Evoked compound action potentials during spinal cord stimulation: effects of posture and pulse width on signal features and neural activation within the spinal cord

Objective. Evoked compound action potential (ECAP) recordings have emerged as a quantitative measure of the neural response during spinal cord stimulation (SCS) to treat pain. However, utilization of ECAP recordings to optimize stimulation efficacy requires an understanding of the factors influencing these recordings and their relationship to the underlying neural activation. Approach. We acquired a library of ECAP recordings from 56 patients over a wide assortment of postures and stimulation parameters, and then processed these signals to quantify several aspects of these recordings (e.g., ECAP threshold (ET), amplitude, latency, growth rate). We compared our experimental findings against a computational model that examined the effect of variable distances between the spinal cord and the SCS electrodes. Main results. Postural shifts strongly influenced the experimental ECAP recordings, with a 65.7% lower ET and 178.5% higher growth rate when supine versus seated. The computational model exhibited similar trends, with a 71.9% lower ET and 231.5% higher growth rate for a 2.0 mm cerebrospinal fluid (CSF) layer (representing a supine posture) versus a 4.4 mm CSF layer (representing a prone posture). Furthermore, the computational model demonstrated that constant ECAP amplitudes may not equate to a constant degree of neural activation. Significance. These results demonstrate large variability across all ECAP metrics and the inability of a constant ECAP amplitude to provide constant neural activation. These results are critical to improve the delivery, efficacy, and robustness of clinical SCS technologies utilizing these ECAP recordings to provide closed-loop stimulation.


Introduction
Evoked compound action potential (ECAP) recordings have been utilized as a quantitative measure of the neural response to spinal cord stimulation (SCS) for treating specific chronic pain conditions [1][2][3]. The ECAP is a bioelectrical signal reflecting the summation of action potentials generated by SCS and thus represents a quantitative measure of neural recruitment in the spinal cord. By automatically adjusting stimulation parameters to maintain a relatively constant ECAP amplitude, the ostensible goal of this approach is to maintain a consistent level of neural activation in the spinal cord despite changes in body position and activity [3,4].
Unlike cardiac pacemakers, which routinely incorporate electrogram sensing to inform a more physiologic, automatic control of the heart rhythm (so-called 'closed-loop' control) [5,6], SCS has traditionally been programmed in an 'open-loop' manner [3]. That is, the stimulation parameters are fixed unless manually changed. This approach may lead to sub-optimal therapeutic outcomes as the SCS is under-or over-delivered due to frequent movement of the spinal cord relative to the SCS electrodes [7,8].
To address this challenge, one approach is to utilize spinal ECAPs recorded from inactive (nonstimulating) electrodes as a feedback signal to provide real-time, closed-loop control of the stimulation [2,3]. As described above, these recordings can theoretically be used to maintain more consistent neural activation despite changes in body position and activity. However, several factors present challenges to the utility of this ECAP-based approach. First, the microvolt-amplitude ECAP must be distinguished from several sources of electrical (e.g., stimulation artifact) and biological noise in the recorded signal that are typically several orders of magnitude larger than the underlying neural response [9,10]. Second, this approach relies on the fundamental assumption that a constant ECAP amplitude equates to a constant degree of neural activation or dosing in the spinal cord [3,4]. This assumption may be an oversimplification as the ECAP is influenced by motion of the spinal cord relative to not only the stimulating electrodes, but the recording electrodes as well [11]. Finally, it remains unclear how ECAP recordings vary over stimulation parameters and across patients and postures. These unanswered questions complicate the broad application of ECAP-controlled, closed-loop SCS and its utility to contemporary SCS modalities.
To answer these questions, we utilized a combined experimental and computational modeling approach. We used experimentally acquired ECAP recordings in 56 patients undergoing a trial of SCS to quantify the variability in ECAP features. Then, we used computational models to interpret the observed experimental trends and to investigate the assumption that a constant ECAP amplitude equals a constant level of neural activation across various spinal cord positions. Our experimental results demonstrate dramatic variability in ECAP recordings across patients that must be accounted for in clinical systems utilizing this closed-loop approach. Furthermore, our computational modeling results demonstrate that maintaining a constant ECAP amplitude, the approach currently utilized in ECAP-controlled, closed-loop SCS [4], may not provide a constant degree of neural activation or dosing in the spinal cord.

