View source for Stress State and Strain Rate Dependence of the Human Placenta

== Abstract ==
Maternal trauma in automotive collisions is a source of injury, morbidity, and mortality for both mothers and fetuses. The primary associated pathology is placental abruption in which the placenta detaches from the uterus leading to hemorrhaging and termination of pregnancy. In this study, we focused on the differences in placental tissue response to different stress states (tension, compression, and shear) and different strain rates. Human placentas were obtained (n = 11) for mechanical testing and microstructure analysis. Specimens (n = 4+) were tested in compression, tension, and shear, each at 3 strain rates (9 testing protocols). Microstructural analysis included SEM, histology, and interrupted mechanical tests to observe tissue response to various loading states. Our data showed the greatest placenta strength in tension, followed by compression, and then by shear. The study concludes that mechanical behavior of human placenta tissue (i) has a strong stress state dependence and (ii) behaves in a rate dependent manner in all three stress states, which had previously only been shown in tension. Interrupted mechanical tests revealed differences in the morphological microstructure evolution that was driven by the kinematic constraints from the different loading states. Furthermore, these structure-property data can be used to develop high fidelity constitutive models for maternal trauma simulations.

== Materials and Methods ==
=== Sample Preparation ===
Human placentas from eleven donors were used in this study. All samples were obtained from uncomplicated singleton vaginal deliveries at Oktibbeha County Hospital in accordance with the Mississippi State University (MSU) Institutional Review Board (#08-275). Donating patients were screened for the presence of sexually transmitted diseases (including HIV, HBV, and HCV) and unclear perinatal history. Samples were placed in 4 °C Ringers lactate buffered saline (LBS) and transported immediately after delivery to MSU where all tests were performed in a BSL2 certified laboratory. All tests were performed within 24 hours of delivery. Note that we used vaginally delivered placentas, because placentas obtained by caesarean delivery are pulled from the uterine wall and are usually already mechanically damaged. Due to the size limit of the placenta tissue, we were not able to perform tests for each strain-rate and stress-state condition within a single donor. However, donor placentas were randomly assigned to loading modalities (tension, compression, and shear). Within a loading modality, there were between three and four donors, each donor placenta contributed at least one test to each strain rate.

=== Mechanical Testing ===
Specimens were rinsed in LBS and dissected in preparation for mechanical testing. All samples were prepared such that each specimen was dissected from within a single placental lobe as previously described.27, 28 This prevents issues with underestimation of placental strength due to the thinner regions between lobes. Specimens were dissected to their appropriate shape by scalpel dissection using a guide to allow consistent shape. No specimens were frozen prior to testing since we found that the placenta tissue properties changed greatly after freezing and thaw procedures. Specimens were mechanically tested using the Mach 1 Micromechanical Testing System (Biomomentum, Laval, Quebec, Canada) shown in Figure 1-A. As mentioned above, tension, compression, and shear mechanical tests were performed under three different strain rates to investigate the stress state dependence of placenta tissue. Each donor was tested in a single stress-state and contributed at least one test to each strain-rate. All mechanical tests were conducted in a water bath containing LBS. All tensile and compression tests included a preloading of 1 gram, preconditioning of 10 cycles at 10% strain, and a re-preload of 1 gram.

[[File:Placenta fig1.PNG]]

Tensile Testing. Dogbone shaped samples (Fig. 1-B) were prepared with a grip-to-grip length of 40 mm, a width of 10 mm at the center of the dogbone, and a thickness of 5 mm. Following preconditioning, samples were pulled to failure; all tensile specimens failed in the middle region of the dogbone and the majority of the ends of the dogbone specimens were within the grips. The tensile failure tests were conducted at rates of 40, 400, and 4000 μm/s (N = 4+ for each rate).  In tensile testing, the displacement rates of 40, 400, and 4000 μm/s correspond to strain rates of 0.001, 0.01, and 0.1 /s, respectively.
  
