UNIVERSITY OF CINCINNATI
______, 20 _____
I,______, hereby submit this as part of the requirements for the degree of:
______in: ______It is entitled: ______
Approved by: ______
Ultrasonic Surgical Instruments: A Multi-Variate Study for Cutting-Rate Effects
A Dissertation submitted to the
Engineering Mechanics division of the Aerospace Engineering and Engineering Mechanics Department
in partial fulfillment of the requirements for the degree of
DOCTORATE OF PHILOSOPHY (Ph. D.)
in the College of Engineering at the University of Cincinnati
June, 2003
by
Jeffrey J. Vaitekunas
B.S., Purdue University, 1985 M.S., Northwestern University, 1988
Committee Chair: Dr. Edward S. Grood, Ph.D.
ABSTRACT
In spite of the proven efficacy and safety of ultrasonic surgical systems, the mechanisms
for cutting and coagulation are not well understood. Preferred operating parameters and ranges
should be used if clinical benefit can be shown. Therefore this research was designed to
determine whether frequency, normal force, velocity and blade shape affect the cut-rate of an
ultrasonic surgical instrument.
Test velocities covered the range available from current ultrasonic surgical systems.
Three values for normal force were selected based on previous testing. A low value
corresponded to a “light” touch typically applied in fine dissection between tissue planes, and a
heavy value typically used in skin incisions such as a laparotomy. Two specimens were chosen
for evaluation: wax and liver.
The basic behaviors of the observed cut-rates obtained at 55.5 kHz with a 2.1 mm
diameter round blade were similar for wax and liver. Using analysis of variance (ANOVA), normal force, ultrasonic velocity and their first order interaction are shown to significantly affect cut-rate up to 5 N in wax and 2.5 N in liver.
In wax, cut-rate is shown to be independent of frequency, and in liver the data indicate that cut-rate is independent of frequency, but are not sufficient to draw a statistical conclusion.
In liver above a threshold, cut-rate increases significantly and depends on blade shape.
A model for wax cutting was developed based on melting and removal of wax. Several
assumptions were made and two parameters were determined by a regression. Still, the model
predictions were accurate for the data on which the regression was performed. The model also
predicts with reasonable accuracy the behavior observed at other frequencies for other blade shapes.
The model can certainly be improved by more rigorous development; nonetheless, it does demonstrate the basic mechanisms involved in wax cutting.
The results from the liver experiments and data analysis suggest that much more work is needed to accurately determine the underlying mechanisms of complex behavior of cutting tissue.
The outcome of this research on liver cutting is the identification of promising directions for future research.
ACKNOWLEDGEMENT
As completion of this work became evident, I thought of someone I wanted to thank in my acknowledgement. I sat and wrote the name on a piece of paper, hoping not to forget the individual's contribution to my work. In setting down that first name, I realized that I should list
all the people I wanted to recognize, because without them this work would not have succeeded.
To my surprise, the list filled a page. As I continued to add names over time, remembering one
event or another, I also realized I would almost certainly forget some contributors over the eight- year time-period this dissertation represents. So, to all those who contributed, my sincere thanks.
To my wife, Lisa, and daughters, Winona and Anna, I dedicate this work. I hope that I was also successful in not allowing this Ph.D. to supercede something much more important, my family.
I want to thank my committee: Dr. Ed Grood, my committee chair, whose clarity of
thought and levelheaded style I will continue to strive to emulate; Dr. Foster Stulen, my research
advisor, whose collaboration led me through this work that I am proud to present; Dr. Peter
Nagy, whose demand for precision and thoroughness was necessary to drive this work to its
current level; and Dr. David Butler, whom I first sought out when thinking about starting this
endeavor, and whose guidance was always thoughtful and well-intended. Their combined input
was invaluable and appreciated. I cannot imagine a better committee.
From a corporate perspective, no work of this cost, in terms of both effort and money,
can succeed without champions and supporters outweighing those trying to redirect resources to
other areas. My thanks to Johnson & Johnson, and specifically Ethicon Endo-Surgery, for
support of this work. Two individuals were champions deserving my gratitude. Mr. Richard
Dakers, who supported my ideas and sold the concept to the board of directors, lives the J&J
Credo and has earned my respect. Dr. Sharbel Noujaim, vice-president of R&D at the time of
this work, was steadfast in support of my efforts. Finer leaders I have never known.
During the time I was designing experiments, performing tests, and developing models, I
have reported to six different managers through three re-organizations at Ethicon Endo-Surgery, each time requiring me to re-sell the project and re-gain grass-roots support. I am indebted to Pat
Hider, Steve Neuenfeldt and John Wright for their efforts and support in helping me keep this work alive over a time-period of eight years, when institutional memory can fade in a quarter. I am also indebted to Lou Capezzuto for both supporting my Ph.D. work and leading me through the side-trip of passing the Patent Bar exam right in the middle of my Ph.D. efforts.
I have often wondered why it’s called a Doctorate of Philosophy, when the work is science and engineering. However, having now traversed the process, I recognize how much philosophical pondering is necessary in taking a scientific query into minutia. My thanks to
Scott Wampler and the late Ron Brinkerhoff, with whom many a philosophical discussion ensued. These individuals delighted with me in the sheer quest for truth and understanding, contributing without any desire other than my “getting it right.”
Finally, I want to thank my parents Walt and Trudy Vaitekunas, for instilling in me the desire to learn. Their willingness to field my incessant questions as I was growing is a trait that I hope to equal as my children are now growing. Also, my wife’s late aunt, Ms. Edith Miller, deserves more credit than I could have ever understood on the day I promised her I would not quit and give up on this quest.
TABLE OF CONTENTS
Chapter Description Page
List of Tables 5
List of Figures 6
List of Terms and Symbols 9
1. Introduction 12
1.1 Motivation 13
1.2 Research Objective / Questions 15
2. Literature Review 17
2.1 Overview 17
2.2 Historical Perspective 17
2.2.1 Koening and Human Hearing 18
2.2.2 Piezoelectricity 18
2.2.3 The Langevin Stack 19
2.2.4 Bio-Effects 19
2.2.5 Phacoemulsification 20
2.2.6 Neurosonic Surgery, Predecessor to HIFU 20
2.3 Ultrasonics 21
2.3.1 The Physics of Ultrasound 21
2.3.2 Diagnostic Ultrasound 21
2.3.3 Therapeutic Ultrasound 25
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Chapter Description Page
2.4 Therapeutic Ultrasound 26
2.4.1 High Intensity Focused Ultrasound (HIFU) 26
2.4.2 KHz Frequency Studies 29
2.4.3 Bio-Effects from Ultrasonic Scalpels 30
3. Model for Cutting Wax with Ultrasonically Activiated Blade 34
3.1 Introduction 34
3.2 Background for Modeling 35
3.3 Factors Known to Affect Cutting 38
3.4 Development of a Wax Cutting Model 40
3.4.1 Conservation of Energy 43
3.4.2 Energy Generated 44
3.4.3 Energy Stored 47
3.4.4 Equating Energies 48
3.5 Model Predictions 51
3.6 Comparison of Model to Empirical Data 55
3.6.1 Background of Cutting Experiments 55
3.6.2 Results from Wax-Cutting Experiments 57
3.6.3 Comparing Wax Cutting Results to Model 59
3.6.4 A-Posterori Evidence of Melt-Zone 64
3.7 Conclusion 65
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Chapter Description Page
4. Experimental Materials and Methods 67
4.1 Design of Experiments 67
4.1.1 Hypotheses 67
4.1.2 Treatment Factors 67
4.1.3 Response Measure 73
4.1.4 Determination of Statistics 73
4.2 System Performance under Load 73
4.3 Mechanical Testing 76
4.4 Specimen Fixture and Preparation 80
4.5 Data Acquisition and Analysis 82
4.6 Screening Experiments 85
5. Experiment Results 97
5.1 Wax Results 97
5.1.1 Data Collection 97
5.1.2 Effects of Force, Velocity and Frequency 98
5.1.3 Effects of Blade Shape 101
5.2 Liver Results 106
5.2.1 Effects of Force, Velocity and Frequency 107
5.2.2 Effects of Blade Shape 110
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Chapter Description Page
6. Discussion 114
6.1 Behavior of Wax Cutting 114
6.2 Liver Cutting 117
7. Conclusion 121
7.1 Research Questions 122
7.2 Wax Cutting 124
7.3 Liver Cutting 124
8. Proposed Directions of Future Research 126
Bibliography 128
Appendix A: Dissertation-Related Publications 134
Appendix B: Specific Heat of Freeman Wax 135
Appendix C: Translated Manuscripts 137
4
LIST OF TABLES
Name of Table Table Number Page
Cutting Model: Physical Parameters 3.3.1-1 39
Model Parameters 3.5-1 54
Cutting Forces per Unit Length 4.1.2-1 72
Measured Load Data 4.3.3-1 79
Factors in Blade Cleaning Analysis 4.6.1-1 85
ANOVA Data for Cleaning Analysis 4.6.1-2 86
Wax-Cutting Experimental Data 5.1.1-1 98
ANOVA Results for Cut-Rate in Wax 5.1.2-1 101
ANOVA Results for Wax-Cutting Including Blade Shape 5.1.3-1 102
ANOVA Results for Force, Velocity, and Interaction 5.2.1-1 107
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LIST OF FIGURES
Name of Figure Figure Number Page
Ultrasonic Surgical System 1.1-1 14
Shear-cutting with an Ultrasonic Blade 3.2-1 38
Shear-Cutting Side View 3.4-1 40
Wax-Cutting Thermodynamic System 3.4-2 42
Wax-Cutting Geometry 3.4-3 43
Magnified View of End-effector / Specimen Interface 3.4.2-1 44
Melted-wax Zone in Front of the End-effector During Cutting 3.4.4-1 49
Melt-Zone, ∆, Plotted as a Function of Force and Velocity 3.5-1 55
Model Predictions of Cut-Rate 3.5-2 56
Harmonic Scalpel Surgical System 3.6.1-1 57
Data from Wax-Cutting 3.6.2-1 59
Comparison of Model Prediction and Experimental Data 3.6.3-1 61
Round versus Angled Blade Cut-Rate Predictions 3.6.3-2 63
Cut-Rate versus Peak Tip Velocity for Wax Cutting 3.6.3-3 64
Micrograph of Wax Specimen after Testing 3.6.4-1 66
Cross-section of Blades Used in Studies 4.1.2-1 70
Laser Vibrometer Excursion Measurement System 4.2-1 74
Ultrasonic Blade in Loading Test Fixture 4.2-2 75
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Name of Figure Figure Number Page
Correlation of Current to Excursion under Load 4.2-3 76
Fixture Loading Positional Arrangement 4.3.3-1 78
Liver Specimen Preparation 4.4.2-1 80
Liver Fixture 4.4.2-2 81
Wax-Cutting Data Set 4.5.1-1 83
Graphical Data Set for Ultrasonic Blade Cutting Liver 4.5.1-2 83
Ultrasonic Blade Encountering Connective Tissue 4.5.2-1 84
Cut-Rate versus Slot Number for Cleaning Study Data Set 4.6.2-1 88
Cut-Rate versus Slot Number for Culled Cleaning Study Data Set 4.6.2-2 89
Analysis of Lobe-to-Lobe Variation 4.6.2-3 90
Graphical Data Set for Ultrasonic Blade Creep Test in Liver 4.6.3-1 92
Regression Analysis of Creep Between 3-to-6 Seconds 4.6.3-2 93
IR Camera Set-up 4.6.4-1 94
IR Camera Image of Wax-cutting 4.6.4-2 95
IR Camera Image of Wax-cutting 4.6.4-3 96
Cut-Rate versus Velocity and Force, 55.5 kHz and 75 kHz 5.1.2-1 99
Force and Velocity affect Cut-Rate 5.1.2-2 100
Cut-Rate is a Function of Velocity 5.1.2-3 101
Angled Blade versus Round Blade at 55.5 kHz 5.1.3-1 103
Angled Blade Cuts Slower in Wax 5.1.3-2 104
Blade Geometry affects Cut-Rate 5.1.3-3 105
55.5 kHz Statistical Analysis 5.2.1-1 108
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Name of Figure Figure Number Page
Cut-Rate as a Function of Velocity and Normal Force 5.2.1-2 109
Cut-Rate as a Function of Velocity and Normal Force in Liver 5.2.1-3 110
Angled Blade Cuts Faster in Liver 5.2.2-1 111
Angled Blade versus Round Blade in Liver 5.2.2-2 112
Frequency Confounded with Blade Shape 5.2.2-3 113
Stress-Relaxation in Liver 6.2.1-1 119
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TERMS AND SYMBOLS
ANOVA Analysis of variance
CUSA Cavitron Ultrasonic Surgical Aspirator
EES Ethicon Endo-Surgery
Harmonic Scalpel A trademark name for a family of ultrasonic surgical instruments.
HIFU High-intensity focused ultrasound
Langevin stack A high-power ultrasound transducer, sometimes referred to as a sandwich transducer.
MTS Materials Testing Systems, Inc.
Phaco (phacoemulsification) A procedure in which sound waves are used to shatter a cataract
PID Proportional-Integral-Differential
Q A measure of resonant bandwidth
A1 Elemental area 1
A2 Elemental area 2
Am Area of Melt
Av Area of blade in contact with sample inside thermodynamic boundary
a Ambient distance
a2 Arbitrary coefficient used to fit analytical model to experimental results
B5 Blade shape, circular cross-section
C Cut-rate
D Diameter of blade cross-section
Ec Energy conducted
Eg Energy generated
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Er Energy through A1 at location r
Er+∆r Energy through A2 at location r+ ∆r
Es Energy stored
F Normal force
Fl Load-cell force
Fv Viscous force fc Center frequency f1 Frequency at lower ½ power point f2 Frequency at upper ½ power point g Heat-generation rate per unit volume h Specimen width
K5 Blade shape having 120º included angle cross-section k Thermal conductivity
L Latent heat of fusion l Length of cut m Mass
Pa Average power
Pi Instantaneous power p Pressure
Q Heat energy r Radial distance r1 Radial distance 1 r2 Radial distance 2
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rm Melt zone radius rt Blade radius s Specific-heat
T Temperature
Ta Ambient temperature
Tb Blade temperature
Tm Melt temperature t Time
V Blade velocity
Vrms RMS blade velocity w Slot width in rheological flow opening
∆ Melt Zone thickness or height of rheological-flow slot
η Viscosity in a Newtonian fluid
ξ Effective viscosity assuming shear force in wax approximated by a newtowian fluid
θ Angle in Radians
ρ Wax density
τ Period of Vibration
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1. INTRODUCTION
Surgical devices such as the Harmonic Scalpel, a trademark name for a family of
ultrasonically activated surgical instruments currently manufactured and sold by Ethicon Endo-
Surgery (EES), are gaining popularity in the operating room due to the unique properties
inherent in ultrasound and its delivery modes. Many times, these properties significantly
differentiate therapeutic ultrasound from other energy modalities, such as electrosurgery, used to cut
and coagulate tissue. In addition, the ultrasonic surgical instruments provide clinical advantages over other instruments including: reduced tissue damage, decreased operating times, fewer instrument exchanges and more rapid healing.
While there is much reported clinical research on the subject of the clinical effectiveness of ultrasonic surgical systems, little attention has been given to the underlying characteristics of the ultrasound energy, specifically frequency and velocity. (Gossot, 1999; McCarus 1996;
Kanehira, 1999; Heili, 1999) Since the system is resonant, naturally the question arises as to what is the optimal frequency. The thought is that there may be a preferential transmission of energy into the tissue and / or an amplified desired tissue effect at a specific frequency.
Therefore, this dissertation was designed to evaluate effects of frequency and velocity on the performance of ultrasonic surgical devices operating in the 20 kHz to 75 kHz regime.
The depth of tissue cut by a surgeon depends on tissue type and on the proxmity of sensitive structures embedded or near the cut. The surgeon controls the aggressiveness of cutting by the applied force of the end-effector against the tissue. Because applied force is an important factor in cutting speed, force is included in the study.
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1.1 Motivation
While therapeutic ultrasonic systems provide a means to hemostatically cut tissues and
coagulate vessels, medical professionals may derive additional benefits from their use. For instance, ultrasound eliminates some potential hazards that exist with the modalities of electrical
and laser energies. One hazard of electrosurgery stems from the possibility that electrical
currents from electrosurgical devices may take unobserved paths, leading to necrosis of tissue
outside the surgeon’s view. Laser surgery is not without hazards. The depth of penetration of a
cut made via laser is difficult to control, and damage can occur to underlying tissue. On the
other hand, ultrasonic instruments have demonstrated an ability to minimize lateral tissue
damage, leading to faster healing and greater postoperative patient comfort (Amaral et al., 1995;
Ohtsuka et al., 1997).
Motivation for investigating the effects of multiple variables on ultrasonic cutting and
coagulation comes from a desire to design more effective surgical instruments with improved
surgical outcomes. An increased understanding of how variables such as system frequency, force
and velocity affect cutting speed allows more informed decisions about design tradeoffs,
eliminates the need for cut-and-try development, reduces number of animals used in pre-clinical
trials, and shortens time to market. The work performed in this dissertation is the first significant
effort to acquire this knowledge, and its results will help direct future research efforts to
ultimately achieve a complete quantitative understanding of the interaction of ultrasonic
instruments with tissue to improve surgical outcomes and improve patient health.
EES was especially interested in understanding the performance of its Harmonic
Scalpel system, depicted in Figure 1.1-1. The system operates at 55.5 kHz and consists of a
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generator; a hand piece, which houses the ultrasonic transducer; and an instrument. The handpiece basically contains the ultrasonic transducer that transforms the electrical energy from the generator to ultrasonic energy. The instrument includes a waveguide that transmits the ultrasonic energy and a tip, that is the end-effector in contact with tissue. A sheath covers the waveguide to eliminate patient or surgeon contact along the vibrating waveguide. Only the tip,
also referred to as the end-effector or blade, delivers ultrasonic energy to tissue.
Figure 1.1-1: Ultrasonic Surgical System
Surgeons ultimately control the performance of the Harmonic Scalpel. First, they select an instrument for the procedure being performed. Currently, more than 20 different instruments are available for open and laparoscopic procedures and are designed and indicated for specific surgical procedures. Second, they select one of five power settings to be available at one pedal
of a two-pedal foot switch. The second pedal is always set to the maximum power level. While
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referred to as a power setting, these actually set the current driving the piezoelectric elements.
The generator is designed so that the current basically determines the ultrasonic tip velocity. The surgeon controls the rate of coagulation and speed of cutting by the time and force that the end- effector is applied to the tissue at the selected power level.
The objective of the design of newer generations of systems and instruments is to make informed decisions to reduce development costs and time and to achieve even better clinical outcomes. Unfortunately, quantitative information or analytical models for the mechanisms of cutting and coagulation are unavailable in the literature to guide these decisions. However, the design goal remains to deliver the best system possible to the surgeons.
The investment in the development of an existing family of instruments, hand piece and generator is immense. While the knowledge from the initial development should help reduce investment costs in a second family at a different frequency, the cost in terms of dollars and time would still be enormous. Therefore, any decision to change system parameters of an existing system needs to be soundly based on better results from the underlying mechanisms that govern cutting and coagulation. This research originated from the questions of whether to change frequencies in subsequent generations of the Harmonic Scalpel or to develop systems for specific procedures.
1.2 RESEARCH OBJECTIVE AND QUESTIONS
1.2.1 Objective and Definitions The objective is to determine the effects of frequency, force and velocity on the cutting performance of an ultrasonic surgical instrument. Load means the force at which the blade is pushed against the tissue. Excursion is the ultrasonic displacement of the blade
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tip. The product of frequency in radians per second and excursion amplitude is velocity. Frequency is the ultrasonic frequency of the energy generated by the system.
1.2.2 Questions
Does the frequency of an ultrasonic surgical instrument affect the rate of cutting?
Does the force on an ultrasonic surgical instrument affect the rate of cutting?
Does the velocity of an ultrasonic surgical instrument affect the rate of cutting?
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2. LITERATURE REVIEW
2.1 OVERVIEW
For the purpose of this discussion, the field of ultrasonics is conveniently divided into three
areas. First, the physics of ultrasound encompasses the fields of acoustics and stress wave
propagation. The second and third areas, diagnostic ultrasound and therapeutic ultrasound,
combine to create the field of medical ultrasound.
