Bioheat model of spinal column heating during high-density Spinal Cord Stimulation

Abstract

Introduction:

High density spinal cord stimulation (HD-SCS) delivers higher charge per time by increasing frequency and/or pulse duration, thus increasing stimulation energy. Previously, through phantom studies and computational modeling, we demonstrated that stimulation energy drives spinal tissue heating during kHz-SCS. Here, we predicted temperature increases in the spinal cord by HD-SCS, the first step in considering the potential impact of heating on clinical outcomes.

Materials and Methods:

We adapted a high-resolution CAD-derived spinal cord model, both with and without a lead encapsulation layer, and applied bioheat transfer Finite Element Method (FEM) Multiphysics to predict temperature increases during SCS. We simulated HD-SCS using a commercial SCS lead (eight contacts) with clinically relevant intensities (voltage-controlled: 0.5–7 V_rms) and electrode configuration (proximal bipolar, distal bipolar, guarded tripolar [+ − +], and guarded quadripolar [+ − + − +]). Results were compared with the conventional and 10 kHz-SCS (current-controlled).

Results:

HD-SCS waveform energy (reflecting charge per second) governs joule heating in the spinal tissues, increasing temperature supra-linearly with stimulation RMS. Electrode configuration and tissue properties (an encapsulation layer) influence peak tissue temperature increase - but in manner distinct for voltage-controlled (HD-SCS) compared to current-controlled (conventional / 10 kHz-SCS) stimulation. Therefore, depending on conditions, HD-SCS could produce heating greater than 10 kHz-SCS. For example, with an encapsulation layer, using guarded tripolar configuration (500 Hz, 250 μs pulse width, 5 V_peak HD-SCS), the peak temperature increases were 0.36 °C at the spinal cord and 1.78 °C in the epidural space.

Conclusions:

As a direct consequence of the higher charge, HD-SCS increases tissue heating; voltage-controlled stimulation introduces special dependencies on electrode configuration and lead encapsulation (reflected in impedance). If validated with an in vivo measurement as a possible mechanism of action of SCS, bioheat models of HD-SCS serve as tools for programming optimization.

INTRODUCTION

To optimize pain control and patient acceptance, novel approaches for spinal cord stimulation programming are being developed. High density spinal cord stimulation (HD-SCS) delivers higher charge per second by increasing duty cycle (increasing frequency and/or pulse width) [1]–[4]. Duty cycles of HD-SCS are 9–50% [1], [5]–[7], compared to 2–4% for conventional SCS and 40–80% for kHz-SCS [1], [2], [8], [9]. Charge per second increases with duty cycle times the stimulation peak intensity. Note that when only one pulse phase is used in calculation (i.e., counting pulses of one phase and disregarding pulses of the other phase), these reported duty cycles are halved. Stimulation energy increases with duty cycle times the square of intensity [10]. Clinically, HD-SCS allows pain relief without paresthesia by administering subthreshold intensity; nonetheless, charge per second and energy applied are relatively high compared to conventional SCS [4], [6], [10], [11].

We previously showed using phantom measurements and bio-heat FEM computational models that increased SCS energy – whether by frequency and pulse duration (duty cycle) or intensity-contributes to increasing spinal tissue temperature through joule [8], [9]. Here, we simulate spinal tissue heating by HD-SCS including consideration of the impact of voltage-controlled stimulation, multipolar guarded electrode configurations, and an encapsulation layer (from scar tissue formation around the lead; [12], [13]). We predict that the high charge per time characteristic of HD-SCS increases spinal tissue heating, and that voltage-controlled stimulation introduces special sensitivity to electrode configuration and lead encapsulation.

