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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Accurate filtering of physiological tremor is extremely important in robotics assisted surgical instruments and procedures. This paper focuses on developing single stage robust algorithms for accurate tremor filtering with accelerometers for real-time applications. Existing methods rely on estimating the tremor under the assumption that it has a single dominant frequency. Our time-frequency analysis on physiological tremor data revealed that tremor contains multiple dominant frequencies over the entire duration rather than a single dominant frequency. In this paper, the existing methods for tremor filtering are reviewed and two improved algorithms are presented. A comparative study is conducted on all the estimation methods with tremor data from microsurgeons and novice subjects under different conditions. Our results showed that the new improved algorithms performed better than the existing algorithms for tremor estimation. A procedure to separate the intended motion/drift from the tremor component is formulated.

Tremor is defined as “a rhythmic, involuntary movement of a body part” [

The general assumption is that tremor has a single dominant frequency [

Physiological hand tremor lies in the band of 8–12 Hz with an amplitude of 50

Physiological tremor presents a technical challenge because of the high frequency band and its application in real-time. The error compensation control loop has to be executed in real-time. The system has to sense the tremor motion, distinguish between voluntary and undesired components, and generate an out-of-phase movement of the effector (hardware or software) to nullify the erroneous part, all in one sampling cycle. This approach will only work when there is a distinctive and accurate separation between the desired and unwanted motion. For example, dominant frequency of physiological hand tremor lies in the band of 6–15 Hz while hand movement of surgeon during microsurgery is almost always less than 0.5–1 Hz. Due to presence of accelerometers in tremor sensing equipment, physiological tremor filtering is more challenging with the presence of drift, noise and gravity in acceleration measurements [

Although linear filters [

Band limited multiple Fourier linear combiner (BMFLC) [

In this paper, a study is conducted on 6 micro surgeons and 6 healthy subjects to analyze time-frequency tremor characteristics. Existing methods on tremor estimation are first reviewed and the two improved methods are discussed. We improve the existing BMFLC algorithm by modifying the adaption procedure. Instead of relying on LMS for adaptation, we combine BMFLC with recursive least squares (RLS) and Kalman Filter to develop two new methods for accurate tremor estimation. All the existing and proposed methods are reviewed for performance on the data collected. The estimation accuracy is validated over several trails of data to show the effectiveness of the proposed methods.

Tremor recordings are performed through the Micro Motion Sensing System (M^{2}S^{2}) [^{2}S^{2} consists of a pair of orthogonally placed position sensitive detectors (PSD) and an infra-red (IR) diode to track the 3D displacement of the tip of microsurgical instrument in real-time. The IR diode is used to illuminate the workspace. A ball is attached to the tip of an intraocular shaft to reflect IR rays onto the PSDs. Experimental setup is shown in ^{2}S^{2} are 0.7

The tremor data recorded from 6 healthy subjects and 6 microsurgeons is considered for analysis in this paper. All subjects gave informed consent prior to the test and reported no physical or cognitive impairments. The subjects had their wrists rested on a small platform of the (M^{2}S^{2}) and were asked to take a comfortable seating position. They had to hold the stylus between their index finger and thumb in order to ensure that all subjects have similar grip across trials. The tip of the stylus was pointed near the center of the M^{2}S^{2} workspace. Two types of tasks are performed by the subjects:

The subjects performed two trials for each task with approximately one minute break between each trail.

In [

The analysis of tremor frequency characteristics can be performed with the single sided amplitude spectrum. Using the amplitude spectra, the dominant frequencies and the bandwidth of the tremor can be identified. However, the time-frequency characteristics of the tremor cannot be quantified with the amplitude spectrum. Existence of multiple peaks in amplitude spectrum of healthy subjects can also be related to dynamic changes in tremor frequency in the given band. It was not clear whether the single dominant frequency changes or there exists multiple dominant frequencies at any given time instant. To further analyze the tremor characteristics, we employ the BMFLC [

To study the time-frequency characteristics of tremor, the data of 6 microsurgeons and 6 healthy subjects are analyzed with BMFLC. For illustration, time-frequency mapping, FFT spectrum analyzer and spectrogram for surgeon #1 and novice subject #1 are shown in the

In this section, we first discuss the existing methods on tremor and later propose two improved methods. Existing methods for tremor can be categorized as single frequency based tremor estimation methods and multiple-frequency based tremor estimation methods. Weighted Fourier Linear Combiner (WFLC) [

The WFLC [_{k}_{0k} estimates the unknown frequency of the input signal. _{0} are adaptive gain parameters that govern the adaptation process of frequency and amplitude respectively. In usual practice, the combination of WFLC and FLC is employed for tremor filtering. The main advantage of WFLC is that it can adapt to changes in frequency of the signal. However, if the frequency variations are fast enough (signal frequency does not remain constant over time), the performance of WFLC will be degraded.

Recently a two stage algorithm was developed to improve the performance of the WFLC by employing a Kalman Filter (KF) to minimize the estimation error [

Presence of multiple peaks in the fast Fourier transform (FFT) spectrum is the result of modulation of multiple frequency components in tremor. Existing methods FLC and WFLC algorithms adapt to a single frequency present in the incoming signal. For the tremor signal consisting of multiple dominant frequencies closely, the accuracy in tremor estimation decreases with WFLC [

To overcome the problems with tremor signals comprising of multiple dominant frequencies, BMFLC [_{1} − _{n}_{k}_{rk}_{rk}_{r}_{1}_{n}_{1} − _{n}_{rk}_{rk}

LMS update:
_{k}_{k}_{k}

Input signal amplitude and phase are estimated by the adaptive vector _{k}

As LMS algorithm [

The recursive least squares algorithm (RLS) [

Compute Kalman gain _{k}

Update the BMFLC weights

Update correlation matrix _{k}

The main purpose of the forgetting factor

Kalman filter [_{k}_{k}_{k}_{k}_{k}_{k}_{k}_{1:k−1} = [_{1}, _{2}, ⋯, _{k−1}]. In this section, we employ the following notation:
_{1:k−1}, the estimated state_{k}_{k}

Compute Kalman gain _{k}

Update BMFLC weights

Update covariance matrix

_{0}and

_{0}.