Diagnostic ultrasound uses low-intensity energy in the 0.1-to-20-MHz region to determine
pathological conditions or states by imaging. Therapeutic ultrasound produces a desired bio-
effect, and can be divided further into two regimes, one in the region of 20 kHz to 100 kHz,
sometimes called low-frequency ultrasound, and the other in the region from 0.1 to 10 MHz,
where the wavelengths are relatively small so focused ultrasound can be used for therapy. At high intensities of energy, this application is referred to as HIFU for High Intensity Focused
Ultrasound. (Christensen, 1988; Sanghvi, 1993; Crum, 1999)
Examples of therapeutic ultrasound applications are: HIFU for tumor ablation and
lithotripsy, phacoemulsification, thrombolysis, liposuction, neural surgery and the use of ultrasonic
scalpels for cutting and coagulation. In low-frequency ultrasound, direct contact of an
ultrasonically active end-effector or surgical instrument delivers ultrasonic energy to tissue, creating bio-effects. Specifically, the instrument produces heat to coagulate and cut tissue, and cavitation to help dissect tissue planes. Other bio-effects include: ablation, accelerated bone healing and increased skin permeability for transdermal drug delivery.
This chapter gives a brief history of the development of medical ultrasound with a primary focus on therapeutic applications. From this review, one observes the steady progress in
17
the number and sophistication of applications. New medical applications will continue to drive
the development of ultrasound technology.
2.2 HISTORICAL PERSPECTIVE
A short chronology of the use of ultrasonic energy in medicine provides insight to the
evolution of therapeutic ultrasound systems. While diagnostic imaging is considered by many to be
the first medical application of ultrasonic energy, a dramatic ultrasonic bio-effect, the killing of fish,
was observed and published before the invention of diagnostic imaging.
2.2.1 Koening and Human Hearing: In 1865, Koening sought to discover the highest pitch
that humans could hear. He developed tuning forks and resonators from 4,096 Hz to 90,000 Hz
(Frederick, 1965). Using these sources, Koening was able to map the upper range of the human
hearing response, and he was the first to determine the upper limit of approximately 20,000 Hz.
This upper limit of audible sound is now accepted as the lower limit for therapeutic ultrasound.
Otherwise, therapeutic devices operated at audible frequencies could cause undesired outcomes ranging from annoyance to hearing impairment.
2.2.2 Piezoelectricity: About 1880, the piezoelectric effect was discovered in naturally- occurring quartz crystals by Jacque and Pierre Curie (Frederick, 1965). Piezoelectricity permitted the convenient generation of ultrasonic waves, and hence significant advancements in ultrasonic instruments and their applications soon ensued. For example, Altberg (1907) developed an early instrument for detecting and measuring ultrasonic waves using these quartz crystals.
18
2.2.3 The Langevin Stack: The use of natural crystals was limited to higher frequencies because
of their relative size at the time, and lower power because the crystals were small and weak in
tension. In 1917, Langevin was the first to develop a high-power ultrasound transducer, now
commonly referred to as a "Langevin stack" (Frederick, 1965). The stack is a sandwich of
piezoelectric crystals compressed between resonating masses. An electric field oscillating across
the poles of the crystals excites the stack, transforming the electrical energy into mechanical motion.
The Langevin construction allows lower frequency resonant transducers to be constructed, with
high power capability due to the pre-compression. Today, all transducers in low-frequency
ultrasonic surgical systems use the Langevin stack.
Langevin was working on anti-submarine warfare when he developed the stack. He was
performing underwater acoustics research to detect the presence of submarines, and noted the death
of small fish swimming in front of his transducers. This may be the first notation of an ultrasonic
bio-effect. However, at the time, Langevin seemed to consider it little more than an annoying side effect from his research.
2.2.4 Bio-Effects: In 1927, Wood and Loomis cite the Langevin bio-effect as prompting their
research into high-power applications ranging from bio-effects to materials science (Wood and
Loomis, 1927 a and b). Working with quartz crystals excited to 50,000 volts, they describe particle
agglomeration, emulsification, atomization, destruction of red blood cells and various frictional
effects. The frequencies they used ranged from 100 kHz to 700 kHz. The naturally occurring
piezoelectric crystals needed extreme voltages to produce high-power ultrasonic devices. Not until
the development of piezoelectric ceramics in the mid-1900’s could high-power ultrasonic devices be
produced readily and driven at much lower voltages.
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The above publications describing ultrasonic bio-effects predate the suggestion of ultrasound for diagnosis by at least a year. In 1928, Soviet physicist Sokolov suggested using ultrasonic energy to examine inside opaque objects for hidden flaws (Goldberg et al., 1988; Sokolov et al., 1929). And in 1944, Firestone received a patent on a reflectoscope for non-destructive testing, a device related to sound navigation and ranging (SONAR) equipment developed during
World War II (Goldberg et al., 1988; Firestone, 1942). The principles of SONAR technology were then later applied to develop early diagnostic ultrasound imaging systems.
2.2.5 Phacoemulsification: In 1962 Kelman, an ophthalmologist, developed a tissue emulsifier
(Devine et al., 1991). This phacoemulsifier (phaco) removed the lens of the eye to facilitate replacement during cataract surgery. Emulsifiers were the first medical devices employing a waveguide to deliver ultrasonic stress waves from a transducer into tissue (Devine et al., 1991).
Note that if the phaco is considered the first successful surgical application of high power ultrasound, 45 years passed from the first observed bio-effect to the first useful application of high-power ultrasound for a therapeutic bio-effect.
2.2.6 Neurosonic Surgery: Fry and Fry (1954a and b) performed the first thorough analysis of the interaction of ultrasound and tissue, and assessed whether therapeutic ultrasound could destroy deep-seated brain tumors. Their work describes models of ultrasound tissue interaction and experimental apparatus used to validate the models. They developed a method wherein deep portions of the brain were necrosed while sparing tissue between the necrosed area and the exterior of the brain, by delivering the energy from outside the brain. This work has continued to evolve into what is now called high-intensity focused ultrasound, or HIFU.
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2.3 ULTRASONICS
2.3.1 The Physics of Ultrasound: The fields of acoustics and stress wave propagation
encompass applications ranging from non-destructive testing in materials science, to beer packaging
in high-volume manufacturing (Ensminger, 1988; Kinsler et al., 1982; Morse et al., 1968;
Krautkramer et al., 1990). Many texts are available on acoustics and wave propagation, and provide the necessary physics, analytical background and insight for the development of models for ultrasonic devices, and potentially for models applicable to ultrasonically-induced tissue bio-effects.
Achenbach and Graff present a good base of general theory for acoustic wave propagation in elastic
solids in their texts (Achenbach, 1990; Graff, 1975). Nayfeh (1995) extends the concepts to layered anisotropic media. In addition, there are texts that specifically address the thermal and mechanical effects of ultrasound. Young reviews many of the theories and models for cavitation in high-power applications (Young et al., 1989).
2.3.2 Diagnostic Ultrasound: Diagnostic and therapeutic ultrasound encompass the
applications of ultrasound in the field of medicine. Diagnostic ultrasound uses ultrasonic energy
to perform a procedure that will help determine pathological conditions or states. Diagnostic
ultrasound typically transmits a propagating burst of ultrasonic energy from a contact transducer
into the tissue. When the energy encounters a change in the acoustic impedance such as from
one organ to another some of the energy is reflected back. The reflected energy is received by the same transducer and used to from an image. Research in the field of diagnostic ultrasound
produced valuable information applicable to therapeutic ultrasound; therefore, an understanding
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of the effects of diagnostic ultrasound gives a good background for understanding research in the
field of therapeutic ultrasound.
One of the main concerns about using ultrasonic energy for diagnostic purposes manifests
itself in the form of bio-effects. Several mechanisms of ultrasound-tissue interaction can contribute
to bio-effects. Generally, these mechanisms are separated into thermal effects and mechanical
effects (Ziskin et al., 1992; AAPM, 1995). While the power levels used in diagnostic ultrasound
remain low in comparison with the levels used in therapeutic devices, mechanical effects such as
cavitation created during diagnostic procedures (e.g., sonograms) might cause unintentional bio-
effects. These concerns have prompted organizations such as the Food and Drug Administration
(FDA), the American Institute of Ultrasound in Medicine (AIUM) and the National Electrical
Manufacturers Association (NEMA) to adopt measurement standards to limit the dose of ultrasound to tissue. Indices such as the Thermal Index (TI) and the Mechanical Index (MI) have been developed as measurement standards for diagnostic devices (Holland et al., 1989; NCRP, 1992).
Both the MI and TI used in diagnostic ultrasound dosimetry are frequency dependent (NCRP,
1992). Though these indices were developed for megahertz-frequency diagnostic ultrasound devices, and are not generally considered in the low kHz range for high-power devices, the impetus behind their development should not be discounted. Clearly, ultrasonic energy produces changes in human tissue. Several of the known bio-effects of ultrasonic energy are discussed below.
2.3.2.1 Thermal Mechanisms for Bio-Effect: Absorption is one of the processes by which
mechanical energy is converted into heat (Ziskin et al., 1992). Absorption, along with reflection
and scattering, leads to attenuation of ultrasound when propagating through tissue. Absorption
in tissue is generally specified via an attenuation coefficient in units of dB/cm/MHz and there are
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tabulated values for different types of tissues (Duck, 1990). Attenuation coefficients are very
important in diagnostic ultrasound, because attenuation limits the depth of penetration that can be
achieved. Unfortunately, these values cannot be directly applied to HIFU, since at high acoustic
intensities wave propagation is highly non-linear. These nonlinearities cause a sinusoidal
compressional wave to steepen into an N-shaped wave. This represents a multi-frequency component wave that can be divided into its individual components, and the corresponding
attenuation coefficients can be applied for each component in calculations. In addition,
wavelengths for low-kHz frequencies are very long, and much longer than the treatment zone,
therefore the absorption mechanism is not a significant contributor to heating in low frequency
therapeutic ultrasound.
As diagnostic ultrasound intensities increased in the 1970’s, heating of tissue became
more of a concern to the radiologists performing procedures. However the introduction of
phacoemulsifiers and surgical aspirators caused acute heating to become a major concern with their use. As Kelman was developing the phaco for cataract removal, significant local heating of
the eye occurred where tissue came in contact with the vibrating ultrasonic end-effector.
Instruments such as the phaco and Cavitron Ultrasonic Surgical Aspirator (CUSA) therefore
evolved to include cooling water jackets and protective sleeves to deal with undesired heating
effects (Devine et al., 1991; Wuchinich, 1977).
Balamuth (1962) and Wuchinich (1977), pioneers of high-power ultrasonic surgical
systems, have contributed significantly to the understanding of possible mechanisms for both
thermal and non-thermal effects. Potential mechanisms for tissue heating include frictional heating
between the vibrating blade and tissue, acoustic absorption and visco-elastic heat generation derived
from fluid dynamics. The early work by Balamuth suggests that tissue cutting can be attributed to
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thermal energy, though more recent publications from Cimino and Bond (1995 a and b) suggest
only non-thermal mechanisms are important in CUSA-like devices.
2.3.2.2 Mechanical Mechanisms for Bio-Effects: Ultrasound-induced mechanical events
such as cavitation, micro-streaming and free radical production produce bio-effects not necessarily
related to the bulk generation of heat (Roy, 1996). Cavitation occurs in liquids when the peak rarefactional pressure exceeds a threshold and out-gassing and vapor formation occur. When this occurs in tissues, the growing cavity containing the gas and vapor can burst. These cavities also collapse and release a significant amount of mechanical energy in a very small volume. Effective temperatures of 5,200 K and higher have been measured in solutions of metal carbonyls through the use of comparative rate thermometry (Suslick et al., 1995).
When a cavity collapses near a surface a micro-jet is formed, a mechanism known to cause damage to metals such as ship propellers (Young, 1989). The collapse itself leads to cell disruption.
Therefore, cavitation has the potential to create significant bio-effects. Young presents several definitions of cavitation thresholds, all of which have frequency as a dominant parameter (Young et al., 1989).
Micro-streaming occurs around cavitation bubbles as well as through hydro-dynamics associated with the passage of ultrasound around structures of differing mechanical impedances
(Verdaasdonk et al., 1998). Microstreaming, a mechanism by which there is bulk movement of
fluid, has been suggested as one of the mechanisms by which accelerated bone-healing occurs.
Researchers believe microstreaming increases the nutrient flow to the damaged area and aids in
removal of damaged tissue.
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Free radical production is known to occur under conditions sufficient to produce cavitation
(Suslick et al., 1995). Free radicals can cause cell death, and are capable of initiating sound-
activated chemistry (sonochemistry).
Therefore these thermal and mechanical mechanisms contribute to tissue bio-effects.
Depending on the application, one or more may be important to the desired outcome. Many of
the effects described above have some frequency dependence and can be enhanced by proper
selection of frequency and amplitude. All of the mechanisms are relevant in the field of
therapeutic ultrasound.
2.3.3 Therapeutic Ultrasound Systems: Therapeutic ultrasound is defined as the delivery of
ultrasonic energy at a frequency greater than 20 kHz to tissue in order to provide a therapeutic or
beneficial clinical effect. Therapeutic ultrasound divides into two regimes. Low-frequency
ultrasound, occurring in the low kHz region of 20 kHz to 100 kHz, uses Langevin stacks to produce
ultrasonic stress waves that are delivered to tissue using instruments as waveguides. HIFU
transmits relatively high-frequency ultrasonic energy from a transducer through the tissue to a small
focal volume where intense ultrasound energy locally raises temperature.
In ultrasonic surgical devices, blades or other end-effectors are attached to the transducer via an instrument. The instrument including the blade resonates at the same frequency as the
transducer, and therefore, the overall system frequency remains the same. The instruments take the form of long rods or tubes that act as waveguides to receive the ultrasonic energy from the transducer and deliver it to the end-effector that contacts the tissue.
The displacement of the ultrasonic vibration at the tip, denoted as d, behaves as a simple sinusoid at the resonant frequency as given by Equation 2.3.3-1:
25
d = A sin (ωt) (Eq. 2.3.3-1)
where:
ω = the radian frequency that equals 2π times the cyclic frequency, f
A = the zero-to-peak amplitude
The excursion of the tip is defined as the peak-to-peak (p-t-p) amplitude, which is just twice the
amplitude of the sine wave, or 2A.
At the tip of the end-effector, the energy is delivered to tissue to create several effects within
the tissue. These include the basic gross conversion of mechanical energy to both frictional heat at
the blade-tissue interface, and bulk heating due to viscoelastic losses within the tissue. In addition,
there may be the ultrasonically induced mechanical mechanisms of: cavitation, microstreaming, jet
formation and sonoluminescence (Ensminger et al., 1988; Young et al., 1989; Christensen et al.,
1988; Dyson et al., 1982).
2.4 THERAPEUTIC ULTRASOUND – HIFU AND KHZ FREQUENCY STUDIES
Driven by clinical needs, there is active research in both HIFU and low-frequency ultrasound. The objective is to gain deeper understanding of the interaction of tissue with
ultrasound to ultimately deliver improved therapies and improve patient outcomes.
2.4.1 High Intensity Focused Ultrasound: Many of the mechanisms of HIFU are also a
consideration in low frequency applications, and therefore worthwhile visiting here. HIFU
utilizes the propagation of a focused beam of ultrasound, resulting in very high intensities within a
small focal region to perform surgical procedures and treat tissue. Currently, significant effort
26
from many universities is directed towards understanding and achieving tissue bio-effects utilizing
HIFU. Understanding both how ultrasonic energy affects the tissue and how tissue changes affect
the ultrasound are important for treatment planning and development of future HIFU devices.
The use of HIFU to stimulate neural structures has been proposed by Gavrilov et al. (1996)
to diagnose and treat neural disorders. He studied somatic sensations in humans using ultrasonic
frequencies from 480 kHz to 2.67 MHz, reporting sensations at intensities ranging from 8 to 3000
W/cm2. They observed that induction of tactile sensation is independent of frequency within the
tested range. Therefore they suggest that mechanical mechanisms are the primary factors of
ultrasound as a physiological stimulus. Heating is discounted as a mechanism, because it would
depend on velocity and hence frequency if displacement is fixed.
Shock wave lithotripsy is the oldest application of high-intensity focused ultrasound in surgery. Acoustic pressure is sufficient to break up stones, and thermal effects are negligible for the tissues surrounding the stones. However, Howard et al. (1996) presented lithotriptor histology results that show tissue cell damage due to high stresses associated with shock waves propagating through the tissue. Also at the high acoustic pressures in lithotripsy, cavitation can produce ultraviolet and x-ray emissions, which are known to affect cells (Vona et al., 1995).
Early work by Lele (1963), using continuous wave insonification, suggested that ultrasound effects on nerves are thermal in nature, primarily through absorption. Lele's studies were done using HIFU transducers with frequencies above 500 kHz. Lele demonstrated that the nerve damage was consistent with damage from an equivalent simple heat source. The intent of the studies was to deliver enough ultrasonic energy to produce heat, therefore any stimulus effects were presumably overwhelmed and not studied.
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While described as high intensity, bio-effects can actually occur at relatively low levels.
The demarcation between diagnostic ultrasound and therapeutic ultrasound is fuzzy at best.
Coakley and Morris (1977) have reported damage to plant roots by ultrasound intensities as low as
3.3 watts/cm2 for 2 minutes at 0.8 MHz. Sarvazyan shows that at acoustic intensities as low as 5-7
watts / cm2 the nonlinear properties of tissue contribute significantly to energy delivery and dose
(Rudenko et al., 1996).
Ter-Haar has presented evidence for ultrasonically-induced cavitation in-vivo at 80
watts/cm2 (ter-Haar et al., 1982). Crum and Fowlkes (1986) have shown that a single cycle of ultrasound at 1 MHz can produce cavitation. Thus bio-effects associated with cavitation can occur in very short time periods as well as at relatively low intensities.
Dyson et al. (1982) specifically separated cellular effects of ultrasound into thermal and non-thermal mechanisms. The stated non-thermal effects include changes associated with standing waves, acoustic streaming, microstreaming and cavitation, as discussed earlier. She suggested that some of Lele's work was done at therapeutic levels where those events of thermal origin masked those of non-thermal origin. She states that at lower dose levels, thermal and non-thermal changes may occur simultaneously, where some effects may have both a thermal and non-thermal basis
(Dyson et al., 1982). Dyson presents experimental evidence of non-thermal cellular mechanisms, both in vitro and in vivo.
Several groups are currently working on surgical applications of HIFU. Hynynen et al.
(1992) have produced significant work on HIFU for surgical applications. Their earlier work was centered on hyperthermia for oncology. Hynynen’s current research includes the simultaneous measurement of ultrasound-induced temperature rise using magnetic resonance imaging to quantify and control the treatment volume. A number of researchers have published clinical results from
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HIFU used to treat benign prostatic hyperplasia (BPH) (Sanghvi et al., 1993; Ebert et al., 1995;
Uchida et al., 1995; Nakamura et al., 1995; Madersbacher et al., 1995; Gelet et al., 1993). Other
groups have presented studies for treatments of fibrocystic breast (Damianou et al., 1993; Zimmer et
al., 1993; AAPM, 1995). The overall conclusion from these studies is that HIFU can be an effective
therapy.
Hill and ter-Haar and their co-workers are performing studies to look at other surgical uses of HIFU as a part of oncological treatments (Chen et al., 1993; Hill et al., 1994[1]). They have also looked at models for HIFU lesion rate production, and optimum ultrasonic frequencies for HIFU ablation (Hill et al., 1994[1]; Hill et al., 1994[2]). These studies were looking to optimize tradeoffs between depth of penetration, focal spot size and the ability to increase tissue temperature within the focal zone.
2.4.2 KHz Frequency Studies: O’Brien and Zachary (1996) have shown that there is a species dependency in observed effects of 30 kHz continuous wave ultrasound exposure. Their studies compared lung tissue damage between species for mouse, rabbit and pig models. Ratios of damage scores up to 14.4 were shown between mouse and pig models at equivalent acoustic pressure exposures.
Koch et al. (2002) have published results for determining the acoustic output characteristics of a harmonic scalpel. Their work is directed more toward possible bioeffects to the operator or operating room personnel than to tissue bioeffects of the patient. They suggest there might be high levels of air-borne acoustic pressure that could result in hearing loss of the operator if the instrument was held too close to the operator’s ear for a long period of time, however the results were inconclusive.
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Nagy and Nayfeh have produced a body of work examining rods immersed in fluids, and
their resulting viscosity-induced attenuation (Nagy and Nayfeh, 1996; Nagy, 1995; Nayfeh and
Nagy 1995). They report a frequency-dependent attenuation in highly viscous liquids for steel wires of 2.35 mm diameter coated in honey. This suggests the possibility of a similar effect for
2.1 mm diameter titanium blades immersed in tissue.
2.4.3 Bio-effects from Ultrasonic Surgical Scalpels: The International Electrotechnical
Commission (IEC) recognized that lack of consistent measurable operational parameters hindered
progress in understanding mechanisms and bio-effects from ultrasonic surgical instruments. The
IEC published a standard detailing how high-power ultrasonic devices operating at kHz frequencies
can be measured (IEC-61847). The IEC developed this standard, in part, to allow comparisons
between kHz-range high-power surgical devices. At the time, the IEC stated that little is known
about the mechanisms of tissue cutting and coagulation from ultrasonic instruments (IEC-
61847).
