This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TNSRE.2014.2379594, IEEE Transactions on Neural Systems and Rehabilitation Engineering

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT)
REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < extract the desired neural signal. This particular spatial processing method, namely the delay and sum beamforming, greatly enhances capturing action potentials propagating at a desired velocity while suppressing the action potentials travelling with other speeds in addition to noise and other interfering signals. Despite prominent features of the delay and sum beamforming method compared to model based methods its major drawbacks such as low selectivity in extracting action potentials at higher velocities and its non-uniform frequency response have made its results unreliable [8],[10]. Inspired by the popular Frost space-time beamformer used in broadband phased array techniques [16],[17], we have modified the delay and sum beamforming method by adding a set of Tapped Delay Line (TDL) filters to each branch of the beamformer. Together with an appropriate pattern synthesis technique, it is shown that this new design technique overcomes the inherent problems of the delay and sum beamformer by creating a uniform frequency-velocity beampattern. We follow three specific goals in this article: a) bring to light the pitfalls of the delay and sum beamformer in an analytic form, b) propose an alternative beamforming method for neural signal extraction which resolves the issues of the delay and sum beamformer, c) clarify further on potential applications of the velocity selective beamforming in neural signal analysis. To reach these goals we first present the principles of the delay and sum beamforming along with its theoretical analysis and shortcomings in Section II. The structure of our proposed beamforming method and its associated design technique to create a uniform frequencyvelocity beampattern are explained in Section III. The performance of the proposed method is evaluated in Section IV by means of three comprehensive examples. Finally, complementary remarks regarding further characteristics and applications of the proposed method are presented in Section V. To distinguish easily between different collections of 



signals at the same point in the system we use () , () , and () for scalar values, vectors, and matrices, respectively. The operator ()T will denote transposition. II. DELAY AND SUM VELOCITY SELECTIVE BEAMFORMER A. Principles of the Delay and Sum Beamforming Fig 1 illustrates a conventional delay and sum electrode array with N electrodes and inter-electrode spacing d [7],[9],[11]. The recorded signal of the nth electrode, xn (t ), n  1,, N which is a composite signal of neural signals of different fibers is passed through a delay block  n . By appropriate tuning of  n , based on the time delay between electrodes, only the set of action potentials travelling with the velocity matched to  n will appear at the output of the beamformer [7]. That is why we call the structure of Fig 1 delay and sum velocity selective beamformer (or simply delay and sum beamformer). This structure has also been called velocity selective recording

2

system [13].

Σ #1

#2

#3

#N

d

Nerve

Fig. 1. Delay and sum velocity selective beamformer.

Selectivity of the delay and sum beamformer depends upon the travelling speed of the desired action potentials and the length of the array [8]. For a given length, the best selectivity is achieved for the lowest velocity. For this reason, the delay and sum beamformer was primarily used for small caliber fibers which exhibit low propagation speeds. For example, using an array with 16 electrodes and 600 m electrode spacing, Huang and his colleagues used delay and sum beamforming to discriminate different neural spikes from a synthetic abdominal nerve cord of Cricket Acheta domestica [7]. Using this arrangement they could separate synthetic neural signals of four fibers with propagation speeds of 2, 3, 4, and 5 m/sec, respectively. In [8] an MEC with a length of 3 cm and 11 ring electrodes was used to analyze the performance of the delay and sum beamformer in extracting the action potentials travelling with the speed of 20-120 m/sec in a model of a nerve fiber using the tripolar method. The selectivity of this structure was later analyzed in [9]. Animal experiments of the delay and sum beamformer were further conducted using: an MEC with a length of 38 mm and 11 ring electrodes on the median nerve of a pig for the velocity range of 43-60 m/sec [14], an MEC with a length of 40 mm and 11 ring electrodes on the sciatic nerve of a frog for the velocity range of 20-40 m/sec [18], and an MEC with a length of 30 mm and 11 electrodes on median and lateral giant fibers of an earthworm for the velocity range of 7.5 to 45 m/sec [11]. It was shown by these researchers that the detection of the propagation velocity of the slow fiber population from the composite signal was difficult because the fast and the slow activities seem to melt into each other in the velocity profile. It was also shown that tripolar and biplolar methods both have the same selectivity but the tripolar method may exhibit larger signal amplitudes. It is worthwhile mentioning that in addition to using delay and sum beamforming in neural signal analysis, this method has also been used in extracting evoked potentials in the median nerve of a human with a great improvement in SNR [19] and in motor unit conduction velocity measurement using surface electrodes [20]. Since the delay and sum beamformer has been widely employed by different groups and it has been the basis for developing more recent methods [10],[13], its characteristics

1534-4320 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TNSRE.2014.2379594, IEEE Transactions on Neural Systems and Rehabilitation Engineering