_{k}

Accurate separation of voluntary motion from raw data is extremely important for successful compensation in robotics applications. To deal with this problem, in our proposed algorithm a bias weight [_{0} > 0 to track the intentional component in the LMS algorithm as follows:
_{k}_{k}_{1k} ⋯ _{nk} _{1k} ⋯ _{nk} _{0k}]^{T} are the new reference vector and adaptive weight vectors respectively. Since the high frequency components track their respective frequencies, the weight vector corresponding to 1 will adapt to the voluntary motion/drift in the motion. Therefore, the components can obtained as
^{th}

Robotics based surgical devices such as Micron [

As the algorithm provides the weight vectors of all the sine and cosine components, the non-drifting position information can be obtained with

In this section, we first discuss the separation of voluntary motion with BMFLC-Kalman filter on the raw data recorded during our trails and later compare the performance of all algorithms on the filtered data.

With addition of the extra weight as discussed in Section 3.2, the algorithm tracks the low-frequency component (voluntary movement). The raw data recorded from a healthy subject performing a tracing task is shown in

Similarly, for the raw data recorded with surgeon #1 performing a pointing task is shown in

To evaluate the performance of all algorithms, the tremor data of all subjects is bandpass filtered with zero-phase 5th order butterworth filter having pass band 6–14 Hz. The time-frequency map and FFT in

The following parameters and initial conditions are set for all the algorithms:

WFLC algorithm: _{0} = 1.10^{−5}, ^{−4}, _{0} = 7 Hz

WFLC-Kalman: _{0} = 1.10^{−5}, ^{−4}, _{0} = 7 Hz, _{0} = 0.01

BMFLC: _{1} = 2_{n}

BMFLC-RLS: _{1} = 2_{n}_{0} = 0.1

BMFLC-Kalman: _{1} = 2_{n}_{0} = 0.01

To further quantify the performance of all algorithms, the data recorded for two tasks (pointing task and tracing task with two trails/task) is considered for analysis. The analysis is performed separately for surgeons and novice subjects. All the algorithms are prediction based and only rely on output measurement _{k}_{k}_{+1} estimate.

Accuracy of cancellation of tremor in robotics instruments mainly depends on separation of tremulous motion from the raw data. It is necessary to develop novel methods for accurate filtering and estimation of physiological tremor in real-time for surgical applications. The proposed algorithm with a constant weight filters the low-frequency component,

As healthy subjects tremor characteristics display a band with multiple dominant frequencies, WFLC based algorithms fail to model tremor accurately. The single frequency component in WFLC has to adapt to all the frequency changes in the signal and high accuracy cannot be obtained. An improvement in the performance can be seen by integrating WFLC with Kalman filter. BMFLC based algorithms outperform the rest of the algorithms due to inherent nature of tremor with multiple dominant frequencies. It should be noted that WFLC based methods can be employed for pathological tremor filtering as the tremor consists of a single dominant frequency.

As tracing task involves more control, subject tend to display larger variations in tremor amplitude compared to pointing task. To study the difference in performance for pointing and tracing tasks, the analysis is performed separately for two tasks. The error bars with mean and standard deviation are shown in

As part of our continuing research in developing smart surgical device such as Micron [

This paper presents an improved single stage algorithm for estimating tremor for data sensed with accelerometers. The voluntary motion and involuntary motion can be separated from raw data accurately with the proposed method. Existing method BMFLC with LMS algorithm is improved by replacing LMS algorithm with Kalman filter. To analyze the performance of all the algorithms, a comprehensive comparative study is conducted on the data recorded from 6 healthy subjects and 6 microsurgeons. To highlight the performance of the proposed methods, we evaluate both the state of the art algorithms with the two novel-methods developed in this paper. The proposed methods BMFLC-Kalman and BMFLC RLS performed better than the existing methods WFLC, WFLC-Kalman and BMFLC-LMS. Among the five algorithms BMFLC-Kalman performed better producing an accurate estimate of tremor with an average RMS error of 0.003

Following are results of a study on the “Human Resource Development Center for Economic Region Leading Industry” Project, supported by the Ministry of Education, Science & Technology (MEST) and the National Research Foundation of Korea (NRF).

Micro Motion Sensing System (M^{2}S^{2}) setup.

Time-Frequency mapping of surgeon #1 and novice subject #1 in the band of 7–14 Hz.

BMFLC Architecture.

Block diagram for BMFLC-Kalman tremor filtering.

Performance of all algorithms with Surgeon #1 (pointing task).

Average RMS tracking error (

Average RMS error on all trails for tremor estimation algorithms.

WFLC | WFLC-Kalman | BMFLC | BMFLC-RLS | BMFLC-Kalman | |
---|---|---|---|---|---|

6 Novice subjects | 1.065 |
0.747 |
0.512 |
0.08 |
0.004 |

6 Surgeons | 0.956 |
0.632 |
0.408 |
0.076 |
0.003 |