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ABSTRACT
A Linked-plane Obstacle-set Algorithm for Modeling Broad Muscle Paths: Application to the Deltoid Muscle Bo Xu, M. S. B. M. E. Mentor: Brian A. Garner, Ph. D. Computer modeling is commonly used to simulate muscle paths for the study of human biomechanics. Because some muscles, such as broad muscles, have complex morphology, modeling the paths of these muscles can be challenging. The aim of this study is to develop a new algorithm that quickly and realistically models the wrapping paths of broad muscles. The algorithm treats the muscle as a series of elastic bands wrapping around sphere-shaped obstacles. Each band is constrained to lie in its own plane and wrap around its own sphere. Each band plane forms a given angle with respect to the adjacent band plane, with the first band plane forming an optimized angle with respect to a fixed reference plane. The optimization seeks to minimize the sum total of all band lengths. The new algorithm accounts for tissue connectivity between muscle fibers in broad muscles, and can reproduce realistic muscle moment arm simulations.
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A Linked-plane Obstacle-set Algorithm for Modeling Broad Muscle Paths: Application to the Deltoid Muscle by Bo Xu, B. S. E. E. A Thesis Approved by Department of Mechanical Engineering
William Jordan, Ph. D., Chairperson Submitted to the Graduate Faculty of Baylor University in Partial Fulfillment of the Requirements for the Degree Master of Science in Biomedical Engineeringof
Approved by the Thesis Committee
Brian Garner, Ph. D., Chairperson
James B. Farison, Ph. D ___________________________________Qin Sheng, Ph. D
Accepted by the Graduate School August 2008
J. Larry Lyon, Ph.D., Dean
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TABLE OF CONTENTS
LIST OF FIGURES..................................................................................................... vi LIST OF TABLES ...................................................................................................... viii
- CHAPTER ONEIntroduction ACKOWLEDGEMENTS xi - Musculoskeletal Biomechanics - Overview of Human Musculoskeletal System - Basics of Human Musculoskeletal Biomechanics - Experimental and Computational Methods in Musculoskeletal BiomechanicsExperimental Methods - Complementary Role of Computer Modeling........................................... - Importance of Modeling Paths of Muscles - Challenge of Modeling Broad Muscles..................................................... - Purpose and Overview of Thesis Research .....................................................Brief Summary of Previous Types of Algorithms - Purpose - Overview of Thesis
- CHAPTER TWOBroad Muscles in the Human Anatomy - Types of Muscle Geometries........................................................................... - Definitions of Muscle Origin and Insertion - Examples of Broad Muscles............................................................................ - Gluteal Muscles.........................................................................................Abdominal and Back Muscles - Shoulder Muscles
- Previous Muscle Wrapping Algorithms................................................................Straight-line Algorithm CHAPTER THREE
- Line-segments with Via-points Algorithm......................................................
- Obstacle-set Algorithm
- 3D Finite-element Algorithm
- The Linked-plane Obstacle-Set Algorithm CHAPTER FOUR
- Principles of Single Band Wrapping Around Sphere...................................... iv
- Principles of Solving for All Bands Simultaneously
- Parameters Required for Defining Muscle Path..............................................Variations of Algorithm
- A Case Study: Modeling the Human Deltoid....................................................... CHAPTER FIVE
- Overview .........................................................................................................Experimental Studies of Deltoid Moment Arm
- Moment Arm Calculation
- Three Heads of Deltoid
- Arm Movements Studied
- Computer Model of the Deltoid Muscle .........................................................Three Studies from Which Moment Arm Comparisons Were Made........
- Bones and Muscles Reconstructed from the Medical Images...................
- Kinematics Model
- Deltoid Origin and Insertion Sites.............................................................
- Obstacle Sphere Centers and Radii ...........................................................Orientation of the Global Reference Plane
- Angle Phi Between Each Muscle Band Plane...........................................
- Simulations of Moment Arm Data
- Comparing Simulated with Experimental Data
- Optimizing Parameters to Match Experimental Data ...............................Tricks to Improve Simulated Reproduction of Experimental Data...........
