# Analysis of Cardiac Motion and Deformation

## Paper List

Acrobat .pdf Format Gzipped Postscript Format.
See note below for access restrictions.

## Papers

### The Active Elastic Model

Xenophon Papademetris, E. Turan Onat, Albert J. Sinusas, Donald P. Dione, R. Todd Constable and James S. Duncan.
To appear in the proceedings of Information Processing in Medical Imaging (IPMI), 2001.

#### Abstract

Continuum mechanical models have been used to regularize ill-posed problems in many applications in medical imaging analysis such as image registration and left ventricular motion estimation. In this work, we present a significant extension to the common elastic model which we call the \emph{active elastic model}. The active elastic model is designed to reduce bias in deformation estimation and to allow the imposition of proper priors on deformation estimation problems that contain information regarding both the expected magnitude and the expected variability of the deformation to be estimated. We test this model on the problem of left ventricular deformation estimation, and present ideas for its application in image registration and brain deformation during neurosurgery.

#### BibTeX Entry

@INPROCEEDINGS{xPapademetris2001,
author = "X.  Papademetris and  E. T. Onat and A.  J.  Sinusas  and
D.  P.  Dione and R. T. Constable, J. S.  Duncan",
title = "The Active Elastic Model",
booktitle = "Information Processing in Medical Imaging (IPMI)",
year = "2001",
month = "June"}


### Estimation of 3D Left Ventricular Deformation from Echocardiography

Xenophon Papademetris, Albert J. Sinusas, Donald P. Dione and James S. Duncan.
Medical Image Analysis. In-press (March 2001)

#### Abstract

The quantitative estimation of regional cardiac deformation from 3D image sequences has important clinical implications for the assessment of viability in the heart wall. Such estimates have so far been obtained almost exclusively from Magnetic Resonance (MR) images, specifically MR tagging. In this paper we describe a methodology for estimating cardiac deformations from 3D echocardiography (3DE). The images are segmented interactively and then initial correspondence is established using a shape-tracking approach. A dense motion field is then estimated using an anisotropic linear elastic model, which accounts for the fiber directions in the left ventricle. The dense motion field is in turn used to calculate the deformation of the heart wall in terms of strain in cardiac specific directions. The strains obtained using this approach in open-chest dogs before and after coronary occlusion, show good agreement with previously published results in the literature. They also exhibit a high correlation with strains produced in the same animals using implanted sonomicrometers. This proposed method provides quantitative regional 3D estimates of heart deformation from ultrasound images.

#### BibTeX Entry

@article{xPapademetris2001b,
author ="X.  Papademetris and  A.  J.  Sinusas  and D.  P.  Dione and J. S.  Duncan",
title ="Estimation  of {3D} Left Ventricular Deformation from Echocardiography",
journal="Medical Image Analysis",
year ="in-press"}
The accompanying quicktime movies are also available.

### Estimating 3D Strain from 4D Cine-MRI and Echocardiography: In-Vivo Validation

Xenophon Papademetris, Albert J. Sinusas, Donald P. Dione, R. Todd Constable and James S. Duncan.
In the proceedings of MICCAI' 2000 to-appear

#### Abstract

The quantitative estimation of regional cardiac deformation from 3D image sequences has important clinical implications for the assessment of myocardial viability. The validation of such image-derived estimates, however, is a non-trivial problem as it is very difficult to obtain ground truth. In this work we present an approach to validating strain estimates derived from 3D cine-Magnetic Resonance (MR) and 3D Echocardiography (3DE) images using our previously-developed shape-based tracking algorithm. The images are segmented interactively and then initial correspondence is established using a shape-tracking approach. A dense motion field is then estimated using a transversely linear elastic model, which accounts for the fiber directions in the left ventricle. The dense motion field is in turn used to calculate the deformation of the heart wall in terms of strains. The strains obtained using our algorithm are compared to strains estimated using implanted markers and sonomicrometers, which are used as the gold standards. These preliminary studies show encouraging results.

