck cancer. Based on the multistage theory of carcinogenesis, cells harboring an intermediate number of mutations are not cancer cells yet but have a higher risk of becoming cancer than normal cells. This study constructed a mathematical model for cancer initiation and recurrence by combining the Moran and branching processes in which cells require two specific mutations to become malignant. There are three populations in this model: (i) normal cells with no mutation, (ii) premalignant cells with one mutation, and (iii) cancer cells with two mutations. The total number of healthy tissue is kept constant to represent homeostasis, and there is a rare chance of mutation every time a cell divides. If a cancer cell with two mutations arises, the cancer population proliferates, violating the homeostatic balance of the tissue. Once the number of cancer cells reaches a certain size, we conduct computational resection and remove the cancer cell population, keeping the ratio of normal and premalignant cells in the tissue unchanged. After surgery, we considered tissue dynamics and eventually observed the second appearance of cancer cells as recurrence. Consequently, we computationally revealed the conditions where the time to recurrence became short by parameter sensitivity analysis. Particularly, when the premalignant cells’ fitness is higher than normal cells, the proportion of premalignant cells becomes large after the surgical resection. Moreover, the mathematical model was fitted to clinical data on diseasefree survival of 1,087 patients in 23 cancer types from the TCGA database. Finally, parameter values of tissue dynamics are estimated for each cancer type, where the likelihood of recurrence can be elucidated. Thus, our approach provides insights into the concept to identify the patients likely to experience recurrence as early as possible.
Locoregional recurrence after surgery appears in many cancer types. About 8% of invasive breast cancer patients exhibited local recurrence after surgical resection with free resection margins (
A major cause of local recurrence is field cancerization (
Theoretical studies have investigated field cancerization impacts on the emergence of recurrent tumors (
This study developed a novel mathematical model of recurrent tumor evolution. We employed a stochastic process of a multistage model to represent the accumulation of mutations in a tissue, leading to cancer relapse after surgical resection of the first tumor. Particularly, we focused on the relationship between the tissue compositions at the time of surgery and the time until the emergence of recurrent tumors. Our approach provided insights on how to predict the time of recurrence from the tissue dynamics at the time of surgery and how to intervene patients to prevent the recurrence.
Let us consider the dynamics of three types of cells in a tissue (
The schematic diagram of our model.
Initially,
To integrate the Moran process and branching process, we adopted stochastic simulations based on Gillespie’s algorithm (
When the event of cell turnover in a healthy tissue occurs, one of
First of all, the case (i) occurs through two ways: (a) A Type0 cell dies, and a Type1 cell divides without a mutation; and (b) a Type0 cell dies, and another Type0 cell divides with a mutation to be a Type1 cell. Exceptionally, when a Type0 dies, and a Type1 cell divides with a mutation to be a Type2 cell, an additional selection of a cell to divide is done because a Type2 cell cannot reside in a normal tissue under the assumption of the model. In this situation, if a Type1 cell is selected to divide without a mutation, the number of Type1 cells increases by one. The probabilities of these three events are given by
Secondly, the case (ii) occurs in such a way that a Type1 cell dies and a Type0 cell divides without a mutation. Exceptionally, when a Type1 cell dies, and another Type1 cell divides with a mutation to be a Type2 cell, an additional selection for a cell division is done. In this case, if a Type0 cell is selected for the additional cell division, the number of Type1 cells decreases by one. The probabilities of the two events are given by
Finally, the probability that the number of Type1 does not change [case (iii)] is given by
In summary, the time of one step in simulations is calculated using Eq. (1), and in one step, one of the following three processes occurs: (i) cell turnover in a tissue, (ii) the death of a Type2 cell, or (iii) the birth of a Type2 cell. When case (i) happens, there are three possibilities in tissue dynamics. The number of type1 cells increases by one, decreases by one, or does not change. Initially, all the cells are Type0. Once the number of Type2 cells reaches 10^{9}, computational surgical resection to set the number of Type2 cells to be 0 again will be conducted. After that, the time until the number of Type2 cells reaches 10^{9} again is measured as recurrence time.
As for the calculation of the Type2 growth, we assumed that when the number of cells is small, the stochastic effect should be considered. When the number of Type2 cells exceed twice as large as the size of the normal tissue, 2
During Δ
The data used in our analysis were downloaded from TCGA PanCancer Clinical Data Resource provided in the previous publication (
Diseasefree survival of clinical data were calculated using the Kaplan–Meier method from diseasefree intervals mentioned in
The whole process of our model was conducted on C++. Parameter optimization was conducted using the Nelder–Mead method on R (version 3.6.2). The survival time analysis was conducted on Prism (version 8.4.3).
First of all, we conducted stochastic simulations of the model for the initial cancer progression, and the time courses of three populations: Type0, Type1, and Type2 were shown (
Three patterns of cancer initiation. Gray, blue, and red curves describe Type0, Type1, and Type2 cells, respectively (the full growth dynamics are not shown). Each panel contains three trials of the same parameter sets distinguished by the type of lines: Joined, dashed, and longdashed. Cancer initiates from:
Next, we examined the time to recurrence after surgical resection and the proportion of premalignant (Type1) lesions at the time of surgery in a vast parameter range (
Parameter dependence on recurrence time. Mean values obtained from the simulations are shown by dots, and standard deviations are indicated by bars. Pie charts in the panels indicate the proportion of Type1 cells in normal tissue at the first treatment. Light blue, blue, dark blue represent small (
To investigate the relationship between the proportion of Type1 cells during initial treatment and time to recurrence comprehensively, we conducted computational simulations with parameter sets randomly picked (
The relationship between the number of Type1 cells in the normal tissue at the first treatment and time to recurrence with various parameter values.
We confirmed that recurrence time was significantly different among the proportion of Type1 cells during the first treatment (
Results of recurrence time
Fitting of our model to clinical data of diseasefree survival in 23 cancer types. Results of diseasefree survival
Estimated parameters and pvalues by fitting the outputs from our simulations to clinical data.
Cancer type 


