Jared Barber- Seminar, Oct 4, 2011 Joint work with Ivan Yotov and Gilles Clermont

 Background on pneumonia and inflammation  ODE Model ◦ Model ◦ Desired behaviors ◦ Results  PDE Model ◦ Model additions ◦ Results  Conclusions  Future Work

 A condition where inflammation in the lung compromises lung function  A leading cause of death in elderly, very young, chronically ill, and third world  Caused by bacteria, virus, fungi, parasites ◦ Bacteria associated with most severe cases ◦ Flu can cause pneumonia  Associated with coughing, fever, chills, lack of breath, confusion in elderly.  Treated with fluids, antibiotics, oxygen therapy, breathing treatments

 Players ◦ Pathogen-introduced via air  Bacteria-b ◦ Immune cells  Neutrophils-n  Macrophages-m ◦ Cytokines  Pro-inflammatory-c p  Anti-inflammatory-c a  Process (to right)

 Parameters chosen so that ◦ Healthy steady state is stable ◦ Neutrophils outkill/outnumber macrophages ◦ At maximal anti-inflammation levels, immune response is reduced by 75-80% ◦ Pro and anti-inflammatory cytokine levels are of the same order ◦ Anti-inflammatory cytokines delayed wrt pro- inflammatory cytokines  There are some rarer desired behaviors that are not currently reproducible by the model

 Bacterial infection is cleared by local immune response without needing to activate macrophages and neutrophils t in hrs

 Bacterial infection grows initially and then is destroyed by activated immune cells which subsequently decay to zero  Note: We have all desired behaviors t in hrs

 Bacterial infection is initially reduced but recovers once anti-inflammatory cytokines kick in t in hrs

 Introduction of additional bacteria later on can turn a healthy situation (Simulation 2) into an unhealthy one

 Patients seen are usually Type II or Type III  We want O(Type II) ≈ O(Type III), not the case

 Diffusion ◦ All species ◦ Smaller species (cytokines) diffuse more than larger species (inflammatory cells)  Chemotaxis ◦ Macrophages migrate towards regions of high bacterial and cytokine concentration ◦ Neutrophils migrate towards regions of high cytokine concentration

 Lung made up of three components: ◦ Air/Alveolar region (A-90% of the lung) ◦ Blood (B-5% of the lung) ◦ Tissue (T-5% of the lung)  Inflammation indicator function  Local saturation function

 Saturation for other components:

 Effective diffusion/chemotaxis coefficients depend on air, blood, and tissue saturation:  For macrophages:

 Bacterial infection is cleared and immune system returns to original steady state Note: Actual Comp Domain 20x20 cm

 Time: Each profile 2hrs apart Note: Actual Comp Domain 20x20 cm

 Bacterial infection is not cleared and system proceeds to death Note: Actual Comp Domain 20x20 cm

 Bacterial infection is not cleared and system proceeds to death Note: Actual Comp Domain 20x20 cm

 Both models can produce desired behavior  PDE model allows more Type II simulations ◦ PDE system starts with less bacterial load ◦ Diffusion lessens virility of bacterial growth ◦ Chemotaxis allows inflammatory cells to gang up on the bacteria  PDE model gives much more flexibility PDEODE vs

 X-rays pick up mostly water

 X-ray density = S T + S B  Use Kalman Filter to compare with actual data

 Further refine ODE model to obtain more desired behaviors  Consider including other members ◦ Damage ◦ Adaptive immune response  For chemotaxis and diffusion coefficients, ◦ Maximize number of physiologically realistic simulations ◦ Find conditions to limit pattern formation from occurring ◦ Use smaller initial size of infection  Obtain average values of neutrophils and cytokines in addition to x-rays to use for parameter estimation