Materials and methods
In this study, we acquired a library of spinal ECAP recordings and perceptual thresholds (PTs) from subjects already undergoing commercial SCS trials according to approved labeling. We performed recordings over a wide assortment of postures and stimulation parameters. We then processed the recordings to reduce stimulation artifact (a common noise signal associated with ECAP recordings) and assess relevant ECAP features. Finally, we used a computational model of ECAPs to simulate the effects of SCS pulse width (PW) and dorsal cerebrospinal fluid (dCSF) thickness on the ECAP recordings. We then related our model findings back to the experimentally acquired ECAP dataset. We provide the in-depth methodology for these steps below.

Experimental data acquisition
In this study, we analyzed data obtained from 56 subjects. These experimental data were acquired as part of a non-significant risk feasibility trial assessing the effects of stimulation parameters, electrode choice, and subject activity on both spinal ECAPs and the control characteristics of an investigational closed-loop SCS system. For these ECAP recordings, we used a custom, investigational research system to connect to the subjects' conventional, eight-electrode, 60 cm long, percutaneous leads (Model #977D260, Medtronic plc). The research system delivered cathodic-leading, symmetric, biphasic stimulation with an interphase interval of 30 µs and recorded the ECAP elicited by the stimulus pulse. The details of the stimulating and recording functions of this system are described elsewhere [12].
Similar to other studies [9,11], we used the research system to acquire ECAPs from the subjects' trial leads at the end of their commercial trial and immediately prior to removal of the leads. The ECAPs were elicited at a fixed rate of 50 Hz with a selection of PWs (90-300 µs) while the subject assumed various postures (seated, supine, right and/or left lateral recumbency, standing) (see table S1 for descriptions of the subsets of trials for each experimental condition). The lead position was selected by the implanting physicians to optimize the subjects' therapeutic outcomes during the trial and in general consisted of two staggered leads near the T9 spinal level. However, one subject had two staggered leads placed near C4 and another subject had a single lead implanted. We delivered stimulation on either end (rostral or caudal) of one lead via a guarded cathode configuration, or adjacent and/or skipped electrode bipolar electrode pairs. The bipolar recording electrodes were allocated to the opposite end of the same lead. The stimulation consisted of 'growth curve sweeps' in which the SCS amplitude was ramped up from either 0 mA or from a stimulation amplitude below subject perception in 0.1 mA increments until the subject perceived the stimulation (perception threshold, or PT). We then ramped the stimulation up further until the subject reported discomfort (discomfort threshold, or DT). We defined the DT as the stimulation amplitude at which the subject would not want to experience the stimulation for more than 30 s. The time at each stimulation amplitude interval varied, with a median time of 0.64 s (range: 0.08-50.66 s). The dwell time at each amplitude step was chosen collaboratively between the subject and the researcher. For instance, subjects often needed very little dwell time to assess if there was perceptible stimulation with very low SCS amplitudes. However, they requested longer intervals with supra-threshold SCS when describing the perception of the stimulation. We did not assess all postures, PWs, and electrode choices in each subject owing to time constraints, the inability of the subjects to comfortably assume all postures, and the desire to limit subject fatigue. We performed all measurements and data analyses identically between subjects; no specific randomization or investigator blinding was employed. Following data collection, we disconnected the subjects' leads from the research system and the subjects exited the study.

