Author
Submitted to the Department of Electrical Engineering and Computer Science in Partial Fulfillment of the Requirements for the Degree of
Master of Engineering in Electrical Engineering and Computer Science at the Massachusetts Institute of Technology
August 30, 2002
Copyright 2002, Sneha Thakkar. All rights reserved.
The author hereby grants to M.I.T. permission to reproduce and distribute publicly paper and electronic copies of this thesis and to grant others the right to do so.
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
I
JUL 30 2003
Departmentof Electrical Engineering and Computer Science, Aug 22, 2002
Certified by
_
Accepted by
Hugh M. Herr
Instructor, Harvard-MIT Division of Health Sciences and Technology
Thesis Supervisor
~ur C. Smith
Chairman, Department Committee on Graduate Theses
BARKER

by
Submitted to the
Department of Electrical Engineering and Computer Science
August 30, 2002
Submitted to the Department of Electrical Engineering and Computer Science in Partial Fulfillment of the Requirements for the Degree of
Master of Engineering in Electrical Engineering and Computer Science at the Massachusetts Institute of Technology
ABSTRACT
For trans-femoral amputees the energy expenditure required for ambulation is significantly greater than that required for non-amputated individuals. The Leg
Laboratory at MIT, in conjunction with Ossur, has developed an autoadaptive, electronic, magnetorheological (MR) prosthetic knee (Rheo) to address this problem. Unlike currently available prosthetic knee technologies that utilize hydraulic valves, the Rheo controls knee damping by adjusting magnetic field strength through the modulation of electromagnetic current. A study at Spaulding Rehabilitation Hospital with eight established unilateral trans-femoral amputees was conducted to test the hypothesis that
MR technology improves metabolic economy. The Rheo and the electronic, hydraulic based C-LEG were compared along three axes-metabolic cost, kinematics and kinetics, and muscle activity. A significant metabolic improvement using the Rheo was found, although evaluation of the speculated mechanisms for energy conservation was inconclusive. The results are encouraging in that the Rheo knee promises to enable unilateral trans-femoral amputees to lead more active lives.
2

To my parents, sisters, and buddy for their endless love.
Srini, you're like 74* and clear skiesperfect.
3

As this project and my career at MIT draw to an end, I think it only appropriate to stop and acknowledge the many people who have guided and supported me along the way.
First I would like to thank all the participants of this study for their time, and for giving me a glimpse into their world. And of course Professor Herr for giving me this project, pushing me to the limit, and having an enthusiasm that is contagious. I would also like to thank Ossur for funding this study and the close friends that I developed at the Gait Lab, especially Jen, for their unlimited patience, and without whom this study would have never gotten off the ground. Dr. Shal Gozani for his vision and faith. And then there are my friends, who are more appropriately labeled my second family. I cannot even begin to express what they have done for me and what they mean to me-they're the part of
Boston that I will miss the most.
I YS, jj \ Ar; , A;) NE.

TABLE O F FIG URES ................................................................................................................................ 7
LIST O F TABLES ........................................................................................................................................ 8
1 INTRODUCTION ...................................................................................................................................... 9
THE AMPUTATION, AMPUTEE, AND PROSTHESIS ..................................................................................... I I
S c .................................................................................................................................................
1 3
K n e e ...................................................................................................................................................
1 3
S h a n k .................................................................................................................................................
1 4
F .................................................................................................................................................... 1 5
GAIT CYCLE ............................................................................................................................................. 15
S ta n c e P h a s e ...................................................................................................................................... 1 6
S w in g P h a s e ....................................................................................................................................... 1 7
Variations Seen in Trans-femoral Amputees ..................................................................................... 18
11 EXPERIM ENTAL OVERVIEW .......................................................................................................... 20
C-LEG AND RHEO OVERVIEW ................................................................................................................. 20
HYPOTHESIS DEVELOPMENT .................................................................................................................... 21
H ......................................................................................................................................... 2 2
APPROACH AND DATA COLLECTION ........................................................................................................ 22
Kinematics and Kinetics Data Collection .......................................................................................... 24
Surface Electromyography Data 25
Oxygen Consumption ......................................................................................................................... 26
III M ETABO LIC REQUIREM ENTS ...................................................................................................... 28
M ETHODS ................................................................................................................................................ 29
D a ta C lu sterin g ................................................................................................................................. 2 9
D efining Steady State ......................................................................................................................... 30
Participating ........................................................................................................................ 30
M ethod ]: M inimizing Point-to-Point Variability ............................................................................ 31
M ethod 2: M inimizing Large-Scale Variability ................................................................................ 33
DISCUSSION ............................................................................................................................................. 35
IV K INEM ATICS AND KINETICS ........................................................................................................ 37
BACKGROUND
37
M ETHODS AND RESULTS .......................................................................................................................... 38
DISCUSSION ............................................................................................................................................. 40
V ELECTRO M YO G RAPH Y .................................................................................................................... 42
M ETHODs/RESULTS ................................................................................................................................. 42
DISCUSSION .............................................................................................................................................
46
VI CLO SING REM ARK S ......................................................................................................................... 48
FUTURE W ORK ........................................................................................................................................ 48
Time Constraints 48
Varying Gait Speed ............................................................................................................................ 49
Treadmill Walking ............................................................................................................................. 49

Qualitative Improvem ents ............................................................................ I 50
Accommodation Period 50
Other Approaches .............................................................................................................................. 50
VII R EFERENCES .................................................................................................................................... 52
APPEN DIX A - EM G ANALY SIS CO DE .............................................................................................. 55
6

Figure 1 H istoric Prosthesis.....................................................................................
Figure 2 Trans-femoral Amputee Prosthesis Components..................................................
Figure 3 Current prosthetic knee technologies................................................................
Figure 4 G ait C ycle Phases......................................................................................
Figure 5 Definitions of cycle, stride, and step length.........................................................
Figure 6 Knee flexion during a single gait cycle..............................................................
Figure 7 Three-dimensional view of a gait cycle..............................................................
Figure 8 Pictorial Knee Flexion/Extension.....................................................................
Figure 9 Graphical Illustration of Hypothesis..................................................................
Figure 10 Anatomical view of Flexors and Extensors studied...............................................
Figure 11 Metabolic Pathway Overview....................................................................... 28
Figure 12 Adenosine Tri-Phosphate............................................................................. 28
Figure 13 Steady State Identification and Comparison Method............................................. 31
Figure 14 Visual representation of Minimizing Large-Scale Variability .................................. 33
Figure 15 Example of embedded data creeping and multiple plateaus ................................... 35
Figure 16 Illustration of linear mapping between time and %gait cycle domains ....................... 38
Figure 17 Sample EMG Filtering Process..................................................................... 43
22
26
17
17
18
13
15
16
10
12

Table 1 The subjects' age, sex, and anthropometrical data..........................................................
23
Table 2 Session Two Temporal Subject's Knee Usage Information..............................................
27
Table 3 Metabolic Data Results: Minimizing Point-to-Point Variability Method...............................
32
Table 4 Statistical results of Metabolic Economy Testing.......................................................
32
Table 5 Metabolic Data: Minimizing Large-Scale Variability Method........................................
34
Table 6 Statistical results of Metabolic Economy Testing ......................................................
34
Table 7 R ange of norm al knee m otion ................................................................................
37
Table 8 Knee angle correlation comparing biological and affected knee. .....................................
39
Table 9 Paired Two Sample for Means t-Test on the Correlation Numbers...................................
40
Table 10 EMG Results for Semitendinosus...........................................................................
44
Table 11 EMG Results for Biceps Femoris.........................................................................45
Table 12 EMG Results for Rectus Femoris........................................................................
46

