1. A mathematical model of necrotizing enterocolitis Jared Barber Department of Mathematics, University of Pittsburgh Work with Ivan Yotov and Mark Tronzo May 10, 2011 1/24

2. Outline Background Necrotizing Enterocolitis Model Results Summary and future directions 2/24

3. Necrotizing Enterocolitis Disease characterized by wounds in intestinal wall of premature infants Mortality: 2% of premature infants die Initiation of wounds – Ischemia/trauma Worsening of wounds – Bacterial invasion Communal bacteria: 10 3 -10 12 per mL – Elevated immune response What’s causing the damage/how can we make things better? 3/24

4. Normal Intestine Lumen Epithelial Cells Tissue Blood Available: http://www.pearsonsuccessnet.com/snpapp/iText/products/0-13-115075-8/text/chapter29/concept29.2.html 4/24

5. Simplified System-Flattened intestine Available: http://www.foodmuseum.com/exgutparts.html 5/24

6. Simplified System-Four Layers 6/24

7. Simplified System-Players in the disease Epithelial cells ZO1 gap/tight junction protein Bacteria Macrophages Activated macrophages Damage Activated Neutrophil Cytokines Nitric Oxide 7/24

8. Inflammatory Cascade 8/24

9. Partial Differential Equations Epithelial Layer – Diffusion enhanced by More epithelial cells Fewer bacteria – Proliferation – Death enhanced by more activated neutrophils, pro-inflammatory cytokines, and bacteria 9/24

10. Partial Differential Equations Bacteria Diffusion Proliferation Death by: – “Passive” local innate immune response – Activated killing by immune cells 10/24

11. Partial Differential Equations Activated Macrophages Diffusion Chemotaxis up gradients of bacteria and cytokines Natural death Recruitment via bacteria, cytokine, and damage interactions with macrophages 11/24

12. Vertical Diffusion-Epithelial layer permeability ZO1 levels (epithelial barrier effectiveness) – Are low when number of epithelial cells are low – Decrease when epithelial cells die – Decrease in the presence of nitric oxide Vertical diffusion coefficient modified: 12/24

13. Numerics Use a cell-centered finite difference approach Periodic boundary conditions in x and y Top and bottom, no flux boundary conditions Initial conditions, zero except – Constant source of neutrophils from blood – Macrophages nonzero except in lumen and blood – Epithelial layer held at 1 everywhere except in the wound as is ZO1 13/24

14. Partial Circular Wound Epithelial Cell Integrity in Epithelial Layer 14/24

15. Circular Hole: Partial Wound Dynamics in epithelial layer for healthy case Time in hours 15/24

16. Circular Hole: Complete Wound Increasing wound severity should lead to more unhealthy outcomes Epithelial Cell Integrity in Epithelial Layer 16/24

17. Circular Hole: Complete Wound Dynamics in epithelial layer for healthy case Time in hours 17/24

18. Circular Hole: Complete Hole with Breast-feeding Add in anti-inflammatory cytokines and anti- microbial peptides Time in hours 18/24

19. Irregular shape (formula fed) Same area as large circular wound with same ICs inside and outside wound 19/24

20. Formula Fed Irregular (dashed) vs Circular Wound (dotted) Irregular hole is more healthy Time in hours 20/24

21. Irregular vs Circular Hole: Considering different wound severities Initial epithelial integrity: 12.2% Note: Reason for reopening—damage-activated macrophage positive feedback loop in tissue 21/24

22. Irregular vs Circular Hole: Considering different wound severities Healthy outcomes – For circular wounds if epithelial IC > 12% – For irregular wounds if epithelial IC > 11% In some cases (<1%) irregular wounds may be healthy when circular wounds do not PDE model can capture some dynamics that ODE models cannot 22/24

23. Summary Model produces physiologically consistent results – Hole severity – Breast feeding Model predicts small but significant dependence of outcomes on shape of wound 23/24

24. Future Directions Finer scale features – Villi – Vasculature Model calibration—Parameter estimation Additional species/layers – Different types of epithelial cells – Mucous layer – TLR4 receptor activity Investigate effects of these changes on the pathogenesis of NEC 24/24

25. Thank you! 25/24

26. Physiological consistent results Both healthy and unhealthy results possible Healthiness of outcome increases when – Wound severity decreases – Breast feeding is used instead of formula feeding Do results depend on shape of wound? 26/24

27. Irregular vs Circular Wounds: Reason for differences Why are irregular wound simulations healthier? – Wound closure governed by diffusion – Less distance to travel, more quickly the wound closes, and the more healthy the situation Qualitatively, outcomes are the same. Are there any situations where the outcome of the simulation (healthy vs unhealthy) depends on the shape of the wound? 27/24