C23: Tissue Engineering

1. C23: Tissue Engineering Lecture 4 Dr Julian F Dye Julian.dye@eng.ox.ac.uk

2. Overview of Lectures • General Introduction to Tissue Engineering; • Extracellular matrixengineering • Bioreactor technologies • Enabling technologies - Cryopreservation of cells and engineered tissues - Mass transfer in cell/tissue culture - Mathematical modelling of fluid flow and mass transport in growing tissues Tissue Engineering - L1

3. Cell Preservation • Needs for cell preservation – e.g. stem cell banking • Needs for engineered tissue preservation • Off-the-shelf availability • Long production cycle • Quality control • Product distribution

4. Techniques • Slow cooling • Cooling rate differs between cells of differing size and water permeability: a typical cooling rate around 1°C/minute • Vitrification • Instead of crystallising, the solution turns into an amorphous ice • increase in the viscosity and a depression of the freezing temperature • Freeze-drying • Not possible for mammalian cells at the moment Tissue Engineering - L4

5. Freezing Damage to Cells Survival % With a Cryopresevation agent (CPA) Dehydration Intracellular Ice Formation Freezing Rate

6. Effects of cooling rate on cell survival Cooled to -196 C and thawed rapidly (from Mazur, P. 1970, Science, 939-949)

7. Cell Cryopreservation Requirements • Cell survival (the more the better) • No functional loss (which functions?!) • Well defined cryoprotecting agents (no serum) • Animal product free (ideally no animal proteins) • Reduced dimethyl sulfoxide (DMSO) content (better no DMSO for some cell types) • Simple protocol (CPA loading and removal, freezing and thawing)

8. Specific Problems in Cryopreservation of TECs Tissue Engineering - L4

9. Features of a Growing Engineered Tissue • Cells consume nutrient and produce waste • Mass transport is by diffusion, and/or perfusion, and/or convection • Cells can proliferate • Cells make extracellular matrix • Cells can degrade scaffold Tissue Engineering - L4

10. Transport in Cell/Tissue Culture • Diffusion/Convection • Interface mass transfer gas – liquid (oxygen) • Diffusion in porous medium • Transport through cell membrane with cells Culture medium Tissue Engineering - L4

11. Diffusion • Net transport of molecules from a region of higher to one of lower concentration by random molecular motion. • The result of diffusion is a gradual mixing of material. In a phase with uniform temperature, no external net forces acting on the particles, the diffusion process will eventually result in complete mixing or a state of equilibrium. • Molecular diffusion is typically described mathematically by Fick's laws.

12. Fick’s First Law DA is the Diffusion coefficient or Diffusivity of solute A The greater D, the faster the diffusion Typical values are 10-5 cm3/s in water, 10-1 cm3/s in air Tissue Engineering - L4

13. Convective Mass Transfer b – bulk s –surface δ – boundary layer thickness Film theory simplifies convective transfer to the boundary layer or interface Tissue Engineering - L4

14. c2i c1b c2b c1i Z1 Z2 Interface Mass Transfer Gas Phase O2/Air Culture Medium Direction of mass transfer Flux = NA NA = kc1 (C1b – C1i) = kc2 (C2i – C2b) bulk bulk interface interface Z is the interface zone K is the mass transfer coefficient Tissue Engineering - L4

15. Interface Mass Transfer Where NA is flux Tissue Engineering - L4

16. Interface Mass Transfer Mass transfer coefficient is a measure of resistance to flow Treat like resistors in series Tissue Engineering - L4

17. Diffusivity in porous media • Depending on porosity, pore size distribution, and tortuosity • Diffusion through solid is much slower than through liquid • Can be modelled using Darcy’s Law • Can be approximated using solid content for small molecules • Affected by temperature Tissue Engineering - L4

18. Darcy’s Law Darcy's Law is a generalized relationship for flow in porous media. It shows the volumetric flow rate is a function of the flow area, elevation, fluid pressure and a proportionality constant. It may be stated in several different forms depending on the flow conditions. Since its discovery, it has been found valid for any Newtonian fluid where,Q = volumetric flow rate (m3/s),A = flow area perpendicular to L (m2),K = hydraulic conductivity (m/s),l = flow path length (m),h = hydraulic head (m), andΔ = denotes the change in h over the path L. Tissue Engineering - L4

19. Effective Diffusion Coefficient in porous media l For a solute diffusing across a porous material (e.g. membrane or scaffold) Pore area < surface area Ap/At < 1 • De=D x material correction factor • Correction factor depends on the nature of the porous medium • Generally: • totuosity of pores symbol τ • porosity symbol φ (solid vol/total vol or pore area/surface area) • adsorption Pathlength > l τ > 1 Tissue Engineering - L4

20. Mass transport through cell membranes • Cell membranes • is a selectively permeable lipid bilayer coated by proteins which comprises the outer layer of a cell. • In essence membranes are essential for the integrity and function of the cell. • control the input and output of the cell

21. Transport through cell membranes Three types: • Passive transport • Diffusion • Simple diffusion (Fick’s law) • Facilitated diffusion • Osmosis: • Water transport • Active transport

22. Simple diffusion through cell membrane • Heat energy causes molecules to move randomly • The higher the concentration gradient the more rapid the net diffusion • Simple diffusion across a membrane is called permeability • Hydrophobic chemicals cross membranes faster than hydrophilic ones • Energy from ATP is not required • The higher the partition coefficient the higher the permeability

23. Facilitated diffusion K and Vmax depend on properties of the diffusing molecule, maximum rate of diffusion (Vmax): when all the carrier proteins are saturated How quickly the carrier proteins become saturated can be described by the variable K, the concentration gradient at which the rate of diffusion is 1/2 Vmax.