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < need more investigation. Our approach in this investigation, however, will be based on sensor array signal processing principles. As it will be shown in subsequent sections, the beampattern of a delay and sum beamformer has a nonuniform shape in both velocity and frequency dimensions. Unlike the phased array communication systems in which the angle of arrival of the signal (or more precisely cos of the angle) has a linear relationship with the delay [16], in delay and sum velocity selective beamforming the delay has an inverse relationship with the velocity. On the other hand, in most phased array systems the desired signal is a narrowband signal whereas a neuronal spike signal is a wideband signal. B. Transfer Function of the Delay and Sum Beamformer Let us assume that in Fig 1, M active fibers exist in a nerve each having a neural signal sm (t ), m  1,, M consisting of action potentials travelling with the speed of vm . Therefore, the signal captured by the nth electrode with respect to a reference electrode will be, M  (n  1)d    zn (t ), xn (t )   sm  t  vm  m1 

n  1,2,, N

(1)

where zn (t ) denotes the captured noise or other interfering signals. To extract the desired signal sd (t ) which travels with the speed of vd from this composite signal the delay at the nth branch should be tuned to  n  (n  1)d / vd . Consequently, 1

the output signal of the beamformer will be given by , N

y (t )   n 1

1 xn (t   n )  N

that the desired signal sd (t ) captured by each electrode will be added constructively with those of other electrodes and the sum will appear at the beamformer output whereas the interfering signals sm (t ) will be added with different delays in a destructive manner. This is also true for zn (t ) which is assumed independent on different electrodes. C. Analysis of the Delay and Sum Beamformer Response To find out how a delay and sum beamformer behaves in extracting the desired neural signal and suppressing unwanted signals we now analyze its different characteristics. Beampattern To obtain the frequency-velocity transfer function (beampattern) of the delay and sum beamformer we apply Fourier transform to (2) assuming a neural signal s(t ) The sign of  n in (2) is taken positive here for the sake of analysis.

Y( f ) 1  S( f ) N

N

e

1 1  i 2f  n 1d     v vd 

n 1

(3)   1 1  sin  fNd     1  v vd     N   1 1  sin  fd      v vd    in which Y ( f ) and S ( f ) are Fourier transforms of y (t )

and s(t ) , respectively. This is the same result as in [9]. For v  vd we get H DS ( f , vd )  1 which creates the maximum response of the beamformer to the desired signal. However, as it will be shown subsequently, the delay and sum beamformer demonstrates a highly non-uniform frequency-velocity beampattern which results in poor interference suppression and eventually corruption of the desired signal. It is worthwhile mentioning that the plot of the peak amplitude of the beamformer output as a function of velocity, is called Intrinsic Velocity Spectrum (IVS) and has also been used to characterize the beamformer response [13]. H DS  f , v  can be interpreted as IVS at different frequencies. If v I denotes the speed of an undesired action potential (interference) travelling at a speed very close to vd then we can define u  vd  vI , u 2  vI vd and re-write (3) as, H DS ( f , u ) 

1 N

N

e

 u   i 2 f ( n 1) d  2  u 

(4)

n 1

(2)

M

For the desired velocity we set vm  vd in (2). This means

1

H DS  f , v  

v . Therefore,

Derivative of (4) with respect to u gives,

  (n  1)d (n  1)d   1  sm t       zn (t ), N n1 m1   vm vd   N

travelling with the speed of

3

 u 

i 2f ( n1) d  2  H DS ( f , u ) 1  i 4fdu  N u     (n  1)e 3 u N u  n1

(5)

It is easy to show that an increase in u greatly decreases the magnitude of H DS ( f , u) / u in (5). This means that the selectivity of the beamformer in suppressing the undesired spike signals severely degrades at higher speeds. Also (5) implies that the number of sample points in a given velocity band decreases with increasing velocity. This has been referred to as velocity resolution in the current literature [21]. Eq (5) also shows that H DS ( f , u) / u reduces by decreasing f which in turn means further reduction in the beamformer selectivity for lower frequencies. This analysis is supported by Fig 2 which plots the frequency-velocity beampattern at two different speeds, 30 m/sec and 80 m/sec, and two different frequencies, 1 kHz and 5 kHz, for an electrode array with 5 cm length and d=2.5 mm. While the beampattern in Fig 2(a) exhibits a narrow mainlobe at 30 m/sec and 5 kHz, the beampattern in Fig 2(b) displays a wide mainlobe at the speed of 80 m/sec and the same frequency. The mainlobe width in Fig 2(a) greatly decreases if the frequency of the signal decreases from 5 kHz to 1 kHz as it is illustrated in Fig 2(c). Likewise, the mainlobe width of Fig 2(b) significantly increases with a change in frequency from

