Improved Electrically Evoked Auditory Steady-State Response Thresholds in Humans

Abstract

Electrically evoked auditory steady-state responses (EASSRs) are EEG potentials in response to periodic electrical stimuli presented through a cochlear implant. For low-rate pulse trains in the 40-Hz range, electrophysiological thresholds derived from response amplitude growth functions correlate well with behavioral T levels at these rates. The aims of this study were: (1) to improve the correlation between electrophysiological thresholds and behavioral T levels at 900 pps by using amplitude-modulated (AM) and pulse-width-modulated (PWM) high-rate pulse trains, (2) to develop and evaluate the performance of a new statistical method for response detection which is robust in the presence of stimulus artifacts, and (3) to assess the ability of this statistical method to determine reliable electrophysiological thresholds without any stimulus artifact removal. For six users of a Nucleus cochlear implant and a total of 12 stimulation electrode pairs, EASSRs to symmetric biphasic bipolar pulse trains were recorded with seven scalp electrodes. Responses to six different stimuli were analyzed: two low-rate pulse trains with pulse rates in the 40-Hz range as well as two AM and two PWM high-rate pulse trains with a carrier rate of 900 pps and modulation frequencies in the 40-Hz range. Responses were measured at eight different stimulus intensities for each stimulus and stimulation electrode pair. Artifacts due to the electrical stimulation were removed from the recordings. To determine the presence of a neural response, a new statistical method based on a two-sample Hotelling T ² test was used. Measurements from different recording electrodes and adjacent stimulus intensities were combined to increase statistical power. The results show that EASSRs to modulated high-rate pulse trains account for some of the temporal effects at 900 pps and result in improved electrophysiological thresholds that correlate very well with behavioral T levels at 900 pps. The proposed statistical method for response detection based on a two-sample Hotelling T ² test has comparable performance to previously used one-sample tests and does not require stimulus artifacts to be removed from the EEG signal for the determination of reliable electrophysiological thresholds.

Appendix

A implementation of Hotelling T ² test

One measurement with complex frequency bins B corresponding to the modulation frequencies was represented by a matrix D defined as

$$ {{D}_{{k,l}}} = \left[ {\begin{array}{*{20}{c}} {{{B}_{{k,l,1,1}}}} & \cdots & {{{B}_{{k,l,1,N}}}} \\ \vdots & {} & \vdots \\ {{{B}_{{k,l,M,1}}}} & \cdots & {{{B}_{{k,l,M,N}}}} \\ \end{array} } \right] $$

(1)

with the number of modulation frequencies K, number of measurements L, number of epochs M, and number of recording electrodes N. Different sample sets with the same modulation frequency were combined into a matrix X with dimensions M × O

$$ {X_k} = \left( {{x_{{k,m,o}}}} \right) = \left[ {{D_{{k,1}}}^{{ \cdot \cdot \cdot }}{D_{{k,_L}}}} \right] $$

(2)

and normalized into a matrix $\mathop{X}\limits^{ \cdot }$ obtained by column-wise division with the standard deviation S

$$ {S_k} = \left( {{s_{{k,o}}}} \right) = \sqrt {{{\text{E}}\left( {\left( {{x_{{k,o}}} - \overline {{x_{{k,o}}}} } \right)\left( {{x_{{k,o}}} - \overline {{x_{{k,o}}}} } \right) } \right)^\dag}} $$

(3)

$$ {\mathop{\text{X}}\limits^{ \cdot }_k} = \left( {{{\mathop{x}\limits^{ \cdot } }_{k,m,o}}}\right) = \left( {{{\mathop{x}\limits}_{{k,m,o}}}/{s_{{k,o}}}} \right) $$

(4)

