An agent based model of intracellular ice formation and propagation in small tissues

Abstract Successful cryopreservation of tissues and organs would be a critical tool to accelerate drug discovery and facilitate myriad life saving and quality of life improving medical interventions. Unfortunately success in tissue cryopreservation is quite limited, and there have been no reports of successful long term organ cryopreservation. One principal challenge of tissue and organ cryopreservation is the propagation of damaging intracellular ice. Understanding the probability that cells in tissues form ice under a given cryopreservation protocol would greatly accelerate protocol design, enabling rational model-based decisions of all aspects of the cryopreservation procedure. Established models of intracellular ice formation (IIF) in individual cells have previously been extended to small linear (one-cell-wide) arrays to establish the theory of intercellular ice propagation in tissues. However these small-scale lattice-based tissue ice propagation models have not been extended to more realistic tissue structures, and do not account for intercellular forces that arise from the expansion water into ice that may cause mechanical disruption of tissue structures during freezing. To address these shortcomings, here we present the development and validation of a lattice-free agent-based stochastic model of ice formation and propagation in small tissues. We validate our Monte Carlo model against Markov chain models in the linear two-cell and four-cell arrays presented in the literature, as well as against new Markov chain results for 2 × 2 arrays. Moreover we expand the existing model to account for the solidification of water into ice in cells. We then use literature data to inform a model of ice propagation in hepatocyte disks, spheroids, and tissue slabs. Our model aligns well with previously reported experiments, and demonstrates that the mechanical effects of individual cells freezing can be captured. Author summary The widespread ability to successfully store, or cryopreserve, tissues and organs in liquid nitrogen temperatures would be game changing for human and animal medicine and drug discovery. However, success is limited to a select number of small tissues, and no organs can currently be stored in a frozen or solid state and survive thawing. One major contributor to damage during this process is the formation of intracellular ice, and its associated cell level damage. This ice formation is complicated in tissues by the number of intercellular connections facilitating intercellular ice propagation. Previous researchers have developed and experimentally validated simple one dimensional models of ice propagation in tissues, but these fail to capture complex tissue geometries, and have many fewer intercellular connections compared to three dimensional tissues. In this paper, we adopt previous models of ice formation and propagation to a model capable of capturing arbitrary cell orientations in three dimensions, allowing for realistic tissue structures to be modelled. We validated this tool on simple models and with experimental data, and then test it on three structures made of digital liver cells: disks, spheroids, and slabs. We show that we can capture new information about the interaction of cooling the tissue, the formation of intracellular ice, the movement of ice from one cell to another, and the mechanical disruption that occurs during this process. This allows for novel insights into a mechanism of damage during cryopreservation that is cooling rate and tissue structure dependent.

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