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.

References

References
1.
Midgett
,
D. E.
,
Pease
,
M. E.
,
Jefferys
,
J. L.
,
Patel
,
M.
,
Franck
,
C.
,
Quigley
,
H. A.
, and
Nguyen
,
T. D.
,
2017
, “
The Pressure-Induced Deformation Response of the Human Lamina Cribrosa: Analysis of Regional Variations
,”
Acta Biomater.
,
53
, pp.
123
139
.
2.
Midgett
,
D. E.
,
Pease
,
M. E.
,
Quigley
,
H. A.
,
Patel
,
M.
,
Franck
,
C.
, and
Nguyen
,
T. D.
,
2017
,
Regional Variations in the Mechanical Strains of the Human Optic Nerve Head
,
Springer International Publishing
, New York, pp.
119
127
.
3.
Bay
,
B. K.
,
Smith
,
T. S.
,
Fyhrie
,
D. P.
, and
Saad
,
M.
,
1999
, “
Digital Volume Correlation: Three-Dimensional Strain Mapping Using X-Ray Tomography
,”
Exp. Mech.
,
39
(
3
), pp.
217
226
.
4.
Rohlfing
,
T.
,
Maurer
,
C. R.
,
Bluemke
,
D. A.
, and
Jacobs
,
M. A.
,
2003
, “
Volume-Preserving Nonrigid Registration of MR Breast Images Using Free-Form Deformation With an Incompressibility Constraint
,”
IEEE Trans. Med. Imaging
,
22
(
6
), pp.
730
741
.
5.
Smith
,
T. S.
,
Bay
,
B. K.
, and
Rashid
,
M. M.
,
2002
, “
Digital Volume Correlation Including Rotational Degrees of Freedom During Minimization
,”
Exp. Mech.
,
42
(
3
), pp.
272
278
.
6.
Franck
,
C.
,
Hong
,
S.
,
Maskarinec
,
S. A.
,
Tirrell
,
D. A.
, and
Ravichandran
,
G.
,
2007
, “
Three-Dimensional Full-Field Measurements of Large Deformations in Soft Materials Using Confocal Microscopy and Digital Volume Correlation
,”
Exp. Mech.
,
47
(
3
), pp.
427
438
.
7.
Elen
,
A.
,
Choi
,
H. F.
,
Loeckx
,
D.
,
Gao
,
H.
,
Claus
,
P.
,
Suetens
,
P.
,
Maes
,
F.
, and
D'hooge
,
J.
,
2008
, “
Three-Dimensional Cardiac Strain Estimation Using Spatio-Temporal Elastic Registration of Ultrasound Images: A Feasibility Study
,”
IEEE Trans. Med. Imaging
,
27
(
11
), pp.
1580
1591
.
8.
Legant
,
W. R.
,
Miller
,
J. S.
,
Blakely
,
B. L.
,
Cohen
,
D. M.
,
Genin
,
G. M.
, and
Chen
,
C. S.
,
2010
, “
Measurement of Mechanical Tractions Exerted by Cells in Three-Dimensional Matrices
,”
Nat. Methods
,
7
(
12
), pp.
969
971
.
9.
Neu
,
C. P.
, and
Genin
,
G. M.
,
2014
,
Handbook of Imaging in Biological Mechanics
,
CRC Press
, Boca Raton, FL.
10.
Boyle
,
J. J.
,
Kume
,
M.
,
Wyczalkowski
,
M. A.
,
Taber
,
L. A.
,
Pless
,
R. B.
,
Xia
,
Y.
,
Genin
,
G. M.
, and
Thomopoulos
,
S.
,
2014
, “
Simple and Accurate Methods for Quantifying Deformation, Disruption, and Development in Biological Tissues
,”
J. R. Soc. Interface
,
11
(
100
), p. 20140685.
11.
Bayly
,
P. V.
,
Clayton
,
E. H.
, and
Genin
,
G. M.
,
2012
, “
Quantitative Imaging Methods for the Development and Validation of Brain Biomechanics Models
,”
Annu. Rev. Biomed. Eng.
,
14
(
1
), pp.
369
396
.
12.
Zhang
,
Z.
,
Zhu
,
M.
,
Ashraf
,
M.
,
Broberg
,
C. S.
,
Sahn
,
D. J.
,
Song
,
X.
, and
Sahn
,
D. J.
,
2014
, “
Right Ventricular Strain Analysis From Three-Dimensional Echocardiography by Using Temporally Diffeomorphic Motion Estimation
,”
Med. Phys.
,
41
(
12
), p. 122902.
13.
De Craene
,
M.
,
Piella
,
G.
,
Camara
,
O.
,
Duchateau
,
N.
,
Silva
,
E.
,
Doltra
,
A.
,
D'hooge
,
J.
,
Brugada
,
J.