1534-4320 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TNSRE.2014.2379594, IEEE Transactions on Neural Systems and Rehabilitation Engineering

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1

|H(f,v)|

|H(f,v)|

1

0.5

vsl 

20

40

60

80

Velocity (m/sec)

100

0

120

By substituting (9) in (3) it can be shown that 20

40

H DS ( f , vsl ) / H DS ( f , vd )  2 /(3 ) . This is identical to 13.5 dB

100

120

1

|H(f,v)|

|H(f,v)|

80

(b)

0.5

0

60

Velocity (m/sec)

(a) 1

20

40

60

80

Velocity (m/sec)

100

0.5

0

120

20

40

60

80

Velocity (m/sec)

100

120

(c) (d) Fig. 2. Frequency-velocity beampattern of an array with 5 cm length and 21 electrodes for, (a) vd = 30 m/s and f = 5 kHz, (b) vd = 80 m/sec and f = 5 kHz, (c) vd = 30 m/sec and f = 1 kHz , (d) vd = 80 m/sec and f = 1 kHz.

5 kHz to 1 kHz as it can be seen in Fig 2(d). To further justify this non-uniform behavior in a delay and sum beamformer we next obtain the equation of the mainlobe width. Mainlobe Width One of the most important factors in the characteristics of a beampattern is the mainlobe width which determines the selectivity of the array in separating different signals [16]. The mainlobe width is determined by using either the 3 dB beamwidth or its null-to-null counterpart [22] (see Fig 2(b) as an example). Based on (3) it is easy to show that the null-tonull beamwidth vnull null and the 3 dB beamwidth v3dB3dB [9] are given by (6) and (7), respectively. v null null 

2 Ndfv d

2

( Ndf ) 2  v d

2

2

2

vd Ndf

(6)

2.6 Ndfvd v  2.6 d 2 2 ( Ndf )  (1.32vd ) Ndf 2

v3dB3dB 

2

(7)

The approximation in (6) and (7) is valid when Ndf  v d . Clearly Nd in (6) and (7) represents the length of the array which renders that in the delay and sum beamformer increasing the length of the array reduces the mainlobe width. A related quantity called velocity quality factor Qv has also been introduced in the literature [9] for the same purpose as, Qv 

vd

(9)

BW3dB

0.5

BWnull-null

0

2 fNdv d 3vd  2 fNd

4

(8)

v3dB 3dB

We use both these criteria for comparing different methods later.

attenuation for the maximum sidelobe level compared to the mainlobe. There is no way for the delay and sum beamformer to reduce this level any further. Grating Lobes If the antenna spacing in a phased array system increases beyond half the wavelength of the desired signal spurious lobes with the same height of the main lobe may appear in the beampattern [22] . These lobes which are called grating lobes allow interfering signals at other directions than the desired signal enter the beamformer and mix up with the desired signal. The same phenomenon can happen in a velocity selective beamformer when inter-electrode spacing in the array goes beyond a certain length. If the travelling speed of a fiber is larger than the desired fiber, its successive action potentials will always add up destructively due to their small propagation delays between electrodes and the pre-steering delays tuned to the desired fiber. However, since we normally assume that all action potentials have the same shape, for the non-desired fiber with lower speed than the desired fiber, the combination of interelectrode spacing, the value of pre-steering delays, and the travelling speed of the spikes could be such that a number of successive action potentials appear simultaneously at the output of the pre-steering delay of each electrode and add up constructively at the output. This will be manifested as a grating lobe in the beampattern but its origin is of course different from the desired fiber in which only one of its action potentials appear at different times at each branch of the beamformer but due to the matched pre-steering delays will add up constructively with its replicas. The successive action potentials of a non-desired fiber could add up with each other constructively if the following condition is met.

 I   d  k.T f ,

(10)

in which  d  d / vd and  I  d / v I are the delay values of the desired and interfering signals between two adjacent electrodes and T f denotes the interspike interval (inverse of the firing rate) of the action potentials which is assumed to be the same for both fibers. From (10) we conclude that the first grating lobe (k=1) would appear if d is given by, d

Sidelobe Levels The maximum sidelobe level appears when the numerator of (3) becomes (almost) unity (peak is roughly in the middle of two adjacent nulls) [22]. It is easy to show that the first sidelobe level appears at the velocity vsl given by (9),

k  1,2,

Tf

(11)

1 1     v I vd 

This implies that the inter-electrode spacing must satisfy the following condition in order not to have any grating lobe in the beampattern.

