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Nonhomogeneous strain from sparse marker arrays for analysis of transmural myocardial mechanics
Linköping University, Department of Biomedical Engineering, Biomedical Modelling and Simulation. Linköping University, The Institute of Technology.
Linköping University, The Institute of Technology. Linköping University, Department of Biomedical Engineering, Biomedical Modelling and Simulation.ORCID iD: 0000-0001-5526-2399
Stanford University Medical Center.
Texas AM University.
2007 (English)In: Journal of Biomechanical Engineering, ISSN 0148-0731, Vol. 129, no 4, 603-610 p.Article in journal (Refereed) Published
Abstract [en]

Background: Knowledge of normal cardiac kinematics is important when attempting to understand the mechanisms that impair the contractile function of the heart during disease. The complex kinematics of the heart can be studied by inserting radiopaque markers in the cardiac wall and study the pumping heart with biplane cineradiography. In order to study the local strain, the bead array was developed where small radiopaque beads are inserted along three columns transmurally in the left ventricle. Method: This paper suggests a straightforward method for strain computation, based on polynomial least-squares fitting and tailored for combined marker and bead array analyses. Results: This polynomial method gives small errors for a realistic bead array on an analytical test case. The method delivers an explicit expression of the Lagrangian strain tensor as a polynomial function of the coordinates of material points in the reference configuration. The method suggested in this paper is validated with analytical strains on a deforming cylinder resembling the heart, compared to a previously suggested finite element method, and applied to in vivo ovine data. The errors in the estimated strain components are shown to remain unchanged on an analytical test case when evaluating the effects of one missing bead. In conclusion, the proposed strain computation method is accurate and robust, with errors smaller or comparable to the current gold standard when applied on an analytical test case.

Place, publisher, year, edition, pages
2007. Vol. 129, no 4, 603-610 p.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-41891DOI: 10.1115/1.2746385ISI: 000248737000016Local ID: 59323OAI: diva2:262746
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2016-03-14
In thesis
1. Invasive and Non-Invasive Quantification of Cardiac Kinematics
Open this publication in new window or tab >>Invasive and Non-Invasive Quantification of Cardiac Kinematics
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The ability to measure and quantify myocardial motion and deformation provides a useful tool to assist in the diagnosis, prognosis and management of heart disease. Myocardial motion can be measured by means of several different types of data acquisition. The earliest myocardial motion tracking technique was invasive, based on implanting radiopaque markers into the myocardium around the left ventricle, and recording the marker positions during the cardiac cycle by biplane cineradiography. Until recently, this was the only method with high enough spatial resolution of three-dimensional (3D) myocardial displacements to resolve transmural behaviors. However, the recent development of magnetic resonance imaging techniques, such as displacement encoding with stimulated echoes (DENSE), make detailed non-invasive 3D transmural kinematic analyses of human myocardium possible in the clinic and for research purposes.

Diastolic left ventricular filling is a highly dynamic process with early and late transmitral inflows and it is determined by a complex sequence of many interrelated events and parameters. Extensive research has been performed to describe myocardial kinematics during the systolic phase of the cardiac cycle, but not by far the same amount of research has been accomplished during diastole. Measures of global and regional left ventricular kinematics during diastole are important when attempting to understand left ventricular filling characteristics in health and disease.

This thesis presents methods for invasive and non-invasive quantification of cardiac kinematics, with focus on diastole. The project started by quantification of changes in global left ventricular kinematics during diastolic filling. The helical myocardial fiber architecture of the left ventricle produces both long- and short-axis motion as well as torsional deformation. The longitudinal excursion of the mitral annular plane is an important component of left ventricular filling and ejection. This was studied by analyzing the contribution of mitral annular dynamics to left ventricular filling volume in the ovine heart.

In order to quantify strains for a specific body undergoing deformation, displacements for a set of internal points at a deformed configuration relative to a reference configuration are needed. A new method for strain quantification from measured myocardial displacements is presented in this thesis. The method is accurate and robust and delivers analytical expressions of the strain components. The developed strain quantification method is simple in nature which aids to bridge a possible gap in understanding between different disciplines and is well suited for sparse arrays of displacement data.

