An automated algorithm for measurement of surgical tip excursion in ultrasonic vibration using the spatial 2 dimensional fourier transform in an optical image

An Automated Algorithm for Measurement of Surgical Tip Excursion in Ultrasonic Vibration Using the Spatial 2 Dimensional Fourier Transform in an Optical Image Physics Procedia 87 ( 2016 ) 139 – 146 Av[.]

Physics Procedia 87 ( 2016 ) 139 – 146 Available online at www.sciencedirect.com

1875-3892 © 2016 The Authors Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license

( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).

Peer-review under responsibility of the Ultrasonic Industry Association.

doi: 10.1016/j.phpro.2016.12.021

ScienceDirect

44th Annual Symposium of the Ultrasonic Industry Association, UIA 44th Symposium, 20-22 April 2015, Washington, DC, USA and of the 45th Annual Symposium of the Ultrasonic Industry

Association, UIA 45th Symposium, 4-6 April 2016, Seattle, WA, USA

An automated algorithm for measurement of surgical tip excursion

in ultrasonic vibration using the spatial 2-dimensional Fourier

transform in an optical image

Prakash Manandhar*,a.b, Andrew Warda, Patrick Allena and Daniel J Cottera

a

Integra LifeSciences, N Billerica, MA, 01862, USA

b

Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

Abstract

The International Electrotechnical Commission (IEC) has defined a standard IEC 61847 (First Edition, 1998) for characterization of ultrasonic surgical systems This standard prescribes several methods for measurement of primary tip vibration excursion The first method described in the standard uses an optical microscope and relies on the motion blur of a vibrating object as it is imaged at low frame rates (e.g 30 Hz) of conventional video equipment This is a widely used method, that predates the standard, in ultrasonic surgical instrument design, and it is one of the key parameters that surgeons who use these devices are aware of It is relatively easily measured using a microscope system Although this method is widespread, the accuracy of this method is highly dependent on multiple factors such as operator training, microscope lighting and modulation of surgical tip motion It is also a manual and time consuming measurement such that a continuous measurement that describes dynamics at the scale

of micro-seconds becomes impossible Here we describe an algorithm to automate this measurement so that it can

be done at high speed without operator training, reducing human error and operator variation The algorithm derives from techniques used in motion blur estimation and reduction in the image processing literature A 2 dimensional spatial Fourier transform is computed from the microscope image of an ultrasonically vibrating tip A peak detection algorithm is used along with pre-processing to reduce noise Separation of peaks in the Fourier domain is used to estimate tip excursion We present data that shows an error of about 1% between manual and automated methods, when measurements are in the range of 300 microns and about 20% when the measurements are in the range of 30 microns

© 2016 The Authors Published by Elsevier B.V

Peer-review under responsibility of the Ultrasonic Industry Association

Keywords: ultrasonic surgical aspirator; stroke; Fourier transform; measurement, CUSA, cavitation

© 2016 The Authors Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license

( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).

Peer-review under responsibility of the Ultrasonic Industry Association.

* Corresponding author Tel.: +1-508-441-9155 E-mail address: prakashm@mit.edu

1 Introduction

Ultrasonic surgical devices have been used for many decades for various surgical applications starting with dental plaque removal in 1947 (Jallo, 2001) When the Cavitron Ultrasonic Surgical Aspirator (CUSA) devices are used in neurosurgery or liver surgery, the combined effect of cavitation, mechanical impact and other mechanisms is to selectively ablate very soft tissue or very hard tissue such as calcified tumors, and have a lower effect on fibrous elastic tissue like blood vessels (Verdaasdonck et al., 1998) An important parameter that determines tissue effect is the extent of longitudinal vibration of the distal end of the tip; this is also known as the stroke of the tip

Fig 1 depicts a typical setup that is used to measure the stroke optically For a sinusoidal vibration of frequency ݂ and zero-to-peak amplitude ܷ, disregarding phase, the equation of motion at the distal end of the surgical tip is given by:

When the measurement is made optically, the stroke is measured as the peak-to-peak amplitude of vibration, ʹܷ,

as shown in Fig 1 Three methods of measurement of vibration amplitude are listed in the international standard for measurement and declaration of basic output characteristics of ultrasonic surgical systems, IEC 61847:1998 (IEC, 1998) The first is the optical method mentioned above The other two methods are (1) laser Doppler vibrometry and (2) feedback voltage if a feedback system is employed (IEC, 1998) Both of these alternative methods are not as favorable as the optical method The laser vibrometry method requires precision setup which is time consuming to perform routinely Laser vibrometry is better for measuring very low amplitudes Commercially available instrumentation can be out of range for the typical amplitudes and frequencies used in CUSA devices For example,

10 m/s is a common peak velocity that commercially available vibrometers can measure; for a CUSA device operating at 23 kHz, 310 μm peak-to-peak stroke, the peak velocity is ʹߨ ൈ ʹ͵ ൈ ͳͲଷൈ ͵ͳͲ ൈ ͳͲି଺ൈ ͲǤͷȀ• ൌ ʹʹȀ• Feedback voltage is not a direct measurement and it is often difficult to ascertain whether the data is corrupted by phenomena like cross-talk with drive signals Given that optical measurement is very practical, it is widely used in the ultrasonic surgical tissue ablation device community However, the process of measuring stroke is

a very manual method that can be time consuming and dependent on operator training and setup, e.g magnification, lighting and display system The IEC 61847:1998 standard depicts this measurement method but does not delve into nuances that can make measurements subtly inconsistent when done in different labs Some of these nuances are explained in the section 1.1 below to build a case for automating and standardizing these measurement techniques

Nomenclature

ܷ zero-to-peak amplitude of vibration

1.1 Nuances of optical measurement of stroke

Optical measurement of stroke depends on the presence of micron scale geometric features, such as machining marks, that are present in the surgical tip surface that reflect the illuminating light in a specular fashion When the tip is vibrating, the specular dot features are transformed into lines with thickened ends that the operator has to align

to the lines using a video caliper system (Fig 2) This is due to the frame rate of video capture being very small compared to the frequency of ultrasonic vibration Usually, there are a multitude of these features in a measurement sample and some of the features can blend together to create larger features and too much light can be reflected off some features to create a halo effect (Fig 3) As multiple operators can choose to align the features in the images

Prakash Manandhar et al / Physics Procedia 87 ( 2016 ) 139 – 146 141

differently (Fig 4), there can be further variance in measurement In our experience, with operator training, a consistency of about +/- 5 μm can be achieved between various operators when making measurements in the range

of 20 μm to 400 μm However, this measurement usually takes tens of seconds and it is not possible to continuousl y take readings It is common to have stroke modulations that are in the order of micro-seconds to achieve different tissue effects such as increased selectivity (Verdaasdonck et al., 1998; Packer et al., 2005; Gardiner et al., 2015) An automated method of continuous measurement could alleviate some of these concerns In the rest of this paper, we will describe an automated algorithm and show that the accuracy is comparable to measurement by a human operator

Fig 1 (a) Microscope and lighting setup for stroke measurement (b) Longitudinal vibration of surgical tip, when seen under a microscope with

appropriate illumination appears as a motion-blur which can be measured

Fig 2 The optical measurement setup includes a calibrated video calipers system that superimposes lines on the image that the operator can align

to perform a measurement

Fig 3 (1) Halo effect makes precise measurement difficult when lighting is not correct (2) Some points can blend with nearby features to create larger points that reduce precision of measurement The operator has to pick the smallest distinct set of points for aligning to the measurement