- Results CHAPTER SIX
- Optimized Deltoid Model Parameters.............................................................Origin and Insertion Sites..........................................................................
- Obstacle Sphere Centers, Radii, and Phi Values.......................................
- Simulated vs. Experimental Deltoid Muscle Data
- Linked-plane Computational Performance and Robustness
- Discussion and Conclusions.................................................................................. CHAPTER SEVEN
- Advantages of the Linked-plane Algorithm....................................................
- Elegant Simplicity
- Realistic Representation of Broad Muscles ..............................................Fast Computational Performance
- Flexibility
- Limitations of the Linked-Plane Algorithm
- Many Parameters to Define.......................................................................
- Conclusion.......................................................................................................Comprehensive Matching of Experimental Data
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LIST OF FIGURES
Figure 1.1 Basic components of the musculoskeletal system .................................... 2 Figure 1.2 Muscle length-force property.................................................................... 3 Figure 1.3 Experimental methods to study musculoskeletal biomechanics............... 4 Figure 1.4 Computer modeling methods to study musculoskeletal biomechanics.. .. 6 Figure 2.1 (a) Gluteus maximus. (b) Gluteus medius ............................................... 13 Figure 2.2 (a) Abdominal external oblique. (b) Latissimus dorsi. ............................ 14 Figure 2.3 (a) Pectoralis major. (b) Deltoid .............................................................. 15 Figure 3.1 Straight-line muscle path model. .............................................................. 16 Figure 3.2 Via-points muscle path model .................................................................. 17 Figure 3.3 Obstacle-set muscle path model for biceps brachii .................................. 19 Figure 3.4 3D finite-element model for the gluteus maximus and the gluteus medius 21 Figure 4.1 A single band wraps around a sphere ....................................................... 22 Figure 4.2 Multiple bands wrap over sphere obstacles .............................................. 23 Figure 5.1 The thoracic system defined by the Mayo Clinic ..................................... 30 Figure 5.2 (a) one cross-section CT image of the trunk of human body, resource from Visible Human Project. (b) Frontal view of the upper limb reconstructed for this study, with the global coordinates origin fixed at the middle top of manubrium sterni. (c) Lateral view of the reconstructed three dimensional image of the deltoidmuscle.................................................................................................................. 33
Figure 5.3 Ground coordinates locates at the center of the glenohumeral joint. A framed plane is also pictured to represent the global reference plane. ............... 37 Figure A.1 Four typical types of obstacle-sets for modeling the constraining anatomical structures ............................................................................................................. 59
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Figure B.1: Illustration of a single muscle path wrapping around a sphere obstacle. 60 Figure C.1 Geometry illustration for calculating cross-section’s center and radius.. 62 Figure C.2: Point Q is a tangent point from P lying in the muscle path plane on the cross-section circle of the wrapping sphere. Point T (not shown) is a similar tangent point from S............................................................................................ 63 Figure C.3: Illustration of tangent points q and t computed based on points p, s, and c, all expressed in the local coordinate system of the muscle band plane .............. 65 Figure D.1 Steps to calculate the optimal reference angle value ............................... 66 Figure E.1 The origin and insertion sites of the deltoid muscle................................. 67 Figure E.2 Sphere obstacles for all the muscle bands ................................................ 68 Figure E.3 Top back view of the muscle bands lying within the deltoid musclereconstructed from the VHP dataset.................................................................... 69
Figure E.4 Muscle path lengths for each head of the deltoid during abduction, scaption and flexion........................................................................................................... 70 Figure E.5 Moment arm graphs for each head of the deltoid during abduction, scaption and flexion........................................................................................................... 71 Figure E.6 Lateral view of the deltoid muscle, showing all of the nine modeled muscle bands ................................................................................................................... 72 Figure E.7 Lateral view of the deltoid muscle with the humerus flexed 80 degrees. 73 Figure E.8 Lateral view of the deltoid muscle, with the humerus raised 80 degrees in the scapular plane...................................................................................................... 74 Figure E.9 Frontal view of the deltoid muscle, with the humerus abducted 90 degrees 75 Figure E.10 Side view of the humerus rotating in the sagittal pane: a) Extension. b) Neutral position. c) Flexion................................................................................ 76
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ACKNOWLEDGMENTS
I thank Baylor University School of Engineering and Computer Science for having me here. I am grateful for support from Dr. James Farison, my friend Dan Shen and my dear parents. I especially thank Dr. Brian Garner for introducing me to this fun area of research, and for patiently guiding me through the past two years.
