Spline surface interpolation for calculating 3-D ventricular strains from MRI tissue tagging

1996 ◽  
Vol 270 (1) ◽  
pp. H281-H297 ◽  
Author(s):  
M. J. Moulton ◽  
L. L. Creswell ◽  
S. W. Downing ◽  
R. L. Actis ◽  
B. A. Szabo ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Reference Image ◽  
Line Detection ◽  
Elasticity Solution ◽  
Surface Interpolation ◽  
Spline Surface ◽  
Tissue Tagging ◽  
Measurement Analysis ◽  
Displacement Reconstruction ◽  
Rms Errors

A method is developed and validated for approximating continuous smooth distributions of finite strains in the ventricles from the deformations of magnetic resonance imaging (MRI) tissue tagging "tag lines" or "tag surfaces." Tag lines and intersections of orthogonal tag lines are determined using a semiautomated algorithm. Three-dimensional (3-D) reconstruction of the displacement field on tag surfaces is performed using two orthogonal sets of MRI images and employing spline surface interpolation. The 3-D regional ventricular wall strains are computed from an initial reference image to a deformed image in diastole or systole by defining a mapping or transformation of space between the two states. The resultant mapping is termed the measurement analysis solution and is defined by determining a set of coefficients for the approximating functions that best fit the measured tag surface displacements. Validation of the method is performed by simulating tag line or surface deformations with a finite element (FE) elasticity solution of the heart and incorporating the measured root-mean-square (rms) errors of tag line detection into the simulations. The FE-computed strains are compared with strains calculated by the proposed procedure. The average difference between two-dimensional (2-D) FE-computed strains and strains calculated by the measurement analysis was 0.022 +/- 0.009 or 14.2 +/- 3.6% of the average FE elasticity strain solution. The 3-D displacement reconstruction errors averaged 0.087 +/- 0.002 mm or 2.4 +/- 0.1% of the average FE solution, and 3-D strain fitting errors averaged 0.024 +/- 0.011 or 15.9 +/- 2.8% of the average 3-D FE elasticity solution. When the rms errors in tag line detection were included in the 2-D simulations, the agreement between FE solution and fitted solution was 24.7% for the 2-D simulations and 19.2% for the 3-D simulations. We conclude that the 3-D displacements of MRI tag lines may be reconstructed accurately; however, the strain solution magnifies the small errors in locating tag lines and reconstructing 3-D displacements.

A Smooth Contact Algorithm Using Cubic Spline Surface Interpolation for Rigid and Flexible Bodies

2013 ◽  
Author(s):  
Juhwan Choi ◽  
Jin Hwan Choi
Keyword(s):  
Contact Force ◽  
Cubic Spline ◽  
Surface Representation ◽  
Flexible Bodies ◽  
Contact Algorithm ◽  
Surface Interpolation ◽  
Spline Surface ◽  
Smooth Contact ◽  
Representation Method ◽  
Detailed Search

The contact analysis of multi-flexible-body dynamics (MFBD) has been an important issue in the area of computational dynamics because the realistic dynamic analysis of many mechanical systems includes the contacts among rigid and flexible bodies. But, until now, the contact analysis in the multi-flexible-body dynamics has still remained as a big, challenging area. Especially, the most of contact algorithms have been developed based on the facetted triangles. As a result, the contact force based on the facetted surface was not accurate and smooth because the geometrical error is already included in the contact surface representation stage. This kind of error can be very important in the precise mechanism such as gear contact or cam-valve contact problems. In order to resolve this problem, this study suggests a cubic spline surface representation method and related contact algorithms. The proposed contact algorithms are using the compliant contact force model based on the Hertzian contact theory. In order to evaluate the smooth contact force, the penetration depth and contact normal directions are evaluated by using the cubic spline surface interpolation. Also, for the robust and efficient contact algorithm development, the contact algorithms are divided into four main parts which are a surface representation, a pre-search, a detailed search and a contact force generation. In the surface representation part, we propose a smooth surface representation method which can be used for smooth rigid and flexible bodies. In the pre-search, the algorithm performs collision detection and composes the expected contact pairs for the detailed search. In the detailed search, the penetration depth and contact reference frame are calculated with the cubic spline surface interpolation in order to generate the accurate and smooth contact force. Finally in the contact force generation part, we evaluate the contact force and Jacobian matrix for the implicit time integrator.