I
Extremity loss is a functionally, psychologically, and socially debilitating condition with a U.S. prevalence of approximately one million people. About 90% of all amputations involve the lower extremity from foot to femur with an annual U.S. incidence of
125,000. Of all amputees, trans-femoral amputees are the second largest group. The majority of lower extremity amputations are warranted as treatment for disease
most commonly diabetes mellitus type 1 (50-80%). As a consequence of this systemic etiology, patients undergoing one amputation are at significantly higher risk of undergoing a second, further undermining their functional status. Other causes of lower extremity limb loss include trauma (which may account for as much as one quarter of amputations), malignancy, infection, and congenital malformation. 29,30
Most patients undergoing lower extremity amputation require prosthetic training in an effort to restore as much functionality as possible. Most currently available lower limb prostheses are passive devices and require amputees to compensate with proximal and contralateral musculature. This is substantially more energy-intensive and unsafe.
Furthermore, compensation is especially challenging for trans-femoral amputees who retain significantly less balance and ambulatory function, and exceedingly difficult for bilateral amputees who often relinquish ambulatory function altogether. 29,30
Historically, the use of prostheses dates back to ancient civilizations where simple crutches or wooden leather cups were used. For practical reasons, the lower extremity

f-'RG A NAM fs) () 2\
A Ut, ADAP1!\'f
KNITITRDCTO prosthetic evolved into a type of modified crutch or peg to free the hands for functioning.
Over the next few centuries, variants of the peg leg theme took on the form of, for example, armor extensions for knights during battle and various cosmetic means of disguising disability.
Figure 1 Historic prostheses.
Left: image from 1865 during the Civil War. Center: drawing from the 16th century. Right: a German wood and rawhide prostheses.46'47
Fueled by the significant increase in lower limb amputees during World War II, more resources were devoted to the development of functional prostheses. It was during this time that the concept of the hinge knee was taken a step further through the implementation of hydraulics - the hydraulics were designed to provide a means for resistance during swing.
48
Today, with the improvement of electronics and digital information a new movement in lower limb prosthetics is underway. Two electronic knees currently available on the market are the Endolite Intelligent Prosthesis and the
Otto Bock C-leg (discussed in Chapter Two).
fr
ONOMY (jAl ANALYSIS 01 AN
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10

The fusion of increasing biomechanics understanding with advances in biomedical engineering promises to enhance functional restoration of lower extremity amputees. By developing cooperative prostheses using biomechanical gait models, balance, safety and self-image can all be improved and energy expenditure will likely be reduced.
Nevertheless, the translation from biomechanical principles and design to clinical benefit is often unpredictable, and biomedical devices are typically products of iterative design refinement. The Leg Laboratory at MIT, in conjunction with Ossur, is currently developing an auto-adaptive knee prosthesis which promises to improve ambulatory function for trans-femoral amputees. The purpose of this project is to serve this iterative refinement process by outlining the mechanics and energetics of ambulation, describing the consequent design of this auto-adaptive knee prosthesis and characterizing the clinical impact that this prosthesis has on the ambulatory function of trans-femoral amputees.
Particular emphasis will be placed on energetics and this project seeks to verify the hypothesis that the invocation of an auto-adaptive knee reduces energy expenditure during ambulation.
The Amputation, Amputee, and Prosthesis
Losing a limb can be a devastating experience, with emotional and social ramifications as well as the obvious physical loss. However, with an intact personal will, and in conjunction with technology and the care of seasoned practitioners, the amputee's functional status can be dramatically improved.
11

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LUtNOMY
6.M! AN,,\ IYSISU
AU
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KM I. i loN,
After amputation surgery, the healing process takes approximately two weeks. During this time it is imperative that the residual limb be exercised to avoid muscle contraction; the residual limb should also be massaged, bandaged, and fit with a temporary prosthesis to avoid peripheral edema-swelling due to accumulation of interstitial fluid. The
preparatory prosthesis is typically worn for a few weeks providing a limb stabilization period, thereby maximizing proper definitive prosthesis fitting and alignment-both critical for amputee comfort and effectiveness while walking.
The definitive prosthesis is a four-component system composed of a socket, knee, shank, and foot as seen in Figure 2 below. There are a variety of designs for each component that can be assembled to match the unique needs of the individual. Although an extensive overview is beyond the scope of this thesis, a brief overview is provided here for orientation.
SOCKET
LESAN
S INGLE-AXIS
KNEEE
N'
HYDRAULIC x
CRUSTACEAN
SHANK
FOOT-ANt.
SNK IMYLOflS.
SACH FOOT
: sIIAGL-AxiS FOOT
Figure 2Trans-femoral amputee prosthesis components. Components may be interchanged to fulfill the specific needs of the individual.
2 9
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.'\\AI YS~
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12
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Socket
The interface between the residual limb and the prosthesis is the socket. The most common method of holding the socket in place is to create a vacuum between the socket and the limb. Good socket design and fit will allow residual limb muscles to be efficiently utilized.
2 9
Knee
As mentioned previously, there are a variety of knee systems. In increasing order of complexity these include the single-axis constant friction (hinge) knee, the locking knee, the weight actuated knee, the polycentric knee, the pneumatic/hydraulic knee, and the electronic knee.
2 9 Most knees actually incorporate a combination of the above-mentioned features; e.g., the electronic C-LEG knee described in Chapter Two also uses hydraulics.
A brief overview of the various knee systems will be provided here.
Figure 3 Current prosthetic knee technologies. Pictured from left to right-single axis, lock knee, weight actuated, polycentric, hydraulic, and electronic knees.
49
Single axis knees behave like a door hinge. They lack stance control and therefore require more energy on the part of the amputee to ensure their safety during stance.
Furthermore, they behave optimally only at one speed. A locking knee is used for amputees who require greater stance stability than the single axis knee can provide. A lever or cable is pulled to lock the knee in place. This can be very dangerous if the knee
[NERGY I-CONOMY GAII ANALYSIS i \\ A I 1A1A1 VI PMA
KNI
13

is locked and the individual falls-the direction of the fall cannot be controlled.
Additionally, a pronounced limp results. Weight actuated, or safety knees, are single axis knees that swing freely when no weight is applied and lock when weight is put on the prosthesis. This is beneficial if the amputee is tired and steps with a flexed knee, as the knee will not buckle under him/her. However, stance flexion (described in the next section) is not possible. Polycentric knees mechanically allow multiple axes of rotation.
The length of the prosthetic shortens with each step aiding in preventing toe stubbing.
This knee is stable during stance, yet still allows easy flexion for swing. Multiple speeds can be achieved through the use of hydraulics. Pneumatic (air) and hydraulic (fluid) knees control knee flexion by movement through a piston, thereby allowing variable speeds. As such, more natural gait is seen. Electronic knees have the potential for mimicking natural gait more accurately than any purely mechanical system. Electronic knees can practically perform instantaneous changes in speed. Moreover, they can aid in controlling swing and stance stability. Amputees do not have to think about every step.
For the purposes of this study the electronic knee is of primary importance to us. 49
Shank
The shank provides the mechanical connection between the knee and foot. There are two types of shanks: exoskeleton and endoskeleton. Exoskeleton shanks are shaped like a leg with a hollow interior; accordingly, load is transferred through the walls. Endoskeleton shanks have central load-bearing tubes also called pylons. This second type of shank is used for more advanced knee systems, and in the study we conducted an endoskeleton shank was used for each subject.
29
H' '. '-H
14

Foot
There are a variety of foot systems, each providing different benefits and uses; for example, there are feet that are specific for running. The two categories of feet are articulated and unarticulated.
2 9 In our study, we used Flex-Foot's Allurion, articulated foot.
Gait Cycle
In order to further characterize the scope of this project it is necessary to have an understanding of "normal" gait. By normal it is meant that generalizations across race, age, sex, etc. have been made to allow for parameterization.
43
In this section we review the phases of a gait cycle focusing on one particular phase that will be of interest in formulating and proving our hypothesis. For ease of explanation we will discuss the gait cycle duration in terms of the right leg. Throughout this discussion refer to Figure 4.
T;IlAKK. iAN
Rght heel
Left toe- contact off
0%
Leoft heel
O
Rght toe-
Ocontact
50% ime, percent of cycle
Double Aie r Double L a
R. Stai P se G.
L ___
Chas.
a04- swiit in hs
Cycle (stride) duati
Time Dimensions at Walking Cycle
Figure 4 Gait Cycle Phases
2 ht Left heel toeoff
100%
Double
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The gait cycle, or stride (refer to Figure 5), consists of two phases-stance phase followed
by swing phase.
ke contact
IPhase contact wf ft. Stop. thr
.
L S~te ff Mrentha
CYCle longth
It
Figure 5 Definitions of cycle, stride, and step length.
2
Stance Phase
Stance phase begins as the right heel makes contact with the ground, heel strike, and ends when the right toe lifts off the ground, toe off. Moreover, the initiation and termination of stance are delimited by a period of double support, when both feet are on the ground.
During double support weight is shifted from one leg to another in preparation for swing.
Another important attribute of stance is knee flexion. As illustrated in Figure 6 and Figure
7, during the time interval from right heel contact (the knee being extended at this point) until the foot is flat, the right knee flexes slightly to a maximum angle of approximately fifteen degrees. The purpose of this stance flexion is to absorb some of the impact of heel strike and to aid in preventing large vertical gyrations of the center of mass as weight is shifted from one leg to another. After stance flexion the knee begins to extend, stance
extension, and then flexes again in preparation for the swing phase.2
N
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A ADAPNVE
PROS'n IC KNIE 16

