Low-frequency tibial neuromodulation excites bladder activity in humans

Before statistical analysis was conducted, several data points had to be removed from the dataset due to:

• A failure to abstain from caffeine/nicotine before participation (n=1, group A)

• Presence of an ongoing treatment for relevant comorbidities (n=1, group A)

• Several participants reporting the urge to urinate before the end of the digestion period, preventing administration of neuromodulation (n=3, n_GroupA = 1, n_Groupb = 2)

Unfortunately, exclusion of these participants did lower the statistical power of the analysis, resulting in a final final sample distribution of N_A = 14, N_B = 14, N_C = 15. The non-normality and relatively small sample size of this distribution required that non-frequentist statistical techniques be used.

Despite this, the results of the study were nonetheless promising. Analyzing the effects of the intervention, it was clear that there was a differential effect of stimulation frequency on urge-onset time. To account for the small sample size and non-normality of the dataset, a Bayesian robust linear regression was conducted, rather than a typical frequentist approach.

Given the potential for outliers arising as a result of the sample size, a Student’s t distribution was selected during likelihood calculation (N_draws = 12,000). The model indicated that group A (low-frequency TTNS) had a mean time to first urge of 937 s (HDI_3%=575.88 s, HDI_97%=1291.88 s, see Figure 1A). Posterior distribution comparison indicated an 89.28% probability that individuals exposed to low-frequency TTNS experienced urge onset more rapidly than placebo control (group B, mean = 1277.7 s, HDI_3%=880.68 s, HDI_97%=1648.17 s). As detailed in Figure 1, it also indicated that group C (high-frequency TTNS) displayed a delayed urge onset compared to placebo control (mean = 2301.93 s, HDI_3%=1931.67, HDI_97%=2642.83 s) with posterior analysis indicating a 99.94% chance that high-frequency intervention delayed urge onset in individuals within group C when compared to those in group B. All parameters indicated excellent model convergence (Rˆ=1.00). These results indicate the likely presence of a promising frequency-dependent trend; however, additional analysis is critical as the sample size remains too small to make any certain claims at this stage.

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Nevertheless, an additional region of practical equivalence (ROPE) analysis was conducted to assess whether the difference in urge-onset time between groups A and B (which would indicate a novel effect of TTNS) was clinically relevant. A range of ±60 s was selected as the region of practical equivalence for the analysis. Doing so revealed that 7.49% of the posterior distribution of the difference in urge onset fell within the region of equivalence, indicating a considerable likelihood of potential clinical relevance (see Figure 1—figure supplement 1).

Of all experimental participants (including those removed from statistical analysis), only one individual declined the offer to take part in the washout period, resulting in a participation rate of 98%.

A factorial ANOVA suggested there was a significant main effect of the washout period (F_(1,79) = 17.625, p<0.00001) but not group allocation (F_(2,79) = 1.276, p=0.28) on urge intensity. In addition, there was no significant interaction between the factors reported (F_(2,79) = 1.076, p=0.35). In all cases, there was an increase in the average urge intensity reported by the participants before and after the washout period (see Figure 1B). At the end of the washout period, the three conditions finished with a similar intensity score. However, the variability within this data makes any robust inferences impossible.

There was a small but observable relationship between urge intensity and sensory response (i.e., time elapsed to urge sensation). While urge intensity at the first reporting point (i.e., before the washout period) was similar across groups, those in the excitatory condition reported the sensation earlier compared to those in the inhibitory condition (see Figure 1C).

Under baseline (unmodulated) conditions, the behavior of the model was promising. The model accurately simulated normal bladder function and the associated efferent nervous activity. Specifically, it was able to reproduce the expected filling and voiding cycle (see Figure 2, top trace). During the filling phase, the efferent projections associated with urine storage (hypogastric and pudendal) were tonically active, while the pelvic projections associated with voiding were silent.

Figure 2

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In contrast, during void events, bursts of pelvic efferent activity silenced the hypogastric and pudendal projections. This change in activity was associated with a decrease in bladder volume, indicative of a switch in the system from a storage state to voiding (see Figure 2). These results suggest that the model was able to mimic the complex switching behaviors required to mediate the behavior of the lower urinary tract, allowing it to serve as an accurate baseline upon which to test the impact of modulation.

