The shape of the urine stream--from biophysics to diagnostics

Is the time right for a new initiative in mathematical modeling of the lower urinary tract? ICI-RS 2023

INTRODUCTION

A session at the 2023 International Consultation on Incontinence - Research Society (ICI-RS) held in Bristol, UK, focused on the question: Is the time right for a new initiative in mathematical modeling of the lower urinary tract (LUT)? The LUT is a complex system, comprising various synergetic components (i.e., bladder, urethra, neural control), each with its own dynamic functioning and high interindividual variability. This has led to a variety of different types of models for different purposes, each with advantages and disadvantages.

METHODS

When addressing the LUT, the modeling approach should be selected and sized according to the specific purpose, the targeted level of detail, and the available computational resources. Four areas were selected as examples to discuss: utility of nomograms in clinical use, value of fluid mechanical modeling, applications of models to simplify urodynamics, and utility of statistical models.

RESULTS

A brief literature review is provided along with discussion of the merits of different types of models for different applications. Remaining research questions are provided.

CONCLUSIONS

Inadequacies in current (outdated) models of the LUT as well as recent advances in computing power (e.g., quantum computing) and methods (e.g., artificial intelligence/machine learning), would dictate that the answer is an emphatic "Yes, the time is right for a new initiative in mathematical modeling of the LUT."

Fluid Ejections in Nature

From microscopic fungi to colossal whales, fluid ejections are universal and intricate phenomena in biology, serving vital functions such as animal excretion, venom spraying, prey hunting, spore dispersal, and plant guttation. This review delves into the complex fluid physics of ejections across various scales, exploring both muscle-powered active systems and passive mechanisms driven by gravity or osmosis. It introduces a framework using dimensionless numbers to delineate transitions from dripping to jetting and elucidate the governing forces. Highlighting the understudied area of complex fluid ejections, this review not only rationalizes the biophysics involved but also uncovers potential engineering applications in soft robotics, additive manufacturing, and drug delivery. By bridging biomechanics, the physics of living systems, and fluid dynamics, this review offers valuable insights into the diverse world of fluid ejections and paves the way for future bioinspired research across the spectrum of life.

Fluid ejections in nature

From microscopic fungi to colossal whales, fluidic ejections are a universal and intricate phenomenon in biology, serving vital functions such as animal excretion, venom spraying, prey hunting, spore dispersal, and plant guttation. This review delves into the complex fluid physics of ejections across various scales, exploring both muscle-powered active systems and passive mechanisms driven by gravity or osmosis. We introduce a framework using dimensionless numbers to delineate transitions from dripping to jetting and elucidate the governing forces. Highlighting the understudied area of complex fluid ejections, this work not only rationalizes the biophysics involved but also uncovers potential engineering applications in soft robotics, additive manufacturing, and drug delivery. By bridging biomechanics, the physics of living systems, and fluid dynamics, this review offers valuable insights into the diverse world of fluid ejections and paves the way for future bioinspired research across the spectrum of life.

A Velocity-Based Approach to Noninvasive Methodology for Urodynamic Analysis

PURPOSE

To date, invasive urodynamic investigations have been used to define most terms and conditions relating to lower urinary tract symptoms. This invasiveness is almost totally due to the urethral catheter. In order to remove this source of discomfort for patients, the present study investigated a noninvasive methodology able to provide diagnostic information on bladder outlet obstruction or detrusor underactivity without any contact with the human body.

METHODS

The proposed approach is based on simultaneous measurements of flow rate and jet exit velocity. In particular, the jet exit kinetic energy appears to be strongly related to bladder pressure, providing useful information on the lower urinary tract functionality. We developed a new experimental apparatus to simulate the male lower urinary tract, thus allowing extensive laboratory activities. A large amount of data was collected regarding different functional statuses.

RESULTS

Experimental results were compared successfully with data in the literature in terms of peak flow rate and jet exit velocity. A new diagram based on the kinetic energy of the exit jet is proposed herein. Using the same notation as a Schäfer diagram, it is possible to perform noninvasive urodynamic studies.

CONCLUSION

A new noninvasive approach based on the measurement of jet exit kinetic energy has been proposed to replace current invasive urodynamic studies. A preliminary assessment of this approach was carried out in healthy men, with a specificity of 91.5%. An additional comparison using a small sample of available pressure-flow studies also confirmed the validity of the proposed approach.