1534-4320 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TNSRE.2014.2379594, IEEE Transactions on Neural Systems and Rehabilitation Engineering

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < T f ,min

1.4

(12)

 1 1     vmin vd 

1.2

If d becomes larger than (12) then at least one grating lobe will appear in the beampattern. This analysis is a confirmation to what has been reported in [13] as spurious velocity spectral responses. An example is shown in Fig 3 for a delay and sum beamformer with a length of 12 cm and 4 electrodes at vd  50 m/sec and 1 / T f  600 Hz. Signal to Interference Plus Noise Ratio (SINR) As it was mentioned previously,  n of each electrode is selected such that the desired action potentials become aligned with each other. This means that undesired signals will appear at different time instants and therefore will attenuate each other. The amount of attenuation depends on the location of a given velocity with respect to the desired velocity and is exactly given by the beampattern. The beam pattern basically determines the filtering characteristics of the beamformer. For example, a magnitude of 0.1 for an undesired velocity compared to 1 for the desired velocity means 10 dB attenuation for the signal travelling at the undesired velocity. An important factor which demonstrates the discrimination capability of the beamformer in extracting the desired signal from all unwanted signals not just a particular velocity is its signal to interference plus noise ratio. SINR is the ratio of the power of the desired signal to the power of all undesired signals. Based on (2), the SINR of the delay and sum beamformer is given by, SINR 

Grating Lobes

1

 

N E sd2 t 

(13)

2  N M    (n  1)d   (n  1)d (n  1)d        E   sm t     zn  t   n 1 m 1, m  d   vm vd   vd     

where E represents the expectation operator. Eq (13) implies that increasing N will increase SINR. D. Parameters Affecting Delay and Sum Beamformer Response From the analysis of the previous section we conclude that the following factors directly affect the response of a delay and sum beamformer. 1) Length of the Array

It is clear from (6) and (7) that the selectivity of the array is a function of its length Nd. Longer length means better selectivity, however, in practical scenarios the length of the array is limited by anatomical considerations of the nerve. 2) Desired Speed

Unfortunately, the response of the delay and sum beamformer highly depends on the desired speed vd . While the array has a narrow beamwidth at lower speeds it exhibits a

|H(f,v)|

d

5

0.8 0.6 0.4 0.2 0 0

20

40

60

80

100

120

Velocity (m/sec)

Fig. 3. Cross-section of the frequency-velocity beampattern of an array with 4 electrodes and 12 cm length at f=600Hz.

large beamwidth at higher speeds. 3) Frequency Effect

According to (5) the beampattern shows a highly nonuniform frequency-velocity response. Although the beampattern shows uniform response for the desired signal, it exhibits different attenuation levels for different frequency components of non-desired signals. 4) Inter-Electrode Spacing

For a fixed array length the number of electrodes should be chosen such that (12) is satisfied. This gives the maximum value for d. More number of electrodes is of course preferred to improve SINR as suggested by (13). However, smaller d means smaller values for pre-steering delays and more quantization error [23] unless a higher sampling frequency is chosen. Eventually, d is limited by the thickness of the electrodes. As mentioned above, the length of the array is often dictated by anatomical considerations. Consequently, it is not possible to create a beampattern with arbitrarily narrow mainlobe width regardless of the beamformer type. However, as it will be shown subsequently the non-uniform effect of other factors (e.g. velocity, frequency) can be compensated and a desired beampattern can be obtained by employing a space-time velocity selective beamformer and an appropriate design technique. III. SPACE-TIME VELOCITY SELECTIVE BEAMFORMER A. The Beamformer Structure Space-Time broadband beamforming is a well-known technique for spatial filtering of broadband signals in phased array antennas [16],[22]. In this method, TDL filters are added to each branch of the beamformer after the pre-steering delays to create a uniform frequency-angle beampattern. The same idea can be applied to a velocity selective electrode array as it is shown in Fig 4. Similar to Fig 1, front-end delay blocks are used to compensate for the propagation delay of the desired neural signal. The signals out of the delay blocks, assumed to be sampled with interval Ts , enter a set of TDL filters each with J weights. These weights can manipulate the response of the beamformer such that a uniform frequencyvelocity beampattern is obtained.

1534-4320 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TNSRE.2014.2379594, IEEE Transactions on Neural Systems and Rehabilitation Engineering

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT)
REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1

1 

 i 2f ( n 1) d    1 N  v vd  H ST ( f , v)   H n ( f )e N n 1

(25)

J

In this equation H ( f )  w e i 2f ( m1)T is defined. Comparing  nm n s

m1

(25) with (3) shows that an extra term H n ( f ) is now involved in the beampattern response. This term is actually used to create a uniform frequency-velocity response which could not be achieved by the delay and sum beamformer. Although optimal beamformer weights are rigorously determined by (21) to (24), obtaining closed form equations for the beampattern characteristics such as mainlobe width and sidelobe levels is not easily possible as they depend on the actual values of the weights. Once the optimal weights are found these pattern characteristics can be determined by replacing the beamformer weights in (19) and using regular numerical procedures (e.g. zero finding, applying derivative, etc.). E. Design Steps of a Space-Time Beamformer Design of a space-time beamformer requires performing the following steps which some of them are the same as in the delay and sum beamformer. 1) Length of the Array Similar to a delay and sum beamformer the length of the array is dictated by anatomical considerations.

