Finite element modeling and in vivo analysis of electrode configurations for selective stimulation of pudendal afferent fibers
© Woock et al; licensee BioMed Central Ltd. 2010
Received: 24 September 2009
Accepted: 25 May 2010
Published: 25 May 2010
Intraurethral electrical stimulation (IES) of pudendal afferent nerve fibers can evoke both excitatory and inhibitory bladder reflexes in cats. These pudendovesical reflexes are a potential substrate for restoring bladder function in persons with spinal cord injury or other neurological disorders. However, the complex distribution of pudendal afferent fibers along the lower urinary tract presents a challenge when trying to determine the optimal geometry and position of IES electrodes for evoking these reflexes. This study aimed to determine the optimal intraurethral electrode configuration(s) and locations for selectively activating targeted pudendal afferents to aid future preclinical and clinical investigations.
A finite element model (FEM) of the male cat urethra and surrounding structures was generated to simulate IES with a variety of electrode configurations and locations. The activating functions (AFs) along pudendal afferent branches innervating the cat urethra were determined. Additionally, the thresholds for activation of pudendal afferent branches were measured in α-chloralose anesthetized cats.
Maximum AFs evoked by intraurethral stimulation in the FEM and in vivo threshold intensities were dependent on stimulation location and electrode configuration.
A ring electrode configuration is ideal for IES. Stimulation near the urethral meatus or prostate can activate the pudendal afferent fibers at the lowest intensities, and allowed selective activation of the dorsal penile nerve or cranial sensory nerve, respectively. Electrode location was a more important factor than electrode configuration for determining stimulation threshold intensity and nerve selectivity.
Pudendal nerve stimulation is a potential means of restoring bladder function to persons with spinal cord injury (SCI). Stimulation of sensory (afferent) fibers either in the dorsal penile branch (DNP) or the cranial sensory branch (CSN) of the pudendal nerve can evoke stimulation frequency-dependent contraction or relaxation of the urinary bladder in cats [1, 2]. However, the existence of comparable reflexes in persons with SCI remains unclear. In both experimental and clinical settings, intraurethral electrical stimulation (IES) has been utilized as a minimally invasive method to investigate these reflexes. However, the activation of multiple nerve pathways (pudendal and pelvic) by this approach did not enable identification of the specific sensory nerves responsible for the evoked bladder reflexes. The present study used a finite element model (FEM) and parallel in vivo measurements in the male cat to quantify the effects of electrode configuration and position on intraurethral activation of pudendal afferent nerve fibers. The primary aim of this study was to determine the optimal IES electrode configuration and stimulation locations for selectively activating pudendal afferents to aid future preclinical and clinical investigations.
Clinical evaluation of the bladder response to pudendal nerve stimulation is difficult because of the limited access to the pudendal nerve. The pudendal nerve trunk is located in the ischiorectal fossa, where it exhibits a complex and highly variable branching pattern that provides the motor and sensory innervation of the genitalia, urethra, rectum and the pelvic floor [3–8]. As a result of the complex nerve anatomy, clinical investigation of specific pudendal afferent fibers has been difficult. Transcutaneous stimulation (with external surface electrodes) of the DNP in humans can evoke robust bladder relaxation and promote continence [9–11], but this approach is limited to activation of superficial pudendal afferent branches. Percutaneous stimulation can activate the pudendal nerve [12, 13] in humans, but it is unclear which branches of the nerve are activated. In contrast, surgically implanted cuff electrodes enable selective activation of the different pudendal nerve branches in the cat . IES in the proximal urethra can evoke bladder contraction in humans , but the conflicting results between the human and cat [15, 16] suggests that further analysis of the effects of intraurethral stimulation is necessary.
The goal of this study was to develop a computer model of IES that can be used to interpret data and guide design of IES electrode geometries for selective stimulation of pudendal afferents. We developed three-dimensional (3-D) FEMs to determine the electric potentials generated along the DNP and CSN by IES. The potentials were used to calculate the second spatial derivative of the extracellular potential along the nerve fibers (the 'activating function', AF ). The model and in vivo stimulation thresholds provide insight into the effects of electrode geometry and location valuable for future clinical and preclinical experiments investigating the ability to restore control of bladder function in persons with spinal cord injuries or other neurological disorders via stimulation of pudendal afferents.
