Optimal control in cryopreservation of living cells and tissues (renewal proposal)

Size: px

Start display at page:

Download "Optimal control in cryopreservation of living cells and tissues (renewal proposal)"

Egbert Parks
6 years ago
Views:

1 DFG Priority Program SPP 1253/2 Optimization with partial differential equations Optimal control in cryopreservation of living cells and tissues (renewal proposal) Prof. Dr. K-H. Hoffmann Technische Universität München, Zentrum Mathematik Chair of Mathematical Modelling Garching, Germany Review Process Freising, March 30-31

2 Objectives of the renewal proposal Development of mathematical models describing processes occurring in frozen cells and tissues during warming and thawing. The models have to account for effects of recrystallization, devitrification, cell dehydration, and rehydration. Application of control theory to design of optimized thawing protocols that essentially reduce injuring factors of thawing. Optimization will improve such biological indexes as viability, fresh level, and the level of pluripotency. Implementation of optimized thawing protocols as stable software in freezing plants such as IceCube devices. It is very important that the proposal will be worked out in cooperation with practicing biologists to calibrate the models and verify the efficiency of the optimized thawing protocols experimentally.

3 Some cell-damaging factors of thawing 1. Recrystallization of small ice crystals into large ones (rapid cooling but slow thawing) 2. Devitrification resulting into formation of irregular ice crystals (rapid thawing) 3. Further osmotic dehydration occurring during the warming phase, if the osmotic equilibrium was violated because of the rapid cooling (rapid cooling but slow thawing) 4. Rehydration and swelling of cells when as more ice melts.

Processes occurring in frozen cells during warming and thawing and their modeling Dendrites. Allen-Cahn and Cahn- Hilliard equations (Cahn, Garcke, Hoffmann) Ice nuclei.

4 Processes occurring in frozen cells during warming and thawing and their modeling Dendrites. Allen-Cahn and Cahn- Hilliard equations (Cahn, Garcke, Hoffmann) Ice nuclei. Thermodynamic models of nucleation (Toner, Karlsson, Mazur, Muldrew) Bulk ice. Phase-field models (Frémond, Caginalp, Hoffmann, Xu) Vitrified water. Molecular dynamics simulations (Brockbank) Osmotic flows

What is vitrification? How to study it? Vitrification can be achieved by developing a hydrogen bonding network within water that needs to be broken down for crystal growth.

5 What is vitrification? How to study it? Vitrification can be achieved by developing a hydrogen bonding network within water that needs to be broken down for crystal growth. A hydrogen bond is the attractive force between one electronegative atom and a hydrogen covalently bonded to another electronegative atom. It results from a dipole-dipole force with a hydrogen atom bonded to oxygen. Molecular dynamics simulations of the formation of hydrogen bonding networks in pure water. M. Matsumoto & I. Ohmine. J. Chem. Phys. 104 (7), 15 February Molecular dynamics modeling of the promotion of vitrification by intracellular macromolecules and cryoprotective agents. G. Morra. Dissertation, Berlin, 2005

6 Coupled controlled model of thawing are the volume fractions of bulk ice, dendritic ice, ice nuclei, vitrified solute, and liquid phase.,, is the temperature. Free energy: gradient part (surface energy) generalized quartic free energy deviation from the thermodynamical equilibrium

7 Heat equation: are linear functions of the temperature θ and controls c; these functions define the rates of transition between phases. is a vector of controls associated with cryoprotective agents that vary eutectic properties of solutions., - specific activation energies. Dynamics of the phase functions: Allen-Cahn system Cahn-Hillard system Appropriate for the description of the aggregation of ice nuclei into larger dendritic ice crystals. Numerical implementation and design of optimal controls suppressing dendrite growth assumes cooperation with H. Garcke and L. Blank.

8 Examples of objective functionals, - volume fractions of the dendritic ice and the liquid phase, respectively - the temperature in the extracellular space (control function) - vector of parameters associated with cryoprotective agents (controls) - prescribed rate of the intracellular temperature 1. Minimization of the dendritie ice content with accounting for the rate of the mean intracellular temperature: 2. The same meaning but with point-wise index and state constraints : s. t. 3. Minimization of the thawing duration with accounting for the temperature rate: Minimization of the last functional is favorable for the reduction of cell swelling caused by the rehydration. It is observed in experiments that rapid thawing is also preferable in many other aspects., s. t.

simulation of thawing intracellular bulk ice when the extracellular

9 First simulations for a simplified model are functions of the temperature, simplified phase transition equations = bulk ice = dendrite ice 2D simulation of thawing intracellular bulk ice when the extracellular temperature grows Formation of dendritic ice on the moving boundary of thawing bulk ice

Osmotic rehydration of cells during thawing -the normal velocity of the cell boundary - the intracellular salt concentration - the extracellular salt concentration - the unfrozen extra- and

10 Osmotic rehydration of cells during thawing -the normal velocity of the cell boundary - the intracellular salt concentration - the extracellular salt concentration - the unfrozen extra- and intracellular water contents c out c in solid extracellular matrix thawed extracellular ice (liquid) with decreasing salt concentration cell with intracellular liquid osmotic inflow tends to balance intra- and extracellular salt concentrations - the Stefan condition with curvature, where Frémond, M. Non-smooth thermomechanics. Springer-Verlag: Berlin, 2002.

11 Cell swelling caused by the rehydration end shape initial shape initial shape All snapshots Movie

Cooperation partners Cooperation with the SPP project Optimization Problems Governed by Cahn- Hilliard

The common point here is adopting the Cahn-Hilliard model to the description of the recrystallization of

Dr. Gert Fränzl, Managing director of SY-LAB Geräte GmbH.

