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Development and evaluation of a method and apparatus to measure shoulder instabilities Lecarpentier, Karine 1997

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Development and Evaluation of a Method and Apparatus to Measure Shoulder Instabilities by Karine Lecarpentier Engineer Degree, Ecole Nationale Superieure des Techniques Avancees, France. 1996 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF Master of Applied Science in T H E F A C U L T Y OF G R A D U A T E STUDIES (Department of Electrical Engineering) We accept this thesis as conforming to the required standard The University of British Columbia August 1997 © Karine Lecarpentier, 1997 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I. agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. -Department of The University of British Columbia Vancouver, Canada Date ^ , d r /ft, f g ? DE-6 (2/88) Abstract The shoulder is now subject to a rapidly increasing number and variety of surgical proce-dures. However, the results of these procedures in terms of improved patient life are subjectively reported. No precise, objective and non-invasive method is currently available to assess the dynamic function of the shoulder. The two major bones involved in the shoulder are the scapula (shoulder blade) and the humerus (upper arm). The extremity of the scapula in contact with the humeral head is called the glenoid. Together they form the glenohumeral joint. The articulating surface of the humeral head is spherical. The glenoid is congruent to the humeral head, but its small dimension allows small translations to occur. If translations become too large (typically 2 or 3 cm), the joint can dislocate, damaging surrounding tissues. The shoulder is then said unstable. Stability and mobility of the shoulder can be characterized by the amount and direction of translations in the glenohumeral joint. The goal of this thesis was to develop a system that gives a quantitative and precise assess-ment of shoulder laxity at the time of diagnosis, and again after surgical intervention. This system should be non-invasive, objective, relatively inexpensive, easy to use and to set up, and should fit any sized patient. It should give quantitative information and be repeatable and accurate within 1 or 2 mm. The system we developed measures shoulder translations using the trajectory of the elbow relative to the shoulder. An electro-magnetic sensor was incorporated in the system to measure the position of the elbow and the position of a reference point on the shoulder (acromion). We modeled ii the humeral head as a sphere and the glenoid as a small planar surface. From this model, we developed an algorithm that measures shoulder translations, assuming that the distance R between the sensor on the elbow and the center of the humeral head, and the orientation 6 of the glenoid are known. A method was developed to assess the accuracy and calibration of the electro-magnetic sensor. The maximum error was 1.5 mm. We validated the' system on an artificial model. On patients, the system showed a significant difference in the shape of the translation curve between the stable and unstable shoulder of a patient with serious shoulder instability. However, the rotation of the scapula, that we neglected, induced significant errors and prevented any useful quantitative information. The system as it stands now is a useful tool to supplement existing methods, but additional work is necessary for the system to be used routinely and replace existing methods. In particular, a more precise tracking of the scapula is necessary to measure its rotation. Immobilization of the scapula may be an alternate solution. Some suggestions were made to improve the accuracy of the electro-magnetic sensor. A better estimation of the parameter R may be obtained from radiography. Once the system gives the required quantitative information, the system will contribute to improve objectivity and accuracy in assessment which we trust will improve outcomes in shoulder surgery. The system could be adapted to measure other joint instabilities such as the knee and the hip and be the base for the development of other technologies for general improved patient outcome. 111 Contents Abstract ii Contents iv Remerciements vii Medical Terminology viii 1 Introduction 1 1.1 Motivation for the Research . . 1 1.2 Scope of the Thesis 4 1.3 Contributions of the Research . 4 1.4 Thesis Overview 5 2 Background 7 2.1 Clinical Background 7 2.1.1 The Shoulder Mechanism and Causes of Instabilities 7 2.1.2 Definitions of Anatomical Plans and Joint Movements 12 2.1.3 Literature Review on Translations in Glenohumeral Joints . 14 2.1.4 Current Methods to-Assess Shoulder Instabilities and Specifications for a Novel Method and System 16 2.2 Technical Background 18 2.2.1 Specifications for Position Sensors 18 iv 2.2.2 Review of Different Types of Position Sensors 18 3 Electro-magnetic Position Sensors 25 3.1 Introduction '. . 25 3.2 Electro-magnetic Sensors Technology 25 3.3 Definition of Terms and Characteristics 28 3.4 Overview of the "Flock of Birds" ™ 30 3.5 Errors with the Default Filter Setting 32 3.5.1 Static Error 32 3.5.2 Error Due to the Time-Varying Noise and to the Interaction between the Receivers 33 3.5.3 Errors Due to Time-Lag 34. 3.6 Modification of the System Setting 35 3.7 Influence of Metallic Environment 38 3.8 Results, Possibility of Calibration and Extension to a Broader Range of Related Medical Applications 40 3.9 Possible Improvements to the Sensor 45 4 Mathematical Model of the Shoulder and Algorithm 47 4.1 Introduction 47 4.2 Model of the Glenohumeral Joint and Introduction to the Algorithm 48 4.3 Algorithm 50 4.4 Simulations 54 4.5 Study of the Errors and of their Propagation on the Model 57 4.5.1 Propagation of error in estimation of R 57 4.5.2 Propagation of Errors in Estimation of 6 (Glenoid angle) 59 4'5.3 Propagation of Sensor and Sensing Errors • • 60 4.6 Summary 66 v 5 Evaluation of the Model and Clinical Application 68 5.1 Introduction 68 5.2 Evaluation on an Artificial Model 69 5.3 Clinical Set-up 71 5.3.1 Placement of the Sensors 71 5.3.2 Position of the Patient and the Tester . . 