Lulu Chu & Chenhong Zhu CHSL

Rationale: Nonlinear Functional Changes in Aortic Banding Heart Failure Animal Model

Project Objective 1 and Method Objective: To understand how functional changes in SERCA or NCX influence the Cai oscillation and the transient amplitude/frequency in a compartmental model using parametric studies and bifurcation analysis based on experimental data Method: – Identify a good minimal ODE model for Ca dynamics including targets of interest and simulate in XPP – Include realistic buffering effect in cytosol and SR (Greenstein & Winslow 2006) – Replace PMCA with NCX formulation from Luo&Rudy 1994 or Weber et al – Parametric studies of SERCA, NCX, and determine which has a more profound impact on Ca oscillation amplitude and frequency in heart failure conditions

Preliminary Results: Calcium Dynamics Cytosol SR SERCA Leak RyR LCC PMCA/NCX Model replication

Preliminary Results normal Reduced SERCA Increased Extrusion Normal Cai vs vSERCA Cai vs vPMCA normal

Project Objective 2 and Method Objective: Better understand Cai traveling wave in 1D space with the fire-diffuse-fire model and investigate how SERCA or NCX or RyR changes results in wave propagation failure. Method: – Derive a new 1D PDE for Cai which includes the buffering effect in cytosol based on rapid buffer approximation (RBA) and fluxes of interests – Implement the model using finite difference scheme in XPP or Matlab to do numerical integrations with new parameters set from the first objective – Parametric studies of SERCA and NCX functions and investigate how they change normal behavior of Cai wave speed and propagation

Model Plan for 1D Ca Traveling Model RBA Treat all the fluxes as point sources Use finite difference method

Anticipated Difficulties XPP numerics issue Implementation with 1D PDE model and position of Ca reaction (influx/efflux)