Tumor proliferation and diffusion on percolation clusters

Abstract

We study in silico the influence of host tissue inhomogeneity on tumor cell proliferation and diffusion by simulating the mobility of a tumor on percolation clusters with different homogeneities of surrounding tissues. The proliferation and diffusion of a tumor in an inhomogeneous tissue could be characterized in the framework of the percolation theory, which displays similar thresholds (0.54, 0.44, and 0.37, respectively) for tumor proliferation and diffusion in three kinds of lattices with 4, 6, and 8 connecting near neighbors. Our study reveals the existence of a critical transition concerning the survival and diffusion of tumor cells with leaping metastatic diffusion movement in the host tissues. Tumor cells usually flow in the direction of greater pressure variation during their diffusing and infiltrating to a further location in the host tissue. Some specific sites suitable for tumor invasion were observed on the percolation cluster and around these specific sites a tumor can develop into scattered tumors linked by some advantage tunnels that facilitate tumor invasion. We also investigate the manner that tissue inhomogeneity surrounding a tumor may influence the velocity of tumor diffusion and invasion. Our simulation suggested that invasion of a tumor is controlled by the homogeneity of the tumor microenvironment, which is basically consistent with the experimental report by Riching et al. as well as our clinical observation of medical imaging. Both simulation and clinical observation proved that tumor diffusion and invasion into the surrounding host tissue is positively correlated with the homogeneity of the tissue.

Invasiveness of Cancer Populations in a Two-dimensional Percolation cluster: a Stochastic Mathematical Approach

“…Paget (1889) has proposed the ‘seed-soil’ hypothesis to explain the organ-specificity of cancer metastasis, marking the beginning of a journey of query spanning more than a century. Jiang et al (2014, 2016) have computed the diffusion exponent of cancer cell population in 2D percolation cluster to evaluate the invasiveness quantitatively. However, the Logistic growth model they used proved inaccurate when cell density is low (Johnson et al, 2019; Korolev et al, 2014; Neufeld et al, 2017).…”

“…In the studies of (Jiang et al, 2014, 2016) and (Liang et al, 2019), the used parameters were cited from various references and thus lacked consistency. As a result, uncertainty assessment of the parameters could be hindered.…”

In vivo mimicking model for solid tumor towards hydromechanics of tissue deformation and creation of necrosis

“…In this study, we attempt an extension of the isolated solid tumor model where the tumor possesses a normal tissue layer surrounding the tumor tissue. This mathematical model is represented as an in vivo tumor analogous model [38][39][40][41]. There must be some physiological differences between normal and tumor tissues [26,42,43].…”