Though the model does display the ability to accurately capture bladder-like behavior, it should be noted that there were several limitations that may limit its generalizability. The model displayed a much smaller bladder capacity (mean 112 ml, ±11.6) than observed physiological values in humans (300 − 500 ml; Boron and Boulpaep, 2017). Additionally, the model displayed poor voiding efficiency. Under normal (unmodulated) conditions, the average voiding efficiency was 14.5% (±31.4%). The low average efficiency coupled with the relatively large variance limits the direct physiological comparisons that may be drawn from the model.

These limitations are likely due to the training data used during model fitting. The original dataset was obtained from male Wistar rats (Jabbari and Erfanian, 2019). The average capacity across the dataset was 0.7 ml (±0.09). Moreover, it also displayed a similarly poor voiding efficiency throughout (mean = 9.54%,±2.59)—likely due to the tightly constrained nature of the recorded bladder behavior.

While the reduced capacity and voiding efficiency of the training dataset were partially overcome (as the performance of our model outperformed in these metrics slightly), the limited generalizability of the model should be kept in mind when interpreting the results.

Despite this limited generalizability, the model nevertheless serves as a more than acceptable foundation for drawing proof-of-concept conclusions and examining potential mechanistic explanations for tibial nerve stimulation.

Analyzing the effects of TNS on the computational model revealed an intriguing trend. Under baseline conditions, the model produced a cycle of storage and voiding in accordance with expectations from previously obtained animal data (see Jabbari and Erfanian, 2019, Figure 3A). Applying high-frequency (20 Hz) stimulation to the system completely inhibited the voiding action (according to the expected effect of TNS on bladder behavior). However, if low-frequency (1 Hz) TNS was applied to the system, voiding occurred earlier (baseline mean = 426 s, ±14.6; low-frequency mean = 410 s, ±9.9) and with greater voiding efficiency (baseline mean = 9.54%, ±2.59; low-frequency mean = 41.44%, ±21.72), causing larger drops in stored volume for a given voiding event (see Figure 3, Figure 3—figure supplement 1).

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To do so, the research team conducted a further exploration of the system during low-frequency TNS. To guide this exploration, an initial hypothesis was generated. In theory, to drive any increase in voiding activity without considerably changing the time elapsed before voiding (i.e., the time of void-onset), one or more of the following changes may be occurring:

• The intensity of bladder contraction is increased.

• The duration of bladder contraction is increased.

• The system-level mechanisms that control urine storage are being inhibited.

Further analyzing the behavior of the system under a range of different stimulation conditions, the research team discovered a frequency-dependent relationship between TNS and contraction duration. For a given simulation, at low frequencies, the average effective duration of contraction—that is, bladder contractions that successfully induced a voiding event—was increased significantly, while at high frequencies, it was eliminated completely, resulting in a contraction duration of 0 ms (as voiding became impossible, see Figure 3B). These findings confirm the presence of a frequency-dependent effect of TNS on bladder behavior and indicate that the low-frequency effect may be driven by the extension of bladder contraction, causing a greater intensity of voiding for a given simulation run, altering bladder capacity (see Figure 3—figure supplement 2).

As the duration of contraction was highlighted as a measure of interest by the initial computational analysis, we sought to understand the nature of this frequency-dependent effect by analyzing the specific projections that may mediate it. To do so, an analysis of bladder contraction was performed in a range of connective states (where specific tibial nerve projections were severed) during low- and high-frequency stimulation.

A one-way ANOVA revealed a significant effect of the connective state on the total duration of contractions (i.e., across all voiding events) over a 500-s simulation during low-frequency (F_(5,54) = 16.975, p<0.0001) and high-frequency conditions (F_(5,54) = 55.269, p<0.0001).

