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Computer-assisted Large-scale Visualization and Quantification of Pancreatic Islet Mass, Size Distribution and Architecture
Published on: March 4, 2011
Cell-size distribution and scaling in a one-dimensional Kolmogorov-Johnson-Mehl-Avrami lattice model with continuous
Zoltán Néda1, Ferenc Járai-Szabó1, Szilárd Boda1
1Babeş-Bolyai University, Department of Physics, RO-400084, Cluj-Napoca, Romania.
Abstract:
The Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth model is considered on a one-dimensional (1D) lattice. Cells can grow with constant speed and continuously nucleate on the empty sites. We offer an alternative mean-field-like approach for describing theoretically the dynamics and derive an analytical cell-size distribution function. Our method reproduces the same scaling laws as the KJMA theory and has the advantage that it leads to a simple closed form for the cell-size distribution function. It is shown that a Weibull distribution is appropriate for describing the final cell-size distribution. The results are discussed in comparison with Monte Carlo simulation data.
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