ECAP processing
Stimulation artifact is an electrical noise contaminant that manifests both coincident with and shortly after the delivery of a stimulation pulse. Reducing this artifact is critical for accurate and consistent ECAP measurement and characterization [9]. In this study, we adopted previously described methods for reducing artifact and quantifying ECAP amplitudes (figure 1) [11]. Briefly, we averaged 50 consecutive recordings in a growth curve sweep (corresponding to 1 s of data) to limit non-synchronous noise (figure 1(B)), then we used an artifact model (AM) scheme to reduce the stimulation artifact [9]. The AM scheme consisted of fitting an exponentially shaped 'model' to the stimulation artifact, and then digitally subtracting the model from the recording to isolate the neural response ( figure 1(C)). For the ECAP amplitude estimate (the voltage difference between the N1 and P2 features of the polyphasic ECAP), we defined N1 as the minimum ECAP amplitude in the window from 0.75 ms to 1.05 ms following the leading edge of the stimulation waveform. Similarly, we defined P2 as the maximum ECAP amplitude in the window from 1.05 ms to 1.45 ms following the leading edge of stimulation. As changes in SCS parameters influence the ECAP latency [12], we shifted our N1 and P2 search windows as needed to account for delayed ECAP initiation with widened PWs.
Following ECAP denoising and amplitude estimation, we plotted growth curves representing the ECAP amplitudes for each sweep of the stimulation amplitude (figure 1(E)) [13]. Growth curves are a convenient tool for summarizing the changes in neural activation reflected by the ECAP as stimulation amplitudes are varied. The curvilinear transition point in the growth curve from sub-threshold stimulation (no neural activation) to supra-threshold stimulation (linear growth) is of particular interest. By fitting the growth curves, we were able to derive a parameter at this curvilinear transition point, the ECAP threshold (ET) ( figure 1(E)). The ET tightly tracks with the patient PT across SCS PWs and postures [11]. The ET and the supra-threshold slope of the growth curve (ECAP growth rate) depend on a multitude of factors, including variable thickness of the cerebrospinal fluid (CSF) between both the recording and stimulating electrodes and the spinal cord [11], the distribution and type of fibers contributing to the ECAP [14,15], and the selected stimulation parameters [16]. See the appendix for a detailed description of the methods used in the AM, growthcurve fitting, and ET calculation.

Computational modeling
We improved upon a previously published computational modeling infrastructure of spinal ECAPs generated during SCS [14]. This modeling infrastructure included a finite element method (FEM) model consisting of a spinal cord (both gray and white matter), CSF, dura, epidural tissue, spine, and surrounding bulk tissue previously described by Anaya et al [14]. We defined the gray and white matter boundaries of the spinal cord model using human cadaver samples of the lower thoracic spinal cord [17]. We did not include explicit representations of the dorsal roots because a previous study found that the inclusion of dorsal roots had a minimal effect on simulation results [18]. Our initial dCSF thickness was 3.2 mm [14,19,20]. Within the epidural tissue along the anatomical midline, we embedded a cylindrical SCS electrode array with a total length of 75 mm. The distal end included eight electrodes, each with a length of 3 mm, diameter of 1.3 mm, and an edgeto-edge spacing of 4 mm. This electrode design was the same design used in our experimental dataset. We surrounded the electrode by a 0.3 mm thick encapsulation layer [14].
We discretized our FEM model into tetrahedral elements using 3-matic (Materialise NV, Belgium) and exported the final volume mesh into COMSOL Multiphysics (COMSOL Inc., USA). Next, we assigned electrical properties to the tissues using the conductivities described in Anaya et al [14]. To match the average bipolar electrode impedance measured in our experimental dataset, we set the electrical conductivity of the encapsulation layer to be 0.089 S m −1 [21,22]. We used the conjugate gradient method to calculate the electrostatic potential fields generated in the FEM model. As described below, we used these potential fields to estimate both the neural We estimated the stimulation artifact and subtracted the artifact from the averaged raw recording to produce the predicted ECAP. (D) Experimental ECAPs at various stimulation amplitudes. Note, the P1, N1, and P2 peaks in the waveform. As stimulation amplitude increases, the timing of the peaks remains relatively constant, yet the ECAP amplitude increases. (E) Experimental growth curve generated from the ECAP recordings shown in D. The experimental growth curve (blue) and a curve fit (brown) to the experimental data using the method described in the appendix. We used this curve fitting to estimate the ECAP threshold (ET). response to SCS as well as the corresponding ECAP recording.
In contrast to the previous version of this model [14], we divided our population of axon models into 100 unique fiber-diameter groups (one fiberdiameter group for every 0.1 µm between 6 and 15.9 µm), for a total of 10 000 fibers per simulation. As axons in the ventral half of the white matter of the spinal cord did not contribute significantly to ECAP recordings (data not shown), we exclusively distributed axons in the dorsal half of the spinal cord using Lloyd's algorithm (figure 2) [18,23].
We performed axon simulations using the software package, NEURON, in a Python programming environment [24]. Our axon models consisted of multicompartment cable models of dorsal column sensory axons described in previous studies [14,[25][26][27][28]. Unless otherwise stated, we evaluated models using a pulse frequency of 50 Hz, a biphasic, cathodic-leading guarded cathode (E5+/E6−/E7+) stimulation configuration, a PW of 150 µs, and a bipolar recording configuration. We utilized a reciprocity-based approach to calculate the SCSinduced ECAPs recorded from the implanted electrode array (figure 2) [29][30][31]. To calculate model ECAP recordings, we scaled the signal contribution of each fiber diameter group according to the physiological densities observed in the cadaveric human spinal cord [14,15,18].
Following previous SCS computational modeling studies, for each model, we defined the model PT (mPT) as the minimum stimulation amplitude to activate ⩾10% of dorsal column axons [32,33]. We defined the model DT (mDT) as 1.4 * mPT [19,32,33]. For each set of stimulation parameters, we generated a model growth curve by incrementing the applied stimulation amplitudes from 0.1 mA to the mDT, in 0.1 mA increments (figure 3).

