USF Libraries
USF Digital Collections

Biomechanical model of transhumeral prostheses

MISSING IMAGE

Material Information

Title:
Biomechanical model of transhumeral prostheses
Physical Description:
Book
Language:
English
Creator:
Freilich, Rebekah
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:

Subjects

Subjects / Keywords:
Socket-residual limb interface
Motion analysis
Validation
Reliability
Dissertations, Academic -- Biomedical Engineering -- Masters -- USF   ( lcsh )
Genre:
non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: It has been shown that the interface between the prosthetic socket and residual limb (S-RL) interface is an important factor in determining acceptance and outcomes of upper limb prostheses. 1 Among the most common complaint from amputees is that the prosthesis is uncomfortable due to developing skin irritation which is usually attributed to poor fit (Nielson 1990). In order to understand why skin irritations can and do occur it is imperative to examine the biomechanical properties of the S-RL interface. A primary reason behind the development of skin irritation is instability of the socket upon the residuum. Alley (2009) asserts that excess slip, axial rotation, and translation are the facets of instability that cause skin irritations due to friction and shear. Measuring the motion at the S-RL interface is not commonly done and therefore there is still no valid and reliable method to quantify the motion clinically. A licensed prosthesis fabricated a transhumeral residual limb model to fit within a typical, harness suspended transhumeral prosthesis. A custom testing apparatus was built to hold the residual limb model and prosthesis for testing. Eight infrared markers were placed on the prosthesis and residual limb model: Two each respectively on the "wrist", elbow axis, socket, and on the residual limb model. The model consists of 3 rigid segments, the forearm, socket, and residual limb. Pearson r correlations were done to see how strongly correlated the motion analysis calculated values were to the accepted values. All results were significant with a r <= .95 and p<.05.
Thesis:
Thesis (M.S.B.E.)--University of South Florida, 2009.
Bibliography:
Includes bibliographical references.
System Details:
Mode of access: World Wide Web.
System Details:
System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by Rebekah Freilich.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 51 pages.

Record Information

Source Institution:
University of South Florida Library
Holding Location:
University of South Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 002069317
oclc - 608212434
usfldc doi - E14-SFE0003199
usfldc handle - e14.3199
System ID:
SFS0027515:00001


This item is only available as the following downloads:


Full Text

PAGE 1

Biomechanical Model of Transhumeral Prostheses by Rebekah Freilich A thesis submitted in partial fulfillment Master of Science in Biomedical Engineering of the requirements for the degree of Department of Chemical & Biomedical Engineering College of Engineering University of South Florida Major Professor: Rajiv Dubey, Ph.D. William E. Lee, III, Ph.D. M. Jason Highsmith, DPT Stephanie L. Carey, Ph.D. Date of Approval: October 22, 2009 Keywords: Socket Residual Limb Interface, Motion Analysis Validation, Reliability Copyright 2009, Rebekah Freilich

PAGE 2

DEDICATION I would like to dedicat e this thesis to my family who never gave up on me. Love you all lots.

PAGE 3

ACKNOWLEDGMENTS I would first like to thank everyone on my committee for all of their help and support through the entire process of completing my thesis. I could not have finished without their willingness to help. Secondly I would like to thank Greg Bauer and his team at West Coast Brace and Limb for creating the residual limb used for testing.

PAGE 4

i T ABLE OF CONTENTS L IST OF TABLES iii LIST OF FIGURES iv ABSTRACT vi C HAPTER 1 I NTRODUCTION 1 Problem Statement 1 Importance of Socket Residual Limb (S RL) Interface 2 Evolution of Socket Design 5 Motion Analysis as a Tool to Measure Motion 6 Goals of the Thesis 8 Hypothesis 8 C HAPTER 2 M ATERIALS AND METHODS 9 Testing Protocol 9 Experimental Design 11 Reliability and Validity 11 Data Processing 12 Marker Set 12 Segments 15 Angle Measurements and Calculations 18 Displacement 23 C HAPTER 3 RESULTS 25 Elbow Angle 25 Inferior Displacement 27 Medial/Lateral Tilt 29 Axial Rotation 30 Shoulder Angle Verification 31 C HAPTER 4 DISCUS SIONS, LIMITATIONS AND RECOMMENDATIONS FOR FUTURE WORK 32 R EFERENCES 35

PAGE 5

i i APPENDICES 37 Appendix A : Marker File 38 Appendix B : Vicon BodyBuilder Program for Rig 42 Appendix C: Vicon BodyBuilder Program 47

PAGE 6

iii LIST OF TABLES Table 1 Marker set used by Carey et al. [15] which also represents a typical marker set based on anatomical landmarks 7 Table 2 Data from a single trial of elbow angle calculations 19 Table 3 Example of data and statistical calculations for inferior displacement from a single trial 24 Table 4 Data from all of the elbow angle calculations 25 Table 5 Data from all of the inferior displacement trials 27 Table 6 Data from all of the tilt trials 29

PAGE 7

iv LIST OF FIGURES Figure 1 Custom Testing Apparatus 9 Figure 2 Marker set for residual limb and prosthetic socket 12 Figure 3 Marker placement on front of body 14 Figure 4 Marker placement on back of body 14 Figure 5 The 3 segments representing arm and prosthesis 15 Figure 6 Coordinate system that defines the residual limb segment 16 Figure 7 Coordinate system that defines the socket segment 17 Figure 8 Position of t he goniometer on the prosthesis while measuring elbow angles 18 Figure 9 Graph of elbow component angles from a single trial 19 Figure 10 Set up for axial rotation and tilt trials 20 Figure 11 Marks on the residual limb to measure inferior displacement of the socket on the residual limb 23 Figure 12 The i nferior translation is equal to the change of position of the FSckt marker 24 Figure 13 Regression Analysis between the accepted angle values and the VICON calculated angles 26 Figure 14 Regression Analysis between the accepted displacement values and the VICON calculated distances 28 Figure 15 Regression Analysis between the accepted tilt angle and the VICON calculated distances 29 Figure 16 Regression Analysis between the accepted axial rotation angle and the VICON calculated distances 30 Figure 17 Comparison between the v alidated marker set and the experimental marker set during shoulder flexion 31

PAGE 8

v Figure 18 Comparison between the validated marker set and the experimental marker set during shoulder abduction 31

