Publications (underlined titles are hyperlinks to pre/re-prints): Analytic time optimal boundary control of the diffusion equation with applications in cryobiology. (with AJ Kearsley) In preparation. The main idea of this work is that the optimization of cryo-protocols depends on cost functions defined only in the bio-domain and the exterior of the system. For example, when determining optimal cooling protocols, we ultimately only care to minimize ice-related cell death in the tissue,without regard to the state outside of the tissue. This allows for a “decoupling” of optimization problems into a (typically) state constrained boundary control problem, and an inverse problem. In this manuscript we use ideas from inverse problem theory to analytically determine the optimal boundary control for a coupled mass transport system with a 1D linear diffusion equation in the extratissue domain. We then show that this system is not exactly controllable, and prove the optimality of an analytic regularized control. Finally, we compare results of the regularized control to a direct numerical method. Optimal control of a coupled heat and mass transfer model with applications in rapid freezing of tissues. (with AJ Kearsley) In preparation. Here we extend and refine ideas described in a paper with Han et al (#13 below). We model heat transport in a tissue enclosed in a “cryotube” to determine the spatial dependence of cooling rate when the system is plunged into liquid nitrogen. We then use the glass transition phase diagram to determine minimal concentrations needed to ensure the exclusion of ice formation in the tissue at the modeled cooling rates. We then determine the optimal boundary concentration control (minimizing the time- and toxicity- cost functionals defined in papers #5 and #4, respectively) to achieve this two-dimensionally spatially dependent concentration distribution. On the choice of cryoprotectant toxicity cost functionals for a state constrained cellular mass transport optimal control problem. (with AJ Kearsley) In preparation. Here we prove some results on the insensitivity of optimal trajectory to the cost functional in the setting of optimal concentration control in cryobiology. In particular, we show that for all monotonic cost functions in concentration, the optimal cryopreservative addition strategy is to first increase total volume to the state constraint. We then give an analytic approach to determine optimal switching times for the remainder of the trajectory. Identification and minimization of a toxicity cost function for the optimal addition and removal of cryoprotectants. (with AZ Higgins and AJ Kearsley) (In review: Biotechnology and Bioengineering). Here we use published time dependent toxicity values to determine the functional relationship between intracellular concentration and cumulative toxicity by fitting a power law equation to data. We then use a numerical approach to determine toxicity-optimal cryoprotective agent (CPA) equilibration strategies. We compare these to previously determined time-optimal continuous (#5 below) and stepwise (e.g. #14,19, 20 below) strategies. 5. Analytical optimal controls for the state constrained addition and removal of cryoprotective agents. (with CC Chicone and JK Critser) (In review: Bulletin of Mathematical Biology) 6. Mathematical model formulation and validation of water and cryoprotective agent transport in whole hamster pancreatic islets. (with CT Benson and JK Critser) (In review: Journal of Biomechanical Engineering) 7. A calorimetric method to measure water-cryoprotectant mutual diffusivity in biological tissues at both super- and sub-zero temperatures. (with X Han, Y Liu, JK Critser) (In review: Int. J. Heat and Mass Transfer). 8. Stability analysis of several non-dilute multiple solute transport equations. (In press: Journal of Mathematical Chemistry). 9. A general model for the dynamics of cell volume, global stability, and optimal control. (with CC Chicone and JK Critser) (In press: Journal of Mathematical Biology). 10. Melting point equations for the ternary system water-sodium chloride-ethylene glycol revisited. (with A Bagchi, X Han, JK Critser, EJ Woods) (In press: Cryobiology). 11. MEMS-based Coulter counter for cell counting and sizing using multiple electrodes (with Y Wu, JK Critser, M Almasri.). J. Micromech. Microeng. 20, 085035. 2010. 12. Note: Microelectromechanical systems Coulter counter for cell monitoring and counting (with Y Wu, JK Critser, M Almasri). Review of Scientific Instruments. 81, 076103. 2010. 13. Measurement of the apparent diffusivity of ethylene glycol in mouse ovaries through rapid MRI and theoretical investigation of cryoprotectant perfusion procedures. (with X Han, L Ma, A Brown, JK Critser). Cryobiology. 58 (3), 2009. 14. Osmotic Tolerance Limits and Membrane Permeability Characteristics of Stallion Spermatozoa Treated with Cholesterol (with AI Glazar, SF Mullen, J Liu, JK Critser, EL Squires, JK Graham). Cryobiology. 59 (2), 2009. 15. Osmotic characteristics and fertility of murine spermatozoa collected in different solutions (S Wei, H Men, JK Critser). Reproduction, 137, 215-223, 2009. 16. *The History of Sperm Cryopreservation (with Walters E.M., Woods E., Critser J.K.). In: A Practical Guide to Sperm Banking. Ed: Allan Pacey and Matthew Tomlinson. 2009. 17. A MEMS based Coulter counter for cell sizing. (with M Korampally, Y Wu, JK Critser, M Almasri). In: Proceedings of SPIE: Microfluidics, BioMEMS, and Medical Microsystems VI. 22 January 2008, San Jose, CA, Vol. 6886, p 68860A 18. Development of a micro-scale differential scanning calorimeter for single cell measurements (with WG Zhao, GL Solbrekken, SF Mullen, X Han, JK Critser). In: Proceedings of HT2007: 2007 ASME-JSME Thermal Engineering Summer Heat Transfer Conference. July 8-12, 2007, Vancouver, British Columbia, Canada. Paper number HT2007-321555. 19. Improved cryopreservation methods for a mouse embryonic stem cell line. (with CM Kashuba Benson, JK Critser). Cryobiology. 56 (2) 2008. 20. Osmotic tolerance limits and effects of cryoprotectants on the motility, plasma membrane integrity and acrosomal integrity of rat sperm.(with S Wei, H Men, JK Critser). Cryobiology. 53 (3), 336-348. 2006. 21. Mercury free operation of a Coulter Counter Multisizer II sampling stand(with MA Haidekker, CM Kashuba Benson, JK Critser). Cryobiology. 51 (3), 344-7. 2005. 22. Exact solutions of a two parameter flux model and cryobiological applications(with CC Chicone and JK Critser). Cryobiology 50 (3), 308— 316. 2005. 23. Fundamental cryobiology of reproductive cells and tissues (with EJ Woods, Y Agca, JK Critser). Cryobiology. Apr; 48 (2), 146-56. 2004. 24. *Fundamental Cryobiology (with JK Critser). In: Proceedings of a Workshop on Transporting Gametes and Embryos. (2004) Havemeyer Monograph Series No. 12. Suffolk, UK. 25. Effects of Percoll separation, cryoprotective agents, and temperature on plasma membrane permeability characteristics of murine spermatozoa and their relevance to cryopreservation (with MJ Phelps, J Liu, CE Willoughby, JA Gilmore, JK Critser). Biol Reprod. 61 (4), 1031-41. 1999. 26. 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 (with CT Benson, C Liu, DY Gao, ES Critser, JK Critser). Cryobiology. 37 (4) 290-9. 1998. *Not peer reviewed