ECAP variability due to PW
Previous experimental work has shown that increasing the stimulus PW linearly increases the delay of (1) Stimulation is applied to the spinal cord. We used a finite element method model to estimate the potential fields generated during SCS (isopotential lines shown near the proximal electrodes). (2) Stimulation induces action potentials in spinal neurons (only a single axon is shown for clarity). In our model, we distributed multicompartment cable models of axons in the dorsal white matter and simulated their response to the applied stimulus. (3) Action potentials propagate rostrally and caudally from the site of initiation. As the action potentials travel past the recording electrodes, the voltage difference between the recording electrodes will measure a (4) spinal ECAP. We used a reciprocity-based approach to calculate the model ECAP recordings. * Importantly, the measured ECAP represents the summation of all active fibers passing by the recording configuration, rather than the single fiber shown here.
the ECAP relative to the stimulus onset [12]. In our experiments, we built on this work by characterizing the effect of different PWs (90-300 µs) on the growth curve.
We compared experimental growth curves for multiple PWs obtained from within a single subject with consistent posture, stimulation configuration, and recording configuration. If a subject had measurements for at least three independent PWs, we generated both strength-duration and charge-duration curves using the ET from each trial. Then, we estimated the chronaxie and rheobase from the chargeduration curve (see the appendix for details describing the charge-duration curve fitting) and analyzed fits with an R 2 above 0.50.
We performed simulations for eight PWs ranging from 90 µs to 300 µs in 30 µs increments. We calculated the ECAP amplitude, growth curve and corresponding metrics (e.g. ECAP amplitudes, model ET (mET), ECAP growth rate), and directly compared these model predictions to trends in the experimental dataset. Finally, we generated model-based strengthduration and charge-duration curves and compared these curves to the corresponding experimental data.
2.5. ECAP variability due to posture dCSF thickness, a parameter that varies by millimeters during postural changes, strongly influences the ECAP amplitudes and perception of the . The evoked compound action potential (ECAP) growth curve. The ECAP growth curve is the relationship between the stimulation amplitude and the corresponding ECAP amplitude. The left column shows the applied stimulus (top), example neural activation (2nd row), and simulated ECAP response (3rd row) at a low stimulus amplitude (1.7 mA) in which no neural activity/ECAP is generated. The middle and right columns show the same parameters for both a moderate stimulus (6.0 mA) and high stimulus (10.8 mA), respectively. The bottom row shows the growth curve summarizing the relationship between the stimulation amplitude and ECAP response. Each dashed vertical line shows the corresponding point on the growth curve to the column above. stimulation (figure 4) [7,14,34]. Therefore, we focused our analyses on differences in ET and ECAP growth rate for alternate postures in our experimental dataset and analogously for various dCSF thicknesses in our computational models.
In the experimental dataset, our analysis exclusively compared seated versus supine postures due to a limited number of experimental trials for other postures. For consistency in the applied waveform, we restricted this analysis to trials with guarded cathode stimulation with PWs ranging from 100 to 200 µs. To simulate the effects of changes in posture, we developed two computational models with dCSF thicknesses of 2.0 mm and 4.4 mm (in addition to our 3.2 mm dCSF model) ( figure 4) [7,14,19,20]. We characterized model ECAP recordings The growth curve summarizing the relationship between the stimulation amplitude and the ECAP amplitude. Each growth curve corresponds to a different dorsal CSF thickness. Postures that result in more dorsal CSF (e.g., prone) exhibit a less steep growth curve that is shifted to the right (i.e., more current is required to generate a given ECAP amplitude). Conversely, postures that result in less dCSF thickness (e.g., supine) exhibit a steeper growth curve and require less current for ECAP generation. We generated this example data using our computational modeling infrastructure. by calculating the ECAP amplitude, growth curve, and corresponding metrics (e.g., ECAP amplitudes, mET, ECAP growth rate). We then compared these model predictions to trends in the experimental data. Using these models, we also evaluated changes in neural activation resulting from the alternate dCSF thicknesses.

