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Kinetics of Intracellular Ice Formation in One-Dimensional Arrays of Interacting Biological Cells

Daniel Irimia ^* and Jens O. M. Karlsson 

^* Center for Engineering in Medicine and Surgical Services, Massachusetts General Hospital, Shriners Hospital for Children, and Harvard Medical School, Boston, Massachusetts 02129; and Woodruff School of Mechanical Engineering, and Petit Institute for Bioengineering and Bioscience, Georgia Institute of Technology, Atlanta, Georgia 30332

Correspondence: Address reprint requests to Dr. Jens O. M. Karlsson, Georgia Institute of Technology, Woodruff School of Mechanical Engineering, Atlanta, GA 30332-0405. Tel.: 404-385-4157; Fax: 404-385-1397; E-mail: karlsson{at}alum.mit.edu.

Although cell-cell interactions are known to significantly affect the kinetics of intracellular ice formation (IIF) during tissue freezing, this effect is not well understood. Progress in elucidating the mechanism and role of intercellular ice propagation in tissue freezing has been hampered in part by limitations in experimental design and data analysis. Thus, using rapid-cooling cryomicroscopy, IIF was measured in adherent cells cultured in micropatterned linear constructs (to control cell-cell interactions and minimize confounding factors). By fitting a Markov chain model to IIF data from micropatterned HepG2 cell pairs, the nondimensional rate of intercellular ice propagation was found to be = 10.4 ± 0.1. Using this measurement, a new generator matrix was derived to predict the kinetics of IIF in linear four-cell constructs; cryomicroscopic measurements of IIF state probabilities in micropatterned four-cell arrays conformed with theoretical predictions (p < 0.05), validating the modeling assumptions. Thus, the theoretical model was extended to allow prediction of IIF in larger tissues, using Monte Carlo techniques. Simulations were performed to investigate the effects of tissue size and ice propagation rate, for one-dimensional tissue constructs containing up to 100 cells and nondimensional propagation rates in the range 0.1 1000.