Publications (underlined titles are hyperlinks to pre/re-prints):

1.Analytic time optimal boundary control of the diffusion equation with applications in cryobiology. (with AJ Kearsley) In preparation.

The main idea of this work is that the optimization of cryo-protocols depends on cost functions defined only in the bio-domain and the exterior of the system. For example, when determining optimal cooling protocols, we ultimately only care to minimize ice-related cell death in the tissue,without regard to the state outside of the tissue. This allows for a “decoupling” of optimization problems into a (typically) state constrained boundary control problem, and an inverse problem. In this manuscript we use ideas from inverse problem theory to analytically determine the optimal boundary control for a coupled mass transport system with a 1D linear diffusion equation in the extratissue domain. We then show that this system is not exactly controllable, and prove the optimality of an analytic regularized control. Finally, we compare results of the regularized control to a direct numerical method.

2.Optimal control of a coupled heat and mass transfer model with applications in rapid freezing of tissues. (with AJ Kearsley) In preparation.

Here we extend and refine ideas described in a paper with Han et al (#13 below). We model heat transport in a tissue enclosed in a “cryotube” to determine the spatial dependence of cooling rate when the system is plunged into liquid nitrogen. We then use the glass transition phase diagram to determine minimal concentrations needed to ensure the exclusion of ice formation in the tissue at the modeled cooling rates. We then determine the optimal boundary concentration control (minimizing the time- and toxicity- cost functionals defined in papers #5 and #4, respectively) to achieve this two-dimensionally spatially dependent concentration distribution.

3.On the choice of cryoprotectant toxicity cost functionals for a state constrained cellular mass transport optimal control problem. (with AJ Kearsley) In preparation.

Here we prove some results on the insensitivity of optimal trajectory to the cost functional in the setting of optimal concentration control in cryobiology. In particular, we show that for all monotonic cost functions in concentration, the optimal cryopreservative addition strategy is to first increase total volume to the state constraint. We then give an analytic approach to determine optimal switching times for the remainder of the trajectory.

4.Identification and minimization of a toxicity cost function for the optimal addition and removal of cryoprotectants. (with AZ Higgins and AJ Kearsley) (In review: Biotechnology and Bioengineering).

Here we use published time dependent toxicity values to determine the functional relationship between intracellular concentration and cumulative toxicity by fitting a power law equation to data. We then use a numerical approach to determine toxicity-optimal cryoprotective agent (CPA) equilibration strategies. We compare these to previously determined time-optimal continuous (#5 below) and stepwise (e.g. #14,19, 20 below) strategies.

