Urine flow curves of healthy males: a mathematical model of bladder and urethal function during micturition

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Inadequacies in current (outdated) models of the LUT as well as recent advances in computing power (e.g., quantum computing) and methods (e.g., artificial intelligence/machine learning), would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."

Mathematical modeling of the lower urinary tract: A review

AIMS

Understand what progress has been made toward a functionally predictive lower urinary tract (LUT) model, identify knowledge gaps, and develop from them a path forward.

METHODS

We surveyed prominent mathematical models of the basic LUT components (bladder, urethra, and their neural control) and categorized the common modeling strategies and theoretical assumptions associated with each component. Given that LUT function emerges from the interaction of these components, we emphasized attempts to model their connections, and highlighted unmodeled aspects of LUT function.

RESULTS

There is currently no satisfactory model of the LUT in its entirety that can predict its function in response to disease, treatment, or other perturbations. In particular, there is a lack of physiologically based mathematical descriptions of the neural control of the LUT.

CONCLUSIONS

Based on our survey of the work to date, a potential path to a predictive LUT model is a modular effort in which models are initially built of individual tissue-level components using methods that are extensible and interoperable, allowing them to be connected and tested in a common framework. A modular approach will allow the larger goal of a comprehensive LUT model to be in sight while keeping individual efforts manageable, ensure new models can straightforwardly build on prior research, respect potential interactions between components, and incentivize efforts to model absent components. Using a modular framework and developing models based on physiological principles, to create a functionally predictive model is a challenge that the field is ready to undertake.

Age is associated with reduced urethral pressure and afferent activity in rat

Age-related changes in the lower urinary tract (LUT) can affect the coordination of reflexes and increase the incidence of bladder disorders in elderly. This study examines the age-related loss of urethral signaling capability by measuring the afferent activity directly. We find that less urethral pressure develops in response to fluid flow in old rats compared to young rats and that pressure and flow evoke less urethral afferent activation. These findings are consistent with our previous study demonstrating that the urethra-to-bladder reflex, which is required for efficient voiding, becomes weaker with age. We measured the pudendal afferent response in young (4-7 months) and old (18-24 months) rats to fluid flow in the urethra across a range of flow rates. We used paraffin embedding and hematoxylin and eosin staining to quantify age-related changes in the sensory branch of the pudendal nerve. Urethral afferent signaling in response to the same urethral flow rates was weaker in older animals. That is, the sensitivity of urethra afferents to flow decreased with age, and higher flow rates were required in older animals to recruit urethra afferents. There was also a reduction in the myelin thickness of pudendal afferents in old rats, which is a possible contributing factor to the sensory activity. Furthermore, the same flow rates evoked less pressure in the urethras of old animals, indicating there is an age-related change of the urethral tissue that reduces the pressure stimulus to which these afferents respond. These results help characterize the underlying changes in LUT system with age.

Risk factors for stress urinary incontinence after native-tissue vaginal repair of pelvic organ prolapse

OBJECTIVE

To identify risk factors for postoperative stress urinary incontinence (POSUI) after native-tissue prolapse repair without a concomitant anti-incontinence procedure.

METHODS

The present single-center retrospective study included women with genital prolapse who underwent high uterosacral ligament suspension without a concomitant anti-incontinence procedure during 2008-2013. Univariate and multivariate analyses were performed to identify risk factors for POSUI (identified through clinical interview and International Consultation on Incontinence Modular Questionnaire-Short Form [ICIQ-SF] self-administration) at 6 months.

RESULTS

In total, 87 (20.9%) of 417 women developed POSUI. Preoperative stress urinary incontinence (SUI) and urodynamically diagnosed SUI were significantly associated with POSUI; moreover, women with POSUI had a higher preoperative ICIQ-SF score, a lower opening detrusor pressure, and a lower detrusor pressure at maximum flow than did women without POSUI (P<0.05 for all comparisons). In the multivariate analysis, preoperative SUI (odds ratio 3.11), a detrusor pressure at maximum flow of less than 30 cm H₂ O (odds ratio 2.93), and urodynamically diagnosed SUI (odds ratio 2.26) were independent risk factors for POSUI.

CONCLUSION

Preoperative urodynamic parameters, obtained before prolapse repair surgery, were associated with POSUI and could be useful in providing adequate counseling to facilitate decision making on whether to add a concomitant anti-incontinence procedure.

Clinically relevant modeling of urodynamics function: the VBN model

BACKGROUND

For the past two decades, a mathematical model of micturition was built step by step. Fundamental studies, presentations of the model and several applications to various male and female lower urinary tract dysfunctions have been published. We expect now that other teams will be interested in using it. In order to do so, a VBN pack (software in Linux and tutorial) is freely available.

AIMS

The purpose of this review is to describe the model and to show its practical usefulness.

MATERIALS AND METHODS

After a short description of the basis of the model and of how to use it, some published applications were summed up. The main application of the VBN model is to obtain a coherent modelling for a given patient from a set of several recordings (free uroflows and pressure-flow study) obtained either during the same session or in follow up.

RESULTS

This experience gradually led us to study what information could be extracted from a free uroflow. In addition, the model is valuable to quickly compute the effect of some additional condition; thus, it can predict the effect of an experimental artefact (urethral catheter, penile cuff).