CHAPTER ONE
Introduction Musculoskeletal Biomechanics
Overview of Human Musculoskeletal System The musculoskeletal system of our human body is very complex. From a biomechanics perspective it may be considered to involve a passive system and an active system. Coordination of the two systems helps to permit certain body movements while also maintaining body center of gravity and balance. The passive system is composed of the skeleton and the associated connective tissues such as cartilage and ligaments. It is termed “passive” because it only generates forces in response to movements and forces produced by the active system. Bone is a rigid mertialbody that supports our body, transmits forces, and acts as levers for force transmission. Cartilage is an elastic and flexible tissue that cushions the bones during motions. Finally, ligament connects bone to bone, and is designed to restrict movements to certain directions to maintain both stability and flexibility within joints. The active system is mainly composed of muscles and the attached tendons (Figure 1.1). When stimulated by the neural system, muscles are able to generate forces directly by contracting. Muscle forces are transmitted by tendons to the skeleton to control movement and to help maintain body posture.
Muscle produces forces both due to passive elastic properties and to active contraction in response to neural stimulation (i.e., “activation”). The passive force- length response represents the steady-state force at zero activation for various isometric lengths. The fully active force-length response represents steady-state force at full activation for different isometric lengths. This response diminishes with less-than-full activation, and also with increasing muscle-shortening velocity. The total muscle force is the sum of the active force and the passive force (Figure 1.2). The capacity of a muscle to produce force may be considered as the steady-state force of a muscle, given its current length and shortening velocity, when fully activated by the neural system.
Figure 1.2 Muscle length-force property. Experimental and Computational Methods in Musculoskeletal Biomechanics
Experimental Methods Many aspects of musculoskeletal biomechanics can be revealed using experimental methods (Figure 1.3). The methods may involve living human subjects,
cadavers, or animals. Quantities such as gross body motions (by motion capture systems), external reaction forces (by force plates, load cells, or other force transducers), and even electrical signals (by electromyography, or EMG electrodes) generated by muscles when they activate can be recorded experimentally from live subjects [2]. Studies of human cadaver specimens can reveal much about the anatomy and the structure of anatomical tissues including bones, muscles, articulating joint surfaces, ligaments, tendons, and many other components. Studies involving animals may be used, for example, to simulate human response to surgical methods, orthopedic implants, exercise regimes, and the like.
Figure 1.3: Experimental methods to study musculoskeletal biomechanics: (a)Electromyography [3]; (b) Reflective motion markers [4].
Figure 1.4 Computer modeling methods to study musculoskeletal biomechanics: (a) Anybody Tech—occupational health [6]. (b) Computer modeling of a leg, with 9degrees of freedom. (c) & (d) Mathematical model of the vocal folds and the glottal flow for studying vocal folds deformation, and glottal fluid-structure interaction [7].
activity, and then these may be compared with similar data measured experimentally. In either case, the computer model provides insights into what is happening inside the body to produce what is observed outside the body. Computer modeling offers a convenient platform to manipulate the data from experiments, and to simulate the data that is not accessible during experiments. Of course, the results of a computer model and simulation are only as good as the model is able to accurately reproduce the actual biomechanics occurring in the body. Therefore, it is desirable to derive and validate a model based on as much experimentally available information about the real system as possible. For example, many computer models are now derived from medical images such as CT or MRI, which provide a snapshot of the internal anatomy. A series of two-dimensional medical
images may be taken at very high resolutions, and then reconstructed to recreate the three-dimensional geometry of anatomical structures such as bones and muscles. In this way, a computer model may be derived and constructed based on actual anatomical dimensions.