PAGE 9

vi BIOMECHANICAL MODEL OF TRANSHUMERAL PROS THESES Rebekah Freilich ABSTRACT It has been shown that the interface between the prosthetic socket and residual limb (S RL) interface is an important factor in determining acceptance and outcomes of upper limb prostheses. [1] Among the most common complaint from amputees is that the prosthesis is uncomfortable due to developing skin irritation which is usually attributed to poor fit (Nielson 1990). In order to understand why skin irritations can and do occur it is imperative t o examine the biomechanical properties of the S RL interface. A primary reason behind the development of skin irritation is instability of the socket upon the residuum. Alley (2009) asserts that excess slip, axial rotation, and translation are the facets o f instability that cause skin irritations due to friction and shear. Measuring the motion at the S RL interface is not commonly done and therefore there is still no valid and reliable method to quantify the motion clinically. A licensed prosthesis fabrica ted a transhumeral residual limb model to fit within a typical, harness suspended transhumeral prosthesis. A custom testing apparatus was built to hold the residual limb model and prosthesis for testing.

PAGE 10

vii Eight infrared markers were placed on the prosthesis and residual limb model: Two each respectively on the wrist, elbow axis, socket, and on the residual limb model. The model consists of 3 rigid segments, the forearm, socket, and residual limb. Pearson r correlations were done to see how strongly correlated the motion analysis calculated values were to the accepted values. All results were significant with a r <= .95 and p<.05.

PAGE 11

1 CHAPTER 1 INTRODUCTION Problem Statement Technological advancements in upper limb prosthetics have lead to improved prosthetic function and design. However, currently the ability to quantify the motion of particularly upper limb prosthetics is lagging. The marker sets for the upper body are based on anatomical l andmarks which may or may not be present depending on the location of the amputation. Another problem basing the marker sets on anatomical landmarks is that the residual limb and socket are grouped together as one segment. By grouping the prosthetic socket and residual limb together one is assuming that the long axis of the socket and residual limb are always aligned, which would not be the case if there was any medial/lateral tilt in the frontal plane of the socket on the residual limb. Despite the fact that the motion at interface between the residual limb and socket has become an important discussion topic there is currently no valid and reliable way to quasi statically measure the motion at the interface.

PAGE 12

2 Importance of Socket Residual Limb (S RL) Int erface It has been shown that the interface between the prosthetic socket and residual limb (S RL) interface is an important factor in determining acceptance and outcomes of upper limb prostheses. [1] Among the most common complaint from amputees is that the prosthesis is uncomfortable due to developing skin irritation which is usually attributed to poor fit [2] In order to understand why skin irritations can and do occur it is imperative to examine the biomechanical properties of the S RL interface. A primary reason behind the development of skin irritation is instability of the socket upon the residuum. The skin irritations occur due to the biomechanical properties at the S RL interface. These properties include the load distribution, transmission of forces from the user to the prosthesis, and the stability of device. These properties rely on proper fit of the socket as well as have an effect on the positional control of the pr osthetic device. Load distribution and transmission has been an important topic in both upper and lower limb prosthetics. The main principles of the current loaddistribution models are the same when it comes to load bearing for both upper and lower limb: uniform distri bution of load around the residual limb and concentration of load on loadtolerant parts of the limb. Alley [3] presents both the current model described above as well as his model, known as the highfidelity or compressionstabilization model. The main difference between his

PAGE 13

3 model and the current m odel is his involves more skeletal control through targeted soft tissue relief. [3] Transmission of the forces from the user to the prosthetic device via the interface is also very important. In lower limb prostheses, it is particularly important because the soft tissues in the residual limb are not well suited for bearing the load of the body weight and inertial forces. [4] The S RL interfaces ability to transmit these forces greatly a ffects the volitional control of the prosthesis. In many current socket models there is a delay between the movement of the residual and the socket caused by the time it takes for the soft tissue between the bone and the socket to compress to the point o f realizing interface response of sufficient magnitude to effect movement. [3] A properly designed socket will not only allow for efficient transmission of the forces from the user to the prosthesis but also optimize stability. This means that the socket will not exceed the movement needed for mobility on the residual limb, which has yet to be defined. Stability has 3 main facets: slip, axial rotation, and translation. Slip refers to the intrinsic movement of the soft tissue to overcome the frictional force at the S RL interface. When discussing creati ng new sockets it is important to talk about all of the different properties of the tissue and not just slip. Sensinger J and Weir F [5] looked at the rotational stiffness of the S RL inter face and how much it can be modulated by the user by co contracting their muscles. They looked at how variables such as socket length, co contraction levels, residual limb diameter, and bone diameter affected the affected the

PAGE 14

4 rotational stiffness of the S RL interface. [5] They found that the rotational stiffness of the S RL interface can vary over a wide range of values and that the floor and ceiling of this range depended significantly on s ocket length and co contraction levels. They suggested that a distal window cut in the socket could possibly decrease the discomfort without affecting the users ability to create torque in cases with a high rotational stiffness such as requiring a long s ocket. [5] The challenge is not only to attempt to decrease the discomfort caused by the rotational stiffness of the S RL interface but also to limit the amount of slip without impinging on th e range of motion the prosthetic device allows. Rotation around the soft tissue or the long axis of the primary bone is referred to as axial rotation. Just like with slip a properly designed socket should limit the amount of axial rotation that occurs but there is no data on how much axial rotation is to be accepted. Traditional transhumeral sockets rely on auxiliary straps to control the axial rotation which subjects patients to excessive harness pressure in the axilla. [3] Any other movement of the socket on the residual limb relative to the skeletal structure of the limb is referred to as interface translation. A lot of translation is occurs through soft tissue compression and often involves friction and shear. [3] Not only can translation lead to skin irritation but it can also complicate the control of the device. Some of the newer sockets are being designed to help minimize the slip, translation, and axial rotation at the S RL interface. [3, 5 9]

PAGE 15

5 Evolution of Socket Design It was not until the 20th century that upper limb socket design entered the literature. In the 60s and 70s the sockets were characterized as by a reduction in the lateral trim line which caused greater stability and mobility. This was followed by an aggressive modification i nto the deltopectoral groove and a flattened region posteriorly just inferior to the spine of the scapula providing greater rotation control and enhanced range of motion. [8] Slowly as the 20th Anatom ical socket design is more than just simply matching the volume and surface shape of the residual limb. When it comes to amputations above the elbow there is a lot more unstable tissue that needs to be contained and supported than bone. However, it is st ill important to attempt to grab the bony structure to allow for greater stability and control. [6] This is where art and science take place in creating a socket. century ended more presentations focused on anatomical socket design.