Statistical analysis
We quantified variations in ETs and suprathreshold ECAP growth rates using a linear mixed effects model. We fit the statistical model using fitlme in MATLAB (MathWorks, USA). This statistical model had a fixed intercept for posture and PW and a random effect to account for variability between subjects.

Results
From our experimental data, we considered a total of 479 trials from 56 subjects. Of these 479 trials, 195 did not have sufficient maximum ECAP amplitude (i.e., >4 µV) to be used for growth curve fitting or had poor growth curve fits (28 subjects had at least one trial that was included in analysis and one that was excluded; 11 subjects had all trials excluded from analysis). Therefore, our analyses considered 284 datasets obtained from 45 subjects. For the subjects with low maximum ECAP amplitudes observed during our measurements, it is important to note that these subjects were not entirely without ECAPs. Detectable ECAPs may have manifested with other electrode configurations or during activities, such as a back arch, that transiently resulted in a detectable ECAP.

ECAP strength-and charge-duration relationships
We examined how the stimulus PW affected the ECAP growth curves with respect to both the stimulation amplitude and the charge per phase. In both our experimental and modeling data, increasing the PW shifted the growth curve to the left, with longer PWs requiring lower stimulation amplitudes to elicit an equivalent ECAP amplitude (figures 6(A) and (C)). With regards to charge per phase, increasing the PW shifted the ECAP growth curve to the right, with longer PWs requiring higher charge per phase to elicit an equivalent ECAP amplitude (figures 6(B) and (D)). We also used our ET calculations to examine the rheobase and chronaxie in both our experimental data and modeling predictions. To estimate the rheobase and chronaxie, we fit the charge-duration plots with Weiss' equation (see the appendix for details regarding the charge-duration curve fitting) (figures 6(E) and (F)) [35]. For a stimulation amplitude corresponding to ET, the experimental group had a median rheobase of 1.  (R 2 = 0.964). Across subjects considered in our PW analysis, we observed a general decrease in PTs, DTs, and ETs as the PW increased (figure S1).