7

F. Practical Implementation of the Space-Time Beamformer In real experiments, signals captured by each electrode are first passed through some stages of analog signal conditioning such as amplification and filtering prior to digitization. As mentioned before, both bipolar and tripolar recording techniques can be used for velocity selective beamforming. Since pre-steering delays are implemented in digital domain, higher sampling rates are recommended to minimize the effect of quantization error particularly when higher vd is requested. Interpolation of the data or other similar methods can also be used to reduce the effect of quantization error. Once the signals are recorded in digital domain, neural signal extraction can be performed for any desired velocity by designing an appropriate beamformer and applying it to the recorded data. The weights obtained from (24) are generally complex numbers whereas the recorded electrode signals are real. Therefore, a quadrature filter (Hilbert transform) is required in the actual implementation [16] to create a complex signal from the original real signal as it is illustrated in Fig 5. The complex signal xn (t   n )  ixn (t   n ) is now used in the space-time  beamformer of Fig 4 where x denotes the Hilbert n (t ) transform of xn (t ) .

2) Number of Electrodes and Inter-Electrode Spacing Choosing the number of electrodes and d follow the same rules as explained in the design of a delay and sum beamformer. 3) Length of the TDL Although increasing the number of taps in the TDL provides more degrees of freedom to reach the desired pattern, it imposes high computational load and sometimes numerical inaccuracy with large size matrices. Similar to a phased array system a value between 40-90 taps is a reasonable compromise between array performance and computational complexity [16],[22],[25]. For an MEC length of 3-5 cm we also found that this number of taps ensures having the desired beampettern without being entangled with the computational load or numerical ill-conditioning. The best way is to increase the number of taps from a low value and plot the beampattern until it meets the desired characteristics over the frequency band of the desired signal. 4) Desired Pattern For the desired pattern Pd  f , v  a two dimensional uniform frequency-velocity pattern should be assumed. Velocity range of interest can be as small as zero and can be as large as the maximum speed of the nerve fiber. However, if the propagation velocities of the fibers of a particular nerve are concentrated in a specific range then the design of the array can be better suited to that velocity range. The frequency band of interest should cover the frequency components of the desired neural signal.

Fig. 5. Using Hilbert transform in an actual implementation of a space-time beamformer.

IV. SIMULATION RESULTS We have tried to construct our simulation scenarios based on true values of human nerve parameters. Myelinated human peripheral nerve fibers typically conduct action potentials in the range of 35-75 m/sec, but this range could be as large as 10-120 m/sec [26],[27]. The conduction velocity of unmyelinated axons rarely exceeds 3-5 m/sec [26],[27]. The frequency distribution of a typical neural signal could be as wide as 100 Hz to 20 kHz but its frequency components are mainly distributed in the range of 300 Hz to 5 kHz [8]. Three examples are presented in this section. Our goal in the first example is to extract a desired spike signal from compound nerve action potential (CNAP). When there are a handful of fibers in a nerve [7],[11] extracting the desired signal from the interfering spike signals is possible only when the beamformer has enough selectivity and interfering signals are not too close to the desired signal. It is shown in this example that the space-time beamformer is able to faithfully

1534-4320 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TNSRE.2014.2379594, IEEE Transactions on Neural Systems and Rehabilitation Engineering

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT)
REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT)
REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT)
120

>120

0

0

37.7

37.8

7.2

7.2

23.2

24.0

5.4

5.4

TDNN

15.7

Erroneous peak

6.6

Erroneous peak

However, the space-time beamforming method creates a uniform beampattern for the entire band of frequency and it uses the components of the desired signal over this entire band to detect a particular velocity. Consequently, depending on the maximum frequency components of the signal, the BPF method can exhibit better or worse selectivity compared to the space-time beamforming method. If the received signal has high frequency components the BPF method may exhibit better selectivity than the space-time beamforming method. However, these high frequency components must be selected with caution and based on some a priori knowledge of the actual signals otherwise it may be corrupted by the background noise. Furthermore, as it is noted in [13] the presence of grating lobes must be avoided accordingly. Of course, the simple structure of the BPF method is definitely a privilege for this method compared to the more complex structure of the space-time beamformer. Since the TDNN works based on feature classification principles, it produces an excellent result in the single fiber experiment because it can greatly match the signal with its previous trainings. However, with a large number of action potentials travelling at the same speed in different fibers, this method cannot find a good match between the received signals and the training signals. That is why it produces erroneous results for the actual velocity in the second experiment and in all cases where there is a large difference between the shape of received signals and the ones used for training. This is typical of artificial neural network classifiers based on training signals (supervised learning). Importantly, the space-time beamforming method does not need any prior information or training based on the shape of the action potentials or its other characteristics. It is important to mention that both the BPF and TDNN methods are fiber activity detector not a fiber signal extractor.

