A computer model of the neural control of the lower urinary tract

Model-based analysis of the acute effects of transcutaneous magnetic spinal cord stimulation on micturition after spinal cord injury in humans

AIM

After spinal cord injuries (SCIs), patients may develop either detrusor-sphincter dyssynergia (DSD) or urinary incontinence, depending on the level of the spinal injury. DSD and incontinence reflect the loss of coordinated neural control among the detrusor muscle, which increases bladder pressure to facilitate urination, and urethral sphincters and pelvic floor muscles, which control the bladder outlet to restrict or permit bladder emptying. Transcutaneous magnetic stimulation (TMS) applied to the spinal cord after SCI reduced DSD and incontinence. We defined, within a mathematical model, the minimum neuronal elements necessary to replicate neurogenic dysfunction of the bladder after a SCI and incorporated into this model the minimum additional neurophysiological features sufficient to replicate the improvements in bladder function associated with lumbar TMS of the spine in patients with SCI.

METHODS

We created a computational model of the neural circuit of micturition based on Hodgkin-Huxley equations that replicated normal bladder function. We added interneurons and increased network complexity to reproduce dysfunctional micturition after SCI, and we increased the density and complexity of interactions of both inhibitory and excitatory lumbar spinal interneurons responsive to TMS to provide a more diverse set of spinal responses to intrinsic and extrinsic activation of spinal interneurons that remains after SCI.

RESULTS

The model reproduced the re-emergence of a spinal voiding reflex after SCI. When we investigated the effect of monophasic and biphasic TMS at two frequencies applied at or below T10, the model replicated the improved coordination between detrusor and external urethral sphincter activity that has been observed clinically: low-frequency TMS (1 Hz) within the model normalized control of voiding after SCI, whereas high-frequency TMS (30 Hz) enhanced urine storage.

CONCLUSION

Neuroplasticity and increased complexity of interactions among lumbar interneurons, beyond what is necessary to simulate normal bladder function, must be present in order to replicate the effects of SCI on control of micturition, and both neuronal and network modifications of lumbar interneurons are essential to understand the mechanisms whereby TMS reduced bladder dysfunction after SCI.

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.

Anatomy and physiology of the lower urinary tract

Functions of the lower urinary tract to store and periodically eliminate urine are regulated by a complex neural control system in the brain, spinal cord, and peripheral autonomic ganglia that coordinates the activity of smooth and striated muscles of the bladder and urethral outlet. Neural control of micturition is organized as a hierarchic system in which spinal storage mechanisms are in turn regulated by circuitry in the rostral brainstem that initiates reflex voiding. Input from the forebrain triggers voluntary voiding by modulating the brainstem circuitry. Many neural circuits controlling the lower urinary tract exhibit switch-like patterns of activity that turn on and off in an all-or-none manner. The major component of the micturition switching circuit is a spinobulbospinal parasympathetic reflex pathway that has essential connections in the periaqueductal gray and pontine micturition center. A computer model of this circuit that mimics the switching functions of the bladder and urethra at the onset of micturition is described. Micturition occurs involuntarily during the early postnatal period, after which it is regulated voluntarily. Diseases or injuries of the nervous system in adults cause re-emergence of involuntary micturition, leading to urinary incontinence. The mechanisms underlying these pathologic changes are discussed.

Neural control of the lower urinary tract

This article summarizes anatomical, neurophysiological, pharmacological, and brain imaging studies in humans and animals that have provided insights into the neural circuitry and neurotransmitter mechanisms controlling the lower urinary tract. The functions of the lower urinary tract to store and periodically eliminate urine are regulated by a complex neural control system in the brain, spinal cord, and peripheral autonomic ganglia that coordinates the activity of smooth and striated muscles of the bladder and urethral outlet. The neural control of micturition is organized as a hierarchical system in which spinal storage mechanisms are in turn regulated by circuitry in the rostral brain stem that initiates reflex voiding. Input from the forebrain triggers voluntary voiding by modulating the brain stem circuitry. Many neural circuits controlling the lower urinary tract exhibit switch-like patterns of activity that turn on and off in an all-or-none manner. The major component of the micturition switching circuit is a spinobulbospinal parasympathetic reflex pathway that has essential connections in the periaqueductal gray and pontine micturition center. A computer model of this circuit that mimics the switching functions of the bladder and urethra at the onset of micturition is described. Micturition occurs involuntarily in infants and young children until the age of 3 to 5 years, after which it is regulated voluntarily. Diseases or injuries of the nervous system in adults can cause the re-emergence of involuntary micturition, leading to urinary incontinence. Neuroplasticity underlying these developmental and pathological changes in voiding function is discussed.