ECAP variability due to posture
We evaluated how the experimental ET and ECAP growth rate changed for recordings performed in seated versus supine positions. For 12 of the 45 subjects, growth curve sweeps were acquired in both seated and supine postures. In the seated group, the median ET was 4.5 mA with a median ECAP growth rate of 18.4 µV mA −1 (figures 7(A) and (B)). In contrast, the supine position had a median ET of 2.0 mA with a median ECAP growth rate of 32.0 µV mA −1 (figures 7(A) and (B)). When using a linear mixed effects model to account for inter-subject variability, we found that the ET for the supine posture was estimated to be 65.7% lower than the ET for the seated posture (95% confidence interval 59.1%-73.0%). The ECAP growth rate was also 178.5% larger for the supine position versus the seated positions (95% confidence interval of 157.1%-202.7%). In our computational model, we evaluated three spinal cord positions to mimic different postures. We generated model ECAP recordings for dCSF thickness of 2.0, 3.2, and 4.4 mm (figure 7(C)) [20]. The model with 2.0 mm of dCSF had a 50.0% decrease in mET and a 92.5% increase in the ECAP growth rate relative to the base model with 3.2 mm of dCSF. In contrast, the model with 4.4 mm of dCSF increased mET by 78.1% and decreased the neural slope by 42.0% relative to the base model with 3.2 mm of dCSF. Overall, our modeling trends showed strong alignment with the experimental trends.
In addition to evaluating growth curve parameters, we used our computational model to estimate the number of fibers that must be activated to generate the same ECAP amplitude for different postures. We focused our analyses on two ECAP amplitudes: 4 µV (representing stimulation near PT/ET) [11], and 25 µV (an approximate amplitude of a paresthesia-centric closed-loop SCS system) [1]. To generate a 4 µV ECAP, we applied Model predicted neural activation (G) and corresponding percent differences (H) throughout the spinal cord with an equivalent ∼25 µV ECAP recording. At physiological fiber densities, 1467 and 2847 fibers were activated for a dorsal CSF thickness of 2.0 and 4.4 mm, respectively. This difference corresponded to a 94.1% increase in the number of fibers necessary to generate the same ECAP amplitude. In C and F, darker colors indicate increased neural recruitment of fibers with diameters between 7.0 and 15.9 µm. Note, fibers smaller than 7.0 µm were excluded from this visualization as they were not activated at the given stimulation amplitudes.

Discussion
The electrophysiologic insight afforded by spinal ECAP sensing holds promise as a tool for optimizing the configuration and delivery of SCS. However, realizing this promise requires an understanding of the technical challenges, biophysical factors, and realworld effects influencing the acquisition and interpretation of the spinal ECAP. In our work, we used findings from 45 human subjects in conjunction with computational modeling to develop insight into these phenomena and the clinical utility of ECAP sensing with SCS. We discuss these considerations below.

ECAP variability
Unlike other bioelectric signals (e.g., the electrocardiogram) that are consistently observable and exhibit comparatively similar attributes (i.e., signal amplitudes and morphologies) between patients, spinal ECAPs exhibit both inter-and intra-patient variability that depend on several factors. These factors include the choice of stimulating and recording configurations, lead position, the patient's perception of SCS, the artifact rejection capability of the recording system, the type of SCS therapy selected, prescribed medication, and the patient's posture and activity [9,11,12,36]. This variability is plainly evident in figure 5 which provides an aggregate view of the ECAP growth curves and properties from our experimental dataset. With regards to the ECAP amplitude at DT (figure 5(C)), the median ECAP amplitude was 19.4 µV with a range from 3.4 µV to 235.4 µV. This observation speaks clearly to the need for robust systems that can consider this variability and customize the stimulation for the unique needs of each patient.
Of equal interest are the cases in which we detected no measurable ECAP above the 4 µV noise floor for a particular stimulation configuration or posture (156/479 trials; 33% of the trials in our dataset), or subjects in which we detected no measurable ECAP for any stimulation configuration or posture (4/56 subjects in our dataset). Several possible explanations exist for this observation. First, we included allcomers irrespective of SCS trial success or lead location. The lead placement was at the discretion of the implanting physician, and we did not enforce a strict midline placement (i.e., to maximize ECAP amplitudes). We believe that collecting ECAPs from such a heterogeneous population affords a more comprehensive view of what may be reasonably anticipated when acquiring ECAPs in a 'real-world' clinical setting. Second, for some patients receiving SCS, the PT is either the same as, or closely approximates, the DT. With these patients, the perception of any sensation associated with SCS for a given posture/electrode combination may be unacceptable and represent a potential limitation for ECAP-controlled, closed-loop SCS systems that rely on the continuous delivery of paresthesia-centric SCS [3]. Finally, the ability to resolve the µV-level ECAP is influenced by the signal shunting effect of the CSF layer, and potentially other factors, such as the proximity of the electrodes to the laminar bone [14]. For patients with comparatively large spinal canals and dCSF thickness, insufficient ECAP signal-to-noise ratios may mean that ECAP-controlled, closed-loop SCS is not possible in some patients.