MATERIAL AND METHODS

We adapted a computer-aided design (CAD) model of the of lower thoracic (T8-T12) spinal cord with seven tissue compartments including vertebrae, intervertebral disc, soft-tissues, epidural fat, dura, CSF, and spinal cord (white matter and gray matter combined) in SolidWorks 2016 (Dassault Systemes AmericasCorp., MA, USA) (Fig. 1). A simulated Medtronic Vectris SureScan HD-SCS lead (1×8 Compact (977A2); electrode diameter: 1.3 mm; electrode length: 3.0 mm; edge-to-edge inter-electrode spacing: 4 mm) was positioned in the epidural fat (approximately 5.1 mm away from the dorsal surface of the spinal cord, along the mediolateral midline of the spine). We modeled only a single lead, while SCS may also be applied with multiple leads. The dimensions of the individual tissues, modeled here as an isotropic homogeneous volume conductors, were based on our prior studies [8], [9]. The entire CAD model assembly was then manually segmented and meshed into a finer mesh using a built-in voxel-based adaptive meshing algorithm of Simpleware ScanIP (Synopsys Inc.,CA, USA) . Mesh density was refined until additional model refinement produced less than 1% difference in peak temperature change and peak electric field. The resulting mesh consisted of > 13.5 million tetrahedral elements. The final finite element method (FEM) model was later imported and computationally solved in COMSOL (COMSOL Multiphysics. MA, USA).

Figure 1: SCS FEM bioheat model design.

(A) CAD derived human spinal cord anatomy of the lower thoracic spine (T8-T10) with seven segmented spinal tissue compartments, and an epidurally implanted commercial eight contact SCS lead. (B, C) Different views of the meshed spinal cord FEM model. (D) Predicted maximum temperature increase at the epidural space (electrode surface) and spinal cord.

During HD-SCS, joule heating is produced by an electrical current flow through the tissue. This thermal energy source was modelled as σ|∇V|² where V (Volts) is an induced local potential by stimulation and σ (Sm⁻¹) is the electrical conductivity of the tissue. We assumed a quasi-static electrical conduction model, which allowed us to apply Laplace ‘s equation to compute the electric potential V (Volts) as follows [14]–[16]:

$$\nabla ·\left[\sigma \nabla V\right] = 0$$ (1)

Consequently, a constant voltage/current was administered corresponding to the stimulation RMS (at the anode, with the cathode grounded). Based on our prior analysis, providing an electrode boundary condition with the appropriate constant RMS value correctly predicts resulting temperature change [8], [9], [15], [17]. RMS SCS intensities were calculated based on corresponding peak intensities and stimulation waveform parameters, as previously derived [8], [9], [15], [17]. The relationship between stimulation RMS and duty cycle, DC, is shown in Equation 2

$$X_{RMS} =X_{\mathit{\text{Peak}}}\sqrt{DC}$$ (2)

where $DC=\frac{Pulse Width}{Pulse Duration}$ ,X_Peak is the peak bipolar stimulation intensity, and X_RMS is the corresponding RMS value for current-controlled or voltage-controlled stimulation.

We coupled joule heating during SCS (1) and solved the Pennes bio-heat transfer equation to approximate temperature distribution throughout a perfused tissue as:

$$\rho C_p\frac{\partial T}{\partial t}=\nabla .\left(\kappa \nabla T\right)-{\rho }_b{C}_b{\omega }_b\left(T-T_b\right)+Q_{met}+\sigma {\left|\nabla V\right|}^2$$ (3)

where ρ,ρ_b,C_p,T_b,κ,ω_b,C_b and Q_met are spinal tissues density (kg m⁻³), blood density, specific heat capacity of spinal tissues (J kg⁻¹ K⁻¹), core/blood temperature (K), thermal conductivity of spinal tissues (W m⁻¹ K⁻¹), blood perfusion rate (s⁻¹), blood specific heat capacity, and metabolic heat generation rate (Wm⁻³), respectively [15], [18]. We solved the model under steady state assumption $\left(\frac{\partial T}{\partial t}=0\right)$.

The biophysical and thermo-electrical properties of biological tissues were based on prior studies [6], [8], [9], [19]–[23]. The assigned properties for different spinal tissues are listed in Table 1.

Table 1: Biophysical and thermo-electrical properties of the modelled biological tissues.

Note in avascular tissues, blood properties and Q_met are set to zero.