Unconfined Compression Testing. Cylindrical samples (Fig. 1-C) were prepared with a grip-to-grip length of 16 mm and a radius of 19 mm. Specimens were mounted and secured with a small dot of PermaBond cyanoacrylate ester adhesive (Permabond, Pottstown PA) to prevent slipping from the compression head. The very small amount of glue did not prevent the specimens from deforming as unconfined compression. Following preconditioning, samples were loaded to 3000 grams. Tests were conducted at rates of 40, 400, 4000 μm/s (N = 5+ for each rate). In compression testing, the displacement rates of 40, 400, and 4000 μm/s correspond to strain rates of 0.0025, 0.025, and 0.25 /s, respectively.  

Shear Testing. Rectangular samples (Fig. 1-D) were prepared to have a width of 20 mm, length of 50 mm, and thickness of 10 mm. All samples were prepared such that the shear loading occurred through the thickness of the placenta. These samples were glued to the shear test setup using a minimal amount of PermaBond adhesive. Compressive load between the parallel shear loading surfaces was limited to the minimum necessary to secure the samples with glue. Samples were sheared to 100 grams in the positive and negative directions for 10 cycles. The data from the final cycles were used for analysis, as that data represents the tissue behavior after preconditioning. Tests were conducted at rates of 40, 400, 4000 μm/s (N=5+ for each rate). In shear testing, the displacement rates of 40, 400, and 4000 μm/s correspond to strain rates of 0.004, 0.04, and 0.4 /s, respectively. Data was recorded at sampling rate of 100 /s. All data was processed for further comparison using a custom software tool.

=== Mechanical Data Analyses ===
All data were first analyzed by engineering stress and engineering strain in each stress state at each displacement rate. Briefly, engineering stress was calculated as the loading force over the undeformed cross-sectional area, and engineering strain was calculated as the displacement divided by the initial grip-to-grip distance (gauge length at 1 gram preload after preconditioning). The engineering stress and engineering strain were then converted to true stress and true strain using the following formulas:
     
[[File:Placenta eq1.PNG]]

where σ_eng and ε_eng are the engineering stress and strain, and σ_true and ε_true are the true stress and strain, respectively.  For these formulas, tensile strain is positive, and compressive strain is negative. These formulas also assume material incompressibility.

In order to accurately compare shear data to compression and tension, an effective stress conversion was applied to shear stress and strain as follows:

[[File:Placenta eq2.PNG]]

Similar to other types of soft tissues, stress-strain curve of placenta tissues consists of a nonlinear region and a linear region. For each mechanical test, a linear fit was applied in the linear region of the stress-strain curve to determine the slope and x-intercept of the fitted line. The slope of this fitted line represents the tissue’s tensile modulus in the linear region (maximum tensile modulus) and the x-intercept represents the tissue’s extensibility.

=== Scanning Electron Microscopy ===
Scanning Electron Microscopy (SEM) was performed to visualize the microstructure of placentas. Samples were prepared by common SEM preparation methods. Briefly, specimens were fixed in Karnovsky’s Fixative (2% paraformaldehyde, 2.5% glutaraldehyde, in 0.1M Phosphate Buffer). Samples were further fixed in 1% osmium tetroxide and then dehydrated in a critical point dryer (Polaron E 3000 CPD). Dried samples were sputter coated with gold-palladium and observed using a Zeiss EVO 50 SEM (Zeiss, Thornwood NY) equipped with a LaB6 electron gun and secondary electron detector.

=== Interruption Mechanical Testing and Histology ===
Interruption mechanical tests were performed to reveal the microstructural evolution of the placenta tissue as the applied load increased.  Samples were prepared, as described earlier, for each stress state. After being mounted in the appropriate configuration for their stress state, each sample was deformed to a desired engineering strain value and held at that strain; the water bath was replaced with 10% neutral buffered formalin and the sample was allowed to fix for 24 hours. The interrupted mechanical tests were performed at two strain levels for each stress state, the first near the transitional region (heel region) of the nonlinear stress-strain curve (25%, 30%, 39% for tension, compression, and shear, respectively), and the second in the linear region of the stress-strain curve (50%, 60%, 79% for tension, compression, and shear, respectively).

After fixation, samples were prepared for histology analysis. Samples were embedded in paraffin and cut into 5 μm sections. Samples were then stained with Haematoxylin & Eosin (H&E) and examined by light microscopy (Nikon EC600) to assess internal microstructural changes in response to the external loading, especially the alteration of blood vessel alignment and morphology.

