Mathematical modelling of the lower urinary tract

Onset of Spontaneous Filling and Voiding Cycles in the Lower Urinary Tract: A Modeling Study

Spontaneous filling and voiding cycles represent a key dynamical feature of the healthy lower urinary tract. Some urinary tract dysfunctions, such as over-flow incontinence, may alter the natural occurrence of these cycles. As the function of the lower urinary tract arises from the interplay of a multitude of factors, it is difficult to determine which of them can be modulated to regain spontaneous cycles. In this study, we develop a mathematical model of the lower urinary tract that can capture filling and voiding cycles in the form of periodic solutions of a system of ordinary differential equations. After experimental validation, we utilize this model to study the effect that several physiological quantities have on the onset of cycles. We find that some parameters have an associated numerical threshold that determines whether the system exhibits healthy cycles or settles in a state of constant overflow.

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.

Computational Tools for the Investigation of the Male Lower Urinary Tract Functionality in Health and Disease

Purpose

This paper aims to show the potentialities of computational bioengineering in the field of lower urinary tract pathophysiology. Engineering methods allow the investigation of urine flow in healthy and pathologic conditions and the analysis of urethral occlusion by means of artificial urinary sphincters.

Methods

Computational models of bladder and urethra were developed and exploited to investigate the lower urinary tract physiology in health and in disease. Average male morphometric configurations were assumed, together with typical properties of both biological tissues and fluids. The reliability of the models was assessed by the mutual comparison of results and the investigation of data from experimental and clinical activities.

Results

The developed models allowed to analyze typical situations, such as the micturition in health and in disease, and the lumen occlusion by external devices. The models provided information that clinical and experimental tests barely provide, as the occurrence of turbulent phenomena within urine flow, the shear stresses at the lumen wall, the external pressure that is strictly required to occlude the lumen.

Conclusions

The methods of bioengineering allow broadening and deepening the knowledge of the lower urinary tract functionality. More in detail, modeling techniques provide information that contributes to explain the occurrence of pathological situations, and allows to design and to optimize clinical-surgical procedures and devices.

System-on-chip design of the cortical-diencephalic centre of the lower urinary tract

This article presents the design of a field programmable gate array (FPGA)-based prototype of a system on chip (SoC) capable of behaving as one of the nerve centres comprising the neuroregulatory system in humans: the cortical-diencephalic nerve centre. The neuroregulatory system is a complex nerve system consisting of a heterogeneous group of nerve centres. These centres are distributed throughout the length of the spinal cord, are autonomous, communicate via interneurons, and govern and regulate the behaviour of multiple organs and systems in the human body. As a result of years of study of the functioning and composition of the neuroregulatory system of the lower urinary tract (LUT), the centres that regulate this system have been isolated. The objective of this study is to understand the individual functioning of each centre in order to create a general model of the neuroregulatory system that is capable of operating at the level of the actual nerve centre. This model represents an advancement of the current black box models that do not allow for isolated or independent treatment of system dysfunction. In this study, we re-visit our research into the viability of the hardware design of one of these centres-the cortical-diencephalic centre. We describe this hardware because functioning of the centre is completely configurable and programmable, which validates the design for other centres that comprise the neuroregulatory system. In this document, we succinctly present the formal model of the centre, propose a hardware design and an FPGA-based prototype, construct a testing and simulation environment to evaluate it and, lastly, analyse and contrast the results using data obtained from real patients, verifying that the functional behaviour fits that observed in humans.

Quantitative multiphoton microscopy of murine urinary bladder morphology during in situ uniaxial loading

Urodynamic tests are the gold standard for the diagnosis of bladder dysfunction, and the mechanical compliance of the bladder is an important parameter in these tests. The bladder wall has a layered structure, differentially affected by pathology, so knowledge of the contribution and role of these layers and their constituents to overall bladder compliance will enhance interpretation of these clinical tests. In this study we document the functional morphology of the detrusor and lamina propria of the murine bladder wall using a custom in-situ tensile loading system under multiphoton microscopy (MPM) observation in unloaded state and under incremental uniaxial stretch. Features in the stress-stretch curves of bladder samples were then directly related to corresponding MPM images. Collagen organisation across wall depth was quantified using image analysis techniques. The hypothesis that the lamina propria deformed at low strain by unfolding of the rugae and rearranging collagen fibrils was confirmed. A novel 'pocket' feature in the detrusor was observed along with extensive rearrangement of fibrils in two families at different depths, providing higher stiffness at high stretches in the detrusor. The very different deformations of detrusor and lamina propria were accommodated by the highly coiled structure of collagen in the lamina propria. Imaging and mechanical studies presented here allow gross mechanical response to be attributed to specific components of the bladder wall and further, may be used to investigate the impact of microstructural changes due to pathology or aging, and how they impair tissue functionality.

STATEMENT OF SIGNIFICANCE

This article reports the first in-situ multiphoton microscopy observations of microstructural deformation under uniaxial tensile loading of ex vivo bladder. We describe collagen rearrangement through the tissue thickness and relate this directly to the stress-stretch behaviour. We confirm for the first time the unfolding of rugae and realignment of fibrils in the lamina propria during extension and the rapid stiffening as two fibril families in the detrusor are engaged. This technique provides new insight into microstructure function and will enhance understanding of the impact of changes due to pathology or aging.

Hardware design of the cortical-diencephalic centre of the lower urinary tract neuroregulator system

The neuroregulator system in humans controls organ and system functioning. This system comprises a set of neural centres that are distributed along the spinal cord and act independently together with their nerve interconnections. The centres involved in this task were isolated in previous studies through investigations of the functioning and composition of the neuroregulator system of the lower urinary tract to elucidate their individual performances and enable the creation of a general neuroregulator system model capable of operating at the neuronal level. Although the long-term goal of our research is the development of a system on chip (SoC) capable of behaving as a fully programmable neuroregulator system, this work is another step in which we test the viability of the hardware design of one of these neuroregulator centres (specifically the cortical-diencephalic centre) to achieve a first prototype and architectural proposal. To this end, the behaviour of this centre has been isolated, a hardware design implemented on FPGA has been proposed to create a prototype, a simulation environment has been built for the evaluation, and finally, the results have been analysed. This system verified that the functional behaviour corresponded to the expected behaviour in humans and that the operational requirements for the implementation were technically and architecturally viable.