CAUCHY

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SimBio-NeuroFEM is based on the code developments of the CAUCHY project. CAUCHY, a Fortran77 code, was developed from 1991 until 1997 by an interdisciplinary research team (H.Buchner, G.Knoll, A.Rienäcker, R.Beckmann, R.Pohlmeier, J.Pesch, C.Wolters, J.Silny) at the Institute for Machine Elements and Machine Design and the Clinic for Neurology at the RWTH Aachen. The CAUCHY code was based on a generic Fortran77 FEM library of the Institute for Machine Elements and Machine Design which was until 1991 mainly used for simulation processes in machines such as car motors etc.. The CAUCHY project was supported by the VW-foundation and is named by the french mathematician Augustin Louis Cauchy (1789-1857), who developed principles of different mathematical problems valid also for the FEM method. The documentation of the CAUCHY code from 1997 that you can study below was mainly written and managed by R.Beckmann. It is thus the original version from 1997 that we did not adapt and update.

Introduction

The main purpose of brain mapping is to chart the internal structure of the brain and to localize areas of certain function or dysfunction using non-invasive measurement techniques. Over the last two decades structural imaging techniques, X-ray computer tomography (CT) and magnetic resonance tomography (MRT), have became precise enough to depict the brain with a resolution of roughly one millimeter. Functional imaging techniques, measuring metabolism and blood flowing, positron-emission-tomography (PET) and functional magnetic resonance tomography (fMR), were shown to be able to localize functional areas of the brain with a sufficient resolution.

A second technique to measure the functional state of the brain is to record the electro-magnetic activity of the brain (EEG and MEG) at the surface of the head and to perform source reconstruction for localizing the actually active brain area(s). This approach has the advantages of a very high time resolution (msec) [PET and fMR approximately 1-2 sec] and dramatically lower costs (EEG cheaper by a factor 10 to 30 in comparison to PET and fMR).

During the last years multichannel EEG and MEG systems became available and source localization of cerebral activity with respect to the individual anatomy became a prominent goal of electroencephalography. A mathematical treatment of this problem on the basis of physical principles and computer techniques was first proposed by Brazier 1949 [9] and implemented by Henderson et al. [8]. Their approach bases on representing the head by a spherical volume conductor model and the locus and orientation of the source by an equivalent dipole. However, a sphere or multiple layer spheres are an oversimplified model because the geometry of the head is not properly represented by a sphere, the thickness of skin and skull are not uniform, electric conductivity varies in different parts of the head, and the conduction properties of the compartments of the head are dependent on the direction of current flow. Recent studies demonstrated, that head modeling with respect to the individual head anatomy is required for exact localization.

While the finite element method (FEM) is known to be able to treat geometries of arbitrary complexity and is able to model variable material properties and anisotropy in computer simulations, it was rarely applied to the problem discussed here.

Our interdisciplinary research team started in 1993 developing the finite element based program CAUCHY supported by the VW-foundation. The major goal was to prepare the tools for source reconstruction within the individual anatomy for experimental use.

This manual or better description of the functionality of CAUCHY was written mainly for documentation of our work, but also for possible new users. We want CAUCHY to be available for everyone accepting the user agreements.