Spinal Tissues	Soft Tissue	Vertebrae	IV Disc	Epidural Fat	Dura	CSF	Spinal Cord	Encapsulation
Conductivity, σ (S m−1)	0.004	0.04	0.6	0.04	0.368	1.77	0.1432	0.13
Thermal Conductivity, κ (W m −1 k−1)	0.47	0.32	0.49	0.21	0.44	0.57	0.51	0.21
Blood density, ρb (kg m−3)	1057	1057	0	1057	1057	0	1057	1057
Specific heat capacity of blood, Cb ( J kg −1 K −1 )	3600	3600	0	3600	3600	0	3600	3600
Blood perfusion rate, ωb (s −1 )	0.00009	0.00048	0	0.00008	0.009	0	0.009	0.00008
Metabolic heat generation rate, Qmet ( Wm−3 )	368	26.1	0	302	15575	0	15575	302

The thermoelectric properties of the HD-SCS lead were given as: Platinum/Iridium contact (σ = 4 × 10⁶ S m⁻¹; κ = 31 W m⁻¹ K⁻¹) and polyurethane inter-electrode gap (σ = 2 × 10⁻⁶ S m⁻¹; κ = 0.026 W m⁻¹ K⁻¹). The role of scar tissue formation (encapsulation), an inflammatory response after a SCS implant, has been previously studied [12], [24]. The resistivity of the encapsulation tissue alters the electric field generation and distribution around chronically implanted electrodes [22], [23]. Here, we simulated and contrasted the effect of an encapsulation layer on spinal tissues heating for the undermentioned stimulation conditions. Thermo-electric properties of the lead encapsulation layer were assigned as indicted in Table 1 [12], [22], [23], [25], [26].

In studies comparing HD-SCS, Conventional SCS, 10 kHz-SCS, a proximal bipolar configuration was simulated by energizing the third electrode of the stimulation lead or E3 (cathode) and E4 (anode). Additional HD-SCS electrode configurations were distal bipolar (E1 (cathode), E8 (anode)), guarded quadripolar (E3 (anode), E4 (cathode), E5 (cathode), E6 (anode)), and guarded tripolar (E4 (anode), E5 (cathode), E6 (anode)). The remaining external boundaries of the spinal cord and surrounding tissues were electrically insulated [15], [17], [24]. For thermal boundary condition, the temperature at the outer boundaries of the model was fixed at core body temperature (37 °C), assuming no convective heat loss to the ambient temperature, no convective gradients across spinal surrounding tissues, and no SCS-induced heating at the model boundaries. The initial temperature of the tissues was set to the core body temperature [15], [17], [24]. To ensure model boundaries and mesh resolution did not impact results, we confirmed 1) <0.01 °C increase in temperature at the model boundaries when SCS was activated; 2) <0.001 % increase in current density at the model boundaries during SCS; and 3) <5% temperature increase when relative tolerance was decreased by 100X. Note that monopolar stimulation was not simulated in this work; therefore, the outer boundaries were not grounded.

Using clinically relevant HD-SCS intensities (0.5 – 7 V_peak) [1], [6], [10] and electrode configurations (proximal bipolar, distal bipolar, guarded tripolar [+ − +], and guarded quadripolar [+ − + − +]), we predicted the maximum temperature increase by a commercial SCS lead, both with and without lead encapsulation layer (Fig. 1). Wherever stated, the RMS SCS intensities were calculated based on corresponding peak intensities and stimulation waveform parameters, as previously derived [8, 9]. For stimulation RMS values calculations purposes, we assumed that all SCS systems waveform outputs were biphasic symmetric. The maximum temperature increases by voltage-controlled HD-SCS (frequency =500 Hz, pulse width = 250 μs, V_peak = 5 V) were compared with current-controlled conventional SCS (f = 50 Hz, pulse width= 200 μs, I_peak = 3.5 mA) [1], [2], [27] and 10 kHz-SCS (frequency =10 kHz, pulse width = 30 μs, I_peak = 3.5 mA) [2], [8], [9], [28] for a proximal bipolar electrode configuration, both with and without lead encapsulation conditions. Note that for each SCS approach, we evaluated clinically applicable (but relatively high) stimulation doses [1], [3], [4], [7], [9], [11], [29]. In a sperate analysis, we simulated the sensitivity of maximum temperature increase with various RMS intensities (Table 2).

