Two-dimensional computational fluid dynamics study of urine flow in the prostatic fossa after benign prostatic hyperplasia surgery: a single-patient model

Introduction

Benign prostatic hyperplasia (BPH) is a common benign urinary system disease in middle-aged and elderly men. Surgical intervention remains the main treatment for patients with moderate to severe BPH (1). Minimally invasive procedures such as transurethral resection of the prostate (TURP) and laser enucleation have become the preferred clinical options due to their advantages of minimal trauma, less bleeding, and rapid recovery. However, postoperative urinary retention is still a common complication (2). Studies have suggested that the structural morphology of the prostatic fossa after surgery is one of the key factors affecting urinary function (3). Nevertheless, conventional non-invasive imaging techniques such as ultrasound or magnetic resonance imaging (MRI) fail to provide detailed information on the intraluminal urinary flow dynamics. Traditional urodynamic examinations, while capable of evaluating parameters including maximum urinary flow rate (Qmax) and post-void residual volume, cannot directly quantify local hydrodynamic effects in vivo (4).

The clinical puzzle is that variable postoperative fossa geometry—shaped by the extent of resection or enucleation, the configuration of the bladder neck, and preservation of the median lobe—likely drives persistent lower urinary tract symptoms (LUTS), but conventional urodynamics cannot localize the corresponding hydrodynamic disturbance. Computational fluid dynamics (CFD) solve the conservation equations of mass and momentum for a defined geometry and boundary conditions, yielding spatially resolved estimates of pressure, velocity, and turbulence-derived energy loss (5,6). In urology, CFD has been applied to model flow in the ureter, urethra, and prostatic cavity, including idealized post-transurethral-surgery geometries (4,7,8). The metrics used here are: outlet velocity at the external urethral meatus, a surrogate for Qmax under the fixed-inflow assumption; inlet pressure at the bladder neck, reflecting the detrusor pressure required to drive flow; turbulent kinetic energy (TKE), representing local velocity fluctuations; and turbulent dissipation rate (ε), representing the rate at which TKE is converted to heat.

This study employed CFD modeling to systematically determine the pressure distribution and flow velocity characteristics of mid-term micturition under different prostatic urethral diameter ratios after transurethral surgery (9).

Methods

General data

The study enrolled a 63-year-old male patient from Peking University People’s Hospital who underwent prostate MRI for evaluation of BPH. Prostate dimensions were as follows: transverse diameter 5.8 cm, anteroposterior diameter 3.6 cm, craniocaudal diameter 4.0 cm, and prostate volume 43.4 ml. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. This study is a non-invasive CFD simulation using anonymized retrospective imaging data with no identifiable patient information. Ethical approval and informed consent were waived by the Ethics Committee of Peking University People’s Hospital.

Geometric modeling

To investigate the effect of different prostatic urethral diameters on urinary flow after TURP, key structures of the lower urinary tract in elderly men were simplified. The lower urinary tract consists of the bladder neck, prostatic urethra, and the remaining urethra. The prostatic urethra was spatially approximated as a curved ellipsoid, and the urethra as an “S” shape. The spatial relative position and angle between the prostatic urethra and the urethra were determined using sagittal prostate MRI. According to the literature (5), the bladder neck diameter during micturition was set at 1.0 cm, urethral diameter 0.6 cm, longitudinal prostatic urethral diameter 4.0 cm, and length of the remaining urethra 16.4 cm. Two-dimensional modeling was performed using COMSOL Multiphysics 6.1 software (Appendix 1). The closed two-dimensional object was converted into a solid to form a composite domain, distinguishing between solid and fluid domains. Meshing was performed under physical field control. Grid independence was confirmed by comparing outlet velocity across meshes of 11,048, 18,904 and 22,186 elements (difference <2%). A mesh with 11,048 elements was used for subsequent CFD simulations (Figure 1).

