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Thermal Modeling and Validation for Transcutaneous Spinal Cord Electrical Stimulation

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Thermal Modeling and Validation for Transcutaneous Spinal Cord Electrical Stimulation

Chih-Wei Chang 1, Reggie Edgerton 2, and Wentai Liu 1,3,4

1Department of Bioengineering 2Department of Integrative Biology and Physiology 3Department of Electrical Engineering 4California NanoSystems Institute, University of California at Los Angeles, Los Angeles, CA 90095 USA


Transcutaneous electrical spinal cord stimulation has been shown promising but requires a careful study for the thermal management. Temperature rising can lead to possible damage in the body tissue caused by the inevitable electrical power dissipation at the electrode-skin interface. A new electrode is thus proposed to significantly reduce the interface impedance and consequently suppress the heating effect due to electrical stimulation. We report the performance and validation of the newly electrode by a realistic physical model for transcutaneous stimulation using Pennes’ Bio-heat transfer equation.

Pain-Points and Solutions

Electrode/Skin Interface Impedance Reduced by Spiked Electrode

Electrical stimulation delivers large stimulation current to effectively modulate the circuitry of spinal cord for pain relief and motor function recovery. This large current inevitably results in large electrical power dissipation at the electrode/skin interface due to the high interface impedance characteristics of the skin when using traditional surface electrodes. We developed a novel electrode which significantly lowers the tissue spread resistance when bypassing the Stratum Corneum layer (SC layer, the very outer skin layer that consist of dead cells) as shown in Fig. 1 (A). The equivalent circuit model (Fig. 1B) also shows that the double layer capacitance is increased over the conventional electrode at the same footprint because the increase of the effective electrode surface of the spiked structures. Consequently the overall electrode impedance can be significantly reduced. The spike structure can be made by various materials such as silicon, metal or polymer (Fig. 1C). Preliminary impedance test on skin demonstrates the reduction of the electrode/skin impedance by the spike electrode by 5.7x at the stimulation frequency of 10 KHz (Fig. 1D).  


Realistic 3D Spinal Cord Modeling

Whole body finite element volume conductor model is implemented to compare the heat dissipation when applying the conventional electrode and proposed spike electrode onto skin. Structural MRI images are used to reconstruct the three dimensional model to simulate the temperature rising under electrical stimulation. The sliced images has 3 mm offset distance between each scan. The components including muscle, fat, vertebrae, CSF, and spinal cord are marked by contours in the sliced images and reconstructed in 3D CAD tools. The multi skin layers and abdomen are manually added into the model, as shown in Fig. 2. The 3D model is then imported into COMSOL to simulate the collaborated electrical joule heating and bioheat transfer.

During the electrical stimulation, the tissue temperature begins rising due to the power dissipation into the tissue from joule heating. The heat transfer in the bio tissue is then calculated by the Bio-heat equation, where the metabolism heating, blood perfusion, and blood heating are computed in COMSOL model, as well as air convection effect.

Simulation Condition

The stimulation and return electrodes are placed on dorsal and ventral side of the trunk. Planar electrode with 1 cm in diameter is attached onto the outer skin layer in the model, while the spike electrode has 50 spikes with 40μm in bottom width, 60μm in height, evenly distributed on the electrode surface. Pulsed current stimulation (3 ms of 10 KHz biphasic pulse train at 100Hz) with 100mA current intensity is applied to the electrode. The initiate body temperature and the blood temperature are set as 37˚C, with ambient temperature = 25˚C.


Fig. 3 shows the simulated temperature rising of the planar and spike electrode after 1hr stimulation. The degree of burning is calculated by the fraction of necrosis tissue based on the Arrhenius equation, which irreversible damage reaction according to time length, temperature, and activation energy/ frequency factor of the tissue. 

The result shows that the planar electrode reaches first-degree burn after 27.6 minutes (fraction=0.411, 48.35°C), second degree burn after 45 minutes (fraction=0.632, 48.6°C), and its steady state (48.8°C , 11.8°C rising) after 50 minutes of stimulation. The spike is still in the safe range till temperature get to steady state (42.2°C, 5.2°C rising) after 60 minutes. In contrast, it takes the planar electrode only 80 seconds to reach 42°C. Spike electrode reduce the temperature rising by 55.9% at the steady state, compared with traditional planar electrode. 


Realistic physical model demonstrates the performance of the proposed spike electrode in the transcutaneous electrical stimulation. Comparing to the planar electrodes, proposed design can significantly reduce the tissue heating. The stimulation safety margin is thereby improved and possible heat damage can be minimized when high intensity, long-term stimulation treatment is required.


This project was partly supported by the California Capital Equity LLC. 

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