\ .
....
Figure 6 Knee flexion during a single gait cycle.
2
Figure 7 Three-dimensional view of a gait cycle. Notice in particular the knee flexion as described in the text. 2
Swing Phase
The swing phase of the cycle commences when the right toe is no longer in contact with the ground and concludes with the second heel strike. As the right toe lifts, the knee continues to flex until it reaches a critical angle, after which it extends forward in preparation for heel strike. The angle to which the knee flexes must be great enough to avoid toe stubbing, yet small enough so that the knee has time to extend before heel strike. With the second heel strike at the conclusion of the swing phase, the gait cycle for the right leg is complete.2
THAKKAR FNIRG YC AP 'I I .ISOI- ANA oST'ET 17

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Variations Seen in Trans-femoral Amputees
Although it is difficult to concretely define what is "good" versus "poor" gait, one obvious important feature is gait symmetry. If gait is symmetrical it follows that:
1
Ts=t~ _T9 ds
1
T
SW = ge
-T d gc d(1.1)
1t = stance phase time
1, = swing phase time tgc = gait cycle time
1ds = double support time
What is often seen in unilateral amputees is the tendency to favor their unaffected side, resulting in asymmetrical gait. All of the subjects who participated in this study are unilateral amputees, as described in Chapter Two.
Another difference in lower limb amputee gait is revealed when examining the stance phase. As Figure 8 illustrates, there is often a diminution or complete absence of flexion during stance.
Figure 8 Pictorial Knee Flexion/Extension. The solid line represents biological norms. Dashed line represents affected side for a trans-femoral amputee.
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Throughout the remainder of this paper we will be discussing how two prosthetic knees,
Ossur/MIT's Rheo knee and Otto Bock's C-leg, compare in aiding ambulation of transfemoral amputees. We will focus on the performance differences during the late stance/pre-swing phase of each system.
19

The goal in the design and implementation of a prosthetic knee for trans-femoral amputees is to safely and efficiently enable "normal" gait. Difficulty arises in accurately describing "normal" because of the intrinsic interplay between biomechanics, physiology, and the environment. The complexity of the problem is compounded by requiring knowledge of the effects of stumbling, climbing stairs, sitting, etc when developing a model. With the introduction of microprocessors into the prosthetic knee many of the phases and obstacles described in Chapter One and here can be detected and compensated for by modifying intrinsic parameters like resistance.
C-LEG and Rheo Overview
The most advanced electronic knee available on the market today is the C-LEG.
Developed in Germany by Otto Bock Orthopedic Industry, it is recommended for amputees with moderate to higher functional level. When a subject is fitted with the knee a prosthetist uses software on a laptop to set various parameters such as maximum flexion angle, resistance, etc. As the patient walks, sensors on the C-leg record data such as knee angle, velocity, moment, and stance stability. This information is collected at a frequency of 50 Hz. The data is then passed on to a hydraulic system, thereby inducing appropriate adjustments-actuators adjust the positions of hydraulic valves to control knee damping. With this technology patients have been able to walk on slopes, down stairs, and on uneven surfaces for up to 30 hours, limited only by the lifespan of the knee's rechargeable lithium-ion battery.
14 15
The engineers at Ossur and MIT have sought to develop an electronic knee of their own.
Unlike the hydraulic system implemented in the C-LEG and other conventional prosthetic knees, the Rheo knee consists of parallel steel plates that slide past one another. The knee damping process is slowed when a magnetic field is applied

perpendicular to the plates by an electromagnet. Furthermore, a magnetorheological
(MR) fluid residing between the plates provides resistive torque. The knee collects sensor data like the C-LEG and is able to detect the various phases of the gait cycle.
Unlike the C-LEG however, the Rheo knee enables amputees to climb stairs and is autoadaptive. By auto-adaptive we mean that as the amputee walks the knee is able to detect and self calibrate its parameters to the individual's particular needs and desires. If adjustments need to be made, variables can be modified using software available on a handheld computer. The benefit of such a system is that unwanted variability introduced
by prosthetist technique can be avoided, while variability can be employed if desired.
Additionally, it usually takes a few visits with the prosthetist to get the parameters set properly because the prosthetist cannot anticipate all the obstacles the amputee will face once he leaves the office. Auto-adaptation expedites this process and provides the amputee with more comfort and confidence by refining variables in real time.6,26
In the rest of this chapter we will develop a hypothesis and describe the methodology employed to verify our hypothesis.
Hypothesis Development
Among the electronic knees currently available, the MIT knee is unique in that the knee resistance is automatically adjusted during the swing and stance phases for different speeds and enables stance flexion without buckling. Moreover, in conventional prosthetic knees the torque about the knee during late stance/early swing is proportional to angular velocity (F = b L-0). In contrast, torque in the MIT knee can be approximated at as constant (F= C). At low speeds only a slight difference may be apparent. However, with increasing speed the increasing angular velocity will cause the torque in the conventional knee system to dramatically increase, resulting in a substantial difference in torques between the two systems. Torque being proportional to force, and force to work, this suggests that the energy requirements will vary between the two different systems.
21

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Hypothesis
Due to differences in knee torque during the late stance/early swing phase, we hypothesize that there will be an energy savings during gait with the MIT knee over gait with a conventional prosthesis.
Exp Enrgy vs. Torque
As illustrated in Figure 9 we expect the difference in energy expenditure between the conventional knee and the MIT knee to be magnified with increasing speed.
Therefore, ideally, when testing our hypothesis, data should be collected for slow, normal, and fast speeds.
Tarque
(Q
Figure 9 Graphical Illustration of
Hypothesis
Approach and Data Collection
A study at the Gait Laboratory in Spaulding Rehabilitation Hospital was conducted to verify our hypothesis. A total of eight unilateral trans-femoral amputees, all well established, participated-five male, three female (Table 1). Study participants were between the ages of 25 and 52 with mean 41, body mass range of 53 and 110.8kg (mean
-79kg), and heights ranged from 165 to 196m (mean -178m).
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22

Table 1 The subjects' age, sex, and anthropometrical data
Subject
Label Sex Age
Rheo Rheo C-LEG C-LEG
Mass Height Mass Height
[yr] [kg] [i] [kg] [m]
JB
BE
DF
CH
GH
DO
JR
TO
Mean
SD
F
M
M
F
M
M
M
F
35
37
42
48
52
43
46
25
41.0
8.5
55.6
97.0
84.0
58.2
110.8
87.0
88.1
53.0
79.2
21.3
167
183
183
165
193
181
188
167
178.4
10.6
54.9
97.2
84.0
57.8
110.8
86.4
87.7
53.0
79.0
21.4
167
182
183
165
196
177
188
165.5
177.9
11.4
Conventional
Prosthesis
C-LEG
C-LEG
Maunch
Maunch low profile
C-LEG
C-LEG
Tae Len
Otto Bock Hydraulic
Subjects were asked to dedicate two sessions-the first to be fitted with both the Rheo and the C-LEG, and a subsequent visit to Spaulding where quantitative data was collected. Fitting for each amputee was conducted at Next Step Orthotics and
Prosthetics, Inc by a trained prosthetist. It was essential that the same prosthetist align each subject to decrease differences in alignment styles. During the fitting process the prosthetist set C-LEG parameters using a laptop computer by verbally communicating and visually inspecting the amputee's gait. Rheo parameters were set to their default parameters and the amputee was asked to walk, enabling the knee to auto-adapt to the individual. Any necessary adjustments were made at the time. Furthermore, all subjects used Flex-Foot's low profile, high-energy return Allurion foot for the duration of the study, per recommendation by the prosthetist.
Protocol approval to evaluate the biomechanical differences between the Rheo and C-
LEG during the second session was provided by the Spaulding Rehabilitation Hospital and Boston University School of Medicine institutional review board. Moreover, a
A'.
~<~Afl1H(
'L
~23

written informed consent was obtained from each participant before data collection commenced. At Spaulding, quantitative information was obtained primarily along three axes-kinematics and kinetics, muscular activity, and energy consumption.
Kinematics and Kinetics Data Collection
Looking at the kinematics and kinetics is important in understanding differences in metabolic needs for several reasons. By examining symmetry and biological realism, both the higher and lower level mechanisms of apparent energy differences can potentially be appreciated. Armed with this understanding of mechanism, refinements can be made to approach the goal of efficiently achieving biological gait.
Subjects were asked to stand and walk along a 10-meter platform with two embedded, staggered force plates from Advanced Mechanical Technology, Inc. (AMTI).
Two conditions were tested: (1) walking at a comfortable pace with the C-LEG and (2) walkig at a comfortable pace with the Rheo knee. The order of these testing conditions was randomized, and the subject was provided with ample time to acclimate to each knee before being tested. 10 complete gait strides for each condition provided lower extremity kinematics, kinetics, and EMG (discussed in the next section) data. Additionally, during each testing condition the subject was timed to ensure a fairly constant speed between trials and conditions. Analysis procedures used for pelvic and bilateral lower extremity joint motion and joint kinetics have been previously well described, but will briefly be described here.
2 3 2 4
To measure the three-dimensional position of the reflective markers at 120 frames per second, the VICON 512 System (an eight camera video-based motion analysis system) was used. The reflective markers were placed on various bony structures of the pelvis and lower extremities while walking-bilateral anterior superior iliac spines, lateral femoral condyles, lateral malleoli, forefeet, and heels. Additional markers were placed over the sacrum and rigidly attached to wands over the mid-femur and mid-shank. The embedded force plates measured motion analysis data and ground reaction forces simultaneously. The VICON 'Plug-In-Gait' application calculated joint torques using a
24

