Data-driven variational multiscale reduced order modeling of vaginal tissue inflation.

The vagina undergoes large finite deformations and has complex geometry and microstructure, resulting in material and geometric nonlinearities, complicated boundary conditions, and nonhomogeneities within finite element (FE) simulations. These nonlinearities pose a significant challenge for numerical solvers, increasing the computational time by several orders of magnitude. Simplifying assumptions can reduce the computational time significantly, but this usually comes at the expense of simulation accuracy. This study proposed the use of reduced order modeling (ROM) techniques to capture experimentally measured displacement fields of rat vaginal tissue during inflation testing in order to attain both the accuracy of higher-fidelity models and the speed of simpler simulations. The proper orthogonal decomposition (POD) method was used to extract the significant information from FE simulations generated by varying the luminal pressure and the parameters that introduce the anisotropy in the selected constitutive model. A new data-driven (DD) variational multiscale (VMS) ROM framework was extended to obtain the displacement fields of rat vaginal tissue under pressure. For comparison purposes, we also investigated the classical Galerkin ROM (G-ROM). In our numerical study, both the G-ROM and the DD-VMS-ROM decreased the FE computational cost by orders of magnitude without a significant decrease in numerical accuracy. Furthermore, the DD-VMS-ROM improved the G-ROM accuracy at a modest computational overhead. Our numerical investigation showed that ROM has the potential to provide efficient and accurate computational tools to describe vaginal deformations, with the ultimate goal of improving maternal health.

History-Dependent Deformations of Rat Vaginas under Inflation.

The vagina is a highly inhomogeneous, anisotropic, and viscoelastic organ that undergoes significant deformations in vivo. The mechanical attributes of this organ facilitate important physiological functions during menstruation, intercourse, and birthing. Despite the crucial mechanical role that the vagina plays within the female reproductive system, the deformations that the organ can sustain over time under constant pressure, in both the longitudinal direction (LD) and circumferential direction (CD), have not been fully characterized. This experimental study focuses on quantifying the creep properties of the vagina via ex vivo inflation testing using the rat as animal model. Toward this end, rat vaginas were subjected to three consecutively increasing constant luminal pressures (28 kPa, 55 kPa, and 83 kPa) using a custom-built experimental setup and the resulting inhomogeneous deformations were measured using the digital image correlation (DIC) method. The vagina was found to deform significantly more in the CD than the LD at any constant pressure, suggesting that the organ primarily adapts to constant pressures by significantly changing the diameter rather that the length. The change in deformation over time (i.e., creep) was significantly higher during the 1st inflation test at a constant pressure of 28 kPa than over the 2nd and 3rd inflation tests at constant pressures of 55 kPa and 83 kPa, respectively. The findings of this study on the mechanical behavior of the vagina could serve to advance our limited knowledge about the physiology and pathophysiology of this important reproductive organ.

Mechanical properties of tissue-mimicking composites formed by material jetting additive manufacturing.

Capitalizing on features including high resolution, smooth surface finish, large build volume, and simultaneous multi-color/multi-material printing, material jetting additive manufacturing enables the fabrication of full-scale anatomic models. The ability to print materials that resemble relevant, compliant tissues has especially motivated implementation of material jetting for patient-specific surgical planning or training models. In an effort to broaden the material selection for the material jetting process, and to provide materials that more closely mimic the functional needs for a wider variety of tissues, a composite material system is explored that uses non-curing fluid dispersed into a photo-curable medium. The material properties of the composites are examined through both thermal and mechanical analysis (dynamic mechanical analysis, Shore hardness testing, puncture testing, and tensile testing). Higher contributions of non-curing fluid generally reduce part strength and stiffness, and exponential and second-order polynomial expressions are appropriate fits for many of the mechanical properties as functions of non-curing fluid concentration. Through the fundamental exploration of the impact of an added diluent on material properties, the study advances knowledge on the process-property relationship for multi-material jetting. Additionally, better understanding of the mechanical property space offered by these materials will expand the capabilities of material jetting in the context of biomedical applications. The collection of mechanical properties serve as reference data sets to facilitate quicker screening for tissue-mimicking, medical models.

Tear propagation in vaginal tissue under inflation.

Vaginal tearing at childbirth is extremely common yet understudied despite the long-term serious consequences on women's health. The mechanisms of vaginal tearing remain unknown, and their knowledge could lead to the development of transformative prevention and treatment techniques for maternal injury. In this study, whole rat vaginas with pre-imposed elliptical tears oriented along the axial direction of the organs were pressurized using a custom-built inflation setup, producing large tear propagation. Large deformations of tears through propagation were analyzed, and nonlinear strains around tears were calculated using the digital image correlation technique. Second harmonic generation microscopy was used to examine collagen fiber organization in mechanically untested and tested vaginal specimens. Tears became increasingly circular under pressure, propagating slowly up to the maximum pressure and then more rapidly. Hoop strains were significantly larger than axial strains and displayed a region- and orientation-dependent response with tear propagation. Imaging revealed initially disorganized collagen fibers that aligned along the axial direction with increasing pressure. Fibers in the near-regions of tear tips aligned toward the hoop direction, hampering tear propagation. Changes in tear geometry, regional strains, and fiber orientation revealed the inherent toughening mechanisms of the vaginal tissue. STATEMENT OF SIGNIFICANCE: Women's reproductive health has historically been understudied despite alarming maternal injury and mortality rates in the world. Maternal injury and disability can be reduced by advancing our limited understanding of the large deformations experienced by women's reproductive organs. This manuscript presents, for the first time, the mechanics of tear propagation in vaginal tissue and changes to the underlying collagen microstructure near to and far from the tear. A novel inflation setup capable of maintaining the in vivo tubular geometry of the vagina while propagating a pre-imposed tear was developed. Toughening mechanisms of the vagina to propagation were examined through measurements of tear geometry, strain distributions, and reorientation of collagen fibers. This research draws from current advances in the engineering science and mechanics fields with the goal of improving maternal health care.