,
Sitges
,
M.
, and
Frangi
,
A. F.
,
2012
, “
Temporal Diffeomorphic Free-Form Deformation: Application to Motion and Strain Estimation From 3D Echocardiography
,”
Med. Image Anal.
,
16
(
2
), pp.
427
450
.
14.
Veress
,
A. I.
,
Weiss
,
J. A.
,
Huesman
,
R. H.
,
Reutter
,
B. W.
,
Taylor
,
S. E.
,
Sitek
,
A.
,
Feng
,
B.
,
Yang
,
Y.
, and
Gullberg
,
G. T.
,
2008
, “
Measuring Regional Changes in the Diastolic Deformation of the Left Ventricle of SHR Rats Using microPET Technology and Hyperelastic Warping
,”
Ann. Biomed. Eng.
,
36
(
7
), pp.
1104
1117
.
15.
Veress
,
A. I.
,
Phatak
,
N.
, and
Weiss
,
J. A.
,
2005
, “
Deformable Image Registration With Hyperelastic Warping
,”
Handbook of Biomedical Image Analysis
,
J. S.
Suri
,
D. L.
Wilson
, and
S.
Laxminarayan
, eds.,
Springer
,
Boston, MA
, pp.
487
533
.
16.
Phatak
,
N. S.
,
Sun
,
Q.
,
Kim
,
S.-E.
,
Parker
,
D. L.
,
Sanders
,
R. K.
,
Veress
,
A. I.
,
Ellis
,
B. J.
, and
Weiss
,
J. A.
,
2007
, “
Noninvasive Determination of Ligament Strain With Deformable Image Registration
,”
Ann. Biomed. Eng.
,
35
(
7
), pp.
1175
1187
.
17.
Young
,
A. A.
, and
Axel
,
L.
,
1992
, “
Three-Dimensional Motion and Deformation of the Heart Wall: Estimation With Spatial Modulation of Magnetization—A Model-Based Approach
,”
Radiology
,
185
(
1
), pp.
241
247
.
18.
Young
,
A. A.
,
Fayad
,
Z. A.
, and
Axel
,
L.
,
1996
, “
Right Ventricular Midwall Surface Motion and Deformation Using Magnetic Resonance Tagging
,”
Am. J. Physiol.
,
271
(
6
), pp.
H2677
H2688
.
19.
Papademetris
,
X.
,
Sinusas
,
A. J.
,
Dione
,
D. P.
, and
Duncan
,
J. S.
,
2001
, “
Estimation of 3D Left Ventricular Deformation From Echocardiography
,”
Med. Image Anal.
,
5
(
1
), pp.
17
28
.
20.
Tustison
,
N. J.
, and
Amini
,
A. A.
,
2006
, “
Biventricular Myocardial Strains Via Nonrigid Registration of Anatomical NURBS Models
,”
IEEE Trans. Med. Imaging
,
25
(
1
), pp.
94
112
.
21.
Decerck
,
N.
,
Ayache
,
J.
, and
Mcveighb
,
E. R.
,
1999
, “
Use of a 4D Planispheric Transformation for the Tracking and Analysis of LV Motion With Tagged MR Images
,”
Imaging
,
3660
, pp.
69
80
.
22.
Han
,
S. J.
,
Oak
,
Y.
,
Groisman
,
A.
, and
Danuser
,
G.
,
2015
, “
Traction Microscopy to Identify Force Modulation in Subresolution Adhesions
,”
Nat. Methods
,
12
(
7
), pp.
653
656
.
23.
Lubinski
,
M. A.
,
Emelianov
,
S. Y.
, and
O'Donnell
,
M.
,
1999
, “
Speckle Tracking Methods for Ultrasonic Elasticity Imaging Using Short Time Correlation
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
,
46
(
1
), pp.
82
96
.
24.
Baker
,
S.
, and
Matthews
,
I.
,
2004
, “
Lucas-Kanade 20 Years on: A Unifying Framework
,”
Int. J. Comput. Vis.
,
56
(
3
), pp.
221
255
.
25.
Bower
,
A. F.
,
2009
,
Applied Mechanics of Solids
,
CRC Press
, Boca Raton, FL.
26.
Eshelby
,
J. D.
,
1957
, “
The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems
,”
Proc. R. Soc. London A
,
241
(
1226
), pp. 376–396.
27.
Tada
,
H.
,
Paris
,
P. C.
, and
Irwin
,
G. R.
,
2000
,
The Stress Analysis of Cracks Handbook
,
3rd ed.
,
ASME Press
, New York.
28.
Soepriatna
,
A. H.
,
Damen
,
F. W.
,
Vlachos
,
P. P.
, and
Goergen
,
C. J.
,
2018
, “
Cardiac and Respiratory-Gated Volumetric Murine Ultrasound
,”
Int. J. Cardiovasc. Imaging
,
34
(
5
), pp.