From these results, it is clear that brainstem, rather than spinal cord, targeting projections are necessary for the manifestation of the low-frequency effect, though it cannot be said at this stage how each module contributes to the effect (as both were required to produce a large-magnitude increase in contraction duration). The effect size of the PAG-only condition was larger than that of the PMC condition, providing some evidence that this region may be playing a greater role in the process; however, further research is required to disentangle the individual effects of each region. Intriguingly, it appears that the inclusion of spinal-targeting tibial projections has a pronounced influence on voiding efficiency, with the elimination of these projections (leaving only brainstem projections intact) causing a more consistent increase in voiding efficiency.

In contrast, the combination of projections that underlie high-frequency stimulation is more opaque. Bladder contractions were extinguished by any combination of spinal or brainstem targeting tibial projections when 20 Hz TNS was applied (see Figure 3Cii). This finding makes it difficult to pinpoint the exact mechanism that underlies high-frequency inhibition of bladder activity (as all tested configurations were able to induce the effect). These findings require further analysis, but nevertheless provide additional evidence for a clear inhibitory effect of high-frequency TNS on bladder function.

The results of the present study demonstrate that TTNS is able to impart a frequency-dependent effect on bladder function. They corroborate preliminary animal data within the literature (Li et al., 2020; Moazzam et al., 2016; Theisen et al., 2018) and for the first time demonstrate evidence for a frequency dependence in humans. The results suggest that the main effect of the intervention on the healthy population was sensation.

Changes in the time taken for participants to experience the urge to urinate were the primary change in bladder behavior, in contrast to the effects on urge intensity, which were minimal, though significant variance within the data makes any conclusions difficult. Although 20 Hz stimulation appeared to increase the average intensity of the urge after treatment, this is unlikely to indicate the presence of any lingering effect. Rather, it is more likely that this difference compared to 1 Hz stimulation was due to more time elapsing before participants reported any feeling of urgency (see Figure 1C). In other words, while a similar intensity was reported upon feeling the urge to urinate, the time taken to produce this feeling could be modulated—either reducing it (via 1 Hz stimulation) or increasing it (via 20 Hz stimulation). This result is surprising, as it would be expected that any modulation in one aspect of afferent bladder sensation (the urge onset) would reasonably drive a change in the other (the urge intensity).

While this juxtaposition undoubtedly warrants further exploration, it is possible to hypothesize a potential explanation of the effect. As will be shown by the results of the computational modeling, it may be the case that any afferent sensory changes observed are secondary to the primary effect of TTNS—the modulation of efferent bladder activity. TTNS has been shown to alter the activity of a number of regions of the brainstem and cortex associated with bladder function (Krhut et al., 2023) in different ways dependent on bladder volume (Li et al., 2023), suggesting a complex state-dependent sensory effect. Though not explored in the present publication, it is possible these secondary effects (i.e., those outwith the PAG and PMC targets modeled here) influence the conscious perception of bladder sensation in a complex and temporally specific manner.

The limitations of the pilot study are somewhat remedied by the results of the computational modeling work, which provide considerable mechanistic context to the experimental study. The unmodulated behavior of the model was promising, suggesting that it was able to accurately mimic the complex switching behavior employed by the micturition control system (de Groat et al., 2015). The system produced tonic storage-related efferent activity indicative of a guarding reflex during periods of lower bladder volume that transitioned to void-promoting pelvic activation and silence of storage-related activity at appropriate times. The switch in the circuit state aligned with voiding events in the data. These results suggest the model is able to capture both aspects of micturition (upper circuit activity and lower-bladder behavior), providing an accurate overview of the system for further research. Although the average bladder capacity of the model was lower than would be expected in vivo (simulated capacity was approximately 100–150 ml compared to a physiological range of 300–400 ml; Lukacz et al., 2011), the accuracy of the high-level behavior of the system allowed the effects of TTNS to be studied in silico. The impact of TTNS on the system was clear: By varying solely the frequency of stimulation, it was possible to up- or downregulate simulated bladder activity. This was in line with the hypothesis stated in the article, confirming the presence of a frequency-dependent effect highlighted by the experimental study.

