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.

Fluid mechanics approach to analyzing collagen fiber organization.

SIGNIFICANCE: The spatial organization of collagen fibers has been used as a biomarker for assessing injury and disease progression. However, quantifying this organization for complex structures is challenging. AIM: To quantify and classify complex collagen fiber organizations. APPROACH: Using quantitative second-harmonic generation (SHG) microscopy, we show that collagen-fiber orientation can be viewed as pseudovector fields. Subsequently, we analyze them using fluid mechanic metrics, such as energy U, enstrophy E, and tortuosity τ. RESULTS: We show that metrics used in fluid mechanics for analyzing fluid flow can be adapted to analyze complex collagen fiber organization. As examples, we consider SHG images of collagenous tissue for straight, wavy, and circular fiber structures. CONCLUSIONS: The results of this study show the utility of the chosen metrics to distinguish diverse and complex collagen organizations. We find that the distribution of values for E and U increases with collagen fiber disorganization, where they divide between low and high values corresponding to uniformly aligned fibers and disorganized collagen fibers, respectively. We also confirm that the values of τ cluster around 1 when the fibers are straight, and the range increases up to 1.5 when wavier fibers are present.

Investigation of Murine Vaginal Creep Response to Altered Mechanical Loads.

The vagina is a viscoelastic fibromuscular organ that provides support to the pelvic organs. The viscoelastic properties of the vagina are understudied but may be critical for pelvic stability. Most studies evaluate vaginal viscoelasticity under a single uniaxial load; however, the vagina is subjected to dynamic multiaxial loading in the body. It is unknown how varied multiaxial loading conditions affect vaginal viscoelastic behavior and which microstructural processes dictate the viscoelastic response. Therefore, the objective was to develop methods using extension-inflation protocols to quantify vaginal viscoelastic creep under various circumferential and axial loads. Then, the protocol was applied to quantify vaginal creep and collagen microstructure in the fibulin-5 wildtype and haploinsufficient vaginas. To evaluate pressure-dependent creep, the fibulin-5 wildtype and haploinsufficient vaginas (n = 7/genotype) were subjected to various constant pressures at the physiologic length for 100 s. For axial length-dependent creep, the vaginas (n = 7/genotype) were extended to various fixed axial lengths then subjected to the mean in vivo pressure for 100 s. Second-harmonic generation imaging was performed to quantify collagen fiber organization and undulation (n = 3/genotype). Increased pressure significantly increased creep strain in the wildtype, but not the haploinsufficient vagina. The axial length did not significantly affect the creep rate or strain in both genotypes. Collagen undulation varied through the depth of the subepithelium but not between genotypes. These findings suggest that the creep response to loading may vary with biological processes and pathologies, therefore, evaluating vaginal creep under various circumferential loads may be important to understand vaginal function.

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.

Inflation and rupture of vaginal tissue.

Around 80% of women experience vaginal tears during labour when the diameter of the vagina must increase to allow the passage of a full-term baby. Current techniques for evaluating vaginal tears are qualitative and often lead to an incorrect diagnosis and inadequate treatment, severely compromising the quality of life of women. In order to characterize the failure properties of the vaginal tissue, whole vaginal tracts from rats (n = 18) were subjected to free-extension inflation tests until rupture using a custom-built experimental set-up. The resulting deformations were measured using the digital image correlation technique. Overall, the strain and changes in curvature in the hoop direction were significantly larger relative to the axial direction. At a failure pressure of 110 ± 23 kPa (mean ± s.d.), the hoop and axial stresses were computed to be 970 ± 340 kPa and 490 ± 170 kPa, respectively. Moreover, at such pressure, the hoop and axial strains were found to be 12.8 ± 4.4 % and 6.4 ± 3.7 % , respectively. Rupture of the vaginal specimens always occurred in the hoop direction by tearing along the axial direction. This knowledge about the rupture properties of the vaginal tissue will be crucial for the development of clinical approaches for preventing and mitigating vaginal tearing and the associated short- and long-term traumatic conditions.

Swine Vagina Under Planar Biaxial Loads: An Investigation of Large Deformations and Tears.

Vaginal tears are very common and can lead to severe complications such as hemorrhaging, fecal incontinence, urinary incontinence, and dyspareunia. Despite the implications of vaginal tears on women's health, there are currently no experimental studies on the tear behavior of vaginal tissue. In this study, planar equi-biaxial tests on square specimens of vaginal tissue, with sides oriented along the longitudinal direction (LD) and circumferential direction (CD), were conducted using swine as animal model. Three groups of specimens were mechanically tested: the NT group (n = 9), which had no pre-imposed tear, the longitudinal tear (LT) group (n = 9), and the circumferential tear (CT) group (n = 9), which had central pre-imposed elliptically shaped tears with major axes oriented in the LD and the CD, respectively. Through video recording during testing, axial strains were measured for the NT group using the digital image correlation (DIC) technique and axial displacements of hook clamps were measured for the NT, LT, and CT groups in the LD and CD. The swine vaginal tissue was found to be highly nonlinear and somewhat anisotropic. Up to normalized axial hook displacements of 1.15, no tears were observed to propagate, suggesting that the vagina has a high resistance to further tearing once a tear has occurred. However, in response to biaxial loading, the size of the tears for the CT group increased significantly more than the size of the tears for the LT group (p = 0.003). The microstructural organization of the vagina is likely the culprit for its tear resistance and orientation-dependent tear behavior. Further knowledge on the structure-function relationship of the vagina is needed to guide the development of new methods for preventing the severe complications of tearing.