Foundations of modeling in cryobiology-III: Inward solidification of a ternary solution towards a permeable spherical cell in the dilute limit

A three-dimensional lattice-free agent-based model of intracellular ice formation and propagation and intercellular mechanics in liver tissues

A successful cryopreservation of tissues and organs is crucial for medical procedures and drug development acceleration. However, there are only a few instances of successful tissue cryopreservation. One of the main obstacles to successful cryopreservation is intracellular ice damage. Understanding how ice spreads can accelerate protocol development and enable model-based decision-making. Previous models of intracellular ice formation in individual cells have been extended to one-cell-wide arrays to establish the theory of intercellular ice propagation in tissues. The current lattice-based ice propagation models do not account for intercellular forces resulting from cell solidification, which could lead to mechanical disruption of tissue structures during freezing. Moreover, these models have not been expanded to include more realistic tissue architectures. In this article, we discuss the development and validation of a stochastic model for the formation and propagation of ice in small tissues using lattice-free agent-based model. We have improved the existing model by incorporating the mechanical effects of water crystallization within cells. Using information from previous research, we have also created a new model that accounts for ice growth in tissue slabs, spheroids and hepatocyte discs. Our model demonstrates that individual cell freezing can have mechanical consequences and is consistent with earlier findings.

Rational synthesis of total damage during cryoprotectant equilibration: modelling and experimental validation of osmomechanical, temperature, and cytotoxic damage in sea urchin (Paracentrotus lividus) oocytes

Sea urchins (e.g., Paracentrotus lividus) are important for both aquaculture and as model species. Despite their importance, biobanking of urchin oocytes by cryopreservation is currently not possible. Optimized cryoprotectant loading may enable novel vitrification methods and thus successful cryopreservation of oocytes. One method for determining an optimized loading protocol uses membrane characteristics and models of damage, namely osmomechanical damage, temperature damage (e.g., chill injury) and cytotoxicity. Here we present and experimentally evaluate existing and novel models of these damage modalities as a function of time and temperature. In osmomechanical damage experiments, oocytes were exposed for 2 to 30 minutes in hypertonic NaCl or sucrose supplemented seawater or in hypotonic diluted seawater. In temperature damage experiments, oocytes were exposed to 1.7 °C, 10 °C, or 20 °C for 2 to 90 minutes. Cytotoxicity was investigated by exposing oocytes to solutions of Me2SO for 2 to 30 minutes. We identified a time-dependent osmotic damage model, a temperature-dependent damage model, and a temperature and time-dependent cytotoxicity model. We combined these models to estimate total damage during a cryoprotectant loading protocol and determined the optimal loading protocol for any given goal intracellular cryoprotectant concentration. Given our fitted models, we find sea urchin oocytes can only be loaded to 13% Me2SO v/v with about 50% survival. This synthesis of multiple damage modalities is the first of its kind and enables a novel approach to modelling cryoprotectant equilibration survival for cells in general.

Loading equine oocytes with cryoprotective agents captured with a finite element method model

Cryopreservation can be used to store equine oocytes for extended periods so that they can be used in artificial reproduction technologies at a desired time point. It requires use of cryoprotective agents (CPAs) to protect the oocytes against freezing injury. The intracellular introduction of CPAs, however, may cause irreversible osmotic damage. The response of cells exposed to CPA solutions is governed by the permeability of the cellular membrane towards water and the CPAs. In this study, a mathematical mass transport model describing the permeation of water and CPAs across an oocyte membrane was used to simulate oocyte volume responses and concomitant intracellular CPA concentrations during the exposure of oocytes to CPA solutions. The results of the analytical simulations were subsequently used to develop a phenomenological finite element method (FEM) continuum model to capture the response of oocytes exposed to CPA solutions with spatial information. FEM simulations were used to depict spatial differences in CPA concentration during CPA permeation, namely at locations near the membrane surface and towards the middle of the cell, and to capture corresponding changes in deformation and hydrostatic pressure. FEM simulations of the multiple processes occurring during CPA loading of oocytes are a valuable tool to increase our understanding of the mechanisms underlying cryopreservation outcome.

Mathematical Modeling and Optimization of Cryopreservation in Single Cells

Cryobiology is a multiscale and interdisciplinary field. The scope and scale of interactions limit the gains that can be made by one theory or experiment alone. Because of this, modeling has played a critical role in both explaining cryobiological phenomena and predicting improved protocols. Modeling facilitates understanding of the biophysical and some of the biochemical mechanisms of damage during all phases of cryopreservation including CPA equilibration and cooling and warming. Moreover, as a tool for optimization of cryopreservation protocols, modeling has yielded many successes. Modern cryobiological modeling includes very detailed descriptions of the physical phenomena that occur during freezing, including ice growth kinetics and spatial gradients that define heat and mass transport models. Here we reduce the complexity and approach only a small but classic subset of these problems. Namely, here we describe the process of building and using a mathematical model of a cell in suspension where spatial homogeneity is assumed for all quantities. We define the models that describe the critical cell quantities used to describe optimal and suboptimal protocols and then give an overview of classical methods of how to determine optimal protocols using these models. We include practical considerations of modeling in cryobiology, including fitting transport models to cell volume data, performing optimization with cell volume constraints, and a look at expanding cost functions to cooling regimes.