Note: See links for new open graduate positions in interdisciplinary biology and mathematical biology.

Cryobiology is the study of life at low temperatures. A major branch of cryobiology is cryopreservation where cold is used to preserve life for extended amounts of time. Stored carefully and processed appropriately, samples preserved in liquid nitrogen can be stored for thousands of years. Cryopreservation requires the suppression of intracellular ice, which nearly always requires equilibration of cells and tissues with high concentrations of chemicals called cryoprotective agents or CPAs. These CPAs are similar to antifreeze in that they reduce the melting/freezing temperature of the cells and the solution, but they also contribute to the system's ability to form a solid without ice-crystals. Safely achieving this ice-free, glassy, state is the biggest challenge in the science of cryopreservation. 

My research focuses on using mathematical models to understand and minimize mechanisms of damage caused by the protocols used to achieve this glassy state. There are two major processes I focus on: the equilibration of cells with and from the high concentrations of CPAs needed to avoid intracllular ice, and the prediction of the formation of ice within cells and tissues. 

I use either cell or tissue mass-transport models to predict responses to exposure to CPAs, and am developing damage models to predict which protocols cause the least damage during this process. These damage models relate the accumulation of cellular toxicity due to exposure to CPAs and equilibration protocols. Note that higher toxicity accumulation rates happen at higher concentrations and temperatures,  but these temperatures have shorter exposure times. Therefore, the prediction of optimal protocols depends on an accurate model of temperature dependent transport and damage, and uses optimization and optimal control theory to predict CPA equilibration protocols that minimize this damage. 

The tissue damage models that I am presently developing are cell-based: each individual cell's state is tracked, and allowed to both chemically and physically interact with other cells as well as the interstitium. This allows the accurate prediction of both chemical (toxicity) and mechanical damage caused by cryopreservation protocols. I am developing mass transport models as well as intercellular ice-propagation models as well, where predictions of the movement of ice from one cell to another can aid in the determination of needed cryoprotectant concentrations.  