A literature search has uncovered a few pertinent publications relating to the
mechanisms of therapy from ultrasonic surgical instruments in the low-kHz regime. Two of
these are publications from Russian journals for which translations are provided in Appendix C
for the reader’s convenience.
The Russian publications are of primary interest because they relate to ultrasonic cutting
of biological tissues (Nabibekov et al., 1980; Sarkisov et al., 1982). These publications
developed a tissue-cutting model for both ultrasonically active and non-active cutting
instruments. This work considered plunge insertion, or cutting at an angle normal to the surface
of the tissue. While beneficial for procedures such as phacoemulsification, their model is not
appropriate for shear-cutting that is the action of the Harmonic Scalpel.
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Cimino and Bond (1995) have proposed a model for tissue fragmentation produced by
the CUSA device, also used for plunge-cutting of soft tissues. As previously stated, the CUSA device incorporates a water-cooling jacket to minimize thermal effects. This cooling water flows
in front of the end-effector, thereby reducing other effects such as cavitation damage. The
CUSA device cuts tissue in the same direction as the longitudinal excursion of the tip. Both
systems investigated by Nabibekov and his co-workers, and Cimino and Bond approach the
tissue in the normal direction.
The system examined in this dissertation applies the ultrasonic vibration along the surface
of the tissue being cut. It is best described as shear-cutting. So both bodies of the previous
works by Nabibekov and Cimino and Bond are not directly applicable to the system here.
Verdaasdonk et al. (1998) disputed Cimino and Bond’s suggestion that cavitation had
little or no effect on the fragmentation capability of the CUSA device. Verdaasdonk’s results
from studies on the mechanisms of action of the CUSA showed combined effects from
cavitation-induced fragmentation, mechanical cutting and thermal deterioration. Their high-
speed photography clearly shows cavitation at the tip to tissue interface contributing to
fragmentation. Shock waves emanating from the collapsing cavitation bubbles were also clearly
identified, but no tissue effects were discernable from the shock wave propagation.
An attempt was made by Tsuda et al. (1982) to begin to study the effect of frequency on
cutting and heating of biological tissue. Two frequencies were selected, 20 kHz and 50 kHz.
Unfortunately, different end-effectors were used at each frequency, making analysis between
frequencies difficult. No subsequent publication by Tsuda reporting results with respect to
frequency has been uncovered.
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An attempt to measure the heat generated by an ultrasonic instrument shear-cutting tissue was published by Okada et al. (1988), wherein a thermal camera was used to measure temperature while cutting bone. They compared cutting bone using a reciprocating saw with cutting bone using an ultrasonic saw. In effect, the comparison was of 60 Hz versus 28 kHz cutting of bone. Their study was medical in nature, and discussion of results was limited to clinical efficacy and did not address the issue of frequency effects. They saw a 20º C temperature rise with the ultrasonic saw operated at 28 kHz compared with the 60 Hz saw. They considered the temperature rise to be an undesirable effect, and controlled it to a less than 10º C rise using water injection to the cutting site as a coolant. Results from this study suggest that significantly less effort is needed to cut bone utilizing an ultrasonically-energized saw.
Olympus Optical Company has published an Internet web site on ultrasonic surgical instrumentation at www.olympus.co.jp/LineUp/Endoscope/eneE.html. On this site, Olympus is claiming that low-frequency ultrasound (23.5 kHz) enables faster coagulation and cutting than higher-frequency systems. No rationale or substantiation is provided for this statement with regard to frequency effects. In spite of their claim, Olympus has recently introduced a 40 kHz system.
EES actively researches tissue effects from ultrasonic instruments, and has since before the introduction of its Harmonic Scalpel in 1995. Some of the studies published by Vaitekunas and his co-workers (1996, 1997) describe bio-effects from ultrasonic surgical devices used for cutting and coagulation of tissues. In 1997, Vaitekunas et al. showed that an ultrasonic ball coagulator in tissue never exceeded about 70 ºC when coagulating tissue, determining that tissue did not reach the boiling point of water when it was used. This was a continuation of their work
32
presented in 1996, that discussed tissue / blade interactions of the then newly introduced
Harmonic Scalpel.
In conclusion, current research in the area of therapeutic ultrasound focuses largely towards understanding the various bio-effects of the interaction of ultrasonic energy and tissue. Yet research
in both HIFU and low-kHz frequency ultrasonic surgical instruments is still seeking accurate
understanding of the interactions of ultrasonic parameters, their bioeffects and the resulting clinical
outcomes.
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3. A MODEL FOR CUTTING WAX WITH AN ULTRASONICALLY ACTIVATED BLADE
3.1 Introduction
Shear-cutting is an important function of modern ultrasonic surgical systems, especially in laparoscopic instruments. These systems consist of a generator that converts standard line electrical power to electrical energy at the ultrasonic frequency. The generator drives a hand- piece that converts the electrical energy to ultrasonic mechanical energy. Single-use or limited- use surgical instruments are connected to the hand-piece. The mechanical vibrations produced by the hand-piece are transmitted by a waveguide in the instrument that usually provides some displacement gain. A sheath surrounds the waveguide to protect the surgeon and patient from direct contact with the ultrasonic energy. Only the distal tip of the instrument is exposed, and brought into contact with tissue to coagulate and cut. The main advantage of an ultrasonic surgical system is the ability to provide good hemostasis while simultaneously cutting tissue. In laparoscopy, another advantage is the instrument is dull for use as a tissue grasper and dissector, and only made sharp in terms of ability to cut when activated.
One type of instrument that continues to gain in popularity with surgeons is the coagulating shear. This instrument has a rod-like distal end with an opposing clamp-arm operated by the surgeon. The clamp-arm can be closed without ultrasound energy to act as a simple tissue grasper. The backside of the blade (the side opposite the clamp arm) is used to cut tissue and dissect planes. This is referred to as back cutting, which cuts tissue in a shear-cutting process. Finally, tissue can be grasped between the active tip and clamp arm to coagulate tissue as it is transects. This last function is very useful for sealing arteries and veins.
34
Ultrasonic surgical instruments have been used by surgeons for over a decade and have
been proven safe and effective. During this period, there has been much advancement in the design, testing, and manufacturing of these instruments in terms of ultrasonic performance.
However, there remains a lack of understanding of how the ultrasound energy interacts with
tissue. Though instruments can be readily designed to operate at the desired frequency with
desired tip-displacements, in-vitro and in-vivo testing must be performed to verify desired tissue-
effects, which is both time and resource intensive.
A first step is to develop a comprehensive model is to consider shear-cutting, which is the
most basic function of the instrument. An effective shear-cutting model could then be used to
guide the development of a model for clamped coagulation. Generating a model that represents
the embodiment of the fundamental understanding of the cutting process is useful for predicting
the performance of an ultrasonic surgical instrument. The model could provide an analytical tool
for the designer to quickly screen surgical-instrument concepts. The designer could then focus
on instrument concepts that promise to be effective, and thereby, significantly reduce product
development time and costs while delivering safe and effective instruments.
3.2 Background for Modeling of Ultrasonic Cutting
While a model that accurately describes the interaction of ultrasonically-active blades and
tissue is highly desirable, surprisingly few efforts are reported in the literature. There are two
groups that have reported models for tissue cutting with ultrasonic instruments. Cimino and
Bond (1995) developed a model for the CUSA. Nabibekov, Sarkisov and their co-workers
(Nabibekov et al., 1980a and b; Sarkisov et al., 1982) developed a model for an ultrasonically
35
active scalpel blade. Both devices are basically used in plunge-cutting, which is defined as
cutting tissue by driving an end-effector into tissue, analogous to a jack-hammer plunging into pavement.
Nabibekov divides the cutting process into phases when the blade is driving into and cutting the tissue, and when it is retracting away from tissue. During the cutting phase
Nabibekov assumes that the ultrasonic force supplied by the surgeon must overcome a failure force for tissue. The model predicts a leveling off with velocity due to viscous and hydrodynamic drag of the blade against the tissue. The Nabibekov model ultimately relies on fitting coefficients for the instrument-to-tissue reaction forces.
The Cimino and Bond model was developed for the CUSA device, which cuts tissue in the same direction as the longitudinal excursion of the tip. They examined the mechanism of plunge-cutting, and confirmed Nabibekov’s assumptions for tissue-contact phase-relationships; however, they did not provide a predictive model. Cimino and Bond were successful, through the use of high-speed photography, in verifying their analysis of how ultrasonic plunge-cutting occurs. Their videos clearly showed distinct phases of contact and non-contact between the end- effector and tissue during the cutting process.
Shear-cutting, on the other hand, is defined as cutting tissue with the end-effector
vibrating perpendicularly to the direction of cutting (see Figure 3.2-1). Shear cutting is analogous
to an electric carving-knife cutting through a turkey. Shear-cutting is continuous in that the blade is always in contact with the tissue even though the motion of the blade is alternating. The force imparted to the specimen in shear-cutting is also different from plunge-cutting by the fact that the direction of the end-effector’s vibratory motion is perpendicular to the direction of
36
cutting of the instrument through the specimen. This requires a coupling mechanism between the end-effector and the specimen for the shear-cutting model.
Thus there are basic differences in the interaction of the ultrasonically active end- effectors for plunge cutting and shear cutting. So while the models for plunge cutting provide some insight, they are not directly applicable to shear cutting.
There are many articles published on the clinical effects of the ultrasonic surgical instruments. These typically report clinical outcomes in terms of application to a procedure, improved hemostasis when cutting, increased burst pressure for sealed vessels, and smaller damaged tissue margins compared with other energy modalities. There are however very few articles that report either results from well-designed experiments or modeling efforts to determine the basic mechanisms of the interaction of ultrasonically-active shear instruments with tissue.
One study on shear cutting was reported by Okada et al. (1988). They compared cut rates obtained with a reciprocating saw with an ultrasonically driven blade. They made the observation that the ultrasonic blade heated up, so they cooled it to eliminate temperature effects.
No substantive conclusions were drawn, and no reports of a continuation of their work could be found in the literature.
Thus there are few models or experimental results reported in the literature to determine tissue effects in ultrasonic shear cutting at a fundamental level. But the need for a model grows as more and more instruments are designed. The model developed here is for cutting wax as a tissue surrogate. It is basic and does not account for all of the behavior observed in tissue.
Nonetheless, it is an important first step.
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Figure 3.2-1: Shear-Cutting with an Ultrasonic Blade
3.3 Factors known to affect cutting
3.3.1 Factors and controls: Ultrasonic surgical systems have been in use for over a decade. So their performance in terms of cutting and coagulating tissue are well known, if not well understood. Both the manufacturer and the surgeon control the delivery of ultrasonic energy to the tissue, and consequently the outcome for a particular tissue.
Table 3.3.1-1 is a list of factors that affect cutting with ultrasonic instruments and how it is controlled. The parameters may be controlled: by the manufacturer in terms of the performance they design into their system and instruments, by the user who selects the output levels of the generators and the instruments being used, and by the properties of the material or tissue and how they are affected by the mechanical and thermal effects of ultrasonic energy.
38
Table 3.3.1-1: Cutting Model: Physical Parameters
Factors Control
Normal Force (Load) User Controls
Excursion Amplitude (Tip Velocity) User Selects
Frequency of Vibration Manufacturer Controls
Blade Geometry Manufacturer Controls
Material Properties Material Specific
Failure Criteria Material Specific
Isotropy / Inhomogenaity Material Specific
Energy Dissipation Heat and Other Losses
In surgery, the surgeon selects the instrument(s) needed for a particular procedure, and
selects an output level to drive the instrument when activated. That level can be selected for each action taken by the surgeon with the instrument. The surgeon through his / her experience and “feel” applies a force to the tissue that in conjunction with the particular instrument and tip velocity creates the desired effect in an acceptable amount of time. Once the ultrasonic system and instrument are chosen for cutting a particular tissue, velocity and force primarily determine cut rate.
Instruments that have relatively sharp blades compared with other blades are known to cut faster for a given normal force or to achieve the same cut rate with lesser force. Thus blade performance can be tailored for a specific application by balancing cutting speed for hemostasis.
Therefore any model needs to explicitly account for blade shape and or sharpness.
39
3.4 Development of an Ultrasonic Shear-Cutting model for Wax
The objective of this modeling effort is to first understand the interaction of ultrasound with a well-behaved material in this mode of cutting. This will allow model predictions to be compared with empirical laboratory data without the obscuring scatter in data due to tissue variability. Therefore the approach taken in this research is to first consider shear-cutting in wax. With an understanding of the basic mechanisms, then the model can be extended to tissue, and finally to clamped coagulation.
Development of the model begins by considering the two-dimensional geometry of a round blade shear-cutting a specimen illustrated in Figure 3.4-1. The blade’s end-effector, seen in side view, is vibrating horizontally along the x-axis, and in contact with the specimen seen in section.
Figure 3.4-1: Shear-Cutting Side View
40
Observation of ultrasonic instruments shear-cutting through wax shows that after a short initial dry-contact period, the end-effector continuously melts the wax preceding the cut and moves through the wax. As the end-effector cuts through the specimen, there is a melt zone observable immediately in front of the end-effector. Behind the blade there is an observable melt track. A viscous melted layer of wax surrounds the blade when cutting at steady-state.
Therefore, the wax-cutting model is developed assuming steady-state viscous heating of this melt layer, after all start-up transients have ceased.
An energy balance approach is used in the model development. Energy terms of the system as shown in Figure 3.4-2 are: energy generation in the wax from the viscous heating due to the ultrasonically activated blade; heat conduction into the wax; heat conduction into the blade; latent heat for the phase change from solid to liquid wax; convection; and radiation.
Virgin wax is constantly being introduced to the blade as it advances. Therefore the elevated temperatures occur in a narrow zone around the front half of the blade. The convection of heat to the surrounding air and the radiation from the wax in front of the blade only occurs in this narrow melt zone. The melt temperature of wax is relatively low and the area of the melt zone is small. Therefore the amount of heat loss by convection and radiation are expected to be small and are neglected.
41
Figure 3.4-2: Wax-Cutting Thermodynamic system
Conductive heat loss into the solid wax in front of the blade is limited, because solid wax at ambient temperature is continuously being introduced to the melt zone. IR camera images confirm that there is little heat flow into the solid wax in front of the melt zone.
The geometry assumed by the model is illustrated in Figure 3.4-3. Using a cylindrical
coordinate system with r=0 at the center of the blade, rt is defined as the radius of the blade, and
rm is defined as the distance from the blade’s center locating the melt / solid-wax interface. Now
the melt zone thickness, ∆, may also be defined as ∆ = rm – rt. The sample thickness is assumed
for simplicity to be constant and is denoted by h. The radius rm is assumed constant for a given
cut-rate and assumed not to vary with angle θ.
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Figure 3.4-3: Wax-Cutting Model Geometry
3.4.1 Conservation of Energy: Energy terms are lumped into the rate of energy generation
(Eg’), rate of energy storage in specific heat (Es’) and latent heat (EL’) and rate of energy
conduction (Ec’). Conservation of energy for a closed thermodynamic system states:
Eg’ + W’ = Es’+ EL’+ Ec’ (Equation 3.4.1-1)
Eg’ is the rate energy is delivered into the system through viscous heating of the wax by the end-
effector. W’ is the rate work is done as the blade moves through the melted wax. Es’ is the rate
energy is stored in the wax as specific heat. EL’ is the rate energy is stored in the wax as latent
heat from the conversion of solid wax to liquid wax through a phase change. Ec’ is rate energy is conducted into the solid wax from the liquid wax and energy conducted into the blade.
43
3.4.2 Energy Generated: Figure 3.4.2-1 depicts the interface between the end-effector and
the specimen illustrating the viscous layer where heat-generation occurs. From the first law of
thermodynamics, the heat generated is equal to the force times the distance moved. The force,
Fv, is the viscous force generated by the motion of the blade in the melted wax, and the distance
traveled is the blade velocity multiplied by the time.
Figure 3.4.2-1: Magnified View of End-Effector / Specimen Interface
Consider a Newtonian viscous liquid layer between two solid surfaces moving at a constant rate with respect to one another depend on a material constant as illustrated in Figure
3.4.2-1. Non-slip conditions at the stationary and moving boundaries are assumed. The point a in the solid wax is assumed stationary, and the point d moves from d to d′ at velocity υ with
no slip between the wax and the blade. Therefore the simplest form of the velocity distribution
through the melt-zone is that of a Newtonian fluid with a viscous force Fv defined by:
(University Physics, 1980)
Fv = ηAv (υ/∆) (Equation 3.4.2-1)
44
Where η denotes the coefficient of viscosity, a material constant. Equation 3.4.2-1 assumes that
the viscosity is a constant, and that the change of velocity with respect to distance is constant for
simplicity. Viscosity of wax is known to vary with temperature, pressure and velocity, and is
therefore not Newtonian (Sors, 1981). In actuality, the viscosity in the melt zone changes from a
solid at rm to some minimum viscosity at the location of highest temperature. For modeling
purposes, the molten wax is assumed to behave as a Newtonian fluid, and the viscosity is
assumed to be an effective overall viscosity, designated as ξ to differentiate it from the material-
property η.
In Equation 3.4.2-1, Fv is the force coupled from the ultrasonic vibration of the end-
effector into the specimen, Av is the area of contact between the end-effector and the specimen, υ
is the velocity of the end-effector excursion (assumed to be constant along the length of the end-
effector in the x direction).
Equation 3.4.2-1 is a basic equation of viscous force from a continuously moving surface,
such as a viscometer employing a rotating disk supported by a viscous layer over a flat solid-
surface. However, for the ultrasonic surgical instruments the motion is sinusoidally
reciprocating. Considering the sinusoidal excursion of the end-effector, the force is described as:
d ⋅ω ⋅ cosω ⋅t F = ξ ⋅ A ⋅ v v (Equation 3.4.2-2) ∆
where d ⋅ω ⋅ cos()ω ⋅ t describes the instantaneous velocity of the ultrasonic end-effector.
Simply substituting the sinusoidal motion ignores the dynamics of the system. The molten wax
moving in one direction must first be decelerated and then accelerated in the opposite direction.
Nonetheless, Equation 3.4.2-2 captures the basic phenomenon of viscous force for a vibrating
45
plate. One would expect the effects dynamics would be accounted for to some degree by the effective viscosity given all other factors are constant.
Only half the end-effector is inside the system boundary shown in Figure 3.4-3. Any heat generation behind the blade is assumed not to contribute to the melting / cutting process.
The area, Av, is therefore half the circumference of the blade times the wax thickness given by:
Av = ½ (2 π rt) h = π rt h (Equation 3.4.2-3)
Instantaneous power, Pi, is defined by the product of force time velocity, and for this case is given by:
V 2(t) P = ξ ⋅ A ⋅ i v ∆ (Equation 3.4.2-4)
The average power, Pa, is determined by integrating the instantaneous power over one period, τ, of vibration:
ξ ⋅ A 1 τ P = v ⋅ V 2 (t) ⋅ dt a ∫ (Equation 3.4.2-5) ∆ τ 0
which reduces to:
V 2 P = ξ ⋅ A ⋅ rms a v ∆ (Equation 3.4.2-6)
where Vrms is the root mean squared value of velocity.
The total energy delivered is the sum of the heat generated by the blade and the mechanical work done by the blade. The heat delivered is simply the product of power and
46
period of time over which it is delivered. The mechanical work is the product of the normal force and the distance traveled in the same period of time. The total energy delivered is therefore given by
2 Eg + W = (ξ π rt h V rms t / ∆ ) + F ⋅l (Equation 3.4.2-7)
The second term above is the mechanical work done to by moving the blade through molten wax. From experiments, a blade with 5 N normal force moved about 3 millimeters distance in 6 seconds, and therefore represents a maximum of about 2.5 milliwatts of power.
This is the power required to move through molten wax and continuously remove the molten wax out from in front of the advancing blade. This amount of power is an order of magnitude less than the power delivered from the blade to continuously melt wax, as measured by a Clarke-
Hess power meter. In all tests, the power was well above 1 W. Therefore the second term, F ⋅l , is neglected in Equation 3.4.2-7.
3.4.3 Energy Stored: The total heat delivered to the system is the sum of the heat needed to raise the wax from ambient temperature to (at least) the melt point, plus the latent heat (also called the heat of fusion) needed to transform the wax from solid to liquid through the phase change, plus the heat conducted into the blade and surrounding solid wax.
The total volume of wax melted is the area melted as the blade advances through the wax, times the length of the cut:
Total Volume of Wax Melted = 2 rm h • C t (Equation 3.4.3-1) where the area melted is 2 rm h and C t is the length. C denotes cut-rate and t represents the time to cut. Therefore the total mass of wax melted is given by:
47
m = 2 rm h C t ρ (Equation 3.4.3-2) where ρ is the density of the molten wax.
