We developed a mathematical representation of ventricular geometry
and muscle fiber organization using three-dimensional finite elements
referred to a prolate spheroid coordinate system. Within elements,
fields are approximated using basis functions with associated parameters
defined at the element nodes. Four parameters per node are used to
describe ventricular geometry. The radial coordinate is interpolated
using cubic Hermite basis functions that preserve slope continuity,
while the angular coordinates are interpolated linearly. Two further
nodal parameters describe the orientation of myocardial fibers. The
orientation of fibers within coordinate planes bounded by epicardial
and endocardial surfaces is interpolated linearly, with transmural
variation given by cubic Hermite basis functions. Left and right
ventricular geometry and myocardial fiber orientations were characterized
for a canine heart arrested in diastole and fixed at zero transmural
pressure. The geometry was represented by a 24-element ensemble with
41 nodes. Nodal parameters fitted using least squares provided a
realistic description of ventricular epicardial root mean square
(RMS) error less than 0.9 mm and endocardial (RMS error less
than 2.6 mm) surfaces. Measured fiber fields were also fitted (RMS
error less than 17 degrees) with a 60-element, 99-node mesh obtained
by subdividing the 24-element mesh. These methods provide a compact
and accurate anatomic description of the ventricles suitable for
use in finite element stress analysis, simulation of cardiac electrical
activation, and other cardiac field modeling problems.
%0 Journal Article
%1 Niel_1991_H1365
%A Nielsen, P. M.
%A Grice, I. J. Le
%A Smaill, B. H.
%A Hunter, P. J.
%D 1991
%J Am. J. Physiol.
%K 2012234 Animals, Artificial, Biocompatible Connective Design, Dogs, Endocardium, Equipment Gov't, Heart Heart, Materials Materials, Mathematics, Mechanical, Membranes, Models, Non-U.S. Research Stress, Structural, Support, Swine, Testing, Tissue, Ventricles,
%N 4 Pt 2
%P H1365--H1378
%T Mathematical model of geometry and fibrous structure of the heart.
%U http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=2012234&query_hl=17
%V 260
%X We developed a mathematical representation of ventricular geometry
and muscle fiber organization using three-dimensional finite elements
referred to a prolate spheroid coordinate system. Within elements,
fields are approximated using basis functions with associated parameters
defined at the element nodes. Four parameters per node are used to
describe ventricular geometry. The radial coordinate is interpolated
using cubic Hermite basis functions that preserve slope continuity,
while the angular coordinates are interpolated linearly. Two further
nodal parameters describe the orientation of myocardial fibers. The
orientation of fibers within coordinate planes bounded by epicardial
and endocardial surfaces is interpolated linearly, with transmural
variation given by cubic Hermite basis functions. Left and right
ventricular geometry and myocardial fiber orientations were characterized
for a canine heart arrested in diastole and fixed at zero transmural
pressure. The geometry was represented by a 24-element ensemble with
41 nodes. Nodal parameters fitted using least squares provided a
realistic description of ventricular epicardial root mean square
(RMS) error less than 0.9 mm and endocardial (RMS error less
than 2.6 mm) surfaces. Measured fiber fields were also fitted (RMS
error less than 17 degrees) with a 60-element, 99-node mesh obtained
by subdividing the 24-element mesh. These methods provide a compact
and accurate anatomic description of the ventricles suitable for
use in finite element stress analysis, simulation of cardiac electrical
activation, and other cardiac field modeling problems.
@article{Niel_1991_H1365,
abstract = {We developed a mathematical representation of ventricular geometry
and muscle fiber organization using three-dimensional finite elements
referred to a prolate spheroid coordinate system. Within elements,
fields are approximated using basis functions with associated parameters
defined at the element nodes. Four parameters per node are used to
describe ventricular geometry. The radial coordinate is interpolated
using cubic Hermite basis functions that preserve slope continuity,
while the angular coordinates are interpolated linearly. Two further
nodal parameters describe the orientation of myocardial fibers. The
orientation of fibers within coordinate planes bounded by epicardial
and endocardial surfaces is interpolated linearly, with transmural
variation given by cubic Hermite basis functions. Left and right
ventricular geometry and myocardial fiber orientations were characterized
for a canine heart arrested in diastole and fixed at zero transmural
pressure. The geometry was represented by a 24-element ensemble with
41 nodes. Nodal parameters fitted using least squares provided a
realistic description of ventricular epicardial [root mean square
({RMS}) error less than 0.9 mm] and endocardial ({RMS} error less
than 2.6 mm) surfaces. Measured fiber fields were also fitted ({RMS}
error less than 17 degrees) with a 60-element, 99-node mesh obtained
by subdividing the 24-element mesh. These methods provide a compact
and accurate anatomic description of the ventricles suitable for
use in finite element stress analysis, simulation of cardiac electrical
activation, and other cardiac field modeling problems.},
added-at = {2009-06-03T11:20:58.000+0200},
author = {Nielsen, P. M. and Grice, I. J. Le and Smaill, B. H. and Hunter, P. J.},
biburl = {https://www.bibsonomy.org/bibtex/27a1911016f638cd44d72f7046c946f12/hake},
description = {The whole bibliography file I use.},
file = {Niel_1991_H1365.pdf:Niel_1991_H1365.pdf:PDF},
interhash = {20661e90d9eeb1c756b898406f79eac6},
intrahash = {7a1911016f638cd44d72f7046c946f12},
journal = {Am. J. Physiol.},
key = 60,
keywords = {2012234 Animals, Artificial, Biocompatible Connective Design, Dogs, Endocardium, Equipment Gov't, Heart Heart, Materials Materials, Mathematics, Mechanical, Membranes, Models, Non-U.S. Research Stress, Structural, Support, Swine, Testing, Tissue, Ventricles,},
month = Apr,
number = {4 Pt 2},
pages = {H1365--H1378},
pmid = {2012234},
timestamp = {2009-06-03T11:21:24.000+0200},
title = {Mathematical model of geometry and fibrous structure of the heart.},
url = {http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=2012234&query_hl=17},
volume = 260,
year = 1991
}