Design of a novel midstream fluid waste sample collection device for patients

Reducing the contamination rates in mid-stream urine samples is a challenge. A novel design for a mid-stream urine sample collection device, which uses a novel mechanism to separate the mid-stream flow from the fore-stream and end-stream flows based on flow speed, is presented. The device, supplied in two parts, is designed to be clipped to a toilet and used in a seated position, which improves ease of use for disabled patients. As there is no mixing of the flow types during use, it is hypothesised that contamination rates should be lower than many competing designs. The all-polymer design is easy to use by both men and women, due to the addition of a form-fitting funnel and is designed to collect samples directly into containers of the same standard currently issued, allowing easy and hygienic collection. Due to its complex shape, the main body of the device is produced by a non-conventional injection moulding process. The holder can be produced using standard injection moulding technology. The two parts are designed to be assembled together by the user by means of a simple interference fit, which removes the cost of assembly altogether.

Novel CFD modeling approaches to assessing urine flow in prostatic urethra after transurethral surgery

Assessment of the pressure and velocity of urine flow for different diameter ratios of prostatic urethra (RPU) after transurethral surgery using computational fluid dynamics (CFD). A standardized and idealized two-dimensional CFD model after transurethral surgery (CATS-1st) was developed for post-surgery mid-voiding. Using CATS-1st, 210 examples were amplified according to an array of size [3][5][14], which contained three groups of longitudinal diameters of prostatic urethra (LD-PU). Each of these groups contained five subgroups of transverse diameters of the bladder neck (TD-BN), each with 14 examples of transverse diameters of PU (TD-PU). The pressure and velocity of urine flow were monitored through flow dynamics simulation, and the relationship among RPU-1 (TD-PU/TD-BN), RPU-2 (RPU-1/LD-PU), the transverse diameter of the vortex, and the midpoint velocity of the external urethral orifice (MV-EUO) was determined. A total of 210 CATS examples, including CATS-1st examples, were analyzed. High (bladder and PU) and medium/low (the rest of the urethra) pressure zones, and low (bladder), medium (PU), and high (the rest of the urethra) velocity zones were determined. The rapid changes in the velocity were concentrated in and around the PU. Laminar flow was present in all the examples. The vortices appeared and then gradually shrank with reducing RPU on both the sides of PU in 182 examples. In the vortex examples, minimum RPU-1 and RPU-2 reached close to the values of 0.79 and 0.02, respectively. MV-EUO increased gradually with decreasing RPU. In comparison to the vortex examples, the non-vortex examples exhibited a significantly higher (p < 0.01) MV-EUO. The developed CFD models (CATS) presented an effective simulation of urine flow behavior within the PU after transurethral surgery for benign prostatic hyperplasia (BPH). These models could prove to be useful for morphological repair in PU after transurethral surgery.

Novel measurement tool and model for aberrant urinary stream in 3D printed urethras derived from human tissue

Background

An estimated 10% of male adults have split or dribbled stream leading to poor hygiene, embarrassment, and inconvenience. There is no current metric that measures male stream deviation.

Objective

To develop a novel method to measure spray in normal and abnormal anatomical conformations.

Design, setting, and participants

We developed a novel platform to reliably describe spray. We used cadaveric tissues and 3D Printed models to study the impact of meatal shape on the urinary stream. Cadaveric penile tissue and 3D printed models were affixed to a fluid pump and used to simulate micturition. Dye captured on fabric allowed for spray detection.

Outcome measurements and statistical analysis

Spray pattern area, deviation from normal location, and flowrates were recorded. Computational fluid dynamic models were created to study fluid vorticity.

Results and limitations

Obstructions at the penile tip worsened spray dynamics and reduced flow. Ventral meatotomy improved flowrate (p<0.05) and reduced spray (p<0.05) compared to tips obstructed ventrally, dorsally or in the fossa navicularis. 3D models do not fully reproduce parameters of their parent cadaver material. The average flowrate from 3D model was 10ml/sec less than that of the penis from which it was derived (p = 0.03). Nonetheless, as in cadavers, increasing obstruction in 3D models leads to the same pattern of reduced flowrate and worse spray. Dynamic modeling revealed increasing distal obstruction was correlated to higher relative vorticity observed at the urethral tip.

Conclusions

We developed a robust method to measure urine spray in a research setting. Dynamic 3D printed models hold promise as a methodology to study common pathologies in the urethra and corrective surgeries on the urine stream that would not be feasible in patients. These novel methods require further validation, but offer promise as a research and clinical tool.

"Fossa navicularis" and "septum glandis": A "flow-control chamber" for the male urethra?

