Inferring rates of metastatic dissemination using stochastic network models

The circulation stage of the metastatic cascade: A mathematical description and its clinical implications

Metastatic cascade is a multi-stage process that starts with separation of a cancer cell from the primary tumor and ends with the emergence of a detectable metastasis. In the process the initiator cancer cell enters the circulatory system (intravasates), flows with the blood, and exits the circulation (extravasates) into an organ or tissue. The time period between intravasation and extravasation constitutes the circulation stage of the metastatic cascade. This stage is unique in that it lends itself naturally to various non-invasive observations and measurements in an individual cancer patient. This creates an opportunity for gaining insight into metastasis, its mathematical modeling, and designing diagnostic/prognostic tools and new cancer therapies. Although mechanisms of intravasation, survival and extravasation of circulating tumor cells (CTCs) are very complex and largely unknown, mathematical modeling of the circulation stage of the metastatic cascade is facilitated by two inter-related factors: a relative simplicity of the circulatory network and the cyclic nature of blood flow. The article presents a single-subject stochastic model of CTC dynamics that leads to simple formulas, applicable to any homogeneous CTC population, for organ-specific extravasation probabilities, the distribution and expected value of the number, X, of circulation cycles completed by a CTC prior to extravasation, and the average circulation time. In particular, we found that the distribution of random variable X is geometric G(x), where parameter x is measurable, at least in principle, in an individual subject. We also discuss implications of our results for cancer research and treatment.

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.

Drug Sensitivity Testing for Cancer Therapy, Technique Analysis and Trends

The techniques and qualities of drug sensitivity testing (DST) for anticancer treatment have grown rapidly in the past two decades worldwide. Much of DST progress came from advanced systems of technical versatility (faster, highly-throughput, highly-sensitive, and smaller in tumor quantity). As the earliest drug selective system, biomedical knowledge and technical advances for DST are mutually supported. More importantly, many pharmacological controversies are resolved by these technical advances. With this technical stride, the clinical landscape of DST entered into a new phase (>500 samples per testing and extremely low quantity of tumor cells). As a forerunner of the drug selection system, DST awaits a new version that can adapt to complicated therapeutic situations and diverse tumor categories in the clinic. By upholding this goal of pathogenic and therapeutic diversity, DST could eventually cure more cancer patients by establishing high-quality drug selection systems. To smoothen DST development, there is a need to increase the understanding of cancer biology, pathology and pharmacology (cancer heterogeneity, plasticity, metastasis and drug resistance) with well-informative parameters before chemotherapy. In this article, medicinal and technical insights into DST are especially highlighted.

Drug Sensitivity Testing for Cancer Therapy, Key Areas

AIMS

Cancer is a high-mortality disease (9.6 million deaths in 2018 worldwide). Given various anticancer drugs, drug selection plays a key role in patient survival in clinical trials.

METHODS

Drug Sensitivity Testing (DST), one of the leading drug selective systems, was widely practiced for therapeutic promotion in the clinic. Notably, DSTs assist in drug selection that benefits drug responses against cancer from 20-22% to 30-35% over the past two decades. The relationship between drug resistance in vitro and drug treatment benefits was associated with different tumor origins and subtypes. Medical theory and underlying DST mechanisms remain poorly understood until now. The study of the clinical scenario, sustainability and financial support for mechanism and technical promotions is indispensable.

RESULTS

Despite the great technical advance, therapeutic prediction and drug selection by DST needs to be miniature, versatility and cost-effective in the clinic. Multi-parameters and automation of DST should be a future trend. Advanced biomedical knowledge and clinical approaches to translating oncologic profiles into drug selection were the main focuses of DST developments. With a great technical stride, the clinical architecture of the DST platform was entering higher levels (drug response testing at any stage of cancer patients and miniaturization of tumor samples).

DISCUSSION

The cancer biology and pharmacology for drug selection mutually benefit the clinic. New proposals to reveal more therapeutic information and drug response prediction at genetic, molecular and omics levels should be estimated overall.

CONCLUSION

By upholding this goal of non-invasive, versatility and automation, DST could save the life of several thousand annually worldwide. In this article, new insights into DST novelty and development are highlighted.

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.