• JD Benson, AZ Higgins, K Desai, A Eroglu. A toxicity cost function approach to optimal CPA equilibration in tissues. Cryobiology. In Press. https://doi.org/10.1016/j.cryobiol.2017.09.005
• PA Blankenship, SL Stuebing, SS Winter, JL Cheatwood, JD Benson, IQ Whishaw, and DG Wallace. The medial frontal cortex contributes to but does not organize rat exploratory behavior. Neuroscience, 336, 1-11, 2016. doi:10.1016/j.physbeh.2016.04.027
• PA Blankenship, AA Blackwell, N Ebrahimi, JD Benson, and DG Wallace. A History of adolescent binge drinking is associated with impaired self-movement cue processing on manipulatory scale navigation tasks. Physiology and Behavior. 161, 130-139, 2016. doi: 10.1016/j.physbeh.2016.04.027
• AF Davidson, C Glasscock, DR McClanahan, JD Benson, AZ Higgins. Toxicity- Minimized Cryoprotectant Addition and Removal Procedures for Adherent Endothelial Cells. PLOS One 10(11): e0142828, 2015. doi:10.1371/journal.pone.0142828
• JD Benson. Global stability and exact solution of an arbitrary-solute nonlinear cellular mass transport system. Mathematical Biosciences 258,176–181, 2014 doi:10.1016/j.mbs.2014.09.014
• DM Anderson, JD Benson, and AJ Kearsley. Foundations of modeling in cryobiology—I: Concentration, Gibbs energy, and chemical potential relationships Cryobiology, 69 349– 360, 2014. doi:10.1016/j.cryobiol.2014.09.004
• JD Benson, CT Benson, and JK Critser. Mathematical model formulation and validation of water and cryoprotective agent transport in whole hamster pancreatic islets. Mathematical Biosciences. 254, 64–75, 2014 doi:10.1016/j.mbs.2014.06.003
•    AF Davidson, JD Benson, and AZ Higgins. Mathematically Optimized Cryoprotectant Equilibration Procedures for Cryopreservation of Human Oocytes. Theoretical Biology and Mathematical Modeling, 11 (13) 2014. doi: 10.1186/1742-4682-11-13
•    CM Kashuba, JD Benson, and JK Critser. Rationally optimized cryopreservation of multiple mouse embryonic stem cell lines: I—Comparative fundamental cryobiology of and implications for embryonic stem cell cryopreservation protocols. Cryobiology 68 (2) 166-175, 2014. doi:10.1016/j.cryobiol.2013.12.007
•    CM Kashuba, JD Benson, and JK Critser. Rationally optimized cryopreservation of multiple mouse embryonic stem cell lines: II— Mathematical prediction and experimental validation of optimal cryopreservation protocols. Cryobiology 68 (2) 176- 184, 2014. doi:10.1016/j.cryobiol.2013.12.003
• RE Lusianti, JD Benson, JP Acker, AZ Higgins. Rapid removal of glycerol from frozen- thawed red blood cells. Biotechnology Progress, 29 609-620, 2013. onlinelibrary.wiley.com/doi/10.1002/btpr.1710
• JD Benson, EM Walters, EJ Woods and JK Critser. The cryobiology of spermatozoa. Theriogenology, 78 1682-1699, 2012. doi:10.1016/j.theriogenology.2012.06.007
• JD Benson, CC Chicone, and JK Critser. Analytical optimal controls for the state constrained addition and removal of cryoprotective agents. Bulletin of Mathematical Biology 74 (7) 1516-1530, 2012. link.springer.com/article/10.1007/s11538-012-9724-2
• JD Benson. Some comments on recent discussion of the Boyle van't Hoff relationship. Cryobiology 64 (2) 118-120, 2012. doi:10.1016/j.cryobiol.2011.12.001
• Y Wu, JD Benson, M Almasri. Micromachined Coulter counter for dynamic impedence study of time sensitive cells. Biomed Microdevices 14 739-750, 2012. link.springer.com/article/10.1007/s10544-012-9655-6
• JD Benson, AJ Kearsley, and AZ Higgins. Mathematical optimization of procedures for cryoprotectant equilibration using a toxicity cost function Cryobiology 64 (3) 144-151, 2012. doi:10.1016/j.cryobiol.2012.01.001
• JD Benson. Stability analysis of several non-dilute multiple solute transport equations. Journal of Mathematical Chemistry 49 (4) 859-869, 2011. link.springer.com/article/10.1007/s10910-010-9783-2
• JD Benson, CC Chicone, and JK Critser. A general model for the dynamics of cell volume, global stability, and optimal control.Journal of Mathematical Biology 63 (2) 339-359, 2010. ink.springer.com/article/10.1007/s00285-010-0374-4
• JD Benson, A Bagchi, X Han, JK Critser, EJ Woods. Melting point equations for the ternary system water-sodium chloride-ethylene glycol revisited. Cryobiology 61 (3) 352- 356, 2010. doi:10.1016/j.cryobiol.2010.10.001
• Y Wu, JD Benson, JK Critser, M Almasri. MEMS-based Coulter counter for cell counting and sizing using multiple electrodes. J. Micromech. Microeng. 20, 085035. 2010. doi:10.1088/0960-1317/20/8/085035
• Y Wu, JD Benson, JK Critser, M Almasri. Note: Microelectromechanical systems Coulter counter for cell monitoring and counting. Review of Scientific Instruments. 81, 076103. 2010. dx.doi.org/10.1063/1.3462327
• X Han, L Ma, JD Benson, A Brown, JK Critser Measurement of the apparent diffusivity of ethylene glycol in mouse ovaries through rapid MRI and theoretical investigation of cryoprotectant perfusion procedures. Cryobiology. 58 (3), 2009. doi:10.1016/j.cryobiol.2009.02.005
• AI Glazar, SF Mullen, J Liu, JD Benson, JK Critser, EL Squires, JK Graham Osmotic Tolerance Limits and Membrane Permeability Characteristics of Stallion Spermatozoa Treated with Cholesterol. Cryobiology. 59 (2), 2009. doi:10.1016/j.cryobiol.2009.07.009
• S Wei, H Men, JD Benson, JK Critser Osmotic characteristics and fertility of murine spermatozoa collected in different solutions. Reproduction, 137, 215-223, 2009. www.reproduction-online.org/content/137/2/215
• CM Kashuba Benson, JD Benson, JK Critser Improved cryopreservation methods for a mouse embryonic stem cell line. Cryobiology. 56 (2) 2008. doi:10.1016/j.cryobiol.2007.12.002
• S Wei, JD Benson, H Men, JK Critser. Osmotic tolerance limits and effects of cryoprotectants on the motility, plasma membrane integrity and acrosomal integrity of rat sperm. Cryobiology. 53 (3), 336-348. 2006. doi:10.1016/j.cryobiol.2006.09.001
• JD Benson, MA Haidekker, CM Kashuba Benson, JK Critser. Mercury free operation of a Coulter Counter Multisizer II sampling stand. Cryobiology. 51 (3), 344-7. 2005. doi:10.1016/j.cryobiol.2005.08.004
• JD Benson, CC Chicone and JK Critser Exact solutions of a two parameter flux model and cryobiological applications. Cryobiology 50 (3), 308-316. 2005. doi:10.1016/j.cryobiol.2005.03.003
• EJ Woods, JD Benson, Y Agca, JK Critser. Fundamental cryobiology of reproductive cells and tissues. Cryobiology. Apr; 48 (2), 146-56. 2004. doi:10.1016/j.cryobiol.2004.03.002
• MJ Phelps, JD Benson, J Liu, CE Willoughby, JA Gilmore, JK Critser. Effects of Percoll separation, cryoprotective agents, and temperature on plasma membrane permeabil- ity characteristics of murine spermatozoa and their relevance to cryopreservation. Biol Reprod. 61 (4), 1031-41. 1999. www.biolreprod.org/content/61/4/1031
• CT Benson, C Liu, DY Gao, ES Critser, JD Benson, JK Critser. Hydraulic conductivity (Lp) and its activation energy (Ea), cryoprotectant agent permeability (Ps) and its Ea, and reflection coefficients (sigma) for golden hamster individual pancreatic islet cell membranes. Cryobiology. 37 (4) 290-9. 1998. http://europepmc.org/abstract/MED/9917345