1534-4320 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TNSRE.2014.2379594, IEEE Transactions on Neural Systems and Rehabilitation Engineering

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < In other words, if the purpose of velocity selective beamforming is just detecting the firing rate of the spikes, the BPF and TDNN methods can also be used similar to spacetime velocity selective beamforming method. However, for applications where the actual waveform of the spike is required the space-time beamforming method will be preferable. V. DISCUSSION AND CONCLUSION Localizing different neural fiber activities (SFAP) of a peripheral nerve, in addition to helping us to better understand the underlying mechanisms of physiological control systems, could lend itself to a variety of important applications. Primarily such technology can greatly help us to upgrade the functionalities of our implantable neuroprosthetic devices that interact with the peripheral nervous system and help to restore disabled functions in patients with spinal cord injuries, strokes, and amputations. Unfortunately, current technology mostly relies on the techniques which could only detect the gross activity of the nerve [30]. The main limitation of such technology is the lack of a more selective neural interface which could discriminate between the activities of different pathways within a nerve. The existing diagnostic methods also suffer from the same limitation. Traditional analysis of the compound muscle action potentials (CMAPs), sensory nerve action potentials (SNAPs), and motor unit action potentials (MUAPs) which are obtained during routine motor conduction, sensory conduction, and needle EMG (Electromyography) recordings are often used to diagnose disorders of the peripheral nervous system [27]. The target peripheral nerve is stimulated by surface electrodes and CMAP or SNAP are captured by other surface electrodes. Then parameters such as latency, amplitude, duration, and area of the captured signal graphs are studied to provide useful information about the type of neuromuscular disorder. However, nerve latency (conduction velocity) can only reflect the activity of the fastest conducting fibers; the effect of small myelinated and unmyelinated fibers cannot be observed in such traditional nerve conduction velocity measurements. Therefore, neuropathies that affect only small fibers may not be seen in such nerve conduction studies [27]. On the other hand, the action potential of a single sensory or motor fiber usually has either a biphasic or triphasic shape. Both CMAP and SNAP are compound action potentials representing the summation of fast and slow conducting fibers. Following nerve stimulation, the slower fibers lag behind the faster fibers at the recording site. This may cause the negative phase of the slower fibers overlap with the positive trailing phase of the fastest fibers and results in phase cancellation and time dispersion in the recorded CMAP and SNAP signals [27]. By separating activities of individual fibers in a peripheral nerve with low fiber density or illustrating different fiber group activities in nerves with high fiber densities, a velocity selective beamformer can be used to resolve the above issues. Although in this article we focused on the cuff electrode recording, the space-time beamformer can be used with other types of electrodes such as surface electrodes similar to [19].

11

By providing the 3D plot of the nerve activity over the time, much greater information can be provided by such beamforming technique than what is currently provided by traditional CMAP or SNAP analysis. By study of this 3D plots we can not only observe which fiber types are actually involved in a specific task but we can also determine their time correlation and their strength. Furthermore, due to the well-known beamforming algorithm used in space-time beamformer, analysis of the neural activity can be performed in real-time. This could provide valuable information for clinical investigations. On the other hand, an electrode array can be chronically implanted around a peripheral nerve and sends its recorded signals through a wireless link (inductively or by a radio frequency) to a remote station for further processing. Another prominent feature of the velocity selective recording is its ability to discriminate between afferent and efferent neural activities which travel with the same conduction velocity. In traditional methods different experiments are required for sensory, motor, and mixed conduction studies [27] whereas velocity selective beamforming can separate simultaneous motor (efferent) versus sensory (afferent) neural activities. To develop velocity selective beamforming algorithms some simplifying assumptions are normally made [7]. First, it is assumed that the structural and biophysical characteristics of the axons and the nerve do not vary over the length of the electrode array. This in turn means that the action potential waveforms do not vary over the length of the measurement, appear identically at all recording electrodes, and travel with a constant speed along the fiber. Although, some variations in these parameters are quite normal, they do not significantly affect the premises of the velocity selective beamforming. When the goal of the beamformer is extracting a desired neural signal (in a nerve with low density fiber), any other secondary processing can be performed on the output signal of the beamfomer (y(t) in Fig 4). This processing could be matched filtering [11], bandpass filtering [8] , or even neural spike sorting. Our results show that for the nerves with low fiber density, the TDNN [10] can be the best activity detector with highest velocity selectivity but it may produce incorrect results for the nerves with high density fibers. The BPF method is a simple yet effective activity detector which can produce satisfactory results for both high and low density fibers, although its performance depends on frequency contents of the signal. On the other hand, the space-time beamforming method appears to be the best signal extractor or activity detector in all scenarios with the cost of more complexity compared to the BPF method. Furthermore, the space-time beamforming method does not need any training phase like the TDNN. Although, the TDNN and space-time beamformer both use TDL filters in their structures and look very similar from this viewpoint, their working principles are entirely different. TDNN works based upon artificial neural network theory and uses feature classification principles (sigmoid nonlinear element) to implement a velocity selective recording technique. On the other hand, the space-time beamforming method uses the principles of sensor array signal