Figure 1 Steps of computational fluid dynamics analysis. (A) Sagittal MRI. (B) Prostatic urethra. (C) Two-dimensional simplified model. (D) Solid domain and fluid domain formed after solid conversion. (E) Meshing. (F) Transient study performed. Velocity zone: red = high, light blue = medium, dark blue = low. MRI, magnetic resonance imaging.

Material properties and model setup

Material properties were defined: urine was assumed to be a steady-state, homogeneous, incompressible, and adiabatic Newtonian fluid. At 37 ℃, urine density was set to 1,035 kg/m3 and dynamic viscosity to 0.8583×10−3 Pa·s. The average urinary flow rate in healthy men is 15–25 mL/s. With a bladder neck diameter of 1 cm, the inlet cross-sectional area A = πr2 m2. The calculated inlet velocity at a length of 1 cm was approximately 0.19–0.32 m/s. The inlet boundary condition was set to a normal inflow velocity of 0.25 m/s (equivalent to an average urinary flow rate of 20 mL/s), and the outlet pressure was 0 Pa, representing free outflow to atmosphere and neglecting distal urethral resistance from the external urethral sphincter. The Reynolds number based on the maximum prostatic urethral diameter (1.4 cm) and inlet velocity is Re = ρUD/μ ≈ (1,035 × 0.25 × 0.014)/0.0008583 ≈ 4,221, placing the flow in the transitional-to-turbulent regime (Re spans ~2,412–6,632 across the 0.8–2.2 cm diameter range). The realizable k−ε turbulence model based on the Reynolds-averaged Navier-Stokes (RANS) equation was adopted because it has been used in prior CFD studies of post-transurethral prostatic urethral flow (7) and is well suited to capturing flow separation and recirculation in this transitional-to-turbulent regime (8). A turbulence intensity of 0.05 (5%) was prescribed at the inlet. This value matches the 5% turbulent intensity adopted in a prior CFD study of post-transurethral prostatic urethral flow (7), is consistent with mildly disturbed physiological inflow, and aligns with standard COMSOL defaults for internal flows.

Study design

A transient study was constructed with output time steps set from 0 s to 2 s at 0.1 s intervals. This interval captures the initial flow establishment while keeping file size manageable. A boundary probe was placed at the external urethral orifice to measure the average flow velocity, and another at the bladder neck inlet to measure the average pressure, reflecting resistance changes in the fluid domain. To evaluate the influence of prostatic urethral morphological differences on urinary flow after various transurethral procedures, the prostatic urethral diameter was adjusted from 0.8 to 2.2 cm at 0.2 cm increments, yielding 8 groups: 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, and 2.2 cm. The prostatic urethral diameter ratio is defined as the prostatic urethral diameter divided by the fixed urethral diameter of 0.6 cm. The 0.8–2.2 cm diameters were selected to span the clinical spectrum of postoperative prostatic cavities—from the smaller lumen typical of tissue-sparing TURP to the larger cavity produced by anatomical holmium laser enucleation of the prostate (HoLEP) enucleation. In clinical practice, enucleated cavities can exceed 2.2 cm; however, because the simulations already revealed the diameter-dependent trend within this range (rising inlet pressure and intensified turbulence once the diameter exceeded ~1.4 cm), models with diameters beyond 2.2 cm were not constructed. Identical hydrodynamic simulations were applied to all models. For post-processing, a horizontal cut line was drawn at the midpoint of the prostatic urethra—the cross-section where the prostatic urethral width varies most and where low-velocity recirculation and maximal TKE were observed in pilot runs—to sample TKE (k) and turbulent dissipation rate (ε) along the cavity axis. Line graphs were plotted at 0, 0.3, 0.6, 0.9, 1.2, 1.5, and 1.8 s.

Statistical analysis

Modeling and hydrodynamic simulations were performed using COMSOL Multiphysics 6.1 with the k−ε turbulence model interface. Turbulence was modeled using the standard k−ε two-equation model with realizability constraints, and near-wall flow was modeled using wall functions. Scatter plots of velocity and pressure were generated using RStudio 4.4.2.