PAGE 16

6 Motion Analysis as a Tool to Measure Motion Despite the interest in upper extremity motion, the analysis of the motion is still considered to be at an early stage. [10, 11] Since the 1990s there has been a large increase of the number of studies using motion analysis to measure the motion of the upper extremities. [10] Th e VICON Motion analysis was first use to measure motion in nonimpaired persons. Small et.al. [13] showed that a 3D optoelectronic motion analysis is as accurate as stereoradiographic analysis of bone segments. Lowe [14] used motion analysis to validate the accuracy of observational estimates of shoulder and elbow posture Motion Analysis System is used by a number of medical and biomedical industries for capturing and measuring motion. [1 2] Motion analysis has also been used to measure upper limb motion in individuals with prostheses. Most of these studies have looked at task completion with either an actual prosthesis or a simulated prosthesis. [15 17] Highsmith et al. [18] looked at different terminal devices designed to kayak. In their study they used the same marker set as Carey et al. [15] shown below in Table 1 However, the elbow calculated by the motion analysis was off by 10 degrees. This was one of the main reasons the experimental marker system is not based on landmarks.

PAGE 17

7 Table 1 Marker set used by Carey et al. [15] which also represents a typical marker set based on anatomical landmarks

PAGE 18

8 The two main goals of the thesis are: Goals of the Thesis 1) Create a valid and reliable biomechanical model that can measure the movement at the S RL interface. 2) Create a valid and reliable biomechanical model that can correctly measure the kinetics of transhumeral prostheses on a rigid body residual limb model in a laboratory setting. Hypothesis 1) The measurements calculated via motion analysis in the laboratory on the rigid residual model will have a strong positive correlation (r>.95 p<.05) to the measurements of already shown to be reliable and valid tools to measure motion (Validity). 2) The measurements calculated for a certain construct by the motion analysis in the laboratory on the rigid residual model will not significantly differ from each other. The standard deviations of each angle and distance will be looked at as well as graphical representations of each (Reliability).

PAGE 19

9 CHAPTER 2 MATERIALS AND METHODS Testing Protocol A licensed prosthesist fabricated a transhumeral residual limb model to fit within a typical, harness suspended transhumeral prosthesis. A custom testing apparatus was built to hold the residual limb model and prosthesis for testing. Figure 1 Custom Testing Apparatus

PAGE 20

10 For the axial rotation and medial/lateral tilt testing a different residual limb was created out of plaster for easier measuring of the rotation and maneuvering. The residual limb created by the licensed prosthesist has a lip on the back that would not ex ist o n a residual limb, which does not allow for any axial rotation of the socket on the residual limb.

PAGE 21

11 Experimental Design Reliability and Validity The main goal of this study, as mentioned above, are to create a valid and reliable marker set to measure the motion of the prosthetic arm including the motion at the S RL interface. Reliability is the consistency of the measurements. In order for the experimental marker set to be considered reliable the standard deviation (SD) of each of the particular measurements must be less than the error of the accepted measuring device. Validity is the degree to which the measurements are measuring what they are supposed to be. In order for the experimental marker set to be considered valid a strong positive correl ation (r<=.95 p<.05) mush exist between the VICON calculated measurements and the actual measurements. In Equation 1 the X refers to the actual measurements and the Y refers to the VICON calculated measurements. Equation 1 Pearsons r correlation

PAGE 22

12 Data Processing Marker Set The marker set for the residual limb and prosthesis consists of 8 infrared markers: two each respectively on the wri st component, elbow axis, socket of prosthesis, and on the residual limb model. One marker to simulate the shoulder joint center (not shown in figure below) was added to define the axis direction for the residual limb segment. The torso and shoulder mar kers are consistent with those shown in table 1. The marker file for VICON can be seen in Appendix A. Figure 2 Marker set for residual limb and prosthetic socket

PAGE 23

13 The front and back residual limb markers, FResL and BResL respectively, are located on the residual limb right above the prosthetic socket. Below them on the socket are the front and back socket markers, FSckt and BSckt respectively. On the elbow component of the prosthesis there is a marker on the medial and la teral sides of the elbow on the axis of rotation, MEComp, and LEComp respectively. The markers for the wrist component are labeled the same way as MWComp, and LWComp respectively, along the flexion / extension axis of the wrist. The placement of the markers on the residual limb and the socket are very important to ensure that the marker set will work on all trim lines. The FResL and Fsckt markers and the BresL and BSckt markers do not need to be lined up as seen in the figure but the center points between the two sets need to be lined up in all three planes. The marker set for the torso and shoulder are consistent with those in Table 1. In the figures below the white tape represents the trim line of a prosthesis to help demonst rate the placement of the markers on the torso as well as the residual limb and prosthesis. The figures below only show the markers for the torso, residual limb, and prosthesis since the other side would be consistent with Table 1. It is imperative to not e that even though the white tape and the trim line of the prosthesis used in the experiment are not the same that the ResLC and ScktC are still lined up in all three planes. As long these two virtual points are aligned and there is a marker on the anteri or and posterior parts of the residual limb and socket then the segments will be calculated correctly.

PAGE 24

14 Figure 3 Marker placement on front of body Figure 4 Marker placement on back of body

PAGE 25

15 Segments The biomechanical model of an arm with a transhumeral prosthesis is made up of 3 rigid segments: the forearm, socket, and residual limb. The main change from traditional segments is the separation of the upper arm into two segments one representing the residual limb and the other the socket. Each segment is defined by an origin and a coordinate system which are defined below. Figure 5 The 3 segments representing arm and prosthesis The residual limb segment origin is at the ResLC which is half way between the FResL and the BResL markers. The first defining line of the segment is defined as the line from the ResLC to the shoulder joint center (SJC), which becomes the Z axis. The seco nd defining line of the residual limb segment is from the FResL marker to the BResL marker. The Y axis, as defined by the Residual Limb Socket Forearm

PAGE 26

16 program, is the line perpendicular to both the first defining line and the second defining line that meets the right hand rule. Theref ore using the right hand rule the Y axis would be coming out of the paper. The X axis is the line that satisfies the right hand considering the other two axes. The coordinate system for the residual limb segment is shown in Figure 6 Figure 6 Coordinate system that defines the residual limb segment The origin of the socket segment is at the elbow joint center (Ecomp C) which is defined as the point half way between the MEcomp and LEcomp markers. The first defining line of the socket segment is from the E Comp C to the

PAGE 27

17 socket center (ScktC). The second defining line of the segment is from the center of the wrist (WrstC) to the E lbwJC. Using the same definitions of each axis as described above the coordinate system for the residual segment as shown in Figure 7 Figure 7 Coordinate system that defines the socket segment For both the pseudo joint between the residual limb and the socket and the elbow rotation around the X, Y, and Z axis represent abduction (if possible), flexion/extension, and axial rotation respectively.

