Moment of inertia as a means to evaluate the biomechanical impact of pelvic organ prolapse


Correspondence: Renato Natal Jorge Ph.D., Institute of Mechanical Engineering, Faculty of Engineering, University of Porto, Rua Dr Roberto Frias, Porto 4200-465, Portugal. Email:



To present an alternative measure (moment of inertia) to describe the anatomical features of the pelvic organ prolapse.


A total of 30 women (21 diagnosed as having pelvic organ prolapse and 9 as controls) were evaluated by clinical scales and magnetic resonance imaging. Imaging biometric measures were carried out. Moment of inertia, pubovisceral muscle thickness and area, and levator hiatus anterior-to-posterior and lateral measures were compared by means of non-parametric tests, as well as their correlation with demographic features of the two sample groups.


Moment of inertia, muscle area and levator hiatus diameters were statistically different between patients and controls. Furthermore, they were also well correlated with prolapse-associated factors, such as the number of vaginal deliveries and age, as well as Pelvic Organ Prolapse Quantification system and imaging staging of levator ani defects.


Moment of inertia can be used as a new parameter to evaluate pelvic floor damage resulting from prolapse.

Abbreviations & Acronyms



fecal incontinence


moment of inertia


magnetic resonance imaging


pelvic floor dysfunction


pelvic floor muscles


pelvic organ prolapse


Pelvic Organ Prolapse Quantification system


pubovisceral muscle




urinary incontinence




PFD includes clinical problems affecting a woman's pelvic organs and the structures that support them, such as the pelvic fascia and the PFM. The most common types of female PFD comprise POP, UI and FI. Its high prevalence and impact on quality-of-life makes it a focus of different specialities, such as primary care doctors, gynecologists, urologists and, because of its relationship with biomechanical features, also engineers.

The overall model for PFD in women includes family history, heavy work, high-impact sports activity, chronic straining or hormonal status.[1, 2] Pregnancy and vaginal delivery were also proven to relate to nerve and PFM damage, connective tissue or ligament disruption, increasing the risk for both urinary and defecatory symptoms or vaginal bulging. Among the predisposing factors to developing PFD, vaginal delivery is, in fact, the most relevant independent risk factor.[3-7] Evidence of muscle physical damage, denervation and changes in morphology has been reported in women with UI and POP, and progress is being made to assess what specific role levator ani muscle injury plays in the pathogenesis of these common problems.[8-11] The consequences of levator ani damage might depend on which and how its components were damaged. Injury to each component might be expected to have a different functional effect. Pubovisceral muscle includes pubococcygeal and puborectal muscles, which form a sling around the rectum and vagina to promote urogenital hiatus closure.[7, 12] Its disruption or thickness abnormalities are associated with UI and POP.[10, 12-15]

Anatomical features of PFD were previously described by using US and MRI, with great success.[16, 17] Even with a direct association between pubovisceral muscle thinning or defects and the increase of levator hiatus and POP diagnosis,[18] a case–control study showed that women with prolapse had an equal likelihood of having minor defects as asymptomatic normal women.[19] Additionally, a recent study showed that defects and loss of muscle bulk in the puborectal muscle were not seen by MRI in women with POP.[20] Despite the advantages of clinical US and MRI, it must be emphasized that most imaging analysis on axial static MRI describes muscle loss, but not its biomechanical impact. So, in a biomechanical perspective, a new predictive measure of prolapse event or severity based on static images would be very useful.

Muscle atrophy, changes in morphology or disruption cause functional weakness and might relate to the reduction of MOI.[21] MOI is a geometrical property of a structure's cross-sectional area that constitutes an important geometrical parameter to define bending or deflection characteristics of that structure. This measure is associated with several morphological properties, such as the area, the thickness and, in a lesser degree, other dimensions of the muscle cross-sectional area, such as the diameters, as described by Young.[22] The greater the MOI, the increased resistance to deformation, which means that less strength is necessary to compensate for positional shifts. The MOI of a cross-sectional area can change according to its morphological features, as shown on Figure 1. For example, when the thickness (t → t') and area of the structure decrease, and the diameters increase (a → a' and 2b → 2b'), MOI is reduced. In this case, a higher probability of deformation is related to the lower stiffness, and the force necessary to counteract pressure is superior.

