Collaboration with Craig Henriquez’ laboratory at Duke University Multi-scale Electro- physiological Modeling

Contents Overview of projects with Duke University Software infrastructure to support collaboration Preliminary results Goals and development plans for next year

Multi-scale electrophysiological modeling ‣ Collaborator: prof. dr. Craig Henriquez ‣ Group: 2 Postdocs, 3 PhD students, several master students. ‣ Duke University: Biomedical Engineering Department

Multi-scale electrophysiological modeling Primary goal: Create tools and investigate methods for doing multi-scale electro- physiological modeling Projects: ‣ Creating a bidomain model of a heart coupled to a full torso model (Applied to the mouse) ‣ Creating a model of propagation at a tissue level, using discrete compartments in 3D. (Applied to cardiac tissue) ‣ [Creating a model of electroporation] ‣ Creating a model of field stimulation of cardiac and neuronal cells. project part of the CIBC center separately funded projects

Multi-scale electrophysiological modeling Discrete bidomain Realistically shaped intra and extracellular spaces that do not overlap in space Realistically shaped membrane model (2D) connecting to volumetric spaces (3D) Our approach: Continuous bidomain Intracellular space Extracellular space Space with conductivity adjusted for the volume fraction of modeled space Membrane model connecting each point in space to the other domain (total domain = 4D) Traditional approach:

Creating discrete multi-domain models Simulating propagation in cardiac tissue Simulating field stimulation in tissue [Simulating electroporation efficiency] All have in common that we need to have tools for defining the geometry, coupled with a solver that solves the membrane equations (reaction) and the domain equations (diffusion) simultaneously.

Creating discrete multi domain models (2) Creating domain defining tissue domains defining membrane properties Adding stimulus, reference and recording sites (electrodes) Creating a system of linear equations to represent data a 11 x 1 +a 12 x 2 + a 13 x 3... = b..... Solving system of equations CardioWave (Solver package developed at Duke)

Software infrastructure SCIRun: visually building models, generating diffusion reaction equations and displaying results. CardioWave: diffusion-reaction equation solver using parallel computing. Matlab: building simplified models for initial set of simulations.

Project Progress ‣ Building basic infrastructure in SCIRun for model creation and interfacing CardioWave. ‣ Upgrade CardioWave to run simulation in parallel and using adaptive time stepping. ‣ Create geometrically shaped models (3D) and run field stimulation simulation. ‣ Refine tools depending on needs ‣ Create realistically shaped models and do comparison with continuous bidomain models.

SCIRun/Matlab Interface (1)

SCIRun/Matlab Interface (2) Matlab in SCIRun for generating geometries

SCIRun: Separation of algorithms and modules SCIRun Very flexible Less user friendly PowerApp Less flexible User friendly Old SCIRun dataflow model: Up to 80 different modules needed for one simple model. Hugh overhead in memory due to dataflow paradigm. Solution: Create modules with less granularity. Automate large parts of the creation of the model. We want to be here: Limit the number of modules needed Enough flexibility for both field stimulation and propagation simulation

SCIRun: Separation of algorithms and modules Algorithm Algorithm SCIRun Toolbox Algorithm Algorithm Algorithm... Algorithm Code reusing SCIRun’s algorithms Module that deciphers the geometry of the model and invokes the proper algorithms to build the diffusion reaction equations. Currently containing about 50% of SCIRun’s Core algorithms

Software pipeline/workflow SCIRun: model construction CardioWave: mpi solver of diffusion reaction equations SCIRun: visualization of results Desktop machine with nice graphics card Cluster or Multiprocessor shared memory machine Save model files in format compatible with CardioWave CardioWave is exporting SCIRun compatible files

SCIRun: CardioWaveInterface Definition of a hexahedral mesh Assigning domains to each element Extracting the surface between cells and interstitial space Defining gap junctions as connections between cells perpendicular to fiber along fiber Each colored domain is a different cell

SCIRun: CardioWaveInterface (2) Define a change a gap junction properties Define a reference potential Select an area of the membrane for stimulation

SCIRun: CardioWaveInterface (3) Geometries and properties of recording electrodes, membranes, reference electrodes, stimulus electrodes, and domain conductivities Process everything and build the tissue model and generate the diffusion-reaction equations All files needed to run the CardioWave solver and mappings to project solutions back onto geometries

Propagation simulation (1) Model of a piece of cardiac tissue: One myocyte Gap junctions

Propagation simulation (2) ADD MOVIE I MADE OF PROPAGATION Propagation of an action potential in a 3D bundle of cardiac tissue

Field stimulation Stimulation electrode What is the effect of the local tissue architecture on the efficiency of stimulation of neurons? i.e. the cells disturb the local field.

Software engineering “to do” list (1) ‣ BioPSE developments Improving memory and resource management ‣ Visualization developments Tools for filtering, interpolating, loading and editing tensor fields. Improve widgets for fine-tuning models. 2D graphics and histograms ‣ Simulation / CardioWave developments Implement improvements from discrete multi domain CardioWave Core into continuous bidomain CardioWave Core. Add more membrane models to CardioWave Distribution model for CardioWave with SCIRun. Generating tissue layout from tissue statistical parameters

Software engineering “to do” list (2) ‣ Imageprocessing and geometric processing: Segmentation tools for segmentation micro CTs. Surface Remesher for mouse model. Rendering abstract shapes (cylinders, cones, etc.) Merging of surface meshes. Warping of meshes. Improvements to interface of tetrahedral mesh generator.

Connection with other projects Modeling Cardiac Defibrillation in children (John Triedman) Dr. Alonso Moreno’s lab: Studying Propagation in Cardiac Tissue Preparations Dr. Cameron McIntyre’s lab: Computational Stimulation of Deep Brain Stimulation Neuron field stimulation simulations Cardiac propagation simulations at microscopic scale Model building tools Meshing tools Microscopic origin defibrillation Tools for labeled maps Tools for estimating impedance... Microscopy Image Analysis and Visualization (NCMIR) Segmentation of microscopic images Mouse Skeleton Phenotyping (The Cappechi Lab) Epilepsy Detection: EEG Source Localization and MR imaging (Scott Makeig and Greg Worrell ) Multi-scale Electro- physiological Modeling (Craig Henriquez) Finite Element Modeling tools