full-inverse dynamic model. The combination of inertial characteristics and mass of each lower extremity, derived linear and angular velocities and accelerations of each lower extremity segment, and ground reaction force and joint center position estimates formed the basis for power and joint torque calculations. Furthermore, these parameters were normalized over height and body weight. Additionally, foot contact times and distance measures were derived from temporal data such as stride length and velocities. These temporal data, in turn, were obtained from force plate and kinematics information. As previously mentioned, 10 trials per foot per condition were obtained for a total of 40 trials per subject. Refer to Chapter 3 for the results and analysis of this data.
Surface Electromyography Data
It has been previously shown that stress induces increased muscle activity. For example, when an individual is performing an energy intensive activity, such as running, we would expect to see an increase in muscle action compared to a relaxed walk. Therefore, by using surface electrodes to test muscle activity we can verify our hypothesis that energy expenditure is decreased when using the Rheo knee, as compared to the C-leg.
Surface electromyography (EMG) places electrodes on the surface of the skin over muscles of interest, thereby allowing amplification and visualization of motor unit depolarization. Activity of hip flexors and extensors were measured for both the affected and unaffected side. In particular, the rectus femoris (flexor), biceps femoris (extensor), and semintendinosus (extensor) were monitored (Figure 10).
"'4.
25

E
NHR(Y
F,,NOMY 6A I AN A I
VA IAXI
KN I IIXPRIMN
Muscles of Thigh
Anterior View Superficial Dissection
Muscles of Hip and Thigh
Posterior View Superficial Dissection
N IA!,
Semitendinosus muscle
Rectus femoris muscle
Biceps femoris muscle
Figure 10 Anatomical view of Flexors and Extensors studied. 50
A 16-channel EMG system developed by Motion Lab Systems was used to measure
EMG signal of the flexors and extensors (described above) for both the subject's affected and unaffected sides. Motion Lab pre-amplifier surface electrodes with a gain of 20 were placed over the muscles of interest on the unaffected side. Before applying electrodes to the affected side it was necessary to prepare the skin by light sanding and alcohol to maintain reasonable impedance. Nicolet Biomedical 20 mm diameter, one-meter length leads, stripped of their connectors were placed on the residual limb underneath the subject's socket. These were then connected to Motion Lab pre-amplifiers for fine-wire electrodes (gain of 20), which in turn interfaced with the EMG multi-channel system.
Data was collected at 3000 Hz throughout the subject's walking trials.
23
Oxygen Consumption
Oxidation of glucose has been shown to be directly proportional to the body's energy requirements.
2 Therefore, decreases in calculated oxygen consumption and carbon dioxide emission from measured expiratory volumes and concentrations are indicative of decreased energy needs. As a result, after completion of the gait analysis phase of the session, the subject's oxygen consumption was measured with both the Rheo and the C- leg.
26
TI AKKA ENERGY E(ONOMY GiAi
ANAtIYIviS AN V:)A!aiWVI Pi-m:T
KNi

A Cosmed K-4, lightweight telemetric system measured oxygen consumption for the duration of this portion of the study. Subjects breathed through a portable, non-rebreathing facemask which attached to an anatomic harness. These harnesses contained the portable unit that housed the oxygen and carbon dioxide analyzers, barometric sensors, sampling pump, transmitters, and electronics.
2 3 Each subject was first asked to rest for five minutes. Subjects were then instructed to walk at a constant, comfortable pace in an unobstructed hallway until steady state was achieved. During the walking portion amputees were timed to ensure that a constant pace was indeed being held. After walking with the first knee, subjects were asked to rest again. During this time knees were switched and the process repeated for the second knee. Data were collected throughout the experiments and averaged over thirty-second intervals to identify any twoand-a-half minute spans of steady state.
Refer to Table 2 for information on the order of conditions tested for each subject.
Subject
JB
BE
DF
CH
GH
DO
JR
TO
Table 2 Session Two Temporal Subject's Knee Usage Information.
Knee 1 Knee 2
C-LEG
Rheo
Rheo
Rheo
C-LEG
C-LEG
C-LEG
Rheo
Rheo
C-LEG
C-LEG
C-LEG
Rheo
Rheo
Rheo
C-LEG
Knee 1 Knee 2
C-LEG
Rheo
Rheo
Rheo
C-LEG
C-LEG
C-LEG
Rheo o %1' i. , s27

Catabolism of food sources provides us with the energy we need to function. As seen in Figure 11, the conversion of the energy stored in the chemical bonds of food to a usable form is complicated. In overview, complex molecules
(proteins, polysaccharides, and lipids) are hydrolyzed to their building blocks (amino acids, monosaccharides, and fatty acids), which in turn are converted to acetyl-CoA. Acetyl-CoA then enters the citric acid cycle, followed by oxidative phosphorylation. The final product of these metabolic pathways is adenosine tri-phosphate
Figure 11 Metabolic Pathway Overview
4
(ATP) which serves as a common energy source. For a more extensive overview refer to
Lipponcott's Biochemistry
4 .
The phosphate-
High-energy phosphate bonds
Adenine phosphate bonds seen in ATP are high-energy bonds
NH
2
2N that drive many reactions forward. For example, cleavage of ATP to adenosine di-phosphate,
N N o o. 0 0I
It o
0- O- o
0inorganic phosphate, and energy
(A TP ADP+P + energy) allows muscles to
HO HO contract. Lodish describes muscle physiology in
Ribose greater detail
3
. The muscles utilized when walking
Figure 12 Adenosine Triphosphate
4 are described in Chapter Five.
The oxidation of carbohydrates and fats to ATP can be either aerobic (Equation (3.1)), with oxygen, or anaerobic (Equation (3.2)), without oxygen. 1,
C
6
H
12
0
6
T+36ATP+42H20 (3.1)
C
6
H
12
0
6
-+ 2Lactate+
TP
-+
+C0
2
1
(3.2)

As seen in the above equations, anaerobic oxidation of glucose is much less efficient in
ATP production than aerobic oxidation. Therefore, during exercising the body will use aerobic oxidation-resorting to anaerobic only when the need for ATP outweighs the availability of oxygen, occurring at more strenuous work levels. Because subjects in this study were asked to walk at a comfortable pace, we can assume that oxidation of glucose was strictly aerobic. Under this assumption Equation (3.1) illustrates that oxygen consumption is linearly proportional to ATP production (energy usage).
Methods
As mentioned in Chapter Two, to test the hypothesis that MR-based technology is more energy efficient than hydraulic systems, an open spirometry system was used, and the metabolic data for each subject was reported as oxygen consumption (ml/min) time points averaged over 30second intervals. Two major issues arise in analyzing this data:
(1) data clustering (2) defining steady state. Two analysis methods were employed to try and correct for these concerns, each with its own benefits and flaws.
Data Clustering
The use of clustered data protocols is often seen in clinical situations. A cluster is defined as data that cannot be viewed as independent because of strong intra-correlation.
The need to cluster data is often seen when patients are stratified by physician for example. Subjects treated by the same physician would be considered a cluster because the physician's treatment nuances may influence the outcome. Donner and Kelly, as well as Wears, thoroughly outline this problem and describe several methods that can be used to account for clustering. Typical methods used include those based on Mantel-Haenszel,
Woolf, ratio estimator, robust variance GEE, and multiple logistic regression procedures.
Although necessary, the effect of cluster randomization is to increase standard errors and hence widen confidence intervals. The result is a reduced sample size and a loss of power. This effect is magnified by fewer, but larger clusters.
29

