Grand Valley State University

ScholarWorks@GVSU Masters Theses

Graduate Research and Creative Practice

4-2007

An Upper Extremity Biomechanical Model: Application to the Bicep Curl Adam Miller Grand Valley State University

Follow this and additional works at: http://scholarworks.gvsu.edu/theses Part of the Engineering Commons Recommended Citation Miller, Adam, "An Upper Extremity Biomechanical Model: Application to the Bicep Curl" (2007). Masters Theses. Paper 686.

This Thesis is brought to you for free and open access by the Graduate Research and Creative Practice at ScholarWorks@GVSU. It has been accepted for inclusion in Masters Theses by an authorized administrator of ScholarWorks@GVSU. For more information, please contact [email protected].

An Upper Extremity Biomechanical Model: Application to the Bicep Curl A thesis by Adam Miller, M.S.E. Presented April 2007

In partial fulfillment of the requirements for the Master of Science in Engineering degree

Advisor: Dr. Jeff Ray, Director of Engineering

School of Engineering Grand Valley State University

•Adam Miller 2007

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Grand Valley State University Padnos College of Engineering and Computing CERTIFICATE OF EXAMINATION

Examining Board

Advisor

)r. Shirley Fleischmann

Dr. Princewill Anyalebechi

The Thesis By

Adam Miller

entitled

Development of an Upper Extremity Biomechanical Model: Application to the Bicep Curl

is accepted in partial fulfillment of the requirements for the degree of Master of Science in Engineering

I H / V I a v ^00 f Date:

Dr. C. Standridge, Graduate Director

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Development of an Upper Extremity Biomechanical Model: Application to the Bicep Curl a Padnos College of Engineering and Computing M.S.E Thesis Presentation by Adam Miller ABSTRACT: An upper extremity biomechanical model was developed based on recommendations provided by the International Society of Biomecbanics. The model was used to investigate biomecbanical differences between two variations of the bicep curl exercise: the standing and incline dumbbell curls. An 8-camera Vicon motion capture system was used to collect data on five subjects that executed 10 repetitions of each type o f curl. Four key biomecbanical indicator variables were investigated: range of motion, maximum elbow flexion moment, mean elbow flexion moment, and the flexion angle at which the maximum flexion moment occurs. On average, the range of motion at the elbow was 11.9° less for the incline curl. Both the mean and maximum elbow flexion moments were significantly higher for the incline curl. Finally, the flexion angle at which the maximum flexion moment occurred was 71.9° for the standing bicep curl and 35.1° for the incline bicep curl, a difference of 36.8°.

GRANDVkLII'Y Stai i . U m v i R s n V

11

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

DEDICATION

For my family, my friends, and all those who have supported me through my journey thus far. To my loving fiancée, Nikki, for keeping me sane, believing in me, and putting up with the long hours I’ve spent working on my computer monitor tan.

Ill

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

ACKNOWLEDGEMENTS

The author would like to express his sincere gratitude to his co-workers and peers at Mary Free Bed Rehabilitation Hospital’s Motion Analysis Center: Dr. Krisanne Chapin, Mitch Barr, and Dr. Gordon Alderink. I would especially like to thank Dr. Krisanne Chapin for her advice and support throughout the entirety o f my graduate education. Without her I would not have reached this point.

IV

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Table of Contents

List of Tables.......................................................................................................................... vii List o f Figures........................................................................................................................viii List o f Symbols and Abbreviations..........................................................................................x 1

2

Introduction........................................................................................................................1 1.1

Upper Extremity Anatomy........................................................................................ 1

1.2

Description of Joint A ngles...................................................................................... 5

1.3

Estimation o f Joint Centers of Rotation................................................................. 12

1.4

Application o f Upper Extremity M odels............................................................... 16

Methods........................................................................................................................... 21 2.1

3

Upper Extremity M odel.......................................................................................... 21

2.1.1

Thorax Coordinate System ............................................................................ 23