Though these results are promising, there are several key limitations to our computational approach that should be kept in mind when interpreting any results. As previously mentioned, the model displayed a bladder capacity and voiding efficiency considerably lower-than-normal human physiological ranges. Though this may be explained by the training data used during the fitting process, it nevertheless reduces the physiological generalizations that may be drawn from the model. Moreover, the model did not simulate nociceptive afferent projections. Therefore, at present it cannot be used to test the efficacy of TTNS on a pathologically active lower urinary tract system. As such, care should be taken when directly comparing the computational findings to biological reality as they cannot directly inform us of any therapeutic clinical effects. Rather, the present findings should be viewed through the lens of a systems-level proof-of-concept approach. Nevertheless, even with a relatively narrow system-level perspective, our results still provide further evidence and a potential mechanistic explanation for an underexplored excitatory effect. These findings are more than sufficient to serve as an initial foundation for future clinical work.

Though these results are evidently promising, when the computational and human findings are taken together, they appear to paint different pictures of the frequency-dependent effect. The pilot study indicates a primary effect of the intervention on afferent sensation (with urge sensation being the primary measure) while the computational model primarily indicates an efferent effect through a change in contraction duration (though there was a minor afferent effect present). Analyzing the computational results, it is tempting to assume the primary effect of TTNS was on efferent behavior as the change in contraction duration observed in silico was considerably greater than the equivalent shift in void onset time, mirroring the relatively small effect size seen in the pilot study where 1 Hz stimulation was found to induce the urge slightly earlier, but not at a considerably greater sensory magnitude. However, the relatively small sample size of the pilot study and the simplified afferent model (which did not include nociceptive C-fibers) preclude this conclusion at the present time.

The two measures are not unrelated. Both pertain to different aspects of bladder function, and as such further research must critically assess how the two outcome measures are connected, as the present work indicates that both may be affected by the TTNS in a frequency-dependent manner (though to varying degrees of functional efficacy). Nevertheless, these findings undeniably indicate the presence of some form of complex frequency-dependent effect of TTNS on bladder-related function.

The future clinical research directions of this frequency dependence are particularly important when considering the treatment of non-obstructive urinary retention (NOUR). Currently, the treatment of NOUR remains rather limited. Invasive sacral stimulation is the only approved neuromodulatory treatment option available to patients (Elkelini et al., 2010). Previous attempts to use TTNS to treat NOUR have returned mixed results (Coolen et al., 2021; Gaziev et al., 2013). However, this may be due to the use of inappropriate stimulation parameters. Previous research did not alter the stimulation parameters of the standard interventions used in the treatment of incontinence and, as such, may have in fact had a deleterious effect on NOUR symptomatology.

Moreover, at present, TTNS is typically applied to treat incontinence prophylactically, with weekly sessions promoting long-term improvement in symptomatology (Agost-González et al., 2021; Te Dorsthorst et al., 2021). However, these findings suggest that if TTNS is to be applied in the treatment of urinary retention, it may be more effective to administer the treatment in an acute manner, that is, at the point of voiding. Doing so could upregulate the bladder and facilitate unassisted voiding. If shown to be effective when implemented in this way, it could serve as an effective means of reducing the dependency of urinary retention patients on catheters, reducing the rates of urinary tract infections, and improving overall quality of life (Letica-Kriegel et al., 2019; Youssef et al., 2023).

In addition to providing evidence for therapeutic value in the treatment of retention, the present work may also shed light on the mechanistic underpinnings of this frequency-dependent effect. Our results indicate that low-frequency excitation is mediated by brain stem-specific projections. However, this does not preclude an influence of spinal projections. We found a minor but observable influence of spinal cord projections on voiding efficiency. Keeping spinal projections intact during low-frequency stimulation seemingly reduced the magnitude of the observed increases in voiding efficiency (when compared to the same experiment run with only brainstem projections in place). It cannot be said at this time what the specific interaction between spinal and brainstem projections but it is clear there is a complex relationship between the two that should be explored in future work.

Regardless of the interaction between the spinal and brainstem projections, it may be possible to characterize the clear role of the brainstem in low-frequency excitation from a system-level perspective by characterizing the region as a filter. The inhibitory feedback mechanisms within the PAG and PMC (see Figure 5, labels 1–4) allow the modules to act as a set of high-pass filters connected in series, preventing efferent void signaling until a sufficient afferent firing rate is reached. Low-frequency TNS can induce an excitatory effect by inhibiting feedback mechanisms within the PAG, reducing the threshold of the filters, thus allowing a smaller afferent signal to pass through to the PMC (the primary micturition control region; de Groat et al., 2015), triggering void-promoting efferent activity.

