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Research Papers

A Parameterized Ultrasound-Based Finite Element Analysis of the Mechanical Environment of Pregnancy

[+] Author and Article Information
Andrea R. Westervelt

Department of Mechanical Engineering,
Columbia University,
New York, NY 10027
e-mail: arw2181@columbia.edu

Michael Fernandez

Department of Mechanical Engineering,
Columbia University,
New York, NY 10027
e-mail: mjf2152@columbia.edu

Michael House

Department of Obstetrics and Gynecology,
Tufts Medical Center,
Boston, MA 02111
e-mail: mhouse@tuftsmedicalcenter.org

Joy Vink

Department of Obstetrics and Gynecology,
Columbia University Medical Center,
New York, NY 10032
e-mail: jyv2101@cumc.columbia.edu

Chia-Ling Nhan-Chang

Department of Obstetrics and Gynecology,
Columbia University Medical Center,
New York, NY 10032
e-mail: cn2281@cumc.columbia.edu

Ronald Wapner

Department of Obstetrics and Gynecology,
Columbia University Medical Center,
New York, NY 10032
e-mail: rw2181@cumc.columbia.edu

Kristin M. Myers

Mem. ASME
Department of Mechanical Engineering,
Columbia University,
New York, NY 10027
e-mail: kmm2233@columbia.edu

1Corresponding author.

Manuscript received July 15, 2016; final manuscript received March 3, 2017; published online April 5, 2017. Assoc. Editor: Steven D. Abramowitch.

J Biomech Eng 139(5), 051004 (Apr 05, 2017) (11 pages) Paper No: BIO-16-1296; doi: 10.1115/1.4036259 History: Received July 15, 2016; Revised March 03, 2017

Preterm birth is the leading cause of childhood mortality and can lead to health risks in survivors. The mechanical functions of the uterus, fetal membranes, and cervix have dynamic roles to protect the fetus during gestation. To understand their mechanical function and relation to preterm birth, we built a three-dimensional parameterized finite element model of pregnancy. This model is generated by an automated procedure that is informed by maternal ultrasound measurements. A baseline model at 25 weeks of gestation was characterized, and to visualize the impact of cervical structural parameters on tissue stretch, we evaluated the model sensitivity to (1) anterior uterocervical angle, (2) cervical length, (3) posterior cervical offset, and (4) cervical stiffness. We found that cervical tissue stretching is minimal when the cervical canal is aligned with the longitudinal uterine axis, and a softer cervix is more sensitive to changes in the geometric variables tested.

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Figures

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Fig. 1

Uterine and cervical dimensions taken via transabdominal and transperineal ultrasound at 25 weeks of gestation. UD: uterine diameter, UT: uterine thickness, CD: cervical dimension, and CA: cervical angle.

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Fig. 2

Three-dimensional representation of the environment of pregnancy. The cervix was separated into three sections for analysis: the upper cervix, lower cervix, and internal os region.

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Fig. 3

Sample mesh for baseline geometry. The fetal membrane was meshed with hexahedral elements, while all other volumes were meshed with tetrahedral elements.

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Fig. 4

Boundary and loading conditions. Outside of abdomen was fixed in x, y, and z directions (dashed lines in figure). Uniform intrauterine pressure (IUP) was applied on inner surface of FM. Tied contact was applied between FM (cyan) and uterine wall (purple) and between FM and upper cervix (green). Sliding contact was applied between FM and cervix internal os region (yellow). (For interpretation of the color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 5

The color map reports the first principal right stretch for the baseline geometry evaluated with IUPs of (a) 25 weeks = 0.817 kPa, (b) 40 week = 2.33 kPa, and (c) contraction = 8.67 kPa. The percentage reports the volume fraction of the cervical internal os region above a 1.05 stretch. The membrane is removed for clarity. (For interpretation of the color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 6

Baseline results with vector plots to show stretch directions for (a) first principal right stretch, (b) second principal right stretch, (c) third principal right stretch, and (d) maximum shear strain. For first principal right stretch, circumferential stretch is exhibited at the internal os while radial stretch is observed at the anterior and posterior sections of the uterocervical interface.

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Fig. 7

Uterine and cervical stretch patterns as AUCA (shown top left) is varied. The color map reports the first principal right stretch for not remodeled cervix with AUCA of (a) 90 deg, (b) 100 deg, and (c) 110 deg, and remodeled cervix with AUCA of (d) 90 deg, (e) 100 deg, and (f) 110 deg. The percentage reports the volume fraction of the cervical internal os region above a 1.05 stretch. The membrane is removed for clarity. (For interpretation of the color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 8

Uterine and cervical stretch patterns as CL (shown top left) is varied. The color map reports the first principal right stretch for not remodeled cervix with CL of (a) 25 mm, (b) 30 mm, (c) 35 mm, and (d) 40 mm, and remodeled cervix with CL of (e) 25 mm, (f) 30 mm, (g) 35 mm, and (h) 40 mm. The percentage reports the volume fraction of the cervical internal os region above a 1.05 stretch. The membrane is removed for clarity. (For interpretation of the color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 9

Uterine and cervical stretch patterns as PCO (shown top left) is varied. The color map reports the first principal right stretch for not remodeled cervix with PCO of (a) 0 mm, (b) 5 mm, (c) 10 mm, (d) 15 mm, (e) 20 mm, and (f) 25 mm, and remodeled cervix with PCO of (g) 0 mm, (h) 5 mm, (i) 10 mm, (j) 15 mm, (k) 20 mm, and (l) 25 mm. The percentage reports the volume fraction of the cervical internal os region above a 1.05 stretch. The membrane is removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 10

Uterine and cervical stretch patterns as cervical fiber stiffness is varied. The color map reports the first principal right stretch for the baseline geometry evaluated with a cervical fiber stiffness (ξ) value of (a) 1.71, (b) 7.89, (c) 36.3, (d) 167, and (e) 769 kPa. The percentage reports the volume fraction of the cervical internal os above a 1.05 stretch. The membrane is removed for clarity. (For interpretation of the color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 11

Principal right stretch plots of the MRI geometry model (a1) and the parameterized geometry model (a2) under an IUP of 0.817 kPa applied to the fetal membrane. First principal stretches ((a1) and (a2)) reflect the areas of highest tension and are concentrated around the internal os and the proximal portion of the cervix. Third principal strains ((c1) and (c2)) represent areas of compression, which are most prominent in the MRI model (c1). Shear strains are shown in figures (d) and are also concentrated over the internal os, but are approximately twice as large in the MRI-derived model due to the irregular surface of the geometry.

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