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FieldML: concepts and implementation.

Christie GR, Nielsen PM, Blackett SA, Bradley CP, Hunter PJ - Philos Trans A Math Phys Eng Sci (2009)

Bottom Line: It comprises a rich set of operators for defining generalized fields as functions of other fields, starting with basic domain fields including sets of discrete objects and coordinate systems.It is extensible by adding new operators and by their arbitrary combination in expressions, making it well suited for describing the inherent complexity of biological materials and organ systems.It outlines current implementations in established, open source computation and visualization software, both drawing on decades of bioengineering modelling software development experience.

View Article: PubMed Central - PubMed

Affiliation: Auckland Bioengineering Institute, University of Auckland, Auckland 1142, New Zealand. r.christie@auckland.ac.nz

ABSTRACT
The field modelling language FieldML is being developed as a standard for modelling and interchanging field descriptions in software, suitable for a wide range of computation techniques. It comprises a rich set of operators for defining generalized fields as functions of other fields, starting with basic domain fields including sets of discrete objects and coordinate systems. It is extensible by adding new operators and by their arbitrary combination in expressions, making it well suited for describing the inherent complexity of biological materials and organ systems. This paper describes the concepts behind FieldML, including a simple example of a spatially varying finite-element field. It outlines current implementations in established, open source computation and visualization software, both drawing on decades of bioengineering modelling software development experience.

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Visualization of a deforming heart in Cmgui, from a simulation performed using CMISS (see Nash & Hunter 2001). Here the coordinate field is defined in a prolate spheroidal coordinate system, and interpolated over finite elements using different basis functions for each component. Streamlines show the muscle fibre coordinate system with respect to which material properties for the simulation were defined; it is defined by interpolating Euler angles over elements, which transform an orthonormal coordinate system relative to an initial orientation aligned to the gradients of the coordinate field with respect to the element chart coordinates. Displacement gradient operators applied to the coordinate field at various simulation times and relative to the initial state are further converted into large strains; eigenvalues and eigenvectors of the resulting matrix give the principal strains, which are visualized as arrows, blue and outward pointing for extension, red and inward pointing for compression.
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fig7: Visualization of a deforming heart in Cmgui, from a simulation performed using CMISS (see Nash & Hunter 2001). Here the coordinate field is defined in a prolate spheroidal coordinate system, and interpolated over finite elements using different basis functions for each component. Streamlines show the muscle fibre coordinate system with respect to which material properties for the simulation were defined; it is defined by interpolating Euler angles over elements, which transform an orthonormal coordinate system relative to an initial orientation aligned to the gradients of the coordinate field with respect to the element chart coordinates. Displacement gradient operators applied to the coordinate field at various simulation times and relative to the initial state are further converted into large strains; eigenvalues and eigenvectors of the resulting matrix give the principal strains, which are visualized as arrows, blue and outward pointing for extension, red and inward pointing for compression.

Mentions: A significant influence on FieldML has been the CMISS modelling software (www.cmiss.org), which supports complicated representations of finite-element fields using basis functions with high-order continuity and flexible parameter mappings. CMISS models use fields to express most simulation variables, including geometry, material properties as well as dependent variables. It is able to use different basis functions for each field component defined over the same topology. This contrasts with conventional finite-element representations, which restrict fields to using just a few simple element types, mixing function with topology. In addition, they often treat geometry and material properties as special cases, distinct from other fields. Examples include the General Mesh Viewer format (http://www-xdiv.lanl.gov/XCM/gmv) and EXODUS II format (http://endo.sandia.gov/SEACAS/Documentation/exodusII.pdf). The authors consider these formats to be limiting for many of the problems being encountered in bioengineering. Christie et al. (2002) showed the benefits of defining fields by mathematical operations on other fields including cases where the fields have a nonlinear relationship to field parameters, as illustrated later by the muscle fibres in figure 7. It is noted that the more varied field representations in CMISS come at the cost of greater software complexity, which FieldML intends to reduce by replacing fixed-functionality codes with modular combinations of basic field operations.