While inhibition of the PMC or PAG alone did not result in the same magnitude of excitation, this filtering hypothesis may explain the slight difference in both contraction duration and voiding efficiency between the two conditions. In both cases, contraction duration and voiding efficiency were greater when the PAG was targeted over the PMC. As the first filter in series (the PAG), it is possible that when left fully operational (i.e., where only intact PMC targeting tibial projections were active) it is capable of eliminating afferent activity before it can reach the PMC. In this configuration, the inhibitory state of the PMC matters little.

Although this filtering hypothesis effectively explains the relationship between spinal and brainstem projections during low-frequency TTNS, it cannot explain the complex interactions that may be at play during high-frequency TTNS. The results from the present study were unclear in this respect, as all conditions resulted in the same extinguishing of bladder behavior, making the formation of any explanation difficult. It is unclear if high-frequency inhibition occurs at the spinal level, silencing afferent activity before it reaches the filters (Figure 5, label 5), or at the level of the brainstem, silencing communication between the modules that allows the production of void-promoting efferent activity (Figure 5, labels 2–4) or even the efferent activity itself (Figure 5, label 1). Preliminary evidence from the literature paints a picture of a complex relationship between spinal and brainstem tibial projections. Specifically, TTNS has been shown to have a directly inhibitory effect on spinal activity (Yecies et al., 2018) that is nevertheless insufficient to induce bladder changes in cases of spinal cord injury (de Groat and Tai, 2015). Although this effect may be due to a rewiring of the bladder control system (as there is evidence that early application of TTNS has some effect; Birkhäuser et al., 2020), coupled with the results from the present work, it is clear there is a need for further research to explore how the spinal and supraspinal aspects of the system interact to inhibit bladder function during high-frequency TTNS.

Future research should primarily focus on confirming if these system-level proof-of-concept results generalize from an in silico demonstration to real-world effects in a pathological population. Specifically, subsequent work should maintain a clear focus on exploring the clinical efficacy of low-frequency TTNS as a treatment option for urinary retention. Specifically, it would be prudent to determine if administration of the intervention in an acute manner, at a lower frequency, induces an objective, measurable change in bladder physiology. If followed through to completion, this research direction may remedy the mixed results seen previously. Additionally, these findings may contribute to the ongoing development of a wearable neuromodulatory treatment device, which may provide a user-friendly method of administering the intervention (Ju et al., 2025).

Despite some limitations surrounding the methodology of the experimental study and the need for further research in this direction, the present findings nonetheless provide vital evidence for a frequency-dependent effect of TTNS in human beings. Moreover, they suggest a complex and not-necessarily solely brainstem-specific role of the tibial nerve in bringing about this unexpected, but critically important excitatory effect. We propose that these findings would lay the groundwork for a number of future research efforts, which may elucidate the precise neural mechanisms underlying the complex effects of TNS on bladder function in both healthy and diseased states.

A graphical overview of the study can be seen in Figure 4. In summary, the study was a single-blind design between subjects. Participants were pseudo-allocated to one of three groups such that the sample size across groups remained equally distributed (see below). Participants were not informed of this decision to ensure blinding was maintained.

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Figure 4—source data 1

Example urge-intensity survey.

Shown is an example of the survey that was given to the participants in printed form.

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To ensure a relatively stable bladder baseline across the sample, several measures were taken. First, participants were asked to restrict their fluid intake for 2 h and caffeine or nicotine for 12 h before the beginning of the experiment—caffeine or nicotine affect urination (Maughan and Griffin, 2003; Burn et al., 1945). Second, participants were asked to empty their bladder as much as they were reasonably able upon arrival, before ingesting 750 ml of water.

