Transport through Core-Shell Fibrous Biomaterials and Biological Systems

1. Transport through Core-Shell Fibrous Biomaterials and Biological Systems by Manolis M. Tomadakis and Kunal Mitra Florida Institute of Technology Melbourne, FL, USA

2. Core-Shell Fibrous Media • Source: Hills, Inc., our industrial partner

3. Core-Shell Fibrous Biomaterials and Biological Systems • Myelinated nerve fibers in regenerated nerve tissues • Chavez-Delgado et al., J Biomed Mater. Res. Part B: Appl. Biomater 74B, 589-600, 2005. • Core-shell hollow biopolymer nanofibers • Agarwal et al., Adv. Funct. Mater., 19, 2863–2879, 2009.

4. Core-Shell Fibrous Biomaterials Applications • Tissue-engineering scaffolds for tissue repair and regeneration: • Sustainable, controllable, and efficient release of • bioactive agents: drugs, proteins, enzymes • Potential applications of such scaffolds: • Local cancer treatment • Stem cell attachment on biocompatible nanofibers • Endovascular stents preventing restenosis • Manipulation and segregation of viruses and bacteria

5. Cardiac Papillary Muscle and Chordae Tendinae, Native or Tissue-Engineered • Cardiac papillary muscle: • Myocardial core surrounded by a thin • endocardial sheath rich in collagen • Chordaetendinae: • Dense collageneous core enclosed in • an outer sheath of elastin • SEM micrographs of human papillary muscle and • chordaetendinae with disengaged elastinlayer • Gusukuma et al., Int. J. Morphol. 22, 267-272, 2004.

6. Transport Properties of Core-Shell Fibrous Biomaterials and Biological Systems • Electric field effects on myelinated nerve fibers: • Electrical conductivity • Electrical activity in cardiac tissue: • Electrical conductivity • Cardiac radiofrequency ablation: • Thermal and electrical conductivity • Controlled delivery of drugs and other bioactive agents in • tissue-engineering scaffolds: • Effective diffusivity and/or • thermal conductivity and/or • electrical conductivity

7. 1-d, 2-d, and 3-d Fibrous Media

8. Transport Properties Investigated • Effective diffusivity, De • Viscous permeability, k • Effective thermal and electrical conductivity, • magnetic permeability and dielectric constant, pe

9. Effective Transport Property ComputationThrough Random Walks in Porous Media < 2>: mean square displacement of random walkers t : travel time in the porous medium

10. Random-Walk Trajectories in Beds of Non-conducting 1-d Fibers

11. Viscous Permeability Computation • Conduction-based method (Johnson et al., 1986) For random fiber structures:

12. Effective Diffusivity and Permeabilityof Random Fiber Structures

13. Permeability for Flow through 3-d Random Fibers Experimental data Ref. 36: Stainless steel wire crimps Ref. 37: Glass wool, fiberglass Ref. 38: Glass wool Ref. 39: Collagen membranes Ref. 40: Collagen membranes Ref. 41: Bronze and copper wire Ref. 42: Agarose hydrogels Tomadakis, M.M, and Robertson, T.J., J. Compos. Mater., 39, 163-188 (2005).

14. Biological Applications of Random-Walk Simulation Results • Controlled-release drug delivery systems • Plant physiology, plant-fiber composites • Bacterial migration in porous media • Targeting cancerous cells by radiated nanotubes • Nanoparticle-assisted delaying of toxin binding • Diffusion in hydrogels, protein crystals, immobilized cell • systems, biopolymer nanofibers, human stratum corneum.

15. Core-Shell Fiber Topology Model

16. Phase Volume Fractions and Specific Surface Areas

17. Phase Mean Intercept Lengths

18. Core-Shell Model Predictions for the Relative Diffusivity

19. Core-Shell Model Predictions for the Relative Permeability

20. Relative Diffusivity and PermeabilityCorrelations for Core-Shell Fibrous Media

21. Relative Permeability for Cross-Plane Flow through Core-Shell Fiber Structures

22. Relative Diffusivity for Cross-Plane Flow through Core-Shell Fiber Structures

23. Predicting Effective Transport Properties with the Law of Mixtures ? Fiber-Matrix Systems: Core-Shell Fibrous Media: : Volume fraction, bulk transport property of phase i

24. Sample Predictions by the Law of Mixtures

25. Key Random-Walk Parameters inCore-Shell Fiber Structures

26. Elements of Random Walks in Random Core-Shell Fiber Structures Mean Free Path: Interface Crossing: Mean Step Check: 0.01 (i = c, s, m)

27. Thermal Imaging Camera Beam Splitter Short Pulse Laser Irradiated Sample Optical Path Power Meter Photo Detector Oscilloscope Laser Ablation Experiments

28. Conclusions • Experimentally validated numerical methods were extended to model transport through random core-shell fibrous media capturing the topology of biomaterials and biological systems. • The resulting predictions for the effective diffusivity and viscous permeability of such systems with transport in the matrix phase agree with earlier analytical predictions and experimental data of the literature for systems of similar topology. • Random walk algorithms are being developed to derive the effective thermal and electrical conductivity, dielectric constant and magnetic permeability of core-shell fibrous media with transport in one, two, or all three phases.

29. Acknowledgements Hills, Inc. NASA Glenn Research Center Florida Solar Energy Center