PAGE 28

18 Both quasi static and static tests were conducted for each angle being tested. For the elbow angle a goniometer was attached to the prosthesis as shown in the figure below to determine the actual angle(s) for each test. The center of the goniometer was placed at the center of rotation of the elbow joint to ensure the most accurate measurements. The elbow was locked from 50 to 120 degrees in 10 degree increments. Quasi static tests were also conducted from 50 to 90 degrees and then 90 to 120 degrees in 10 degree increments. The static test was conducted at each angle independently while the quasi static test stopped at a number of angles during a single testing session. Angle Measurements and Calculations Figure 8 Position of the goniometer on the prosthesis while measuring elbow angles

PAGE 29

19 Results of a single trial of elbow component angle measurements would look as follows. Table 2 Data from a single trial of elbow angle calculati ons Angle (deg) Goniometer ( 2) VICON 90.0 90.9 80.0 80.6 70.0 70.3 60.0 60.3 50.0 50.5 Mean 70.0 70.5 Std. Dev. 15.8 16.0 Pearsons r 0.99995 Figure 9 Graph of elbow component angles from a single trial 40 50 60 70 80 90 100Angle (deg)Time (sec)Elbow Component Angles

PAGE 30

20 Figure 10 Set up for axial rotation and tilt trials For the testing of axial rotation and tilt of the prosthetic socket on the residual limb a residual limb made out of paper mache was used (shown in Figure 10). Both static and quasi static trials were conducted for axial rotation and tilt. For axial rotation 5 and 10 degrees were tested and for tilt 5 and 10 degrees were measured. Each of the axial rotation and tilt trials will result in a chart link that seen in Table 2 The shoulder angle testing was done by running tri als with both the marker set described in [15] and the experimental marker set described in this

PAGE 31

21 study. The calculated shoulder angles for each of the marker sets were compared graphically on the same chart. These tests ensured that the resi dual limb segment was moving with the prosthesis segment since the experimenter does not have a prosthesis. BodyBuilderTMEquati on 2 calculates angles using Euler angles. Euler angles are used to describe the rotation between two 3D coordinate systems in terms of three angles. Each of the Euler angles describes a transformation as seen in Equation 2 Euler angle definitions The order of rotation of the elbow angle per the program I wrote is yxz. Euler angles describe rotation with respect to a rotating frame. [19] The rotation matrix for a yxz ro t ation is shown in Equation 3 The 1, 2, and 3 represent the angles of rotation around y, x, and z respecti vely. The transformation matrix

PAGE 32

22 which is the rotational matrix times the position vector is shown in Equation 4 The R11 etc in the transformation matrix correspond wi th that position in the rotational matrix. Equation 3 Rotational matrix for elbow angle calculations Equation 4 Transformation matrix for elbow angle calculations Since the final position vector is know and the X, Y, Z are also known, the elbow angles can be calculated using inverse kinematics. All of the angles are calculated in a similar fashion with the rotational matrix being determined by the definition of the rotation in the program.

PAGE 33

23 Displacement Both static and quasi static testing were completed for inferior displacement of the socket on the residual. Marks were placed on the residual limb in increments of .5 in from 0 to 2 inches as measured by a ruler. For the static testing the prosthesis was heal at each mark independently. During the quasi static testing the prosthesis was pulled down stopping at each mark for about 10 seconds then moving on to the next. The inferior displacement is measured by calculating the change in distance between the BResL and BSckt markers along the z axis. Figure 11 Marks on the residual limb to measure inferior displacement of the socket on the residual limb

PAGE 34

24 Results from a single trial for inferior displacement are shown below. Table 3 Example of data and statistical calculations for inferior displacement from a single trial Distance (in) Ruler ( .1) VICON ( .02) 0.5 0.4 1.0 0.9 1.5 1.4 2.0 1.9 Mean 1.3 1.2 SD 0.6 0.6 Pearson r 0.99999 Figure 12 The i nferior translation is equal to the change of position of the FSckt marker

PAGE 35

25 CHAPTER 3 RESULTS Elbow Angle A strong positive correlation (r= .99 p< .0001) also exists between the elbow angles measured using goniometry and the elbow angles calculated by motion analysis. Since the error of the goniometer is two degrees, in order for the calculated angles from motion analysis to be reliable all of the results for a particular angle must have a difference in standard deviation less than 2 degrees. Table 4 Data from all of the elbow angle calculations Actual Angle (deg) Calculated Angle (deg) 1 2 3 4 5 6 7 8 9 10 Mean SD 120 2 120.9 121.3 120.2 119.6 119.8 121.0 120.9 119.4 118.9 119.9 120.2 0.8 110 2 111.0 110.3 109.2 110.9 109.0 111.3 109.4 111.5 109.0 110.5 110.2 1.0 100 2 100.6 99.8 98.9 100.6 99.4 101.3 99.6 100.9 99.2 101.4 100.2 0.9 90 2 90.9 90.7 88.8 89.3 90.7 90.8 90.9 91.4 89.5 90.3 90.3 0.8 80 2 80.6 78.7 80.7 79.7 80.0 81.2 79.4 81.0 79.9 80.3 80.2 0.8 70 2 70.3 69.8 68.9 70.4 69.7 72.0 69.8 71.7 70.0 70.5 70.3 0.9 60 2 60.3 59.7 59.8 60.0 59.8 60.4 59.2 60.7 59.5 59.4 59.9 0.5 50 2 50.5 49.7 50.2 49.9 49.5 51.0 49.0 49.4 49.0 50.9 49.9 0.7