2.1.2

Scapula Coordinate System........................................................................... 24

2.1.3

Humerus Coordinate System......................................................................... 25

2.1.4

Forearm Coordinate System .......................................................................... 25

2.1.5

Hand Coordinate System............................................................................... 26

2.1.6

Dumbbell Coordinate System........................................................................ 27

2.1.7

Estimation o f Shoulder Joint Center............................................................. 28

2.1.8

Joint Rotations................................................................................................ 29

2.2

Experimental Methods............................................................................................ 30

2.3

Statistical Methods...................................................................................................35

Results..............................................................................................................................37

V

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

3.1

Bicep Curl Kinematics and Kinetics.....................................................................37

3.2

Statistical Test Results...........................................................................................40

4

Discussion......................................................................................................................44 4.1

Limitations..............................................................................................................45

4.2

Recommendations.................................................................................................. 52

5

Conclusion......................................................................................................................54

6

References...................................................................................................................... 55

Appendix A : Center of Rotation Calculation.......................................................................57 Appendix B ; Vicon BodyLanguage C ode........................................................................... 60 Appendix C : MATLAB Code for Center of Rotation Caleulation.................................... 67 Appendix D : Bicep Curl Kinematies and Kinetics............................................................. 70 Appendix E : Biomechanical Indicator Box Plots................................................................75

VI

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

List of Tables

Table 1: Upper Extremity Model Marker Locations........................................................... 22 Table 2: Thorax Coordinate System......................................................................................24 Table 3: Scapula Coordinate System.....................................................................................24 Table 4: Humerus Coordinate System.................................................................................. 25 Table 5: Forearm Coordinate System................................................................................... 26 Table 6: Hand Coordinate System.........................................................................................27 Table 7: Dumbbell Coordinate System................................................................................. 28 Table 8: Shoulder Joint Angles..............................................................................................29 Tahle 9: Elbow Joint Angles.................................................................................................. 30 Table 10: Wrist Joint Angles................................................................................................. 30 Table 11 : Descriptive Statistics for Range of M otion......................................................... 40 Table 12: Descriptive Statistics for Maximum Flexion M oment....................................... 41 Table 13: Descriptive Statistics for Flexion Angle at Maximum Moment........................ 41 Table 14: Descriptive Statistics for Mean Flexion Moment................................................42 Table 15: Independent Samples t-test for Equality of Means..............................................43

Vll

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

List of Figures

Figure 1: Shoulder Girdle Anatomy^^^.................................................................................... 3 Figure 2: Elbow Joint Anatomy^^^............................................................................................4 Figure 3; Hand and Wrist^^^...................................................................................................... 5 Figure 4: Body Planes^^^............................................................................................................6 Figure 5: Euler Angles^"^^...........................................................................................................7 Figure 6: Globographic Shoulder Representation^^^.............................................................. 9 Figure 7: Definition of Globograpbie Joint Angles^^^............................................................ 9 Figure 8: Elbow Joint Articulation^'^.....................................................................................11 Figure 9: Wrist Artieulation^^^................................................................................................ 12 Figure 10: Spherical Joint Center.......................................................................................... 14 Figure 11: Scapulotboracic M o tio n ^....................................................................................19 Figure 12: Elbow Flexor MuseW^^.......................................................................................20 Figure 13: Upper Extremity Bony Landmarks Proposed by the ISB^^^..............................21 Figure 14: Thorax Coordinate System^^^............................................................................... 23 Figure 15: Scapula Coordinate System^*^.............................................................................. 24 Figure 16: Humerus Coordinate System^*^............................................................................ 25 Figure 17: Forearm Coordinate System^^^............................................................................. 26 Figure 18: Hand Coordinate System......................................................................................27 Figure 19: Dumbbell Coordinate System ............................................................................. 28 Figure 20: Subject Marker Placement....................................................................................32 Figure 21: 8-Camera Vicon Motion Capture System.......................................................... 33