Now consider the simplified case when: heat conduction into the blade and surrounding solid wax are assumed to be negligible, wax is raised to its melt temperature, melts, and the melted wax does not substantially increase above the melt temperature in the narrow melt zone.
This is equivalent to all heat going into melting the wax. So additional energy stored in the molten wax compared with room temperature solid wax is:
Es +EL=2 rm h C t ρ [ L + s (Tm − Ta ) ] (Equation 3.4.3-3)
where L is the Latent Heat, s is the specific-heat, Tm is the melt temperature and Ta is the ambient temperature.
3.4.4 Equating Energy Generated to Energy Stored
Equating the first term of Equation 3.4.2-6 with Equation 3.4.3-3, and solving for cut- rate, C, finds:
2 (ξ ⋅π ⋅ rt ⋅ ) C = V rms (Equation 3.4.4-1) 2 ⋅ rm ⋅ ρ ⋅ ∆ ⋅[]L + s ⋅ ()Tm − Ta
Equation 3.4.4-1 provides good insight into the effects relevant to cut-rate. As velocity increases or the viscosity increases, cut-rate increases as heat-rate increases. In the denominator, increased melt-point for the wax (Tm), and increased melt zone (rm) all predict a decrease in cut-rate.
Equation 3.4.4-1 does not explicitly include the normal force applied to the blade. Yet experimental data and many years of experience clearly demonstrate that normal force has a significant effect on the cut-rate in wax. In addition, the cut-rate is dependent on the melt zone thickness, ∆, that is not one of the control variables of either force or ultrasonic velocity. This leads to the conjecture that melt thickness depends at least in part on normal force.
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The molten wax must be continuously removed from in front of the blade so that the blade can continuously melt solid wax. Extrusion of a viscous fluid depends on the pressure gradient driving the fluid, and the normal force is supported by the pressure distribution it creates in the melt zone. Therefore, the extrusion of the molten wax was considered to be the mechanism for the dependence of melt zone thickness and normal force.
To incorporate the extrusion into the model, consider the melt zone immediately in front of the end-effector as illustrated in Figure 3.4.4-1. For a constant cut-rate and end-effector velocity, this zone is assumed to be constant.
Figure 3.4.4-1: Melted-wax Zone in Front of the End-effector During Cutting
The filled area of Figure 3.4.4-1 is the area where melted wax may be removed as the end- effector moves through the wax. Wax may be removed from the two rectangular segments on top of the figure and the two annular sections in the front and backside of the figure. For modeling purposes, this area will be approximated as a slot having a width w and a thickness ∆.
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The width w corresponds to the perimeter of the blade in contact with the molten wax, and is given by
w = 2⋅ h + 2 ⋅π ⋅ rt (Equation 3.4.4-2) where the melt zone is assumed to be small compared with the radius rt. Again, the melt zone thickness is simply:
∆ = rm − rt (Equation 3.4.4-3)
A volume flow-rate equation is assumed to be of the form of Equation 3.4.4-4. Equation
3.4.4-4 is an equation for flow, where the flow is dominated by the melt zone thickness:
a ⋅ F ⋅ ∆3 Q = 2 (Equation 3.4.4-4) η where Q is the flow rate per unit time, the test force is F, and a2 is a coefficient to fit the model to empirical data. The viscosity, η, is problematic in this case, because the wax varies from a solid to a liquid within the melt zone, with the viscosity varying accordingly. As described earlier, the viscosity η is replaced with ξ, representing an effective viscosity and the new form becomes:
a ⋅ F ⋅ ∆3 Q = 2 (Equation 3.4.4-5) ξ and multiplying by the density, Equation 3.4.4-5 becomes a mass flow rate:
ρ ⋅ a ⋅ F ⋅ ∆3 Q ⋅ ρ = 2 (Equation 3.4.4-6) ξ
Now the melted-wax produced is set equal to the melted-wax removed by setting
Equation 3.4.4-6 equal to Equation 3.4.3-2. Note that Equation 3.4.3-2 needs to be first transformed into a rate by dividing by time. The resulting relation is:
ρ ⋅ a ⋅ F ⋅ ∆3 2 ⋅ r ⋅ h ⋅C ⋅ ρ = 2 (Equation 3.4.4-7) m ξ
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Now, recognizing that rm=rt+∆, Equation 3.4.4-1 may be re-written as:
2 (ξ ⋅π ⋅ rt ⋅ ) C = V rms (Equation 3.4.4-8) 2 ⋅ ()rt + ∆ ⋅ ρ ⋅ ∆ ⋅[]L + s ⋅ (Tm − Ta ) and substituting Equation 3.4.4-9 for C in Equation 3.4.4-8, simplifying, and solving for ∆ one obtains:
0.25 h ⋅ξ 2 ⋅π ⋅ r ⋅V 2 ∆ = t rms (Equation 3.4.4-9) a2 ⋅ ρ ⋅[]L + s ⋅ ()Tm − Ta ⋅ F
Equation 3.4.4-9 provides a model for how the melt zone in front of the end-effector changes as a function of blade velocity, blade diameter, material properties and most importantly as a function of normal force. Equation 3.4.4-9 can be substituted back into Equation 3.4.4-8, so that cut-rate is a function of the control variables of this study, as well as geometric and materials parameters.
The model for the cut-rate in wax is now complete. Cut-rate in the model explicitly depends on the control variable normal force and ultrasonic velocity. There are two parameters,
ξ and a2 that are not precisely known a-priori. In the development, ξ represents an effective viscosity, and a2 is the effective geometry factor that allows the simple wax removal model to be applied. The model has effectively coupled three mechanisms: 1) the generation of heat; 2) the melting of wax; and 3) the removal of wax by extrusion.
3.5 Model Predictions
Equations 3.4.4-9 and 3.4.4-11 were programmed in MS-EXCEL. Values used in the equations are given in Table 3.5-1. The value for rt was the actual radius of the 55.5 kHz round
51
2.1 mm diameter blade used in the study. Width, h, was the measured wax thickness using
Mitutoyo calipers. Melt temperature is taken as the value published by the manufacturer.
Ambient temperature was taken as 70 °F, converted to K. Wax density was calculated by the weight measured by a calibrated scale divided by the volume determined by caliper measurements of thickness, width, and length. Latent Heat, L, was taken as the value from
Walnut Hills Waxes.(Walnut Hills, 2003) Specific-heat, s, was measured using a calorimeter using the procedure attached in Appendix B.
Coefficient a2 and effective viscosity ξ were determined by treating them as regression coefficients in a least-square error analysis with the empirical data obtained with a 55.5 kHz, 2.1
-2 mm diameter round blade. Coefficient a2 is equal to 154 (in units of meters ) based on the value obtained from the least-squares regression. The effective viscosity, ξ, is set to 1.98 Pa-s, also determined through the least-squares fit to the empirical data. These values will be further discussed after comparison of the model to empirical data. The experiments are described in the experimental results section below.
Using the parameters found in Table 3.5-1 below, the three-dimentional plots seen in
Figure 3.5-1 and Figure 3.5-2 are generated. Figure 3.5-1 shows how the characteristic melt thickness, ∆, varies with force and velocity. Figure 3.5-2 predicts cut-rate as a function of ultrasonic velocity and normal force. Both surfaces demonstrate nonlinear behavior with the control paramters as reflected in Equations 3.4.4-9 and 3.4.4-11.
The melt thickness increases as velocity increases and force decreases. This is because there is less relative extrusion of wax with lower force while more wax is melted due to the higher viscous heating with higher velocity. Cut-rate, on the other hand, increases with both
52
velocity and force as seen in Figure 3.5-2. This is because as more wax is melted with higher velocities, the higher forces extrude out molten wax at a greater rate.
Table 3.5-1: Model Parameters
Description Variable Unit Value
*1 Blade Radius rt M 0.00105
Specimen Width*1 h M 0.00473
Melt Temperature*2 K 410 Tm
*3 K 293 Ambient Temperature Ta Wax Density*4 ρ kg/m3 930
Specific-heat*4 s J/kg/K 2,400
J/kg 406,000 Latent Heat of Fusion*5 L Effective Viscosity*6 ξ Pa-s 1.98
*6 -2 Geometric Coefficient a2 m 154
*1 Determined in Design of Experiment
*2 Manufacturers published value
*3 Assumed room temperature of 20° C
*4 Experimentally measured
*5 Published value for waxes
*6 Least Squares fit to empirical data
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∆-Values Characteristic Melt-Zone Thickness
3.5e-4
3.0e-4
) s
r 2.5e-4
e t
e 2.0e-4
m
(
-
1.5e-4 ∆
1.0e-4 5.0 4.5 5.0e-5 4.0 3.5 ) 10 (N 3.0 e 8 2.5 rc R 6 2.0 o MS F Ve 4 1.5 loci 2 ty (m /s) Model Predictions for ∆ r0_values.jnb
Figure 3.5-1: Melt Zone Thickness, ∆, Plotted as a Function of Force and Velocity
54
Figure 3.5-2: Model Predictions of Cut-Rate
3.6 Comparison of Cutting Model to Empirical Data
3.6.1 Background of Wax-Cutting Experiments: One of the most popular ultrasonic cut and coagulation surgical systems is the Harmonic Scalpel manufactured by EES, illustrated in
Figure 3.6.1-1. It operates at 55.5 kHz, and there are a number of instruments that can be used with it, including ball coagulators, dissecting hooks and blades, and Laparosonic Coagulating
Shears (LSC). There are two shapes of shear blade-tips utilized in this study. The LCS-B5 has a blade that is of round cross-section, where the 5 denotes an instrument that can be introduced through a 5mm trocar. The LCS-K5 is the same as the B5 but with the circular cross-
55
section machined along two cords to create a 120° angled blade. All the LCS instruments include a clamp arm to squeeze the tissue against the active blade. The backside of the blade, the side opposite the clamp arm, is used to dissect and cut tissue, which is referred to as back-cutting and is the focus of this dissertation.
Figure 3.6.1-1 Harmonic Scalpel Surgical System
Most of the experiments at 55.5 kHz used the LCS-B5 in the back-cutting mode. This blade was chosen because of its simple shape and the fact that there are similar blade cross- sections offered by other manufacturers. Some data were obtained with the LCS-K5 to begin to delineate the relative contributions of heat and stress in tissue cutting.
Three different frequency systems were evaluated: 23.5 kHz, 55.5 kHz and 75 kHz. The
23.5 kHz system was an existing medical device, but this system used an instrument with a blade diameter half that of the LCS-B5. The 55.5 kHz system is the Harmonic Scalpel system. The
75 kHz hand piece was specifically designed for this research and along with custom fabricated blades. It operated with a modified Harmonic Scalpel generator.
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3.6.2 Results from Wax-Cutting Experiments: The results from wax-cutting experiments, to be described in following chapters, are presented in Figure 3.6.2-1. As an overall observation, the data are consistent with intuition and experience. As force and velocity increase, the cutting- rates increase. The cut-rates for 55.5 kHz and 75 kHz are nearly identical at a given velocity, indicating that frequency does not significantly affect cutting rate. In fact, frequency has been accounted for in the sense that the ultrasonic velocity is the product of frequency and displacement. The data for the thinner-diameter blade at 23.5 kHz has higher cutting-rates for the same force. This would be expected because of the resulting higher pressure at the contact between the blade and the wax. The figure includes data from the LCS-K5 blade, which was cutting with its knife-edge into the wax. The data from the angled blade (K5) is very similar to the round blade (B5). This similarity indicates that ultrasonic wax-cutting is wax melting, and stress concentrations do not play a significant role in wax.
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Wax Cutting - All Data
0.40
0.35
) s
/ 0.30 m
c 0.25
(
e
t 0.20 a
R 0.15
t 6
u 0.10 ) C 5 0.05 4 tons 3 0.00 ew 18 N 16 2 ( 14 12 e 10 1 8 c Ti 6 p P 4 0 or eak 2 F Velo city (m/s) 55.5 kHz Round - Blue Circles 75 kHz Round - Red Squares 23.5 kHz 1 mm - Black Triangles n = 6 for each condition 55.5 kHz - Angled Blade, Pink Triangles 288 total tests Regression of 55.5 kHz round blade data round_wax_master_withK5.jnb
Figure 3.6.2-1: Data from Wax-Cutting
A plane was initially used to fit the 55.5 kHz data and is included in Figure 3.6.2-1. The plane is an adequate representation of the data itself; however it does not capture the fact that there is no cutting at zero force. If one extends the plane to zero force, it predicts non-zero cut-
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rates. The lack of the capture of basic behavior was motivation for the development of a model based on the underlying physical mechanisms.
3.6.3 Comparison of Wax-Cutting Experiments to the Predictive Model: The known materials properties and dimensions reported in Table 3.5-1 were used in the model to predict cut-rates.
But two parameters, a2 and ξ, were determined from the experimental data. A minimum least squared error regression was performed using the model and data obtained with the round 2.1mm blade at 55.5 kHz to determine estimates of values of a2 and ξ. The resulting values were a2=154 m-2 and ξ= 1.98 Pa-s.
The resulting model predictions are shown in Figure 3.6.3-1. Note that the range of data acquired is a subset of the range illustrated in the model predictions presented in Figure 3.5-2.
The model predictions seem to agree overall even though only two parameters were determined from 15 test conditions of velocity and force.
From the regression, the effective viscosity was calculated as 1.98 Pa-sec, which if one assumes is the actual material viscosity would correspond to a temperature of molten wax at about 243º F based on manufacturer data. This temperature is consistent with the IR camera data.
A constant velocity-gradient was assumed through the melted wax. However, the predicted melt thickness was much larger than the shear skin layer for the exponential decay of sinusoidal shear waves in a viscous medium (Nagy, 1995). The constant gradient assumption is not valid. Likewise, viscosity and other physical parameters are functions of temperature. So even though the estimate of the coefficient of viscosity, ξ, appears to be reasonable, it may have contributed to an unreasonable estimate of extrusion area.
The estimated area through which wax is extruded is proportional to the reciprocal of the
59
2 a2 coefficient in the model. The area calculated based on a2 is on the order of 10 cm , which is much larger than any corresponding physical area. This discrepancy may in part be due to the basic form assumed for the extrusion equation that came from squeeze flow between flat plates.
The actual geometry approaches two concentric cylindrical walls. One wall is the surface of the blade, and the other is the interface between solid and liquid wax. The pressure distribution in this geometry can be significantly different from that of flat plates and may account for some of the discrepancy.
The above considerations suggest that a better understanding of the strain-rate field in the melted wax, pressure distribution in the wax, the local viscosity of the wax over the melt region, and the flow of the wax around the blade are prime areas for future improvement in the model.
Figure 3.6.3-1: Comparison of Model Prediction and Experimental Data
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As seen in Figure 3.6.3-1, the predicted cut-rates were nearly identical in terms of both overall cut-rate and behavior with respect to velocity and force. For example, the curvature in the data with respect to force, as observed at the highest velocity, was neither apparent nor appreciated until the model predications demonstrated this behavior.
The model was used to predict the angled blade geometry at 55.5 kHz. In the model, the knife-edge changes the perimeter through which wax is removed and the contact area for the calculation of viscous heating. The projected area of the angled blade is the same as the round so calculated contact pressure is the same based on the model assumptions.
The model predictions are compared with data obtained with the angled blade in Figure
3.6.3-2. The model predicts a slight decrease in cut-rate for the angled blade, which is clearly evident in the empirical data. The main difference between the blades is that the contact area of the angled blade is approximately 10% less than the contact area of the round blade due to the flats machined into the K5 blade to produce the 120º included angle. (See the blade cross- sections illustrated in Figure 3.6.3-2.) Therefore less heat and a subsequent lower cut-rate should be expected, as is observed. However, the fact that the angled cuts at a slower rate is counter- intuitive, because of the sharper tip. General experience shows that the sharper a blade is, the faster and easier it cuts. This further supports the conclusion that wax cutting is really wax melting.
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Figure 3.6.3-2: Round versus Angled Blade Cut-Rate Predictions
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0.35
0.30
0.25
0.20
0.15
0.10 Cut Rate (cm/s) 0.05
0.00 246810121416 Peak Tip Velocity (m/s)
55.5 kHz 75 kHz 23.5 kHz Model Prediction for 1.2 mm diameter round blade. Model Prediction for 2.1 mm diameter round blade.
round_wax_5N_2DB.jnb
Figure 3.6.3-3: Cut-Rate versus Peak Tip Velocity for Wax Cutting
Finally the geometry of the 23.5 kHz blade was then input into the model. As seen in
Figure 3.6.3-3, the wax-cutting model predicts that the 1.2 mm diameter 23.5 kHz blade will have a higher cut-rate for a given velocity than the 2.1 mm diameter 55.5 kHz. However, the observed cut-rate for the 23.5 kHz blade is higher than the model predictions. So while the
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model predicts the current direction of change, the magnitude of the change is under-estimated by the model. The discrepancy indicates some limitations to range of validity of the assumptions made to develop this simplified model. However, based on the overall performance of the model, the mechanisms from which the model is developed are indeed operating.
3.6.4 A-posteriori Evidence of Melt Zone Thickness: The wax was available for examination after testing. Figure 3.6.4-1 is a micrograph of the wax taken under polarized top- lighting. In the image, the round hole from where the blade was removed is centered in the image. Around the open hole is a dark region of melted wax. Outside the melted region are the diagonal lines of machining marks in the surface of the wax, made when the wax was planed to 4 mm thickness. Unfortunately, the melted region could only be measured after the specimen was removed from the test fixture, after the test was completed. The blade sat in the wax under no- load conditions, and the dimensions of the melt zone during actual testing are unknown.
However, the measured melt zone in the micrograph is approximately 400 micrometers, which does not refute the model predictions of the melt zone varying from approximately 100 micrometers to 350 micrometers under load.
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Figure 3.6.4-1 Micrograph of Wax Specimen After Testing
3.7 Conclusion
A model was developed to understand material cutting using ultrasonic energy. The model is based on the continuous melting of wax by viscous heating of a molten layer and the extrusion of the molten wax from the melt zone as the blade advances. Many assumptions went into the model and a regression was performed to determine two parameters. Even so, the model accurately reflected the behavior of the experimental data, and after the initial regression, the model could be extended to other conditions with reasonable accuracy.
The model for wax-cutting demonstrates fundamental understanding of the mechanisms
65
involved. This understanding has identified key material and dimensional properties that control cut-rate in wax. The wax model can be used as a starting point or as guidance to develop useful models for cutting in tissue and should help delineate melting (possibly phase changes) mechanisms and stress or other mechanical failure mechanisms.
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4. EXPERIMENTAL MATERIALS AND METHODS
This chapter describes the materials and methods for the experiments performed with machinist’s wax and porcine liver. First, the overall design of experiments is presented and then the materials and methods are described. Second, screening tests are presented that determined procedures for minimizing variance in liver data.
4.1 Design of Experiments
4.1.1 Hypothesis: This research was designed to determine the effects of force, velocity and frequency of vibration on the cut-rate of an ultrasonic surgical instrument. The hypothesis, stated in null form, is: Frequency of vibration, force, and velocity do not affect the cut-rate of an ultrasonic surgical instrument.
4.1.2 Treatment Factors
Frequency of Vibration (3 levels – fixed factor):
23.5-kHz 55.5-kHz 75-kHz
Sandwich-type ultrasonic transducers, also called Langevin transducers, are well known and established for the production of high-intensity ultrasonic motion. In United Kingdom
Patent No. 145,691, issued in 1921, Langevin describes how a sandwich of piezoelectric material positioned between metal plates generates high-intensity ultrasound. Sandwich transducers are
67
basically mechanically tuned resonators. Delivery of ultrasonic energy at a given frequency requires a mechanical resonator designed specifically for that frequency. Therefore each frequency must have its own transducer.
Sandwich-type transducers are relatively high-Q devices with Q’s typically greater than
100. The Q of a resonant system is the measure of the resonant bandwidth. During operation, high-Q devices are driven at resonance and maintained within a relatively narrow frequency range by established feedback control methods. See, for example, US Patents No. 5,630,420 and
No. 5,026,387, which describe systems incorporating and controlling sandwich-type transducers.
The bandwidth of a resonant system may be calculated as:
Q = fc / f2 – f1 (Eq. 4.2.1-1)
Where fc is the center frequency of vibration, and f1 and f2 are the half-power points on each side of fc, where the amplitude is 0.707 times the amplitude at fc.
The relative high-Q nature of these resonant devices requires that each transducer be tuned to resonate at precisely the correct frequency. Even with the tight tolerances currently available with modern manufacturing processes, tolerance “stack-up” issues present challenges to designers of sandwich-type transducers. Stack-up issues occur when variations in design tolerances of each individual part sum together to produce a significant total variation. Variations in individual parts occur due to variations in material properties for different lots of material, assembly variation and/or dimensional variations. The instruments too must be designed at a specific frequency to vibrate in a desired mode and achieve relatively high displacements without failing the material. Transverse and other parasitic modes must be avoided, because these type of
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vibrations lead to internal heating of the instrument and mechanical failure. Therefore, designing and manufacturing transducers and the instruments to operate with them is a painstaking exercise.