Importance of Modeling Paths of Muscles Common to all the various approaches for modeling musculoskeletal biomechanics is the need for defining a mathematical model for the muscle path. The description of the muscle path is a foundation upon which many other aspects of the computer model builds. Representation of the muscle paths determines the muscle’s attachment sites and trajectory between attachment sites. These factors directly influence both the point of and direction of the force applied to the bone. In addition, the muscle path influences how large the muscle force can be because it determines the muscle length, which, by virtue of a muscle’s force-length properties, determines a muscle’s force capacity. Failure to model the muscle paths realistically could greatly distort the research results from musculoskeletal modeling studies. A muscle path is the line-of-action of a muscle fiber as it wraps over bones and other tissues on its way from origin to insertion. A muscle fiber starts from one attachment site on the origin bone, deforms its shape to wrap around the joint, and inserts onto another articulating bone, generating a torque to pull one articulating bone toward another. A proper definition of muscle paths in musculoskeletal models includes the specification of the origin and insertion sites, a description of the joint and joint motion, and a description of the wrapping shape of the muscle fibers between attachment sites. A good model of muscle paths will permit ready calculation of the
conditions need to be simulated in the model. Quantifying the parameters required to describe these types of anatomical constraints for each section of a broad muscle can be very challenging. Another challenge in modeling broad muscles is simulating the coordination of the muscle fibers within a muscle. Muscle fibers run generally parallel to each other along the line-of-action, held together by connective tissues such as the epimysium, endomysium, and perimysium, which serve to ensheath the muscle fibers within different layers (shown in Figure 1.1). Because of these connective tissues the muscle fibers generally move together as a solid, yet deformable, shape. Most previous efforts to model muscle paths have ignored this connectivity, and have assumed that each section of muscle fibers, or muscle band, wraps around underlying structures somewhat independently from the others. Results from some of these previous studies (such as [11]) indicate that ignoring the connectivity between muscle fibers can lead to unreasonable behavior of the muscle paths during motion simulation. Previous efforts, such as Blemker et al. [10], using methods that do account for interconnectivity between muscle fibers tend report very slow computation times that are not practical for in-depth simulation. The challenge, therefore, lies in how to account for the internal connectivity between muscle fibers in a way that the model can be realistic, robust, and computationally efficient.
Brief Summary of Previous Types of Algorithms A number of algorithms have been developed so far to model muscle paths, including the straight-line model, line-segments with via-points model, obstacle-set model, and three dimensional, finite elements model, [9]-[11].
All of these algorithms except the finite element algorithm model muscle paths as a single band through which muscle force is assumed to be transmitted. Broad muscles are often modeled using multiple, independent bands. Since the internal connectivity between muscle tissues is not taken into account, these algorithms lack a certain degree of realism. The finite element model accounts for the connection of tissues within a muscle by modeling the entire structure of the muscle with finite elements. This approach is especially relevant for broad muscles whose shape is clearly influenced by adjacent fibers within the muscle. As will be described more fully in Chapter Three, each previous model has its advantages and disadvantages. The simple method of the straight line model is very easy to implement and solves extremely quickly, but only provides an accurate muscle path representation for very short and simple muscle fibers that traverse essentially straight lines between attachment sites. The via-points model introduces additional points of traversal so that the muscle path is a connected series of straight lines between attachment sites. This method is also simple and speedy, but still lacks geometric realism for many types of muscles. The obstacle-set model, which simulates muscle fibers as independent elastic bands wrapping frictionlessly around simple geometric shapes, offers nice simulations of thin muscles, but can have problems modeling broad muscles realistically due to the fact that each band is considered independently without regard to interconnectivity. The finite element algorithm can offer good realism, but is fairly complex to implement and is very expensive in terms of computational time.