Results

CFD simulations were conducted on 8 groups of two-dimensional prostatic urethral models. Model structure and velocity data demonstrated that when the prostatic urethral diameter exceeded 6 mm (i.e., larger than the urethral diameter), the urethra became a high-velocity zone and the prostatic urethra a medium-velocity zone. When the prostatic urethral diameter was smaller than the urethral diameter, the high-velocity zone shifted to the prostatic urethra. When the prostatic urethral diameter further increased to 1.4 cm, a low-velocity zone appeared in the prostatic urethra (Figure 2). In all groups, the external urethral orifice velocity and bladder neck pressure stabilized after 0.02 s (Figure 3).

Figure 2 Model velocity vector diagram. Velocity zone: red = high, light blue = medium, dark blue = low. (A) When the prostatic urethral diameter is 0.4 cm, the prostatic urethra region is a high-velocity zone. (B) When the prostatic urethral diameter is 0.8 cm, the urethra is a high-velocity zone, while the prostatic urethra is a medium-velocity zone. (C,D) When the prostatic urethral diameter is 1.6 cm, the region is in a low-velocity zone, and the velocity field shows reverse-direction arrows, indicating the presence of turbulent flow.

Figure 3 Velocity-time curve when the prostatic urethral diameter is 1.6 cm; velocity stabilizes after 0.02 seconds.

At 2 s, the minimum velocity was 0.5152 m/s, the maximum 0.5180 m/s, the absolute change 0.0028 m/s, and the overall relative change rate 0.54% (Table 1, Figure 4). This magnitude is physiologically negligible and indicates that, under constant inlet velocity, prostatic urethral diameter has little effect on outlet flow rate. The average inlet pressure at 2 s first decreased and then increased with increasing prostatic urethral diameter, reaching the lowest value of 292.5 Pa at 1.4 cm (Figure 5).

Figure 4 Scatter plot of prostatic urethral diameter versus mean flow velocity at the external urethral orifice at 2 seconds.

Figure 5 Scatter plot of prostatic urethral diameter versus average inlet pressure; the lowest pressure occurs at a prostatic urethral diameter ratio of 2.33.

Turbulence occurred above a prostatic urethral diameter of 1.4 cm, located in the low-velocity zone of the prostatic fossa. Turbulence intensity, TKE (k), and turbulent dissipation rate (ε) peaked at 0.6 s, after which turbulence gradually stabilized (Figures 6,7). Larger prostatic urethral diameters were associated with longer stabilization times, higher TKE, and higher turbulent dissipation rate.

Figure 6 Spatial distributions of turbulent kinetic energy and turbulent dissipation rate along the mid-prostatic cross-sectional line for each model group. (A) Prostatic urethral diameter 0.8 cm. (B) Prostatic urethral diameter 1.0 cm. (C) Prostatic urethral diameter 1.2 cm. (D) Prostatic urethral diameter 1.4 cm. (E) Prostatic urethral diameter 1.6 cm. (F) Prostatic urethral diameter 1.8 cm. (G) Prostatic urethral diameter 2.0 cm. (H) Prostatic urethral diameter 2.2 cm.

Figure 7 Time-series line plots of turbulent kinetic energy and dissipation rate along the mid-prostatic-urethral cut line.

Discussion

The primary goal of transurethral surgical procedures—including TURP, enucleation, prostate suspension and dilation, and transurethral vaporization of the prostate—is to relieve bladder outlet obstruction (BOO) secondary to BPH. The key underlying mechanism does not depend on the extensive removal of prostatic tissue, but instead on restoring the physiological luminal morphology of the prostatic urethra to optimize urodynamic function. Clinical evidence has consistently shown that significant improvement in LUTS can be achieved even when the volume of resected tissue constitutes less than half of the total prostate volume. This observation strongly supports the conclusion that restoring urethral patency and normal luminal geometry is more critical than merely reducing prostatic gland volume (6,9,10).