Vlll

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Figure 22: Incline Curl Bench (Preacher Bench)..................................................................35 Figure 23: Incline and Standing Bicep Curl Average Kinematics and Kinetics................ 39 Figure 24: Varying Moment Arm of Biceps^'^......................................................................45 Figure 25: Link Segment Model^^^.........................................................................................46 Figure 26: Subject #1 Bicep Curl Average Kinematics and Kinetics.............................. 70 Figure 27: Subject #2 Bicep Curl Average Kinematics and Kinetics.............................. 71 Figure 28: Subject #3 Bicep Curl Average Kinematics and Kinetics.............................. 72 Figure 29: Subject #4 Bicep Curl Average Kinematics and Kinetics.............................. 73 Figure 30: Subject #5 Bicep Curl Average Kinematics and Kinetics.............................. 74 Figure 31: Elbow Flexion Range of Motion Box Plot......................................................... 75 Figure 32: Maximum Flexion Moment Box P lo t.................................................................76 Figure 33: Flexion Angle for Maximum Moment Box Plot................................................76 Figure 34: Mean Flexion Moment Box Plot......................................................................... 77

IX

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

List of Symbols and Abbreviations

ISB...................................................................... International Society of Biomeehanies EMG....................................................................Electromyography CoR..................................................................... Center of rotation R .......................................................................... Rotation matrix between two segments Rx(0)....................................................................Rotation about axis “x” by an angle 0 n ...........................................................................Total number of time frames m ..........................................................................Total number of markers Pij......................................................................... Position of marker] at time frame i ij...........................................................................Radius of sphere on which marker] moves Cgeom.....................................................................Geometric error Caig........................................................................Algebraic error

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

1

Introduction

Application of upper extremity biomechanical modeling in both clinical and nonclinical settings has been hindered by the complex range of movements at the shoulder girdle and by the limitations of available technologies. This is not to say that there have not been any useful motion analyses of the upper extremity, but the underlying problems that have prevented widespread use still exist. Consequently, there is no general standard to guide the development of upper extremity models. However, as motion analyses prove to be ever more valuable in fields such as gait analysis, sport biomechanics, and ergonomics, innovative modeling techniques and standards are being developed to overcome the hurdles of upper extremity biomechanical modeling.

1.1 Upper Extremity Anatomy The upper extremity consists of the trunk, head, neck, shoulders, arms, and hands. The complex anatomy and range of motion of the upper extremity is largely responsible for prohibiting the development of robust models. For this reason it is important to be familiar with upper extremity anatomy, particularly the shoulder girdle, to gain insight into the problem at hand. The shoulder has the greatest range of motion of any joint in the body. Many people mistakenly consider shoulder joint as one joint, when in actuality shoulder motion eomes fi-om four distinct articulations. Figure 1 shows the anatomy of the shoulder girdle, including its four major joints. These include the sternoclavicular, acromioclavicular, and glenohumeral joints. The sternoclavicular joint is a saddle type joint that links the

1

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

upper extremity to the torso. Artieulation oeeurs between the medial end of both clavicles, the cartilage of the first ribs, and the sternum. The acromioclavicular joint functions as a pivot point between the lateral end of the clavicle and the scapula, allowing for movement of the arm above the head. This joint is held together by various ligaments that run between both the coracoid and acromion processes of the scapula and the clavicle. The extremely mobile glenohumeral joint, commonly called the shoulder, is a ball and socket joint and links the humerus to the glenoid fossa of the scapula. Finally, although the scapula and thorax do not have the structure of a typical joint, articulation between these segments, or scapulothoracic motion, also contributes to shoulder motion. These four separate articulations all contribute simultaneously to shoulder motion. Understanding and describing the impact of any of these particular joint’s articulation on the overall range o f motion o f the shoulder is one of the many challenges of upper extremity modeling. In fact, many upper extremity models simply do not account for these individual articulations. The shoulder is certainly the most challenging aspect of upper extremity modeling.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Acromioclavicular joint

