Reduced Order Model of a Human Left and Right Ventricle Based on POD Method

The paper aims to build a reduced order model (ROM) of the left and right ventricle of a human heart. The input heart model is build from 3D sets of registered, flexible surface meshes for the left and right ventricle, resulting from the MRI data. Spatial and temporal variables are separated using Proper Orthogonal Decomposition. It enables data reduction and works as a data-driven filter, separating similar and alternative properties of the left and right ventricle movement, which is diagnostically essential in cardiology studies. Each mode can be correlated with a corresponding heart movement. The temporal coefficients reflect the functioning of the heart, and comparing them may reveal and distinguish pathologies. We have proven that complex heart motion can be modeled with relatively small number of degrees of freedom. The model spanned on a few POD modes allows the analysis of the crucial movement data and better identification of possible failures.

[1]  Andreas Daffertshofer,et al.  PCA in studying coordination and variability: a tutorial. , 2004, Clinical biomechanics.

[2]  Hua Yu,et al.  A direct LDA algorithm for high-dimensional data - with application to face recognition , 2001, Pattern Recognit..

[3]  Daniel Rueckert,et al.  Segmentation of cardiac MR and CT image sequences using model-based registration of a 4D statistical model , 2007, SPIE Medical Imaging.

[4]  Chandan Chakraborty,et al.  Application of principal component analysis to ECG signals for automated diagnosis of cardiac health , 2012, Expert Syst. Appl..

[5]  James F. O'Brien,et al.  Variational Implicit Surfaces , 1999 .

[6]  Alistair A. Young,et al.  Atlas-Based Quantification of Cardiac Remodeling Due to Myocardial Infarction , 2014, PloS one.

[7]  Daniel Rueckert,et al.  Construction of a Statistical Model for Cardiac Motion Analysis Using Nonrigid Image Registration , 2003, IPMI.

[8]  Ali Ghaffari,et al.  Heart arrhythmia detection using continuous wavelet transform and principal component analysis with neural network classifier , 2010, 2010 Computing in Cardiology.

[9]  James V. Stone.  Independent Component Analysis , 2015 .

[10]  Siep Weiland,et al.  Model Reduction by Proper Orthogonal Decomposition , 2002 .

[11]  Denis Noble,et al.  The Cardiac Physiome: perspectives for the future , 2009, Experimental physiology.

[12]  Marc A Simon,et al.  A new approach to kinematic feature extraction from the human right ventricle for classification of hypertension: a feasibility study , 2012, Physics in medicine and biology.

[13]  Maxime Sermesant,et al.  vtkINRIA3D: A VTK Extension for Spatiotemporal Data Synchronization, Visualization and Management , 2007, The Insight Journal.

[14]  Hans-Peter Meinzer,et al.  Statistical shape models for 3D medical image segmentation: A review , 2009, Medical Image Anal..

[15]  L. Sirovich.  Turbulence and the dynamics of coherent structures. III. Dynamics and scaling , 1987 .

[16]  Hervé Delingette,et al.  An Integrated Platform for Dynamic Cardiac Simulation and Image Processing: Application to Personalised Tetralogy of Fallot Simulation , 2008, VCBM.

[17]  A. Hoes,et al.  Predicting mortality in patients with heart failure: a pragmatic approach , 2003, Heart.

[18]  Nicholas Ayache,et al.  Non-parametric Diffeomorphic Image Registration with the Demons Algorithm , 2007, MICCAI.

[19]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[20]  R. Tibshirani,et al.  Sparse Principal Component Analysis , 2006 .

[21]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control) , 2005 .

[22]  Antonio Daniele,et al.  Treatment of motor and non-motor features of Parkinson's disease with deep brain stimulation , 2012, The Lancet Neurology.

[23]  L. Glass,et al.  Theory of heart : biomechanics, biophysics, and nonlinear dynamics of cardiac function , 1991 .

[24]  Gilles Barone-Rochette,et al.  Mechanisms of cardiac dysfunction in obstructive sleep apnea , 2012, Nature Reviews Cardiology.

[25]  Steven L Fischer,et al.  A simple approach to guide factor retention decisions when applying principal component analysis to biomechanical data , 2014, Computer methods in biomechanics and biomedical engineering.

[26]  Michal Rychlik,et al.  Application of Modal Analysis for Extraction of Geometrical Features of Biological Objects Set , 2008, BIODEVICES.

[27]  Haiping Lu,et al.  MPCA: Multilinear Principal Component Analysis of Tensor Objects , 2008, IEEE Transactions on Neural Networks.

[28]  Guillaume Houzeaux,et al.  A massively parallel computational electrophysiology model of the heart , 2011 .

[29]  M Boulakia,et al.  Reduced-order modeling for cardiac electrophysiology. Application to parameter identification. , 2012, International journal for numerical methods in biomedical engineering.

[30]  Witold Stankiewicz,et al.  Genetic Algorithm-based Calibration of Reduced Order Galerkin Models , 2011 .

[31]  S. Plein,et al.  Normal human left and right ventricular dimensions for MRI as assessed by turbo gradient echo and steady‐state free precession imaging sequences , 2003, Journal of magnetic resonance imaging : JMRI.

[32]  Heiko Hoffmann,et al.  Kernel PCA for novelty detection , 2007, Pattern Recognit..