PAGE 36

26 Figure 13 Regression Analysis between the accepted angle values and the VICON calculated angles. The error bars represent standard error mean (SEM) y = 1.004x 0.1876 R = 1 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 130.0 40 50 60 70 80 90 100 110 120 130Calculated Angle (deg)Actual Angle(Deg)Actual vs. Mean Calculated Angles

PAGE 37

27 Inferior Displacement A strong positive correlation (r= .99 p<=.0001) also exists between the inferior displacement measured using a ruler and the distances calculated by motion analysis. Since the error of the ruler is 0.1 in, in order for the calculated distances from motion analysis to be reliable all of the results for a particular angle must have a standard deviation less than 0.1. Table 5 Data from all of the inferior displacement trials Actual Distance (in) Calculated Distance (.02) 1 2 3 4 5 6 7 8 9 10 Mean SD 0.5 .1 0.5 0.4 0.5 0.4 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.03 1 .1 0.9 0.9 1.1 0.9 1.1 1.0 1.0 1.0 1.0 1.0 1.0 0.06 1.5 .1 1.5 1.4 1.6 1.4 1.5 1.5 1.6 1.5 1.5 1.5 1.5 0.05 2 .1 2.0 1.9 2.0 1.9 2.1 1.9 2.0 1.9 2.0 2.0 2.0 0.06

PAGE 38

28 Figure 14 Regression Analysis between the accepted displacement values and the VICON calculated distances. The error bars represent SEM y = 1.0026x 0.0101 R = 0.9998 0.000 0.500 1.000 1.500 2.000 2.500 0 1 2 3Calculated Distance (in)Actual Distance (in)Actual vs. Mean Calculated Distances

PAGE 39

29 Medial/Lateral Tilt A strong positive correlation (r=. 99 p< .0001) between the actual or accepted value for tilt and the VICON calculated angles for tilt of the socket on the residual limb. The error on the protractor is 1 degree therefore the difference between the two standard deviations should be less than 1 degree. Table 6 Data from all of the tilt trials Protractor Tilt (deg) VICON calculated tilt (deg) 1 2 3 4 5 6 7 8 9 10 average SD 5 2 5.0 5.3 4.8 4.9 6.0 5.7 4.8 5.5 5.2 6.3 5.4 0.5 10 2 9.5 10.0 10.6 9.4 10.4 10.2 9.7 10.3 10.3 9.9 10.0 0.4 Figure 15 Regression Analysis between the accepted tilt angle and the VICON calculated distances. The error bars represent SEM y = 0.9343x + 0.6811 R = 1 0.0 5.0 10.0 15.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0VICON calculated tilt (deg)Actual tilt measurements (deg)Actual Vs. Mean VICON calculated tilt values

PAGE 40

30 Axial Rotation A strong positive correlation (r=. 99 p< .0001) between the actual or accepted value for axial rotation and the VICON calculated angles for tilt of the socket on the residual limb. The error on the protractor is 1 degree therefore the difference between the two standard deviations should be less than 1 degree. Figure 16 Regression Analysis between the accepted axial rotation angle and the VICON calculated distances. The error bars represent SEM

PAGE 41

31 Shoulder Angle Verification The calculations for the shoulder angles were the same for both the validated marker set and the experimental marker set. Figure 17 Comparison between the validated marker set and the experimental marker set during shoulder flexion Figure 18 Comparison between the validated marker set and the experimental marker set during shoulder abduction 20 0 20 40 60 80 100Calculated Angle (Deg)TimeShoulder Angle Calculations during Flexion Validate Marker Set Experimental Marker Set 0 20 40 60 80Calculated Angle (Deg)Time (sec)Shoulder Angle Calculations during Abduction Validated Marker Set Experimental Marker Set

PAGE 42

32 CHAPTER 4 DISCUSSION, LIMITATIONS AND RECOMMENDATI ONS FOR FUTURE WORK As mentioned in the introduction the analysis o f upper extremity motion is still considered to be at an early stage. [10, 11] This study will add to the current research of upper extremity motion by starting the conversation about how to quantify the motion at the S RL interface. It is imperat ive to keep in mind that this is just a preliminary study and limited to laboratory studies at this time. The ability to quantify the motion at the S RL interface will improve studies involving tranhumeral prostheses, socket design, and socket fit. The b iomechanical model discussed in this paper is able to provide both valid and reliable measurements for the motion at the residual limb. Not only will this provide an objective way to quantify fit but also provide some insight as to how much motion provides the stability and control required without causing too much skin irritation that the patient chooses not to wear the prosthesis. The most obvious limitation is the lack of any human subjects in the study. However, it is imperative to at least test the concept of the model before going through the long process of getting IRB approval and finding subjects for the test. Also due to the fact that the model was not tested on humans the experimental marker set has only been shown to be reliable and valid on a rigid body residual

PAGE 43

33 model. Despite this fact this study has shown that it is possible to get valid and reliable measurements of the motion at the S RL interface using motion analysis. Other limitations include using only one trim line and one residual li mb length. However, as mentioned above, as long as the ResLC and ScktC are s till aligned the trim line will not affect the results. In terms on residual limb length, issues would arise if the residual limb was very short or if the amputation occurred at t he shoulder joint. Depending on the size of the markers and the resolution of the cameras there may not be enough room to separate the residual limb and socket into two different segments. Another limitation is that I did not take into consideration properties of skin. In order to quantify accepted values for the motion at the S RL limb interface human subject testing needs to occur. The use of an electronic goniometer would provide an easier way to collect the accepted values of the motion rather than t rying to attach both a goniometer and protractor to the individual. Also since this method is only practical in a laboratory setting it is important to try to create a tool that is more user friendly for a clinical setting. Another aspect not considered in this study is the correlation between the she forces created by the motion which is what causes the skin irritation and sores on the residual limb. In order to study the forces and pressure caused by the motion, sensors would need to be added to measur e the amount of force and pressure. The ability to measure the motion and forces at the S RL interface is very important to the study of prosthetics. This will help researchers not only

PAGE 44

34 understand how and why skin irritation can and does occur on the residual limb but also help them determine how much motion is necessary to create the perfect balance between control and skin irritation.

