Consolidated mathematical growth model of the primary tumor and secondary distant metastases of breast cancer (CoMPaS)

A Role of Effector CD 8 + T Cells Against Circulating Tumor Cells Cloaked with Platelets: Insights from a Mathematical Model

Cancer metastasis accounts for a majority of cancer-related deaths worldwide. Metastasis occurs when the primary tumor sheds cells into the blood and lymphatic circulation, thereby becoming circulating tumor cells (CTCs) that transverse through the circulatory system, extravasate the circulation and establish a secondary distant tumor. Accumulating evidence suggests that circulating effector CD 8 + T cells are able to recognize and attack arrested or extravasating CTCs, but this important antitumoral effect remains largely undefined. Recent studies highlighted the supporting role of activated platelets in CTCs's extravasation from the bloodstream, contributing to metastatic progression. In this work, a simple mathematical model describes how the primary tumor, CTCs, activated platelets and effector CD 8 + T cells participate in metastasis. The stability analysis reveals that for early dissemination of CTCs, effector CD 8 + T cells can present or keep secondary metastatic tumor burden at low equilibrium state. In contrast, for late dissemination of CTCs, effector CD 8 + T cells are unlikely to inhibit secondary tumor growth. Moreover, global sensitivity analysis demonstrates that the rate of the primary tumor growth, intravascular CTC proliferation, as well as the CD 8 + T cell proliferation, strongly affects the number of the secondary tumor cells. Additionally, model simulations indicate that an increase in CTC proliferation greatly contributes to tumor metastasis. Our simulations further illustrate that the higher the number of activated platelets on CTCs, the higher the probability of secondary tumor establishment. Intriguingly, from a mathematical immunology perspective, our simulations indicate that if the rate of effector CD 8 + T cell proliferation is high, then the secondary tumor formation can be considerably delayed, providing a window for adjuvant tumor control strategies. Collectively, our results suggest that the earlier the effector CD 8 + T cell response is enhanced the higher is the probability of preventing or delaying secondary tumor metastases.

Intermetastatic and Intrametastatic Heterogeneity Shapes Adaptive Therapy Cycling Dynamics

Adaptive therapies that alternate between drug applications and drug-free vacations can exploit competition between sensitive and resistant cells to maximize the time to progression. However, optimal dosing schedules depend on the properties of metastases, which are often not directly measurable in clinical practice. Here, we proposed a framework for estimating features of metastases through tumor response dynamics during the first adaptive therapy treatment cycle. Longitudinal prostate-specific antigen (PSA) levels in 16 patients with metastatic castration-resistant prostate cancer undergoing adaptive androgen deprivation treatment were analyzed to investigate relationships between cycle dynamics and clinical variables such as Gleason score, the change in the number of metastases over a cycle, and the total number of cycles over the course of treatment. The first cycle of adaptive therapy, which consists of a response period (applying therapy until 50% PSA reduction), and a regrowth period (removing treatment until reaching initial PSA levels), delineated several features of the computational metastatic system: larger metastases had longer cycles; a higher proportion of drug-resistant cells slowed the cycles; and a faster cell turnover rate sped up drug response time and slowed regrowth time. The number of metastases did not affect cycle times, as response dynamics were dominated by the largest tumors rather than the aggregate. In addition, systems with higher intermetastasis heterogeneity responded better to continuous therapy and correlated with dynamics from patients with high or low Gleason scores. Conversely, systems with higher intrametastasis heterogeneity responded better to adaptive therapy and correlated with dynamics from patients with intermediate Gleason scores.

SIGNIFICANCE

Multiscale mathematical modeling combined with biomarker dynamics during adaptive therapy helps identify underlying features of metastatic cancer to inform treatment decisions.

Novel models by machine learning to predict prognosis of breast cancer brain metastases

BACKGROUND

Breast cancer brain metastases (BCBM) are the most fatal, with limited survival in all breast cancer distant metastases. These patients are deemed to be incurable. Thus, survival time is their foremost concern. However, there is a lack of accurate prediction models in the clinic. What's more, primary surgery for BCBM patients is still controversial.