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.

Mathematical modelling of the lower urinary tract

The lower urinary tract is one of the most complex biological systems of the human body as it involved hydrodynamic properties of urine and muscle. Moreover, its complexity is increased to be managed by voluntary and involuntary neural systems. In this paper, a mathematical model of the lower urinary tract it is proposed as a preliminary study to better understand its functioning. Furthermore, another goal of that mathematical model proposal is to provide a basis for developing artificial control systems. Lower urinary tract is comprised of two interacting systems: the mechanical system and the neural regulator. The latter has the function of controlling the mechanical system to perform the voiding process. The results of the tests reproduce experimental data with high degree of accuracy. Also, these results indicate that simulations not only with healthy patients but also of patients with dysfunctions with neurological etiology present urodynamic curves very similar to those obtained in clinical studies.

Organization of the neural switching circuitry underlying reflex micturition

The functions of the lower urinary tract to store and periodically eliminate urine are regulated by a complex neural control system in the brain and spinal cord that coordinates the activity of the bladder and urethral outlet. Experimental studies in animals indicate that urine storage is modulated by reflex mechanisms in the spinal cord, whereas voiding is mediated by a spinobulbospinal pathway passing through a coordination centre in the rostral brain stem. Many of the neural circuits controlling micturition exhibit switch-like patterns of activity that turn on and off in an all-or-none manner. This study summarizes the anatomy and physiology of the spinal and supraspinal micturition switching circuitry and describes a computer model of these circuits that mimics the switching functions of the bladder and urethra at the onset of micturition.

Smooth muscle modeling and experimental identification: application to bladder isometric contraction

This paper presents an original smooth muscle model based on the Huxley microscopic approach. This model is the main part of a comprehensive lower urinary track model. The latter is used for simulation studies and is assessed through experiments on rabbits, for which a subset of parameters is estimated, using intravesical pressure measurements in isometric conditions. Bladder contraction is induced by electrical stimulation that determines the onset and thus synchronizes simulation and experimental data. Model sensitivity versus parameter accuracy is discussed and allows the definition of a subset of four parameters that must be accurately identified in order to obtain good fitting between experimental and acquired data. Preliminary experimental data are presented as well as model identification results. They show that the model is able to follow the pressure changes induced by an artificial stimulus in isometric contractions. Moreover, the model gives an insight into the internal changes in calcium concentration and the ratio of the different chemical species present in the muscle cells, in particular the bounded and unbounded actin and myosin and the normalized concentration of intracellular calcium.

Afferent bladder nerve activity in the rat: a mechanism for starting and stopping voiding contractions

The objective of this work was to study the relation between afferent bladder nerve activity and bladder mechanics and the mechanisms that initiate and terminate bladder contractions. Bladder nerve activity, pressure and volume were recorded during the micturition cycle in the rat. The highest correlation was found between afferent nerve activity and stress (pressure x volume). Afferent nerve activity depended linearly on stress within 6%, and both slope and offset were independent of the bladder-filling rate. The levels of afferent bladder nerve activity at the onset and cessation of efferent firing to the bladder were highly reproducible with coefficients of variation of <or=17%. We propose a model in which afferent activity is proportional to bladder wall stress, and bladder contraction is initiated when afferent activity exceeds a threshold due to an increasing pressure and volume. The contraction continues until afferent activity drops below a threshold again as a result of a decreasing volume.

[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.

