Research Papers

Regularization-Free Strain Mapping in Three Dimensions, With Application to Cardiac Ultrasound

[+] Author and Article Information
John J. Boyle

Department of Biomedical Engineering,
Washington University in St. Louis,
St. Louis, MO 63130;
Department of Orthopaedic Surgery,
Columbia University,
Black Building 1406, 650 W 168 Street,
New York, NY 10032
e-mail: john.boyle.87@gmail.com

Arvin Soepriatna

Weldon School of Biomedical Engineering,
Purdue University,
206 S. Martin Jischke Drive, Room 3025,
West Lafayette, IN 47907
e-mail: asoepria@purdue.edu

Frederick Damen

Weldon School of Biomedical Engineering,
Purdue University,
206 S. Martin Jischke Drive, Room 3025,
West Lafayette, IN 47907
e-mail: fdamen@purdue.edu

Roger A. Rowe

Department of Mechanical Engineering and
Materials Science,
Washington University in St. Louis,
Jolley Hall, CB 1185, 1 Brookings Drive,
St. Louis, MO 63130
e-mail: rowe.wustl@gmail.com

Robert B. Pless

Department of Computer Science,
George Washington University,
800 22nd Street NW Room 4000,
Washington, DC 20052
e-mail: pless@gwu.edu

Attila Kovacs

Department of Internal Medicine,
Cardiovascular Division,
Washington University School of Medicine,
660 S. Euclid Avenue, CB 8086,
St. Louis, MO 63110
e-mail: akovacs@dom.wustl.edu

Craig J. Goergen

Weldon School of Biomedical Engineering,
Purdue University,
206 S. Martin Jischke Drive, Room 3025,
West Lafayette, IN 47907
e-mail: cgoergen@purdue.edu

Stavros Thomopoulos

Department of Orthopaedic Surgery,
Columbia University,
New York, NY 10032;
Department of Biomedical Engineering,
Columbia University,
Black Building 1408, 650 W 168 Street,
New York, NY 10032
e-mail: sat2@cumc.columbia.edu

Guy M. Genin

Fellow ASME
Department of Biomedical Engineering,
Washington University in St. Louis,
St. Louis, MO 63130;
Department of Mechanical Engineering and
Materials Science,
Washington University in St. Louis,
St. Louis, MO 63130;
NSF Science and Technology Center
for Engineering Mechanobiology,
Washington University in St. Louis,
Green Hall, CB 1099, 1 Brookings Drive,
St. Louis, MO 63130
e-mail: genin@wustl.edu

1Contributed equally.

Manuscript received April 1, 2018; final manuscript received September 21, 2018; published online October 22, 2018. Assoc. Editor: Jeffrey Ruberti.

J Biomech Eng 141(1), 011010 (Oct 22, 2018) (11 pages) Paper No: BIO-18-1160; doi: 10.1115/1.4041576 History: Received April 01, 2018; Revised September 21, 2018

Quantifying dynamic strain fields from time-resolved volumetric medical imaging and microscopy stacks is a pressing need for radiology and mechanobiology. A critical limitation of all existing techniques is regularization: because these volumetric images are inherently noisy, the current strain mapping techniques must impose either displacement regularization and smoothing that sacrifices spatial resolution, or material property assumptions that presuppose a material model, as in hyperelastic warping. Here, we present, validate, and apply the first three-dimensional (3D) method for estimating mechanical strain directly from raw 3D image stacks without either regularization or assumptions about material behavior. We apply the method to high-frequency ultrasound images of mouse hearts to diagnose myocardial infarction. We also apply the method to present the first ever in vivo quantification of elevated strain fields in the heart wall associated with the insertion of the chordae tendinae. The method shows promise for broad application to dynamic medical imaging modalities, including high-frequency ultrasound, tagged magnetic resonance imaging, and confocal fluorescence microscopy.

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Grahic Jump Location
Fig. 1

Schematic representation of how 3D-XCOR, 3D-LSF, and 3D-DDE calculate 3D deformation gradient tensors. (a) Representation of a volumetric image divided into eight volumes with original undeformed image (left) and deformed configuration (right). (b) 3D-XCOR estimates how each reference volume maps to an equal number of voxels in the deformed image. Considering the centroid of each region (spheres, inset and vertices of bottom), 3D-XCOR finds a best fit displacement. (c) The 3D-LSF method improves on 3D-XCOR by warping the reference regions before finding the best match in the deformed image. Like 3D-XCOR, it considers the displacements of the centroids of these regions when calculating deformation (inset and bottom row). (d) 3D-DDE accurately calculates the deformation of all eight regions independently (outlines, bottom row), directly from the warping function that maps the undeformed volumes to the deformed volumes.

