Download Modeling Cytomegalovirus Infection

A Mathematical Model of
Cytomegalovirus (CMV) Infection
in Transplant Patients
Grace M. Kepler
Center for Research in Scientific Computation
North Carolina State University
Outline
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Significance
Modeling goals
Mathematical/Biological model
Parameter approximation
Numerical results
Conclusions
Transplantation Numbers
(UNOS, 2005)
The number of individuals waiting for,
receiving, or living with a transplanted
organ(s) is significant.
• More than 27,000 organs transplanted
• Approximately 90,000 waiting for organs
• 153,000 living with functioning organ
transplant
Life-long immunosuppression is the
standard of care for transplant
patients.
Immunocompromised individuals are
susceptible to infections from
• Common pathogens (eg., influenza)
• Opportunistic infections (eg., Listeria)
• Latent infections (eg., HCV, VZV, CMV)
CMV infection
• Most significant threat to patient and graft
health
• Directly or indirectly causes:
– allograft rejection
– decreased graft and patient survival
– predisposition to opportunistic infections
and malignancies
Facts about CMV
• A herpes virus
• 50-90% of adults are infected (geographic
variation)
• Primary infection in immunocompetent individuals
is generally asymptomatic (some get
mononucleosis-like illness )
• Establishes lifelong latent infection
• Latent infection is well control by healthy immune
systems
• Reactivation rare in healthy individuals
CMV Infection Risk In
Transplantation
Donor Recipient
Type
D+
R-
primary
D-
R+
reactivation
D+
R+
superinfection
D-
R-
risk with exposure
Optimal care of individuals with
transplanted organs is important
• No universal agreement among transplant
centers about
– Prophylactic vs. preemptive antiviral treatment
– Optimal duration of antiviral treatment
• Optimal treament may vary among
subpopulations (eg., D+ R- vs D- R+)
Modeling goals
• Create a within-patient dynamic model of
CMV infection
• Describe dynamics of cell and viral
populations with ODEs
x(t )  f ( x, t; )
Model parameters 
Modeling goals
• Individualized medicine
– model equations are the same for each individual
– model parameter values may vary among individuals
– individuals are characterized by their particular set of
parameter values
– parameter values for each individual determine their
particular infection dynamics
– allowing prediction for each individual
Longitudinal data
Viral load data for one individual.
Censored data
Parameter estimation
Estimate model parameters from the data.
Prediction
Use the model and characterstic parameters
to predict infection dynamics.
Modeling goal – Population predictions
• Estimate characteristic parameters for
many individuals using longitudinal data
Modeling goal – Population predictions
• Create a probabilistic model to describe
parameter distributions
Modeling goal – Population predictions
• Use the probabilistic model to create virtual patients
• Predict population behavior (eg., treatment
regimens)
Antiviral treatment
Modeling goal – Population predictions
• Use a stochastic model to sample the parameter
distributions (virtual patients)
• Predict population behavior (eg., treatment
regimens) Antiviral treatment
Modeling goal – Population predictions
• Use a stochastic model to sample the parameter
distributions (virtual patients)
• Predict population behavior (eg., treatment
regimens) Antiviral treatment
Modeling considerations
• Start simply, capture most salient
biological features
– a model that can describe primary, latent,
and reactivated infections in healthy or
immunocompromised individuals
• Use clinical measurements to inform
the model
• Model cell and viral populations in the
blood
Math/Bio model - virions
VIRIONS
(free virus)
Math/Bio model – susceptible cells
SUSCEPTIBLE CELLS
(monocytes)
cell
replication
and death
Math/Bio model actively-infected cells
ACTIVELY INFECTED
CELLS
Math/Bio model –
viral-induce cell lysis
Math/Bio model –
immune response
CMV-SPECIFIC
IMMUNE
EFFECTOR
CELLS
Math/Bio model –
immune suppression
Math/Bio model –
lysing of infected cells
Math/Bio model – latently-infected cells
LATENTLYINFECTED
CELLS
Math/Bio model – reactivation
reactivation of monocytes
upon differentiation
Math/Bio model –
cell replication/death
State Variables
Variable
Description
Units
V
virions
virions/mL-blood
E
cells/mL-blood
RI
virus-specific immune
effector cells
actively-infected cells
RS
susceptible cells
cells/mL-blood
RL
latently-infected cells
cells/mL-blood
cells/mL-blood
Mathematical equations
V  n RI  cV  fkRSV
  E

E  (1  òS ) E 1   E  V 
e
 

RI  kRSV   RI  (1  òS )mERI   0 RL   RI
 RS
RS   1 
rS


 RS  kRSV

 RL
RL   1 
rL


 RL   0 RL   RI

Clinical data
Longitudinal measurements
• Real-time quantitave PCR measurements
of viral DNA in plasma ( V )
• Antigenemia assay ( RI )
• PBMC depleted ELISPOT assay ( E )
Statistical framework
• Intra-subject variation of
observations
– assay errors
– physiological fluctuations
– assay limits (cesored data)
Parameter approximations
• Physiological information
• Experimental measurements
 , 0 , rS , rL
• Auxilliary parameters
Viral load decay
tH , tD , E,V
• Using reduced models for
specific time regimes
k , c, m, E
Unknown parameters
Emery1999
 , n, e, , 
Parameter approximations
• Provide initial values for parameter
estimation when data is available
• Allow exploratory simulations of model
behavior
Immunocompetent ( s  0)
Primary infection
4
2
Initial conditions: (V , E , RI , RS , RL )  (110 , 0, 0, 4 10 , 0)
Immunocompetent ( s  0)
Latent infection
V
E
RI
• The latent infection
state is characterized
by the equilibrium
levels of the state
variables following
primary infection.
(V , E, RI , RS , RL )
Immunosuppression
Primary
infection
s  0
Immunosuppression
Primary
infection
 s  0.4
Immunosuppression
Primary
infection
 s  0.7
Immunosuppression - Latency
D-R+ Transplant Scenario
• The donor tissue has no CMV virions or
latently-infected cells (D-)
• Prior to transplantation, recipient has a
latent CMV infection, characterized by low
levels of V, RI, and RL that is controlled by
the immune effector cells E
• After transplantation, pharmacolgical
immunosuppression can result in a
secondary (reactivated) CMV infection
Reactivation
Immune suppression of
an individual with a
latent CMV infection
V
 s  0.7
E
RI
Conclusion
• Created a mathematical model for CMV infection in both
immunocompetent and immunocompromised individuals
• Identified data that can be collected to inform the model
• Approximated values for most of the model parameters
• Model exhibits primary, latent, and secondary (reactivated)
infections
• Latent infection is characterized by low-level viral load and
actively-infected cells
• Simulation of reactivated infection approximates CMV
infection in D-R+ transplant patients
CMV infection in other
immunocompromised individuals
• Most common congenital infection
– can result in developmental and sensory
disabilites
• Retinitis infection in AIDS patients.
• CMV CTL-inflation may be a cause of
immunosuppression in elderly individuals
Challenges
• Get data
– parameter estimation
– predictive capability
• Further model development
– other transplant situations (eg., D+R-)
– HLA type, antiviral treatment,...
Collaborators
• Tom Banks, CRSC, NCSU
• Marie Davidian, CQSB, NCSU
• Eric Rosenberg, MGH, Harvard