Content

  1. Nomenclature
  2. Principles of Finite Element Modeling
    1. General Description of the Finite Element Method
    2. On the exactness of the finite-element method
  3. General Program Functionality
    1. Batch handling
    2. Volume conductor
      1. Sphere (KUGEN)
      2. Realistically Shaped Head Modeling
        1. Conductivities
          1. Element-related or node-related conductivities
          2. Anisotropy
        2. Local Mesh Refinement (REMESH)
        3. Possible Source Nodes / Influence nodes (EIPP)
          1. Volume
          2. Surface
          3. Excluding of Possible Source Nodes (TEILMA)
    3. Data
      1. Electrode Position (KNOFIN)
      2. MEG-System Description
      3. EEG/MEG data
      4. Excluding Measurement Channels (TEILMA)
    4. Forward Modeling
      1. Dipole Model
      2. Source Simulation
      3. Generating .knw Input Files with EIPP
      4. Reference Solution
      5. Lead Field Matrix
    5. Inverse Reconstruction
      1. Constraints
        1. Volume Search
        2. Surface Search
          1. Normal Constraint
      2. Singular Value Decomposition (SVD) and S/N Representation (TSVD)
        1. Focal Inverse Current Reconstruction- Simulated Annealing (SA) and Deviation Scan (DS)
      3. Regularization: Tikhonov-Philips
        1. Minimum Norm Least Squares -MNLS- (L2-Norm)
          1. L2 Norm Degree of Smoothness
          2. Discrete L2
        2. Non-linear norms
          1. L1-Norm
          2. Entropy
          3. Lambda Iteration
          4. Convergence Test
          5. FOCUSS
    6. Output
    7. Optional Checks
    8. Miscellaneous Features
      1. Heat/Temperature Calculation
      2. Eigenvector Calculation
      3. SVD of the lead-field matrix
      4. Transient Solution
  4. Program proceeding
    1. Batch handling
    2. Volume conductor
      1. Sphere (KUGEN)
      2. Realistically Shaped Head Modeling
        1. Conductivities
          1. Element-related conductivities
          2. Node-related conductivities
          3. Anisotropy
        2. Local Mesh Refinement (REMESH)
        3. Possible Source Nodes / Influence nodes (EIPP)
          1. Volume
          2. Surface
          3. Excluding of Possible Source Nodes (TEILMA)
    3. Data
      1. Electrode Position (KNOFIN)
      2. MEG-System Description (CURMEG, TEILMA)
      3. EEG/MEG Import (MESCNV)
      4. Excluding Measurement Channels (TEILMA)
    4. Forward Modeling
      1. Dipole Model
      2. Source Simulation
      3. Generating .knw Input Files with EIPP
        1. Generation of a scalar source file with EIPP
        2. Generation of a vector source file with EIPP
      4. Reference Solution
      5. Lead Field Matrix
    5. Inverse Reconstruction
      1. Constraints
        1. Volume Search
        2. Surface Search
          1. Normal Constraint
      2. S/N Representation (TSVD)
        1. Focal Inverse Current Reconstruction-Simulated Annealing
        2. Linear Least Squares Methods [16,15]
      3. Regularization: Tikhonov-Philips
        1. L2-Norm
          1. Degree of Smoothness
          2. Discrete L2
        2. L1-Norm
        3. Entropy
        4. Lambda Iteration
        5. Convergence Test
        6. FOCUSS
    6. Output
      1. Visualization - Maps
      2. Visualization - Sources
    7. Optional Checks
    8. Miscellaneous Features
      1. Heat/Temperature Calculation
      2. Eigenvector Calculation
      3. SVD of the lead-field matrix
      4. Transient Solution
    9. Known Problems
  5. Program Control
  6. Programmer’s information
    1. Compact Storage
    2. Memory Allocation
    3. Forward Solution
      1. EEG
      2. MEG
    4. Solvers
  7. Validation
    1. CAUCHY vs. Sphere
      1. EEG
      2. MEG
    2. Head Phantom
      1. The head model
      2. Experimental arrangement and realization
      3. Inverse calculation
      4. Results
      5. Conclusions
    3. Perspectives
  8. Installation
    1. Hardware Requirements
      1. Prerequisites
        1. Platform independent prerequisites
        2. Additional prerequisites for LINUX
        3. Additional prerequisites for SUN-SPARC-STATION
    2. Installing procedure
      1. Unpack the package
        1. Platform independent
      2. Configure the package
      3. Installing the package
      4. Testing CAUCHY:
      5. Recompile the programs
    3. Operating systems
      1. Tested hardware configuration
    4. Known problems
  9. Examples
    1. Geometry 1
      1. Example 1-1
      2. Example 1-2
    2. Geometry 2
      1. Example 2-1
      2. Example 2-2
      3. Example 2-3
      4. Example 2-4
    3. Geometry 3
      1. Example 3-1
      2. Example 3-2
    4. Kugen-Example
    5. Spangl-Example
  10. Appendix A
    1. Generals Concerning Input Files
    2. Formats of Data Files
    3. CAUCHY Input Files
  11. Appendix B -EIPP-
  12. Appendix C
    1. INPCAU
      1. General Description
      2. Program Control
    2. KUGEN
      1. General Description
      2. Program Control
      3. File Formats
    3. REMESH
      1. General Description
      2. Program Control
      3. File Formats
    4. KNOFIN
      1. General Description
      2. Program Control
      3. File Formats
    5. CURMEG
      1. General Description
      2. Program Control
      3. File Formats
    6. TEILMA
      1. General Description
      2. Program Control
      3. File Formats
    7. MESCNV
      1. General Description
      2. Program Control
      3. File Formats
    8. SPANGL
      1. General Description
      2. Program Control
      3. File Format
  13. Appendix D
  14. References
  15. CAUCHY Papers

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