FieldML: concepts and implementation.

Christie GR, Nielsen PM, Blackett SA, Bradley CP, Hunter PJ - Philos Trans A Math Phys Eng Sci (2009)

Visualization of a deforming heart in Cmgui, from a simulation performed using CMISS (see Nash & Hunter 2001). Here the coordinate field is defined in a prolate spheroidal coordinate system, and interpolated over finite elements using different basis functions for each component. Streamlines show the muscle fibre coordinate system with respect to which material properties for the simulation were defined; it is defined by interpolating Euler angles over elements, which transform an orthonormal coordinate system relative to an initial orientation aligned to the gradients of the coordinate field with respect to the element chart coordinates. Displacement gradient operators applied to the coordinate field at various simulation times and relative to the initial state are further converted into large strains; eigenvalues and eigenvectors of the resulting matrix give the principal strains, which are visualized as arrows, blue and outward pointing for extension, red and inward pointing for compression.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2665020&req=5

fig7: Visualization of a deforming heart in Cmgui, from a simulation performed using CMISS (see Nash & Hunter 2001). Here the coordinate field is defined in a prolate spheroidal coordinate system, and interpolated over finite elements using different basis functions for each component. Streamlines show the muscle fibre coordinate system with respect to which material properties for the simulation were defined; it is defined by interpolating Euler angles over elements, which transform an orthonormal coordinate system relative to an initial orientation aligned to the gradients of the coordinate field with respect to the element chart coordinates. Displacement gradient operators applied to the coordinate field at various simulation times and relative to the initial state are further converted into large strains; eigenvalues and eigenvectors of the resulting matrix give the principal strains, which are visualized as arrows, blue and outward pointing for extension, red and inward pointing for compression.
Mentions: A significant influence on FieldML has been the CMISS modelling software (www.cmiss.org), which supports complicated representations of finite-element fields using basis functions with high-order continuity and flexible parameter mappings. CMISS models use fields to express most simulation variables, including geometry, material properties as well as dependent variables. It is able to use different basis functions for each field component defined over the same topology. This contrasts with conventional finite-element representations, which restrict fields to using just a few simple element types, mixing function with topology. In addition, they often treat geometry and material properties as special cases, distinct from other fields. Examples include the General Mesh Viewer format (http://www-xdiv.lanl.gov/XCM/gmv) and EXODUS II format (http://endo.sandia.gov/SEACAS/Documentation/exodusII.pdf). The authors consider these formats to be limiting for many of the problems being encountered in bioengineering. Christie et al. (2002) showed the benefits of defining fields by mathematical operations on other fields including cases where the fields have a nonlinear relationship to field parameters, as illustrated later by the muscle fibres in figure 7. It is noted that the more varied field representations in CMISS come at the cost of greater software complexity, which FieldML intends to reduce by replacing fixed-functionality codes with modular combinations of basic field operations.

Bottom Line: It comprises a rich set of operators for defining generalized fields as functions of other fields, starting with basic domain fields including sets of discrete objects and coordinate systems.It is extensible by adding new operators and by their arbitrary combination in expressions, making it well suited for describing the inherent complexity of biological materials and organ systems.It outlines current implementations in established, open source computation and visualization software, both drawing on decades of bioengineering modelling software development experience.

View Article: PubMed Central - PubMed

Affiliation: Auckland Bioengineering Institute, University of Auckland, Auckland 1142, New Zealand. r.christie@auckland.ac.nz

ABSTRACT
The field modelling language FieldML is being developed as a standard for modelling and interchanging field descriptions in software, suitable for a wide range of computation techniques. It comprises a rich set of operators for defining generalized fields as functions of other fields, starting with basic domain fields including sets of discrete objects and coordinate systems. It is extensible by adding new operators and by their arbitrary combination in expressions, making it well suited for describing the inherent complexity of biological materials and organ systems. This paper describes the concepts behind FieldML, including a simple example of a spatially varying finite-element field. It outlines current implementations in established, open source computation and visualization software, both drawing on decades of bioengineering modelling software development experience.

Show MeSH