Abstract 964: Effect of Volume Overload on Left Ventricular Torsion and Extra Cellular Matrix

Circulation ◽  
2007 ◽  
Vol 116 (suppl_16) ◽  
Author(s):  
Hosakote M Nagaraj ◽  
Thomas S Denney ◽  
Steven G Lloyd ◽  
David Calhoun ◽  
Inmaculada Aban ◽  
...  
Keyword(s):  
Picric Acid ◽  
Three Dimensional ◽  
Volume Overload ◽  
Left Ventricular ◽  
Deformation Model ◽  
Data Set ◽  
Left Ventricular Torsion ◽  
Tissue Tagging ◽  
Ventricular Torsion ◽  
Longitudinal Strains

Background: Muscle fibers are arranged in a spiral network and are connected by extracellular matrix (ECM). LV torsion is increased in the pressure overloaded heart where there is an increase in ECM. However, torsion and its relation to ECM have not been systematically studied in the volume overloaded heart. Hypothesis: The volume overloaded heart has a decrease in LV torsion due a loss of ECM. Methods: Primary mitral regurgitation (MR) (n=29), resistant hypertension (HTN) (n=77) and normal volunteers (NL) (n±37) were studied. Comprehensive cardiac magnetic resonance imaging (MRI) with tissue tagging was performed and analyzed using three-dimensional data set. Torsion was computed by fitting a B-spline deformation model in prolate-spheroidal coordinates to the tag line data. A subset of MR subjects had LV collagen assessed by picric acid Sirius red from biopsy samples taken at the time of surgery. Results: LV ejection fraction was 65% in MR and 70% in HTN. MR demonstrated eccentric remodeling and HTN demonstrated concentric remodeling. HTN had significantly higher torsion angle and systolic twist compared to NL and MR. This was associated with a simultaneous decrease in longitudinal strain. In contrast, MR patients had similar torsion indices, circumferential and longitudinal strains compared to NL. LV biopsy in MR demonstrated a decrease in interstitial collagen compared to NL. Conclusions: As opposed to the pure volume overloaded heart, LV torsional forces are increased in the pressure overloaded heart. This difference may be related to a rearrangement of the laminar structure due to a differential effect on ECM in the volume overloaded versus the pressure overloaded heart.

Parallel B-Spline Surface Interpolation on a Mesh-Connected Processor Array

1995 ◽  
Vol 24 (2) ◽  
pp. 224-229
Author(s):  
F.H. Cheng ◽  
G.W. Wasilkowski ◽  
J.Y. Wang ◽  
C.M. Zhang ◽  
W.P. Wang
Keyword(s):  
Processor Array ◽  
B Spline ◽  
Surface Interpolation ◽  
Spline Surface

Shape Optimization of a Camoid Follower Surface

2008 ◽  
Author(s):  
Karim A. Aguib ◽  
Keith A. Hekman ◽  
Ashraf O. Nassef
Keyword(s):  
Genetic Algorithms ◽  
Shape Optimization ◽  
Three Dimensional ◽  
Characteristic Surface ◽  
Design Constraints ◽  
B Splines ◽  
Surface Interpolation ◽  
Specific Objective ◽  
Interpolation Technique ◽  
Real Coded Genetic Algorithms

Camoids are three dimensional cams that can produce more complex follower output than plain disc cams. A camoid follower motion is described by a surface rather than a curve. The camoid profile can be directly synthesized once the follower surface is fully described. To define a camoid follower motion surface it is required that the surface pass by all predefined constraints. Constraints can be follower position, velocity and acceleration. These design constraints are scattered all along the camoid follower surface. Hence a fitting technique is needed to satisfy these constraints which include position and its derivatives (velocity and acceleration). Furthermore if the fitting function can be of a parametric nature, then it would be possible to optimize the follower surface to obtain better performance according to a specific objective. Previous research has established a method to fit camoid follower surface positions, but did not tackle the satisfaction of derivative constraints. This paper presents a method for defining a camoid follower characteristic surface B-Splines on two steps first synthesizing the sectional cam curves then using a surface interpolation technique to generate the follower characteristic surface. The fitting technique is parametric in nature which allows for its optimization. Real coded Genetic algorithms are used to optimize the parameters of the surface to meet a specified objective function. A demonstration problem to illustrate the suggested methodology is presented.

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