Relating experimental observations to the computational model
Our experimental ECAP data also provided a means to assess the validity of our computational model. We compared ECAP measures (e.g. ET, growth curve slope, ECAP amplitude) as a function of posture/dCSF thickness between the experimental results and the corresponding modeling predictions, as well as the effect of the stimulus PW on the growth curves and strength-and charge-duration curves. In both our experimental ECAP recordings and simulations, we noted a clear dependence of the ECAP on posture and dCSF thickness. Growth curves in the supine posture demonstrated lower ETs and higher growth rates when compared to a seated posture ( figure  S2). Furthermore, the ECAP amplitudes at DT were higher in the supine versus seated position. These trends likely stem from smaller separation between both the stimulating and recording electrodes and the spinal cord when supine versus upright. Our computational model showed similar trends to these experimental findings when we decreased the dCSF thickness (figure 7). Increasing the dCSF thickness, as happens with shifting from a supine to prone posture, exhibited an opposite effect, with larger mETs and reduced growth rates.

Does a constant ECAP amplitude imply constant neural recruitment?
Because our computational model predictions matched the trends observed in our experimental dataset as described above, we could then employ our computational model to answer additional questions regarding the ECAP recordings. One such question is whether adjusting the stimulation amplitude to maintain a constant ECAP amplitude results in a constant level of neural recruitment. A constant degree of neural activation is the ostensible goal employed by some ECAP-controlled, closed-loop SCS systems as a method to improve the comfort and efficacy of paresthesia-centric SCS [3,4]. With our computational model, we demonstrated that the relationship between ECAP amplitude and neural recruitment is more nuanced than previously suggested in the literature.
To help illustrate the relationship between the ECAP recording and the underlying neural recruitment, we analyzed a series of computational models representing different postures by varying the dCSF thickness. In each model, we set the stimulation amplitude to elicit equivalent ECAP amplitudes. We found that each model required vastly different degrees of neural activation to produce equivalent ECAP amplitudes ( figure 8). For instance, to maintain a constant ECAP amplitude of 25 µV, 94% more axons had to be activated in the prone position (dCSF = 4.4 mm) relative to the supine position (dCSF = 2.0 mm). These results suggest that using an ECAP amplitude as a 'target' for closed-loop SCS does not guarantee consistent neural recruitment. This phenomenon results from the fact that the ECAP amplitude is influenced not only by variable distance between the stimulation electrodes and the spinal cord, but also by the variable distance between the recording electrodes and the spinal cord [11]. As the dCSF thickness increases, smaller ECAP amplitudes are noted due to increased distances between the recording electrodes and the neural sources in the spinal cord [14].
Although our models predicted that approximately twice as many fibers were activated in a prone versus supine posture for both target ECAP amplitudes, it is important to consider the change in the absolute number of fibers activated for each target ECAP amplitude. To maintain a target ECAP amplitude of 4 µV, our model predicted that 135 fibers had to be activated in the supine position and 238 fibers in the prone position, corresponding to an absolute difference of 103 fibers ( figure 8(D)). To maintain a constant target ECAP amplitude of 25 µV, our model predicted that 1467 fibers had to be activated in the supine position and 2847 fibers in the prone position, corresponding to an absolute difference of 1380 fibers ( figure 8(H)). This result means that 13 times as many fibers were activated to maintain the larger target ECAP amplitude of 25 µV relative to the lower target ECAP amplitude of 4 µV. Recognizing that perceived intensity of stimulation grows linearly with fibers activated, our modeling suggests a supine-to-prone postural shift would result in a larger change in perceived stimulation intensity with a closed-loop SCS system configured to maintain a fixed 25 µV ECAP versus a 4 µV ECAP. Further, differential changes in neural activation (figure 8(D)) with the modeled postural shifts in this work are constrained to the dorsal columns when stimulation is configured to maintain a constant 4 µV ECAP. In contrast, the differential neural activation with a 25 µV ECAP (figure 8(H)) spreads laterally past the dorsal columns toward the dorsal root entry zone. The clinical implications of this phenomenon are unknown but may be related to the stimulation-related events seen in some ECAP sensing SCS systems [2].
Clinically, these results suggest that system operation at a lower target ECAP amplitude, such as near ET (which closely tracks PT)-an approach employed with some contemporary SCS therapies [37], and potentially enhanced further with closedloop control using ECAPs [8]-would provide more consistent dosing in the spinal cord and better approximate perceptual and electrophysiologic equivalence over posture and activity. Furthermore, it may be an option for patients that prefer paresthesiafree stimulation and help avoid complications associated with SCS-induced paresthesia, which can disturb sleep, or be experienced as excessive or uncomfortable [38,39].