The above issues are in fact the motivation for this research. If there is a preferred frequency of operation, then certainly surgical instruments should be designed to operate at that frequency. However, it requires a significant effort to design an ultrasonic transducer and a family of instruments for a specific frequency.
The experimental design faced the same difficulties in terms of conducting experiments at a number of different frequencies each requiring its own generator, hand piece and instruments. There are in fact only two frequencies at which available ultrasonic surgical systems operate.
Two systems were used, one from EES operating at 55.5 kHz, and one from Olympus operating at 23.5 kHz. In order to have a third frequency, a special transducer was designed to operate at 75 kHz with a modified generator supplied by EES. Due to these issues, the operational frequency of an ultrasonic surgical system is the most difficult parameter to change when developing instruments for surgical applications. This research is therefore limited to three frequencies: 23.5 kHz; 55.5 kHz; and 75 kHz.
Tip Peak Velocity (3 to 6 levels, depending on frequency):
23.5 kHz: (3 levels) 55.5 kHz: (6 levels) 75 kHz: (4 levels)
The amplitude of vibration of ultrasonic surgical systems is relatively simple to control, and depends on the feedback control algorithm of the system. The feedback employed by the
69
systems used for this research worked under current control. Any amplitude within the available stress range of the ultrasonic surgical instruments is obtained by programming the feedback circuitry of the generator for a corresponding current set-point.
The maximum peak-to-peak (p-t-p) vibration amplitude for a given frequency was chosen based on the available ranges from the generators used. The 23.5 kHz system was only driven to
80% of the maximum generator setting due to blade limitations. The blade of the 23.5 kHz system would not maintain pure longitudinal motion at the 100% generator setting.
Tip Geometry: (2 levels – fixed factor):
For the cutting analysis, the chosen shape of blade tip is that of a circular cylinder.
Figure 4.1.2-1: Cross-Section of Blades
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The only available 23.5 kHz system blade diameter was 1.2mm thick flat blade with semi-circular rounded edges. Also, a 120º included-angle blade (designated the LCS-K5) was available and tested only at 55.5 kHz.
Specimens (2 levels – fixed factor):
Wax
Porcine Liver
Two materials were studied, porcine liver and wax as a tissue surrogate. Porcine liver was selected for study due to: the growing incidence of liver cancer, the relative homogeneity of the tissue and its relatively low collagen content. Liver is considered to be a relatively easy material to cut, a relatively large organ, and therefore represents a convenient tissue to study.
Tissue was not selected as the initial medium for modeling due to its complexity and variability, which demands a significantly greater number of samples to achieve modest statistical power.
Wax was selected as the medium for initial modeling. Wax has been utilized at EES as a cutting standard for qualifying transducer output. Wax is homogeneous, readily available and easy to cut. Understanding how cutting occurs in the homogeneous medium of wax may provide some insight about cutting tissue. Considerable historic information is available for reference relative to cutting speed, repeatability and variation in wax. While wax can not be considered a tissue surrogate because of the vastly different material properties and structure, the cut-rate in wax is similar to tissue for similar forces and velocities.
Several wax types were tested for variability under ultrasonic cutting. Canning wax, although inexpensive, was not selected due to significant variance between wax samples. The wax used in these studies was manufactured by Freeman Corporation and is denoted as blue
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machinable wax. The wax is available from MSC industrial supply under item number
00263343. The Freeman wax was consistent, and did not show significant variance due to wax sample in previous ANOVA analysis of cutting speed.
Force (3 levels – fixed factor):
A constant force of 1.25, 2.5, or 5.0 N was applied to the specimen during cutting. EES has conducted research with an instrumented ultrasonic scalpel. These three forces were subjectively assessed by a veterinary surgeon as representing the low, average and high forces applied when cutting a variety of tissues. The low value corresponded to a “light” touch that the surgeon would typically apply in fine dissection between tissue planes, and a heavy force that might be used in a skin incision such as a laparotomy.
The depth of tissue cut by a surgeon varies as tissue type varies, depending on vascularity and relative location with respect to sensitive structures embedded or near the tissue being transected. Liver specimens are cut to a depth of 8 mm, corresponding to a relatively deep cut typical in a liver resection to remove cancerous tissue. The wax thickness is 4mm. The nominal load distribution assumes that the force is distributed uniformly over the length of the sample and is given in Table 4.1.2-1 for liver and wax.
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Table 4.1.2-1: Cutting Forces per Unit Length
Load-Cell Reading Nominal Distribution in Wax Nominal Distribution in Liver
(N) (N/mm) (N/mm)
1.25 0.313 0.156
2.5 0.625 0.313
5 1.25 0.625
4.1.3 Response Measure
Cutting Speed: An Instron mechanical test system adapted by Materials Testing Systems, Inc.
(MTS) with both force-control and rate-control software was utilized to perform constant-force and constant-velocity cutting of the specimens. The measure was crosshead motion of the test system over a specified time of transection. An MTS internal-rate function was used to calculate cut-rates for each specimen.
4.1.4 Determination of Statistical Significance: Fixed-factor Analysis of Variance
(ANOVA) was used to test significance of independent variables relative to the cutting speed of the ultrasonic surgical system. An α level of 0.05 was selected as the Type I error determination level, to define statistical significance.
4.2 Ultrasonic System Performance under Load
One of the most important treatment factors is the ultrasonic velocity of the vibration at the blade tip. Therefore, it is important to have fixed levels of velocity. However, the control algorithms in ultrasonic systems are typically based on electrical current, voltage or impedance.
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The generators used in this study control current, which nominally corresponds to ultrasonic velocity.
The question arises as to how good is the correlation of velocity to current under varying mechanical load. Therefore an experiment was designed and conducted to determine the affect of load on the correlation of current and velocity. Figure 4.2-1 is a picture of an ultrasonic transducer and blade assembly within a load fixture, utilizing a laser vibrometer to continuously measure tip excursion while varying load. The laser vibrometer used was a Polytec OFV3001 controller with a Polytec OFV511 fiber interferometer. Current measurements were taken with a
Clarke-Hess Model 2330 sampling V-A-W meter, or with HP 34401 Multimeters, illustrated in the figures.
Figure 4.2-1: Laser Vibrometer Excursion Measurement System under Load Conditions
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Figure 4.2-2 is a magnification of the blade lying within a water-bath enclosure. Water is continuously fed into chamois, used as a loading element on the blade. The load is applied through a ram, seen immediately above the blade in the figure. A water-spray shield is fabricated to protect the laser lens from water vapor produced by the blade within the test system.
Figure 4.2-2: Ultrasonic Blade in Loading Test-Fixture for Excursion Measurement
Figure 4.2-3 is a data set exemplary of the output from tests with the excursion calibration system. Four runs of the system are plotted with each set of points representing one
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loading cycle of the blade. As load increases, excursion is seen to decrease slightly. However, note that the correlation of excursion to current has an r2 correlation coefficient of 0.99. As long as current can be monitored or controlled, excursion can be determined with sufficient precision.
Figure 4.2-3: Correlation of Current to Excursion under Loading
4.3 Mechanical Testing
4.3.1 Test Machine and Analysis Software: An Instron test system, adapted by MTS with both force-control and rate-control software, performed constant-force and constant-velocity specimen cutting. Instron/MTS test system #832800, was utilized for this study. The specimen fixture for wax or liver was attached to 20 lb. load-cell C-004190B. MTS Testworks software version 4.04C Build 333 was used to measure the output of the load-cell.
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Cutting speed was determined from average crosshead velocity during a one to two- second period that commenced after the start-up transients ceased. An MTS internal function was used to calculate cut-rates for each specimen. The maximum crosshead speed of this particular test machine was 0.8 cm/sec. This of course meant that if tissue-cutting exceeded this level, the force could never maintain its preset value.
4.3.2 Test Procedure
The test procedure was:
Calibrate the load-cell
Attach fixture to load-cell
Zero the load-cell
Activate an ultrasonic blade
Initiate a force-controlled cut
Measure load-cell output and record readings
The final two steps are repeated a number of times during an experiment, to acquire multiple data points.
4.3.3 Lateral Loading through the Test Fixture: Measurement errors can corrupt and confound the results of studies utilizing the liver test fixture. One measurement error of concern is variation of measured load due to non-axial loading conditions of the measurement system. A study was performed to determine if any corrective actions are necessary when making
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measurements on the Instron/MTS system to correct for inaccuracies due to lateral change of load position when testing.
The procedure started with the standard calibration of the load-cell. Then a known load was applied to the test fixture. The load added during the experiment measured 1.935 N on a
Mettler / Toledo precision scale model number PB153 under calibration protocol C-16072 (ESI).
The load of fixture plus added load should be read by the Instron/MTS system as 8.275 N. The load was applied to the center-point and the load-cell output was recorded. Then the load was moved to one side of the fixture, and the load-cell output was again measured. The same measurement was made for the opposite side. Figure 4.4.4-1 illustrates the loading positions on a fixture relative to a standard test arrangement. The average results of the measurements according to the above procedure are presented in Table 4.3.3-1
Figure 4.3.3-1: Fixture Loading Positional Arrangement Relative to a Standard Test
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All the data were entered into Sigmaplot version 7.1 for analysis, which showed that measured load varies about 2% as the offset of the load moves from the left-most position to the right-most position of the fixture. A 2% error is small relative to the large variances due to tissue inhomogenaity observed in subsequent testing. The force used in this study is within the range of loading conditions for other research conducted using this fixture. Therefore, corrections for lateral loading are not made.
Table 4.3.3-1: Measured Load Data
Load Condition Measured Loads
Fixture only 6.34 N average
Fixture and Load 8.276 N
Fixture loaded at left-most 8.119 N average - 1.9 % error position: 6.5 cm left of center
Fixture loaded center position 8.233 N average - 0.5 % error
Fixture loaded at right-most 8.329 N average +0.6 % error position: 6.5 cm right of center
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4.4 Specimen Fixture and Preparation
4.4.1 Wax: The wax specimens were nominally 4 cm by 7.5 cm and 4mm thick. They were mounted in basically a bar clamp mounted to the load-cell as depicted in Figure 4.2.3-1. During the test, the test machine moved the wax sample down onto the ultrasonically active blade. The transducer was clamped to the base of the test machine, positioned so that the blade extends about one millimeter beyond the backside of the wax.
4.4.2 Liver: Porcine livers were harvested from pigs being used in other studies performed at
EES. The livers were stored in a refrigerator and used within 3 days. Two test specimens could be obtained from the largest lobes of one liver as indicated in Figure 4.4.2-1. The figure is actually a polymeric cast of the vascularity of a porcine liver. The two specimens are acquired at the anterior portion of the lobes were the vasculature is fine and somewhat homogenous.
Figure 4.4.2-1: Liver Specimen Preparation
The liver test fixture is shown in Figure 4.4.2-2, assembled in the Instron/MTS load frame and attached to the load-cell. The fixture is designed with six parallel slots available for
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cutting tissue, labeled as Slot 1-6. A portion of the Instron/MTS load-cell is seen at the top of the picture. Circled at the bottom left of the picture, the 55.5 kHz ultrasonic blade can be seen.
The blades are held rigidly to the Instron/MTS frame with a clamp, a portion of which is visible at the bottom left of the picture.
Figure 4.4.2-2: Liver Fixture
To load the fixture the liver specimens are first cut from the lobes. Each specimen is trimmed in thickness to be nominally 10 mm thick. The liver is sandwiched between plates held together by screws. The screws are tightened so that there is a slight bulge of the liver within the slot. This procedure helps to ensure a reasonably consistent thickness and minimizes the amount of interaction of the tissue from the slots on either side of the one in which cutting is occurring.
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4.5 Data Acquisition and Analysis
4.5.1 Data Acquisition and Analysis: The response measure of the design of experiments is cut- rate. Cut-rate is taken as the average rate of the crosshead movement over a one to three second period of time. The average rate is available as a function from the MTS software. The data capture period is started after the initial transients from the constant force algorithm ceased. In wax the period is from 2.75 to 3.75 seconds. In liver, the transients lasted longer and the data fluctuated more, so the period is two second from 3.5 to 5.5 seconds.
The basic behaviors of force and crosshead speed as a function of time are shown in
Figures 4.5.1-1 and 4.5.1-2 for wax and liver, respectively. As seen in Figure 4.5.1-1, the force is held reasonably constant after the initial transient and the crosshead position continuously advances in a linear fashion. The basic behaviors of force and crosshead position are not as good for the liver data as seen in Figure 4.5.1-2. The start-up transient has a large initial overshoot followed by a relatively prolonged period of undershoot. Then after the transient has passed, the variation in force and the advance of the crosshead both exhibit higher variance compared with wax.
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Figure 4.5.1-1: Wax-Cutting Data
Figure 4.5.1-2: Liver-Cutting Data
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4.5.2 Connective Tissue Events: Figure 4.5.2-1 illustrates data exemplary of liver-cutting on the Instron/MTS system when connective tissue anomalies occur. During this test run, two connective tissue anomalies are observed, one at about 4.25 seconds and the other at about 5.25 seconds. After this cut was performed, the liver was removed from the fixture and the locations corresponding to roughly 4.25 seconds and 5.25 seconds were examined. Two blood vessels, approximately 0.5 mm in diameter, were observed in the cut area. The load curve reveals two dips in the force corresponding to each blood vessel transected. Immediately after transecting the vessel, a load-release phenomenon occurs in the liver that the PID control loop must overcome. The crosshead position curve is observed to be non-linear throughout this load- release process. Therefore data records that included obvious connective-tissue events were excluded from data analysis.
Figure 4.5.2-1: Ultrasonic Blade Encountering Connective Tissue During a Run
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4.6 Screening Experiments
During initial testing in liver, large variations occurred, and systematic changes in cut- rate seemed to be associated with build-up of debris and subsequent cleaning. Therefore a set of screening experiments were run to determine if the effects were indeed significant and how they could be mitigated in the data capture or analysis. The effects that were analyzed were:
removal and replacement of the blade
removal, cleaning and replacement of the blade
cut number
cut slot
liver lobe
creep
4.6.1 Effects of Blade Removal and Replacement with or without Cleaning: A series of
140 tests were run on two liver lobes over a two-day period. The tests were grouped by lobe and slot number in terms of the treatment (removed and replaced, not removed, or removed, cleaned and replaced). An ANOVA was used to determine what treatments had a significant effect. The factors considered are shown in Table 4.6.1-1.
Table 4.6.1-1: Factors in Blade Cleaning Analysis
Factor Type Levels Values
CUTNUM fixed 2 1 through 22
REMOVED fixed 2 1 2
LOBE fixed 2 1 2
SLOT fixed 6 1 2 3 4 5 6
LOAD fixed 2 1 2
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An initial attempt to analyze the data indicated that the factors “Clean” and “Removed” were highly correlated (R=0.873) and could not both be properly included in the model at the same time. Models were fit with first “Clean” (removed, cleaned, and replaced) and then
“Removed” (removed and replaced) included, and it was found that “Clean” was not statistically significant, but that “Removed” was shown to be highly statistically significant. This result, that cleaning was not statistically significant in this study, demonstrates that the cleaning methodology keeps the blade sufficiently clean during the experiments. If cleaning showed up as a significant factor, then the blade would behave differently before and after cleaning. So in subsequent ANOVA analysis, only “Removed” was considered in the ANOVA model.
The magnitude of an initial ANOVA model residuals correlated to the magnitude of the fitted values, suggesting that a log transformation of the Cut-Rate response was required. All data from the first cut in each slot (CUTNUM =1) were removed because the cut-rates showed the highest variation attributed to the initial loading of the liver in a slot. The results from the final ANOVA are included in Table 4.6.1-2.
Table 4.6.1-2: Analysis of Variance ANOVA Data
Source DF Seq SS Adj SS Adj MS F P
CUTNUM 20 0.45786 0.24317 0.01216 0.60 0.906
REMOVED 1 0.03403 0.29917 0.29917 14.74 0.000
LOBE 1 0.07694 0.56713 0.56713 27.94 0.000
SLOT 5 1.56912 1.42350 0.28470 14.03 0.000
LOAD 1 0.54422 0.54422 0.54422 26.81 0.000
Error 111 2.25308 2.25308 0.02030
Total 139 4.93524
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Removing and replacing the blade produces statistically significant variance. In order to mitigate the effects of removal and replacement the first two test runs after replacement are ignored. This was verified by running the same ANOVA on a subset of data with those data removed.
Based on this experiment the following procedure was adopted for all testing. The blade should be cleaned after every five to eight cuts to avoid excessive build up of debris. After replacement, the data from the first two cuts are not included in the data set. Finally, ANOVA’s performed on the liver data will use the log transformation.
4.6.2 Effects of Cut Number, Slot Number and Lobe: The procedure for removing, cleaning and replacement of the blade developed above helped reduce the overall variation in data. This allowed the effects of cut number, slot number and lobe to be evaluated. This was accomplished by culling the original data set shown in Figure 4.6.2-1 of the first two cuts from each slot and the first two cuts after each blade replacement. The data set was also culled of any obvious connective tissue events.
Even after this first filtering of the data, slot variation was significant primarily because of higher and more variable cut-rates observed from Slot 6. When the cut-rate data from Slot 6 were culled from the data, the slot-to-slot variation was no longer significant as can be discerned from the reduced data set in Figure 4.6.2-2.
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Cleaning Study Fresh Liver Cut with 55.5 kHz Round Blade 80 micron Excursion, 0.156 N/mm Load
0.08
0.07
0.06
0.05
0.04
0.03 Cut Rate (cm/s)
0.02
0.01
0.00 01234567
Slot Number livcln7.jnb
Cut Rate vs Slot Number (Col2 vs Col6)
Figure 4.6.2-1: Cut-Rate Versus Slot Number for the Entire Cleaning Study Data Set
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Cleaning Study Fresh Liver Cut with 55.5 kHz Round Blade 80 micron Excursion, 0.156 N/mm Load Graph after Excluding After-Cleaning Data
0.08
0.07
0.06
0.05
0.04
0.03 Cut Rate (cm/s)
0.02
0.01
0.00 0123456
Slot Number livcln8.jnb
Cut Rate vs. Slot Number Col 4 vs Col 2
Figure 4.6.2-2: Cut-Rate Versus Slot Number for the Culled Cleaning-Study Data-Set
Figure 4.6.2-3 shows an analysis of the culled data-set comparing lobe-to-lobe variation.
Along side the data points plotted for each lobe are the means and the standard error of the mean.
Note that each data point graphed may represent multiple replications. Figure 4.6.2-3 shows that for a large number of replications, a small but significant difference is observable between lobes.
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Cleaning Study Fresh Liver Cut with 55.5 kHz Round Blade 80 micron Excursion, 0.156 N.mm Load Graph Excludes After-Cleaning Data
0.022
0.020
0.018
0.016
0.014
0.012
0.010 Cut Rate (cm/s) 0.008
0.006
0.004
0.002 0123
Liver Lobe livcln9.jnb
Cut Rate vs. Lobe Mean and Standard Error Bars for Lobe 1 Data Mean and Standard Error Bars for Lobe 2 Data
Figure 4.6.2-3: Analysis of Lobe-to-Lobe Variation
In summary, the screening experiments determined the following:
1. Cleaning of the blade should be done between 5 to 8 cuts
2. The first two cuts in each slot are not included in the data set
3. The first two cuts following replacement of the blade are not included in the data set
4. Slot 6 is not used
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5. Lobe-to-lobe variation is significant but small and is ignored.
6. Log transformation of the data is used for ANOVA's
4.6.3 Effects of Creep
A potential contributor to error in measured cut-rate is the creep effect of liver tissue in the system. The intent of this study is to determine if any corrective actions are necessary when making measurements on the Instron/MTS system to correct for inaccuracies due to creep from the test machine or from the viscoelastic nature of tissue.
In a creep test, a constant load is applied to an inactive blade embedded into the liver as would normally occur during a cutting test. The blade does not cut because there is no ultrasonic tip excursion. The blade was held at maximum load in tissue for 60 seconds to record the creep characteristics.
Figure 4.6.3-1 illustrates data exemplary of a creep test on the Instron/MTS system. In
Figure 4.6.3-1, force and crosshead position are graphed with respect to time. Crosshead position is the distance, in millimeters, the Instron/MTS load-cell support beam moves during an experimental run. The liver thus exhibits a classic non-linear viscoelastic creep response in
Figure 4.6.3-1.
