To overcome this limitation, researchers are developing multi-electrode tDCS techniques. The electrode configuration is optimized using computational modelling to maximize current density at the target, while minimizing non-target stimulation that can cause unwanted side effects. The computer models of the human brain, which are essential for these techniques, require input of the electrical conductivity of the skull, skin, grey matter and white matter. Measuring these properties, however, is a challenging task resulting in data that's subject to uncertainty.

"The stimulated electric field distribution in the brain depends on parameters such as the chosen stimulation protocol, the brain anatomy and the electrical properties of brain tissue," explained Christian Schmidt from the University of Rostock in Germany. "Knowledge of the influence of the uncertainty in brain tissue properties would enable us to propose more robust tDCS protocols and techniques."

Schmidt and colleagues have now investigated the influence of uncertainties on the optimal electrode configuration and the resulting electric field distribution in multi-electrode tDCS. They examined an example of auditory cortex stimulation, chosen due to its potential as a tinnitus treatment (J. Neural Eng. 12 046028).

Uncertainty impact

For the study, the researchers used a high-resolution head model generated from MR images and segmented into skin, skull, cerebrospinal fluid, grey matter and white matter. An array comprising 74 fixed electrode locations was used to stimulate the auditory cortex.

They first calculated the stimulation protocol for the auditory target and found that the optimized protocol mainly comprised three electrodes: an anode (positive neuronal stimulation) and two cathodes (negative stimulation). The optimization algorithm also injected weaker compensating currents at four other electrodes to minimize non-target current density.

Next, the team employed a multi-variate generalized polynomial chaos (gPC) expansion to compute the sensitivities of the stimulation amplitudes at each electrode to the conductivities of various brain tissues. They used maximum ranges of literature values to model the conductivities: 1.6–33.0 mS/m for the skull; 280.0–870.0 mS/m for skin; 220.0–670.0 mS/m for grey matter; and 90.0–290.0 mS/m for white matter.

The stimulation electrodes were most sensitive to uncertainties in skull conductivity, with large variations seen between electrodes. The anode showed only minor deviations in stimulation amplitude (below 15%), while substantially higher deviations (up to 127.4% and 55%) were seen for the cathodes. Calculating the impact on the resulting current density at the target revealed that the largest effects were of uncertainties in grey and white matter conductivity on the z‑component of the current density.

In addition, sensitivities can arise from combinations of uncertainties – described by Sobol' indices. Calculating the Sobol' indices for the three main electrodes revealed that stimulation amplitudes at the two cathodes were most sensitive to uncertainty in skull conductivity, while those at the anode were influenced most by uncertain conductivities of skull and white matter. Second-order indices showed that the anode was also sensitive to the combined uncertainty in conductivities of skin and skull, and skull and grey matter.

The sum of first- and second-order indices was more than 97.5% for all three main electrodes, suggesting that the total uncertainty in the resulting stimulation protocol can be described almost entirely by those combinations.

Will the therapy work?

An important question in tDCS is whether stimulation with a weak direct current has a therapeutic effect. Previous studies showed that an electric field of about 140 μV/mm can enhance the firing rate of neurons. The mean grey matter conductivity of 445 mS/m used in this study implies that a current density of greater than 0.062 A/m2 is needed to induce therapeutic effects.

As the mean current density (calculated using probability density functions) was approximately 0.041 A/m2, the likelihood of the optimized stimulation protocol inducing above-threshold current densities at the auditory target was less than 50%. The authors note that this may be due to the target's deep location, as well as the large range of conductivity values considered. To improve the probability of effective stimulation, the total current applied to the electrodes could be enlarged, with clinical studies performed to investigate the safety of larger input currents.

The researchers concluded that uncertainty in tissue conductivity must be considered when optimizing stimulation protocols using computational tDCS models. They note that the levels of conductivity uncertainty assumed in this study reflect a "worst-case" scenario and that, in the clinic, use of patient-specific data may help reduce uncertainty in the predicted stimulation protocol.

"The uncertainty quantification revealed that the optimized stimulation amplitudes are differently influenced by the uncertain brain tissue conductivity, resulting in different tolerances for each stimulation electrode," Schmidt told medicalphysicsweb. "This additional knowledge might help clinicians to adjust the stimulation amplitudes based on the chosen target and patient anatomy."

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