#### BibTeX Entry

@INPROCEEDINGS{xPapademetris99b,
author = "X.  Papademetris and  A.  J.  Sinusas  and
D.  P.  Dione and R. T. Constable, J. S.  Duncan",
title = "Estimating 3D Strain from 4D Cine-MRI and Echocardiography: In-Vivo Validation",
booktitle = "Medical Image Computing and Computer Aided Intervention (MICCAI)",
year = "2000",
month = "October"}


### Cardiac Image Analysis: Motion and Deformation

Xenophon Papademetris and James .S. Duncan
In SPIE Handbook on Medical Imaging - Volume III: Medical Image Processing and Analysis. June 2000.

#### Abstract

In this chapter, we describe research in the area of estimation of cardiac motion and deformation from medical images. We focus primarily on the use of 3D mag-netic resonance image sequences, but we will also discuss the application of some methods to ultrafast CT and 3D echo.

#### BibTeX Entry

@incollection(xPapademetris2000,
author = {X. Papademetris and J. S. Duncan},
title =  {Cardiac Image Analysis: Motion and Deformation},
editor = {J. M. Fitzpatrick and M. Sonka},
booktitle =  {SPIE Handbook on Medical Imaging - Volume III: Medical Image Processing and
Analysis},
publisher = {SPIE},
year =  {2000})


### 3D Cardiac Deformation from Ultrasound Images

Xenophon Papademetris, Albert J. Sinusas, Donald P. Dione and James S. Duncan.
In the proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention, Cambridge England, September 1999.

#### Abstract

The quantitative estimation of regional cardiac deformation from 3D image sequences has important clinical implications for the assessment of viability in the heart wall. Such estimates have so far been obtained almost exclusively from Magnetic Resonance (MR) images, specifically MR tagging. In this paper we describe a methodology for estimating cardiac deformations from 3D ultrasound images. The images are segmented interactively and then initial correspondence is established using a shape-tracking approach. A dense motion field is then estimated using an anisotropic linear elastic model, which accounts for the fiber directions in the left-ventricle. The dense motion field is in turn used to calculate the deformation of the heart wall in terms of strain in cardiac specific directions. The strains obtained using this approach in open-chest dogs before and after coronary occlusion related to changes in blood flow, show good agreement with previously published results in the literature. This proposed method provides quantitative regional 3D estimates of heart deformation from ultrasound images.

#### BibTeX Entry

@INPROCEEDINGS{xPapademetris99b,
author = "X.  Papademetris and  A.  J.  Sinusas  and
D.  P.  Dione and J. S.  Duncan",
title = "{3D} Cardiac Deformation from Ultrasound Images",
booktitle = "Medical Image Computing and Computer Aided Intervention (MICCAI)",
year = "1999",
pages =  "420-429",
month = "September"}


### Volumetric Deformation Analysis Using Mechanics--Based Data Fusion: Applications in Cardiac Motion Recovery

Pengcheng Shi, Albert J. Sinusas, R. Todd Constable and James S. Duncan.
International Journal of Computer Vision, November 1999.

#### Abstract

Non--rigid motion estimation from image sequences is essential in analyzing and understanding the dynamic behaviors of physical objects. One important example is the dense field motion analysis of the cardiac wall, which could potentially help to better understand the physiological processes associated with heart disease and to provide improvement in patient diagnosis and treatment. In this paper, we present a new method of estimating volumetric deformation by integrating intrinsic instantaneous velocity data with geometrical token displacement information, based upon continuum mechanics principles. This object--dependent approach allows the incorporation of physically meaningful constraints into the ill--posed motion recovery problem, and the integration of the two disparate but complementary data sources overcomes some of the limitations of the single image source based motion estimation approaches.

#### BibTeX Entry

@article(xShi99,
author = "P. Shi and A.J. Sinusas and R. T.  Constable and J.S. Duncan",
title =  "Volumetric Deformation Analysis Using
Mechanics--Based Data Fusion: Applications in Cardiac Motion
Recovery.",
journal = "International Journal of Computer Vision",
volume = "35",
number = "1",
pages = "65-85",
month = "November",
year = "1999")


### Recovery of Soft Tissue Object Deformation using Biomechanical Models

Xenophon Papademetris, Pengcheng Shi, Donald P. Dione, Albert J. Sinusas, R. Todd Constable, and James S. Duncan.
In the proceedings of Information Processing in Medical Imaging (IPMI)", Visegrad Hungary, 1999.