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Creep Test Zero Excursion of Round Blade in Liver Constant 5 Newton Load
3.0 Blade - Round 5.4 2.9 Frequency - Zero Excursion - Zero 2.8 Specimen - Porcine Liver 5.2
2.7 5.0 2.6 4.8 2.5
2.4 4.6 Load in Newtons 2.3 4.4 Crosshead position in mm position Crosshead 2.2 4.2 2.1
2.0 4.0 0 10203040506070 Time in Seconds Zero5_slow.jnb Crosshead Position ve Time - Col 2 vs Col 3 Load vs Time - Col 2 vs Col 1
Figure 4.6.3-1: Graphical Data Set for Ultrasonic Blade Creep Test in Liver
Figure 4.6.3-2 is a linear regression of the data shown in Figure 5.4.4-1, over the 2.75 to
5.75 second time-period which is the period when cut-rate is to be determined. Any cut-rates determined experimentally in liver will include a comparable creep rate embedded within the measured cut-rate. The creep rate obtained at 5 N in this case was 0.009 mm/s, as seen in Figure
4.6.3-2.
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Creep Test at 5 Newtons load Regression between 3 to 6 seconds Round Blade in Liver
2.355
2.350 Blade - Round Frequency - zero Excursion - Zero 2.345 Load - 5 N
2.340
2.335
2.330 Regression analysis Rsquared=0.98 slope = 0.0091 mm/s 2.325 Crosshead Position in millimeters in Position Crosshead 2.320
2.315 2.53.03.54.04.55.05.56.06.5 Time in Seconds
Time vs Crosshead Position - Col 1 vs Col 2 Zero5_slow_regression.jnb Linear Regression, p<0.0001
Figure 4.6.3-2: Regression Analysis of Creep within the 3-to-6 Second Time-Period
This creep rate at the highest applied force is an order of magnitude below the lowest cut-rate measured in the cut-rate. This experiment at 5 N force was replicated several times with similar rates observed. Creep tests were also run at 1.25 N and 2.5 N forces, and the creep rates were lower at the lower forces as expected. For this reason, data sets were not corrected for creep during cut-rate analysis.
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4.6.4 Infra-Red Camera Measurement of Temperature
An Infra-Red (IR) camera was used to measure the surface temperatures, during wax- cutting with the ultrasonic blades used in this study, to help provide qualitative information about the temperature profiles during wax-cutting. The IR camera is capable of providing a two- dimensional pseudo-color image of the temperature profiles during an experimental run. The profiles are useful for justification of some assumptions made in the wax-cutting model.
An FSR-FLIR (Forward Looking Infra-Red) Prism-DS system, serial no. 550139, was used with AnalyzIR/Tracer software. The experimental set-up is seen in Figure 4.6.4-1.
Figure 4.6.4-1: IR Camera Set-up
Figures 4.6.4-2 and 4.6.4-3 are views from the AnalyzIR software, showing the thermal plot for a wax cut. Figure 4.6.4-2 shows the range of temperature, from ambient to
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approximately 250 °F, in pseudo-color. The blade, at the top of the image, has a 2.1mm diameter. The temperature corona surrounding the blade is seen to be less than 2 millimeters, based on a comparison with the blade diameter. Figure 4.6.4-3 is a re-analysis of the same image, with quantitative information along the line traced in the IR image provided in the associated graph. The 243 °F temperature was the maximum temperature observed for a blade at
5 m/s RMS tip velocity cutting wax. It should be noted that the IR camera shows only surface temperatures, and that the temperature inside the wax immediately in front of the blade could be at a significantly higher temperature than the 243 °F seen at the surface.
Figure 4.6.4-2: IR Camera Image of Wax-Cutting
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Figure 4.6.4-3: Temperature versus position along the indicated line
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5. RESULTS
The results from the experiments are divided into two categories, wax and liver. Several of the wax-cutting results were presented in Chapter 3 to compare with the model predictions.
There, comparisons examined the behavior of cut-rate as a function of normal force and ultrasonic velocity. Here, the results for statistical inference from ANOVA for both the wax and liver data are presented.
5.1 Wax Results
5.1.1 Data Collection: A total of 270 tests were performed which are listed by test conditions in Table 5.1.1-1. As seen from the table, a third of the data were acquired for the round blade at 55.5 kHz data. This is due in part to the facts that: the Harmonic Scalpel system is commercially available, it includes a robust generator and hand piece, and available instruments are field-proven designs. Also the motivation of this research is to determine if there are better frequencies in terms of desired tissue effects. If so, this result would be a powerful justification for a new platform of generators, hand pieces and blades for the Harmonic Scalpel.
The other systems were not as robust, and therefore, data acquisition was limited due to problems with the generators and blade strength at higher ultrasonic displacements.
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Table 5.1.1-1: Wax-Cutting Experimental Data
Fequency Force Velocities Blade Type Number of Total Tests
(netwons) Replicates
55.5 kHz 1.25 5 levels Round (B5) 6 90
2.5 5 levels –2.1 mm 6
5.0 5 levels diameter 6
55.5 kHz 1.25 3 levels Angled (K5) 6 54
2.5 3 levels 2.1 mm 6
5.0 3 levels diameter 6
75 kHz 1.25 4 levels Round (B5) 6 72
2.5 4 levels 2.1 mm 6
5.0 4 levels Diameter 6
23.5 kHz 1.25 3 levels Oblong 6 54
2.5 3 levels round blade 6
5.0 3 levels 1.2 mm 6
diameter
TOTAL 270
5.1.2 Effects of Force, Velocity and Frequency on Wax Cut-Rate: The cut-rates observed for the 2.1 round blade obtained at 55.5 kHz and 75 kHz are shown as a function of velocity and force in the three dimensional plot in Figure 5.1.2-1. A total of 162 points are included in the figure, which represents 6 replicates at 27 test conditions. Drop lines from the individual clusters
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of 6 points each helps make determination of the corresponding velocity and force easy. The velocities for the 75 kHz data are limited to about 11 m/sec, because at the next higher power setting the blades would consistently fail or go into parasitic transverse vibrations.
Figure 5.1.2-1: Cut-Rate versus Velocity and Force at 55.5 and 75 kHz with the 2.1mm
Diameter Round Blade
A two-dimensional plot of cut-rate versus velocity is shown in Figure 5.1.2-2 for the data acquired at 55.5kHz with the round blade. There are three groups of data and three linear regressions seen in the figure corresponding to the same force levels. At a given velocity, the highest force produces the highest cut-rate; the next highest force produces the next highest cut- rate; and the lowest force produces the lowest cut-rate. As force increases, there is clearly an
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increase in the slope of the regression of cut-rate versus velocity. This is evident by the significant interaction of force and velocity.
Figure 5.1.2-2: Cut-Rate versus Velocity at Three Force Levels at 55.5 kHz with the 2.1
mm Diameter Round Blade
The results from an ANOVA performed on data shown in Figure 5.1.2-1 are included in
Table 5.1.2-1. Both force and velocity are significant factors in determining cut-rate as well as the first-order interaction. Frequency does not significantly affect the cut-rate in wax. This is exemplified in Figure 5.1.2-3 that shows cut-rate as a function of velocity at 5 N normal force for both 55.5 and 75 kHz. The 75 kHz data falls about the regression, again demonstrating no frequency dependence.
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Table 5.1.2-1: ANOVA Results for Frequency, Force and Velocity Effects on Cut-Rate in Wax
Factor p level Results
Frequency =0.34 Accept Null Not significant
Force <0.001 Reject Null Significant
Velocity <0.001 Reject Null Significant
Force*Velocity <0.001 Reject Null Significant
Figure 5.1.2-3: Cut-Rate as a Function of Velocity at 5 N Normal Force for Data Acquired at
55.5 and 75 kHz with the 2.1 mm Diameter Round Blade
5.1.3 Effects of Blade Shape on Wax Cut-rate: The data acquired with the angled blade at
55.5 kHz under a normal force of 5 N are shown in Figure 5.1.3-1. The cut-rates observed from
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the angled blade appear to be relatively close to the corresponding data from the round blade but are consistently lower. This slight decrease is obvious in the two-dimensional plot of cut-rate as a function of velocity in Figure 5.1.3-2.
The observation that the angled blade cuts slower is counterintuitive. The angled blade would be expected to cut faster because of the apparent sharpness. This is not the case. The reason for the decrease is that the angled blade has less area in contact with the molten wax compared with the round blade. Therefore, there is less heat generated and less wax melted. As discussed in Chapter 3, this observation supports the conclusion that wax cutting is due primarily to wax melting.
The results from an ANOVA performed on data shown in Figure 5.1.3-1 are included in
Table 5.1.3-1. Velocity, force and blade shape are significant factors in determining cut-rate.
Table 5.1.3-1: ANOVA Results for the Effect of Force, Velocity and Shape (Round versus
Angled) on the Cut-Rate in Wax.
Factor p level Results
Force <0.001 Reject Null Significant
Velocity <0.001 Reject Null Significant
Shape <0.001 Reject Null Significant
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Figure 5.1.3-1: Cut-Rate as a Function of Velocity and Normal Force at Three Force Levels for
Data Acquired at 55.5 kHz with the 2.1 mm Diameter Round and Angled Blades
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Figure 5.1.3-2: Cut-Rate versus Velocity for Data Acquired at 55.5 kHz with the 2.1 mm
Diameter Round Blade and Angled Blade
The 23.5 kHz system has an instrument with a blade denoted as oblong (see Figure 4.2.3-
1). The blade has a 1.2 mm diameter round end that was the end used in the cutting experiments.
The cut-rate data is plotted in Figure 5.1.3-3 with the corresponding data obtained at 55.5 kHz with the round blade. In this case, the cut-rate is clearly greater with the smaller oblong blade compared with the round blade at 55.5 kHz.
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Figure 5.1.3-3: Cut-Rate versus Velocity at 5 N Force for Data Acquired at 55.5 kHz with the
2.1 mm Diameter Round Blade and at 23.5 kHz with the Oblong Blade
The 23.5 kHz system has confounded frequency and blade shape with respect to the 55.5 kHz system with the round blade. However, based on both the results for the angled and round blades at 55.5 kHz and the results from 55.5 and 75 kHz for the round blade, any significant effect observed with the 23.5 kHz system is primarily attributed to shape. Given that the oblong blade represents a shape effect, then the faster cutting is attributed to the smaller projected area.
The smaller area means less wax is melted overall, but less wax needs to be melted because of the smaller blade width and melt zone. The effective driving pressure, normal force over projected area, doubles and therefore the extrusion of the molten wax is much higher, leading to the higher cut-rate.
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5.2 Liver Results
As discussed in Chapter 4, a significant amount of effort was expended to remove various effects that otherwise lead to increased variation in the results. Through that effort, a protocol was developed to mitigate the effects of removing, cleaning and replacing blades, and one of the slots in the liver holding fixture was not used. Connective tissue events were also identified as a major cause of variation in cut-rate. These were readily identified by perturbations in the force, and the cut-rates in these cases were discarded. In spite of all these well-defined methods for accepting or rejecting the data, large variations in the accepted cutting results were observed.
This high degree of variability was in-part the original motivation for testing with a well-behaved manufactured material, wax.
Other problems also arose during the testing. First, the 75 kHz data were judged erratic even with regard to the expected high variance. This was traced to an adaptive algorithm in the generator, which apparently would initiate during the data acquisition period. A “fix” to the existing generator was not practical within the scope of this dissertation. Therefore valid 75 kHz data for liver could not be obtained. Second, at 5 N normal force the cut-rate exceeded the limit of crosshead movement of the Istron Mechanical Test Machine. Even with a 2.5 N normal force at the higher velocities, the limit was occasionally exceeded.
In summary, the extent of the liver data is much less than was originally planned. But in spite of the reduced data set, some valid statistical results were obtained, and differences in behavior compared with the wax results were clearly observed.
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5.2.1 Effects of Velocity and Normal Force on Cut-rate in Liver: The observed cut-rates for
55.5 kHz are shown as a function of velocity and normal force in the three dimensional graph of
Figure 5.2.1-1. The same data are plotted in a two-dimensional plot of cut-rate versus velocity in
Figure 5.2.1-2. Here the data are presented as two sets of points for normal forces 1.25 and 2.5
N. Linear regressions are shown for each set. The slope of the relation increases with normal force. An ANOVA of the data reported in Table 5.2.1-1 indicates that force, velocity and their interaction have significant effects on cut-rate.
Table 5.2.1-1: Results from ANOVA for the Effects of Force and Velocity on Wax Cut-Rate
Factor p level Results
Force <0.001 Reject Null Significant
Velocity <0.001 Reject Null Significant
Force*Velocity <0.002 Reject Null Significant
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Figure 5.2.1-1: Cut-Rate as a Function of Velocity and Normal Force in Liver Acquired at 55.5
kHz with the 2.1 mm Diameter Round Blade
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0.040 0.035 0.030 0.025 2.5 N 0.020 0.015 1.25 N
Cut Rate (cm/s) 0.010 0.005 0.000 6 8 10 12 14 16 18 20 Tip Peak Velocity (m/s)
55 kHz Regression r2=0.76
Figure 5.2.1-2: Cut-Rate as a Function of Velocity and Normal Force in Liver Acquired at 55.5
kHz with the 2.1 mm Diameter Round Blade
Figure 5.2.1-3 is a plot of the data obtained at 1.25 N with a round 2.1mm blade. In addition to the data obtained at 55.5 kHz, there is one cluster of 6 points obtained with a 20 kHz system. The system was a 20 kHz commercial welder that operated over a very narrow amplitude range with a 2.1mm round blade especially designed and fabricated for the system.
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While not a rigorous statistical test of the effect of frequency, the results obtained from 20 kHz system span the extrapolation of the regression for the 55.5 kHz data. This result does not refute the claim that cut-rate is independent of frequency.
Figure 5.2.1-3: Cut-Rate as a Function of Velocity and Normal Force in Liver Acquired at 1.25
N Normal Force at 55.5 kHz and 20 kHz with a 2.1 mm Diameter Round Blade
5.2.2 Effects of Blade Shape on Liver Cut-rate: The data obtained with the angled blade at
55.5 kHz are plotted in Figure 5.2.2-1. Clearly the observed cut-rates with the angled blade behave quite differently in liver compared with wax. In wax, the cut-rates obtained with the angled blade were less than those obtained with the round blade. In liver the behavior is more complex.
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The liver cut-rates obtained with the round and angled blade at a normal force of 2.5 N are plotted as a function of velocity in Figure 5.2.2-2. At a velocity of about 7 m/s the cut-rates from the angled blade fall on top of the cut-rates from the round blades. At a velocity of about
8.5 m/s three points cluster about the regression for the round blade, but the other three points significantly depart from the regression. At a velocity of 10.5 m/s, all the cut-rates obtained with the angled blade are significantly higher than the cut-rates obtained with the round blade.
Figure 5.2.2-1: Cut-Rate in Liver as a Function of Velocity and Normal Force for Data
Acquired at 55.5 kHz with the 2.1 mm Diameter Round and Angled Blades
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Figure 5.2.2-2: Cut-Rate in Liver as a Function of Velocity at a Normal Force of 2.5 N for Data
Acquired at 55.5 kHz with the 2.1 mm Diameter Round and Angled Blades
All the liver data collected at 1.25 N are presented in Figure 5.2.2-3. This includes data collected with 2.1 mm round blades at 20kHz and 55.5 kHz, the angled blade at 55.5 kHz, and the oblong blade at 23.5 kHz. The data from all the blades approach the regression for 55.5 kHz for velocities below 8 m/s. Above 8 m/s, the cut-rates obtained with the angled and oblong blades increase dramatically over the rates obtained with the 55.5 kHz round blades.
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Figure 5.2.2-3: Cut-Rate in Liver as a Function of Velocity for All the Data Obtained at a
Normal Force of 1.25 N
Thus in cutting liver, the observed behavior is delineated into two regimes. The first regime occurs at relatively low ultrasonic velocities. The cut-rate is only weakly dependent on blade shape if at all. Based on both the experimental results and the model for wax, cutting appears to be dominated by a heating mechanism. In the second regime, cutting depends on both heating and a mechanical failure based on the blades with sharper features cutting significantly faster than the 2.1 mm blade. The cut-rate being significantly higher for the angled and oblong blade suggests that the mechanical failure mechanism dominates in this regime.
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6. DISCUSSION
The use of wax as a specimen to evaluate tissue is justified, because of a number of features. First, wax-cutting has been used to qualify the hand pieces of surgical instruments, because a similar rate in tissue cutting is obtained when a hand piece is properly manufactured.
Second, the relatively high variability of results obtained from tissue in mechanical testing is well known in biomedical engineering. Therefore the use of a manufactured material would potentially allow statistical analysis to be performed with less replications due to the lower variance. Third, while the behavior was not expected to predict behavior in tissue, the results could be compared with the tissue results. Thereby any differences from the comparison would be indicative of different mechanisms that would need to be understood.
The behaviors of wax-cutting and liver-cutting from the experiments are very similar in many aspects, but very different in others. This discussion focuses on the comparison of wax and liver results in order to potentially identify the mechanisms and tissue properties that control cut-rate in tissues.
6.1 Behavior of Wax-cutting
6.1.1 Empirical Results: The observed cut-rates in wax were shown to significantly depend on ultrasonic velocity, normal force, and blade shape. Cut-rate was shown not to significantly depend on frequency. As force increases at given velocity, cut-rate continuously increases, and as velocity increases at given force, cut-rate continuously increases.
The oblong diameter blade presents a 1.2 mm diameter contour to the wax that is smaller than 2.1 mm diameter. For the same velocity and force, the smaller blade is observed to cut
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faster than the large round blade. This agrees with intuition that a blade with higher contact pressures should cut faster than one with lower contact pressures.
One of the most interesting findings in wax is that the cut-rate of an angled blade is slower than that of the round blade. The round blade is 2.1 mm in diameter, machined from a titanium rod. The angled blade is made from the round blade by also machining two flats that form adjacent cords with a 120 included angle into the top surface of the round blade. Therefore the angled blade has an apparent sharpness greater than that of a round blade. While the radius at the tip is not known, it is certainly sharper than the round blade with the same surface finish.
Therefore, one would expect a higher cut-rate due to the greater sharpness and higher contact stresses. Given that the rate is slower, cut-rate is not due to stress-induced mechanical failure.
6.1.2 Model for Wax-cutting: The model was developed for wax-cutting based on viscous heating in a liquid layer of molten wax and the extrusion of the molten wax away from the advancing blade. The wax-cutting model is based on an energy balance. Several simplifying assumptions were made to obtain a relatively compact set of equations to solve for cut-rate as a function of velocity and normal force.
While the equations included a number of material properties and geometries that describe the problem, two factors were determined by a regression. One was the effective geometric factor for the extrusion equation, and the other represented an effective viscosity for treating molten wax as a simple Newtonian fluid. This approach is similar to that taken in the
Nabibekov model with a regression to calculate coefficients for a model of the tissue response to an applied force (Nabibekov, 1980). The factors were determined by a least-squares fit to the data obtained at 55.5 kHz with the 2.1mm diameter blade.
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Even with the number of assumptions and basic modeling approach, the model predicted fine behavior of cut-rate with velocity and force not evident when fit with a simple plane. In addition, the model accurately predicted the behavior of the angled blade by only changing those factors related to the geometry difference of the round and angled blades. The material properties and the regression coefficients were not changed.
The cut-rates observed with the oblong blade at 23.5 kHz are greater than those observed at 55.5 kHz with the round blade. In this case, the model predicted the higher cut-rate, but the predictions were less than those observed. The fact that the predicted values are lower than the observed values is likely due a limited range over which the assumptions are valid, or the fact that the oblong blade shape does not behave as a simple round blade.
Based on the ability of the model to predict the observed behavior of angled and round blades, cut-rate in wax is attributed to viscous heating to melt wax and to the extrusion of the molten wax out of the way of the advancing blade.
Although the model is predictive, an unrealistic value for the a2 factor suggesting that the model did not adequately represent the physical problem. Many assumptions were made to allow a set of two algebraic equations to be developed that predicts the basic behavior of the observed cut rate as a function of velocity and force. An analytical model could be derived from a governing set of differential equations that would eliminate the need for a number of the simplifying assumptions and would ultimately be more accurate and general.
While the model was developed specifically for wax and is only used for comparison to observed behavior in liver-cutting, it has potential applications beyond wax-cutting. The model should be applicable to any ultrasonic system that is used to cut or part materials that are
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polymer chains. One recent application has been discussed for the dicing of chocolate confections (Lucas, 2002).
6.2 Liver-cutting
The variability in liver was observed to be higher than expected. In addition, several issues with ultrasonic systems developed for this research limited the amount of data collected.
At 55.5 kHz and normal forces of 1.25 and 2.5 N, an ANOVA using a log representation of the data showed that cut-rate was a function of velocity, normal force and their interaction.
The data obtained at other frequencies is extremely sparse, and only data obtained for one test condition at 20 kHz were obtained. Yet it was consistent with the predicted confidence intervals obtained for 55.5 kHz. While no significant inference can be drawn, the data does not refute the hypothesis that cut-rate at least at lower forces and lower velocities does not depend on frequency. Conversely, if the 20 kHz data had been substantially different, then that would have been an indication that frequency does have an effect.
