Introduction

Lack of urethral support due to weakness in various components of the urethral support system (USS) has been considered as the main etiological factor causing stress urinary incontinence (SUI) [1]. The “hammock hypothesis” describes support of the urethra by a coordinated action of fasciae and muscles, which provides a hammock onto which the urethra is compressed during increases in intra-abdominal pressure (IAP) [1]. In a broad sense, the USS includes the levator ani muscle, vaginal wall, and connective tissues extrinsic to the urethra, as well as the coccygeus muscle, obturator internus muscle, piriformis muscle, and pelvic organs such as the rectum and uterus, as all these structures reside in the female pelvis and interact intimately to support the urethra during pressure events.

Many studies have investigated the pathophysiology of SUI through medical imaging techniques such as ultrasonography (US) [2], anatomical magnetic resonance (MR) imaging [3], and dynamic MR imaging [4]. To assess urethral hypermobility caused by isolated impairment of each specific USS component and to compare components’ relative contribution to urethral support function would require the recruitment of patients with only one impairment condition, which is clinically challenging to identify. Cross-subject differences in female pelvic floor anatomy also affect the objectivity of the comparison. Computer modeling using MR images and simulation using the finite element method (FEM) has proven to be a useful tool [5, 6] due to its ability to conveniently simulate various impairment conditions and keep these comparisons based on the same patient [7, 8]. Several computer models developed from MR images have been reported recently in studies of female pelvic floor dysfunctions, such as pelvic organ prolapse (POP) [9–11], childbirth-related levator ani muscle damage [12], and ligament impairment [13]. However, the clinical application of these models and their comparisons with the true dynamic response of the pelvis is limited due to either (1) missed or simplified important anatomical structures (e.g., bladder, rectum, vaginal canal, uterus are not imaged [12] or buffering fatty tissues are not included [9–13]); or (2) less accurate imaging of boundary conditions (e.g., direct inferior displacement is applied on the uterus [9]; intra-abdominal pressure (IAP) is directly applied on the muscle [13] or vaginal wall [11]). A comprehensive pelvic model incorporating 44 anatomical structures that maintain integrity of the natural female pelvic anatomy was developed in this study to better understand the role of individual structures and their combinations on urethral support in women.

Materials and methods

A 21-year-old healthy woman [nulliparous, nonsmoker, body mass index (BMI) = 22] was recruited according to a protocol approved by the Institutional Review Boards (IRBs) of the University of Minnesota and the University of Houston to undergo a high-resolution pelvic scan in the supine position at rest with a 3T MR imaging scanner (Trio Tim, Siemens, Germany) (slice thickness 3 mm; matrix 320 × 160; field of view 430 mm; pixel size 1.344 mm). For validation purposes, dynamic MR images were acquired in the midsagittal plane approximately every 1.5 s while the patient performed several Valsalva maneuvers.

Image segmentation was first performed on axial images for each anatomical pelvic structure with the guidance of urologists using Mimics 11.0 (Materialise Group, Leuven, Belgium). The closed surfaces were reconstructed for each anatomical structure and exported in stereolithography (STL) format. Those surfaces were imported into MAYA 8.5 (Autodesk, Inc., San Rafael, CA, USA) and Rhinoceros 4.0 (McNeel North America, Seattle, WA, USA) for artifact smoothing and intersecting surface correction and then converted into solid Standard ACIS Text (SAT) geometries. All solid geometries were discretized into finite element meshes with a total number of 126,378 tetrahedral elements in ABAQUS 6.12 (SIMULIA, Providence, RI, USA). The final 3D pelvic model contains 44 anatomical parts, including pelvic muscles, sphincteric muscles, ligaments, bones, fat, bladder, urethra, uterus, vagina, deep perineal pouch, colon, rectum, and anus. In addition, a bodyfill part was created to fill the intra-abdominal space for pressure transmission. A stiff Q-tip swab part was placed in the urethra to simulate the Q-tip swab that has been frequently used in clinical diagnosis and research for SUI [14, 15]. Figure 1 illustrates the reconstructed 3D pelvic model. The bottom of the model was restrained from both translations and rotations. Two uniformly distributed pressures were applied on the front and top surfaces of the bodyfill to simulate Valsalva. IAP was calculated as the averaged contact pressure between the urine and inner bladder wall.

