CRISMA Laboratory UPMC Critical Care www.ccm.pitt.edu Exemplary Care Cut t ing-edge Research World-class Education
Multi-scale modeling of Influenza a virus and its containment Towards System Biology Workshop Grenoble, May 2011 Gilles Clermont, MD CRISMA Center Center for Inflammation and Regenerative Modeling Critical Care Medicine, Mathematics, Industrial Engineering University of Pittsburgh Exemplary Care Cut t ing-edge Research World-class Education
Acknowledgments Colleagues Trainees Baris Hancioglu Ian Price David Dreisigmeyer Sarah Lukens Jay Depasse NIH(GM)/NSF(DMS) Exemplary Care Cut t ing-edge Research World-class Education
Epidemic Influenza In a “normal” season Up to 30 million infections in the US 100,000 attributable hospitalizations 35,000 attributable deaths 3B (direct) -15B (total) in societal costs Most deaths are due to secondary infections (pneumonia) Target population (old, sick and the very young) Exemplary Care Cut t ing-edge Research World-class Education
Pandemic 2009 H1N1 In the US 61M cases, 12,700 deaths Severe illness The Australia-New Zealand experience (NEJM) 722 cases (29 cases/M) 14.3% mortality The Canadian experience (JAMA) 215 cases 14.3% mortality Our own experience Pittsburgh/UPMC 24 admissions to adult ICU starting in august 2009 75% mortality Target population Young adult, pregnant women Exemplary Care Cut t ing-edge Research World-class Education
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Influenza A virus Exemplary Care Cut t ing-edge Research World-class Education
Pandemic influenza is an inflammatory disease 1918 H5N1 Tx/91 H5N1 Perrone et al., PLoS Pathogens 2008 Exemplary Care Cut t ing-edge Research World-class Education
Influenza modeling in Pittsburgh Allegheny county HD Epidemiology Population Social Sciences Data Center (Burke) PSC JHU Genetics (Ghedin-Virology) Host (Clermont/Rosenfeld) Vaccines-In vivo (Ross - CVR) Biodefense (Morel) Exemplary Care Cut t ing-edge Research World-class Education
Multiscale modeling IVA Global pool Containment Human IVA Population level strategies Human IVA Host level Exemplary Care Cut t ing-edge Research World-class Education
Multiscale modeling – MIDAS Exemplary Care Cut t ing-edge Research World-class Education
Multiscale modeling – Population Exemplary Care Cut t ing-edge Research World-class Education
Population-level models (SIR) Susceptibles P(Infection|Environment) Infected P(Duration) ?? P(Death) Recovered P(Susceptible)?=0 Resistant P(immune) • Human activity (travel) • Geography/weather Exemplary Care Cut t ing-edge Research World-class Education
Population-level models Agent-based model (FRED) Sophisticated cellular automata Stochastic - Distribution driven Age, household size, school sizes… Transmission, duration of disease… Computational requirements 32 nodes 75GB (3e8 agents) 5 hours Ferguson et al. Nature 2005 Exemplary Care Cut t ing-edge Research World-class Education
Multiscale modeling – Viral evolution Exemplary Care Cut t ing-edge Research World-class Education
Multiscale modeling - Host Host Lung Tissues Cells Vaccines Virus Therapy Pathways Anti-virals •M2 inhibitors •NA inhibitors Exemplary Care Cut t ing-edge Research World-class Education
The simplest viral model – ever ! (v1.0) dH = − β HV Λ =0 dt Healthy dI cell = β − δ D=0 HV I dt β dV = − pI cV dt Infected Virus cell δ - where active cell killing p is implicit in this death rate c - virus death or shedding Killer cell Exemplary Care Cut t ing-edge Research World-class Education
IVA-host model 2.0 Hancioglu et al, J Theor Biol 2007 Exemplary Care Cut t ing-edge Research World-class Education
Host-level model 3.0 Price et al. JCC 2008 Exemplary Care Cut t ing-edge Research World-class Education
Looking at individuals Baccam et al. Virology 2007 Exemplary Care Cut t ing-edge Research World-class Education