CONCLUSION

Because the process of fitting model computations and real recordings is a powerful way to detect unexpected phenomena, the use of the VBN model provides a method to improve the knowledge of misunderstood dysfunctions of the lower urinary tract.

Are conventional pressure-flow measurements dependent upon filled volume?

OBJECTIVE

To determine, in a prospective study, whether detrusor pressure (p(det.Qmax)) and maximum urinary flow rate (Q(max)) measurements obtained after filling to maximum cystometric capacity (MCC) differ from those obtained with filling restricted to average voided volume (V(void)), as standard protocols for pressure flow studies (PFS) mandate bladder filling until the subject has a strong desire to void, which aids standardization but further divorces the test from real-life experience.

PATIENTS AND METHODS

After calculating the appropriate sample size, 84 patients attending for PFS with an adequately completed 3-day frequency-volume chart were recruited. Each underwent two consecutive PFS with filling to MCC and average V(void) in a random order, and measurements of p(det.Qmax) and Q(max) were compared. For men, the agreement for a diagnosis of obstruction between the tests was also assessed.

RESULTS

Complete data were obtained from 76 (90%) of the patients, with a mean (range) age of 64 (20-94) years. The mean (sd) difference between MCC and average V(void) was 134 (113) mL (P < 0.01). There were no significant differences between estimates of Q(max), at - 0.1 (3) mL/s (P = 0.75), and of p(det.Qmax), at - 1 (13) cmH(2)O (P = 0.91), obtained within each patient. For men there was 91% agreement (32 of 35) in the classification of obstruction.

CONCLUSIONS

Restriction of filling to the average V(void) during PFS allows a closer approximation to normal voiding and results in no clinically relevant change to the value of standard pressure-flow measurements or alters individual classification of obstruction.

[Detrusor activity and motor neurons firing during micturition: analysis by means of modeling of urodynamic tracings]

BACKGROUND

To use a computer assisted analysis of urodynamic tracings (VBN method) in order to propose a quantitative description of the relationship between detrusor activity and firing of efferent motor neurons.

METHODS

Modeling of the nervous control implies three definitions of the detrusor excitation: (1) related to the contractile force (EF), (2) related to the calcium turnover (ECa) and (3) ratio of firing motor neurons (rr). The associate variables have been computed from each uroflow recording of healthy volunteers (male and female) and patients (107 men with lower urinary tract symptoms due to benign prostatic enlargement and 138 women with stress urinary incontinence).

RESULTS

A "standard excitation" governs all the voidings of healthy volunteers. For 47% of male patients and 75% of female patients, a non-standard excitation is observed: beginning as the standard excitation, then sudden break at a time tc (9.7 +/- 2.5 s for male and 4.0 +/- 2.7 s for women). rr has an all-or-none value in case of standard excitation and exhibits a two steps behavior with after tc: = 0.53 +/- 0.21 for men and 0.41 +/- 0.18 for women (non-significant despite the difference in the origin of disease).

CONCLUSION

VBN computer analysis of urodynamic tracings allows to propose a description of the detrusor nervous control: (1) an on-off nervous order rules the "standard" detrusor activity, and (2) a feedback, which probably starts at the urethral level, acts to switch an on-off reduction of the detrusor activity in the other cases.

A mathematical micturition model to restore simple flow recordings in healthy and symptomatic individuals and enhance uroflow interpretation

We describe a model and report a new method to extract quantified data from the simple analysis of whole uroflow curves in healthy and symptomatic individuals. Recorded flow curves were compared with the curves theoretically predicted from a mathematical micturition model. This model was developed by relating each physiological event occurring during micturition to a set of mathematical equations. Due to improvements in speed of computer calculations, a very fast and adaptable mathematical micturition model became available. A total of 302 uroflow curves from 142 patients (61 men and 81 women) were studied. The control group consisted of seven men and 25 women; the symptomatic groups comprised 54 men and 56 women. The mathematical model was applied to analyze all the recorded curves. For patients with lower urinary tract symptoms, specific modelization parameters were introduced according to the clinical condition to be tested. Using two compulsory (patient sex and voided volume) and two optional parameters (clinical condition and urethral catheter size), our mathematical model was able to produce uroflow calculated curves similar to observed curves. In the control group, the calculated and recorded uroflow curves were found to superimpose with an impressive accuracy, i.e., a quadratic error <1%. Test-re-test studies gave the same determination of the specific parameters. In benign prostatic hyperplasia patients, the compressive effect on both prostatic urethra and bladder neck was separately identified. The same intra-individual values were found at 2-week intervals in the group with no treatment (P = no significance), whereas after 3 months of treatment with an alpha-blocker, a decrease in values was noted in responder patients (P < 0.001). In women with various degrees of cystocele, a constrictive effect was identified and found to be identical for successive flows during the same urodynamic testing. This large prospective study demonstrated the relevance of a sophisticated, heavily computerized micturition model, taking into account physiological voiding parameters, to the study of flow in healthy individuals and patients with benign prostatic hyperplasia or cystocele. Curve-fitting led to the determination of critical events during flow such as break point and plateau phase. Determination of these events may enhance uroflow interpretation by providing additional information on the detrusor function. Neurourol. Urodynam. 19:153-176, 2000.