1534-4320 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TNSRE.2014.2379594, IEEE Transactions on Neural Systems and Rehabilitation Engineering

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < processing and spatial filtering theory to extract a desired wideband signal embedded in unwanted (interfering) signals without introducing any frequency distortion to the desired signal. One limiting factor in space-time beamformer is the number of taps. In theory increasing the number of taps will result in a more desired beampettern. However, in practice, increasing the number of taps causes ill-conditioning in the C matrix (Eq. 24) and will adversely affect the weights and consequently the beampattern and will deteriorate the selectivity. One question which may arise in comparing space time beamformer with delay and sum beamformer is the velocity selectivity at lower speeds. As it is shown in Fig 2(a), delay and sum beamformer has a narrow mainlobe at lower speeds whereas space time beamformer seems to produce a uniform beamwidth at all velocities but with wider mainlobe (e.g. Fig 6(d)). In fact, in our design we have intentionally selected a similar mainlobe for both high speeds and low speeds to be able to compare their results directly with each other. As mentioned earlier, the mainlobe width at higher speeds is limited by the length of the array. Similar to the delay and sum beamformer, we can have a space-time beamformer with similar fine selectivity at lower speeds. The simulations presented in this article focused only on fast myelinated fibers with high propagation velocities mainly because velocity selective beamforming for such speeds is much harder to achieve and it can show the merit of our method. Surely, the same method can be applied to extract neural signals from slow unmyelinated fibers. The hardware implementation of the proposed method can be performed similar to other methods. The signal conditioning part (amplification, filtering, ….) can be built by discrete analog components or in ASIC while the beamforming part (delay, applying weights, ….) can be implemented in a DSP processor, FPGA or PC (digital beamforming). Analog delays can also replace the digitally implemented delays [21]. In our view, velocity selective beamforming can play an important role both in neuroscience research as well as in clinical investigations.

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16] [17] [18]

[19]

[20]

[21]

[22] [23]

REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

K. Yoshida, D. Farina, M. Akay, and W. Jensen, “Multichannel Intraneural and Intramuscular Techniques for Multiunit Recording and Use in Active Prostheses,” Proc. IEEE, vol. 98, no. 3, pp. 432–449, March 2010. T. Sinkjaer, K. Yoshida, W. Jenssen, et. al., "Electroneurography", in Encyclopedia of Medical Devices and Instrumentation: Edited by J. G. Webster,Wiley-Interscience, 2006. B. Wodlinger and D. M. Durand, “Localization and Recovery of Peripheral Neural Sources With Beamforming Algorithms,” IEEE Trans. Neural Syst. Rehabil. Eng., vol. 17, no. 5, pp. 461–468, Oct. 2009. P. B. Yoo and D. M. Durand, “Selective recording of the canine hypoglossal nerve using a multicontact flat interface nerve electrode,” IEEE Trans. Biomed. Eng., vol. 52, no. 8, pp. 1461–1469, Aug. 2005. J. Zariffa and M. R. Popovic, “Solution space reduction in the peripheral nerve source localization problem using forward field similarities,” J. Neural Eng., vol. 5, no. 2, pp. 191–202, Jun. 2008. J. Zariffa, M. K. Nagai, M. Schuettler, T. Stieglitz, Z. J. Daskalakis, and M. R. Popovic, “Use of an Experimentally Derived Leadfield in

[24]

[25] [26] [27]

[28]

[29]

[30]