Finite element modeling
Electrical properties of the finite element model of the cat urethra
0.1 nS m-1
Bulbospongiosus m., ischiocavernosus m., ischiourethralis m., inner urethral m., outer urethral m.
0.291 S m-1
Corpus cavernosum, corpus spongiosum
0.6 S m-1
Bulbocavernosus g., prostate g.
0.4 S m-1
Connective tissue, etc.
Prepuce, bounding box
0.05 S m-1
The model was implemented in COMSOL Multiphysics (version 3.4) and partitioned into mesh elements using the finite element method. The internal tissue boundaries were set so that continuity of current was preserved, and the external boundaries were set to ground (V = 0) with the exception of the external boundaries of the prepuce and the adjacent wall of the bounding box, which were set to be electrically insulated (current density = 0). Increasing the mesh density around the electrode or doubling the bounding box size had minimal effect on the maximum potentials generated at the nerves (<5% change). The electrical input was a 1 mA cathodic regulated current for all simulations, and the model was solved using the conjugate gradient method.
The anatomical courses of the DNP and CSN branches of the pudendal nerve were modeled in Matlab (R2007a, Mathworks) based on previous anatomical data [18–21]. The nerves were represented bilaterally as single trunks, and lateral branches of the DNP were later included for further examination of DNP activation in the penile urethra. The potentials generated by IES were exported from the FEM model to Matlab and the potentials along the nerve paths were determined at 0.1 mm increments using interpolation.
The Activating Function
where n is the node of interest and ℓ = 0.5 mm is the internodal length assuming the modeled nerve fibers were 5 μm in diameter . At the termination of the nerve fibers, the activating function was the first spatial derivative of the extracellular potential. The maximum AF was determined for the DNP and CSN bilaterally for each of 5 possible locations of the first (most distal) node in the fiber, and the resulting maximum AFs were averaged.
For analysis of activation of the lateral branches of the DNP in the penile urethra, the AFs were calculated along 5 lateral DNP branches (Figure 1) in addition to the DNP trunk. The branches were initially spaced 3 mm apart  and were located ~1.4 - 2.6 cm from the urethral meatus. The maximum AFs were calculated for each branch for all electrode configurations (Figure 2), and this was repeated for 50 sets of random branch locations generated by randomly varying the location of each branch within ± 1 cm along the longitudinal axis of the urethra. Maximum branch AFs were ordered from greatest to smallest for each of the 50 trials. The AFs were averaged across trials based on their rank (i.e., the maximum AF across the 5 branches was averaged over the 50 trials and so on for the 2nd largest, etc).
An AFR >1.5 combined with a selectivity >1 suggested, conservatively, that activation of a population of fibers under the first set of conditions could be achieved at a lower threshold than under the second set of conditions. If the AFR was <1.5 or selectivity was <1, it is likely that variation in nerve location, anatomical dimensions, and other factors would render stimulation thresholds under the two conditions indistinguishable during in vivo IES.
In vivo experiments
Animal care and experimental procedures were approved by the Duke University Institutional Animal Care and Use Committee. Experiments were performed on 13 sexually intact adult male cats (2.8-4.6 kg) anesthetized with ketamine KCl (35 mg/kg i.m.) and α-chloralose (65 mg/kg i.v. supplemented at 15 mg/kg as needed). Artificial respiration maintained the end tidal CO2 between 3.5 and 4.0%, IV fluids (lactated Ringer's solution or saline/5% dextrose/sodium bicarbonate solution) were delivered at 15 cc/kg/hr via a catheter in the cephalic vein, and a thermostatic heating pad was used to maintain body temperature at ~38°C. Blood pressure was monitored through a catheter in the carotid artery. A catheter was inserted into the bladder dome and the bladder was drained externally to maintain an empty bladder.
A 3.5 or 5 Fr catheter modified with platinum electrodes embedded at 2 cm from the tip was inserted into the urethral meatus. The 3.5 Fr electrode included three 1 mm rings spaced 3.5 mm apart. The 5 Fr electrode included two 2 mm rings spaced 2 mm apart. Electrical stimulation (1 Hz) was applied with the catheter electrodes located 1-7 cm from the urethral meatus. Stimulation intensity varied from 0.5-15 mA, and the intensity threshold to evoke a reflex electromyographic response in the external anal sphincter (EAS EMG) was measured in 0.5 mA increments.
