On Structure-Function Relationships in the Female Human Urethra: A Finite Element Model Approach

Abstract

Remarkably little is known about urethral striated and smooth muscle and vascular plexus contributions to maintaining continence or initiating micturition. We therefore developed a 3-D, multiphysics, finite element model, based on sequential MR images from a 23-year-old nulliparous heathy woman, to examine the effect of contracting one or more individual muscle layers on the urethral closure pressure (UCP). The lofted urethra turned out to be both curved and asymmetric. The model results led us to reject the current hypothesis that the striated and smooth muscles contribute equally to UCP. While a simulated contraction of the outer (circular) striated muscle increased closure pressure, a similar contraction of the large inner longitudinal smooth muscle both reduced closure pressure and shortened urethral length, suggesting a role in initiating micturition. When age-related atrophy of the posterior striated muscle was simulated, a reduced and asymmetric UCP distribution developed in the transverse plane. Lastly, a simple 2D axisymmetric model of the vascular plexus and lumen suggests arteriovenous pressure plays and important role in helping to maintain luminal closure in the proximal urethra and thereby functional urethral length. More work is needed to examine interindividual differences and validate such models in vivo.

Keywords: Arteriovenous anastomoses; Finite element model; Smooth muscle; Striated muscle; Urethra; Urethral closure pressure; Vascular plexus.

Figure 1.

(a) Left view of an illustration of a mid-sagittal section through of a female urethra. (b, left) Axial mid-urethral actin immunoperoxide histologic section for smooth muscle and (b, right) mirrored trichrome histologic section. (c, left) Axial midurethral MRI with mirrored image of the corresponding trichrome-stained histologic section (c, right).

Figure 2.

Construction of a 3D urethral model of a 23-year-old healthy female urethra taken in vivo from MR scans. (a) Mid-sagittal view with bladder outlined by yellow dashed spline (PB: pubic bone) and (b) a segmented axial view of the urethral sphincter. Dark red, yellow and gray regions show an axial cross section of the circular striated muscle, longitudinal smooth muscle and vascular plexus layers respectively. The bright red cross sign marks the center of the lumen. (c) The 3D model was constructed by lofting axial segmented MRI slices in 3D slicer. A: anterior and P: posterior. (d) The final refined 3D model; the segmented compressor urethrae is not shown in the 3D model and its active contraction is excluded from the simulations. STM: circular striated muscle, CSM: circular smooth muscle, LSM: longitudinal smooth muscle, Muc/Vasc: Vascular plexus and submucosa, DN: Detrusor Neck and TR: Trigonal Ring. Asterisk shows the inner surface of the LSM where the pressures in the quasi-radial direction were recorded by the imaginary intraurethral catheter. The innermost red spline is the coapted epithelium of the urethral lumen. (e) Muscle fibers (striated muscle) or line of action (smooth muscle) for each muscle domain. (f) Example of the curvilinear coordinate system for the LSM layer and (g) mid-axial cross section showing the curvilinear coordinate system in the LSM layer. In the simulations, LSM layer contracts along red axes (lines of action) and the pressures change is measured along blue axes (quasi-radial direction).

Figure 3.

(a) Left lateral view of a mid-sagittal section of a cadaveric female lower urinary tract (©DeLancey). The yellow square represents the region of interest in the proximal urethra immediately inferior to the bladder neck. PB represents pubic bone and EM represents external meatus. (b) 2D axisymmetric window (in the region of interest) of the proximal vascular plexus filled with blood, the epithelium separating the plexus from the urine in the proximal urethra. Arterial (P_a), venous (P_v) and vesical pressures (P_u) are variables that were systematically changed in the FE simulation to explore their effect on the closure pressure and the functional length of the urethra. The effective plexus pressure (P_p) is a dependent pressure between the inlet and outlet pressures which determines the closure pressure. (c) 2D axisymmetric meshed domain partially revolved showing the 1.5 mm thick annular shape of the proximal urethra and its vascular plexus. The closed lumen is shown by the black arrow.

Figure 4.

Distribution of the pressure change on the surface between plexus and LSM layer when the STM fibers contracted in length by 4% from the resting state (left), and the plot of the change in UCP along the urethra for the same STM contraction (right).

Figure 5.

(a) Mid-sagittal and (b) mid-axial cross-section of the urethral musculature tissues showing the quasi-radial principal stretch ratio λ_{quasi−radial} when CSM (red regions) is contracted 7% in length (BN: bladder Neck and EM: external meatus). (c) Distribution of the pressure change on the catheter when only the CSM layer contracted up to 7% in length (${\lambda }_{c_{CSM}}=0.93$). CSM contributed three times less to the UCP than STM when contracted by the same contraction stretch ratio.

Figure 6.

(a) Lateral view of the urethra muscle fibers at rest, and (b) when LSM contracts 20% in length. (c) The overall deformed midsagittal cross section of the urethra when LSM contracts 20%. The black outline represents the resting state. The color distribution represents the overall stretch ratio (resultant of active and mechanical) along the quasi-radial direction (BN: bladder neck and EM: external meatus). (d) The anterior and posterior loci of the intersection of the inner surface of the LSM and mid-sagittal plane shows that the urethra is shortened and moved downward when LSM contracts from the rest state. The anterior mid-urethral region of the LSM did not constrict but stretched out the outer STM instead.

Figure 7.

a) Urethral pressure (change) distribution when STM layer was comprised wholly of contractile fibers contracting up to 7% in length (BN: bladder Neck and EM: external meatus). Each profile is associated with a particular stretch ratio of the STM (${\lambda }_{c_{STM}}$). (b) Mid-sagittal and (c) mid-axial (dashed line) cross section of the urethra muscles showing the principal stress distribution along inward quasi-radial direction when STM contracts 3% in length. (d) Urethral pressure (change) distribution when the horseshoe of STM contracted up to 7% in length. The dorsal region of the STM was modeled as a passive tissue without actively contracting. (e) Mid-axial and (f) mid-sagittal cross section of the urethra muscles showing the principal stress distribution along inward quasi-radial direction when STM contracts 3% in length.

Figure 8.

The pressure distribution at different time intervals across the 1.5 mm × 1.5 mm window of the proximal urethra where the vascular plexus (VP) layer starts. Results reveals that the higher blood pressure distribution in the VP compared to the vesical pressure can increase the functional urethral length and promote a hermetic seal. (a) Urine inside the bladder is shown by the yellow triangular region at top left corner. (a) At t = 0 s the arterial pressure of the vascular plexus (inlet) is increased from the initial value equal to the vesical pressure. (b) As pressure distribution continues to increase across the VP, the epithelial boundary slides proximally (up). This further increase in VP inlet and respectively outlet pressures, increases the functional urethral length (or the left axisymmetric boundary of VP). However, when intra-abdominal pressure suddenly rises during stress events such as cough or lifting a heavy object and if the average pressure across the plexus layer fails to overcome the increased vesical pressure in a stress incontinent patient, the functional urethral length is reduced i.e., the epithelial layer expands and is pushed distally (c). This could initiate a leakage episode.