713
724
.
29.
Moore, C. C.
,
Lugo-Olivieri, C. H.
,
McVeigh, E. R.
, and
Zerhouni, E. A.
, 2000, “
Three-Dimensional Systolic Strain Patterns in the Normal Human Left Ventricle: Characterization With Tagged MR Imaging
,”
Radiology
,
212
(2), pp.453–466.
30.
Xu, F.
, 2018, “
Quantitative Characterization of Deformation and Damage Process by Digital Volume Correlation: A Review
,” Theoretical and Applied Mechanics Letters,
8
(2), pp. 83–96.
31.
Yingchoncharoen
,
T.
,
Agarwal
,
S.
,
Popović
,
Z. B.
, and
Marwick
,
T. H.
,
2013
, “
Normal Ranges of Left Ventricular Strain: A Meta-Analysis
,”
J. Am. Soc. Echocardiogr.
,
26
(
2
), pp.
185
191
.
32.
Gabbay
,
U.
, and
Yosefy
,
C.
,
2010
, “
The Underlying Causes of Chordae Tendinae Rupture: A Systematic Review
,”
Int. J. Cardiol.
,
143
(
2
), pp.
113
118
.
33.
Ritchie
,
J.
,
Jimenez
,
J.
,
He
,
Z.
,
Sacks
,
M. S.
, and
Yoganathan
,
A. P.
,
2006
, “
The Material Properties of the Native Porcine Mitral Valve Chordae Tendineae: An In Vitro Investigation
,”
J. Biomech.
,
39
(
6
), pp.
1129
1135
.
34.
Liu
,
Y.
,
Birman
,
V.
,
Chen
,
C.
,
Thomopoulos
,
S.
, and
Genin
,
G. M.
,
2011
, “
Mechanisms of Bimaterial Attachment at the Interface of Tendon to Bone
,”
ASME J. Eng. Mater. Technol.
,
133
(
1
), p.
011006
.
35.
Damen
,
F. W.
,
Berman
,
A. G.
,
Soepriatna
,
A. H.
,
Ellis
,
J. M.
,
Buttars
,
S. D.
,
Aasa
,
K. L.
, and
Goergen
,
C. J.
,
2017
, “
High-Frequency 4-Dimensional Ultrasound (4DUS): A Reliable Method for Assessing Murine Cardiac Function
,”
Tomography
,
3
(
4
), pp.
180
187
.
36.
Gurtin
,
M. E.
,
Fried
,
E.
, and
Anand
,
L.
, 2009,
The Mechanics and Thermodynamics of Continua
, Cambridge University Press, Cambridge, UK.
37.
Carvalho
,
C.
,
Bogaerts
,
S.
,
Scheys
,
L.
,
D'Hooge
,
J.
,
Peers
,
K.
, and
Suetens
,
P.
,
2016
, “
3D Tendon Strain Estimation on High-Frequency 3D Ultrasound Images a Simulation and Phantom Study
,”
International Symposium on Biomedical Imaging
(
ISBI
), Prague, Czech Republic, Apr. 13–16, pp.
172
175
.
38.
Lee
,
V. S.
,
2005
,
Cardiovascular MR Imaging: Physical Principles to Practical Protocols
, Vol.
1
,
Radiological Society of North America
, Oak Brook, IL.
39.
Kettermann
,
M.
,
Grützner
,
C.
,
Van Gent
,
H. W.
,
Urai
,
J. L.
,
Reicherter
,
K.
, and
Mertens
,
J.
,
2015
, “
Evolution of a Highly Dilatant Fault Zone in the Grabens of Canyonlands National Park, Utah, USA—Integrating Fieldwork, Ground-Penetrating Radar and Airborne Imagery Analysis
,”
Solid Earth
,
6
(
3
), pp.
839
855
.
40.
Wen
,
H.
,
Bennett
,
E.
,
Epstein
,
N.
, and
Plehn
,
J.
,
2005
, “
Magnetic Resonance Imaging Assessment of Myocardial Elastic Modulus and Viscosity Using Displacement Imaging and Phase-Contrast Velocity Mapping
,”
Magn. Reson. Med.
,
54
(
3
), pp.
538
548
.
41.
Zuo
,
K.
,
Pham
,
T.
,
Li
,
K.
,
Martin
,
C.
,
He
,
Z.
, and
Sun
,
W.
,
2016
, “
Characterization of Biomechanical Properties of Aged Human and Ovine Mitral Valve Chordae Tendineae
,”
J. Mech. Behav. Biomed. Mater.
,
62
, pp.
607
618
.
42.
Gheorghiade
,
M.
, and
Bonow
,
R. O.
,
1998
, “
Chronic Heart Failure in the United States: A Manifestation of Coronary Artery Disease
,”
Circulation
,
97
(
3
), pp.