24. Transport rate • Simple diffusion of solute into a cell is linearly related to the concentration of solute outside the cell. • Facilitated diffusion, however, approaches a maximum rate as the carrier proteins become saturated with solute (Michaelis menton kinetics)

25. Osmosis What is osmotic pressure? • Movement of water from dilute solution to high osmotic pressure concentrated solution • Osmosis is passive: doesn't require ATP energy • Osmotic flow through most biological membranes is by bulk flow and is similar to the flow caused by a pressure gradient Symbol for osmotic pressure is Π Π = CRT C = mol.m-3 What is the osmotic pressure of isotonic NaCl, 150 mmol at 298 K? C = 150x10-3 x 103 = 150 mol.m-3; Π = 8.31 x 298 x 150 = 371 kPa

26. Osmosis • Isotonic: external solution osmotic pressure equals cytoplasmic • Hypotonic: external solution < cytoplasmic • Hypertonic: external solution > cytoplasmic • Osmosis can produce significant cell volume changes, causing swelling or shrinking. During isolation of white blood cells, pure water exposure of the enriched white blood cell fraction for 60 s is used to burst residual red blood cells, followed by restoration of isotonicity by addition of a measured amount of 1 M NaCl.

27. Active transport • Primary active transport: • use energy (usually through ATP hydrolysis) at the membrane protein itself to cause a conformational change that results in the transport of the molecule through the protein. e.g. Na+-/K+ pump (3 Na+ pumped out for 2 K+ pumped in) • Secondary active transport: • use energy to establish a gradient across the cell membrane, and then utilizing that gradient to transport a molecule of interest up its concentration gradient. e.g. Glucose and amino acid transporters

28. Cell Metabolic Rate • How much consumed (nutrients, oxygen) or produced (metabolites), per cell (or per million cells) per unit time • Depending on conditions, • often assumed to be zero order when difficult to measure! Tissue Engineering - L4

29. Mathematical Modelling in Tissue Engineering • Guide the design • Obtain some difficult to measure values • Save money

30. Modelling of Flow in Individual Pores Flow perfusion culture and fluid shear on monolayer cell cultures in a flow chamber, τ shear stress, Q flow rate, h parallel plate separation CFD model output for sheer stress Through a porous cellular construct. Tissue Engineering - L4 Mekala et al, Asia-Pac. J. Chem. Eng. 2014

31. Fluid Flow in A Perfusion Bioreactor • Two flow domains—the fibres and the space occupied by the scaffold around them—and couple the flows via continuity conditions at the interfaces. • Darcy’s Law was used to model the flow of culture medium through the scaffold. Scaffold modelled as an isotropic porous medium, with a uniform permeability k • The results for configurations A and B suggest that adding fibres perpendicular to the main flow from the inlet and outlet pipes will probably not result in a beneficial change to the flow distribution. C is the best out of three. Upper: A: MicroCT image of a capped porous hydroxyapatite scaffold; B:An SEM image of a transversecross-section through the wall of one of the PLGA fibres, Tissue Engineering - L4 Whittaker et al. J Theor Biol 2009

32. r R3 R2 R1 0 Z Vz L The Krogh cylinder perfusion model:Schematic Diagram of HFMB System Perfused fibre/capillary lumen Solute transport by diffusion Fibre/capillary wall Solute transport by convection cellular matrix Tissue Engineering – L4

33. r Fibre Lumen Equation relating axial convection to radial diffusion of solute Ri r r distance from axis Z is axial axis (direction of flow C concentration Dldiffusion coefficient in lumen Dfeffective diffusion coefficient in fibre wall Ri inner radius of fibre u average velocity of medium in fibre Boundary conditions: at r=0 at r=Ri Chresand, T. J., etc Biotechnol and Bioeng, Vol 32, 1988

34. r Fibre Wall Equation relating radial diffusion through the vessel wall to diffusion coefficient within the perfusing fluid. Ri Ro r Boundary conditions: C concentration Dldiffusion coefficient in lumen Dfeffective diffusion coefficient in fibre wall Daeffective diffusion coefficient in matrix Riinner radius of fibre Roouter radius of fibre at r=Ri at r=Ro

35. r r Cell Matrix Equation relating diffusion through the extravascular matrix to cell consumption V Rc Ro r Boundary conditions: C concentration Dfeffective diffusion coefficient in fibre wall Daeffective diffusion coefficient in matrix Roouter radius of fibre Rc midpoint of interfibre spacing V consumption rate (zero order) at r=Ro at r=Rc

36. Concentration Profiles Oxygen Glucose Tissue Engineering – L4

37. Influence of Fibre Length- Glucose Fibre length = 0.03m Fibre length = 0.3m Tissue Engineering – L4

38. Influence of Flowrate Glucose Oxygen Tissue Engineering – L4

39. Examples • Structure / porosity permeability • Nutrient supply • Krogh’s cylinder Tissue Engineering - L4

40. Further Reading • Walcerz, D. B. and A. M. Karow (1996). "Cryopreservation of cells for tissue engineering." Tissue Engineering 2(2): 85-96. • Fournier, RL. Basic transport phenomena in biomedical engineering. 4th ed. CRC press, Taylor & Francis, Boca Raton, FL, USA. 2017. • Sengers, B. G., M. Taylor, et al. (2007). "Computational modelling of cell spreading and tissue regeneration in porous scaffolds." Biomaterials 28(10): 1926-1940. • Ye, H., D. B. Das, et al. (2006). "Modelling nutrient transport in hollow fibre membrane bioreactors for growing three-dimensional bone tissue." Journal of Membrane Science 272(1-2): 169-178. Tissue Engineering - L4