In this study the unit of analysis is obvious-the subject. However, the same analysis issues arises here as with the physician randomization example because multiple sample points were taken for each subject. As suggested by Wears, because of the small sample size, a simple averaging method (comparing patient mean values) was employed. Such an approach allows comparisons using standard statistical methods. This mean analysis method was used to identify statistical differences in all three dimensions we looked atmuscle activity, kinematics & kinetics, and metabolic economy. The primary pitfall of this analysis technique is that it makes little use of individual measurements. To use more sophisticated statistical methods an increase in trans-femoral amputee participation is needed.
31 45
Defining Steady State
One difficulty in analyzing the oxygen consumption data is to concretely define steady state. In general, steady state is reached shortly after exercise commences at a submaximal work load. During this time, tissue energy demands are met by oxygen delivery and various parameters of physiologic work load plateau.' Ideally, these plateaus would be completely flat, with zero variance. Practically, this is not the case, and an appropriate method for handling this variability is necessary. The two methods described below differ mainly in this respect-one looks at overall trends while the other uses a more restricted view.
Participating Subjects
In both the methods described below, only seven of the eight subjects' metabolic data were used. Subject D.O. is a knee articulate with a very long residual limb.
Modifications to the Rheo are necessary to be able to handle the clearance requirements for such an amputee. Consequently, D.O. experienced toe stubbing with increased walking times-inhibiting him from achieving steady state during the oxygen consumption aspect of this study.
~ ~~~ ~ ~ ~
30

Method 1: Minimizing Point-to-Point Variability
Figure 13 illustrates the method for finding the minimum point-to-point variability.
The first step was to extract "steady state" data from each subject's walking trial with each knee. In this method, steady state was defined as 2.5 minutes of walking (five consecutive 30-second samples) where the percent difference between consecutive readings was less than 5%. These five consecutive 02 consumption values were then averaged and normalized over subject mass and velocity. These results are reported in
Table 3.
Step Identify 2.5 minute subset that best
1 meets steady state definition.
Rest i a) xX
Xi
0
) x 0+e
Xi (j+3)
0
+
4
)
Step Compute average Oxygen consumption over the identified 2.5
2 minute (five sample) interval.
Xi-5
X i(j) ±Xi(j+
1
) +Xi(j+
2
) + Xi(j+
3
) +Xi(j+
4
)
\Y /i n)
-- (k) + Yi(k+1) + Yi(k+2) + Yi(k+3) + Yi(k+4)
Yi 5 MMi n)
3 Compute 02 Cost by normalizing for subject mass and velocity.
Define
Q to be the 02 Cost for subject i using knee x, in m
X
It follows that:
-2X , and =(Y-
Yi2
--
Syi
2
----
Yin
R t 11 yj (k)
(k+2) yi (k+3) yj (k+- ) yi(k+4) where v, is the velocity of subject i in min and mL. is the mass of subject i in kg.
Step 4. Compare the 02 Costs of each knee using a t-test.
-
02 Cost for Knee X
02 Cost for Knee Y
1 Qy5
2
Q -17 Q
Qx,'22 x- 7Q x
Figure 13 - Steady State identification and comparison method
A paired two sample for means student t-Test was run on the 02 cost for each amputee under each condition. Table 4 summarizes these results.
E
. 0kN k)MY 1.
G
A II
A
, ,
Y
I
1
4
KNE31
1T11,KK

Table 3 Metabolic Data Results: Minimizing Point-to-Point Variability Method. 02 cost for the Rheo and
C-LEG were used in a t-Test.
Rheo C-LEG
ID Mass Velocity kg M/s
02 ml/min
02 cost Mass Velocity ml/kg m kg m/s
02 02 cost ml/min ml/kg-m
JB
BE
DF
CH
55.6
97
84
58.2
GH 110.8
JR
TO
88.1
53
Mean 78.1
STD 22.7
1.087
1.068
1.075
1.147
0.751
0.894
1.111
1.019
0.143
658.507
1511.712
1401.876
1316.432
1525.713
1831.571
1038.635
1326.35
379.462
0.182
0.243
0.259
0.329
0.306
0.387
0.294
0.286
0.069
54.9
97.2
84
57.8
110.8
87.7
53
77.9143
22.8807
1.103
1.055
1.077
1.097
0.714
0.84
1.125
1.001
0.159
848.882
1460.872
1471.215
1277.721
1521.542
1760.784
1062.228
1343.32
306.594
0.234
0.237
0.271
0.336
0.320
0.398
0.297
0.299
0.059
Table 4 Statistical results of Metabolic Economy Testing comparing subject 02 cost Table 3 when walking with the Rheo versus the C-LEG.
Rheo 02 Cost C-LEG 02 Cost i
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
Df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
0.285567648
0.004337847
7
0.963295831
0
6
-1.960921622
0.048785207
1.943180905
0.097570414
2.446913641
0.299168788
0.00342553
7
U
32

Method 2: Minimizing Large-Scale Variability
The goal of the method for minimizing large-scale variability was to look for plateaus in subject data and define these to be steady state for the particular subject. Figure 14 is a graphical representation of the oxygen consumption during a portion of metabolic testing.
Portion of Raw Oxygen
1800 -Consumption
1600e 1400 -
. 1200
E .
1000 -
1200 -Plateau
800 o 600 o 400
200 -
0
0 rest
5 10
Steady State
1
15 20
Time (1=30s)
1
25
Outlier!
rest
30 35 40
Figure 114 Visual representation of Minimizing Large-Scale Variability.
From t =0 to t =10 (each data point a 30s average) the subject is in a rest phaseapparent from the low oxygen consumption level. The subject's oxygen level then begins to ramp up as the exercise period commences. It is easy to see in Figure
II by visual inspection that the subject's oxygen consumption data has reached a plateau during the exercise period between t = 13 to t = 23, and is therefore in steady state. However, at t = 17 there is an outlier which could have been caused by an abrupt turn, or statistical noise of other sorts. However, it is visually obvious that the two plateaus are in fact a continuous plateau with added noise. Since the goal is to find a representative value of
02 consumption during the steady-state exercise period, erroneous outliers greater than a standard deviation above or below the mean were thrown out of the calculation. As in the previous method, the mean values for seven subjects were compared on condition (C-
LEG versus Rheo). Table 5 and Table 6 illustrate these results.
33
I IA KKAR NE
YE -i
M
A
01 \- MAAPi, vE PNosf'
ICi

Table 5 Metabolic Data: Minimizing Large-Scale Variability Method. were used in a t-Test.
02 cost for the Rheo and C-LEG
Rheo C-LEG
ID Mass Velocity kg M/s
02 ml/min
02 cost Mass Velocity ml/kg-m kg M/s
02 02 cost ml/min ml/kg'm
JB
BE
55.6
97
DF 84
CH 58.2
GH 110.8
JR
TO
88.1
53
Mean 78.1
STD 22.7
1.087
1.068
1.075
1.147
0.751
708.92
1515.7
0.19548108
0.243853657
54.9
97.2
1405.67
1858.71
1067.08
0.259382023
1334.53 0.333124429 57.8
1524.44 0.305275971 110.8
0.393170782
0.301981755
84
87.7
53
1.103
1.055
1.077
1.097
0.714
0.84
1.125
845.76 0.232854541
1460.22 0.237367381
1485.1
1269.78
0.27371664
0.33387763
1485.86 0.312976265
1758.78 0.398033021
0.894
1.111 1068.79 0.298726588
1.019 1345.007143 0.290324243 77.9143
0.143
1.001 1339.184 0.298221724
367.6191258 0.064395756 22.8807 0.159 304.1143 0.057775728
T
Table 6 Statistical results of Metabolic Economy Testing comparing subject 02 cost Table 5 when walking with the Rheo versus the C-LEG.
Rheo 02 Cost C-LEG 02 Cost
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference df t Stat
P(T<=t) one-tail t Critical one-tail
P(T<=t) two-tail
0.2891
0.0043
7
0.9765
0
6
-1.6939
0.0706
1.9432
0.1412
0.2990
0.0034
7 t Critical two-tail 2.4469
34