A clear understanding of the normal anatomy of the glanular urethra is essential for anatomical reconstruction of the male urethra. In hypospadias surgery, tubularization of the neourethra over a catheter or stent has been the standard method for decades. However, the male urethra is not a tubular structure with uniform configuration and diameter by forming a fossa (navicularis) in the glans penis. We recently investigated the structural anatomy of the glanular urethra using magnetic resonance imaging (MRI). We have shown that the male urethra does not have a uniform tubular structure and not covered by the corpus spongiosum to the end. The glanular urethra that forms the "fossa navicularis" has a wider caliber than the proximal urethra. Its vertical elliptical shape resembles a laterally compressed slit-like passage. The fossa navicularis is covered by a thin layer of fibrous tissue ("septum glandis") which is an extension of tunica albuginea of the corpus cavernosum and the corpus spongiosum. Our hypothesis is based on the results of MRI of the glanular urethra and the basic principles of fluid dynamics. We analyzed the flow dynamics of urine on this particular component of the urethra in terms of shape and structural properties. Because of its wider caliber than the proximal urethra, the glanular urethra (fossa navicularis) should cause an increase in pressure and a decrease in velocity of the urine flow. The navicular shape of the fossa and its elliptical external opening (the meatus) should allow urine to be expelled at higher flow rates and at opposite angles at the upper and lower corners which make the wave-like shape of the urine. It can be said that the changes in the volumetric form, pressure and velocity, as well as the wave-like shape of the urine flow are caused by the "fossa navicularis" covered by the "septum glandis". We propose that the "fossa navicularis" and "septum glandis" play a role as 'flow control chamber" in controlling the flow of the urine exiting the urethra, which must be taken into account for successful functional reconstruction of hypospadias.

Flow resistive forces index (QRF): Development and clinical applicability assessment of a novel measure of bladder outlet resistance, aiming to enhance the diagnostic performance of uroflowmetry

BACKGROUND

Currently, the diagnostic ability of uroflowmetry, the most widely used urodynamic test available for initial assessment of patients with lower urinary tract symptoms (LUTS), is considered limited by its inability to accurately discriminate between the underlying mechanisms of this condition. To improve the diagnostic accuracy of uroflow, we developed a mathematical formula that calculates the flow resistive forces index (QRF), a novel measure of bladder outflow/urethral resistance, and assessed its clinical applicability compared to the maximum flow rate (Q_max ).

MATERIALS AND METHODS

A cross-sectional observational study was conducted in a cohort of 61 adult men presenting with voiding dysfunction symptoms, who all underwent free uroflowmetry followed by pressure flow study. The development of the mathematical formula which contains five key uroflowmetry variables (voided volume, flow time, Q_max , average flow rate, and peak flow time) was based on the assumption that urine volume momentum changes during voiding, the concept of diphasic uroflow pattern (acceleration/deceleration), and the urethral resistance factor (URA) equation. Study subjects were classified either as obstructed or nonobstructed according to established urodynamic criteria (linearized passive urethral resistance relation, LinPURR; Abrams-Griffiths number, AGN [also called bladder outlet obstruction index, BOOI]; and URA). Univariate linear correlations, binary logistic regression model, and receiver operating characteristic (ROC) curve statistical analysis were employed (SPSS-22, MedCalc, GraphPad [P < .05]).

RESULTS

Outflow obstruction was diagnosed in 50.8% (1 in 2) patients. Univariate analysis, and bivariate linear correlation, binary logistic regression, and ROC curve analyses showed that the QRF was a strong independent predictor of bladder outlet/outflow obstruction (BOO), significantly outperforming Q_max .

CONCLUSIONS

QRF index accurately predicts BOO, significantly outperforming the currently widely used bladder outlet obstruction estimator Q_max . Despite potential study limitations (mainly small cohort size and lack of control group), we anticipate that with further study and proper clinical validation, QRF could become a valuable complement to uroflowmetry.

Vorticity in lower urinary tract can be assessed and associates with urinary tract morphology in men

OBJECTIVES

The aim of this study is to develop a method to evaluate the fluid dynamics of urine flow in the lower urinary tract (LUT), especially that of vorticity.

MATERIALS AND METHODS

This investigation included three sub-studies to demonstrate urine flow in the entire LUT. First, we attempted to observe vorticity generation in the urinary bladder during spontaneous voiding using transabdominal color Doppler ultrasonography (CDUS). Second, we performed transrectal CDUS to evaluate the vorticity of urine flow in the prostatic urethra. Patients with prostate cancer were enrolled before robotic surgery and divided into the vorticity and non-vorticity groups based on CDUS findings for comparisons of longitudinal urethral diameter and prostatic urethral angle. Third, the vorticity of the voided urine stream was observed using a high-speed video-camera. Micturition was done in a standing position while synchronously monitored for urine flow using uroflowmetry.

RESULTS

Vorticity formation could be dynamically demonstrated in the urinary bladder and prostatic urethra using CDUS. The prostatic urethral angle of the vorticity group was more than that of the non-vorticity group. High-speed video recording could clearly capture vorticity and spiral shape generation in voided urine. The distance from the external urethral orifice to the first twist changed in accordance with urine flow rate.