Participants underwent a 30-min ‘digestion period’ during which they were able to undertake any activities they wanted as long as they remained seated. During this period, they were prepped for neurostimulation: Any leg hair was shaved from the ankle and lower leg using a sterile disposable razor, and the stimulation site was disinfected using a 70% isopropyl alcohol solution to remove contaminants.

To ensure that the objective outcome of the study could be recorded in all cases, after the digestion period, participants were told to inform researchers when they first felt the urge to urinate. Electrodes (Med-Fit 50 mm × 50 mm Hydrogel Electrodes) were applied to the right leg 1 cm posterior to and 10 cm superior to the medial malleolus in accordance with established TTNS protocols (Li et al., 2024; see Figure 4—figure supplement 1). Participants received stimulation (Digitimer DS7A High-Voltage Constant Current Stimulator) until they felt the urge to urinate. The specific parameters of the stimulation differed according to group allocation (see Figure 4):

• Group A: 1 Hz, 200 µs pulse width, motor threshold.

• Group B: control group, without stimulation, though they still underwent skin preparation.

• Group C: 20 Hz, 200 µs pulse width, motor threshold.

In all cases, any applied stimulation was monophasic and administered at a standard voltage (max 300 V, see Figure 4—figure supplement 2) with a current sufficient to induce flexion or fanning of the big toe. The current was slowly increased until the first sign of this motor activity was observed.

Upon reporting the urge to urinate, the time-elapsed was recorded and the participants were asked to rate how intense they felt their urge according to a validated questionnaire (Blaivas et al., 2007; see Figure 4—source data 1).

The simulated network was composed of a set of interconnected neuronal units, each comprising 100 individual neurons modeled in terms of conductance or Poisson point processes that generated simulated action potentials (see ‘Neuronal model’). The topology of the model was adapted from previous work that simulated reflex voiding (de Groat and Wickens, 2013). The circuit remained broadly unmodified, with the exception of several key modifications, including simulation of the tibial nerve and its projections (see Figure 5). We focus on normal bladder function; therefore, the nociceptive bladder afferents were not included in our model. To simulate the effects of opioidergic and classical inhibition, neurons and synapses were represented in terms of ionic conductance. The biophysical model used to represent the bladder was adapted from Lister et al., 2024 (see ‘Bladder model’).

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The tibial nerve was modeled to project to second-order sensory afferents (via classical inhibitory synapses) and all neuronal units within the PAG and PMC (via opioidergic inhibitory synapses) as shown in Figure 5. To provide fine control over the level of tibial modulation applied to the system, the firing rate of the neuron and its projections was clamped and, if required, could be severed by disconnecting synaptic junctions. This ensured that while in a severed state, the neurons, though still modeled, had no impact on postsynaptic targets.

The model used a biophysical representation of the bladder adapted from the work published by Lister et al., 2024 modified to allow integration with the conductance-based representation of the micturition control circuit used in the present work.

In summary, for each step of the simulation (t), the firing rates of three key efferents: pelvic, hypogastric, and pudendal were used to calculate the internal activation constants—ω_e/i/s—which governed detrusor excitation/inhibition and sphincter activation, respectively. From these values, the bladder state could be calculated and the internal detrusor pressure (P_B(t)) used to update the afferent neuronal activity (the main input for the control circuit; see Figure 5). To ensure computational efficiency, the sampling rate of the model was set at 50 Hz, with each step of the simulation (Δt) representing a 20 ms increment. A detailed description of the model can be found in Lister et al., 2024.

To fit the synaptic weights of the model (see Figure 5—figure supplements 1 and 2), we utilized real bladder pressure and neural data from a previously published work (see Jabbari and Erfanian, 2019). In brief, the training data was obtained from intact adult male Wistar rats. The dataset was comprised of bladder pressure and volume information and extracellular neuronal recordings obtained from between the L6 to S1 spinal cord.

The model was built using the Brian2 package for Python (Stimberg et al., 2019). The relationship between the pelvic afferent firing rate and bladder pressure was calculated according to an empirically derived relationship determined previously (McGee and Grill, 2016), where the firing rate of the primary bladder afferent at each moment F(P_B(t)) was defined as

All neuronal units, with the exception of primary bladder afferents and the tibial nerve, were simulated using a Conductance-Based Adaptive Exponential Integrate-and-Fire (CAdEx) model (Górski et al., 2021), modified to include opioidergic inhibition. Through the inclusion of an additional input current (I_ap), neurons could be made tonically active where required. This was particularly important in the simulation of PAG and PMC, where inhibitory feedback mechanisms reliant on tonic activity were present.