EN 1,R " Y ktN NOY
G iA 1 ANA
I Y 1:AN A: :'( I'II A
I
K
Discussion
Both the analysis methods used have benefits and improvements that can be made. The first method (minimizing point-to-point variability) provides a tight boundary that is successful when your data is evenly distributed about the mean. However, it is extremely vulnerable to creeping illustrated in Figure 15. Although point-to-point differences may be minimal, the overall trend is clearly diminishing over the span identified and should not be considered steady state. Moreover, if there are multiple plateaus there is no convenient way of incorporating them. The
9 Data Creeping and Multiple Plateau Example second method of minimizing large-scale variability is more l 900
E 800
700
0 600
E
S400
robust in this respect because it is designed to look at tendencies. general
However a problematic aspect of a 200
100
0 0
0 10 20 30
Time Sample (1 unit= 30 sec)
40 50 method two is that Figure 15 - Example of embedded data creeping and multiple plateaus intuitively we think of steady state as a span of continuous time. By throwing out outliers, this conception is challenged. Even with these minor flaws both methods have been previously used.
Despite the inherent differences in the point-to-point and large-scale techniques, both produce p-values, for the one-tailed test, between 0.05 and 0.1 (90-95% significant difference between the means) as described in the previous section. Although to be statistically significant a p-value of less than 0.05 is necessary31-45, the results are strongly indicative of an increased metabolic benefit using the Rheo knee versus using the C-LEG, therefore supporting our hypothesis. It is typical for studies such as this to have small sample sizes because of the necessary restrictive selection criteria making it difficult to
35
TIIA K KAR ENIRG kNO
GA\AALYSIS01
A,,- AtiOADAP
IVE PROSTMI"TI
KNEII'

get much power. As a result, the literature often reports p-values upwards of 0.05, as high as 0.1--within our range of significance.
However, there are several things that can be done to more clearly demonstrate the significance seen in improved 02 cost using MR versus hydraulic technology. For example, the adjustments to the Rheo should be made to allow unhindered ambulation over an extended period of time by Subject D.O., so that he would be able to participate in this portion of the study. Adding Subject D.O. would statistically provide a seventh degree of freedom, thereby increasing the study's power.
Increasing the accommodation period is also likely to increase significance. Looking at
Table 3in the Results section of this chapter, Subject BE is the only subject who showed an increase in using the Rheo knee (point-to-point method). This subject said that it was a confidence and comfort difference for him. Being a seasoned C-LEG user B.E. felt that a fair comparison could only be achieved with more extensive usage of the Rheo; this affect has also been previously documented.'16'
7 Therefore, with a longer accommodation period we would expect the differential cost for all subjects to increase in favor of MR technology.
It may also be beneficial to look at amputees' respiratory quotient (RQ) and respiratory exchange ratio (RER). RQ values are taken at rest and are equivalent to the ratio of carbon dioxide production to oxygen consumption. This value could be used to ensure that subject's are adequately resting in between walking periods. The RER is calculated the same way as RQ, but during exercise-a RER greater than 0.9 indicates anaerobic activity. Therefore this measure could be used to guarantee the linear relationship between oxygen and ATP on which our analysis is based.
The results of the metabolic economy portion of this study are promising and relatively significant. Ambulation is markedly more energy intensive for trans-femoral amputees than for individuals without deficits. Therefore, means to decrease this (such as MR technology) enable patient's to lead more active lives.
36

As described in Chapters Two and Three we hypothesized and showed that the use of
MR technology by trans-femoral amputees reduces energy expenditure during walking.
In this chapter and the next we look to explain the mechanism for this result. Two plausible approaches are to look for biological realism and gait symmetry when using one knee versus the other. Unfortunately, biological realism could not be tested in this study because it requires comparing subjects to individuals with normal gait patterns who are similar in height, weight, age, sex, and activity level. However, symmetry can be measured by contrasting data from the subject's biological leg to the action of the residual limb and the prosthetic. In this analysis we focus on knee angle symmetry.
Background
As described in Chapter One, the knee angle goes through periods of varying degrees of flexion (between 0' and 70') throughout the course of the gait cycle. The dynamics of flexion and extension vacillates within a narrow band that is dependent on walking speed, marker placement, and individual differences. For example, according to Perry, increased walking speeds can lead to a greater degree of flexion during the loading phase.
Table 7 relates the range of normal knee motion to percent gait cycle.
Table 7 Range of normal knee motion. Adapted from Perry.
Knee Motion
Motion
Flexion to 18'
Extension to 5*
Flexion to 65*
Extension to 2*
Timing
0-15% Gait Cycle
15-40% Gait Cycle
40-70% Gait Cycle
70-97% Gait Cycle

Methods and Results
The knee angle data reported by the Vicon system were sample points taken at 120Hz.
The beginning and end of the gait cycle for each trial was calculated in the standard way-from time values of first heel strike to second heel strike of the same foot.
These results were in units of seconds and therefore needed to be converted to percent gait cycle to allow for averaging and direct comparison. The mapping was done using a weighted linear approximation between adjacent points for a given percentage as described by
Equation (3.3).
Y =(Y
2
- Y1)x+ y, -(y
2
-Y
1
)x, (3.3)
This approximation method is highly accurate for smooth data such as this. Once each inl
(a
T rial
S.aw
D.ata.
iologi..l aid.)
5i.1.
(a
TS"iN
1 pP- iooi a id.)
Data
U
40
Mapping between Time and % GC
-
+I+
0 20 40 00 S0 100 120 140 1 60
Figure 12 Illustration of linear mapping between time and %gait cycle domains.
trial was transformed from the time domain to percent gait cycle, the ten trials for a given subject, condition (Rheo/C-LEG), and leg (affected/biological) were averaged.
The subsequent four averaged trials per amputee were representative of knee angle data collected during the gait analysis portion of the study.' A correlation (Equation (3.4)) was then run between biological and affected knees for a given condition.
1 Refer to Appendix A for a graphical visualization of the averaged trials for each subject.
FNIKRG\ ENANOMY
GAI
ANALYSIS
0i
ANA
M
DAP ]V PROSIHITKA
KNIK.
38

Px'y cov(X, Y)
(T=
2 = cu = i=1
((3))2
CY y IY ni=1
-Y
A correlation value of 1 indicates complete correlation, 0 means no correlation, and -1 represents anti-correlation. The results of the Rheo and C-LEG correlation between biological and affected knees are summarized in
Table 8.
Table 8 Knee angle correlation comparing biological and affected knees.
Subject Rheo Correlation C-LEG Correlation
GH
DO
JR
TO
JB
BE
DF
CH
0.871779935
0.851331686
0.913320099
0.59809563
0.970559878
0.896177697
0.379242514
0.75860156
0.890476552
0.825834625
0.872998264
0.667569082
0.972520287
0.923541087
0.443223346
0.763815846
A paired two sample for means student t-Test was then conducted. Table 9 outlines the results of this method.
39

Table 9 Paired Two Sample for Means t-Test on the Correlation Numbers in
Table 8
Rheo Correlation C-LEG Correlation
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference df t Stat
P(T<=t) one-tail t Critical one-tail
P(T<=t) two-tail t Critical two-tail
0.7798886
0.0393214
8
0.9887295
0
7
-1.103429
0.1531617
1.8945775
0.3063234
2.3646226
0.7949974
0.0293063
8
Discussion
The results of the t-Test were inconclusive with p-values substantially larger than 0.05.
Although the differences in means for biological and affected knee angle trajectory correlations seems to favor the C-LEG' this statistic has a 70% chance of being completely random. There are several possible etiologies for the inconclusiveness of these results. As previously mentioned, five of the eight subjects were seasoned C-LEG users-only one of whom (Subject D.F.) was equally trained on both knees. Subject D.F.
showed an improvement using the Rheo (correlation= 0.91) versus the C-LEG
(correlation
=
0.87). This again indicates that a longer accommodation period is
In this case a higher mean indicates a greater correlation between affected and biological knee angle trajectories-0 meaning no correlation and 1 representing complete correlation.
1"d iA)P;1TPo;:f~ m
40

required to eliminate the bias in favor of the C-LEG. It is also interesting to note Subject
DO's results. As mentioned in Chapter Three, difficulties in achieving a reasonable gait for DO were insurmountable at the time of 02 consumption testing, but manageable for the short walking distances required for the gait analysis. However, it was apparent with a lack of optimal adjustments there was a deteriation in Rheo functionality; yet there remains only a small difference in correlation coefficients with the two knees. This suggests that with proper adjustments a reversal of favor may be seen.
In addition to knee angle symmetry, symmetry in muscle activity and ground vector reaction forces should be sought. With these three units of measure a regression could be run and the coefficient of multiple correlation, CMC, could be compared.
5 Equation 3.5 describes the CMC.
R= I-
2 T i1
2
I
Yj
_y)
-.
Y )
= 1 (2T - 1)
2
Yi, = tth time point ofjth waveform
Y = average at time t of waveforms 1 and 2
Y = mean of all time points in waveforms 1 and 2
(3.5)
Psw ':m 'v K41

Skeletal muscle is composed of muscle fibers, which in turn are composed of muscle filaments. The basic unit of the muscle filament is the sarcomere. When an action potential is transmitted down a peripheral nerve fiber, the motor end plate is depolarized and a cascade of biological events are triggered, culminating in actin and myosin conformation changes that serve to contract the sarcomere, and hence the muscle fiber
(using ATP in the process). Under increased stress, more action potentials are fired thereby recruiting more muscle fibers to contract. EMG measures the activity of these motor units and can be used as an analysis tool for determining the cost/benefit of ambulation with various prosthetic knees'.
Hip musculature function varies throughout the gait cycle. During stance, stability is the primary concern, while during swing limb control is the primary focus. The semitendinosus and biceps femoris (hip extensors) typically begin action in mid-swing, reaching a maximum intensity during terminal swing. After peaking, action quickly declines and remains off through the remainder of the gait cycle. The adductor longus is the first muscle to begin hip flexion during terminal swing, completing in initial swing.
Additionally, the rectus femoris has a brief period of flexor action during pre-swing and initial swing. The electrical activities of the semitendinosus, biceps femoris, and rectus femoris were measured in this study.'
Methods/Results
As mentioned in Chapter Two, hip flexor (rectus femoris) and extensor (biceps femoris and semitendinosus) data were collected at 3000Hz during the walking trials of the gait analysis sub-session. For each subject, condition, and affected side, raw EMG signal from when the knee begins to flex in late stance to peak flexion angle during swing was
'Lower EMG values at a particular work level indicate that fewer muscle fibers are necessary to accomplish the task--decreased amputee effort.

