Reproduction of patterns in melanocytic proliferations by agent-based simulation and geometric modeling

Abstract

Spatio-temporal patterns of melanocytic proliferations observed in vivo are important for diagnosis but the mechanisms that produce them are poorly understood. Here we present an agent-based model for simulating the emergence of the main biologic patterns found in melanocytic proliferations. Our model portrays the extracellular matrix of the dermo-epidermal junction as a two-dimensional manifold and we simulate cellular migration in terms of geometric translations driven by adhesive, repulsive and random forces. Abstracted cellular functions and melanocyte-matrix interactions are modeled as stochastic events. For identification and validation we use visual renderings of simulated cell populations in a horizontal perspective that reproduce growth patterns observed in vivo by sequential dermatoscopy and corresponding vertical views that reproduce the arrangement of melanocytes observed in histopathologic sections. Our results show that a balanced interplay of proliferation and migration produces the typical reticular pattern of nevi, whereas the globular pattern involves additional cellular mechanisms. We further demonstrate that slight variations in the three basic cellular properties proliferation, migration, and adhesion are sufficient to produce a large variety of morphological appearances of nevi. We anticipate our model to be a starting point for the reproduction of more complex scenarios that will help to establish functional connections between abstracted microscopic behavior and macroscopic patterns in all types of melanocytic proliferations including melanoma.

Multiscale modeling of drug resistance in glioblastoma with gene mutations and angiogenesis

“…Over the past decades, many mathematical models have been developed to simulate tumor evolution, such as ODE models [29] , [30] , stochastic differential equation models [31] , [32] , [33] , partial differential equation models [34] , [35] , agent-based models [36] , [37] , and hybrid models [38] , [39] . These models have shed light on the biological mechanisms underlying tumor growth, offering valuable insights into the intricacies of drug resistance.…”

Front-like expansion and arrest of programmed cell death in brown banana spots

“…Spot expansion and arrest also rule the dynamics of melanocytic nevi (brown moles or birthmarks) on newborn humans [38] as well as the formation of numerous animal skin, fur, and wing patterns [25,28]. A systematic classification of biological spot patterns in terms of their underlying dynamics could be a useful and interesting challenge for future investigations.…”