For decades, TURP has been regarded as the gold standard for medically refractory BPH. With the evolution of tissue morcellators and energy platforms, HoLEP was introduced as an effective alternative to TURP and has gradually emerged as a new gold standard in surgical management of BPH (11). Compared with conventional TURP, transurethral enucleation techniques indeed remove more prostatic tissue, thereby creating a larger prostatic urethral diameter anatomically (2,12). However, current clinical evidence has not definitively established a direct causal relationship between a larger prostatic urethral diameter and superior voiding outcomes. Moreover, some literature suggests that enucleation procedures result in a relatively large prostatic cavity postoperatively, and it has been hypothesized that this structural alteration may induce turbulent flow, potentially exerting adverse effects on urination (2,13). Despite this theoretical concern, existing clinical studies have not consistently demonstrated a significant negative impact of turbulence on voiding outcomes.

To directly observe the urodynamic characteristics within the prostatic urethra and perform actual measurements, current invasive and non-invasive urodynamic assessment methods are insufficient for precise and comprehensive evaluation. CFD, a simulation technique that solves the governing partial differential equations of fluid conservation laws using computers, has been widely applied in industrial engineering. Owing to its non-invasive nature, high fidelity, and reproducibility, CFD offers a superior approach for analyzing physiological and pathological functions within biological lumens in the biomedical field, although its predictions remain simulated estimates that require experimental or clinical validation.

To balance model accuracy and computational efficiency, this study simplified the three-dimensional model into a two-dimensional one. Analyzing of the velocity and pressure characteristics showed that, at a constant inlet velocity, the outlet velocity at the external urethral meatus increased only minimally with increasing prostatic urethral diameter (relative change, ΔV =0.54%), which is clinically negligible. When the prostatic urethral diameter exceeded 1.4 cm, turbulence occurred at the dorsal aspect of the median lobe within the prostatic cavity—a structure formed after BPH surgery. In TURP, the median lobe tissue is often preserved, resulting in a gentle slope from the bladder neck to just anterior to the verumontanum. In contrast, enucleation procedures follow the surgical capsule of the prostate, and the size of the resulting cavity is positively correlated with the volume of the removed adenoma, typically yielding a larger cavity than TURP. This comparison hypothetical in the present idealized model and should be tested in patient-specific three-dimensional reconstructions of actual TURP and HoLEP fossae.

In this study, under constant inlet velocity, urine passing through the prostatic urethra did not reduce the outlet velocity at the external meatus; the 0.54% change is clinically negligible. The low-velocity turbulent regions within the prostatic urethra dissipate kinetic energy before merging into the mid-velocity mainstream. The pressure difference between the inlet and the outlet (set at 0 Pa) indirectly reflects the resistance within the fluid domain. In the absence of turbulence, a larger prostatic urethral diameter corresponded to lower inlet boundary pressure—meaning less bladder contractile force was required to maintain the inlet velocity of 0.25 m/s. However, once turbulence emerged (i.e., when the prostatic urethral diameter exceeded 1.4 cm), further increases in diameter led to higher inlet boundary pressure, demanding greater bladder contractile effort to sustain the same inlet velocity. Although this pressure rise beyond 1.4 cm was modest (≈1.8% at the largest diameter of 2.2 cm), it indicates increased flow resistance; in patients with reduced detrusor contractility, even a small resistance increment may impair effective voiding, although this inference remains to be validated clinically. Because voiding in vivo occurs under variable detrusor pressure rather than fixed flow, these observations should be interpreted as hypothesis-generating rather than proof of clinical harm.