Acromion of scap u la

Sternoclavicular joint

Clavicle

Sternum

S capula

G lenotium eral joint

Hum erus Scapulottioracic articulation

Figure 1: Shoulder Girdle Anatomy[1]

The elbow joint is far simpler than the shoulder in terms of range of motion, but anatomically speaking it is equally as complex. As shown in Figure 2, the two bones of the forearm articulate with the distal end of the humerus at the elbow. Actually, the elbow is composed of two separate joints: the humeroulnar and the humeroradial joints. The humeroulnar joint is a true hinge joint. Articulation occurs between the proximal end of radius and the distal end of the humerus. The radioulnar joint can be classified as a ball-and-socket joint, although ligaments surrounding the elbow joint connect the radius and ulna, preventing abduction or adduction o f the radioulnar joint. However, the structure of the elbow still allows for rotation of the forearm, or pronation and supination.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Humerus

Trochlea

/

Lateral epicondyle

Medial epicondyle

Capitulum

Olecranon Radial notch

Sem ilunar notch

\

H ead

Coronoid p ro cess

Tuberosity —f — ?

Tuberosity

Radius

Ulna

Ulnar styloid pro cess Radial styloid p ro cess

Figure 2: Elbow Joint Anatomy^^^

The hand and wrist compose one of the most complex set o f joints in the human body. Measuring the motion of each bone in the hand requires the development of a specialized biomechanical model. In fact, most general upper extremity studies simply treat the hand as one segment, ignoring movement in the fingers altogether. However, a brief introduction of the anatomy of the hand is appropriate. As shown in Figure 3, the wrist is the connection between the two bones of the forearm and the hand. The wrist is essentially composed of two rows of short bones, called carpals, which allow for motion

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

at the wrist. The metacarpal bones are the five long bones that connect the phalanges, or fingers, to the wrist.

Distal phalanx Middle phalanx Distal phalanx

Proximal phalanx

Proximal phalanx

Metacarpal bone

Carpal-----bones

R adius

U lna

Figure 3: Hand and Wrist^'^

1.2 Description of Joint Angles Calculation o f joint angles, or kinematics, is one of the essential fimctions of a biomecbanical model. Joint angles are typically defined as the angular position of a body segment with regard to the proximal segment. For example, knee joint angles would refer to the angular position of the shank relative to the thigh. Measurement of joint angles in three dimensions is very difficult, if not impossible, to achieve through observation alone. This is one of the driving forces for using motion capture systems and biomecbanical models to measure joint angles. Perhaps the most challenging aspect of upper extremity modeling is the difficulty in describing shoulder joint angles in clinically meaningful terms. Three dimensional

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

rotations can be described using quaternions, Euler angles, or helical axes, however, Euler angles are the only clinically relevant method. Traditionally, joint angles are described in relation to the three body planes: the frontal plane, the sagittal plane, and the transverse plane as shown in Figure 4. Motion in the sagittal plane is called flexion/extension, motion in the frontal plane is called abduction/adduction, and motion in the transverse plane is called intemal/extemal rotation. This convention is used extensively in gait analysis where the primary motion occurs in the sagittal plane.

Sagittal plane

Z

Transverse plane

Figure 4: Body Planes^^^ Euler angles can be used to describe motions in the three body planes. A rotation matrix between two body segments can be decomposed into three elementary rotation matrices, each o f which corresponds to a rotation about a single axis. For example, a rotation about the Z-axis, followed by a rotation about the new x ’-axis, followed by a

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

rotation about the new z”-axis would be designated a (z”, x’, Z) Euler rotation sequence. This is shown graphically in Figure 5 and mathematically in Equation 1.