Study limitations and future work
This study had some potential limitations that should be noted. One potential limitation was that we only performed acute experimental recordings during the externalized trial phase of SCS. It is possible that the results may differ for ECAP recordings performed with chronically implanted SCS systems. Another potential limitation of our modeling work is the absence of sources of stimulation artifact and biological noise. This lack of noise sources causes the model growth curves to have two distinct regions: a sub-threshold stimulation region with no neural activation (i.e., ECAP amplitude of 0 µV below mET) and a supra-threshold stimulation region. This shape differs from the experimental growth curves in the sub-threshold region which contain both an offset and a non-zero slope due to stimulation artifact. Additionally, in the supra-threshold stimulation region, there were often differences between the experimental and model ECAP growth rates. These differences may be due to several factors, such as variations in anatomy, lead placement, and recruitment profiles across individual subjects relative to the generalized model. However, it is important to note that we observed a large amount of variability in the experimental ECAP growth rates (figures 5(A) and (F)), and our model growth rates fell within the experimental range. Finally, the geometrical and electrical properties of our computational model were defined using averaged geometrical values from literature. This generalized approach can be used to investigate technical and anatomical factors (e.g., lead lateralization, dCSF thickness) [14], but future work should examine these factors in more detail and consider a patient-specific modeling approach to fully characterize the influence of sources of interpatient variability on ECAP-based closed-loop SCS [40,41].

Conclusions
Spinal ECAP sensing affords an unprecedented opportunity to optimize SCS therapies by directly assessing the neural response elicited by the stimulation. To further improve this therapy, it is imperative that we fully understand the anatomical and technical factors that influence these ECAP recordings. Therefore, we performed a combined experimental and computational modeling study to address these knowledge gaps. In our experimental data, we found high inter-subject variability across ECAP metrics, and this variability needs to be considered for robust and consistent closed-loop implementations. ECAP-based, closed-loop SCS was developed to provide consistent neural dosing or recruitment by maintaining a consistent ECAP amplitude. However, our computational modeling results demonstrate that maintaining a constant ECAP amplitude does not guarantee constant neural recruitment in the spinal cord and highlights a potential limitation in this closed-loop approach, particularly with paresthesiacentric SCS. These results are critical to improve the delivery, efficacy, and robustness of closed-loop SCS techniques.

Data availability statement
The data cannot be made publicly available upon publication because they contain commercially sensitive information. The data that support the findings of this study are available upon reasonable request from the authors. ) .
The neural transition equation assumes no neural activity below I thr and a linear rate of change of neural activity significantly above I thr . The transition between these two linear regimes is described by the curvature term, σ. In some trials, the subject derived growth curve may predominantly be a result of improper artifact removal. To assess the quality of the artifact removal, we fit a line (with yintercept = N) to the last three quarters of the data from each subject's growth curve. If the growth curve model did not reduce the average error of the linear model by 50%, we assumed that the resulting data was primarily a result of improper artifact removal, and the trial was discarded. Details regarding this growthcurve fitting have been previously published [11].

ET calculation
We calculated the ET from the growth curve using the following equation: Based on the results of Pilitsis et al, we assumed a value of G = 1.5 [11].