Analyses of myocardial kinematics at the level of myocardial fibers require knowledge of cardiac tissue architecture. Temporal changes in myofiber directions during the cardiac cycle have been analyzed in the ovine heart by combining histological measurements of transmural myocardial architecture and local transmural strains.

Rapid early diastolic filling is an essential component of the left ventricular function. Such filling requires a highly compliant chamber immediately after systole, allowing inflow at low driving pressures. Failure of this process can lead to exercise intolerance and ultimately to heart failure. A thorough analysis of the relation between global left ventricular kinematics and local myocardial strain at the level of myocardial fibers during early diastole in the ovine heart was performed by applying the method for strain quantification and the technique for computing temporal changes in myocardial architecture on measures of myocardial displacements and tissue architecture in the ovine heart.

As data acquisition technologies develop, quantification methods for cardiac kinematics need to be adapted and validated on the new types of data. Recent improvements of DENSE magnetic resonance imaging enable non-invasive transmural strain analyses in the human heart. The strain quantification method was first tailored to displacement data from a surgically implanted bead array but has been extended to applications on non-invasive DENSE data measured in two and three dimensions. Validation against an analytical standard reveals accurate results and in vivo strains agree with values for normal human hearts from other studies.

The method has in this thesis been used with displacement data from invasive marker technology and non-invasive DENSE magnetic resonance imaging, but can equally well be applied on any type of displacement data provided that the spatial resolution is high enough to resolve local strain variations.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2010. 49 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1322
National Category
Engineering and Technology
urn:nbn:se:liu:diva-60202 (URN)978-91-7393-375-9 (ISBN)
Public defence
2010-08-17, sal C3, Hus C, Campus Valla, Linköpings universitet, Linköping, 10:15
Available from: 2010-10-07 Created: 2010-10-07 Last updated: 2016-03-14Bibliographically approved
2. Modelling of strain tensors in cardiac kinematics
Open this publication in new window or tab >>Modelling of strain tensors in cardiac kinematics
2006 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The heart wall consists of three distinct layers: the inner endocardium, the middle myocardium and the outer epicardium. The myocardium is the functional tissue that endows the heart with its ability to pump blood, and consists primarily of locally parallel muscle fibers. The orientation of these muscle fibers change with position in the wall. The myofibers have been shown to be arranged parallel in sheets that are rotated around the fiber direction relative to the radial direction of the left ventricle. During a cardiac beat there are local shortenings and lengthenings in the myocardium, both within and between myolaminar sheets. The mechanism by which the local shortening or lengthening is translated into the large and complex motions of the ventricle has to be studied on a local level, by studying deformation. A parameter that describes deformation is strain. The scope of the current project is to perform detailed studies of cardiac strain, particularly during diastole. There exist several definitions of strain tensors and the focus in this project is on the Lagrangian strain tensor.

The myocardial bead array gives kinematic measures of the myocardium toestimate strain in the left ventricular wall of the pumping heart. During surgery, radiopaque beads are inserted into the myocardium along three transmural columns, with typically four to six beads in each column. The 4D coordinates of the beads are acquired with high resolution using time-resolved biplane cineradiography.

This thesis presents a method for strain estimation from myocardial coordinate data. This strain estimation method is tailored for the transmural bead array and fits a polynomial to the bead coordinates. A benefit with the polynomial method is its ability to avoid loss of accuracy for the case of a missing bead, e.g. due to problems sometimes encountered during surgery or during the recovery period. The polynomial strain estimation method is applied to coordinate data from a transmural bead array to quantify diastolic myocardial strain in the ovine heart. This reveals transmural strain inhomogeneities during diastole in the ovine heart.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2006. 36 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1269
National Category
Medical and Health Sciences
urn:nbn:se:liu:diva-35139 (URN)25032 (Local ID)91-85643-89-0 (ISBN)25032 (Archive number)25032 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-11-12

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