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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

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 Exemplary Care  Cut t ing-edge Research  World-class Education 

CRISMA Laboratory UPMC Critical Care

www.ccm.pitt.edu

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 Exemplary Care  Cut t ing-edge Research  World-class Education 

Multi-scale modeling of Influenza a virus and its containment

Gilles Clermont, MD

CRISMA Center Center for Inflammation and Regenerative Modeling Critical Care Medicine, Mathematics, Industrial Engineering University of Pittsburgh

Towards System Biology Workshop Grenoble, May 2011

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 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)

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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)

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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

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Influenza A virus

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Pandemic influenza is an inflammatory disease

Perrone et al., PLoS Pathogens 2008

1918 H5N1 Tx/91 H5N1

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 Exemplary Care  Cut t ing-edge Research  World-class Education 

Influenza modeling in Pittsburgh

Population (Burke) Host (Clermont/Rosenfeld) Biodefense (Morel) Epidemiology Data Center JHU Genetics (Ghedin-Virology) Vaccines-In vivo (Ross - CVR) PSC Social Sciences Allegheny county HD

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Multiscale modeling

IVA Global pool Human IVA Population level Human IVA Host level Containment strategies

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Multiscale modeling – MIDAS

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Multiscale modeling – Population

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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
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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

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Multiscale modeling – Viral evolution

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Multiscale modeling - Host

Host Lung Cells Pathways Tissues Virus Therapy

Vaccines Anti-virals

  • M2 inhibitors
  • NA inhibitors
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The simplest viral model – ever ! (v1.0)

Virus Infected cell Healthy cell Killer cell Λ=0 D=0 δ - where active cell killing is implicit in this death rate p β c - virus death

  • r shedding

dH HV dt dI HV I dt dV pI cV dt β β δ = − = − = −

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IVA-host model 2.0

Hancioglu et al, J Theor Biol 2007

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Host-level model 3.0

Price et al. JCC 2008

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Looking at individuals

Baccam et al. Virology 2007

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The estimation problem

Virus Infected cell Healthy cell Killer cell Λ=0 D=0 δ - where active cell killing is implicit in this death rate p β c - virus death

  • r shedding

dH HV dt dI HV I dt dV pI cV dt β β δ = − = − = −

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Population ensemble models

E(Mn)

E(Mn) ≡ Metamodel or Ensemble

Many many more models than individuals

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Creating the ensemble

Error Probability (density) Parameter axis pA pB pC pD pE

( )

2

( | )

i D H H

L L

M D e

β − Γ +Γ

∝ L

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Calculating the Ensemble

Earl, Deem 2006

Local minima Parameter space

MH-type algorithm Parallel tempering/ Replica exchange as mixing method

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Chain mixing

1

β

2

β

3

β

4

β

5

β

tests

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The population ensemble

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Looking at a population

Baccam et al. Virology 2007

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Probabilistic ensembles – for subpopulations

Sparsity -> pooling “similar” patients may be good enough The clinician does this

E(M)

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A population ensemble

Patient 1 Patient 4

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Host-level models

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V3.0 ensemble

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Probabilistic ensembles – for subpopulations

Sparsity -> pooling “similar” patients may be good enough The clinician does this

E(M)

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Multiobjective estimation

2 2 a b

E E E = +

a b

E E E

α β

=

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Linking scales of description

7 14 Threshold of upper respiratory symptoms

% Infected cells

10 50

B

Dmax

Viral load (log particles/cc) 7 14 12 8 Threshold of infectivity

A

Vtdur Vtmin Vmax

Time (days) 7 14 Threshold of systemic symptoms

IFN-alpha level

100

500 C

Fmin Fdur Ddur

Time (days)

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Linking scales of description

Transmission = infectivity x upper respiratory symptoms Behavior (stay home or not)= systemic symptoms

Viral load (log particles/cc) 7 14 12 8 Threshold of infectivity

A

Vtdur Vtmin Vtmin Vtdur

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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

{ }

{ }

Transmissibility Behavior Resistance Transmissibility Behavior Resistance

(Inputs) , , , , , Inputs Viral load, burst size, viral adhesion, existing antibodies, .. R f R µ µ µ σ σ σ = ∈ ∈ Inputs R

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Predicted impact of therapy

Virulent pathogen Si ifi i i i i

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A multiscale lung model

Inflammation occurs in the tissue barrier between air and blood. Tissue swelling impairs gas

  • diffusion. Extreme inflammation
  • f 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

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Knowledge and successful translation

Empirical Epicycles

  • to XVII century

Kepler/Newton Ellipses First interaction between a physical law and empiric

  • bservation

GR - Einstein Precessing ellipses Discrepancy between predictions and empiric observation

Depth of knowledge

Discrepancy between gravity and other forces of nature

QG - ?? Black hole physics

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UPMC Critical Care

www.ccm.pitt.edu

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 Exemplary Care  Cut t ing-edge Research  World-class Education 