Fig. 1
figure 1

a Front and b back view of all pelvic muscles, ligaments, and bones (fats and organs hidden for better visualization). c Midsagittal view of the entire pelvic model. d Anterior and posterior supports to urethra from pubourethral ligament, vagina, and perineal pouch muscles. Ligaments were modeled using connector elements. The uterosacral ligaments attach the cervix to the posterior pelvic wall. The cardinal ligaments attach the cervix to the lateral pelvic wall. The pubourethral ligaments attach the bladder neck to the symphysis pubis. e Posterior support to urethra from pelvic floor muscles. In a, b, and e, muscles are shown in different colors (green piriformis, orange coccygeus, blue iliococcygeus, yellow obturator internus, magenta pubococcygeus, red puborectalis)

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Although soft tissues show viscoelastic behavior [16–18], a previous study found quasi-linear material property of urological soft tissues when the stress level is under 70 % of the maximal stress value [8]. Soft tissues involved in the pelvic model were modeled as linear elastic solids using material properties from Young’s moduli of the bladder, urethra, uterus, rectum, muscle, ligament, and vaginal tissue (0.05, 0.03, 0.05, 0.1, 2.4, 1.2, and 7.4e–3 MPa) [7]. A soft material (Young’s modulus of 0.04 MPa) was assigned to the bodyfill part. Urine was modeled as an elastic liquid with a Young’s modulus of 1.0e–3 MPa. All soft tissues were considered incompressible considering that they contain abundant water. The bony pelvis was modeled as one rigid and fixed structure considering its negligible deformation under normal pelvic functions due to its much higher stiffness compared with soft tissues [13]. A simplifying condition was created so as to not include voluntary contraction of the pelvic muscles, as it is often the case that, unless the patient is trained to use pelvic floor physical therapy, the pelvic floor responds to acute increase of IAP without voluntary contractions, such as during coughing or sneezing.

The general contact algorithm in ABAQUS was applied to mimic the natural interaction between parts that are in contact but anatomically independent, such as bladder and uterus, uterus and rectum, or pelvic muscles and fatty tissues. Tie constraints in ABAQUS that binds two shared surfaces were used to couple motions of parts that are biologically connected (e.g., coccygeus muscle and coccyx) and to model the connecting effects of fasciae (e.g., tendineus arch of levator ani muscle between iliococcygeus muscle and obturator internus muscle). Connector elements, with the ability to model connective tissues such ligaments [9], were employed to model uterosacral and cardinal ligaments. The Abaqus/Explicit solver was used for finite-element-method implementation.

A validation study was first performed by comparing pelvic floor configurations achieved in computer simulation results with dynamic MR imaging observations along the midsagittal plane at both rest and maximal Valsalva maneuver (Fig. 2). The patient was instructed on how to perform a Valsalva maneuver for the dynamic MR imaging and asked to hold each Valsalva maneuver for at least 2 s. During Valsalva maneuver, abdominal muscles were contracted. Special attention was paid to motions of the bladder, urethra, uterus, and rectum. Results showed that the bladder, uterus, and rectum slide in a posterior direction under the elevated IAP. It was also observed that the increased IAP led to bladder-neck descent and clockwise rotation of the urethra, both of which are important landmarks commonly used in assessing urethral supports. The achieved consistency demonstrated the competence of the computer modeling and simulation method in characterizing pelvic floor responses to increased IAP.

Fig. 2
figure 2

Comparison [dynamic magnetic resonance (MR) imaging vs. dynamic biomechanical analysis] in the sagittal plane of pelvic structures of the female patient at rest and on Valsalva. The black solid line in all images shows the location of the urethra. The red curves in the dynamic MR image outline the bladder. Ut uterus, R rectum, B bladder, PB pubic bone, V vagina, F fat, U urethra)

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The plan of simulation used in this study is listed in Table 1. The first two columns list the test numbers and weakened parts, with their abbreviations in brackets. The impairment of each structure was simulated by reducing the material stiffness by 90 % [13]. Test00 serves as the asymptomatic control test based on the intact model in which no impairment was present. In each test from 01 to 07, a single USS component was weakened (hereafter referred to as single tests); in each test from 08 to 12, a specific group of USS components was weakened (hereafter referred to as group tests). Weakening the levator ani muscle was considered as a group test because the levator ani muscle group is composed of three individual muscle components. SUI is often associated with urethral hypermobility. Transperineal US reveals that the alpha-angle, defined as the angle between the vertical axis and the urethral axis [2], was significantly different on straining (P < 0.05) between the study (SUI) and control groups. In this study, the alpha angle was monitored from the onset of simulation to the final status, at which the IAP reached 100 cmH2O [19]. The urethral excursion angle, defined by the corresponding change in the α angle (Δα) and mathematically equal to the Q-tip excursion in clinical tests [15], was also monitored as an alternative metric to examine the urethral support function. Since the α angle at rest showed no significant difference (P = 0.650) between SUI and control groups [2], and because only urethral support loss attributed to weakness of specific anatomical structure(s) was considered in this computation study, static morphologic variation in the α angle between asymptomatic individuals and patients with SUI was not accounted for.