METHODS

The data used for analysis in this study was obtained from the SEER database (2010-2019). We made a COX regression analysis to identify prognostic factors of BCBM patients. Through cross-validation, we constructed XGBoost models to predict survival in patients with BCBM. Meanwhile, a BCBM cohort from our hospital was used to validate our models. We also investigated the prognosis of patients treated with surgery or not, using propensity score matching and K-M survival analysis. Our results were further validated by subgroup COX analysis in patients with different molecular subtypes.

RESULTS

The XGBoost models we created had high precision and correctness, and they were the most accurate models to predict the survival of BCBM patients (6-month AUC = 0.824, 1-year AUC = 0.813, 2-year AUC = 0.800 and 3-year survival AUC = 0.803). Moreover, the models still exhibited good performance in an externally independent dataset (6-month: AUC = 0.820; 1-year: AUC = 0.732; 2-year: AUC = 0.795; 3-year: AUC = 0.936). Then we used Shiny-Web tool to make our models be easily used from website. Interestingly, we found that the BCBM patients with an annual income of over USD$70,000 had better BCSS (HR = 0.523, 95%CI 0.273-0.999, P < 0.05) than those with less than USD$40,000. The results showed that in all distant metastasis sites, only lung metastasis was an independent poor prognostic factor for patients with BCBM (OS: HR = 1.606, 95%CI 1.157-2.230, P < 0.01; BCSS: HR = 1.698, 95%CI 1.219-2.365, P < 0.01), while bone, liver, distant lymph nodes and other metastases were not. We also found that surgical treatment significantly improved both OS and BCSS in BCBM patients with the HER2 + molecular subtypes and was beneficial to OS of the HR-/HER2- subtype. In contrast, surgery could not help BCBM patients with HR + /HER2- subtype improve their prognosis (OS: HR = 0.887, 95%CI 0.608-1.293, P = 0.510; BCSS: HR = 0.909, 95%CI 0.604-1.368, P = 0.630).

CONCLUSION

We analyzed the clinical features of BCBM patients and constructed 4 machine-learning prognostic models to predict their survival. Our validation results indicate that these models should be highly reproducible in patients with BCBM. We also identified potential prognostic factors for BCBM patients and suggested that primary surgery might improve the survival of BCBM patients with HER2 + and triple-negative subtypes.

Model-based inference of metastatic seeding rates in de novo metastatic breast cancer reveals the impact of secondary seeding and molecular subtype

We present a stochastic network model of metastasis spread for de novo metastatic breast cancer, composed of tumor to metastasis (primary seeding) and metastasis to metastasis spread (secondary seeding), parameterized using the SEER (Surveillance, Epidemiology, and End Results) database. The model provides a quantification of tumor cell dissemination rates between the tumor and metastasis sites. These rates were used to estimate the probability of developing a metastasis for untreated patients. The model was validated using tenfold cross-validation. We also investigated the effect of HER2 (Human Epidermal Growth Factor Receptor 2) status, estrogen receptor (ER) status and progesterone receptor (PR) status on the probability of metastatic spread. We found that dissemination rate through secondary seeding is up to 300 times higher than through primary seeding. Hormone receptor positivity promotes seeding to the bone and reduces seeding to the lungs and primary seeding to the liver, while HER2 expression increases dissemination to the bone, lungs and primary seeding to the liver. Secondary seeding from the lungs to the liver seems to be hormone receptor-independent, while that from the lungs to the brain appears HER2-independent.

NCCBM, a Nomogram Prognostic Model in Breast Cancer Patients With Brain Metastasis

Purpose: Nomogram prognostic models could greatly facilitate risk stratification and treatment strategies for cancer patients. We developed and validated a new nomogram prognostic model, named NCCBM, for breast cancer patients with brain metastasis (BCBM) using a large BCBM cohort from the SEER (Surveillance, Epidemiology, and End Results) database. Patients and Methods: Clinical data for 975 patients diagnosed from 2011 to 2014 were used to develop the nomogram prognostic model. The predictive accuracy and discriminative ability of the nomogram were determined by concordance index (C-index) and calibration curve. The results were validated using an independent cohort of 542 BCBM patients diagnosed from 2014 to 2015. Results: The following variables were selected in the final prognostic model: age, race, surgery, radiation therapy, chemotherapy, laterality, grade, molecular subtype, and extracranial metastatic sites. The C-index for the model described here was 0.69 (95% CI, 0.67 to 0.71). The calibration curve for probability of survival showed good agreement between prediction by nomogram and actual observation. The model was validated in an independent validation cohort with a C-index of 0.70 (95% CI, 0.68 to 0.73). Conclusion: We developed and validated a nomogram prognostic model for BCBM patients, and the proposed nomogram resulted in good performance.