#### Abstract

The estimation of soft tissue deformation from 3D image sequences is an important problem in a number of fields such as diagnosis of heart disease and image guided surgery. In this paper we describe a methodology for using biomechanical material models, within a Bayesian framework which allows for proper modeling of image noise, in order to estimate these deformations. The resulting partial differential equations are discretized and solved using the finite element method. We demonstrate the application of this method to estimating strains from sequences of in-vivo left ventricular MR images, where we incorporate information about the fibrous structure of the ventricle. The deformation estimates obtained exhibit similar patterns with measurements obtained from more invasive techniques, used as a gold standard.

#### BibTeX Entry

@INPROCEEDINGS{xPapademetris99a,
author = "X.  Papademetris and  P.  Shi and D.  P.  Dione
and A.  J.  Sinusas  and J.  S.  Duncan",
title = "Recovery of Soft Tissue Object Deformation using Biomechanical Models. ",
booktitle = "Information Processing in Medical Imaging",
year = "1999",
pages =  "352-357",
month = "June"}


### Point-Tracked Quantitative Analysis of Left Ventricular Motion from 3D Image Sequences

Pengcheng Shi, Albert J. Sinusas, R. Todd Constable Eric Ritman and James .S. Duncan
IEEE TMI January 2000

#### Abstract

We propose and validate the hypothesis that we can use differential shape properties of the myocardial surfaces to recover dense field motion from standard three--dimensional image data (MRI and CT). Quantitative measures of left ventricular regional function can be further inferred from the point correspondence maps. The non-invasive, algorithm--derived results are validated in two levels: the motion trajectories are compared to those of implanted imaging--opaque markers of a canine model in two imaging modalities, where sub--pixel accuracy is achieved, and the validity of using motion parameters (path length and thickness changes) in detecting myocardial injury is tested by comparison to post--mortem TTC staining of myocardial tissue, where the Pearson product--moment correlation value is 0.968.

#### BibTeX Entry

@ARTICLE{xship2000,
author = "P.  Shi and A.  J.  Sinusas and R.  T.  Constable
and E.  Ritman and J.  S.  Duncan",
title = "Point-Tracked Quantitative Analysis of
Left Ventricular Motion from {3D} Image Sequences",
journal = "IEEE Transactions on Medical Imaging",
year = "2000",
month="January",
volume="19",
number="1",
pages="36-50" }


### Physical and geometrical modeling for image-based recovery of left ventricular deformation

J.S. Duncan, P.Shi, R.T. Constable, and A.J. Sinusas.
Progress in Biophysics and Molecular Biology, 69(2-3):333--351, 1998.

#### Abstract

Information about left ventricular (LV) mechanical performance is of critical importance in understanding the etiology of ischemic heart disease. Regional measurements derived from non­invasive imaging to assist in assessing this performance have been in use for decades, and certain parameters derived from these measurements often are useful clinically, as they correlate to some extent with gross physiological hypotheses. However, relatively little work has been done to date to carefully understand the relationship of regional myocardial injury to the local mechanical performance of the heart as derived from image data acquired non- invasively for a particular patient in 3 spatial dimensions over time. This paper describes efforts to take advantage of recent developments in 3D non-invasive imaging and biome- chanical modeling to design an integrated computational platform capable of assembling a variety of displacement and velocity data derived from each image frame to deform a vol- umetric model representation of a portion of the myocardium. A brief description of both the reasoning behind this strategy is put forth, as well as an overview of the approach and some initial results are described.

#### BibTeX Entry

@article(xDuncan98,
author = "J. S.  Duncan and P.  Shi and R. T.  Constable and A.  Sinusas",
title =  "Physical and Geometrical Modeling for Image-Based Recovery
of Left Ventricular Deformation",
journal = "Progress in Biophysics and Molecular Biology",
volume = "69",
number = "2-3",
pages = "333-351",
year = "1998")


### Visually Interactive Cine-3D Segmentation of Cardiac MR Images

Xenophon Papademetris, James Rambo, Donald P. Dione, Albert J. Sinusas and James S. Duncan.
Supplement to the Journal of the American College of Cardiology Volume 31, Number 2 (Supplement A) February 1998.

