Pattern formation of skin cancers: Effects of cancer proliferation and hydrodynamic interactions

Spatial interactions modulate tumor growth and immune infiltration

Direct observation of tumor-immune interactions is unlikely in tumors with currently available technology, but computational simulations based on clinical data can provide insight to test hypotheses. It is hypothesized that patterns of collagen evolve as a mechanism of immune escape, but the exact nature of immune-collagen interactions is poorly understood. Spatial data quantifying collagen fiber alignment in squamous cell carcinomas indicates that late-stage disease is associated with highly aligned fibers. Our computational modeling framework discriminates between two hypotheses: immune cell migration that moves (1) parallel or (2) perpendicular to collagen fiber orientation. The modeling recapitulates immune-extracellular matrix interactions where collagen patterns provide immune protection, leading to an emergent inverse relationship between disease stage and immune coverage. Here, computational modeling provides important mechanistic insights by defining a kernel cell-cell interaction function that considers a spectrum of local (cell-scale) to global (tumor-scale) spatial interactions. Short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects, while asymmetric tumor-immune interaction kernels lead to poor immune response. Thus, the length scale of tumor-immune interaction kernels drives tumor growth and infiltration.

Spatial interactions modulate tumor growth and immune infiltration

Direct observation of immune cell trafficking patterns and tumor-immune interactions is unlikely in human tumors with currently available technology, but computational simulations based on clinical data can provide insight to test hypotheses. It is hypothesized that patterns of collagen formation evolve as a mechanism of immune escape, but the exact nature of the interaction between immune cells and collagen is poorly understood. Spatial data quantifying the degree of collagen fiber alignment in squamous cell carcinomas indicates that late stage disease is associated with highly aligned fibers. Here, we introduce a computational modeling framework (called Lenia) to discriminate between two hypotheses: immune cell migration that moves 1) parallel or 2) perpendicular to collagen fiber orientation. The modeling recapitulates immune-ECM interactions where collagen patterns provide immune protection, leading to an emergent inverse relationship between disease stage and immune coverage. We also illustrate the capabilities of Lenia to model the evolution of tumor progression and immune predation. Lenia provides a flexible framework for considering a spectrum of local (cell-scale) to global (tumor-scale) dynamics by defining a kernel cell-cell interaction function that governs tumor growth dynamics under immune predation with immune cell migration. Mathematical modeling provides important mechanistic insights into cell interactions. Short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects, while asymmetric tumor-immune interaction kernels lead to poor immune response. Thus, the length scale of tumor-immune interactions drives tumor growth and infiltration.

Conditions of acceleration and deceleration of the cancer cell growth under osmotic pressure

In this paper, we study a pattern formation in the epidermal layer of skin during tumor development and appearance of a binary surface consisting of healthy and cancer cells forming Turing patterns under external osmotic pressure. The basic methodology of introducing the external influences, for example, time-targeted drug therapy or radiation exposure, influence of electromagnetic fields, laser radiation or other tumor-targeting physical influences act differently in different phases of the cell cycle. In some cases, this can lead to a slowdown in the growth of cancer cells, and sometimes vice versa. Therefore, it is of particular interest to choose the right parameters such as starting time of external pressure, its magnitude and duration depending on the cell cycle of developing cancer cells. We propose a biologically inspired model that allows us to simulate the growth of cancer cells under conditions of osmotic pressure. We divide this growth into two phases. The first is characterized by active cell division, and the second by their growth. In this article, we introduce two types of pressure: short-term and long-term, and looked at what this leads to in different phases. We have found an interesting result, that there are some resonant points in time both in the first and second phases, when the introduction of additional pressure leads to the most significant slowdown in the growth of cancer cells.

Morphological instability of solid tumors in a nutrient-deficient environment

A phenomenological reaction-diffusion model that includes a nutrient-regulated growth rate of tumor cells is proposed to investigate the morphological instability of solid tumors during the avascular growth. We find that the surface instability could be induced more easily when tumor cells are placed in a harsher nutrient-deficient environment, while the instability is suppressed for tumor cells in a nutrient-rich environment due to the nutrient-regulated proliferation. In addition, the surface instability is shown to be influenced by the growth moving speed of tumor rims. Our analysis reveals that a larger growth movement of the tumor front results in a closer proximity of tumor cells to a nutrient-rich region, which tends to inhibit the surface instability. A nourished length that represents the proximity is defined to illustrate its close relation to the surface instability.

3D models of the dynamics of cancer cells under external pressure

Skin cancer is one of the most frequent cancers worldwide. Recently, it has been shown that the tumor proliferation rate in skin and its dynamics can be changed by an osmotic pressure. However, these findings are rather unstructured. A weak pressure can slow down the tumor growth, while a very high pressure can, on the contrary, lead to accelerated growth and metastases. The magnitude and spatial distribution of osmotic pressures in tumors at present cannot be measured experimentally. Therefore, it is of particular interest to find appropriate models that would simulate the effects of additional osmotic pressures in skin and assess the features of its implementation. In this paper, we suggest an improved model based on the principles of the conventional hydrodynamic model for macrophase separations, which allows one to include not only the properties of healthy and cancer cells but also the microenvironment. We study and analyze the proliferation of cancer cells in 3D models of the epidermal layer of skin under an osmotic pressure. There are two suggested 3D models that are based on the same principles: (1) cellular cubic lattice and (2) cell spheroid. This allows expanding the application of the model depending on a given task. Here, we are focused on the study of melanoma at an early stage when there are not many cancer cells. Additional compressive and expansive pressures are added to the central part of the system. Both systems demonstrate similar results in slowing down the rate of tumor growth with a small pressure.

Clonal pattern dynamics in tumor: the concept of cancer stem cells

We present a multiphase model for solid tumor initiation and progression focusing on the properties of cancer stem cells (CSC). CSCs are a small and singular cell sub-population having outstanding capacities: high proliferation rate, self-renewal and extreme therapy resistance. Our model takes all these factors into account under a recent perspective: the possibility of phenotype switching of differentiated cancer cells (DC) to the stem cell state, mediated by chemical activators. This plasticity of cancerous cells complicates the complete eradication of CSCs and the tumor suppression. The model in itself requires a sophisticated treatment of population dynamics driven by chemical factors. We analytically demonstrate that the rather important number of parameters, inherent to any biological complexity, is reduced to three pivotal quantities.Three fixed points guide the dynamics, and two of them may lead to an optimistic issue, predicting either a control of the cancerous cell population or a complete eradication. The space environment, critical for the tumor outcome, is introduced via a density formalism. Disordered patterns are obtained inside a stable growing contour driven by the CSC. Somewhat surprisingly, despite the patterning instability, the contour maintains its circular shape but ceases to grow for a typical size independently of segregation patterns or obstacles located inside.