Finite element model of intraurethral stimulation
Intraurethral stimulation was applied to electrodes positioned 1-7 cm from the urethral meatus using the electrode configurations shown in Figure 2A. The spatial distribution of the electric potential varied depending on the electrode configuration. Stimulation with the short electrode generated the largest voltage gradient along the urethra, both in maximum value and the volume of tissue that experienced a >1V change in potential, while stimulation with the 1 mm bipolar ring electrode generated the smallest change in potential. The orientation of the short and long electrodes resulted in greater potential changes in the dorsal direction (towards the nerves), whereas the potential changes generated by the ring electrode were more balanced across the dorsal and ventral directions.
Activation threshold depended on electrode location
The maximum AFs, regardless of whether they occurred at the DNP or CSN, also depended on the electrode location (Figure 3C, two-way ANOVA, p < 0.0001). The maximum AFs for stimulation in the membranous urethra (5-7 cm) were significantly larger than those for stimulation in the penile urethra (1-4 cm). Relative stimulation thresholds were determined by inverting the AFs, and the simulation results suggest that the CSN is activated at lower thresholds by stimulation in the membranous urethra than the thresholds necessary to activate the DNP by stimulation in the penile urethra (Figure 3D).
Activation threshold depended on electrode geometry
Comparison of the selectivity and AFR of the 2 mm monopolar and 2 mm bipolar ring electrodes revealed that bipolar stimulation required greater stimulation amplitudes to activate pudendal afferent fibers within the penile urethra (1-4 cm, Figure 6B), while no difference was predicted for stimulation in the proximal urethra. In vivo, the normalized stimulation thresholds for evoking an EAS response were not significantly different for bipolar ring electrodes and the monopolar ring electrodes (Figure 6C, two-way ANOVA, p = 0.17, n = 6 cats). However, the threshold ratios (bipolar electrode threshold divided by monopolar electrode threshold) revealed that thresholds were higher at 2-4 cm for the 2 mm bipolar ring electrode (Figure 6D), as predicted by the model simulations.
The modeled electrode geometries assumed that the electrodes were oriented in the direction of the nerve trunks and that electrode contact was flush with the urethral lumen. The effects of changing the orientation of the short electrode contact and modifying the diameter of the ring electrode were examined. Rotating the short contact electrode to face ventrally (away from the DNP) reduced the maximum AF by 30% for simulation of IES at 2 cm from the meatus. For the ring electrode, reducing the diameter of the stimulation catheter to one-half the diameter of the urethra (and filling the urethral cavity with urine, σ = 1.55) reduced the maximum AF by 20 and 30% for stimulation at 2 and 7 cm, respectively.
DNP branch activation depended on electrode geometry
Number of lateral branches of the dorsal nerve of the penis (DNP) activated before DNP trunk activation as determined by statistical significance (t-test) or selectivity & activating function (AF) ratio
p < .001
Intraurethral electrical stimulation is a minimally invasive method to investigate the bladder responses evoked by activation of pudendal afferent fibers. However, the complex innervation of the urethra and surrounding structures makes it unclear what nerve branches are activated and how this varies with electrode geometry and location. The results of this study show that the location and geometry of the electrode both play significant roles in determining the stimulation threshold and selective activation of the two primary sensory branches (DNP, CSN) of the cat pudendal nerve. In this case, electrode location appears to be the primary factor in determining selectivity of activation. Also, the results indicate IES in the penile urethra activates the DNP trunk and not the lateral branches of the DNP.
This study provides a quantitative analysis of different electrode geometries for intraurethral stimulation, however there are several important limitations. First, the model is a simplified representation of the male feline lower urinary tract with neural innervation by the CSN and DNP. The nerves were represented as single trunks but the DNP has been shown to branch extensively in the area of the glans penis and the CSN typically has a lateral branch along the membranous urethra in addition to the medial branch modeled here . Second, the AF is only an approximation of the relative thresholds for nerve activation by electrical stimulation . Additionally, the fit between the urethra and the electrode contacts in vivo may vary, altering the current density at the different contacts in the multi-contact electrodes and ultimately affecting the thresholds for activation. However, the similarities between the in vivo stimulation thresholds and those predicted by the model demonstrate that the simplifications were justified to support our conclusions.