The tibial nerve and primary bladder afferents were simulated as Poisson point processes that generated simulated neuronal spikes at a prespecified rate. Doing so allowed the firing rate of the pelvic afferent to be set according to the aforementioned mathematical relation and the firing rate of the tibial nerve to be clamped to a specific value (representing external stimulation of the nerve).

Each unit within the network was composed of 100 simulated neurons connected via random synapses (where no autapses were permitted) to introduce noise into the system.

Membrane potential (v) was defined as

where C_m is the membrane capacitance; g_L the leakage current and E_L its associated reversal potential; g_A is the adaptation current and E_A its reversal potential; I_ap the input to tonically firing neurons; and I_syn the input from synaptic connections. Also included were terms that govern the action potential (v_th and Δ_t). As with the original definition proposed by Górski et al., 2021, g_A was defined as

where the rate of change of the current was determined by a rate constant (τ_A), the subthreshold adaptation parameters (v_A and Δ_A), and the maximum subthreshold adaptation conductance (g¯_A). The model also included a post-spike reset mechanism, which too remained unchanged.

Upon spiking, the membrane potential was reset to its resting state (v_R), and the adaptation current increased (δg_A). The purpose of the adaptation current was to allow modeling of the spike-frequency adaptation. Tonically active neurons did not display spike-frequency adaptation to ensure that their activity remained consistent.

To computationally analyze the impact of tibial modulation, simulations were performed in a range of modulatory states. Tibial modulation was applied at 21 different frequencies (0–20 Hz, in 1 Hz increments, N_repeats = 10 in each condition) to a simulation of 500-s duration (where each 500-s simulation was run separately). Any aspect of simulated bladder function or circuit activity could be recorded during these simulations. Where neuronal firing rate activity was analyzed, instantaneous firing rates for each recorded time step were smoothed (first-order Butterworth filter, with a 1 Hz cutoff). To analyze the effect of specific tibial projections, projections to regions of interest could be severed as necessary to prevent the formation of synaptic connections.

The custom code used for the analysis in this study is available in Aidan, 2025. The authors request that any individuals using the code as part of further research cite the present work.

As part of the pilot study statistical analysis, a region of practical equivalence test was conducted. A region of practical equivalence of ±60 s was selected as an appropriate interval. Detailed in Figure 1—figure supplement 1 is the result of the analysis, showcasing a 7.49% overlap in the distribution of differences when comparing groups A and B.

As part of the human study, participants were asked to rate how intense they felt the urge to urinate. This rating was adapted from a validated questionnaire typically used to rank urgency perception as a measure of urological dysfunction (Blaivas et al., 2007; see Figure 4—source data 1).

Shown in Figure 4—figure supplement 1 is an example of the electrode placement. Figure 4—figure supplement 2 is a picture of the parameters set on the DS7A neurostimulator during the experiment.

Each run of the simulation began by specifying a total runtime (in seconds). At t₀, to introduce noise, the initial membrane potential of all neuronal units was randomized between the reversal potential for the leak-current (E_L, –80 mV) and the threshold for action potential (V_th, –50 mV). The bladder was assumed to be empty (V_B = 0) with an initial inflow rate determined via a stochastic process. At each time step (t), the bladder state was updated and the firing rates of the primary pressure-sensitive afferents F(P_B(t)) calculated. This firing rate was then used to update the status of the micturition control circuit and its efferent projections, which would be used to calculate the bladder state for (t+1). The target values for the time step were then saved and the simulation increased to (t+1). Upon reaching the final time step of the specified duration (t_end), any cached data were collated and exported, and the simulation stopped.

Synapses were modeled in terms of conductance using established formulae (Vogels et al., 2011), modified to include opioidergic transmission.