PAGE 45

35 REFERENCES 1. Shultz, AE, Baade, SP, and Kuiken, TA, Expert Opinion on su ccess factors for upper limb prostheses. Journal of Rehabilitation Research and Development, 2007. 44(4): p. 8. 2. Nielson, C, Survey of amputees:functional level and life satisfaction, information needs, and the prosthetist's role. Journal of Prosthetics and Orthotics, 1990. 3: p. 5. 3. Alley, RD, Biomechanical Discussion of Current and Emergent Upper Limb Prosthetic Interface Design. The Academy Today, 2009(June): p. 6. 4. Jia, X, Zhang, M, and Lee, WC, Load transfer mechanics between trans tibial pros thetic socket and residual limb--dynamic effects. J Biomech, 2004. 37(9): p. 13717. 5. Sensinger, JW and Weir, RF, Modeling and preliminary testing socket residual limb interface stiffness of aboveelbow prostheses. IEEE Trans Neural Syst Rehabil Eng, 2008. 16(2): p. 184 90. 6. Andrews, J, Transhumeral and Elbow Disarticulation Anatomically Contoured Socket Considerations. American Academy of Orthotists and Prosthetists, 2008. 20(3): p. 5. 7. Daly, W, Upper extremity socket design options. Phys Med Rehabil Clin N Am, 2000. 11(3): p. 62738. 8. Lake, C, The Evolution of Upper Limb Prosthetic Socket Design. American Academy of Orthotists and Prosthetists, 2008. 20(3): p. 8. 9. Lee, WC and Zhang, M, Using computational simulation to aid in the predict ion of socket fit: a preliminary study. Med Eng Phys, 2007. 29(8): p. 9239. 10. Anglin, C and Wyss, UP, Review of arm motion analyses. Proc Inst Mech Eng H, 2000. 214(5): p. 54155.

PAGE 46

36 11. Drummey, J, Enhancing the Functional Envelope: A Review of Upper Li mb Prosthetic Treatment Modalities. The Academy Today, 2009. June: p. 5. 12. Gironda, RJ, Lloyd, J, Clark, ME, and Walker, RL, Preliminary evaluation of reliability and criterion validity of Actiwatch Score. J Rehabil Res Dev, 2007. 44(2): p. 22330. 13. Small, CF, Bryant, JT, Dwosh, IL, Griffiths, PM, Pichora, DR, et al., Validation of a 3D optoelectronic motion analysis system for the wrist joint. Clin Biomech (Bristol, Avon), 1996. 11(8): p. 481483. 14. Lowe, B, Accuracy and validity of observational estimated of shoulder and elbow posture. Applied Ergonomics, 2004. 35: p. 13. 15. Carey, SL, Jason Highsmith, M, Maitland, ME, and Dubey, RV, Compensatory movements of transradial prosthesis users during common tasks. Clin Biomech (Bristol, Avon), 2008. 23(9): p. 112835. 16. Stein, RB and Walley, M, Functional comparison of upper extremity amputees using myoelectric and conventional prostheses. Arch Phys Med Rehabil, 1983. 64(6): p. 2438. 17. Weekes, DL, Wallace, SA, and Anderson, DI, Training with an upper limb prosthetic simulaor to enhance transfer of skills across limbs. Arch. Phys. Med. Rehabilitation, 2003. 843: p. 7. 18. Highsmith, MJ, Carey, SL, Koelsch, KW, Lusk, CP, and Kinematic evaluation of terminal devices for kayaing with upper extremit y amputation. Journal of Prosthetics and Orthotics, 2007. 19(84): p. 7. 19. Craig, JJ, Introduction to Robotics Mechanics and Contol Third ed. 2005, Upper Saddle River: Pearson Education, Inc.

PAGE 47

37 APPENDICES

PAGE 48

38 Appendix A : Marker File !MKR#2 [Autolabel] C7 Cervical level 7 T10 Thoracic level 10 CLAV Clavicle STRN Sternum RBAK Right back assymetrical marker RSHO Right shoulder WrstM Wrist thumb side WrstL Wrist pinkie side UPA Upper arm ELBM ELBL LSHO Left shoulder MWComp Medial LWComp Left wrist pinkie side ECompL Lateral point on elbow component ECompM Medial Point on elbow component BRESL Back point on res limb FRESL Front point on res limb RSckt Right (medial) point on socket FSckt Left (lateral) point on socket sLSJC simulated LSJC (for rig) LSJC left shoulder joint center CLAV,STRN,C7,T10,RBAK BRESL,FRESL, LSHO RSckt,FSckt,ECompL,ECompM RSHO,RUPA,RELB LWComp,MWComp,ECompL,ECompM ElbM,RWRA,RWRB Torso = C7,T10,CLAV,STRN,RBAK LShoulder = LSHO,CLAV,T1

PAGE 49

39 Appendix A ( Continued) ResLimb = BRESL,FRESL,sLSJC Socket = RSckt,FSckt,ECompL,ECompM LForearm = LWRA,LWRB,ECompL,ECompM RShoulder = RSHO,CLAV,T10 RUpperar m = RSHO,RUPA,RELB RForearm = RELB,RWRA,RWRB Torso,RShoulder Torso,LShoulder RShoulder,RUpperarm RUpperarm,RForearm LShoulder,ResLimb Socket,LForearm [Segment Axes] ORIGINTorso AXISXTorso AXISYTorso AXISZTorso ORIGINTorso,AXISXTorso ORIGINTorso,AXISYTorso ORIGINTorso,AXISZTorso ORIGINRUpperarm AXISXRUpperarm AXISYRUpperarm AXISZRUpperarm ORIGINRUpperarm,AXISXRUpperarm ORIGINRUpperarm,AXISYRUpperarm ORIGINRUpperarm,AXISZRUpperarm ORIGINResLimb AXISXResLimb AXISYResLimb AXISZResLimb O RIGINResLimb,AXISXResLimb ORIGINResLimb,AXISYResLimb ORIGINResLimb,AXISZResLimb