Table 1 Simulation plan and results
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Linear regression analyses were performed for all curves (urethral excursion angles vs. IAP) in MATLAB R2014 (Mathworks Inc., Natick, MA, USA) using a linear model (Δα ~ k × IAP ). The interception of the linear model was set to zero, considering that the urethral excursion angle should be zero at the onset of simulation (IAP = 0 cmH2O). The Δα achieved in the intact test (noted as ΔαIntact) indicates the inherent response to the applied IAP of an asymptomatic USS. A weakening effect index (WEI) (Δα−ΔαIntact) was also employed to elicit the degree of mobility caused solely by the weakened structure in each weakening test.

Results

The α angle at onset of simulation (at rest) was 15.9° for all tests. Table 1 shows the α angles achieved at the final status with the IAP of 100 cmH2O for all tests. The final α angles ranged from 30.3° (intact test) to 50.7° (weakened levator ani muscle and vaginal wall). The corresponding urethral excursion angles (Δα) were calculated based on the difference between onset and final α angles (Table 1); ΔαIntact reached 14.4° for the particular participant in this study. The results further showed that Δα values were <20° when only a single pelvic muscle was weakened (from 15.3° to 19.4°). The vaginal wall, the puborectalis muscle, and the pubococcygeus muscle were found to be the top three most contributing structures. Weakening these parts generated the top three largest urethral excursion angles (Δα = 20.1°, 19.4°, and 18.8°, respectively), while weakening other muscles (the iliococcygeus, piriformis, coccygeus, and obturator internus muscles) generated relatively smaller excursion angles (Δα < 17°). Weakening the levator ani muscle alone (test09) or in combination with other pelvic muscles (test10–12) raised the Δα value >30°. The fitted R-square values for the urethral excursion angle–IAP curves (see Fig. 3) fell into the range of 0.95–0.99, indicating a strong linear relationship between the urethral excursion angle and increased IAP for all tests.

Fig. 3
figure 3

Plots of urethral excursion angle against intra-abdominal pressure for a single and b group tests

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A nonlinearly additive pattern was found among the three levator ani muscle components in terms of weakening effect (WEI = Δα −ΔαIntact). A WEI of 12.0° was achieved when weakening the puborectalis and pubococcygeus muscles together (test08), which is larger than the sum of WEI achieved by weakening these two muscles separately (WEI = 5.0° in test05; WEI = 4.4° in test06). The same nonlinear additive pattern was more remarkable when comparing the WEI obtained from weakening the entire levator ani muscle (WEI = 18.5°, test09) with the sum of WEIs from tests in weakening the three components separately (WEI = 1.4° in test02, WEI = 5.0° in test05, WEI = 4.4° in test06). Such a pattern did not exist for combinations of the levator ani muscle with other muscle groups (test10, 11, 12). This finding suggests that the levator ani muscle is a sophisticated structure that provides support to the urethra in a well-coordinated fashion.

Distinct deformation patterns were found in pelvic floor responses under different weakening conditions (see Fig. 4). When vaginal tissues were weakened, the vaginal canal underwent severe compression and the vaginal wall became extremely thin, yielding more space for extraurethral motion; however, the shape and position of the levator ani muscle did not show evident difference. When the levator ani muscle was weakened, a different pattern was observed: the vaginal wall remained at its normal thickness, while the levator ani muscle showed remarkable backward and downward yielding, especially in the midportion, as the combinational effect of the front and top pressures applied on the bodyfill part on the entire pelvic floor was similar to a body force oriented in the inferoposterior direction and perpendicular to the levator plate. Urethral-axis excursion in this case was attributed more to insufficient support by the weakened levator ani muscle than the collapsed vaginal canal. When the levator ani muscle and the vaginal wall were both weakened simultaneously, both syndromes could be identified.

Fig. 4
figure 4

Deformation patterns of a intact test, b weakened vaginal wall, c weakened levator ani muscle, and d weakened levator ani muscle together with vaginal wall

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Discussion

Our female pelvic model consisting of 44 anatomical structures to mimic the dynamic response to pressure events represents, to the best of our knowledge, the most comprehensive and complete pelvic model in female SUI research. The validation study demonstrated consistency between computer-simulation results and dynamic MR imaging observations along the sagittal plane of the pelvis of the same patient. A parametric study was designed and performed to investigate the relative importance of individual structures or their combination on urethral support in women. The α angles from our computer simulations are in agreement with findings from transperineal US [2].