R^R,.M-RÀfyR,i'p)

( 1)

Where: R = 3-dimensional rotation matrix ip) = rotation about Z-axis by angle (p Rx\o) - rotation about X’-axis by angle 0 = rotation about Z” -axis by angle y/

e about x ' OU T PU T ( H e a d A n g l e s ) N e c k A n g le s = -< T h o r a x ,H e a d ,y x z > OU T PU T ( N e c k A n g l e s ) T h o r a x A n g le s= -< G lo b a l, O U T PU T ( T h o r a x A n g l e s )

T h o r a x ,z x y >

R o t Y X Y ( R H u m e r u s , T h o r a x ,R S H O U L D E R ) R E lb o w A n g le s = -< R H u m eru s, R F o r e a r m ,z x y > R E lb o w A n g le s = < R e lb o w A n g le s ( 1 ) , R e lb o w A n g le s ( 2 ) , R E lb o w A n g le s ( 3 ) -9 0 > O U T PU T ( R E l b o w A n g l e s ) R W r is t A n g le s = -< R F o r e a r m ,R H a n d ,z x y > O U T PU T ( R W r i s t A n g l e s ) R S h o u ld e r A n g le s= -< T h o r a x ,R H u m e r u s, zxy> O U T PU T ( R S h o u l d e r A n g l e s ) {*K IN E T IC S*} {*========*} {*============*} { *= = = = = = = = = = = = *}

{ *ANTHROPOMETRIC DATA*} { * T h is d a t a i s from W in te r (1 9 9 0 ) C h a p te r 3 A n th r o p o m e tr y , a n d M o t o r C o n t r o l o f H u m an M o v e m e n t , S e c o n d E d i t i o n * } { * U n iv e r s it y o f W a terlo o , O n ta r io , C anada, p a g e s: 56 , 57*} A n th ro p o m etricD a ta A n th ro H a n d 0 . 0 0 6 0 . 6 2 05 0 . 2 2 3 0 A n th ro R a d iu s 0 . 0 1 6 0 . 5 7 0 . 3 0 3 0

B io m e c h a n ic s

65

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

A n throH um erus 0 . 0 2 8 0 . 5 6 4 0 . 3 2 2 A n th roT h orax 0 . 3 5 5 0 . 6 3 0 . 3 1 0 A n th r o H e a d 0 . 0 8 1 0 . 5 2 0 . 4 95 0 E n d A n th r o p o m etricD a ta

0

$ % R H u m eru sL en g th = D IS T (R S J C ,R E J C ) PARAM( $ % R H u m e r u s L e n g t h ) $ % R F o rea rm L en g th = D IS T (R E J C ,R U S ) P A R A M ($% R F orearm L en gth ) T horax

=

[T h o ra x ,

A n th roT h orax]

{ * s q u a r e r a d i u s o f g y r a t i o n : . 1 0 3 = . 3 2 2 * * 2 *} R H u m eru s= [R H u m eru s, 0 . 0 2 8 * $ B o d y M a s s , { 0 , 0 . 43 6 * $ % R H u m e r u sL e n g th ,0 } , $% R H u m eru sL en gth *$% R H u m eru sL en gth *{ . 1 0 3 , 0 , . 1 0 3 } * 0 . 0 2 8 * $ B o d y M a ss] R H u m e r u s= [ R H u m e r u s , T h o r a x , RSJC] {* s q u a r e r a d i u s o f g y r a t i o n : . 0 9 1 = . 3 0 3 * * 2 *} R F o rea rm = [R F o rea rm , 0 . 0 1 6 * $ B o d y M a ss, { 0 , 0 . 5 7 0 * $ % R F o r e a rm L en g th ,0 } , $% R H u m eru sL en gth *$% R H u m eru sL en gth *{ . 0 9 1 , 0 , . 0 9 1 } * 0 . 0 1 6 * $ B o d y M a ss] R F o r e a r m = [ R F o r e a r m , R H u m e r u s , REJC] {* s q u a r e r a d i u s o f g y r a t i o n : . 0 8 8 = .2 9 6 * * 2 *} R H and=[R H and, 0 . 0 0 6 * $ B o d y M a s s , { 0 , 0 , 0 } , $R H an d L en g th * $ R H a n d L en g th * ( . 0 8 8 , 0 , . 0 8 8 } * 0 .0 0 6 * $ B o d y M a s s ] R H a n d = [ R H a n d , R F o r e a r m , RWJC] {* s q u a r e r a d i u s o f g y r a t i o n : . 0 8 8 = . 2 9 6 * * 2 D um bbe1 1 = [ D u m b b e ll, $D B M ass, { 0 , 0 , 0 } , { $ D B I n e r t L o n g , $ D B I n e r t T r a n s , $ D B I n e r t T r a n s }] D u m b b e l l = [ D u m b b e l l , R H a n d , RHC] {*