282
289
.
43.
Sutton
,
M. S. J.
,
Pfeffer
,
M. A.
,
Moye
,
L.
,
Plappert
,
T.
,
Rouleau
,
J. L.
,
Lamas
,
G.
,
Rouleau
,
J.
,
Parker
,
J. O.
,
Arnold
,
M. O.
,
Sussex
,
B.
, and
Braunwald
,
E.
,
1997
, “
Cardiovascular Death and Left Ventricular Remodeling Two Years After Myocardial Infarction
,”
Circulation
,
96
(
10
), p. 3294-9.https://www.ahajournals.org/doi/10.1161/01.CIR.96.10.3294
44.
Richardson
,
W. J.
, and
Holmes
,
J. W.
,
2015
, “
Why is Infarct Expansion Such an Elusive Therapeutic Target?
,”
J. Cardiovasc. Transl. Res.
,
8
(
7
), pp.
421
430
.
45.
Zimmerman
,
S. D.
,
Karlon
,
W. J.
,
Holmes
,
J. W.
,
Omens
,
J. H.
, and
Covell
,
J. W.
,
2000
, “
Structural and Mechanical Factors Influencing Infarct Scar Collagen Organization
,”
Am. J. Physiol. Heart Circ. Physiol.
,
278
(
1
), pp.
H194
H200
.
46.
Liu
,
Y. X.
,
Thomopoulos
,
S.
,
Birman
,
V.
,
Li
,
J.-S.
, and
Genin
,
G. M.
,
2012
, “
Bi-Material Attachment Through a Compliant Interfacial System at the Tendon-to-Bone Insertion Site
,”
Mech. Mater.
,
44
, pp.
83
92
.
47.
Liu
,
Y.
,
Thomopoulos
,
S.
,
Chen
,
C.
,
Birman
,
V.
,
Buehler
,
M. J.
, and
Genin
,
G. M.
,
2014
, “
Modelling the Mechanics of Partially Mineralized Collagen Fibrils, Fibres and Tissue
,”
J. R. Soc. Interface
,
11
(
92
), p.
20130835
.
48.
Derwin, K. A.
,
Galatz, L. M.
,
Ratcliffe, A.
, and
Thomopoulos, S.
, 2018, “
Enthesis Repair: Challenges and Opportunities for Effective Tendon-to-Bone Healing
,”
J. Bone Joint Surg. Am.
,
100
(16), p. e109.
49.
Genin
,
G. M.
,
Kent
,
A.
,
Birman
,
V.
,
Wopenka
,
B.
,
Pasteris
,
J. D.
,
Marquez
,
P. J.
, and
Thomopoulos
,
S.
,
2009
, “
Functional Grading of Mineral and Collagen in the Attachment of Tendon to Bone
,”
Biophys. J.
,
97
(
4
), pp.
976
985
.
50.
Thomopoulos
,
S.
,
Birman
,
V.
, and
Genin
,
G. M.
, eds.,
2014
,
Structural Interfaces and Attachments in Biology
,
Springer
,
New York
.
51.
Rubin
,
A. M.
, and
Jerina
,
K. L.
,
1994
, “
Evaluation of Porosity in Composite Aircraft Structures
,”
Mech. Compos. Mater.
,
30
(
6
), pp.
587
600
.
52.
Pelivanov
,
I.
,
Ambroziński
,
Ł.
,
Khomenko
,
A.
,
Koricho
,
E. G.
,
Cloud
,
G. L.
,
Haq
,
M.
, and
O'Donnell
,
M.
,
2016
, “
High Resolution Imaging of Impacted CFRP Composites With a Fiber-Optic Laser-Ultrasound Scanner
,”
Photoacoustics
,
4
(2), pp 55–64.
53.
Freemantle
,
R. J.
,
Hankinson
,
N.
, and
Brotherhood
,
C. J.
,
2005
, “
Rapid Phased Array Ultrasonic Imaging of Large Area Composite Aerospace Structures
,”
Insight - Non-Destructive Test. Cond. Monit.
,
47
(
3
), pp.
129
132
.
54.
Bayly
,
P. V.
,
Cohen
,
T. S.
,
Leister
,
E. P.
,
Ajo
,
D.
,
Leuthardt
,
E. C.
, and
Genin
,
G. M.
,
2005
, “
Deformation of the Human Brain Induced by Mild Acceleration
,”
J. Neurotrauma
,
22
(
8
), pp.
845
856
.
55.
Sabet
,
A. A.
,
Christoforou
,
E.
,
Zatlin
,
B.
,
Genin
,
G. M.
, and
Bayly
,
P. V.
,
2008
, “
Deformation of the Human Brain Induced by Mild Angular Head Acceleration
,”
J. Biomech.
,
41
(
2
), pp.
307
315
.
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