Log_{10}

logSSR  pvalue 

ACC  0.916  1.62  −3.61  0.272  0.2008 
BLCA  0.908  1.43  −3.60  0.717  0.4658 
BRCA  0.922  1.52  −4.02  0.294  <0.0001 
CESC  0.905  1.36  −3.63  0.815  0.8958 
CHOL  0.964  1.52  −3.43  0.113  0.0272 
COAD  0.924  1.40  −3.71  0.564  0.5966 
ESCA  0.934  1.60  −3.42  0.128  0.3458 
HNSC  0.914  1.58  −3.56  0.926  0.3446 
KIRC  0.920  1.27  −3.77  0.314  0.3945 
KIRP  0.908  1.38  −3.62  0.981  0.6651 
LGG  0.905  1.35  −3.62  0.0312  0.0803 
LIHC  0.962  1.72  −3.54  0.647  0.8949 
LUAD  0.920  1.62  −3.62  1.52  0.0039 
LUSC  0.904  1.43  −3.55  0.588  0.4501 
OV  0.905  1.56  −3.37  0.604  <0.0001 
PAAD  0.918  1.54  −3.44  0.139  0.3649 
PRAD  0.913  1.34  −3.80  0.165  0.1207 
SARC  0.930  1.51  −3.42  1.05  0.0036 
STAD  0.917  1.59  −3.59  0.432  0.3859 
TGCT  0.916  1.61  −3.63  1.68  0.4146 
THCA  1.04  1.10  −3.31  7.74  <0.0001 
UCEC  0.909  1.33  −3.65  0.168  0.4777 
UCS  0.904  1.53  −3.49  0.633  0.6923 
ACC, adrenocortical carcinoma; BLCA, bladder urothelial carcinoma; BRCA, breast invasive carcinoma; CESC, cervical squamous cell carcinoma and endocervical adenocarcinoma; CHOL, cholangiocarcinoma; COAD, colon adenocarcinoma; ESCA, esophageal carcinoma; HNSC, head and neck squamous cell carcinoma; KIRC, kidney renal clear cell carcinoma; KIRP, kidney renal papillary cell carcinoma; LGG, brain lower grade glioma; LIHC, liver hepatocellular carcinoma; LUAD, lung adenocarcinoma; LUSC, lung squamous cell carcinoma; OV, ovarian serous cystadenocarcinoma; PAAD, pancreatic adenocarcinoma; PRAD, prostate adenocarcinoma; SARC, sarcoma; STAD, stomach adenocarcinoma; TGCT, testicular germ cell tumors; THCA, thyroid carcinoma; UCEC, uterine corpus endometrial carcinoma; UCS, uterine carcinoma.
In this study, we constructed a mathematical model that could describe cell population dynamics in both normal tissue and cancer tissues. We revealed the relationship between the proportion of premalignant cells and recurrence time (
This model successfully reproduced the diseasefree survivals in 17 out of 23 cancer types (
For the model’s simplicity, we prepared only one population for intermediate cell type as premalignant cells. However, the multistage theory suggested more than two steps to generate a cancer cell from a normal cell (
Conclusively, this model suggests special care of recurrence in the clinic when the fitness of premalignant cells and the growth rate of recurrent tumors is high. Furthermore, this approach can be extended to explore the deviance of recurrence rates among cancer types by introducing the variations of mutational stages and standard adjuvant therapies in each cancer according to growing knowledge.
The original contributions presented in the study are included in the article/supplementary material. Further inquiries can be directed to the corresponding author.
HH supervised the work. MT performed theoretical analysis. MT and HH wrote manuscript. All authors contributed to the article and approved the submitted version.
The work is supported by National Cancer Center Research and Development Fund (2021A7), a research grant from SRL, H.U Group Research Institute, and JSPS KAKENHI Grant Number 20J22335. The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article or the decision to submit it for publication.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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