An inverse stage-shift model to estimate the excess mortality and health economic impact of delayed access to cancer services due to the COVID-19 pandemic

AIM

Decreased cancer incidence and reported changes to clinical management indicate that the COVID-19 pandemic has delayed cancer diagnosis and treatment. This study aimed to develop and apply a flexible model to estimate the impact of delayed diagnosis and treatment on survival outcomes and healthcare costs based on a shift in the disease stage at treatment initiation.

METHODS

A model was developed and made publicly available to estimate population-level health economic outcomes by extrapolating and weighing stage-specific outcomes by the distribution of stages at treatment initiation. It was applied to estimate the impact of 3- and 6-month delays based on Australian data for stage I breast cancer, colorectal cancer, and lung cancer patients, and for T1 melanoma. Two approaches were explored to estimate stage shifts following a delay: (a) based on the relation between time to treatment initiation and overall survival (breast, colorectal, and lung cancer), and (b) based on the tumor growth rate (melanoma).

RESULTS

Using a conservative once-off 3-month delay and considering only shifts from stage I/T1 to stage II/T2, 88 excess deaths and $12 million excess healthcare costs were predicted in Australia over 5 years for all patients diagnosed in 2020. For a 6-month delay, excess mortality and healthcare costs were 349 deaths and $46 million over 5 years.

CONCLUSIONS

The health and economic impacts of delays in treatment initiation cause an imminent policy concern. More accurate individual patient data on shifts in stage of disease during and after the COVID-19 pandemic are critical for further analyses.

A Mathematical Model to Predict Diagnostic Periods for Secondary Distant Metastases in Patients with ER/PR/HER2/Ki-67 Subtypes of Breast Cancer

Previously, a consolidated mathematical model of primary tumor (PT) growth and secondary distant metastasis (sdMTS) growth in breast cancer (BC) (CoMPaS) was presented. The aim was to detect the diagnostic periods for visible sdMTS via CoMPaS in patients with different subtypes ER/PR/HER2/Ki-67 (Estrogen Receptor/Progesterone Receptor/Human Epidermal growth factor Receptor 2/Ki-67 marker) of breast cancer. CoMPaS is based on an exponential growth model and complementing formulas, and the model corresponds to the tumor-node-metastasis (TNM) staging system and BC subtypes (ER/PR/HER2/Ki-67). The CoMPaS model reflects (1) the subtypes of BC, such as ER/PR/HER2/Ki-67, and (2) the growth processes of the PT and sdMTSs in BC patients without or with lymph node metastases (MTSs) in accordance with the eighth edition American Joint Committee on Cancer prognostic staging system for breast cancer. CoMPaS correctly describes the growth of the PT in the ER/PR/HER2/Ki-67 subtypes of BC patients and helps to calculate the different diagnostic periods, depending on the tumor volume doubling time of sdMTS, when sdMTSs might appear. CoMPaS and the corresponding software tool can help (1) to start the early treatment of small sdMTSs in BC patients with different tumor subtypes (ER/PR/HER2/Ki-67), and (2) to consider the patient almost healthy if sdMTSs do not appear during the different diagnostic periods.

Crosstalk between HER2 and PD-1/PD-L1 in Breast Cancer: From Clinical Applications to Mathematical Models

Breast cancer is one of the major causes of mortality in women worldwide. The most aggressive breast cancer subtypes are human epidermal growth factor receptor-positive (HER2+) and triple-negative breast cancers. Therapies targeting HER2 receptors have significantly improved HER2+ breast cancer patient outcomes. However, several recent studies have pointed out the deficiency of existing treatment protocols in combatting disease relapse and improving response rates to treatment. Overriding the inherent actions of the immune system to detect and annihilate cancer via the immune checkpoint pathways is one of the important hallmarks of cancer. Thus, restoration of these pathways by various means of immunomodulation has shown beneficial effects in the management of various types of cancers, including breast. We herein review the recent progress in the management of HER2+ breast cancer via HER2-targeted therapies, and its association with the programmed death receptor-1 (PD-1)/programmed death ligand-1 (PD-L1) axis. In order to link research in the areas of medicine and mathematics and point out specific opportunities for providing efficient theoretical analysis related to HER2+ breast cancer management, we also review mathematical models pertaining to the dynamics of HER2+ breast cancer and immune checkpoint inhibitors.