PAGE 50

40 Appendix A ( Continued) ORIGINSocket AXISXSocket AXISYSocket AXISZSocket ORIGINSocket,AXISXSocket ORIGINSocket,AXISYSocket ORIGINSocket,AXISZSocket ORIGINRForearm AXISXRForearm AXISYRForearm AXISZRForearm ORIGINRForearm,AXISXRForearm ORIGINRForearm,AXISYRForearm ORIGINRForearm,AXISZRForearm ORIGINLForearm AXISXLForearm AXISYLForearm AXISZLForearm ORIGINLForearm,AXISXLForearm ORIGINLForearm,AXISYLForearm ORIGINLFore arm,AXISZLForearm ORIGINRWrist AXISXRWrist AXISYRWrist AXISZRWrist ORIGINRWrist,AXISXRWrist ORIGINRWrist,AXISYRWrist ORIGINRWrist,AXISZRWrist ORIGINLWrist AXISXLWrist AXISYLWrist AXISZLWrist ORIGINLWrist,AXISXLWrist ORIGINLWrist,AXISYLWrist ORIGINLWrist,AXISZLWrist ORIGINGlobal AXISXGlobalAXISY GlobalAXISZGlobal

PAGE 51

41 Appendix A ( Continued) ORIGINGlobal,AXISXGlobal ORIGINGlobal,AXISYGlobal ORIGINGlobal,AXISZGlobal [Joint centers] RSJC LSJC REJC ECompC ScktC ResLC WrstJC WCompJC [Angles] LShoulderAngles ResLScktAngles ElbowCompAngles RShoulderAngles ElbowAngles [Distances] DistResLSocket

PAGE 52

4 2 Appendix B : Vicon BodyBuilder Program for Rig Note: new part highlighted. {* --------------------------------------------------------------------------------*} {* Biomechanical Model Of Transhumeral Prosthesis *} {* Rebekah Freilich 2009 *} {* Master Thesis for Biomedical Engineering *} {* University of South Florida *} {* ----------------------------------------------------------------------------------*} {* ------------------------------*} {*Start of Macro Section*} {* -------------------------------*} {*Display of Segment Axis*} {* ---------------------------------*} Macro AXISVISUALISATION(Segment) ORIGIN#Segment=O(Segment) AXISX#Segment={100,0,0}*Segment AXISY#Segment={0,100,0}*Segment AXISZ#Segment={0,0,100}*Segment output(ORIGIN#Segment,AXISX#Segment,AXISY#Segment,AXISZ#Segment) ENDMACRO {* --------------------*} {*End of Macro Section*} {* --------------------*} {*Define Global Origin*} {* --------------------*} Gorigin = {0,0,0} Global = [Gorigin,{1,0,0},{0,0,1},xyz] {* ---------------------------*}

PAGE 53

43 Appendix B ( Continued) {*Definition of Virtual Points*} {* ---------------------------*} {*Torso*} {* -----*} {* BTorso= (C7+T10)/2 LTorso = (T10+STRN)/2 FTorso = (CLAV+STRN)/2 UTorso = (C 7+CLAV)/2 *} {*Shoulder*} {* --------*} {* {*Temporary local coordinate system*} TempRClav = [RSHO,C7 RSHO,1(Torso),zyx] TempLClav = [LSHO,C7 LSHO,1(Torso),zyx] {* If $Static == 1 Then RSJC = RSHO+{0,0, $RShoulderDepth}*Attitude(Torso) LSJC = LSHO+{0,0, $LShoulderDepth}*Attitude(Torso) $%RSJC = RSJC/TempRClav $%LSJC = LSJC/TempLClav PARAM($%RSJC) PARAM($%LSJC) EndIf *} {*From local coordinate system to global*} RSJC = $%RSJC*TempRClav LSJC = $%LSJC*TempLClav *} {*Elbow Component*} {* ---------------*} ECompC = (ECompL+ECompM)/2

PAGE 54

44 Appendix B ( Continued) {*Wrist*} {* -----*} {*RWJC=(RWRA+RWRB)/2*} LWJC = (LWRA+LWRB)/2 {*Residual Limb*} {* -------------*} ResLC = (BResL+FResL)/2 {*Prosthetic Socket*} {* -----------------*} ScktC = (BSckt+FSckt)/2 {* -------------------------------*} {*Definition of Segments*} {* -------------------------------*} {* Torso = [UTorso,UTorso LTorso,BTorso UTorso,zyx] *} ResLimb = [ResLC,sLSJC ResLC,BResL FResL,zyx] Socket = [ECompC,ScktC ECompC,ECompC LWJC,zyx] {*RUpperm = [REJC,RSJC REJC,REJC RWJC,zyx] RForearm = [RWJC,REJC RWJC,REJC RSJC,zxy]*} LForearm = [LWJC,ECompC LWJC,ECompC sLSJC,zxy] {*RWrist = [RWJC,REJCRWJC,RWRA RWRB,zxy]*} LWrist = [LWJC,ECompCLWJC,LWRA LWRB ,zxy]

PAGE 55

45 Appendix B ( Continued) {* ------*} {*Angles*} {* ------*} {*TorsoAngles = *} {*LShoulderAngles = ( 2) RShoulderAngles = *} ResLScktAngles = ElbowCompAngles = < Socket,LForearm,yxz> {*RElbowAngles = *} {* ---------*} {*Distances*} {* ---------*} DistResLSocket = DIST(ECompL,FResL) {* ------*} {*Output*} {* ------*} {*Joint Centers*} OUTPUT (ECompC,ScktC,ResLC,LWJC) {*Angles*} OUTPUT (El bowCompAngles) OUTPUT (ResFScktAngles) {*Distances*} OUTPUT (DistResLSocket)

PAGE 56

46 Appendix B ( Continued) {*DISPLAY*} {*This calls up the macro to display the segments*} AXISVISUALISATION(Socket) AXISVISUALISATION(ResLimb) AXISVISUALISATION(LForearm) AXISVISUALISATION(LWrist) AXISVISUALISATION(Global)

PAGE 57

47 Appendix C: Vicon BodyBuilder Program Note: new part highlighted. {* ------------------------------------------------------------------------------------*} {* Biomechanical Model Of Transhum eral Prosthesis *} {* Rebekah Freilich 2009 *} {* Master Thesis for Biomedical Engineering *} {* University of South Florida *} {* ------------------------------------------------------------------------------------*} {* ----------------------*} {*Start of Macro Section*} {* ----------------------*} {*Display of Segment Axis*} {* ----------------------*} Macro AXISVISUALISATION(Segment) ORIGIN#Segment=O(Segment) AXISX#Segment={100,0,0}*Segment AXISY#Segment={0,100,0}*Segment AXISZ#Segment={0,0,100}*Segment output(ORIGIN#Segment,AXISX#Segment,AXISY#Segment,AXISZ#Segment) ENDMACRO {* -------------------*} {*End of Macro Section*} {* --------------------*} {*Define Global Origin*} {* --------------------*} Gorigin = {0,0,0} Global = [Gorigin,{1,0,0},{0,0,1},xyz]