The relationship between IAP and induced urethral hypermobility may vary widely across individuals due to differences in anatomy and functional status of the urethral support system [20]. However, simultaneous examination of these two metrics may provide useful information for standardized evaluation of the functional status of the female pelvis. A significant association (p = 0.012) between the ratio of IAP over Q-tip angle (urethral mobility index) and the degree of cystourethrocele was reported in a study that involved 84 incontinence women [21]. The authors proposed this urethral mobility index as a standardized index for crossing-subject comparison. Although it is often intuitively assumed that the extent of urethral hypermobility should be positively related to IAP, this is the first time that this relationship has shown to be linear. The linear relationship over the entire IAP range identified in this study provided substantial ground for the application of the urethral mobility index, which could be obtained consistently at any IAP level with less vulnerability to IAP variations. Moreover, it could provide a comprehensive functional profile of the female pelvic floor in order to discern urethral mobility indices specific to each weakening condition. Any anatomical (such as midurethral sling surgery) or functional (e.g., enhanced pelvic muscle strength) change in the pelvis could also be simulated in the computational model to provide valuable references in presurgery planning, training, or other SUI treatment options.

In our model, the weakening effect was mild when only one single structure was weakened, consistent with Crystle et al., who found patients with good urethral support to have a rotation angle <20° [14]. This finding reveals that the female USS is a stable system and could still provide sufficient support to the urethra under mild impairment. Considering the Q-tip excursion >30° as a criteria for urethral hypermobility [14, 15], we find that weakening the entire levator ani muscle (comprised of the iliococcygeus, puborectalis and pubococcygeus muscles) caused more urethral mobility and could possibly result in urethral hypermobility (Δα = 32.9°). This is consistent with the clinical observation that female SUI patients with urethral hypermobility are often associated with damage to the levator ani muscle [22].

Medical imaging techniques such as MR imaging or US have been widely used for diagnosing SUI characterized by urethral hypermobility, but their application is limited to cases in which morphologic defects of urethral support structures are main causes. However, impairment is not always morphologically observable. Reduced stiffness in pelvic muscles [23] and ligament and vaginal wall tissues due to aging or trauma [24] could also be associated with insufficient support. The computational modeling and biomechanical approach provides a useful tool for those cases in which there is no imaging evidence of morphologic abnormalities in the USS. Moreover, with the capability to reproduce the pelvic floor deformation under different weakening scenarios, and exporting dynamic or static landmarks of interest, our model could be employed to establish a patient-specific SUI profile that manifests the deformation pattern uniquely associated with each possible weakening scenario. The functional status of the urethral support structure could then be assessed by comparing the imaging finding with the established profile. The distinct deformation patterns under different weakening conditions provide valuable references for patient-specific SUI diagnosis, which would be difficult to obtain from other methods considering the particularly challenging requirement that the same patient must develop different weakening syndromes successively, as well as the difficulty in capturing the extremely instantaneous dynamic deformation.

The computational modeling and biomechanical analysis approach presented in this study could also be employed to develop, design, and optimize interventional treatment approaches/devices, such as midurethral slings. Results under different weakening conditions provided in our model could be valuable in simulating worst-case scenarios and determining the safety factor for sling products. Kociszewski et al. [25] showed that success and complication rates of sling surgery were highly associated with implant position. Our model could also be used as a presurgery planning tool to reduce potential postoperative complications and improve treatment success rate on a patient-specific basis.

Limitations of this study are first, it lacks statistical information, as our model was built based on one patient-specific anatomy. The patient-specific-modeling approach provides a tool for personalized diagnosis and treatment outcome prediction for a specific patient. Analyses will be performed in the future based on results from a group of patients in order to provide statistical information. Second, the pelvic model relies on high-resolution MR images, which remains a relatively expensive procedure (approximately US $500/MR scan). Third, the modeling procedure takes about 1–2 weeks for experienced engineers and radiologists. A possible solution to make this approach more accessible is to build a pelvic model template based on features of the patient group and use patient-specific US images for model modification. Fourth, a limitation commonly shared by many other pelvic models is that the voluntary contraction of muscles is not possible in the pelvic model. To do so it would require a nontrivial finite element implementation technique as well as critical physiological calibrations for different levels of voluntary pelvic floor muscle contractions. Very recently, an advanced voluntary pelvic model was proposed that provides a way to model voluntary muscle contractions [26]. Nevertheless, the parameters associated with the voluntary muscle model were not obtained from actual voluntary contraction experiments in this study. A specially designed transvaginal and a transrectal high-density surface electromyogram (EMG) probe [27], along with the internal muscle activity imaging technique [28–30], were recently developed in our group. We are currently using high-density surface EMG measurements to quantitatively characterize voluntary muscle contractions in the female pelvis to further improve our pelvic modeling approach.

In conclusion, a comprehensive computational model of the female pelvis was reconstructed. The vaginal wall, puborectalis muscle, and pubococcygeus muscle were found to be the three most important urethral support structures. Some unique patterns of female pelvic floor deformation were identified, which indicate that the computational modeling and dynamic biomechanical analysis approach presents a powerful tool for female SUI research and clinical diagnosis. It could be potentially employed for patient-specific SUI evaluation and presurgery planning.