FieldML, a proposed open standard for the Physiome project for mathematical model representation

Abstract

The FieldML project has made significant progress towards the goal of addressing the need to have open standards and open source software for representing finite element method (FEM) models and, more generally, multivariate field models, such as many of the models that are core to the euHeart project and the Physiome project. FieldML version 0.5 is the most recently released format from the FieldML project. It is an XML format that already has sufficient capability to represent the majority of euHeart's explicit models such as the anatomical FEM models and simulation solution fields. The details of FieldML version 0.5 are presented, as well as its limitations and some discussion of the progress being made to address these limitations.

Fig. 1

An euHeart aorta model. This is an aortic coarctation model with four vessel branches in the aortic arch: the right subclavian artery, right common carotid artery, left common carotid artery and the left subclavian artery. The figure shows a coarse mesh for demonstration purposes. In the CFD calculation, a much denser mesh was used, with 375695 nodes, 555027 tetrahedral elements and 543720 prism elements, using a different format [4]

Fig. 2

Screenshot of an interactive 3D visualisation of the FieldML version 0.5 representation of the aorta model, embedded in a web page served by the PMR software

Fig. 3

Visualisation of FieldML representation of five patient-specific human left ventricle anatomical models

Fig. 4

FieldML serialisation and communication architecture

Fig. 5

Using an intermediate conversion function to allow for compatible composition of evaluators

Fig. 6

Simple FieldML 0.5 example, colour variation represents the scalar pressure field

Fig. 7

Schematic overview of the example FieldML model XML and mathematical structure, the figures that follow after this show detail on parts of this schematic. Key: CT continuous type, EE external evaluator, ET ensemble type, MT mesh type, PW piecewise evaluator, AE aggregate evaluator, PE parameter evaluator, DS data source, ArgE argument evaluator, RE reference evaluator. Structure is shown for the relevant parts of the standard FieldML library, and for the example model. Each evaluator or type entity’s label consists of the abbreviation of the type according to the legend, a brief description and the symbol used in the mathematical representation describing the example (see line-by-line annotation in supplementary material). See the following figures for details on each of the major sections of this schematic

Fig. 8

Detail of imports from library used in example model (see overview schematic for the explanation of abbreviations)

Fig. 9

More detail of model structure. The structures in the example model are grouped by relevance to the pressure field, the geometric field or shared structures, and detailed schematics for these are presented in the figures that follow

Fig. 10

Detailed schematic for the part of the model shared by both the field definitions for pressure and geometry (see overview schematic for the explanation of abbreviations)

Fig. 11

Detailed schematic for the pressure-specific part of the example model (see overview schematic for the explanation of abbreviations)

Fig. 12

Detailed schematic for the geometry-specific part of the example model (see overview schematic for the explanation of abbreviations)