Figure 1.

Morphological features of a structure and its relationship with MOI. This scheme approximates the shape of semi-elliptical donuts, which can be understood as equivalent to a cross-sectional area of the pubovisceral muscle. When the thickness and diameters vary (from [a] to [b]) the value of MOI changes. 2b, Width, which will correspond to RL diameter; a, height, which will correspond to AP diameter; t, thickness.

POP might be caused by a weaker supportive structure of the PFM that allows viscera to descend through the levator hiatus, a functional gap of the levator ani through which the urethra, vagina and rectum might move down.[23, 24] Straining and coughing increase pressure onto the pelvic floor, inducing muscle deformation and reinforcing levator hiatus opening. The thinner the muscle becomes and the wider the levator hiatus becomes, the resistance to deformation in the cross-sectional area, which defines MOI, is lower. The authors explored the idea that perhaps a thinner or disrupted pubovisceral muscle, which is related to levator hiatus widening and POP, and also to a weaker active and passive response to increase pressure, could be related to a lower MOI. However, to date, there is no measure that relates muscle thickness, area and morphology, which would be important in the clinical setting to assess the real biomechanical impact of POP on the PFM. And so, MOI could be an important tool to describe it. Furthermore, it would be very relevant to predict if nulliparous women with pubovisceral muscle with decreased MOI would be at a higher risk of developing POP, and also, what is the association between the decrease in MOI and the number of vaginal deliveries in POP women.

The aim of the present study was to determine if the MOI parameters of the PFM could be correlated to clinical diagnosis and (static MR) imaging measures of POP; additionally, to compare morphological parameters between women with and without POP.


The present study was approved by the Ethics Committee of the Hospital de São João, Porto. A total sample of 30 women was observed by the same gynecologist. Clinical evaluation and POP–Q were carried out to assess POP. A total of 21 women were diagnosed with POP, whereas nine were used as the control group.

All the women were imaged by means of MRI, using a 3 Tesla scanner. Axial high-resolution T2-weighted images were acquired at rest in the supine position, along the puborectal line.

To carry out image evaluation and measurements, the axial slice closer to the plane of minimal hiatal dimensions was used (Fig. 2). This plane is defined as the minimal AP diameter of the levator hiatus, from the postero-inferior margin of the symphysis pubis to the anterior margin of the pubovisceral muscle, where it defines the anorectal angle.[25-27] In the present study, all the measures were carried out in the pubovisceral muscle, as according to DeLancey et al.,[28] the pubococcygeal and puborectal might not be well differentiated on US or MRI.

Figure 2.

High-resolution T2-w MR images were acquired along (a) the puborectal line (green line) in order to achieve the orientation of the pubovisceral muscle, and (b) the plan of minimal hiatal dimensions on the axial images.

To calculate pubovisceral muscle MOI and cross-sectional area, it was manually segmented using a contour spline. The software Inventor (Autodesk, San Raphael, CA, USA) was used to draw and calculate those variables (Fig. 3). Additionally, three other measures were carried out in the same slice: thickness of right and left portions of pubovisceral muscle at the level of midvagina and levator hiatus AP and RL dimensions, following the methodology described in Majida et al. and Kruger et al. (Fig. 4).[29, 30] Finally, images were evaluated for levator ani defects as proposed by DeLancey et al.,[19] in which women were classified as having “major” (more than half missing), “minor” (less than half of the muscle missing) or no defects.

Figure 3.

Manual procedure to draw the pubovisceral muscle contour using Inventor software.

Figure 4.

Levator hiatus diameters and pubovisceral muscle thickness measures. The anterior-to-posterior and lateral dimensions of (a) the levator hiatus were carried out, (b) along with pubovisceral muscle thickness at the level of midvagina.

Statistical analysis

All continuous variables were expressed as mean ± SD and range. The numerical data were compared by Student's t-test or Mann–Whitney U-test. Correlation between variables was determined by Spearman's correlation analysis. Estimation of MOI decrease was calculated by simple linear regression analysis. A P-value of 0.05 or less was considered to be significant.