12

the Peripheral Nerve Pathway Discrimination Problem,” IEEE Trans. Neural Syst. Rehabil. Eng., vol. 19, no. 2, pp. 147–156, April 2011. Y. Huang and J. P. Miller, “Phased-array processing for spike discrimination,” J. Neurophysiol., vol. 92, no. 3, pp. 1944–1957, Sep. 2004. P. J. Taylor, N. Donaldson, and J. Winter, “Multiple-electrode nerve cuffs for low-velocity and velocity-selective neural recording,” Med. Biol. Eng. Comput., vol. 42, no. 5, pp. 634–643, Sep. 2004. N. Donaldson, R. Rieger, M. Schuettler, and J. Taylor, “Noise and selectivity of velocity-selective multi-electrode nerve cuffs,” Med. Biol. Eng. Comput., vol. 46, no. 10, pp. 1005–1018, Oct. 2008. A. Al-Shueli, C. T. Clarke, N. Donaldson, and J. Taylor, “Improved Signal Processing Methods for Velocity Selective Neural Recording Using Multi-Electrode Cuffs,” IEEE Trans. Biomed. Circuits Syst., vol. 8, no. 3, pp. 401–410, Jun. 2014. K. Yoshida, G. A. M. Kurstjens, and K. Hennings, “Experimental validation of the nerve conduction velocity selective recording technique using a multi-contact cuff electrode,” Med. Eng. Phys., vol. 31, no. 10, pp. 1261–1270, Dec. 2009. J. Taylor, M. Schuettler, C. Clarke, and N. Donaldson, “A summary of the theory of velocity selective neural recording,” in Ann. Int. IEEE EMBS Conf., pp. 4649–4652, 2011. J. Taylor, M. Schuettler, C. Clarke, and N. Donaldson, “The theory of velocity selective neural recording: a study based on simulation,” Med. Biol. Eng. Comput., vol. 50, no. 3, pp. 309–318, Mar. 2012. M. Schuettler, V. Seetohul, et. al., “Fibre-selective recording from peripheral nerves using a multiple-contact cuff: Report on pilot pig experiments,” Ann. Int. IEEE EMBS Conf., pp. 3103–3106, 2011. R. Rieger, J. Taylor, E. Comi, N. Donaldson, et. al., “Experimental determination of compound action potential direction and propagation velocity from multi-electrode nerve cuffs,” Med. Eng. Phys., vol. 26, no. 6, pp. 531–534, Jul. 2004. L. C. Godara, Smart Antennas. CRC Press, 2004. I. Frost, O.L., “An algorithm for linearly constrained adaptive array processing,” Proc. IEEE, vol. 60, no. 8, pp. 926–935, Aug. 1972. M. Schuettler, N. Donaldson, V. Seetohul, and J. Taylor, “Fibreselective recording from the peripheral nerves of frogs using a multielectrode cuff,” J. Neural Eng., vol. 10, no. 3, p. 036016, Jun. 2013. C. A. McKinley and P. A. Parker, “A beamformer for the acquisition of evoked potentials,” IEEE Trans. Biomed. Eng., vol. 38, no. 4, pp. 379–382, April 1991. D. Farina, E. Fortunato, and R. Merletti, “Noninvasive estimation of motor unit conduction velocity distribution using linear electrode arrays,” IEEE Trans. Biomed. Eng., vol. 47, no. 3, pp. 380–388, March, 2000. R. Rieger and J. Taylor, “A Switched-Capacitor Front-End for Velocity-Selective ENG Recording,” IEEE Trans. Biomed. Circuits Syst., vol. 7, no. 4, pp. 480–488, Aug. 2013. H. L. V. Trees, Detection, Estimation, and Modulation Theory, Optimum Array Processing. John Wiley & Sons, 2004. S. Zhang and I. L.-J. Thng, “Robust presteering derivative constraints for broadband antenna arrays,” IEEE Trans. Signal Process., vol. 50, no. 1, pp. 1–10, Jan. 2002. B. D. Carlson and D. Willner, “Antenna pattern synthesis using weighted least squares,” Microw. Antennas Propag. IEE Proc. H, vol. 139, no. 1, pp. 11–16, Feb. 1992. W. Liu and S. Weiss, Wideband Beamforming: Concepts and Techniques. John Wiley & Sons, 2010. J. E. Hall and A. C. Guyton, Textbook of medical physiology. Philadelphia, Pa.; London: Saunders, 2010. D. C. Preston and B. E. Shapiro, Electromyography and Neuromuscular Disorders: Clinical-Electrophysiologic Correlations, Saunders Pub., 3rd Ed, 2012. J. J. Struijk, “The extracellular potential of a myelinated nerve fiber in an unbounded medium and in nerve cuff models,” Biophys. J., vol. 72, no. 6, pp. 2457–2469, Jun. 1997. R. S. Johansson and G. Westling, “Signals in tactile afferents from the fingers eliciting adaptive motor responses during precision grip,” Exp. Brain Res., vol. 66, no. 1, pp. 141–154, Mar. 1987. D. Farina and W. Jensen, Introduction to Neural Engineering for Motor Rehabilitation, 1 edition. Hoboken, N.J: Wiley-IEEE Press, 2013.

1534-4320 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Velocity Selective Neural Signal Recording Using a Space-Time Electrode Array.

Extracting the activity of a particular neural fiber from the extracellular recording of a peripheral nerve is quite important from different clinical...
3MB Sizes 2 Downloads 9 Views