A Handout that was given during the poster session is available on-line.

#### BibTeX Entry

@ARTICLE{xPapademetris98,
author = "X.  Papademetris and  J.  V.  Rambo  and D.  P.  Dione and
A.  J.  Sinusas  and  J.  S.  Duncan",
title = "Visually Interactive Cine-{3D} Segmentation of Cardiac {MR} Images",
journal = "Suppl.  to the J.  Am.  Coll.  of Cardiology",
volume = "31",
number = "2.  Suppl.  A",
month = "February",
year = "1998"} 

### Tracking Myocardial Deformation Using Phase Contrast MR Velocity Fields: A Stochastic Approach

Meyer F.G., Constable R.T., Sinusas A.J., Duncan J.S.
IEEE Transactions on Medical Imaging, Vol. 15, No. 4, August 1996, pages 453-465.

#### Abstract

In this paper, we propose a new approach for tracking the deformation of the Left Ventricular (LV) myocardium from two-dimensional Magnetic Resonance (MR) phase contrast velocity fields. The use of phase contrast MR velocity data in cardiac motion problems has been introduced by others [1] and shown to be po tentially useful for tracking discrete tissue elements, and therefore characteri zing LV motion. However, we show here that these velocity data i.) are extremely noisy near the LV borders and ii.) cannot alone be used to estimate the motion and the deformation of the entire myocardium due to noise in the velocity fields . In this new approach, we use the natural spatial constraints of the endocardia l and epicardial contours, detected semi-automatically in each image frame, to h elp remove noisy velocity vectors at the LV contours. The information from both the boundaries and the phase contrast velocity data is then integrated into a de forming mesh that is placed over the myocardium at one time frame and then track ed over the entire cardiac cycle. The deformation is guided by a Kalman filter t hat provides a compromise between a.) believing the dense field velocity and the contour data when it is crisp and coherent in a local spatial and temporal sens e and b.) employing a temporally smooth cyclic model of cardiac motion when cont our and velocity data are not trustworthy. The Kalman filter is particularly wel l suited to this task as it produces an optimal estimate of the LV's kinematics (in the sense that the error is statistically minimized) given incomplete and no ise corrupted data, and given a basic dynamical model of the LV. The method has been evaluated with simulated data ; the average error between tracked nodes and theoretical position was 1:8% of the total path length. The algorithm has also been evaluated with phantom data ; the average error was 4:4% of the total path length. We show that in our initial tests with phantoms that the new approach sh ows small, but concrete improvements over previous techniques that used primaril y phase contrast velocity data alone. We feel that these improvements will be am plified greatly as we move to direct comparisons in in vivo and three-dimensional datasets.

#### BibTeX Entry


@ARTICLE{xMeyer96,
AUTHOR = "F.  G.  Meyer and R.  T.  Constable and A. J.
Sinusas and J.  S.  Duncan",
TITLE = "Tracking Myocardial Deformation Using Phase Contrast {MR}
Velocity Fields: A Stochastic Approach",
JOURNAL ="IEEE Transactions on Medical Imaging",
VOLUME = "15",
NUMBER = "4",
MONTH = "August",
YEAR = 1996}


### A Model-Based Integrated Approach to Track Myocardial Deformation Using Displacement and Velocity Constraints

Pengcheng Shi, Glynn Robinson, R. Todd Constable, Albert J. Sinusas and James S. Duncan.
Proceedings of the International Conference on Computer Vision (ICCV) 1995.

#### Abstract

Accurate estimation of heart wall dense field motion and deformation could help to better understand the physiological processes associated with ischemic heart diseases, and to provide significant improvement in patient treatment. We present a new method of estimating left ventricular deformation which integrates instantaneous velocity information obtained within the mid-wall region with shape information found on the boundaries of the left ventricle. Velocity information is obtained from phase contrast magnetic resonance images, and boundary information is obtained from shape-based motion tracking of the endo- and epi-cardial boundaries. The integration takes place within a continuum biomechanical heart model which is embedded in a finite element framework. We also employ a feedback mechanism to improve tracking accuracy. The integration of the two disparate but complementary sources overcomes some of the limitations of previous work in the field which concentrates on motion estimation from a single image-derived source.