*}

J O I N T FORCES * }

{*========*}

R W r i s t F o r c e = 1 (R E A C T IO N (R H and)) / $ B o d y M a s s R E lb o w F o r c e = 1 (R E A C T IO N (R F orearm )) / $ B o d y M a ss R S h o u l d e r F o r c e = 1 (R E A C T IO N (R H u m eru s)) / $ B o d y M a ss OUTPUT ( R S h o u l d e r F o r c e , R E l b o w F o r c e , R W r i S t F o r c e )

{*

J O I N T MOMENTS * }

{*========*} {*========*}

R W r is t M o m e n t = 2 (R E A C T IO N (R H an d )) / ( $ B o d y M a s s ) R E lb ow M om en t = 2 (R E A C T IO N (R F o rea rm )) / ($ B o d y M a ss ) R S h o u ld e r M o m e n t = 2 (R E A C T IO N (R H u m eru s)) / ($ B o d y M a s s ) OUTPUT ( R S h o u l d e r M o m e n t , R E l b o w M o m e n t , R W r i s t M o m e n t ) {*

J O I N T POWERS * }

{*========*} {*========*}

R W r i s t P o w e r = P O W E R (R Forearm , R H a n d )/ ($ B o d y M a s s ) R E l b o w P o w e r = P O W E R ( R H u m e r u s, R F o r e a r m ) / ( $ B o d y M a s s ) R S h o u ld e r P o w e r = P O W E R (T h o r a x ,R H u m e r u s)/ ($ B o d y M a ss ) OUTPUT ( R S h o u l d e r P o w e r , R E l b o w P o w e r , R W r i s t P o w e r )

66

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Appendix C: MATLAB Code for Center of Rotation Calculation

%%read marker position data %%Assumes position vectors are row vectors in spreadsheet function CoR = NewtonQ %gather marker data from excel spreadsheet allmarkerposition = xlsread('6340_sjc.xls'); %store marker data in a 3-dimensional matrix %row=frame, columnl=x, column2=y, column3=z, 3D=marker v(:, 1,1 )=allmarkerposition(:, 1); v(: ,2,1 )=allmarkerposition(: ,2) v(: ,3,1 )=allmarkerposition(: ,3) v(:, 1,2)=allmarkerposition(:,4) v( :,2,2)=allmarkerposition( :, 5) v(:,3,2)=allmarkerposition(:,6) %determine number of markers and frames markers = size(v,3); frames = size(v,l); %convergence value maxDistance = .0001; %Initial Guess for CoR and Rj CoR=[l 0,10,10]; ij=zeros(markers); for p=l markers q(p)=400; end notConverged = 1; i = 1; % ith estimate o f CoR while (notConverged) %calculate error matrix E=err(v,ij,CoR(i,:)); %calculate jacobian matrix J=Jacobian(v, CoR(i,:));

67

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

%calculate change in CoR and Rj delta=inv(J'* J) *(J'* E) ; %Detemiine New Values of CoR and Rj CoR=[CoR; CoR(i, :)+[delta( 1,1 ),delta(2,1),delta(3,1)]] ; for j= l markers q(l,j)=ij(lj)+delta(3+j,l); end %Determine if sufficient convergence reached ifi >10000 disp('BC requires over 10000 iterations'); notConverged = 0; end if(i> l) if(norm ( CoR(i,:)-CoR(i-l,:), inf)