Table 2: Sensitivity of HD-SCS intensities (RMS) on maximum temperature increase across different electrode configurations, both without and with encapsulation tissue layer.

Maximum temperature at the epidural space (Electrode) and spinal cord (SC) with and without encapsulation increased with RMS intensities, higher with encapsulation layer and guarded tripolar [+ − +] electrode configuration. Predicted maximum temperature at the epidural space and spinal cord for different electrode configurations at clinically relevant HD-SCS intensities for non-encapsulation stimulation lead (A) and encapsulation lead (B). For each RMS stimulation intensity, the corresponding peak voltage assuming 500 Hz, 250 μs is noted.

A. Non-encapsulated simulation Lead
	Proximal		Distal		Guarded + − − +		Guarded + − +
RMS (V)	Electrode	SC	Electrode	SC	Electrode	SC	Electrode	SC
0.5	0.038	0.000	0.032	0.000	0.039	0.000	0.043	0.000
1.5	0.120	0.009	0.098	0.003	0.	0.019	0.191	0.023
2.5	0.288	0.061	0.218	0.026	0.303	0.076	0.485	0.075
3.5	0.560	0.120	0.424	0.060	0.597	0.148	0.927	0.163
4	0.694	0.141	0.547	0.081	0.760	0.183	1.203	0.215
5	1.068	0.226	0.841	0.132	1.170	0.291	1.865	0.344
7	2.066	0.451	1.623	0.269	2.270	0.577	3.633	0.683
B. Encapsulated simulation Lead
	Proximal		Distal		Guarded + − − +		Guarded + − +
RMS (V)	Electrode	SC	Electrode	SC	Electrode	SC	Electrode	SC
0.5	0.060	0.002	0.047	0.000	0.058	0.005	0.069	0.005
1.5	0.210	0.038	0.140	0.017	0.222	0.052	0.333	0.061
2.5	0.505	0.127	0.337	0.058	0.551	0.158	0.851	0.175
3.5	0.950	0.250	0.650	0.120	1.103	0.300	1.777	0.357
4	1.232	0.294	0.834	0.155	1.352	0.379	2.165	0.456
5	1.902	0.460	1.283	0.246	2.089	0.592	3.337	0.703
7	3.693	0.895	2.483	0.483	4.053	1.157	6.480	1.380

All ΔT values are in °C

Electrode = Sampled at the electrode/Epidural Fat interface

SC = Sampled at the spinal cord surface

RESULTS

We implemented a CAD-derived FEM bioheat computational model of HD-SCS to predict local spinal tissue heating using a commercial eight contact SCS lead at various clinically relevant intensities (voltage-controlled: 0.5 – 7 V_rms), electrode configurations (proximal bipolar, distal bipolar, guarded tripolar [+ − +], and guarded quadripolar [+ − − +]), and under encapsulation or non-encapsulation conditions. These results were compared with predictions for current-controlled conventional SCS and 10 kHz-SCS.