#### BibTeX Entry


@inproceedings{xShi_ICCV95,
author = "P. Shi and G. Robinson and R. T. Constable and A. Sinusas and J. Duncan",
title = "A Model-Based Integrated Approach to Track Myocardial Deformation
Using Displacement and Velocity Constraints",
booktitle =  "Fifth International Conference on Computer Vision",
year =  "1995",
pages =  "687-692"}


### A Unified Framework to Assess Myocardial Function from 4D Images

Pengcheng Shi, Glynn P. Robinson, Amit Chakraborty, Lawrence H. Staib, R. Todd Constable, Albert J. Sinusas and James S. Duncan.
Proceedings of the Computer Vision, Virtual Reality and Robotics in Medicine (CVRMed), Nice, France April 1995.

#### Abstract

This paper describes efforts aimed at developing a unified framework to more accurately quantify the local, regional and global function of the left ventricle (LV) of the heart, under both normal and ischemic conditions, using four--dimensional (4D) imaging data over the entire cardiac cycle. The approach incorporates motion information derived from the shape properties of the endocardial and epicardial surfaces of the LV, as well as mid--wall 3D instantaneous velocity information from phase contrast MR images, and/or mid--wall displacement information from tagged MR images. The integration of the disparate but complementary sources of information overcomes the limitations of previous work which concentrates on motion estimation from a single image--derived source.

#### BibTeX Entry

@inproceedings{xShi_CVRMed95,
author = "P. Shi and G. Robinson and A. Chakraborty and L. Staib and R. T. Constable
and A. Sinusas and J. Duncan",
title = "A Unified Framework to Assess Myocardial Function from {4D} Images",
booktitle =  "Lecture Notes in Computer Science: First
International Conference on Computer Vision, Virtual Reality,
and Robotics in Medicine",
year =  "1995",
pages =  "327-337"}


### A Recursive Filter for Phase Velocity Assisted Shape-based Tracking of Cardiac Non-rigid Motion

J. McEachen, F. Meyer,R. Constable, A. Nehorai and J.S. Duncan
Proceedings of the International Conference on Computer Vision (ICCV) 1995.

### Myocardial Motion and Function Assessment Using 4D Images

P. Shi, G. Robinson, and J. Duncan.
In the proceedings of the IEEE conference on Visualization in Biomedical Computing, Rochester MN, Oct 1994.

#### Abstract

This paper describes efforts aimed at more objectively and accurately quantifying the local, regional and global function of the left ventricle (LV) of the heart from four-dimensional (4D) image data. Using our shape-based image analysis methods, point-wise myocardial motion vector fields between successive image frames through the entire cardiac cycle will be computed. Quantitative LV motion, thickening, and strain measurements will then be established from the point correspondence maps. In the paper, we will also briefly describe an in vivo experimental model which uses implanted imaging-opaque markers to validate the results of our image analysis methods. Finally, initial experimental results using image sequences from two different modalities will be presented.

#### BibTeX Entry

@inproceedings{xShi_VBC94,
author = "P. Shi and G. Robinson and J. Duncan",
title = "Myocardial Motion and Function Assessment Using {4D} Images",
booktitle =  "Visualization in Biomedical Computing",
year =  "1994",
pages =  "148-159"}


### Analysis of Cardiac Motion with Recursive Comb Filtering

J. McEachen, A. Nehorai and J.S. Duncan

#### BibTeX Entry


@inproceedings{xMcEachen,
author = "J. C. McEachen II and A. Nehorai and J. S. Duncan",
title = "A recursive filter for temporal analysis of cardiac motion",
booktitle =  "Proceedings of the IEEE Workshop on Biomedical Image Analysis",
year =  "1994",
pages =  "124-133"}


## Sonomicrometer Papers

This is related work on obtaining cardiac strains from implanted sonomicrometers.