5.Analytical optimal controls for the state constrained addition and removal of cryoprotective agents. (with CC Chicone and JK Critser) (In review: Bulletin of Mathematical Biology)

6.Mathematical model formulation and validation of water and cryoprotective agent transport in whole hamster pancreatic islets. (with CT Benson and JK Critser) (In review: Journal of Biomechanical Engineering)

7.A calorimetric method to measure water-cryoprotectant mutual diffusivity in biological tissues at both super- and sub-zero temperatures. (with X Han, Y Liu, JK Critser) (In review: Int. J. Heat and Mass Transfer).

8.Stability analysis of several non-dilute multiple solute transport equations. (In press: Journal of Mathematical Chemistry).

9.A general model for the dynamics of cell volume, global stability, and optimal control. (with CC Chicone and JK Critser) (In press: Journal of Mathematical Biology).

10.Melting point equations for the ternary system water-sodium chloride-ethylene glycol revisited. (with A Bagchi, X Han, JK Critser, EJ Woods) (In press: Cryobiology).

11.MEMS-based Coulter counter for cell counting and sizing using multiple electrodes (with Y Wu, JK Critser, M Almasri.). J. Micromech. Microeng. 20, 085035. 2010.

12.Note: Microelectromechanical systems Coulter counter for cell monitoring and counting (with Y Wu, JK Critser, M Almasri). Review of Scientific Instruments. 81, 076103. 2010.

13.Measurement of the apparent diffusivity of ethylene glycol in mouse ovaries through rapid MRI and theoretical investigation of cryoprotectant perfusion procedures. (with X Han, L Ma, A Brown, JK Critser). Cryobiology. 58 (3), 2009.

14.Osmotic Tolerance Limits and Membrane Permeability Characteristics of Stallion Spermatozoa Treated with Cholesterol (with AI Glazar, SF Mullen, J Liu, JK Critser, EL Squires, JK Graham). Cryobiology. 59 (2), 2009.

15.Osmotic characteristics and fertility of murine spermatozoa collected in different solutions (S Wei, H Men, JK Critser). Reproduction, 137, 215-223, 2009.

16.*The History of Sperm Cryopreservation (with Walters E.M., Woods E., Critser J.K.). In: A Practical Guide to Sperm Banking. Ed: Allan Pacey and Matthew Tomlinson. 2009.

17.A MEMS based Coulter counter for cell sizing. (with M Korampally, Y Wu, JK Critser, M Almasri). In: Proceedings of SPIE: Microfluidics, BioMEMS, and Medical Microsystems VI. 22 January 2008, San Jose, CA, Vol. 6886, p 68860A

18.Development of a micro-scale differential scanning calorimeter for single cell measurements (with WG Zhao, GL Solbrekken, SF Mullen, X Han, JK Critser). In: Proceedings of HT2007: 2007 ASME-JSME Thermal Engineering Summer Heat Transfer Conference. July 8-12, 2007, Vancouver, British Columbia, Canada. Paper number HT2007-321555.

19.Improved cryopreservation methods for a mouse embryonic stem cell line. (with CM Kashuba Benson, JK Critser). Cryobiology. 56 (2) 2008.

20.Osmotic tolerance limits and effects of cryoprotectants on the motility, plasma membrane integrity and acrosomal integrity of rat sperm.(with S Wei, H Men, JK Critser). Cryobiology. 53 (3), 336-348. 2006.

21.Mercury free operation of a Coulter Counter Multisizer II sampling stand(with MA Haidekker, CM Kashuba Benson, JK Critser). Cryobiology. 51 (3), 344-7. 2005.

22.Exact solutions of a two parameter flux model and cryobiological applications(with CC Chicone and JK Critser). Cryobiology 50 (3), 308— 316. 2005.

23.Fundamental cryobiology of reproductive cells and tissues (with EJ Woods, Y Agca, JK Critser). Cryobiology. Apr; 48 (2), 146-56. 2004.

24.*Fundamental Cryobiology (with JK Critser). In: Proceedings of a Workshop on Transporting Gametes and Embryos. (2004) Havemeyer Monograph Series No. 12. Suffolk, UK.

25.Effects of Percoll separation, cryoprotective agents, and temperature on plasma membrane permeability characteristics of murine spermatozoa and their relevance to cryopreservation (with MJ Phelps, J Liu, CE Willoughby, JA Gilmore, JK Critser). Biol Reprod. 61 (4), 1031-41. 1999.

26.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 (with CT Benson, C Liu, DY Gao, ES Critser, JK Critser). Cryobiology. 37 (4) 290-9. 1998.

*Not peer reviewed