=== Statistical Analysis ===
All experimental data were presented as mean ± standard deviation. One Way Analysis of Variances (ANOVA) was applied for statistical analysis (SigmaStat 3.0, SPSS Inc., Chicago, IL). Comparison among groups was considered significantly different at p < 0.05.

== Results ==
The experimental data were organized by the stress state to assess the strain rate sensitivity of human placenta tissue (Fig. 2). We found that placenta exhibited a strain rate sensitivity in all three loading states (tension: 0.001, 0.01, and 0.1 /s, Fig. 2-A; compression: 0.0025, 0.025, and 0.25 /s, Fig. 2-B; shear: 0.004, 0.04, and 0.4 /s, Fig. 2-C). The larger applied strain rates incurred stiffer (higher stress) tissue responses. 

[[File:Placenta fig2.PNG]]

To better assess the stress-state dependence of human placenta tissue, the experimental data were further organized by the strain rate domains. Significant stress state dependences were exhibited in the placenta for all the examined strain rate domains, i.e., the strain rate domains of 0.001 /s - 0.004 /s (Fig. 3-A), 0.01 /s - 0.04 /s (Fig. 3-B), and 0.1 /s - 0.4 /s (Fig. 3-C). 

[[File:Placenta fig3.PNG]]

For quantitative analyses, the maximum tensile modulus and extensibility of the placenta tissue were compared among different stress states at various strain rates (Fig. 4).  For all three strain rates, the maximum tensile modulus showed an increasing trend in the order of shear, compression, and tension (Fig. 4-A), and the extensibility showed a decreasing trend in the order of shear, compression, and tension (Fig. 4-B).

[[File:Placenta fig4.PNG]]

SEM micrographs (Fig. 5) of the human placenta showed a highly randomized size and distribution of small blood vessels. These vessels varied greatly in alignment leading to a very tortuous (Fig. 5-A, B) and entangled (Fig. 5-C, D) network. 

[[File:Placenta fig5.PNG]]

The interruption mechanical tests (Fig. 6-8) showed that the human placenta tissue exhibited various microstructural behaviors in response to different loading states. The undeformed placenta consists of a relatively disordered network of blood vessels of different sizes with little or no preferred direction and the surrounding blood cells (Fig. 6-A, B). Under tension, as the deformation increased to 25% engineering strain, the blood vessels, especially the larger vessels, were kinematically recruited into tension and align along the primary loading axis (Fig. 6-C, D) much like texture in synthetic polymers. This motion from an initially isotropic orientation to a preferred orientation is the so-called texture effect in which the kinematics from the loading direction reorients the material (blood vessels).  An increase in the appearance of intervascular spaces has also been shown (Fig. 6-C, D). As the tensile strain neared failure at 50% engineering strain, only the largest vessels were still aligned to the direction of loading, while the smaller vessels appeared to have failed, allowing them to return to a recoiled configuration (Fig. 6-E, F). At 50% engineering strain, the intervascular spaces further increased (Fig. 6-E, F). 

[[File:Placenta fig6.PNG]]

The placenta microstructure also showed blood vessels to have a relatively circular cross-section in the undeformed state (Fig. 7-A, B). As the compressive strain increased to 30% engineering strain, the vessels began to collapse, with the vessel cross-sections deformed into elliptical (or elongated) shapes, and the long axes of elliptical (elongated) shapes aligned perpendicular to the loading direction (Fig. 7-C,D), again following kinematic constraints similar to texture evolution in polymers. At 60% compressive engineering strain, the vessels were highly collapsed and elongated, as well as compacted to the point of having almost no space within or between vessels (Fig. 7-E,F). The intervascular space was tremendously reduced at 60% compressive engineering strain. 

[[File:Placenta fig7.PNG]]

The microstructural evolution under shear showed a diagonal vessel alignment towards the shearing direction driven by the kinematics, as well as the presence of vessel morphologies similar to that of tensile and compressive microstructure in local regions (Fig. 8). As the shear loading increased to 39% strain, regions of vessel collapse and intervascular space growth were observed (Fig. 8-C, D). At 79% shear strain, vessels were highly aligned along the diagonal direction of load with significantly larger intervascular spaces (Fig. 8-E, F).

[[File:Placenta fig8.PNG]]