### Three-dimensional regional left ventricular deformation from digital sonomicrometry

D.P. Dione, P.Shi, W.Smith, P.De Man, J.Soares, J.S. Duncan, and A.J. Sinusas.
In 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society}, pages 848--851, Chigago, IL, March 1997.

#### Abstract

Understanding how the left ventricle deforms in 3D and how this deformation is altered with coronary occlusion may lead to the development of non-invasive imaging techniques to determine the extent of permanent injury. To determine regional 3D strains in the left ventricle of the heart we employed digital sonomicrometry, with high temporal and spatial resolution. Two cubic arrays of 8 omni-directional transceiver crystals were implanted in two regions of the left ventricle in an open chest canine preparation ($n=6$). Additional crystals were used to define a fixed external reference space and the long axis of the ventricle. Using ultrasound transit time the distances between all the crystals were recorded. A multidimensional scaling technique was then applied to transform the distances to 3D crystal coordinates. A least squares fit of the displacement field was applied to calculate homogeneous strains for each cube. Cardiac specific directions were determined and strains rotated into the local coordinate space. This technique was applied pre- and post- coronary occlusion. Alterations in strain patterns were evident in the ischemic region and subtle temporal changes in the control region. Thus, digital sonomicrometry, with high temporal and spatial resolution, enhances our ability to analyze regional left ventricular 3D strain patterns.

#### BibTeX Entry

@INPROCEEDINGS{xDione97,
author="D.  P.  Dione and P.  Shi and W.  Smith and P.  De Man and J.  Soares
and J.  S.  Duncan and A.  J.  Sinusas",
title ="Three-Dimensional Regional Left Ventricular Deformation
from Digital Sonomicrometry",
booktitle = "19th Annual International Conference of the IEEE Engineering
in Medicine and Biology Society",
pages = "848-851",
year = "1997",
month="March"}


### Three dimensional digital sonomicrometry: Comparison with biplane radiography

D. Meoli, R. Mazhari, D. P. Dione, J. Omens, A. McCulloch, and A. J. Sinusas.
In Proceedings of IEEE 24th Annual Northeast Bioengineering Conference, pages 64--67, 1998.

#### Abstract

This paper describes a three-dimensional (3D) digital sonomicrometry approach for locating and tracking 3D objects. A commercial digital sonomicrometry system was employed to measure scalar distances between omni-directional sonomicrometers. 3D coordinates were then derived using the statistical technique of multidimensional scaling (MDS). 3D digital sonomicrometry was directly compared with biplane radiography of the ultrasound crystals for estimation of 3D distances in static phantoms and in vivo using an experimental canine preparation. An excellent correlation (r=0.992) was seen when comparing inter-crystal distances derived from biplane radiography and sonomicrometry 3D coordinate data in the gel phantom. A Bland-Altman analysis shows that the average difference in coordinate determined distance between these two different methodologies was only 0.63$\pm$0.46 mm, over a range of inter-crystal distances of 3.14 to 17.28 mm. In the in vivo canine preparation, the correlation between the sonomicrometry derived and biplane derived distances was also excellent (r=0.992) with a slope of 1.05 and an intercept of 0.06. The Bland-Altman analysis shows that the average difference in coordinate determined distance between these two different methodologies was only 0.78$\pm$0.74 mm, over a range of inter-crystal distances of 2.90 to 27.66 mm. We have demonstrated the feasibility of accurately measuring scalar distances using 3D digital sonomicrometry. Digital sonomicrometry combines high spatial and temporal resolution with availability and portability to accurately measure distances in a closely packed array of implanted piezoelectric crystals.

#### BibTeX Entry


@INPROCEEDINGS{xMeoli98,
author = "D.  Meoli and R.  Mazhari and D.  P.  Dione and J.  Omens and
A.  McCulloch and A.  J.  Sinusas",
title = "Three Dimensional Digital Sonomicrometry: Comparison with
booktitle = "Proceedings of IEEE 24th Annual Northeast Bioengineering Conference",
year = "1998",
pages = "64-67" }


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