برآورد توزیع سرعت هدایت با استفاده از برخورد روش تئوری و مطالعه شبیه سازی

Current nerve conduction studies (NCS) are influenced by the activity of the largest active fibers, making it difficult to assess the state of smaller nerve fibers. This study is aimed at alternative diagnostic techniques for assessing carpal tunnel syndrome (CTS). A conduction velocity distribution (CVD) estimator based on the collision technique that incorporates volume conductor modeling is proposed and discussed in this paper. Simulations were run to evaluate the accuracy of the CVD estimator and compare its performance with previous CVD estimators based on the collision technique. Results show the improved accuracy of the proposed approach, which is able to provide estimates with a percent mean square error (PMSE) lower than 1.1% for all CTS cases studied and lower than 2% in the presence of additive white Gaussian noise. Simulations also showed that conduction slowing in the carpal tunnel (CT) segment is detected by the proposed technique and displayed as an increase in the number of low velocity fibers. Results suggest that both CVD estimator and amplitude parameter proposed can help detect the severity of CTS in a patient more accurately than current NCS.

Carpal tunnel syndrome (CTS) is a nerve conduction syndrome caused by localized compression of the median nerve at the wrist. CTS is generally detected using electrophysiological testing such as standard nerve conduction studies (NCS). NCS are performed by placing stimulating electrodes at a distance from the recording electrodes and measuring the peak latency of the compound nerve action potential (CNAP) recorded. The sensory orthodromic response is generally of small amplitude and requires averaging [1]. Typical measurements made are amplitude, area under the waveform, latency and conduction velocity (CV). An average sensory CV of 45 m/s or less indicates the presence of CTS [2] and [3]. NCS evaluate the function of large myelinated nerve fibers with the highest CV, i.e. A beta fibers [2] and [4]. Selective evaluation of nerve fibers based on their diameter or CV is not feasible with these techniques. According to the literature [4], severity of CTS progresses from large nerve fibers to small nerve fibers. This is not a surprising finding given that NCS available are able to evaluate the largest fibers active at the time of recording. An early deficit in the activity of smaller nerve fibers will likely go unnoticed since the contribution of larger fibers to the CNAP recorded is significantly bigger than that coming from the smaller fibers [5]. Hence, a method to assess the diameter or CV of the active nerve fibers traversing the carpal tunnel will improve current CTS diagnostic techniques. Characterizing a nerve in terms of the probability density function (pdf) that describes the distribution of active fibers across a velocity interval can be done by estimating its CV distribution (CVD). If reliable CVD estimates for the median nerve fibers traversing the carpal tunnel are obtained this will be a useful parameter to describe the nerve fibers being affected in a CTS patient. A new method for estimating CVD is proposed in this paper. The estimation of the electrical source needed for the CVD estimator makes use of a deconvolution approach applied to signals recorded using the collision technique as will be described in Section 3. The collision technique can be used to selectively activate nerve fibers of different diameters by varying the delay between two stimuli—a distal supramaximal stimulus and a delayed proximal stimulus [3]. There are two stimulation channels placed on the skin surface, one at the wrist (the distal) and another at the elbow (the proximal). The proximal and distal CNAPs are recorded using a bipolar channel consisting of two surface ring electrodes placed at the middle finger. The inter-stimulus interval (ISI) is the time interval between the delivery of the wrist stimulus pulse and the delivery of the elbow stimulus pulse. When the ISI is relatively large, the proximal CNAP does not collide with the distal CNAP, hence a response from all the nerve fibers activated by the elbow stimulus pulse is obtained. When the ISI is gradually decreased, the contribution from small nerve fibers reduces as the slow traveling action potentials generated at both stimulation sites start colliding and only the faster traveling action potentials get through to the recording electrodes placed on the finger (see Fig. 1). Of the action potentials getting through the one with the lowest CV is determined by the ISI value. This lowest velocity value is calculated as [3]: where CV is the conduction velocity in m/s, D the distance in mm between the two stimulation sites, i.e. wrist and elbow, ISI is the time in ms between delivery of wrist and elbow stimulation pulses.

In previous approaches to CVD estimation based on the collision technique [3] and [8] the SSFAPs used to form the CNAP were considered independent of the conduction velocity. In other words, the SSFAP was considered to be the same for all velocity ranges. However, the response from a single fiber propagates some distance from the stimulation site to the recording site, thus it is dependent on fiber conduction velocity. Also, the SSFAP amplitude and waveshape is dependent on velocity as determined by studies using volume conductor modeling [5]. The CVD estimator proposed in this study uses a volume conductor model to represent the SSFAP such that this velocity dependence is accounted for. To the best of the authors’ knowledge this is the first attempt at incorporating a volume conductor model into a CVD estimator based on the collision technique. The CVD estimations obtained in simulations for all health cases studied were all made with a PMSE smaller than 1.1%. This shows that the CVD estimator can perform well regardless of the nature of the nerve fibers affected during different stages of CTS. Once noise is considered the CVD estimates are accurate within a 2.2% PMSE, which is still well below the 5.4% error displayed by traditional techniques without noise being added. The proposed technique can also offer CVD estimates that indicates the presence of conduction slowing of nerve fibers in the carpal tunnel segment. As results showed, the higher the percent of fibers showing slowing, i.e. suffering from demyelination, the higher the number of fibers the estimator displays on the low velocity end. Even though experimental testing and validation of the proposed technique would be required, simulation results are encouraging. These suggest that with the use of the proposed CVD estimator and amplitude parameter the severity of CTS would be evaluated by observing which velocity range has a relatively reduced number of active fibers and amplitude, respectively, or by matching the patient's CVD estimate to CVD templates identifying the advancement of the disease. It has been reported that as CTS progresses in a patient different fiber sizes/velocities are affected, starting at the high velocity end and affecting fibers with lower velocities as it becomes more severe. This is an aspect that could be further tested with the availability of the technique proposed here and its use in CTS patients. For example, if only small diameter ranges (low CV range) have a relatively reduced number of active fibers, as compared to results from healthy subjects, it may indicate a case of CTS in a patient that would be overlooked by current NCS. Hence, this method could help better describe the type of nerve fibers affected in a patient suffering from CTS or other peripheral neuropathies than current NCS techniques.