Analysis of turbulent spatial distribution along the cross-section of the prostatic cavity showed that no turbulence formed in models with prostatic urethral diameters of 0.8, 1.0, and 1.2 cm. Turbulence was observed in all other five models, consistently located at the dorsal aspect of the median lobe within the prostatic cavity. TKE increased with larger prostatic urethral diameters, indicating a positive correlation between turbulence intensity and cavity size. Additionally, larger cavities required longer time for turbulence to stabilize and exhibited higher turbulent dissipation rates. Under constant inlet velocity, this energy loss due to turbulence manifested as elevated inlet boundary pressure. Conversely, under constant inlet pressure, such energy loss would translate into reduced outlet velocity—i.e., decreased urinary flow rate. A fixed-pressure simulation was not performed here and is an important direction for future work.

In this study, the lowest inlet pressure—and thus the minimal flow resistance across the entire domain—occurred when the prostatic urethral diameter was 1.4 cm (corresponding to a diameter ratio of 2.33). This suggests that, under the constant-flow assumption, enlarging the prostatic urethral diameter beyond a ratio of 2.33 may increase the pressure required to maintain voiding. Whether this ratio translates into superior clinical outcomes requires prospective validation in patient-specific three-dimensional models and correlation with urodynamic parameters such as Qmax and detrusor pressure at Qmax.

This study has several important limitations. Notably, like all CFD studies, the present predictions have not been validated against direct intraurethral flow measurements, so the reported pressures and velocities are simulated estimates rather than in vivo measurements. First, it is based on a single patient’s MRI, so the geometry, angle, and diameter-specific findings cannot be generalized. Second, the model is two-dimensional and idealized; it neglects the asymmetric, three-dimensional anatomy of the prostatic fossa and cannot capture out-of-plane velocities or secondary flows. Third, the realizable k−ε model was used in a transitional-to-turbulent regime; although the realizable k−ε model is appropriate for the turbulent portion, the smaller-diameter cases approach the transitional regime and the predicted turbulence was not benchmarked against laminar or k−ω SST simulations. Fourth, boundary conditions were simplified: a fixed inlet velocity and zero outlet pressure were used, ignoring the dynamic detrusor contraction, external sphincter resistance, and abdominal pressure variations of real voiding. Fifth, no direct experimental or intraurethral validation was performed; CFD provides simulated estimates, not in vivo measurements. Finally, the clinical relevance of small pressure differences and negligible outlet-velocity changes is uncertain. These findings should therefore be viewed as hypothesis-generating and as a basis for larger, patient-specific three-dimensional studies.

Conclusions

Using a single-patient, two-dimensional CFD model, we found that widening the postoperative prostatic urethra above 1.4 cm (diameter ratio ≥2.33) introduced TKE in the prostatic fossa and a small rise in the inlet pressure needed to sustain constant flow, with the lowest inlet pressure occurring at a diameter ratio of 2.33. These findings suggest that an over-enlarged fossa shifts voiding into a turbulent, energy-dissipating regime, offering a mechanistic explanation for persistent LUTS after transurethral prostate surgery. As a preliminary, constant-inflow, single-patient simulation, they require validation in larger cohorts with patient-specific three-dimensional anatomy and urodynamic correlation before any diameter ratio can inform surgical planning.

Acknowledgments

During the preparation of this manuscript, the authors used COMSOL Multiphysics 6.1 for computational fluid dynamics simulation and data analysis, and RStudio 4.4.2 for statistical analysis and graph plotting. The authors have reviewed and edited the output and take full responsibility for the content of this publication.

A preliminary version of this study was presented at the 5th USANZ Functional Urology Symposium & 20th Pan-Pacific Continence Society Annual Meeting (Sydney, Australia; 2026).