1,Ni
R;Y
F'ItoN\tm Y
GAi A iY S!U
AN Ao; AAfif
M extracted. The raw data was then taken into Matlabl where it was full wave rectified and centered about the mean to avoid positive and negative cancellation during further processing. Rectification involves taking the absolute value of all mean-centered negative signals. Rectified data was then passed through a Chebyshev filter to remove high frequency noise. The Chebyshev filter was performed with order 8, a ripple of 0.5 and a cut-off of 0.025. This yielded a cutoff frequency of 37.5 Hz. Figure 17 illustrates this process.
Rectus Femoris - raw data
.
.
.
[.
0
0
0.02
0.015-
E
0.01
0.005
0
0
0 200 400 600 800 1000 1200
Rectus Fsample- rectified
0.04
0.03
.. ... ... .... .. ... ....
0.02
0.01
..
-.. .........
-
. ..
-..
. . . ..-. . . . . .. . . . .
1400
-..
.
.
. ..
1600 1800
.. ... ... ..-
.
2000
-
200
-
0.1
400
-
600
0.2
800 1000 1200
Rectus F!TpI6 filtered
-- -
0.3
sample
0.4
-- -_
1400
0.5
1600
0.6
1800
_
2000
0.7
Figure 137 Sample EMG Filtering Process
The minimum, maximum, and mean values were then computed. A grand average per muscle per subject was calculated and normalized by subject mass and cadence.
Consequently, a paired two sample for means student t-Test was run on the above parameters comparing C-LEG and Rheo-results are shown in the tables below.
Matlab code was adapted from that written by Andreas Hofman in the MIT Leg Laboratory
F GNv; E
ONOMY
Am ANALYSIN ()I N ArAIAi
N).
PWSn KNEl
43

Table 10 EMG Results for Semitendinosus
Mean Maximum Minimum
Rheo C-LEG Rheo C-LEG Rheo C-LEG
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean
Difference df t Stat
P(T<=t) one-tail t Critical one-tail
P(T<=t) two-tail t Critical two-tail
5.38E-06 6.91E-06 1.72E-05 1.66E-05 -4.5E-07 -2.3E-07
4.03E-11 6.16E-11 4.47E-10 2.79E-10 4.04E-13 2.69E-14
6
0.87
6 6
0.901208
6 6
0.345023
0
5
-0.97
0.19
2.02
0.38
2.57
0
5
0.156874
0.440741
2.015049
0.881482
2.570578
0
5
0.86362
0.213635
2.015049
0.427271
2.570578
44

Table 11 EMG Results for Biceps Femoris
Mean Maximum Minimum
Rheo C-LEG Rheo C-LEG Rheo C-LEG
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean
Difference df t Stat
P(T<=t) one-tail t Critical one-tail
P(T<=t) two-tail t Critical two-tail
1.05E-06 6.13E-07 3.83E-06 1.69E-06 -2.2E-07 -3.6E-08
1.97E-12 2.01E-13 :2.72E-11 3.43E-12 1.28E-13 3.26E-15
6 6 6
0.65
6
0.54
6
0.2
0
5
0.93
0.2
2.02
0.4
2.57
0
5
1.16
0.15
2.02
0.3
2.57
0
5
-1.31
0.12
2.02
0.25
2.57
* V
DA'."
45

Table 12 EMG Results for Rectus Femoris
Mean Maximum Minimum
Rheo C-LEG Rheo C-LEG Rheo C-LEG
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean
Difference df t Stat
P(T<=t) one-tail t Critical one-tail
P(T<=t) two-tail t Critical two-tail
2.3 1E-06 2.64E-06 7.34E-06 9E-06 -2E-07 -2.34E-07
8.29E-12 6.69E-12 5.37E-11 8.65E-11 5.2E-14 1.11E-13
8
0.61
8 8
0.43
8 8
0.75
8
0
7
-0.38
0.36
1.89
0.72
2.36
0
7
-0.52
0.31
1.89
0.62
2.36
0
7
0.43
0.34
1.89
0.68
2.36
Only six of the eight subjects' data were used for statistical analysis of the extensors because in two subjects it was unclear based on the anatomy of the residual limb which particular muscle was being utilized for extension.
Discussion
As seen in Tables 10, 11 and 12 the p-values for all tests were substantially greater than
0.05. Therefore no conclusive results can be drawn about the advantages or disadvantages of trans-femoral amputee ambulation using one knee versus the other.
There are several possible etiologies for the inconclusiveness of these results. Firstly, achieving strong, clean signals from the residual limb is extremely difficult. This
46

difficulty is partly due to deterioration of musculature, in conjunction with increased variability in operative muscle attachment. Moreover, extremely thin electrodes (with an unavoidable tradeoff of local amplification) were required on the affected side to allow socket usage. Sanding and alcohol swabbing were used to alleviate the amplification problem, but were constrained in many cases by residual limb sensitivity. Additional noise was also added to the system by the rubbing motion of the socket against electrodes during ambulation. These factors, compounded by the noisy nature of EMG in general, make it difficult to see statistical differences in muscle action. Using an intramuscular, fine-wire protocol in future studies would potentially decrease the noise in the system and provide statistically significant results. It would also enable testing of other flexors and extensors such as the adductor longus'. Although the rectus femoris is the most convenient flexor to obtain with surface electrodes, its action has been shown to be inconsistent across different speeds and subjects.
Given the difficulties associated with surface EMG usage outlined above, it would be advisable to use other measures of effort for analysis. For example, differences in knee torque & power and/or hip torque & power could be studied.
Action of adductor longus is the first and most persistent hip flexor.
A K\" J
47

vI
The results for the study are promising yet incomplete. Our original hypothesis that a magnetorheological prosthetic knee would be more energy efficient for unilateral transfemoral amputees was demonstrated through analysis of subject metabolic data.
Unfortunately, the conclusive results on the mechanism and consequences for this phenomen have yet to be unveiled. Therefore, further analysis and data collection are suggested.
Future Work
One of the main purposes of this study was to serve as a pilot for when a full beta clinical trial is conducted. The purpose of such a beta trial would be to test the viability of the
Rheo so that it may be made commercially available. Some suggestions for future studies are outlined here.
Throughout the duration of this preliminary study several things were learned that could be helpful in a second round study, e.g., learning to fit the knee more appropriately to maximize patient comfort. These slight nuances, which can only be discovered during the actual fitting process, can be used to modify the autoadaption mechanism of the Rheo to minimize the need for outside intervention.
Time Constraints
There are many portions of the study that needed to be conducted on the same day to decrease day-to-day variability. To be able to compare EMG results for different conditions it is necessary that the placement of electrodes be the same. Slight electrode placement differences can result in dramatically different signal amplitudes, thereby biasing the results. Similarly, atmospheric oxygen levels and an individual's baseline energy level can substantially fluctuate between days, therefore requiring oxygen

consumption for both knees to be measured in one session. Moreover, as previously mentioned, walking for trans-femoral amputees is more energy intensive than biological ambulation. As a result, having five hour plus long sessions would not produce representative results. Perhaps the solution to alleviating this time constraint problem is to break up the Spaulding session (our session 2) into two sessions-visit one being strictly gait analysis (kinematics and kinetics with EMG), and visit two focusing on oxygen consumption. Ideally it would be wise to further divide these sessions into two visits-alternating which knee is first. Moreover, before each of these visits the subject should either wear a third party knee (a knee that is not being tested) or alternated which knee was being used to reduce variability due to differences in re-accommodation period.
Under the constraints of our protocol, we tried to correct for which knee the subject started with by randomly dividing subjects into two classes and randomly selecting which knee they would begin with. However, there obviously is variability amongst groups, which is confounded by a small sample size.
Varying Gait Speed
Dividing walking sessions as outlined above would allow testing at multiple gait speeds
(slow, comfortable, and fast). This would allow for clearer evaluation of our hypothesis that the relative metabolic economy with the Rheo is magnified with increasing speed.
Treadmill Walking
Another option that may be tempting for future work is to use treadmill walking instead of the unobstructed hallway walking during oxygen consumption we used. Many studies use treadmill walking to maintain a constant velocity throughout any given trial. We tested using treadmill walking with one trans-femoral amputee, but opted against implementing it as part of out protocol for several reasons. For one, the amputee found it much more difficult to safely walk. The treadmill also prevented the amputee from walking at the same speed that he normally would; this effect has also been seen in other studies with trans-femoral amputees.'"' We felt that this, in conjunction with a lack of comfort, would not provide a good indicator of how the amputee normally walks, and
/ 'I' y.49
*.