A total of 30 women were evaluated (9 nulliparous and 21 multiparous), with an age range of 21–83 years (mean 48.3 ± 24.6). A total of 40%[12] of the women were in menopause. The range of patients' pregnancies was 0–6 (mean 1.8 ± 2.3) and the number of vaginal deliveries was also 0–6 (mean 1.5 ± 2.0). The POP-Q staging resulted in: 30% (9/30) with stage 0, 23.3% (7/30) with stage 1, 23.3% (7/30) with stage 2 and 23.3% (7/30) with stage 3. According to the DeLancey et al. MRI grading system,[19] 10 women were classified as having no defects, nine with “minor” defects and 11 with “major” defects.

The mean values of AP and RL diameters, area, thickness, and MOI of the pubovisceral muscles of the two groups are summarized in Table 1.

Table 1. Measures of levator hiatus diameters, pubovisceral muscle area, thickness and moment of inertia in women with and without prolapse
VariablesWithout prolapse (n = 9)With prolapse (n = 21)P-value
Anterior-to-posterior diameter (cm)4.7 ± 0.565.6 ± 0.710.007
Lateral diameter (cm)2.7 ± 0.583.7 ± 0.610.002
Area of the pubovisceral muscle (mm2)748.3 ± 324.8425.9 ± 111.90.006
Thickness, right side (cm)0.67 ± 0.300.43 ± 0.160.036
Thickness, left side (cm)0.97 ± 0.360.75 ± 0.300.146
Moment of inertia (mm4)162 596.7 ± 81 198.865 505.3 ± 21 820.30.001

Table 2 lists the correlations between MOI and demographic, clinical, and morphological variables. There was a negative correlation, at least moderate, between the MOI with age, pregnancy, vaginal delivery, POP-Q stages and MRI grading system. Pubovisceral muscle area showed very good correlation with MOI (r = 0.907, P = 0.000) and good correlation with POP-Q stages (r = –0.695, P = 0.001), pregnancy (r = -0.677, P = 0.001) and vaginal delivery (r = –0.677, P = 0.001). There were no significant correlations between area and hiatus diameters. Muscle thickness at the level of midvagina, both left and right sides, was positively correlated with MOI (r = 0.552 and r = 0.561, respectively).

Table 2. Correlation between MOI and variables
 AgePregnancyVaginal deliveryMidvagina PVM thicknessArea of PVMPOP-QMRI grading-systemAPRL
  1. aSignificant correlation.
MOIr = −0.534 P = 0.015ar = −0.727 P = 0.000ar = −0.747 P = 0.000ar = 0.561 P = 0.010ar = 0.552 P = 0.012ar = 0.907 P = 0.000ar = −0.790 P = 0.000ar = −0.684 P = 0.001ar = −0.51 P = 0.04r = −0.50 P = 0.042

Mean values of muscle thickness on the right and left sides were superior for the control group, but an unexpected finding was the fact that the right side was thinner for both groups. This might be related to an imaging artifact. The thickness on the right side was correlated with pregnancy, vaginal delivery and POP-Q stages (r = −0.542, P = 0.014; r = −0.549, P = 0.012 and r = −0.530, P = 0.016, respectively). However, it was not possible to establish the same correlations for the left side.

As expected, POP-Q staging was correlated with AP and lateral levator hiatus diameters (r = 0.460 and r = 0.760, respectively).


POP has been associated with avulsion of the levator ani from the pubic arch, the size of levator hiatus and PFM weakness.[19, 31] However, besides traumatic-related features, muscle morphological characteristics might influence mechanical behavior of the PFM, and might contribute to generate less closure force during a contraction. Thus, in addition to scoring levator ani defects and measuring levator hiatus, it is also important to evaluate the morphology of the PMF. MOI values directly establish an important association with pubovisceral muscle area and morphology, allowing complementary information. Similar to what other authors have described,[10] the present study found significantly increased hiatus AP and RL diameters in POP women. The present results showed a moderate correlation between MOI and AP and RL hiatus diameters and thickness, weaker than the correlation obtained for pubovisceral area.