Footnote

Data Sharing Statement: Available at https://tau.amegroups.com/article/view/10.21037/tau-2026-0434/dss

Peer Review File: Available at https://tau.amegroups.com/article/view/10.21037/tau-2026-0434/prf

Funding: This work was supported by the Science and Technology Plan Project of Tongzhou District, Beijing (grant No. KJ2024CX059).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://tau.amegroups.com/article/view/10.21037/tau-2026-0434/coif). The authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. This study is a non-invasive computational fluid dynamics simulation using anonymized retrospective imaging data with no identifiable patient information. Ethical approval and informed consent were waived by the Ethics Committee of Peking University People’s Hospital.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

References

1. Tascı AI, Ilbey YO, Tugcu V, et al. Transurethral resection of the prostate with monopolar resectoscope: single-surgeon experience and long-term results of after 3589 procedures. Urology 2011;78:1151-5. [Crossref] [PubMed]
2. Castellani D, Akand M, Giulioni C, et al. Incidence of Acute Urinary Retention/Failure to Void after Transurethral Interventions for Benign Prostatic Enlargement: Results from a Systematic Review and Meta-Analysis of Comparative Randomized Studies by the FUTURE Collaborative of the Endourological Society. J Endourol 2026;40:726-45. [Crossref] [PubMed]
3. Ishii T, Kambara Y, Yamanishi T, et al. Urine Flow Dynamics Through Prostatic Urethra With Tubular Organ Modeling Using Endoscopic Imagery. IEEE J Transl Eng Health Med 2014;2:1800709. [Crossref] [PubMed]
4. Bhojani N, Bidair M, Kramolowsky E, et al. Aquablation Therapy in Large Prostates (80-150 mL) for Lower Urinary Tract Symptoms Due to Benign Prostatic Hyperplasia: Final WATER II 5-Year Clinical Trial Results. J Urol 2023;210:143-53. [Crossref] [PubMed]
5. Tojo M, Yasuda K, Yamanishi T, et al. Relationship between bladder neck diameter and hydraulic energy at maximum flow. J Urol 1994;152:144-9. [Crossref] [PubMed]
6. Creta M, Russo GI, Bhojani N, et al. Bladder Outlet Obstruction Relief and Symptom Improvement Following Medical and Surgical Therapies for Lower Urinary Tract Symptoms Suggestive of Benign Prostatic Hyperplasia: A Systematic Review. Eur Urol 2024;86:315-26. [Crossref] [PubMed]
7. Zhang B, Liu S, Liu Y, et al. Novel CFD modeling approaches to assessing urine flow in prostatic urethra after transurethral surgery. Sci Rep 2021;11:663. [Crossref] [PubMed]
8. Wang X, Liu P, Zhao S, et al. Dynamic simulation and analysis of the influence of urethral morphological changes on urodynamics after benign prostatic hyperplasia surgery: A computational fluid dynamics study. Comput Methods Programs Biomed 2024;243:107915. [Crossref] [PubMed]
9. Tamalunas A, Keller P, Schott M, et al. Propensity score-matched evaluation of palliative transurethral resection and holmium laser enucleation of the prostate for bladder outlet obstruction in patients with prostate cancer. Prostate Cancer Prostatic Dis 2025;28:153-9. [Crossref] [PubMed]
10. Lerner LB, McVary KT, Barry MJ, et al. Management of Lower Urinary Tract Symptoms Attributed to Benign Prostatic Hyperplasia: AUA GUIDELINE PART II-Surgical Evaluation and Treatment. J Urol 2021;206:818-26. [Crossref] [PubMed]
11. Shvero A, Calio B, Humphreys MR, et al. HoLEP: the new gold standard for surgical treatment of benign prostatic hyperplasia. Can J Urol 2021;28:6-10. [PubMed]
12. Vo LT, Armany D, Chalasani V, et al. Endoscopic enucleation of the prostate versus transurethral resection of the prostate for benign prostatic hyperplasia: a systematic review and meta-analysis. Prostate Cancer Prostatic Dis 2025;28:845-58. [Crossref] [PubMed]
13. Wei JT, Dauw CA, Brodsky CN. Lower Urinary Tract Symptoms in Men: A Review. JAMA 2025;334:809-21. [Crossref] [PubMed]