therefore the energy required when doing so. For the goal of quantifying the amputee's metabolic economy in everyday life, treadmill walking was not suitable.'
Qualitative Improvements
To enable subjects to better qualitatively assess the knees it is imperative that they be able to take the knees out of the lab and test their capabilities/limitations in various settings for which they would use the knee in their daily routines. The amputees are our greatest resource-their suggestions can guide us to focus our efforts on the needs of the end user. It would also be beneficial for the researcher to observe the amputee under various testing conditions (other than the very controlled level of walking) such as stairs, ramps, and different surfaces. This would allow the researchers and subjects to qualitatively assess the knees in real time.
Accommodation Period
It has been shown that energy expenditure increases with stress, whether it is psychological or physical.16,1
7 Increasing a subject's accommodation period may increase the amputee's understanding and utilization of the knee's capabilities, thereby increasing trust in the system. With added confidence comes reduced stress, potentially resulting in reduced metabolic requirements.
Despite the short accommodation period it is interesting to see that the average metabolic data was lower for three of the four/five seasoned C-leg users. This suggests that an adequate training period could produce more significant results.
Other Approaches
There are several other approaches that could be used other than the one used here, that is simply comparing electronic knees head-to-head. A systems approach could also be taken. This would compare the recommended foot/knee combination. However, a systems protocol would put further restrictions on our subject pool-the Ceterus foot
(used with the Rheo) would not be compatible with individuals with very long residual limbs due to the increased minimum length requirement for foot plus knee.
Kvi
50

Another approach would be to incorporate the Maunch hydraulic knee (purely mechanical) into the protocol. This three prong approach would help in pinpointing the differences in metabolic activity-whether it be mechanical (hydraulic versus magnetic), electrical, or some combination of the two.
The goal for the Rheo, as with any prosthetic knee, should be to provide as much functionality to as many people as possible. To enable utilization by the affected population, prosthetic knees also need to be reasonably priced. By introducing the Rheo, the hope is to not only drive down costs, but to take a step in achieving the ultimate goal of a prosthetic knee: To develop a system that models normal gait in all respectspsychologically, physiologically, and usability. The results of this study are promising in that they indicate that further investigation could provide conclusive results showing the benefit of using the Rheo knee.
: AA 1W)A PI; '-*
51

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54

% MATLAB EMG Analyzer --
% Loads EMG data from Excel file
% Signal Processing: Chebyshev filter, followed by Spline Fitting
% Inputs: Excel (.xls) file with specific spreadsheet name
%(identified within code) within xlsread('filename','sheetname') call
% Output: (for each muscle-group)
% Mean EMG value
% Max EMG value
%- Min EMG value echo off file name = 'subject condition.xls'; numtrials = 10;
% Initialize running variables
Mean semi = 0;
Mean biceps =
0;
Meanrectus 0;
Max-semi = 0;
Max biceps 0;
Max rectus 0;
Minsemi = 0;
Min biceps =
0;
Minrectus = 0; for sheetnum =
1 : numtrials
% increment sheet from Sheet 1 to Sheet 10 suffix = int2str(sheetnum); sheetname = strcat(Sheet', suffix);
% Load EMG data
EMGrawdata = xlsread(filename, sheet-name);
[num rows, num cols] = size(EMGrawdata);
% Divide data into muscle-group vectors
Semi rawdata EMGrawdata(:,1);
Biceps rawdata
= EMGrawdata(:,2);
Rectusrawdata = EMGrawdata(:,3);
% Center each muscle-group signal on 0 (using mean) and rectify
Semirect = abs(Semi-rawdata (ones(num rows, 1) * mean(Semi rawdata)));
Biceps rect
= abs(Bicepsrawdata (ones(num rows, 1) * mean(Biceps rawdata)));
Rectus rect
= abs(Rectus rawdata (ones(num rows, 1) * mean(Rectus-rawdata)));

% Filter EMG data per Andreas' configuration parameters
[b,a]= cheby1(8,0.5,0.06);
% Order is 8, ripple is 0.5 (recommended default), and cutoff frequency is 0.1 * sampling freq / 2.
% Sampling freq is 3000, so 0.1 corresponds to a cutoff frequency of about 150 Hz.
Semi filt = filter(b, a, Semirect);
Biceps_filt filter(b, a, Biceps rect);
Rectusfilt = filter(b, a, Rectus-rect);
% update running variables
Mean semi = Meansemi + mean(Semi_filt);
Mean biceps Meanbiceps + mean(Biceps_filt);
Mean rectus Meanrectus + mean(Rectus_filt);
Max-semi = Maxsemi + max(Semi filt);
Max biceps = Max biceps + max(Bicepsfilt);
Maxrectus = Maxrectus + max(Rectus_filt);
Min-semi = Minsemi + min(Semi filt);
Min biceps Min-biceps + min(Biceps_filt);
Minrectus = Min rectus + min(Rectus_filt);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Figures 1-3 provide visual validation that filtering and interpolation are working correctly %
% (no noticeable phase shift or loss of data). %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Semitendinosus Muscle %%%%%%%%%%%%%%%%% figure(1); subplot(3, 1,1); plot(Semi rawdata(:, 1)); plot-title = strcat(' Semitendinosus Trial', suffix, '- raw data'); title(plot title); ylabel('mV'); xlabel('sample'); grid on subplot(3,1,2); plot(Semi rect(:, 1)); plottitle = strcat(' Semitendinosus Trial', suffix,'
rectified'); title(plot title); ylabel('mV'); xlabel('sample'); grid on subplot(3,1,3); plot(sampletimes, Semi_ filt(:, 1)); plottitle = strcat(' Semitendinosus Trial', suffix,
' filtered'); title(plot title); ylabel('mV'); xlabel('sample'); grid on

%% Rectus Femoris Muscle %%%%%%%%%%%%%%%%% figure(2); subplot(3,1,1); plot(Rectusrawdata(:, 1)); plottitle = strcat(' Rectus Femoris Trial', suffix,' raw data'); title(plot title); ylabel('mV'); xlabel('sample'); grid on subplot(3,1,2); plot(Rectusrect(:, 1)); plottitle = strcat(' Rectus Femoris Trial', suffix,' rectified'); title(plot title); ylabel('mV'); xlabel('sample'); grid on subplot(3,1,3); plot(sample times, Rectusfilt(:, 1)); plot-title = strcat(' Rectus Femoris Trial', suffix,' filtered'); title(plot title); ylabel('mV'); xlabel('sample'); grid on
%% Biceps Femoris Muscle %%%%%%%%%%%%%%%%% figure(3); subplot(3, 1,1); plot(Bicepsrawdata(:, 1)); plottitle = strcat(' Biceps Femoris Trial', suffix,' raw data'); title(plot title); ylabel('mV'); xlabel('sample'); grid on subplot(3,1,2); plot(Bicepsrect(:, 1)); plottitle = strcat(' Biceps Femoris Trial', suffix,' rectified'); title(plot title); ylabel('mV'); xlabel('sample'); grid on subplot(3,1,3); plot(sampletimes, Bicepsfilt(:, 1)); plottitle = strcat(' Biceps Femoris Trial', suffix,' filtered'); title(plot title); ylabel('mV'); xlabel('sample'); grid on end;
-\i<w, \r57 I Y ,Lm:A'-'

%output results
Mean semi = Meansemi / numtrials
Mean-biceps Mean-biceps / num trials
Meanrectus = Meanrectus / numtrials
Maxsemi = Maxsemi / numtrials
Max-biceps = Max-biceps / num trials
Maxrectus = Max rectus / numtrials
Minsemi = Minsemi / numtrials
Min-biceps = Minbiceps / numtrials
Minrectus = Minrectus / num trials
58