Multi-response deconvolution of auditory evoked potentials in a reduced representation space.

The estimation of auditory evoked potentials requires deconvolution when the duration of the responses to be recovered exceeds the inter-stimulus interval. Based on least squares deconvolution, in this article we extend the procedure to the case of a multi-response convolutional model, that is, a model in which different categories of stimulus are expected to evoke different responses. The computational cost of the multi-response deconvolution significantly increases with the number of responses to be deconvolved, which restricts its applicability in practical situations. In order to alleviate this restriction, we propose to perform the multi-response deconvolution in a reduced representation space associated with a latency-dependent filtering of auditory responses, which provides a significant dimensionality reduction. We demonstrate the practical viability of the multi-response deconvolution with auditory responses evoked by clicks presented at different levels and categorized according to their stimulation level. The multi-response deconvolution applied in a reduced representation space provides the least squares estimation of the responses with a reasonable computational load. matlab/Octave code implementing the proposed procedure is included as supplementary material.

Auditory brainstem responses obtained with randomised stimulation level.

OBJECTIVE: To present randomised stimulation level (RSL) - a stimulation paradigm in which the level of the stimuli is randomised, rather than presented sequentially as in the conventional paradigm. DESIGN: The value of RSL was evaluated by (i) comparing the morphology of auditory brainstem responses (ABRs) elicited by the conventional and RSL paradigms, and by (ii) an online survey investigating the hearing comfort of the stimulus sequence. STUDY SAMPLE: ABRs were obtained from 11 normal-hearing adults (8 females, 25-29 years). The online survey was administered to 238 adults from the general community. RESULTS: Results showed that (i) both stimulation paradigms elicit ABR signals of similar morphology, (ii) RSL provides a faster comprehensive representation of the ABR session, and that (iii) the general population found RSL stimuli to be more comfortable. CONCLUSIONS: The simultaneous evaluation of all ABR traces of the session provided by RSL has potential to improve the identification of ABR components by enabling clinicians to make use of the response tracking strategy from the start of the test, which is critical in situations where ABRs present an abnormal morphology. New research opportunities and the clinical potential of RSL are discussed.

Subspace-constrained deconvolution of auditory evoked potentials.

Auditory evoked potentials can be estimated by synchronous averaging when the responses to the individual stimuli are not overlapped. However, when the response duration exceeds the inter-stimulus interval, a deconvolution procedure is necessary to obtain the transient response. The iterative randomized stimulation and averaging and the equivalent randomized stimulation with least squares deconvolution have been proven to be flexible and efficient methods for deconvolving the evoked potentials, with minimum restrictions in the design of stimulation sequences. Recently, a latency-dependent filtering and down-sampling (LDFDS) methodology was proposed for optimal filtering and dimensionality reduction, which is particularly useful when the evoked potentials involve the complete auditory pathway response (i.e., from the cochlea to the auditory cortex). In this case, the number of samples required to accurately represent the evoked potentials can be reduced from several thousand (with conventional sampling) to around 120. In this article, we propose to perform the deconvolution in the reduced representation space defined by LDFDS and present the mathematical foundation of the subspace-constrained deconvolution. Under the assumption that the evoked response is appropriately represented in the reduced representation space, the proposed deconvolution provides an optimal least squares estimation of the evoked response. Additionally, the dimensionality reduction provides a substantial reduction of the computational cost associated with the deconvolution. matlab/Octave code implementing the proposed procedures is included as supplementary material.

Latency-dependent filtering and compact representation of the complete auditory pathway response.

Auditory evoked potentials (AEPs) include the auditory brainstem response (ABR), middle latency response (MLR), and cortical auditory evoked potentials (CAEPs), each one covering a specific latency range and frequency band. For this reason, ABR, MLR, and CAEP are usually recorded separately using different protocols. This article proposes a procedure providing a latency-dependent filtering and down-sampling of the AEP responses. This way, each AEP component is appropriately filtered, according to its latency, and the complete auditory pathway response is conveniently represented (with the minimum number of samples, i.e., without unnecessary redundancies). The compact representation of the complete response facilitates a comprehensive analysis of the evoked potentials (keeping the natural continuity related to the neural activity transmission along the auditory pathway), which provides a new perspective in the design and analysis of AEP experiments. Additionally, the proposed compact representation reduces the storage or transmission requirements when large databases are manipulated for clinical or research purposes. The analysis of the AEP responses shows that a compact representation with 40 samples/decade (around 120 samples) is enough for accurately representing the response of the complete auditory pathway and provides appropriate latency-dependent filtering. MatLab/Octave code implementing the proposed procedure is included in the supplementary materials.

Matrix-based formulation of the iterative randomized stimulation and averaging method for recording evoked potentials.

The iterative randomized stimulation and averaging (IRSA) method was proposed for recording evoked potentials when the individual responses are overlapped. The main inconvenience of IRSA is its computational cost, associated with a large number of iterations required for recovering the evoked potentials and the computation required for each iteration [involving the whole electroencephalogram (EEG)]. This article proposes a matrix-based formulation of IRSA, which is mathematically equivalent and saves computational load (because each iteration involves just a segment with the length of the response, instead of the whole EEG). Additionally, it presents an analysis of convergence that demonstrates that IRSA converges to the least-squares (LS) deconvolution. Based on the convergence analysis, some optimizations for the IRSA algorithm are proposed. Experimental results (configured for obtaining the full-range auditory evoked potentials) show the mathematical equivalence of the different IRSA implementations and the LS-deconvolution and compare the respective computational costs of these implementations under different conditions. The proposed optimizations allow the practical use of IRSA for many clinical and research applications and provide a reduction of the computational cost, very important with respect to the conventional IRSA, and moderate with respect to the LS-deconvolution. matlab/Octave implementations of the different methods are provided as supplementary material.

Auditory brainstem and middle latency responses recorded at fast rates with randomized stimulation.

Randomized stimulation and averaging (RSA) allows auditory evoked potentials (AEPs) to be recorded at high stimulation rates. This method does not perform deconvolution and must therefore deal with interference derived from overlapping transient evoked responses. This paper analyzes the effects of this interference on auditory brainstem responses (ABRs) and middle latency responses (MLRs) recorded at rates of up to 300 and 125 Hz, respectively, with randomized stimulation sequences of a jitter both greater and shorter than the dominant period of the ABR/MLR components. Additionally, this paper presents an advanced approach for RSA [iterative-randomized stimulation and averaging (I-RSA)], which includes the removal of the interference associated with overlapping responses through an iterative process in the time domain. Experimental results show that (a) RSA can be efficiently used in the recording of AEPs when the jitter of the stimulation sequence is greater than the dominant period of the AEP components, and (b) I-RSA maintains all the advantages of RSA and is not constrained by the restriction of a minimum jitter. The significance of the results of this study is discussed.