We first considered maximum temperature increases at both the lead surface (epidural space) and spinal cord surface by conventional SCS, HD-SCS, and 10 kHz-SCS, all using proximal bipolar electrodes (Fig. 2). For each SCS approach, we evaluated clinically typical (but relatively high) stimulation doses (conventional: 50 Hz, 200 μs 3.5 mA_peak; HD-SCS: 500 Hz, 250 μs, 5 V_peak; 10 kHz-SCS: 10 kHz, 30 μs, 3.5 mA_peak). Note that HD-SCS is voltage-controlled while conventional and 10 kHz-SCS are current-controlled. In this series, only a proximal bipolar configuration was considered, and both encapsulation layer absent and present conditions were simulated. For the non-encapsulated lead condition (Fig. 2A), maximum temperature increase (ΔT) at the spinal cord was 0.003 °C for conventional SCS, 0.12 °C for HD-SCS, and 0.32 °C for kHz-SCS. For the non-encapsulated lead condition, ΔT at the epidural surface was 0.12 °C for conventional SCS, 0.56 °C for HD-SCS, and 1.50 °C for kHz-SCS. For the encapsulated lead condition (Fig. 2B), ΔT at the spinal cord was 0.0025 °C for conventional SCS, 0.25 °C for HD-SCS, and 0.16 °C for kHz-SCS. ΔT at the epidural surface for the encapsulated lead condition was 0.01 °C for conventional SCS, 1.00 °C for HD-SCS, and 0.8 °C for kHz-SCS. Therefore, addition of lead encapsulation layer increased temperature for the HD-tDCS while decreasing temperature for the conventional and 10 kHz-SCS cases. Using proximal bipolar electrodes, the maximum spinal cord temperature increases of 0.25 °C was predicted for the HD-SCS (500 Hz, 250 μs, 5 V_peak) condition with encapsulation, whereas the maximum epidural temperature increase of 1.50 °C was predicted for the 10 kHz-SCS (10 kHz, 30 μs, 3.5 mA_peak) condition without encapsulation.

Figure 2: Role of encapsulation on spinal tissue heating during conventional SCS, HD-SCS, and 10 kHz-SCS using a clinically typical stimulation programming and a proximal bipolar electrode configuration.

(A) For the non-encapsulated SCS lead condition, the maximum temperature increases for the conventional SCS, HD-SCS, and 10 kHz-SCS were 0.12 °C, 0.56 °C, and 1.50 °C at the epidural fat and 0.003 °C, 0.12 °C, and 0.32 °C, at the spinal cord, respectively. (B) For the encapsulated SCS lead condition, the maximum temperature increases for the conventional SCS, HD-SCS, and 10 kHz-SCS were 0.10 °C, 1.00 °C, and 0.80 °C at the epidural space and 0.0025 °C, 0.25 °C, and 0.16°C at the spinal cord, respectively. For each voltage-controlled simulation the corresponding equivalent current is reported (asterisks).

With computational models one can assess if differences in heating between voltage-controlled and current-controlled stimulation reflect a fundamental difference in processes or are interchangeable, provided the applied voltage is adjusted to a target current (or vice versa). The impedance (measured between the simulated electrodes) encountered by the HD-SCS lead between the proximal bipolar electrodes was 2170 Ω without encapsulation layer and 1130 Ω with encapsulation layer (calculated by Ohms law: I=V/Z). Using these inter-electrode impedances and applying Ohms law, 5 V_peak HD-SCS corresponds to 2.28 mA_peak without encapsulation and to 4.38 mA_peak with encapsulation. In control simulations, we confirmed applying these as current-controlled inputs to the respective models resulting in the same temperature increases as voltage-controlled (not shown). Voltage-controlled and current-controlled are thus interchangeable to the extent lead impedance is accounted for. For each voltage-controlled simulation, we report corresponding equivalent current and for current-controlled simulation, we report the corresponding voltage across the electrodes (values with asterisks, Fig. 2, 3).

Figure 3: Role of electrode configuration on spinal tissue heating without and with lead encapsulation layer during HD-SCS.

(A) For the non-encapsulated SCS lead condition, the whole volume maximum temperature increases at the epidural space and spinal cord were 0.56 °C and 0.12 °C for proximal bipolar, 0.42 °C and 0.06 °C for distal bipolar, 0.60 °C and 0.015 °C for guarded quadripolar, and 0.92 °C and 0.16 °C for guarded tripolar configuration, respectively. (B) For the encapsulated SCS lead condition, the whole volume maximum temperature increases at the epidural space and spinal cord were 1.00 °C and 0.25 °C for proximal bipolar, 0.65 °C and 0.12 °C for distal bipolar, 1.10 °C and 0.30 °C for guarded quadripolar, and 1.78 °C and 0.36 °C for guarded tripolar configuration, respectively. For each of these voltage-controlled simulations the corresponding equivalent current is reported (asterisks).

