The natural history of renal cell carcinoma with pulmonary metastases illuminated through mathematical modeling

Therapeutic options for different metastatic sites arising from renal cell carcinoma: A review

Renal cell carcinoma (RCC) stands among the top 10 malignant neoplasms with the highest fatality rates. It exhibits pronounced heterogeneity and robust metastatic behavior. Patients with RCC may present with solitary or multiple metastatic lesions at various anatomical sites, and their prognoses are contingent upon the site of metastasis. When deliberating the optimal therapeutic approach for a patient, thorough evaluation of significant risk factors such as the feasibility of complete resection, the presence of oligometastases, and the patient's functional and physical condition is imperative. Recognizing the nuanced differences in RCC metastasis to distinct organs proves advantageous in contemplating potential treatment modalities aimed at optimizing survival outcomes. Moreover, discerning the metastatic site holds promise for enhancing risk stratification in individuals with metastatic RCC. This review summarizes the recent data pertaining to the current status of different RCC metastatic sites and elucidates their role in informing clinical management strategies across diverse metastatic locales of RCC.

Mathematical and Machine Learning Models of Renal Cell Carcinoma: A Review

This review explores the multifaceted landscape of renal cell carcinoma (RCC) by delving into both mechanistic and machine learning models. While machine learning models leverage patients' gene expression and clinical data through a variety of techniques to predict patients' outcomes, mechanistic models focus on investigating cells' and molecules' interactions within RCC tumors. These interactions are notably centered around immune cells, cytokines, tumor cells, and the development of lung metastases. The insights gained from both machine learning and mechanistic models encompass critical aspects such as signature gene identification, sensitive interactions in the tumors' microenvironments, metastasis development in other organs, and the assessment of survival probabilities. By reviewing the models of RCC, this study aims to shed light on opportunities for the integration of machine learning and mechanistic modeling approaches for treatment optimization and the identification of specific targets, all of which are essential for enhancing patient outcomes.

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.

Potential Use of CTCs as Biomarkers in Renal Cancer Patients

We demonstrated that the CellCollector is an appropriate tool for detecting CTCs in RCC patients. We examined EpCAM and MUC1 expression levels in RCC tissues and cell lines and analyzed the detection rate of CTCs in blood samples ex vivo using an anti-EpCAM antibody-covered straight or spiraled CellCollector. Eight matched samples were examined for affinity to the anti-EpCAM vs. anti-EpCAM/anti-MUC1 antibody-covered wire. The use of this combination of antibodies allowed us to classify patients with lung metastasis. Finally, four patients were analyzed in vivo. In conclusion, both straight (ex vivo, in vivo) and spiraled (ex vivo) wires detected CTCs.