Furthermore the data obtained from the angled blade at 55.5 kHz and the oblong blade at
23.5 kHz are consistent with the data obtained with the round blade at 55.5 kHz at a normal forces of 1.25 and 2.5 N at velocities below about 8 m/s. This behavior is very similar to the behavior observed in the wax data and predicted by the wax-cutting model. That is, cut-rate is independent of frequency and is dependent on the blade size and contact area as opposed to a blade shape or sharpness per se.
Above velocities of about 8 m/s and at normal forces of 1.25 and 5 N, the cut-rates dramatically increase for the oblong and angled blades compared with the 2.1mm diameter round blade at 55.5 kHz. At a normal force of 5 N, cut-rate could not be observed, because the rates
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exceeded the capacity of the mechanical test machine for all velocities evaluated. Therefore, the statement can be made that at 5 N forces, the cut-rate produced by the 2.1 mm blade at 55.5 kHz is significantly higher than the values that would be obtained based on an extrapolation of the
55.5 kHz data from 1.25 and 2.5 normal force. Clearly there is a threshold for cut-rate in liver that is a function of velocity, normal force and blade type.
Below the threshold, liver behaves similar to wax. In this regime liver-cutting is appears to be due mainly to heat. The heating mechanism likely involves the heating of extracelluar and intracelluar liquid components and blood near the blade. At some temperature or range of temperatures the liquids start to vaporize and burst or melt the cellular walls and matrix of materials forming the liver tissue, allowing the contents to flow and the blade to advance. The need for the continuous transfer of heat limits the cut-rate to a relatively lower value.
6.2.1 Active Stress-Relaxation Tests: In one series of tests, the movement of the crosshead was stopped after achieving a target force, and the force was allowed to approach an equilibrium while the blade remained ultrasonically activated. The results are shown plotted in
Figure 6.2.1-1 for ultrasonic velocities corresponding to 40, 60 and 80 micron excursions at 55.5 kHz. The forces were still decreasing slightly after 60 seconds but appeared to be approaching equilibrium values. The forces at sixty seconds were 1.14, 0.64 and 0.43 N, respectively.
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Liver Cutting-Relaxation Test 55 kHz round blade
6
55 kHz 5 Round Blade Liver Specimen 40, 60 and 80 micron excursion 4
3
Load (Newtons) 2
1 1.14 N 0.64 N 0.43 N 0 0 10203040506070 Time (s) 80 micron excursion relax_5N_Liver.jnb 60 micron excursion 40 micron excursion
Figure 6.2.1-1: Active Stress-Relaxation of Liver
The equilibrium forces appear to be roughly inversely proportional to the ultrasonic velocity. Taking the forces at 60 seconds to be somewhat representative of the equilibrium force, the force velocity products are 12, 13 and 16 for the 80, 60, and 40 micron vibration excursions respectively. These values are in units of power but are not scaled by any coefficient of friction or coupling and are much higher than actual delivered powers.
The observations that the powers are nominally equal, and the cut-rate is zero suggest that a distribution of steady-state temperatures have been reached in the blade and tissue.
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Because the cut-rate is zero, the temperatures in the tissue are now below any phase transition temperatures associated with the potential denaturing of collagen or the boiling of water. This behavior therefore appears to support that tissue cutting is a thermal phenomenon at low forces and low velocities.
Liver is known as a friable material, meaning that it is easily damaged. This is in part due to the relatively low collagen content of the liver compared with other internal organs and skeletal muscle and skin (Gallagher, 2000). In the region above the threshold at nominally 8 m/sec, there is enough induced stress at the blade that the structural components of the liver fail mechanically and quickly. The blade then simply moves through the fluid contents of the mixture of extracellular and intracellular fluids. The stress may be simply the mechanical stresses associated with the dynamic state of stress created by the combination of the contact pressure (normal force) and the ultrasonic movement of the blade. Another mechanism may be pressure induced by cavitation within the cells that are which is know to cause cellular damage.
No matter the underlying mechanism, clearly there is a combination of velocity and force at which a given blade quickly cuts through liver. In this regime, the cut-rate is likely to be a function of blade shape, and may be a function of frequency. However, due to limitations of the machine the cut-rates above the threshold could not be accurately measured, and any such dependences could not be observed or tested.
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7. CONCLUSION
In spite of the proven efficacy and safety of ultrasonic surgical systems, the mechanisms for cutting and coagulation are not well understood. Unaided by any fundamental understanding, new designs must be fabricated and tested on tissue to determine that desired effects can be achieved. This is especially time-consuming and expensive because of the resonant nature of these systems. Instruments must be conceived and designed to resonate at the specific hand- piece frequency, while both avoiding undesirable modes of vibration and developing the ultrasonic displacements within the stress-limits of the instrument material.
This research was designed to determine whether frequency, normal force, velocity and blade shape affect the cut-rate achieved with an ultrasonic surgical instrument. Two specimens were chosen for evaluation. One is a manufactured material, wax, that has been shown to produce consistent rates, which are similar to the rates observed in surgery with these ultrasonic instruments. The other specimen was liver because of its clinical significance in resection of liver cancer, and its relative homogeneity and low collagen content.
The velocities for the tests covered the range available from a 55.5 kHz ultrasonic surgical system that is currently on the market. Three values for normal force were selected based on previous testing. The low value corresponded to a “light” touch that the surgeon would typically apply in fine dissection between tissue planes, and a heavy force that might be used in a skin incision such as a laparotomy.
Therefore the conclusions and directions for future research are made based on data that is representative of ultrasonic surgical systems used in tissue-cutting today.
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7.1 Research Questions
The research was designed to answer specific questions. Given the relatively high repeatability of the wax data, these questions were readily answered using ANOVA analysis. In liver, the data exhibited high variance, and the number of tests were limited due to problems with the custom ultrasonic systems developed for the research. Therefore valid significant results were limited to the base case of 55.5 kHz and an instrument with a diameter of 2.1 mm. Even so, behavior very different from wax cutting was observed that could be of substantial impact in the design of ultrasonic surgical instruments.
7.1.1 Does the Normal Force of an Ultrasonic Surgical Instrument Affect Cut-Rate?
In wax, force was shown to be a significant factor (p<.001) for data obtained at both 55.5 kHz and 75 kHz for round blades of the same diameter. At both frequencies, cut-rate increases continuously with normal force for a given velocity. In liver, the same behavior was observed up to 2.5 N force for the round 2.1 mm blade at 55.5kHz. At a 5 N force, the cut-rates in liver increased dramatically so that the limit of the crosshead speed was exceeded for the particular test machine used in these experiments. The rates at 5 N were much faster than the rates that would be expected based on an extrapolation of the data at 1.25 and 2.5 N.
7.1.2 Does the velocity of an ultrasonic surgical instrument affect the rate of cutting?
In wax, velocity was shown to be a significant factor (p<.001) for data obtained at both
55.5 kHz and 75 kHz for round blades of the same diameter. At both frequencies, cut-rate increases as a continuous function of velocity for a given normal force. In liver, the same
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behavior was observed up to a limit of velocity that depended on blade shape. At 1.25 N normal force and up to 8 m/s velocity, the cut-rates for the round blade, the angled blade and smaller diameter oblong blade were similar for a given force. Above 8m/s, the behavior of the round blade continued on the same trend, while cut-rates observed both with the angled blade and the oblong blade increased dramatically.
7.1.3 Does frequency of an ultrasonic surgical instrument affect the rate of cutting?
In wax, frequency was shown not to be a significant factor (p=0.34) for data obtained at 55.5 kHz and 75 kHz with the round 2.1 mm diameter blade. In liver, the amount of data obtained at different frequencies was extremely limited due to instrumentation issues, and no conclusive statement can be made.
7.1.4 Does blade shape of an ultrasonic surgical instrument affect the rate of cutting?
In wax, the cut-rates obtained with the angled and oblong blades were significantly different compared with the round blade (p<0.001) over the same range of control variables. The angled blade cut-rate was actually lower than that obtained with the round blade in spite of its relative sharpness. The oblong blade had a smaller diameter than the round blade, and it did cut faster than the round blade as expected based on its smaller area and higher contact pressures.
In liver, the cut-rates were similar for all three blades up to nominally 8 m/sec at a normal force of 1.25 N. Above 8m/sec, the oblong and round blades increased significantly above the cut- rate observed with the round blade. So in liver, blade shape has an obvious effect on cut-rate.
Above a threshold velocity at a given normal force, the apparent sharpness can lead to significantly faster cutting rates than a blunter rounder blade.
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7.2 Wax Cutting
The cut-rate was shown to significantly depend on velocity, force, their interaction and blade shape. The observed results are consistent with a model for cut-rate that was based on wax melting and removal of the molten wax. In the development of the model several assumptions were made and two parameters were determined by a regression on a data set. Even so, the model predictions were very accurate for the data on which the regression was performed and predicted some fine features observed in the data. The model was shown to predict with reasonable accuracy the behavior observed at other frequencies for other blade shapes. The model can certainly be improved by more rigorous development; nonetheless, it does demonstrate that the basic mechanisms of wax melting and extrusion are important.
7.3 Liver Cutting
Due to a number of issues with instrumentation and the natural variance observed when testing tissue, conclusions based on statistics can not be made other than for 55.5 kHz and a round blade at forces of 1.25 and 2.5 N. In this limited range of test conditions, cut-rate is shown statistically to be a function of velocity, normal force and their interaction.
Two interesting observations were made in the data. First, when the “sharper” blades were used, the cut-rate dramatically increased with ultrasonic velocity compared with the larger round blade. Second, above a certain normal force, even the larger diameter round blade had a dramatic increase in cut-rate compared with the trend based on the lower forces.
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These two observations and a comparison with the wax data, suggest two hypotheses. First at a given normal force and below a threshold of velocity, cut-rate in tissue is mainly due to thermal effects, and above the velocity threshold at a given force the cut-rate is mainly due to a mechanical effect in which a failure mode may itself be temperature dependent. Second, the observations that this threshold was observed as a function of velocity for the oblong and angled blades at lower forces, and that at the 5 N force the cut-rate for the larger round blade dramatically increases, suggests that the threshold is a function of the interaction of velocity and force for a given blade shape.
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8. PROPOSED FUTURE RESEARCH
The results from the liver experiments and data analysis suggest that much more work is needed to accurately determine the underlying mechanisms of cutting and coagulation of tissue that can be represented in a quantitative model. This research has uncovered promising opportunities for both analytical and experimental research.
Future experimental work needs to commence with the design of a set of transducers that can drive blades to the desired displacements specifically for the research undertaken. The ultrasonic instrumentation needs to be robust over the range of test conditions both in terms of transducers to drive the blades and in terms of blades that are mechanically and acoustically reliable.
That is, the set of transducers, blades, and generators needs to be designed as a “system”. This approach will alleviate issues with ultrasonic instrumentation that hampered this research and will permit experimental protocols to be executed smoothly. This is a significant amount of effort and should not be underestimated.
The wax-cutting model was developed by coupling basic algebraic relations that represented viscous heating, melting, and removal of wax through the two control parameters, velocity and force. The model predictions accurately capture the observed behavior after two parameters were obtained by a least-squares regression on the data. However, the resulting predictions indicate that several assumptions are not entirely valid.
An analytical model for wax cutting needs to be developed based on a fundamental set of differential equations that represent the underlying physics that govern the process. The equations will capture the viscous heat generation, heat transfer, and the removal of wax. The assumptions made to develop the simple algebraic model need not be invoked. Because of the multi-physics
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nature of the problem the analytical problem may be difficult to solve, and finite element analysis may be the best approach to obtain a solution.
The model should also consider the heat input and temperature rise behind the blade. This should allow the melt-zone to be determined as a function of angular position and therefore total power delivered can be compared with measured power.
Controlled experiments need to be performed in liver and other tissues to determine the interplay between cutting and coagulation. Faster cutting without equivalent coagulation has limited clinical usefulness. Experiments should be designed to investigate cutting and coagulation in both the low-velocity low-force and the high-velocity high-force regimes. The data should help elucidate the mechanisms for the low-velocity low-force regime conjectured to be heat dominated and for the high-velocity high-force regime conjectured to be dominated by stress related failure. This information will be crucial in developing an analytical model.
A benchmark for any tissue cutting model will be its ability to predict the conditions where the transition between the two regimes occurs. Another objective of a model should be an ability to predict cut rates and coagulation in different tissues, perhaps as a function of the percent collagen content. This model would be a powerful tool to advance the design of ultrasonic surgical systems.
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Vona D.F., M.W. Miller, H.D. Maillie, "A Test of the Hypothesis that Cavitation at the Focal Area of an Extracorporeal Shock Wave Lithotriptor Produces Far Ultraviolet and Soft X-Ray Emissions", J. Acoust. Soc. Amer., 98 (2), Pt.1, August, 1995.
Walnut Hill Waxes, http://www.walnuthillco.thomasregister.com/olc/walnuthillco/p7.htm
Wood R.W., Loomis A.L., Phys. Rev. 29, 373, 1927-a.
Wood R.W., Loomis A.L., Phil. Mag. 4, 417, 1927-b.
132
Wuchinich, U.S. Patent No. 4,063,557, Issued Dec. 20, 1977.
Young, Cavitation, F. Ronald Young, McGraw-Hill Book Company, QC158.Y68 1989.
Zimmer J.E., Hynynen K., Marcus F., He D.S., “The Feasibility of using Ultrasound for Cardiac Ablation”, I.E.E.E. UFFC 1993 Ultrasonics Symposium, Vol. 2, 1993.
Ziskin, Ultrasonic Exposimetry, Ziskin and Lewin, CRC Press, ISBN # 0-8493-6436-1, 1992.
133
APPENDIX A:
DISSERTATION-RELATED PUBLICATIONS
Ultrasonic Surgical Instruments: A Multi-Variate Study for Cutting Rate Effects, by: Jeffrey J.
Vaitekunas*, Foster B. Stulen**, and Edward S. Grood***, *Ethicon Endo-Surgery,
**BIOMEC, ***University of Cincinnati, Cincinnati, Ohio, Invited lecture to the Acoustical
Society of America, Cincinnati Chapter, May 15, 2001.
Ultrasonic Surgical Scalpels: the Effects of Frequency within the Low kHz Range by J.J.
Vaitekunas and Foster Stulen, presented at the 2000 Ultrasonic Industry Association Symposium,
June 11-13, 2000, Columbus Ohio.
Ultrasonic Cutting of Tissues and Surrogates by J.J. Vaitekunas and Foster Stulen, presented at the
2002 Ultrasonic Industry Association Medical Workshop, May 20, 2002, Atlantic City, NJ.
134
APPENDIX B:
SPECIFIC HEAT OF FREEMAN WAX
Experiment by Curtis Fox, under the direction of Dr. Peter Nagy, at the University of
Cincinnati, aerospace engineering research laboratory.
135 67 best fitting exponential decay 66 before inserting the wax best fitting exponential decay 65 after inserting the wax experimental decay 64
63
62 Temperature [°C] 61
60
59 0 5 10 15 20 25 30 35 40 Time [minutes]
The above figure shows an example of the measured decay curve along with exponential decay curves fit to the experimental data before and after inserting the wax specimen in the water bath. The “instantaneous” temperature drop (δT=1.49 °C) was calculated from the difference between the two best fitting exponential curves by interpolation at the center of the roughly 2-minute-long transient. Then the specific heat of the wax was calculated from the measured masses (weights) of the water (mwater= 0.2 kg) and the wax ∆ (mwax= 0.01284 kg), the measured difference ( T=38.4 °C) between the temperatures of the water bath and the wax specimen at the time of insertion and the known specific heat of water (cwater= 4,186 J/kg/°C) as follows
m δT cc= water , wax water ∆ mwax T which gave 2,530 J/kg/°C. For better accuracy, the same measurement was repeated five times using different pieces of wax. The average specific heat was found to be 2,420 J/kg/°C with a standard deviation of 150 J/kg/°C or 6.2%.
APPENDIX C:
TRANSLATED MANUSCRIPTS
136 MEKHANIKA KOMPOZITNYKH MATERIALOV, 1980, No. 3, pp. 519-524
UDC 611:08:534.6
M. K. Nabibekov, B. D. Plyushchenkov, I. Yu. Sarkisov
INVESTIGATION OF THE PROCESS OF ULTRASONIC CUTTING IN SOFT BIOTISSUES*
The wide-scale use of the ultrasonic method in bone surgery [1-3] faces us with the pressing need to improve the technique and extend it to types of biological objects other than solid biological materials. In particular, efforts are underway to apply ultrasonic energy to cutting soft biotissues [2, 4]. There is as yet still no mechanical model or theory of the cutting process, however, which to a certain extent complicates calculating the acoustic and engineering parameters for the ultrasonic cutting of soft biotissues and precludes efficient experimental and design work. In this article we develop a theory and investigate a physicomathematical model of the process of the ultrasonic cutting of soft biotissues in order to be able to utilize it in the development of the necessary instruments and optimal technology. The process of the ultrasonic cutting of soft biotissues is illustrated schematically in Fig. 1. The electrical vibrations generated by an ultrasonic generator are fed to the magnetostrictor 1, which converts them into mechanical elastic vibrations. After being amplified by the transformer 2 and the concentrator 3 of the instrument, the vibrations are transmitted to its cutting part 4. The elastic support 5 damps the vibrations transmitted to the housing 6 of the acoustic unit. The surgeon cuts biotissue 7 by applying force Fx along the axis of the instrument. To determine the nature of the influence of the acoustic and engineering parameters on ultrasonic cutting, we shall construct a mathematical model of the process. Let us assume that in the cutting process the motion of the instrument is in the same direction as the motion of the ultrasonic vibrations and that it is one-dimensional. We shall represent the instrument with its acoustic unit in the form of an applied point of force of mass M acting along the x axis. The following forces act upon the cutting part of the instrument during the cutting process (Fig. 2): 1) the cutting to USG force Fx, i.e. the force exerted by the surgeon to the instrument and coinciding with the direction of cutting; 2) the effective force of the elastic vibrations Fig. 1. The process of ultrasonic cutting of Fv created by the magnetostrictor of the instrument soft biotissues: 1 — magnetostrictor; 2 — causing the instrument to vibrate sinusoidally; Fv is transformer; 3 — concentrator; 4 — cutting therefore represented in the form: Fv = - part of the instrument; 5 — elastic support; mAω2sin(ωt+φ), where m is the reduced mass of the 6 — housing of the acoustic unit; 7 — vibrating part of the instrument, A and ω are, biotissue; USG — ultrasonic generator. respectively, the amplitude and the frequency of the
* A paper given at the Second All-Union Conference on the Problems of Biomechanics (Riga, April, 1979).
519 cutting part of the instrument, t is the time, φ is the phase of the vibrations; 3) the force of friction Ff of the instrument against the surface of the biotissue; this force is described by the relationship • • Ff = -λsgn x, where λ>0 is a coefficient having the dimensions of force, x is the velocity of the cutting part of the instrument, sgnx• = 1 if x• > 0 and sgnx •= -1 if x• <0; 4) the force of resistance to cutting Fr, which in contrast to the force of friction acts on the instrument only at the times when the biotissue is actually being cut. For certain cutting parameters, the motion of the cutting part of the instrument in biotissue may resemble the motion of a solid body in a viscous liquid. The difference is that for the instrument to begin moving in the biotissue, a force greater than some constant value f0 must be applied. We shall call this force the constant force of resistance of the biotissue. At slow rates of motion of the instrument, the force of resistance is proportional to the velocity. As the velocity increases, the force of resistance becomes proportional to the square of the velocity. Let us • •2 represent it in the form Fr = -(f0+k1x+k2x ). The positive coefficients f0, k1, k2 depend on the geometry of the cutting part of the instrument and the mechanical properties of the biotissue. Taking into consideration all the forces acting on the cutting edge of the instrument and applying Newton's laws, we obtain an equation for the motion of the ultrasonic instrument in the process of severing soft biotissue:
where M is the mass of the instrument with the acoustic unit. The major factor determining the nature of the cutting process is the force exerted by the surgeon Fx. Depending on the magnitude of the force, two significantly different cutting regimes may arise—cutting with detachment of the cutting part of the instrument from the boundary of the cut of the biotissue and cutting without detachment. Let us consider the first case. Equation (1) cannot be solved by a standard method. Therefore let us divide the cutting process into two phases—an active and a passive phase. The active phase of cutting begins at the moment the blade of the instrument engages the unsevered section of the biotissue (Fig. 3) and ceases when the velocity of the instrument becomes equal to zero. It is during this period that cutting occurs. The passive phase of cutting begins when the cutting part of the instrument leaves the edge of the cut in the biotissue, moves in a direction opposite to the direction of cutting and again approaches the edge of the cut. In this period the instrument completes a reverse stroke and no cutting occurs. The friction force clearly acts only during the passive phase. During the active phase it is accounted for in the force of resistance. Having examined the mechanics of the
Fig. 2.* Fig. 3.*
Fig. 2. Forces acting on the instrument during the cutting process: 1—cutting part of the instrument; 2—biotissue. Fig. 3. Phases of cutting: 1—active; 2, 3—passive phase of cutting (2—withdrawal, 3—approach of instrument toward edge of cut in biotissue).