Fig 4 The operator has to align measurement markers to thickened line ends

2 Algorithm

The input of the algorithm is the spatial domain image, ݃ and the output is an estimate of the amplitude, ܷ෡ The image ݃ is taken from a frame of the video feed from the microscope camera and converted to a grayscale image with values at each pixel in the range 0 to 1 The algorithm can be summarized as the series of steps listed in Fig 5 For the purpose of this paper, we are calling this algorithm SRYFT (Stroke by Fourier Transform) The notation used in the listing is borrowed from the Python 2 programming language version 2.7 (Johansson, 2015) The ˆˆ–ɩ and ˆ‹”™‹ functions are from the signal processing toolbox (Johansson, 2015)

Fig 5 The SRYFT algorithm

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Prakash Manandhar et al / Physics Procedia 87 ( 2016 ) 139 – 146 143

2.1 Algorithm discussion

In this section we will make analogies to 1-dimensional functions and their Fourier transforms to illustrate the algorithm as the 2-dimensional functions and their transforms are similar but more complex Consider functions 1 and 2 illustrated in Fig 6 Both functions are rectangular, differing only in width Their Fourier transforms take the

form of a sinc function (Brandwood, 2012) The magnitude or amplitude of the Fourier transform of a rectangular

function is insensitive to the phase of the rectangular function, and the spacing of the nulls of the Fourier transforms are inversely related to the width of the rectangular function This property of the transformed function is maintained even if the original function is slightly noisy or only approximately rectangular This means that the null spacing can

be used to estimate the width of the rectangular function Rekleitis (1996) has proposed the use of this method to calculate optical flow in motion blurred images to create a deburring filter or for video compression More recent reports of similar methods include Moghaddam and Jamzad (2006) and Ji and Liu (2008) We do not believe it has been previously reported for estimation of stroke in ultrasonic devices

Fig 6 1-d Fourier transform of rectangular functions showing the relationship between wide of rectangle function in time domain and null or

peak spacing in the frequency domain

The same principle is applied to two dimensional functions in the SRYFT algorithm A zero-crossing detector on the difference function is used to estimate the locations of the nulls of the transformed function A discrete finite-impulse-response low-pass filter, Šœ in Fig 5, is used to make this detector immune to noise Fig 7 is an example run of the algorithm Referring to the nomenclature in Fig 5, Fig 7(a) corresponds to the original image ‰; Fig 7(b) corresponds to the transformed image

corresponds to the filtered result ɨ; Fig 7(e) corresponds to the difference function †ɨ The image used in this example was of the size 720x480 pixels and the calibration factor was 402.2 pixels/1000 μm The manual measurement using a video scaler was 28 μm, while the automated measurement form the SRYFT algorithm was 33

μm Fig 8 depicts examples for more extreme cases, including a case where there is no vibration (ܷ෡ ൌ Ͳ μm)

Fig 7 An example run of the SRYFT algorithm, illustrating various stages of the algorithm Refer to section 2.1 for details

Fig 8.Example runs depicting, ܷ ෡ ൌ ͵ͷͺ μm (a, b, c) and ܷ෡ ൌ Ͳ μm (d, e, f)

Prakash Manandhar et al / Physics Procedia 87 ( 2016 ) 139 – 146 145

3 Results and discussion

Fig 9 plots the results of a series of experiments The difference between manual measurements and automated measurements are of similar magnitude to the uncertainty in manual measurements of about 5 μm in this system This shows that this algorithm is a feasible approach to automate measurement of stroke without loss of precision

A more obvious alternative approach could be to attempt to replicate the process used by human operators ± identify a pair of points that are not ambiguous or too haloed, estimate their co-ordinates to calculate the distance between them as stroke However, this approach is difficult because of the need for solving complex pattern recognition challenges Taking the Fourier transform results in a simpler algorithm because the Fourier transform is insensitive to phase and the result combines within it all the possible pairs of points joined by lines that form the motion-blur

Fig 9.Comparison of manual and automated measurements from an experimental data series The blue dots are measurement points; the line is a

linear regression fit

Acknowledgements

We would like to thank Peter Gould, Igor Kosenko and the Quality Assurance team at Integra LifeSciences at Billerica, MA, USA for helping us with manual measurements and equipment setup

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