A Mathematical Model of Cytomegalovirus (CMV) Infection in Transplant Patients Grace M. Kepler Center for Research in Scientific Computation North Carolina State University

Outline Significance Modeling goals Mathematical/Biological model Parameter approximation Numerical results Conclusions

Transplantation Numbers (UNOS, 2005) More than 27,000 organs transplanted Approximately 90,000 waiting for organs 153,000 living with functioning organ transplant The number of individuals waiting for, receiving, or living with a transplanted organ(s) is significant.

Life-long immunosuppression is the standard of care for transplant patients. Common pathogens (eg., influenza) Opportunistic infections (eg., Listeria) Latent infections (eg., HCV, VZV, CMV) Immunocompromised individuals are susceptible to infections from

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 DonorRecipientType 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

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

ACTIVELY - INFECTED CELLS Math/Bio model - 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

LATENTLY- INFECTED CELLS Math/Bio model – latently-infected cells

Math/Bio model – reactivation reactivation of monocytes upon differentiation

Math/Bio model – cell replication/death

State Variables VariableDescriptionUnits Vvirions virions/  L-blood Evirus-specific immune effector cells cells/  L-blood RIRI actively-infected cells cells/  L-blood RSRS susceptible cells cells/  L-blood RLRL latently-infected cells cells/  L-blood

Mathematical equations

Clinical data Real-time quantitave PCR measurements of viral DNA in plasma ( ) Antigenemia assay ( ) PBMC depleted ELISPOT assay ( ) Longitudinal measurements

Statistical framework Intra-subject variation of observations –assay errors –physiological fluctuations –assay limits (cesored data)

Parameter approximations Physiological information Experimental measurements Auxilliary parameters Using reduced models for specific time regimes Unknown parameters Viral load decay Emery1999

Parameter approximations Provide initial values for parameter estimation when data is available Allow exploratory simulations of model behavior

Immunocompetent Primary infection Initial conditions:

Immunocompetent The latent infection state is characterized by the equilibrium levels of the state variables following primary infection. Latent infection

Immunosuppression Primary infection

Immunosuppression Primary infection

Immunosuppression Primary infection

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, R I, and R L 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

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