[*Key to Figs. 2 and 3: Fx = Fx—force along x-axis; FK = Fv—vibration force; FT = Ff—friction; FC = Fr— resistance]
520 process, now let us divide equation (1) into two equations describing the active and the passive phases of cutting:
In order to determine how the motion of the ultrasonic instrument depends on the acoustic and engineering parameters we must solve equations (2) and (3) simultaneously. To simplify the • •• calculations, we introduce the dimensionless variables x = Ax~ and z = ωt, then x• = Aωx~ , x• •= Aω2x- x~ and equations (2) and (3) simplify to:
2 2 2 where K = M/m; α = k1/ωm; β = k2A/m; v = Fx/Aω m; µ = f0/Aω m; γ = λ/Aω m. We note that the coefficients α and β are determined by the mechanical properties of the biotissue, the geometry and the mass of the cutting part of the instrument, as well as the acoustic cutting parameters. The coefficients v, µ, and γ are defined, respectively, by the ratio of the cutting force, the force of resistance of the biotissue, and the friction force to the maximum (amplitude) value of the force of the elastic vibrations. These coefficients, unlike coefficients α and β, may change in the course of the cutting process as the cutting force varies. We now introduce simplifications making it possible to solve equations (4) and (5) in analytical form. We note that when ω, α0 and when A0, β0. Since K1, and the duration ∆t of the active phase of cutting is less than the period T of the • ultrasonic vibrations ∆t In equations (6) and (7) the sign ~ above x is omitted. Let us investigate the motion of the instrument during the time of the passive phase of cutting. Without limiting the generality of the argument, we can set the velocity and displacement of the cutting part of the instrument equal to zero at the starting time z0 = 0. The solution of equation (7) describing the motion of the instrument during the passive phase of cutting, when the initial conditions are equal to zero, has the following form: and the rate of motion of the cutting edge -1 where K0 = K . Let us introduce a condition such that, when it is satisfied, cutting proceeds with detachment of the cutting edge of the instrument from the boundary of the cut. To do this, let us consider a 521 • displacement x(z) and velocity x (z) at the time (z0 = 0) of the transition from the passive phase of cutting to the active. Let us expand the displacement and velocity in a Taylor's series of degree z at point z0 = 0. Taking the first terms of the series, we have: Since the cutting edge of the instrument detaches from the edge of the cut of the biotissue, then its displacement and velocity pass through zero and the sign changes to positive, then the condition of detachment, as follows from (10), is of the form: v The displacement and velocity of the cutting edge of the instrument during the active phase of cutting are defined by the solution of equation (12): The expressions for the displacement (13) and velocity (14) of the cutting instrument describe the active phase of a variety of regimes of ultrasonic cutting. One of the regimes most important in practice is the steady-state regime, when after a certain time the instrument begins to move in the biotissue at a constant, predetermined velocity. Let us determine the acoustic and engineering conditions under which the stationary regime occurs. Let us assume that it exists; then the total duration of the active and passive phases is constant and equal to the period of the ultrasonic vibrations T, i.e. where z~ and z¯ are the duration of the active and passive phases, respectively. Let us express the duration of the active and passive phases of cutting as a function of the cutting force. 522 Since the initial moment of the active phase is selected to occur at time zero z0 = 0 and it lasts until the velocity of the cutting edge of the instrument becomes zero, its duration close to the point z0 = 0 is the positive root of equation (14). Solving equations (15) and (14) simultaneously • ~ ~ at x (z¯ ) = 0, we find z¯ = 2 π(1-ξ) and z = 2πξ, where ξ = v/µ = Fx/f0. The equality z /2π = Fx/f0 shows that in the steady-state regime of cutting, the ratio of the duration of the active phase, during which cutting occurs, to the period of the ultrasonic vibrations is equal to the ratio of the force of the surgeon to the force of resistance of the biotissue.* Taking into consideration that the maximum possible duration of the active phase is equal to 2π, we obtain the condition under which the steady-state of cutting occurs: Thus, for any soft biotissue there exists a steady-state of cutting, i.e., a motion of the ultrasonic instrument at a constant predetermined velocity. The steady-state regime of ultrasonic cutting, unlike that of ordinary cutting, occurs at forces exerted by the surgeon that are less than the force of resistance of the biotissue. This is one of the major advantages of the ultrasonic severing of soft biotissues. The surgeon can operate using small cutting forces. The steady-state conditions (16) determine the range of possible forces exerted by the surgeon that allow him to take advantage of the advantage inherent in the principle of applying ultrasonic vibrations to the motion of a cutting instrument. In order to express the dependence of the displacement of the instrument and the velocity of ultrasonic cutting in explicit form, and thereby solve equation (1) for the dynamics of the process, let us set z = z¯ in expression (13). Making the substitutions z¯ = 2 πξ and z¯ = 2 π(1-ξ), we obtain: Let us express cosφ in terms of the parameters of cutting. Since at the end of the passive phase of cutting the cutting edge of the instrument returns to the initial position with coordinates of – – – x(z~ ) = 0, then from expression (8) it follows that vz 2/2+sin(z+φ) – zcosφ – sinφ = 0. Solving this expression for cosφ we obtain: where a = 1 – ξ+(2π)-1sin2πξ; b = a2+π-2sin4πξ. It is not difficult to show that only a minus sign before the root in expression (18) satisfies the physical conditions of the cutting process. Substituting the value of cosφ into expression (17), we obtain in explicit form the dependence of the displacement of the cutting edge of the instrument on the cutting parameters: Let us investigate the displacement x(z~ ) for µ1, i.e., when the force of resistance of the 2 biotissue is much less than the amplitude value of the vibration force (f0Aω m). This is the situation that occurs, for example, in ultrasonic surgery on the soft tissues of the wrist. Expression (19) at µ1 simplifies to: * Here and below, the "force of resistance of the biotissue" is taken to be the constant component f0 of the force of resistance Fr of the biotissue. 523 Using this expression, we can define one of the basic parameters of the cutting process — the average rate of motion of the instrument during the period of the ultrasonic vibrations: where x*(z~ ) = Ax(z¯ ) is the dimensional displacement of the cutting edge of the instrument. The average velocity defined in this way is directly related to the efficiency of the cutting process. Substituting expression (20) in (21) we obtain: Thus we have found, analytically and in explicit form, the functional relationship between the average velocity of the ultrasonic severing of soft biotissues and the acoustic and engineering parameters of the process and the properties of the biotissue. This equation (22) is fairly simple and convenient for practical engineering calculation of optimal cutting parameters. It establishes the relationship between the average velocity of cutting and the following parameters: 1) the force applied by the surgeon Fx to the ultrasonic instrument; 2) the mechanical properties of the biotissue that determine its force of resistance to cutting f0; 3) the amplitude A and frequency ω of the ultrasonic vibrations of the cutting part of the instrument; 4) the inertial properties of the instrument and the acoustic unit, which is determined by what fraction of their mass vibrates. The theory and model described here find application in developing the optimal technology for ultrasonic surgical procedures on soft biotissue and the ultrasonic instruments needed in them. The authors are grateful to G. A. Nikolaev for help in formulating the problem and evaluating the results of the work. REFERENCES 1. Polyakov V. A., Nikolaev, G. A., Volkov M. V., Loshchilov V. I., Petrov V. I. Ultrasonic Welding of Bones and Cutting of Biological Tissues. Moscow, 1973. 136 pp. 2. Loshchilov V. I., Volkov S. M., Zasypkin V. V., Borisov V. P. Ultrasonic Devices for Cutting and Welding Biological Tissues. - In: Ultrasound in Surgery. Moscow, 1973, pp. 24-29. 3. Loshchilov V. I., Volkov S. M. On the question of the mechanism of ultrasonic cutting of biological tissues. Ultrasound in Surgery. Moscow, 1973, pp. 29-33. 4. Borisov V. P. Design and investigation of a the process of ultrasonic cutting of soft biological tissues. Author's abstract of a dissertation submitted for the degree of Candidate of Technical Sciences. Moscow, 1975. 16 pp. All-Union Scientific Research Institute Received 28 May 1979 Of Medical Instrument Building Institute of Applied Mathematics, USSR Academy of Sciences, Moscow Institute of Medical and Biological Problems USSR Ministry of Health, Moscow 524 MEKHANIKA KOMPOZITNYKH MATERIALOV, 1980, No. 4, pp. 703-707 UDC 611:620.179 M. K. Nabibekov, B. D. Plyushchenkov, I. Yu. Sarkisov INCREASING THE EFFICIENCY OF ULTRASONIC CUTTING OF SOFT BIOTISSUES* Clinical experience in the application of ultrasound to cutting a variety of biotissues has shown that the method has many attractive features [1] — the cutting force is reduced and the method offers advantages in terms of hemostasis, asepsis, and reduced pain. The method makes it possible to increase the efficiency of operations, allowing gentler types of procedures to be selected, the operating time to be shortened, and labor- intensiveness to be reduced. The object of this article is examine, theoretically and experimentally, methods for increasing the efficiency of the process of ultrasonic cutting of soft biotissues. In Nabibekov et al. [2] a functional relationship was found between the rate of ultrasonic cutting of soft biotissues and the acoustic and engineering parameters of the process: (1) where A and ω are, respectively, the amplitude and the frequency of the ultrasonic vibrations of the blade of the instrument; K0=m/M is a coefficient characterizing the inertial properties of the instrument; M, m are the mass of the entire instrument and of its vibrating part; ξ=Fx/f0 is a parameter defining the ratio of the cutting force Fx to the resistance of the biotissue f0. The graph of the rate of ultrasonic cutting of soft biotissues is S-shaped (Fig. 1). The behavior of the 2 2 graph in section c is defined by the parabola V/ξ→1 = AωK0[1–π (1–ξ) /3], and in section a by V/ξ→0 = 2 AωK0πξ , i.e. at small values of the cutting force, the cutting rate is proportional to the square of the force applied to the cutting instrument. There is also a section b where V is linearly dependent on ξ. We note that the efficiency of the ultrasonic cutting process is directly related to its speed and the higher the rate the higher the efficiency. At the same time, the duration and the trauma of the procedure increases. It is of practical interest to determine at what values of the acoustic and engineering parameters the efficiency of the process is highest and how it can be controlled. It is obvious that the maximum efficiency occurs at the highest cutting rate. For the same instrument and acoustic parameters, the cutting rate depends on the cutting force applied by the surgeon to the ultrasonic instrument. Its maximum force is determined from the conditions ∂V/∂ξ=0, ∂2V/∂ξ2<0. Differentiating expression (1) and setting it equal to zero, we obtain ξ=n, * A paper given at the Second All-Union Conference on the Problems of Biomechanics (Riga, April, 1979). 703 where n=0, ±1, ±2... Since for there to be a stationary-state cutting regime, i.e., cutting at a constant, predetermined rate, it is necessary, in order that ξ≤1 [2], that there be a unique solution for ξ=n=1 that can be determined from expression (1) using the transition condition when ξ→1: Vmax = AωK0. (2) The maximum cutting rate is proportional to the amplitude and the frequency of the ultrasonic vibrations and does not depend on the biological properties of the biotissue. It is determined solely by acoustic parameters and the force of resistance of the biotissue: Fx=f0. The theoretical assumptions and empirical relationships (1) and (2) were experimentally verified on the laboratory setup shown diagrammatically in Fig. 2. The setup has a base 1 that can be leveled with the aid of adjustment screws 2 and a level 3. A guide 4 is mounted on the base 1 along which a carriage 5 runs. The acoustic unit 6 with the cutting instrument 7 is attached to the carriage. The carriage 5 in put into motion by the action of weights 8 suspended from a cord 9 passing over a pulley 10. A specimen of biotissue 11 is affixed using clamps 12 to a stage 13. Adjusting screws 14 are used to position the specimen 11 along the axis of the instrument 7 during the cutting process. In order to produce a signal proportional to the path covered by the carriage 5 with the instrument 7 during the cutting process, a bridge circuit (Fig. 3) was used. A potentiometer R1 is hooked into one arm of the bridge and the contact is firmly connected to the carriage 5; a variable resistance R2 is hooked into a another arm to balance the bridge prior to the experiment. An N-327 recorder is connected to points a and b (cf. Fig. 3) of the diagonal of the bridge and tracks the electrical signal in time as the carriage 5 with instrument 7 moves along the track. The path covered by the carriage 5 and its rate are determined from the trace recorded on the chart paper. A URSK-7N device [3] is used as the source of ultrasonic vibrations. The experimental procedure used to measure the dependence of the rate of ultrasonic cutting on the nature of the soft biotissue, the cutting force, the amplitude and frequency of the ultrasonic vibrations, and the inertial properties of the instrument was as follows. Before the experiment began, the carriage 5 with the acoustic unit 6 and the instrument 7 was placed in the starting position and held there by a detainer 15. In the Fig. 1. Fig. 2. Fig. 3 Fig. 1. Rate of ultrasonic cutting of soft biotissue as a function of the force exerted by the surgeon Fx: 1, 2 — theoretical and experimental curves. Force of resistance of the biotissue f0=1.8 kg; f=26.5 kHz; A=20 µm; K0=0.04. Fig. 2. Laboratory setup. For explanation, see text. Fig. 3. Bridge circuit. For explanation, see text. 704 starting position the blade of instrument 7 just touches a specimen of biotissue 10x30x70 mm in size. The biotissue is sectioned from muscle of the hind leg of a rabbit. From cord 9 there is suspended a weight 8 simulating the cutting force exerted by the surgeon on the ultrasonic instrument. Then the bridge was balanced and the amplitude and frequency of the ultrasonic vibrations were checked. The amplitude was measured by an optical method using an MG horizontal microscope (resolution 2 µm). The frequency was checked using a CHZ-33 frequency meter. The cutting process began after the carriage 5 was released from the detaining device 15. In the first series of experiments we determined the dependence of the cutting rate on the cutting force. We measured the average rate of motion of the instrument in the biotissue as a function of the mass of the weights simulating the cutting force applied by the surgeon to the cutting instrument. The mass of the weights varied from 0.1 to 1.5 kg, which approximates the range of forces used by a surgeon using the ultrasonic method on the soft biotissue of the wrist. The experimental results are presented in Fig. 1. The theoretical curve 1 reflecting the functional dependence (1) for the following values of the acoustic parameters is plotted in the same coordinates: A=20 µm; f=26.5 kHz; K0=0.04. The force of resistance of the biotissue f0=1.8 kg was also measured experimentally. Comparing curves 1 and 2 it is not difficult to see that they are identical in shape. The experimentally determined value of the maximum cutting rate is approximately the same as the theoretical value V=70 mm/s. The difference between the theoretical values and the measured values does not exceed 20%, evidence of satisfactory agreement between the theoretical and experimental results. The experimental curve 2 differs from the theoretical curve 1 (cf. Fig. 1) by more than the limits of error at cutting forces less than 0.2 kg. We believe this may be due to forces of friction in the laboratory setup that were not compensated for and the force of friction of the instrument against the surface of the biotissue, which were not included in the theoretical calculations. This force was measured experimentally and is equal to 15±5 g. At low cutting force values it begins to play an increasingly great role in the cutting process. Experimental confirmation of the analytical calculations provides evidence that the theoretical approach chosen for calculating the rate of ultrasonic separation of soft biotissues was correct. This allows us to use expressions (1) and (2) both for determining the optimal parameters for the cutting process and for determining its maximum efficiency, which theory predicts is reached when the cutting force is equal to the force of resistance of the biotissue: Fx=f0=1.8 kg. In the second series of experiments we determined the influence of the amplitude of the ultrasonic vibration of the cutting blade on the cutting rate in soft biotissue. By varying the biasing current of the magnetostrictor we allowed the amplitude of the ultrasonic vibrations to vary between limits of 10 and 40 µm. Curve 1 in Fig. 4 is plotted from the theoretically derived equation (2) which establishes a linear relationship between the cutting rate and the amplitude of the ultrasonic vibrations. Line 2 is a best-fit approximation of the experimental data made by the least-squares method. From Fig. 4 it can be seen that when the amplitude increases, for example by a factor of three, the maximum rate that can be achieved also increases by a factor of three. The experimentally determined value for the amplitude is somewhat smaller. 705 Fig. 4. Fig. 5 Fig. 4. Maximum speed for cutting soft biotissue as a function of the amplitude of the ultrasonic vibrations of the cutting part of the instrument: 1, 2 — theoretical and experimental curves. Fig. 5. Family of curves describing the rate of ultrasonic cutting as a function of the cutting force for various biotissues: 1 — fatty, 2 — muscle, 3 — skin. In view of the satisfactory agreement between the theoretical and the experimental results, equation (2) can be used as a theoretical guide in making engineering calculations to determine the maximum efficiency of the cutting process. In addition, it shows that cutting efficiency can be improved by increasing the amplitude of the vibrations of the cutting blade of the instrument. The efficiency of the process can similarly be improved by increasing the frequency of the ultrasonic vibrations and by improving the inertial properties of the tool as defined by the ratio of the mass of the vibrating part of the instrument to the total mass of the acoustic unit together with the cutting instrument. Theoretically, the best should be a value close to unity (K0=1), at which there are minimal losses of acoustic energy. This ratio can be viewed as a criterion for the effectiveness of the transfer of the ultrasonic energy of the cutting edge of the instrument which should be taken as a goal in designing ultrasonic instruments and in improving the efficiency of the cutting process. In the third series of experiments we studied the dependence of the rate of ultrasonic cutting on the type of biotissue. These experiments were conducted because under actual clinical conditions a variety of biotissue are separated — first skin, then fatty tissue and muscle. A family of theoretical curves for various types of biotissue is shown in Fig. 5 that reflects the dependence of the cutting rate on the force applied by the surgeon to the cutting instrument. Curve 1 was plotted for fatty tissue, curve 2 for muscle, and curve 3 for skin. From clinical practice it is known that if the surgeon applies a constant cutting force f0 the cutting rate changes on going from one type of tissue to another. There is a theoretical explanation for this phenomenon. When the instrument passes from skin tissue into the fatty layer, there should be a jump in rate along the vertical axis ab from curve 3 for skin tissue to curve 1 for fatty tissue (cf. Fig. 5). Later, when the instrument goes from fatty tissue into muscle, the cutting rate falls abruptly along the vertical axis bc from curve 1 to curve 2 for muscle. The cutting force is held constant while this is done. If, however, the surgeon attempts to maintain a constant cutting rate, ignoring the fact that the instrument is cutting different biotissues, he will have to 706 make a discontinuous change in the cutting force at the boundary between the two types of tissue (points b, d, e Fig. 5). From graphs 1-3 in Fig. 5 it can be seen that the theoretical maximum cutting rate is the same for the different biotissues and is determined solely by the acoustic parameters of the ultrasonic cutting process: Vmax=AωK0. This rate can be achieved by applying a force to the cutting instrument equal to the force of resistance of the given type of biotissue. Experimentally measured maximum rates of ultrasonic cutting for skin, fatty tissue and muscle proved to be approximately the same and equal to 64±5 mm/s (A=20 µm, f=26.5 s kHz, K0=0.04). This cutting rate was reached with different cutting forces, equal respectively to f0 =3.2 kg, f m f0 =0.16 kg, f0 =1.8 kg. The fact that the maximum cutting rates are the same for cutting the different types of biotissue is evidence that this rate does not depend on the mechanical properties of the biotissue and that theoretically derived equation (2) is correct. The phenomenon described here, as suggested by theory, must hold for any biological tissues in which the force of resistance to cutting is much less than the amplitude 2 value of the force of the ultrasonic vibrations, i.e., Fx REFERENCES 1. Polyakov V. A., Nikolaev, G. A., Loshchilov V. I., Petrov V. I. Ultrasonic Welding of Bones and Cutting of Biological Tissues. Moscow, 1973. 136 pp. 2. Nabibekov M. K., Plyushchenkov B. D., Sarkisov I. Yu. Investigation of the Process of Ultrasonic Cutting of Soft Biological Tissues. Mekhanika Kompozitnykh Materialov, 1980, No. 3, pp. 519-524. 3. Loshchilov V. I., Vedenkov V. G., Volkov S. M., Trofimov A. A. Ultrasonic Devices for Cutting and Welding Biological Tissues. In: Ultrasound in Surgery. Moscow, 1973, pp. 40-44. All-Union Scientific Research Institute Received 8 May 1979 Of Medical Instrument Building Institute of Applied Mathematics, USSR Academy of Sciences, Moscow Institute of Medical and Biological Problems USSR Ministry of Health, Moscow