Grahic Jump Location
Fig. 2

Accuracy and precision of 3D-DDE relative to other regularization-free strain mapping techniques. 3D-DDE was over an order of magnitude more accurate and substantially more precise than other methods for estimating spatially varying strain fields in artificial images. (a) For a 3D rigid body rotated an angle Θ in one plane, 3D-XCOR failed to correctly predict the strain field, with error that was nearly unbounded for large rotation angles (inset). (b) 3D-LSF and 3D-DDE had negligible errors for rigid body rotations. (c) RMS error for a uniaxial stretch E11 scaled with strain for 3D-XCOR. (d) 3D-LSF and 3D-DDE had negligible error for linear, uniform straining. (e) RMS error increased with stretch level λ for both 3D-XCOR and 3D-LSF in a 3D body undergoing nonlinear stretch given by Eq. (1). (f) However, 3D-DDE again estimated strains with minimal error for these nonlinear, nonuniform strain fields. Note that panels (b), (d), and (f) contain data from panels (a), (c), and (e), respectively, zoomed in to focus on results comparing only 3D-LSF and 3D-XCOR.

Grahic Jump Location
Fig. 3

Principal stretch ratio estimations around image volumes of a contracting Eshelby inclusion, generated in silico. (a) Schematic of the Eshelby problem. (b) 3D-SIMPLE detected strain elevation surrounding the inclusion. (c) True values of the stretch ratio in the z-direction matched (d) the 3D-DDE estimated values, while (e) 3D-LSF and (f) 3D-XCOR estimates were successively worse.

Grahic Jump Location
Fig. 4

Principal stretch ratios for image volumes of a preloaded, penny-shaped crack generated in silico. (a) Schematic, (b) 3D-SIMPLE detected the developing crack, ((c) and (d)) 3D-DDE estimates matched the actual fields, while 3D-LSF (e) and 3D-XCOR (f) were successively less accurate.

Grahic Jump Location
Fig. 5

Peak principal strain fields estimated from high frequency ultrasound imaging of a beating mouse heart, showing spatial variations associated with the structure of the heart. ((a) and (b)) Volumetric ultrasound data were acquired over several cycles of a beating mouse heart, then analyzed using 3D-DDE to detect spatial variations in Green–Lagrange strain fields. (c)–(g) These strain fields were segmented to reveal 3D strains in the left ventricle papillary muscle and to track how the myocardial first principal component of the 3D strain fields varied near the insertions of the chordae tendinae. (c) End diastole was taken as a reference configuration. (d) The heart developed strains in the left ventricle as it contracted and blood was ejected from the heart, while the papillary muscles remained unstretched. (e) As the heart cycle reached peak systole and entered isovolumetric relaxation, principal strains in the heart wall reached maximum levels on the order of 0.5. (f) As the heart relaxed during early ventricular filling, strain levels reduced, approaching baseline levels after (g) late ventricular filling. Throughout the cardiac cycle, strains in the papillary muscles (upper arrows yellow online) were lower than those in the surrounding myocardium in the apex (white, lower arrows). LV: left ventricle, RV: right ventricle, and S: skin. Scale bars: 3 mm.

Grahic Jump Location
Fig. 6

Strain patterns in control versus postmyocardial infarction hearts, demonstrating dramatically reduced strains in infarcted heart tissue. ((a) and (b)) Magnetic resonance images of mouse hearts showing the anatomical planes studied using 3D-DDE of ultrasound imaging volumes. (c) A schematic of the heart demonstrating the orientation of the short and long axis as well as the location of the infarction. ((d) and (e)) Peak principal strain at a specific timepoint in control hearts. ((f) and (g)) Peak principal strain at this same timepoint in hearts following myocardial infarction, showing distinctly different strain patterns in both the long and short axis views. (h) Strain as a function of position along the midline of the long-axis view of the heart, showing strain attenuation in the infarcted tissue. Line corresponds to different times; position is measured from the base of the arrow in panel (f). (i) Strain as a function of position along the midline of the short-axis view of the heart, showing strain attenuation in the infarcted tissue, and elevated strain in the tissue surrounding the infarct region. Lines again correspond to different times; position is measured from the base of the arrow in panel (g). Scale bars: 1 mm.



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