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

Abstract

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.

Keywords: checkpoint inhibitors; differential equation; gene signature; machine learning; mathematical modeling; neural network; sunitinib.

Figure 1

Structure of the CNN-Cox model by Yin et al. [61]. Two kernels are used in the CNN-Cox model. The horizontal kernel slides horizontally with the size of a column, and the vertical kernel slides vertically with the size of a row. These two convolutional kernels are applied to the 2D input matrix to extract local features. Then, the output is passed to a max-pooling layer, a flattened layer, a fully connected layer, and an output Cox-regression layer.

Figure 2

Illustration of the RSF-VH algorithm. (A) shows the structure of the RSF-VH algorithm. N bootstrap samples and survival trees are drawn and grown from the dataset. At each node, a randomly selected subset of genes with minimal depths smaller than the mean of estimated minimal depth of the forest is considered to split the branch. This process is repeated until a stopping criterion is met. (B) illustrates the minimal depth of genes b and c in a survival tree. a, b, c, and d are four different randomly selected genes, and the numbers inside each node indicate the depth of the tree. Yellow and green colored points are maximal subtrees for genes b and c, respectively. And the minimal depth for gene b is 3 and for gene c is 2.

Figure 3

The network of interactions between immune and tumor cells including IL-2 and Sunitinib modeled by De Pillis et al. [49]. CD8+ T-cell and NK cell inhibit tumor cells. But NK cells’ action against tumor cells is obstructed by T-reg cells. Tumor cells in turn inhibit CD8+ T-cells and NK cells. Besides tumor cells, T-reg cells along with IL-2 inhibit CD8+ T-cells. CD8+T cells can be recruited by the debris from tumor cells generated by NK cells, and the immune system can be stimulated by the presence of the tumor to create more CD8+T cells. Lymphocytes promote all the immune cells in the model, while IL-2 promotes all other immune cells except lymphocytes. Last but not least, Sunitinib inhibits T-reg cells that have an indirect effect on the tumor microenvironment.

Figure 4

The network of interactions is modeled by Sofia et al. [93]. In this model, CD8+ T-cells, NK cells (cytotoxic cells), and IFN-$\gamma$ inhibit cancer cells. But when the programmed cell death ligand binds with the programmed cell death proteins, CD8+ T-cells’ death rates of cancer cells are reduced. Cytokines such as IL-2 and IL-12 promote cytotoxic, helper, and regulatory T-cells. However, IL-10 inhibits cytotoxic cells and helper T-cells and promotes macrophages. IFN-$\gamma$ also promotes macrophages. On the other hand, macrophages promote helper T-cells. Dendritic cells promote T-reg, helper, and cytotoxic cells. Cancer cells can promote and inhibit dendritic cells, and IL-6 can increase cancer cells’ proliferation. HMGB1, which is mainly produced by cancer and necrotic cells, promotes helper T-cells and dendritic cells. In addition, cancer cells contribute to the necrotic core due to the fast growth and death of cancer cells.