CONCLUSIONS

In a series of sub-studies, this investigation proved vorticity generation in the LUT and voided urine. Vorticity was detectable in the LUT and in voided urine using CDUS and a high-speed video-camera. Vorticity generation might be associated with urethral morphology.

Glans wings are separated ventrally by the septum glandis and frenulum penis: MRI documentation and surgical implications

Objective

In the normal human penis, the glans wings are in apposition in the midline ventrally, and are separated by the "septum glandis" and "frenulum" of the prepuce. However, most of the hypospadias repair techniques include dissection of the glans wings and their approximation enclosing the neourethra within the glans.

Material and methods

In order to obtain detailed information about the normal anatomy of glans penis, magnetic resonance imaging (MRI) findings of the penis were studied in three adults. Transverse, and sagittal sections of the penis were performed with a 1.5-T MRI scanner.

Results

The present MRI study has confirmed that the glans wings do not fuse at the ventral midline and they are seperated by a fibrous tissue (septum glandis). This fibrous tissue is connected to the frenulum, traversing the wings of the glans penis. The glanular urethra forming the fossa navicularis has a wider caliber than the proximal urethra, and its walls are radiologically seen as the extension of that fibrous tissue.

Conclusion

The male urethra is not a uniform tubular structure and has distinct attachments in glans penis. The glans wings are separated ventrally by the septum glandis and frenulum. In hypospadias, the septum glandis and frenulum are entirely missing structures. Therefore, in hypospadias surgery, the anatomical features of the glanular urethra must be taken into consideration.

Hypospadias repair with the glanular-frenular collar (GFC) technique

BACKGROUND

In the normal human penis, the glans wings merge in the midline ventrally, but are separated by the 'septum glandis' in conjunction with the frenulum. The frenulum is also included in the formation of the distal (glanular and subcoronal) urethra, which has a special part known as the 'fossa navicularis'. This has inspired a hypospadias repair technique that simulates the development of the glanular and subcoronal urethra, which can be incorporated into the repair of all cases of hypospadias.

MATERIAL AND METHOD

A total of 121 patients with varying degrees of hypospadias underwent surgery with the described technique: a Y-V plasty was used to dissect the inner foreskin, in a fashion that allowed for its ventral mobilization as a frenular mucosal collar. After tubularization of the proximal urethra, a partial spongioplasty was performed that extended up to the subcoronal level. The glans wings were approximated only at their outermost convexities, with a couple of subepithelial sutures, leaving a slit for the meatus. The cleft-like area between the split wings of the glans penis was filled with the terminal ends of the spongiosum and the dartos of the mucosal collar, which converged to form a septum and a neo-frenulum (glanular-frenular collar, GFC). The midline skin closure of the ventral collar and the circumferential foreskin closure was completed as usual.

RESULTS

At a mean follow-up of 10 months, two patients developed urethral fistula (2%), six had meatal stenosis (5%), and two had glans dehiscence (2%) that resulted in meatal retraction. Overall, patients had a cosmetically satisfying appearance (Figure). Forty-one received secondary circumcision; the parents of 80 (66%) patients were satisfied with the final foreskin appearance obtained with this method.

DISCUSSION

The split wings of the glans penis or so-called ventral cleft between the glans wings that accommodate the frenulum is part of normal anatomy. Hence, in hypospadias surgery, the approximated glans wings should allow for ventral support of the glanular and subcoronal urethra through a reconstructed neo-frenulum. Neither glanular surface enhancement nor extensive dissection of the glans wings and their full-length approximation are necessary, and may in fact be counter-productive.

CONCLUSIONS

The employment of a GFC provided: 1) an anatomical restoration of the distal (glanular and subcoronal) urethra, supported by a frenulum; 2) a protective (undissected) dartos layer over the distal part of the tubularized neourethra; and 3) a space for the re-formation of the fossa navicularis.

Duration of urination does not change with body size

Many urological studies rely on models of animals, such as rats and pigs, but their relation to the human urinary system is poorly understood. Here, we elucidate the hydrodynamics of urination across five orders of magnitude in body mass. Using high-speed videography and flow-rate measurement obtained at Zoo Atlanta, we discover that all mammals above 3 kg in weight empty their bladders over nearly constant duration of 21 ± 13 s. This feat is possible, because larger animals have longer urethras and thus, higher gravitational force and higher flow speed. Smaller mammals are challenged during urination by high viscous and capillary forces that limit their urine to single drops. Our findings reveal that the urethra is a flow-enhancing device, enabling the urinary system to be scaled up by a factor of 3,600 in volume without compromising its function. This study may help to diagnose urinary problems in animals as well as inspire the design of scalable hydrodynamic systems based on those in nature.