12 Cooperation partners Cooperation with the SPP project Optimization Problems Governed by Cahn- Hilliard Variational Inequalities by Prof. Harald Garcke and Dr. Luise Blank is assumed. The common point here is adopting the Cahn-Hilliard model to the description of the recrystallization of intracellular ice nuclei. Design of optimal thawing protocols suppressing dendrite growth is expected. Dr. Gert Fränzl, Managing director of SY-LAB Geräte GmbH. Feezing/thawing experiments using IceCube plants produced by the Firma are assumed. Implementation of optimized thawing protocols as stable software for IceCube freezers is planned.

Univ.- Prof. Dr. med. Dr. med. dent. Dr. med. habil. Robert Sader, Director of the Clinic of Oral and Plastic Facial Surgery at the J. W. Goethe University Frankfurt am Main Prof. Dr. med. Dr. med. dent. Hans-Florian Zeilhofer, Clinic for Reconstructive Surgery.

Christian Morsczeck, Poliklinik für Zahnerhaltung und Parodontologie, Forschungslabor, Universität Regensburg Cooperation with our biology partners is necessary to obtain experimental data required

13 Univ.- Prof. Dr. med. Dr. med. dent. Dr. med. habil. Robert Sader, Director of the Clinic of Oral and Plastic Facial Surgery at the J. W. Goethe University Frankfurt am Main Prof. Dr. med. Dr. med. dent. Hans-Florian Zeilhofer, Clinic for Reconstructive Surgery. Head of the Department for Oral and Facial Surgery, Basel, Switzerland Dr. Christian Morsczeck, Poliklinik für Zahnerhaltung und Parodontologie, Forschungslabor, Universität Regensburg Cooperation with our biology partners is necessary to obtain experimental data required for the model statement and verification of the conformity of our mathematical constructions with the real behavior of cryopreserved living cells under warming and thawing. Such experiments assume treatment of cell cultures, microscopy and Magnetic Resonance (MR) imaging of cells, X-ray scattering, and other hightech methods.

14 Some references K.-H. Hoffmann, N. Kenmochi, M. Kubo, N. Yamazaki. Optimal control problems for models of phase-field type with hysteresis of play operator. Advances in Mathematical Sciences and Applications, 17, (2007). K.-H. Hoffmann, N.D. Botkin. Optimal Control in Cryopreservation of Cells and Tissues. To apper in Advances in Mathematical Sciences and Applications. Gakkotosho, Tokyo, Japan. K.-H. Hoffman, J. Schierholz, N. Brenner, H.-F. Zeilhofer, C. Morsczeck. Pluripotent embryonic-like stem cells derived from teeth and uses thereof. European Patent. Date of publication and mention of the grant of the patent Application number: , International application number: PCT/EP2003/ International publication number: WO 2003/ ( Gazetta 2003/33). N. Botkin, O. Degistirici, B. Faßbender, J. Siemonsmeier, M. Thie. Zahn-Einfrier- Behälter. Deutchen Patent- und Markenamt. Reference number DE A1. Date of publication and mention of the grant of the patent K.G.M. Brockbank, J.R. Walsh, Y.C. Song, M.J. Taylor. Vitrification: Preservation of Cellular Implants. In: Topics in Tissue Engineering, N.A.a.P. Ferretti (ed.), 1-26 (2003). H. Garcke. On mathematical models for phase separation in elastically stressed solids. Habilitationsschrift. Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen Friedrich-Wilhelm-Universität Bonn, Bonn 2000.

15 P. Mazur. Principles of Cryobiology. In: Barry J. Fuller, Nick Lane and Erica E. Benson (eds), Life in the Frozen State, CRC Press, BocaRaton, New York, Washington, D.C., 3-65 (2004). C. Morsczeck, T.W. Götz, J. Schierholz, F. Zeilhofer, U. Kühn, C. Möl, C. Sippel, K.-H. Hoffmann. Isolation of precursor cells (PCs) from human dental follicle of wisdom teeth. Matrix Biology 24, (2005). Indra Neil Mukherjee. A rational design approach for the cryopreservation of natural and engineered tissues. Dissertation, Georgia Institute of Technology, USA, April K. Muldrew, J.P. Acker, J.A.W. Elliott, L.E. McGann. The Water to Ice Transition: Implications for Living Cells. In: Barry J. Fuller, Nick Lane, Erica E. Benson (eds), Life in the Frozen State, CRC Press, BocaRaton, New York, Washington, D.C., (2004). Reinhold T. Pfaff, Yuksel Agca, Jun Liu, Erik J. Woods, Augustine T. Peter, John K. Critser. Cryobiology of Rat Embryos I: Determination of Zygote Membrane Permeability Coefficients for Water and Cryoprotectants, Their Activation Energies, and the Development of Improved Cryopreservation Methods. Biology of Reproduction 63, (2000). J.Y. Tanaka, J.R. Walsh, K.R. Diller, J.J. Brand, S.J. Aggarwal. Algae Permeability to Me 2 SO from 23 to 23 C. Cryobiology 42, (2001). M. Toner, E.G. Cravalho, Marcus Karel. Thermodynamics and kinetics of intracellular ice formation during freezing of biological cells. Journal of Applied Physics 67(3), (1990).

Interspecies Challenges

Cryobiological Challenges of Banking Reproductive Cells, and Tissues Interspecies Challenges Mammals Domestic species Lab animal species Endangered Species Humans (Reproductive Med) Birds Domestic species