Focusing on HD-SCS (500 Hz, 250 μs, 5 V_peak), we next predicted the impact of electrode configuration, both without (Fig. 3A) and with lead encapsulation (Fig. 3B). Without an encapsulation layer, maximum temperature increases predicted in the epidural space and at the spinal cord surface, respectively, using proximal bipolar electrode configurations were 0.56 °C / 0.12 °C, distal bipolar were 0.42 °C / 0.06 °C, guarded quadripolar were 0.60 °C / 0.15 °C, and guarded tripolar were 0.92 °C / 0.16 °C. With an encapsulation layer, maximum temperature increases predicted in the epidural space and at the spinal cord, respectively, using proximal bipolar electrode configurations were 1.00 °C / 0.25 °C, distal bipolar were 0.65 °C / 0.12 °C), guarded quadripolar were 1.10 °C / 0.30 °C), and guarded tripolar were 1.78 °C / 0.36 °C. Therefore, across electrode configurations, temperature increased by HD-SCS (500 Hz, 250 μs, 5 V_peak) was maximum for the guarded tripolar configuration - both without (0.16 °C at the spinal cord; 0.92 °C at the epidural space) and with (0.36 °C at the spinal cord; 1.78 °C at the epidural space). encapsulation

The inter-electrode impedance [anode(s) to cathode(s)] for each SCS electrode configuration, with / without encapsulation layer, respectively were proximal bipolar: 2170 Ω / 1130 Ω (as noted above), distal bipolar: 2325 Ω / 1313 Ω, guarded quadripolar: 1088 Ω / 572 Ω, and guarded tripolar: 1580 Ω / 822 Ω. Based on these impedances, the resulting current produced in each configuration is reported (values with asterisks, Fig. 3). Note that each of these impedance values is measured between active electrodes (so are bipolar impedances rather than single-electrode unipolar impedance) and are then consistent with existing clinical data [1], [10], [29], [30]. The ranking of temperature increase within each electrode configuration is predicted by the resulting current.

We previously showed that heating by SCS depends on stimulation RMS, irrespective of specific waveform parameters (frequency, pulse duration, intensity) [9]. To predict heating by SCS, the RMS can be calculated and applied to the bioheat model (Equation 2). The sensitivity of maximum temperature increase at the epidural space and the spinal cord to the stimulation RMS was predicted, across electrode configurations and both without and with encapsulation (Table 2). For any given intensity and electrode configuration, heating was greater with encapsulation than without. The guarded tripolar electrode configuration produced the maximum heating for any given intensity and encapsulation condition.

Having contrasted clinically relevant SCS parameters, we next systematically explained the impact of the encapsulation layer on current-controlled vs voltage-controlled stimulation. To this end, starting with the non-encapsulated layer condition, we simulated the proximal bipolar HD-SCS under voltage-controlled (V = 5 V_peak; Fig. 4 A.1) and current-controlled with an applied current value matching that result in the voltage-controlled case without encapsulation (I = 1.61 mA_peak; Fig. 4 A.2) – we expected these simulations to produce similar results (see above). Then, the encapsulation layer was added to the voltage-controlled (Fig. 4 B.1) and current-controlled (Fig. 4 B.1) cases. For voltage-controlled stimulation, addition of an encapsulation layer slightly decreased the peak electric field (from 5190 V/m to 4790 V/m) and doubled the peak current density (208 A/m² to 585 A/m²), resulting in an increase in power density (1.08 MW/m² to 2.64 MW/m²) and so an increase in heating (from 0.59 °C to 1.01 °C). For current-controlled stimulation, addition of an encapsulation layer halved the peak electric field (from 5120 V/m to 2470 V/m), and moderately increased peak current density (205 A/m² to 301 A/m²), resulting in a decrease in power density (1.05 MW/m² to 0.7 MW/m²) and so a decrease in heating (from 0.57 °C to 0.30 °C).

Figure 4: Systemic analysis of the impact of an encapsulation layer on voltage-controlled vs current-controlled SCS.