A review of Winkler's foundation and its profound influence on adhesion and soft matter applications.

Few advanced mechanics of materials solutions have found broader and more enduring applications than Emil Winkler's beam on elastic foundation analysis, first published in 1867. Now, 150 years after its introduction, this concept continues to enjoy widespread use in its original application field of civil engineering, and has also had a profound effect on the field of adhesion mechanics, including for soft matter adhesion phenomena. A review of the model is presented with a focus on applications to adhesion science, highlighting classical works that utilize the model as well as recent usages that extend its scope. The special case of the behavior of plates on incompressible (e.g., elastomeric and viscous liquid) foundations is reviewed because of the significant relevance to the behavior of soft matter interlayers between one or more flexible adherends.

Revisiting the generalized scaling law for adhesion: role of compliance and extension to progressive failure.

A generalized scaling law, based on the classical fracture mechanics approach, is developed to predict the bond strength of adhesive systems. The proposed scaling relationship depends on the rate of change of debond area with compliance, rather than the ratio of area to compliance. This distinction can have a profound impact on the expected bond strength of systems, particularly when the failure mechanism changes or the compliance of the load train increases. Based on the classical fracture mechanics approach for rate-independent materials, the load train compliance should not affect the force capacity of the adhesive system, whereas when the area to compliance ratio is used as the scaling parameter, it directly influences the bond strength, making it necessary to distinguish compliance contributions. To verify the scaling relationship, single lap shear tests were performed for a given pressure sensitive adhesive (PSA) tape specimens with different bond areas, number of backing layers, and load train compliance. The shear lag model was used to derive closed-form relationships for the system compliance and its derivative with respect to the debond area. Digital image correlation (DIC) is implemented to verify the non-uniform shear stress distribution obtained from the shear lag model in a lap shear geometry. The results obtained from this approach could lead to a better understanding of the relationship between bond strength and the geometry and mechanical properties of adhesive systems.

Expression, crosslinking, and developing modulus master curves of recombinant resilin.

Resilin is a disordered elastomeric protein found in specialized regions of insect cuticles, where low stiffness and high resilience are required. Having a wide range of functions that vary among insect species, resilin operates across a wide frequency range, from 5Hz for locomotion to 13kHz for sound production. We synthesize and crosslink a recombinant resilin from clone-1 (exon-1+exon-2) of the gene, and determine the water content (approximately 80wt%) and dynamic mechanical properties, along with estimating surface energies relevant for adhesion. Dynamic moduli master curves have been developed, by applying the time-temperature superposition principle (TTSP) and time-temperature concentration superposition principle (TTCSP), and compared with reported master curves for natural resilin from locusts, dragonflies, and cockroaches. To our knowledge, this is the first time dynamic moduli master curves have been developed to explore the dynamic mechanical properties of recombinant resilin and compare with resilin behavior. The resulting master curves show that the synthetic resilin undergoes a pronounced transition with increasing ethanol concentrations, with the storage modulus increasing by approximately three orders of magnitude. Although possibly a glass transition, alternate explanations include the formation of intramolecular hydrogen bonds or that the chitin binding domain (ChBD) in exon-2 might change the secondary structure of the normally disordered exon-1 into more ordered conformations that limit deformation.

Molecular modeling of the elastomeric properties of repeating units and building blocks of resilin, a disordered elastic protein.

The mechanisms responsible for the properties of disordered elastomeric proteins are not well known. To better understand the relationship between elastomeric behavior and amino acid sequence, we investigated resilin, a disordered rubber-like protein, found in specialized regions of the cuticle of insects. Resilin of Drosophila melanogaster contains Gly-rich repetitive motifs comprised of the amino acids, PSSSYGAPGGGNGGR, which confer elastic properties to resilin. The repetitive motifs of insect resilin can be divided into smaller partially conserved building blocks: PSS, SYGAP, GGGN and GGR. Using molecular dynamics (MD) simulations, we studied the relative roles of SYGAP, and its less common variants SYSAP and TYGAP, on the elastomeric properties of resilin. Results showed that SYGAP adopts a bent structure that is one-half to one-third the end-to-end length of the other motifs having an equal number of amino acids but containing SYSAP or TYGAP substituted for SYGAP. The bent structure of SYGAP forms due to conformational freedom of glycine, and hydrogen bonding within the motif apparently plays a role in maintaining this conformation. These structural features of SYGAP result in higher extensibility compared to other motifs, which may contribute to elastic properties at the macroscopic level. Overall, the results are consistent with a role for the SYGAP building block in the elastomeric properties of these disordered proteins. What we learned from simulating the repetitive motifs of resilin may be applicable to the biology and mechanics of other elastomeric biomaterials, and may provide us the deeper understanding of their unique properties.