Modelling the biomechanics and control of sphincters

This paper reviews current mathematical models of sphincters and compares them with a new spatial neuromuscular control model based on known physiological properties. Almost all the sphincter models reviewed were constructed as a component of a more extensive model designed to mirror the overall behaviour of a larger system such as the lower urinary tract. This implied less detailed modelling of the sphincter component. It is concluded that current sphincter models are not suitable for mimicking detailed interactions between a neural controller and a sphincter. We therefore outline a new integrated model of the biomechanics and neural control of a sphincter. The muscle is represented as a lumped-mass model, providing the possibility of applying two- or three-dimensional modelling strategies. The neural network is a multi-compartment model that provides neural control signals at the level of action potentials.The integrated model was used to simulate a uniformly activated sphincter and a partially deficient innervation of the sphincter, resulting in a non-uniformly activated sphincter muscle. During the simulation, the pressure in the sphincter lumen was prescribed to increase sinusoidally to a value of 60 kPa. In the uniformly activated situation, the sphincter muscle remains closed, whereas the partially denervated sphincter is stretched open, although the muscle is intact.

Overview of mathematical computer models of striated sphincter muscles

The present paper compares current mathematical striated sphincter models. Current models are subdivided in four categories: (1) simple models, (2) implementations of the urethral resistance relation, (3) models with realistic muscle dynamics and (4) finite element models. In our research group a neural network model, representing Onuf's nucleus, the spinal motor nucleus that innervates the external urethral and anal sphincters, was developed. A realistic sphincter model is needed to test the neural network. To decide whether or not a model is applicable in our research two requirements should be fulfilled: (1) the presence of realistic muscle dynamics preferably by implementation of a Huxley type muscle model and (2) the model should consist of more than one muscle unit to form a more dimensional model. Reviewing the literature, if a myogenic sphincter is modelled, mainly the Hill-equation is applied. Moreover, single muscle unit models are published. In general a multi-unit muscle model of the sphincter is lacking, prohibiting the study of the inherent properties of sphincter muscles, which could give information on the realistic behaviour of elements in circular muscles. It is concluded that the functionality of current sphincter models is limited for our purpose.

Comparison of different computer models of the neural control system of the lower urinary tract

This paper presents a series of five models that were formulated for describing the neural control of the lower urinary tract in humans. A parsimonious formulation of the effect of the sympathetic system, the pre-optic area, and urethral afferents on the simulated behavior are included. In spite of the relative simplicity of the five models studied, behavior that resembles normal lower urinary tract behavior as seen during an urodynamic investigation could be simulated. The models were tested by studying their response to disturbances of the afferent signal from the bladder. It was found that the inhibiting reflex that results from including the sympathetic system or the pre-optic area (PrOA) only counteracts the disturbance in the storage phase. Once micturition has started, these inhibiting reflexes are suppressed. A detrusor contraction that does not result in complete micturition similar to an unstable detrusor contraction could be simulated in a model including urethral afferents. Owing to the number of uncertainties in these models, so far no unambiguous explanation of normal and pathological lower urinary tract behavior can be given. However, these models can be used as an additional tool in studies of the mechanisms of the involved neural control.

A computer model for describing the effect of urethral afferents on simulated lower urinary tract function

A computer model of mechanical properties of the bladder, the urethra and the rhabdosphincter, as well as their neural control is presented in this paper. The model has a rather simple design and processes sensory information from both the bladder wall tension and urethral stretch. It is assumed that afferent signals from the urethra are involved in a sacral excitatory reflex and a supraspinal inhibitory reflex. Pressure and flow signals that resemble experimentally measured normal human behaviour could be simulated with this model. From these simulations the relation between the neural control mechanisms used in the model and the neural control mechanism in vivo cannot be judged entirely because similar behaviour could be simulated with models that are bas ed on different neural control mechanisms. Also behaviour that resembles detrusor overactivity was simulated with our model after an externally induced rise in detrusor pressure was added. Detrusor overactivity, sometimes in combination with urethral relaxation, can occur during a urodynamic investigation. A possible explanation for this detrusor overactivity might be that the micturition reflex is triggered by unknown disturbances and is inhibited immediately after by the same mechanism that normally ceases voiding. The described model provides such a mechanism. Based on these simulations, therefore, it is concluded that urethral afferent signals might be important in lower urinary tract control.