PAGE 58

48 A ppendix C ( Continued) {* ---------------------------*} {*Definition of Virtual Points*} {* ---------------------------*} {*Torso*} {* -----*} BTorso= (C7+T10)/2 LTorso = (T10+STRN)/2 FTorso = (CLAV+STRN)/2 UTorso = (C7+CLAV)/2 Torso = [UTorso,UTorso LTorso,BTorso UTorso,zyx] {*Shoulder*} {* --------*} {*Temporary local coordinate system*} {*TempRClav = [RSHO,C7 RSHO,1(Torso),zyx]*} TempLClav = [LSHO,C7 LSHO,1(Torso),zyx] IF Static==1 Then {*RSJC = RSHO+{0,0, $RShoulderDepth}*Attitude(Torso)*} LSJC = LSHO+{0,0, $LShoulderDepth}*Attitude(Torso) {*$%RSJC = RSJC/TempRClav*} $%LSJC = LSJC/TempLClav {*PARAM($%RSJC)*} PARAM($%LSJC) End {*From local coordinate system to global*} {*RSJC = $%RSJC*TempRClav*} LSJC = $%LSJC*TempLClav

PAGE 59

49 Appendix C ( Continued) {*Elbow Component*} {* ---------------*} ECompC = (ECompL+ECompM)/2 {*Wrist*} {* -----*} {*RWJC=(RWRA+RWRB)/2*} LWJC = (LWRA+LWRB)/2 {*Residual Limb*} {* -------------*} ResLC = (RResL+LResL)/2 {*Prosthetic Socket*} {* -----------------*} ScktC = (RSckt+LSckt)/2 {* ----------------------*} {*Definition of Segments*} {* ----------------------*} Torso = [UTorso,UTorso LTorso,BTorso UTorso,zyx] ResLimb = [ResLC,LSJC ResLC,RResL LResL,zyx] Socket = [ECompC,ScktC ECompC,ECompC LWJC,zyx] {*RUpperm = [REJC,RSJC REJC,REJC RWJC,zyx] RForearm = [R WJC,REJC RWJC,REJC RSJC,zxy]*} LForearm = [LWJC,ECompC LWJC,ECompC LSJC,zyx]

PAGE 60

50 Appendix C ( Continued) {*RWrist = [RWJC,REJCRWJC,RWRA RWRB,zxy]*} LWrist = [LWJC,ECompCLWJC,LWRA LWRB,zxy] {* ------*} {*Angles*} {* ------*} TorsoAngles = < Global,Torso,xyz> LShoulderAngles =( 2) {*RShoulderAngles =*} ResLScktAngles = ElbowCompAngles = {*RElbowAngles =*} {* ---------*} {*Distances* } {* ---------*} DistResLS = DIST(ECompL,LResL) {* ------*} {*Output*} {* ------*} {*Joint Centers*} OUTPUT(ECompC,ScktC,ResLC,LWJC,LSJC) {*Angles*} OUTPUT(ElbowCompAngles) OUTPUT(ResLScktAngles)

PAGE 61

51 Appendix C ( Continued) {*Distances*} OUTPUT(DistResLS) {*DISPLAY*} {*This calls up the macro to display the segments*} AXISVISUALISATION(Socket) AXISVISUALISATION(ResLimb) AXISVISUALISATION(LForearm) AXISVISUALISATION(LWrist) AXISVISUALISATION(Global)


xml version 1.0 encoding UTF-8 standalone no
record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd
leader nam 2200373Ka 4500
controlfield tag 001 002069317
005 20101007121826.0
007 cr mnu|||uuuuu
008 100421s2009 flu s 000 0 eng d
datafield ind1 8 ind2 024
subfield code a E14-SFE0003199
035
(OCoLC)608212434
040
FHM
c FHM
049
FHMM
090
R856 (Online)
1 100
Freilich, Rebekah.
0 245
Biomechanical model of transhumeral prostheses
h [electronic resource] /
by Rebekah Freilich.
260
[Tampa, Fla] :
b University of South Florida,
2009.
500
Title from PDF of title page.
Document formatted into pages; contains 51 pages.
502
Thesis (M.S.B.E.)--University of South Florida, 2009.
504
Includes bibliographical references.
516
Text (Electronic thesis) in PDF format.
3 520
ABSTRACT: It has been shown that the interface between the prosthetic socket and residual limb (S-RL) interface is an important factor in determining acceptance and outcomes of upper limb prostheses. [1] Among the most common complaint from amputees is that the prosthesis is uncomfortable due to developing skin irritation which is usually attributed to poor fit (Nielson 1990). In order to understand why skin irritations can and do occur it is imperative to examine the biomechanical properties of the S-RL interface. A primary reason behind the development of skin irritation is instability of the socket upon the residuum. Alley (2009) asserts that excess slip, axial rotation, and translation are the facets of instability that cause skin irritations due to friction and shear. Measuring the motion at the S-RL interface is not commonly done and therefore there is still no valid and reliable method to quantify the motion clinically. A licensed prosthesis fabricated a transhumeral residual limb model to fit within a typical, harness suspended transhumeral prosthesis. A custom testing apparatus was built to hold the residual limb model and prosthesis for testing. Eight infrared markers were placed on the prosthesis and residual limb model: Two each respectively on the "wrist", elbow axis, socket, and on the residual limb model. The model consists of 3 rigid segments, the forearm, socket, and residual limb. Pearson r correlations were done to see how strongly correlated the motion analysis calculated values were to the accepted values. All results were significant with a r <= .95 and p<.05.
538
Mode of access: World Wide Web.
System requirements: World Wide Web browser and PDF reader.
590
Advisor: Rajiv Dubey, Ph.D.
653
Socket-residual limb interface
Motion analysis
Validation
Reliability
690
Dissertations, Academic
z USF
x Biomedical Engineering
Masters.
773
t USF Electronic Theses and Dissertations.
4 856
u http://digital.lib.usf.edu/?e14.3199