Selective activation of the DNP was best achieved by stimulation in the distal urethra (near the glans) while selective activation of the CSN was best achieved by stimulation in the proximal urethra (near the prostate). Bladder responses evoked by intraurethral activation of pudendal afferent fibers also exhibit different characteristics for stimulation near the glans penis (high frequency [33-40 Hz] excitation; low frequency inhibition [5-10 Hz]) and near the prostate (excitation at all frequencies [2-33 Hz]) [15, 16]. Further, these in vivo observations highlight the importance of selective DNP or CSN activation because the bladder response to activation of these nerves is different for different stimulation frequencies and involves different neural pathways .
The innervation of the urethra is spatially distinct [19, 20]. IES can activate afferent fibers in the pudendal, pelvic, and hypogastric nerves, and the degree of activation of each nerve is dependent on intraurethral electrode location . Innervation of the proximal urethra by autonomic nerve fibers from the pelvic and hypogastric nerves overlaps with the somatic innervation by CSN fibers [19, 20], and IES in the proximal urethra may result in co-activation of pudendal and autonomic fibers. A previous study of intraurethral stimulation in the cat found that the pudendal and pelvic nerves were both activated by intraurethral stimulation in the membranous urethra . The simulation and in vivo results show that the threshold for pudendal afferent fiber activation for stimulation in the proximal urethra (CSN activation) was lower than the threshold for stimulation in the penile urethra (DNP activation), so future clinical studies should investigate the use of lower amplitude stimuli in the proximal urethra compared to the penile urethra to avoid spillover of activation to neighboring nerves (e.g., autonomic innervation of the proximal urethra). The pudendal and pelvic afferent innervation of the urethra includes myelinated A-fibers and unmyelinated c-fibers. However, the myelinated pudendal urethral afferent fibers are larger, potentially consisting of Aα-, Aβ-, and Aδ-fibers, than the myelinated pelvic urethral afferent fibers, primarily Aδ-fibers [23, 24]. These differences in fiber diameters suggest that it may be possible to limit co-activation of pelvic and hypogastric nerve afferent fibers by minimizing stimulation intensity, but the in vivo thresholds were sufficiently high to suggest co-activation may be difficult to avoid. Pelvic and hypogastric nerves were not modeled here, but should be considered in future work. The inability to distinguish pudendal and autonomic activation in the proximal urethra is of concern for clinical studies investigating the ability to evoke bladder responses via urethral pudendal afferent fiber activation. In a previous study, intraurethral stimulation evoked contractions in persons with spinal cord injuries , but effective stimulation locations were 2-4 cm from the bladder neck, and the roles of pudendal and autonomic nerve fibers in the observed response is unclear.
The different electrode geometries generated different AFs, which suggests that stimulation thresholds would be different for the different electrode geometries (Figure 3D). The short electrode configuration exhibited the lowest stimulation thresholds (determined by the comparing the inverse of the AFs), followed by the ring electrodes (1 and 2 mm), while the bipolar ring electrodes (1 and 2 mm) required higher stimulation intensities to activate the pudendal afferent fibers. The short electrode was directed dorsally, toward the nerve branches, and in practice the orientation of the electrode may be difficult to maintain. Further, the results confirm that improper orientation significantly increases stimulation threshold. Thresholds with the ring electrode would be more consistent although slightly higher than the thresholds for the ideally oriented short electrode. Previous studies of intraurethral activation in the cat found no difference between stimulation thresholds for monopolar and bipolar stimulation. However, one study focused on stimulation in the proximal urethra , which our results predicted would not have different thresholds, while the second study compared thresholds in different animals , which are unlikely to be significantly different because of interanimal variability. Further, contact size and spacing between contacts differentially affect the ability to activate pudendal afferent fibers (e.g., increasing contact length decreases AFs but increasing contact spacing increases AFs) so comparison of electrodes of varying lengths and spacing is complicated. In vivo thresholds were smaller for monopolar stimulation than bipolar stimulation, but the difference in threshold magnitude was less than that predicted by the model. Anatomical variability may confound this measurement in vivo because the location of the stimulation target with respect to the electrodes contributes to threshold differences between monopolar and bipolar stimulation .