DeLancey et al. found that women with POP could contract the PFM with just 43% of the force generated by women with no POP.[19] By knowing that lower MOI values relate to a weaker muscle biomechanical response as a result of the loss of mechanical elasticity, this means that for the same amplitude of movement, the muscle needs higher force during its contraction. The present study also showed that POP women had almost one-third of the MOI mean value when compared with the control group (65 505.3 vs 162 596.7 mm4, respectively). Therefore, despite measuring different aspects of the pelvic floor, they might have very similar clinical meaning. Furthermore, as MOI shows a pattern of biomechanical function, it might be seen as complementary information on the ability to resist to abdominal pressure, which can be obtained in static images through anatomical features of the pelvic floor muscles.

The strongest correlations were obtained with the number of vaginal deliveries, which is the most important independent risk factor for developing POP, and also with POP-Q staging system, which is the most widely used clinical measure of POP. This means that MOI might be able not only to identify POP, but also to predict POP-related morphological defects and functional damage. MOI is strongly associated with muscle area, which in turn is dependent on its thickness, and so, it could be used as its indirect measure. As expected, the results showed a significant correlation between MOI and both muscle area and thickness, and a weaker association between MOI and AP and RL hiatus diameters. The levator hiatus diameters were not significantly correlated with these two morphological characteristics of the muscle (area and thickness), even though they were increased, even at rest, when compared with controls. Additionally, POP women showed decreased values of muscle thickness and area. These findings portray the consequences of demographic and clinical characteristics, such as age, pregnancy and the traumatic event of vaginal delivery.

POP is associated with a disrupted levator ani, and also with a wider levator hiatus. Our control group presented 27% lower RL diameter and 16% AP diameter, and also 56% thicker muscle on the right side and 29% on the left side. The passage of the newborn though the birth canal causes injury to the pelvic floor structures, widening the levator hiatus and stretching of the connective tissue.[32] This might cause pelvic organ downward movement and lead to less vaginal closure force during maximal contraction, modifying the biomechanical mechanism. The present results showed a moderate association between pregnancy and vaginal delivery effects on the size of the levator hiatus, but a stronger negative correlation with MOI, which could therefore be regarded as an alternative measure.

The mechanical effect of pregnancy might induce biomechanical, neurological or neuromuscular changes to the pelvic floor and pelvic organ supports,[33] but the effect of pregnancy itself on pelvic organ support is not well studied. However, the impact of the traumatic event of vaginal delivery is well known.[6] To estimate MOI variation, the regression expression was used (137 871 + [−19 116 × number of vaginal deliveries]) as a means to predict how MOI values would decrease with the increasing number of vaginal deliveries. We were able to say that a women having 3.78 vaginal deliveries has a MOI value of 65 612 mm4, which is, in fact, very close to what we found in our clinically proven POP group (65 505 mm4).

Although MRI is not the routine imaging technique to evaluate pelvic floor dysfunction, the present article aimed to explore the anatomical features of the muscle on high-resolution MRI to obtain a meaningful biomechanical concept that relates MOI to functional and clinical prediction of muscle performance and damage. Similar procedures are being tested by US, which is more commonly carried out, and offers direct anatomical and functional detail.

The present study has certain limitations. First, the sample size was small. Also, MRI is an expensive technique to be used just for this purpose. Second, although POP-Q was used to establish POP diagnosis and staging, the results of the present study should be confirmed by means of dynamic US measures of levator ani and levator hiatus deformation under load. Finally, a larger group and further research are required to confirm the relevance and significance of the present findings.

Future work will focus on MOI measures in different pelvic compartments to establish typical anterior, middle and posterior values; and also to find threshold values for the different POP stages. Furthermore, biomechanical computer-based simulations of contraction and valsalva maneuver will allow to confirm lateral and downward muscle displacement associated with MOI threshold values.

In conclusion, MOI seems to be a reliable measure of POP-related anatomical changes of the pubovisceral muscle morphology. Furthermore, it presented the strongest correlation with demographic and clinical variables.

Conflict of interest

None declared.