Cost-effectiveness of stereotactic body radiation therapy versus video assisted thoracic surgery in medically operable stage I non-small cell lung cancer: A modeling study

OBJECTIVES

Stage I non-small cell lung cancer (NSCLC) can be treated with either Stereotactic Body Radiotherapy (SBRT) or Video Assisted Thoracic Surgery (VATS) resection. To support decision making, not only the impact on survival needs to be taken into account, but also on quality of life, costs and cost-effectiveness. Therefore, we performed a cost-effectiveness analysis comparing SBRT to VATS resection with respect to quality adjusted life years (QALY) lived and costs in operable stage I NSCLC.

MATERIALS AND METHODS

Patient level and aggregate data from eight Dutch databases were used to estimate costs, health utilities, recurrence free and overall survival. Propensity score matching was used to minimize selection bias in these studies. A microsimulation model predicting lifetime outcomes after treatment in stage I NSCLC patients was used for the cost-effectiveness analysis. Model outcomes for the two treatments were overall survival, QALYs, and total costs. We used a Dutch health care perspective with 1.5 % discounting for health effects, and 4 % discounting for costs, using 2018 cost data. The impact of model parameter uncertainty was assessed with deterministic and probabilistic sensitivity analyses.

RESULTS

Patients receiving either VATS resection or SBRT were estimated to live 5.81 and 5.86 discounted QALYs, respectively. Average discounted lifetime costs in the VATS group were €29,269 versus €21,175 for SBRT. Difference in 90-day excess mortality between SBRT and VATS resection was the main driver for the difference in QALYs. SBRT was dominant in at least 74 % of the probabilistic simulations.

CONCLUSION

Using a microsimulation model to combine available evidence on survival, costs, and health utilities in a cost-effectiveness analysis for stage I NSCLC led to the conclusion that SBRT dominates VATS resection in the majority of simulations.

Replication Study: Biomechanical remodeling of the microenvironment by stromal caveolin-1 favors tumor invasion and metastasis

As part of the Reproducibility Project: Cancer Biology we published a Registered Report (Fiering et al., 2015) that described how we intended to replicate selected experiments from the paper 'Biomechanical remodeling of the microenvironment by stromal caveolin-1 favors tumor invasion and metastasis' (Goetz et al., 2011). Here we report the results. Primary mouse embryonic fibroblasts (pMEFs) expressing caveolin 1 (Cav1WT) demonstrated increased extracellular matrix remodeling in vitro compared to Cav1 deficient (Cav1KO) pMEFs, similar to the original study (Goetz et al., 2011). In vivo, we found higher levels of intratumoral stroma remodeling, determined by fibronectin fiber orientation, in tumors from cancer cells co-injected with Cav1WT pMEFs compared to cancer cells only or cancer cells plus Cav1KO pMEFs, which were in the same direction as the original study (Supplemental Figure S7C; Goetz et al., 2011), but not statistically significant. Primary tumor growth was similar between conditions, like the original study (Supplemental Figure S7Ca; Goetz et al., 2011). We found metastatic burden was similar between Cav1WT and Cav1KO pMEFs, while the original study found increased metastases with Cav1WT (Figure 7C; Goetz et al., 2011); however, the duration of our in vivo experiments (45 days) were much shorter than in the study by Goetz et al. (2011) (75 days). This makes it difficult to interpret the difference between the studies as it is possible that the cells required more time to manifest the difference between treatments observed by Goetz et al. We also found a statistically significant negative correlation of intratumoral remodeling with metastatic burden, while the original study found a statistically significant positive correlation (Figure 7Cd; Goetz et al., 2011), but again there were differences between the studies in terms of the duration of the metastasis studies and the imaging approaches that could have impacted the outcomes. Finally, we report meta-analyses for each result.