The selectivity between activation of the DNP and the CSN was dependent on electrode geometry. The narrow bipolar electrode had the greatest selectivity, but selectivity values for all electrodes tended to be high near the urethral meatus and the prostate. No electrode geometry exhibited selectivity >1 at 4 cm from the urethral meatus, suggesting that stimulation in the penile bulb will produce co-activation of the CSN and DNP. In vivo investigations of the bladder response to intraurethral stimulation considered the effect of stimulation location but failed to address the potential for simultaneous excitation of the CSN and DNP [15, 16]. Variability in the bladder response to intraurethral stimulation 4 cm from the urethral meatus led this distance to be excluded from quantification in our previous study of intraurethral stimulation in the cat , while 4-6 cm was grouped together in another study of IES . Bladder responses evoked by IES in the penile and membranous urethra are abolished by bilateral transection of the DNP and CSN, respectively , indicating that IES at different intraurethral location allows minimally invasive selective activation of different pudendal afferent branches. A better understanding of IES will enhance our ability to target pudendal afferent branches selectively in clinical investigations. In addition to providing insight into the ability to restore control of bladder function, selective pudendal afferent activation via IES may be a useful tool for enhancing understanding of the physiology and pathophysiology of urinary dysfunction.
Functional Significance of Lateral Branches of the DNP
A potential benefit of intraurethral stimulation verses transcutaneous (with external surface electrodes) or percutaneous stimulation of the DNP would be selective activation of urethral as opposed to cutaneous DNP fibers. Our results suggest that the range of activation of the lateral branches of the DNP without activation of the DNP trunk varies with electrode geometry. The lateral DNP branches are observed to give off branches that dive towards the urethra (sparsely) , and these urethral offshoots were not modeled, making our estimate of the impact of electrode configuration on urethral activation even more conservative. Based on these results, both clinical and experimental IES studies (which all utilize a ring electrode) are activating the DNP trunk, not the lateral branches. The 3-ring electrode could be further tested in vivo to determine if selective activation of the lateral DNP branches has any influence on the evoked bladder reflexes.
While intraurethral stimulation is an ideal means of activating urethral nerve fibers in the proximal urethra, percutaneous or transcutaneous stimulation of the DNP (or dorsal clitoral nerve) may be achievable at lower thresholds . A previous experiment found that percutaneous, transcutaneous, and intraurethral stimulation (monopolar ring electrode) activated the DNP at 3-5 mA, 10-15 mA, and 15-25 mA, respectively . Anatomical observations in humans and cats identified two populations of DNP axons [1, 19, 28], those travelling laterally on the penile body to the urethra and those travelling down the penile midline to the glans. If these populations play different roles in the inhibitory and excitatory bladder response to DNP stimulation, use of a 3-ring electrode configuration may be valuable for selective activation of the urethral fiber mediated reflex pathway. Transcutaneous DNP stimulation (with external surface electrodes) in humans evokes robust inhibition of the bladder [9–11], but selective activation of the urethral afferent fibers of the DNP may be necessary to evoke robust excitatory bladder responses in humans. This model relied on the detailed description of the innervation of the cat urethra. A thorough description of the innervation of the human urethra is needed to determine the ideal settings (electrode geometry and location) for clinical investigation of the bladder response to IES evoked selective activation of pudendal afferent branches.
The threshold intensity to activate pudendal afferent fibers by IES is dependent on stimulation location and electrode configuration. Additionally, selective activation of the DNP or CSN depends on stimulation location. A ring electrode configuration is ideal for minimizing thresholds and variability in clinical and preclinical IES studies, but use of a multi-contact ring electrode provides a means of examining the specific role of distal urethral afferents in the bladder response to DNP stimulation.
The authors thank Gilda Mills for her technical assistance during the in vivo experiments. This research was supported by the NIH (R01NS050514) a NSF Graduate Student Fellowship.
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