We simulated the proximal bipolar HD-SCS under voltage controlled (V = 5 V_peak) and current controlled with an applied current value matching that resulting in the voltage-controlled case with no encapsulation later (I = 1.61 mA_peak). For voltage-controlled stimulation system (V = 5 V_peak), the maximum electric field, current density, power density, and temperature increase were respectively 5190 V/m, 208 A/m², 1.08 MW/m³, and 0.58 °C for the non-encapsulated lead condition (A1) and 4790 V/m, 585 A/m², 2.64 MW/m³, and 1.01 °C for the encapsulated lead condition (A2). For the current-controlled stimulation system (I = 1.61 mA_peak), the maximum electric field, current density, power density, and temperature increase were respectively 5120 V/m, 205 A/m². 1.05 MW/m³, and 0.569 °C for the non-encapsulated lead condition (B1) and 2470 V/m, 301 A/m², 0.7 MW/m³, and 0.305 °C for the encapsulated lead condition (B2).

DISCUSSION

HD-SCS delivers increased energy (charge per second) by increasing duty cycle (frequency and/or pulse width) [2], [8], [31]. We previously showed through phantom studies and computational modeling that 10 kHz-SCS can increase tissue heating, directly reflecting its higher duty cycle [8], [9]. HD-SCS typically has a lower duty cycle then 10 kHz-SCS, which -all things being equal- would result in less heating by HD-SCS. Using FEM bioheat models (Fig. 1), here we demonstrated the use of voltage-controlled stimulation, (typical for HD-SCS) results in different dependencies on encapsulation layer and electrode configuration than current-controlled stimulation (used in conventional and 10 kHz-SCS). As a result, under some clinically relevant stimulation conditions, HD-SCS can produce spinal tissue heating above 10 kHz-SCS (Fig. 2). For the first phase of this study, the voltage and current-controlled stimulation amplitudes chosen for comparison are not equal in magnitude but based on clinically relevant values. Similar to our prior analysis of 10 kHz SCS [32], our focus here is on heating as an ancillary mechanism of action for HD-SCS pain control [8], not as a safety concern, and predictions remain to be experimentally verified in situ.

The encapsulation layer (reflecting inflammatory response to the lead implantation and leading to scar tissues formation around the electrodes [12], [23], [33], [34]) offers less resistance than epidural fat. Whereas current-controlled stimulation decreased heating with decreasing tissue resistivity, as presented by an encapsulation layer, voltage-controlled stimulation increased heating with decreasing tissue resistivity (Fig. 2; Fig. 4). Under voltage-controlled stimulation, the use of more proximal leads and a tripolar electrode configuration reduced the effective inter-electrode resistance, amplifying temperature increase (Fig. 3).

Tissue properties are complex and dynamic, which makes it intractable to simulate all thermo-electrical properties. Although validated in our previous works using in vitro phantoms ([8], [9]), our simulation results warrant in vivo or ex vivo measurements and validation. Given the importance of electrode design ([8], [15], [17]) and pulse shape ([9], [35]) in heating, precise predictions warrant device specific models.

While the sensitivity of neuronal (e.g., excitability and synaptic efficacy) and metabolic functions (e.g., perfusion) to temperature has been studied experimentally [30]-[33], the impact of potential heating on SCS outcomes remains to be determined [8], [9]. In addition, for HD-SCS (and other SCS approaches using a higher duty cycle and voltage-control), our heating results suggest special consideration for alterations in electrode impedance, including reflecting vertebral level or distance from dural surface, changes over time with scar tissue buildup, (sudden) lead displacement, and patient postural changes [29], [36]–[40]. To the extent heating is an ancillary mechanism of action, modeling pipelines developed previously [8], [9] and applied here for the special cases of HD-SCS and voltage-controlled SCS, will inform programing under divergent strategies than for conventional stimulation. For example, whereas electrode impedance is incidental in conventional SCS programming, for heating, it may be an explicit factor moreover with distinct implications for voltage versus current-controlled stimulation.