For the Hotelling T ² test, $\dot{X}$ was reshaped into a two-column matrix $\ddot{X}$

$$ {{\mathop{X}\limits^{{ \cdot \cdot }} }_{k}} = \left[ {\begin{array}{*{20}{c}} {{\text{Re}}\left( {{{{\mathop{x}\limits^{ \cdot } }}_{{k,1,1}}}} \right)} & {{\text{Im}}\left( {{{{\mathop{x}\limits^{ \cdot } }}_{{k,1,1}}}} \right)} \\ \vdots & \vdots \\ {{\text{Re}}\left( {{{{\mathop{x}\limits^{ \cdot } }}_{{k,M,1}}}} \right)} & {{\text{Im}}\left( {{{{\mathop{x}\limits^{ \cdot } }}_{{k,M,1}}}} \right)} \\ \vdots & \vdots \\ {{\text{Re}}\left( {{{{\mathop{x}\limits^{ \cdot } }}_{{k,1,O}}}} \right)} & {{\text{Im}}\left( {{{{\mathop{x}\limits^{ \cdot } }}_{{k,1,O}}}} \right)} \\ \vdots & \vdots \\ {{\text{Re}}\left( {{{{\mathop{x}\limits^{ \cdot } }}_{{k,M,O}}}} \right)} & {{\text{Im}}\left( {{{{\mathop{x}\limits^{ \cdot } }}_{{k,M,O}}}} \right)} \\ \end{array} } \right] $$

(5)

that contained the real components in the first and the imaginary components in the second column. The Hotelling T ² statistic and the probability of the incorrect rejection of the null hypothesis p was determined from the difference of the means $\Delta \ddot{X}$ of sample sets for two different frequencies in ${\ddot{X}_1}$ and ${\ddot{X}_2}$

$$ \Delta \ddot{X} = E\left( {{{\ddot{X}}_1}} \right) - E\left( {{{\ddot{X}}_2}} \right) $$

(6)

and the pooled covariance matrix $\ddot{C}$

$$ \ddot{C} = {\text Cov}\left( {{{\ddot{X}}_1}} \right) + {\text Cov}\left( {{{\ddot{X}}_2}} \right) $$

(7)

with the cumulative density function of the ${χ^2}$ distribution ${F_{{{χ^2}}}}$, and correction factor r as

$$ {T^2} = LM\Delta \ddot{X}'{\ddot{C}^{{ - 1}}}\Delta \ddot{X} $$

(8)

$$ p = 1 - {F_{{{χ^2}}}}\left( {r{T^2},2} \right) $$

(9)

B determination of r by Monte Carlo simulation

The Hotelling T ² test expects independent samples which is not necessarily true for the EEG recorded from multiple electrodes at the same time. This was mitigated by the calculation of the size of an equivalent sample set of independent samples, represented by the correction factor r which was determined by Monte Carlo simulation.

The dependencies between the recording electrodes were modeled by the covariance matrices for the real and imaginary components C _re and C _im.

$$ {\dot{C}_{{k,{\text{re}}}}} = {\text{Cov}}\left( {{\text Re} \left( {{{\dot{X}}_k}} \right)} \right) $$

(10)

$$ {\dot{C}_{{k,{\text{im}}}}} = {\text{Cov}}\left( {{\text Im} \left( {{{\dot{X}}_k}} \right)} \right) $$

(11)

Correlated random matrices ${\dot{X}_{{R,k}}}$ were calculated from independent normally distributed random data matrices P and Q with dimensions M × O and zero mean by applying the Cholesky decomposition to the covariance matrices

$$ {\dot{X}_{{R,k}}} = {\text Chol}\left( {{{\dot{C}}_{{k,{\text re}}}}} \right)P + {\text Chol}\left( {{{\dot{C}}_{{k,{\text im}}}}} \right)Q{\text i} $$

(12)

For 10,000 trials with different matrices P and Q, Eqs. 5 to 8 were used to characterize the distribution of $T^{2}_{R}$ for normally distributed random data with the specified covariance matrices and to determine the cumulative density function $F_R\left( {T^{2}_{R} } \right)$. Least squares approximation was then used to determine the correction parameter r for the ${χ^2}$ cumulative density function ${F_{{{χ^2}}}}$ with two degrees of freedom by

$$ \left\| {{F_R}\left( {T^{2}_{R}} \right) - {F_{{{χ^2}}}}\left( {rT^{2}_{R}, 2} \right)} \right\| \to \min $$

(13)