The estimation problem dH = − β HV Λ =0 dt Healthy dI cell = β − δ D=0 HV I dt β dV = − pI cV dt Infected Virus cell δ - where active cell killing p is implicit in this death rate c - virus death or shedding Killer cell Exemplary Care Cut t ing-edge Research World-class Education
Population ensemble models E ( M n ) E ( M n ) ≡ Metamodel or Ensemble Many many more models than individuals Exemplary Care Cut t ing-edge Research World-class Education
Creating the ensemble Error ( ) − β Γ +Γ ∝ L L L ( | ) M D e i D 2 H H Probability (density) p A p B p E p C p D Exemplary Care Cut t ing-edge Research World-class Education Parameter axis
Calculating the Ensemble Parameter space Local minima MH-type algorithm Parallel tempering/ Replica exchange as mixing method Earl, Deem 2006 Exemplary Care Cut t ing-edge Research World-class Education
Chain mixing β 5 β 4 β 3 β 2 β 1 tests Exemplary Care Cut t ing-edge Research World-class Education
The population ensemble Exemplary Care Cut t ing-edge Research World-class Education
Looking at a population Baccam et al. Virology 2007 Exemplary Care Cut t ing-edge Research World-class Education
Probabilistic ensembles – for subpopulations E ( M ) Sparsity -> pooling “similar” patients may be good enough The clinician does this Exemplary Care Cut t ing-edge Research World-class Education
A population ensemble Patient 1 Patient 4 Exemplary Care Cut t ing-edge Research World-class Education
Host-level models Exemplary Care Cut t ing-edge Research World-class Education
V3.0 ensemble Exemplary Care Cut t ing-edge Research World-class Education
Probabilistic ensembles – for subpopulations E ( M ) Sparsity -> pooling “similar” patients may be good enough The clinician does this Exemplary Care Cut t ing-edge Research World-class Education
Multiobjective estimation α β = = + 2 2 E E E E E E a b a b Exemplary Care Cut t ing-edge Research World-class Education
Linking scales of description Threshold of Vmax % Infected cells B 12 A infectivity (log particles/cc) Viral load Threshold of upper 8 Vtdur 50 respiratory symptoms Dmax 10 Ddur Vtmin 0 7 14 7 14 Time (days) C IFN-alpha level 500 Threshold of systemic symptoms Fdur 100 Fmin 7 14 Time (days) Exemplary Care Cut t ing-edge Research World-class Education
Linking scales of description Transmission = infectivity x upper respiratory symptoms Behavior (stay home or not)= systemic symptoms Threshold of Vtdur 12 A infectivity (log particles/cc) Viral load 8 Vtdur Vtmin 7 14 Vtmin Exemplary Care Cut t ing-edge Research World-class Education
Linking scales of description Integrated run (explicit hybrid) = not practical Look-up tables = fast but memory hungry Response surfaces = forward simulations, polynomial fit, algebraic computation R Inputs = (Inputs) R f { } ∈ µ µ µ σ σ σ , , , , , R Transmissibility Behavior Resistance Transmissibility Behavior Resistance { } ∈ Inputs Viral load, burst size, viral adhesion, existing antibodies, .. Exemplary Care Cut t ing-edge Research World-class Education
Predicted impact of therapy Virulent pathogen Exemplary Care Cut t ing-edge Research World-class Education Si ifi i i i i
A multiscale lung model Inflammation occurs in the tissue barrier between air and blood. Tissue swelling impairs gas diffusion. Extreme inflammation of a respiratory unit (~25 alveoli) can completely stop gas exchange (shunt). The global impact of inflammation depends on the combined contribution of respiratory units (RU) with diverse anatomical and physiologic properties. Reynolds et al, J Theor Biol 2009 Exemplary Care Cut t ing-edge Research World-class Education
Knowledge and successful translation Empirical Kepler/Newton GR - Einstein QG - ?? Epicycles Ellipses Precessing ellipses Black hole physics - to XVII century First interaction Discrepancy between Discrepancy between between a physical predictions and gravity and other law and empiric empiric observation forces of nature observation Depth of knowledge Exemplary Care Cut t ing-edge Research World-class Education
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