The magnitude of the synaptic current (I_syn) is defined as

where g_ex/in represents the conductance of classical excitatory/inhibitory currents, and E_ex/in their reversal potentials; and g_op/E_op representing the action of opioid currents. Modeled synaptic conductance decayed exponentially according to

Synaptic strength was weighted, so that upon presynaptic spiking, the postsynaptic conductance of either excitatory, inhibitory, or opioidergic currents was incremented according to

where w represents the weighting factor, and δg_ex/in/op the baseline increase in conductance in response to a presynaptic spike. The weights of all synaptic connections were determined by parameter fitting and constrained within a specific range to allow controlled plasticity within the network.

Bayesian optimization was used to fit the parameters of the model (Diessner et al., 2022). To do so, the input to the micturition control circuit had to be carefully controlled. To this end, for the optimization stage, rather than implement a noisy biophysical model, the bladder was represented as a mathematical vector that contained experimentally derived data on internal bladder pressure (P_B(t)) and volume (V_B(t)). The sample rate of the vector was 50 Hz, matching the model. The bladder data used to do so was obtained from previously published work (Jabbari and Erfanian, 2019).

During optimization, the activity of second-order sensory afferents was extracted, downsampled to 10 Hz, and smoothed (first-order Butterworth filter, 1 Hz cutoff frequency). These data were compared to the ground-truth neural data associated with the input bladder data (see ‘Animal model surgery and preparation’), producing a normalized root mean square error (NRMSE) value representing the difference between the simulated activity and expected activity. The algorithm adapted the weights and parameters of the model such that the NRMSE was minimized (acquisition function—Gaussian hedging, acquisition optimizer—LMBFGS, N_calls = 200). After running the algorithm, specific weights were manually adjusted to further optimize the efferent activity of the model, ensuring that it was accurate to typical bladder behavior.

Bayesian optimization of model weights and parameters considerably improved the accuracy of simulated afferent activity, bringing it closer to ground-truth neural data (NRMSE_baseline = 3.367; NRMSE_optimized = 1.454). While subsequent manual tweaking did improve the efferent behavior of the model, it did lead to a slight increase in NRMSE, suggesting that it did so at the cost of afferent accuracy (NRMSE_fitted = 1.599). Despite the minor decrease in global function fit, this methodology nevertheless improved the efferent behavior of the model and allowed the simulation to better capture the peaking pattern of neuronal firing rates in the afferent arm of the circuit (see Figure 5—figure supplement 1), providing an accurate foundation for analyzing the effects of neuromodulation. Notably, the optimization algorithm reached its minimum NRMSE plateau in a reasonable number of calls, suggesting the global function minimum was true (see Figure 5—figure supplement 2).

Although the optimized model did not capture every peak in the firing rate or the physiological noise present in the data, the current level of accuracy is more than sufficient to serve as a foundation for exploring TNS, as noise omission would likely only affect the model’s ability to capture very specific network behaviors irrelevant to the present study.

Where possible, these were matched to the parameters described in the original papers describing the neuronal, synaptic, and lower-urinary tract models (Lister et al., 2024, Górski et al., 2021, Vogels et al., 2011). Key parameters that were fit included the current mediating tonic activity (I_ap), the magnitude of excitatory and inhibitory conductance (g_ex/in/op), and the upper magnitude of spike-frequency adaptation (g¯_A). See Appendix 1—table 1 for the parameters used in the simulation.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

This project was funded in part by the University of Edinburgh and the Engineering and Physical Sciences Research Council (EPSRC) grant number EP/W031493/1.

The study was approved by the local ethics committee of the University of Edinburgh (ID: 977504). Forty-eight people were recruited under three experimental conditions. Before participation, they gave their full informed consent in writing.

1. Preprint posted: January 17, 2025
2. Sent for peer review: March 5, 2025
3. Reviewed Preprint version 1: June 12, 2025
4. Reviewed Preprint version 2: June 30, 2026
5. Version of Record published: September 4, 2026

You can cite all versions using the DOI https://doi.org/10.7554/eLife.106174. This DOI represents all versions, and will always resolve to the latest one.

© 2025, McConnell-Trevillion et al.

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