75 5.4 Initial Study of the Repeatability of the System 78 5.5 Initial Testings on a Patient with an Unstable Shoulder 79 5.6 Introduction of Forces Applied Against the Movement 84 5.7 Analysis of Results and Discussion 89 5.8 Conclusion 90 6 Conclusions 91 6.1 Motivation 91 6.2 Contributions 91 6.3 Conclusions 92 6.4 Suggestions for Future Work 95 Bibliography 97 Appendices 100 vi Remer elements Je remercie tout particulierement Dr. James McEwen pour sa supervision, ses precieux conseils et ses encouragements tout au long de ce travail. Je remercie egalement Dr. Peter Lawrence pour avoir accepte de participer a la supervision de ce travail et pour ses excellentes suggestions. Je suis tres reconnaissante envers Alexei Marko pour son aide et sa participation dans ce projet. Ses commentaires ont ete extremement utiles tout au long de ce travail et particulierement lors de la redaction de cette these. Je tiens a remercier mes amis du departement de Genie Electrique et tout particulierement mon ami Mike Seymour qui m'a supporte pendant la totalite de ce travail et a passe une large portion de son temps a lire et corriger cette these. Enfin, je remercie Kenneth Glinz, Paul Russell et Mike Jameson de Western Clinical Devices pour leur aide technique dans ce projet et Dr. Antony Hodgson pour ses suggestions utiles. Ce projet a ete finance par Western Clinical Devices Inc., I R I S - P R E C A R N , et B C ASI (BC Advanced Systems Institute). K A R I N E L E C A R P E N T I E R The University of British Columbia August 1991 vii Medical Terminology Abduction of the shoulder Elevation of the upper arm in the plane of the body. Adduction of the shoulder Inward motion of the upper arm after abduction of the shoulder. Cross-body movement Motion of the upper arm in the horizontal plane. Glenohumeral joint Joint of the shoulder complex between the humerus and the scapula (see Figure 2.2). Glenoid Shallow distal extremity of the scapula. It forms the glenohumeral joint with the humerus (see Figure 2.2). Glenoid labrum Fibro-cartilage surface covering the glenoid. The glenoid fossa deepens the concavity of the articulation and offers a smooth surface. Humerus Bone that forms the upper arm (see Figure 2.2). Instability Condition of a joint characterized by an abnormal increased amount of mobility sec-ondary to injury of tissues; when applied to the shoulder, instability typically is used to describe a clinical condition characterized by physical signs and related patient symptoms of increased or excessive displacement of the glenohumeral joint [1]. Laxity Lack of tension (slackness or looseness) in a joint, must be further modified to indicate whether the laxity is normal or abnormal. For example, glenohumeral laxity is pathologic only if there is glenohumeral instability [1]. Scapula Triangular bone of the shoulder commonly called the shoulder blade (see Figure 2.2). viii Chapter 1 Introduction 1.1 Motivation for the Research Surgical procedures are rapidly increasing in number and variety. However, few tools are available to assess effectively and non-invasively the patient before surgery and the results of a surgical intervention. There is a general need for better tools to more objectively and more precisely quantify surgical patient outcomes, or the effects of surgical procedure on the patients' lives. Surgical patient outcomes include: • the results of a surgery in term of the nature and extent of any improvement in the patient's life, • the results of surgery , in terms of the relative patient outcomes by alternate surgical proce-dures and different surgeons, • the relative "value for money" achieved within the health care system in term of patient improvement as a result of the selected intervention modality, surgeon and surgical procedure. The number of surgical procedures performed on body joints is especially increasing. Pa-tients with joint pain or symptoms limiting joint strength or mobility are increasingly unwilling to restrict their life activities to accommodate their symptoms. The shoulder, in particular has received little attention until recently, because it does not bear the weight of the body and there-fore is not "vital" for the patient. Also, it is a very complex joint involving several bones and 1 many muscles, ligaments and other tissues. The complete mechanism of the shoulder is not fully understood. However the number and variety of procedures performed on it are rapidly growing and an increasing number of surgeons of varying experience perform these operations. The shoulder is the most mobile joint in the body and is subject to more dislocations than any other joint. Dislocations of the shoulder typically result from an excessive force applied to the joint that forces the arm to exit from the shoulder socket. When a shoulder dislocates, tissue damages usually occur, exposing the shoulder to more successive dislocations, the shoulder is then said unstable. No current precise non-invasive system or method exists to assess the instability of the shoulder, and to assess the results and benefits in terms of improved patient outcomes after surgery. Rather, indications for surgery and subsequent patient improvement are reported subjectively. At present, precise assessment of shoulder instability can be performed only invasively during surgical intervention by manipulation. Non-invasive assessment of laxity through manipulation of the shoulder by a clinician before and after surgery is current practice, but is subjective, imprecise and non-quantitative. Also at present, imaging techniques such as Magnetic Resonance Imaging (MRI) may be used to observe soft tissues for assessment of tissue damage or abnormality, and radiography may be used to observe bone damage and bone positions. Both are expensive and imprecise, both do not allow dynamic examination and manipulation of the shoulder by the clinician and they require the presence of another person with a different skill set to operate the imaging system and interpret the image data. A better method to assess the instability of the shoulder is necessary to improve the assessment of shoulder patient outcomes. A system which quantitatively and precisely assesses shoulder laxity at the time of diagnosis, and again after any surgical intervention, in a non-invasive and systematic way, would: • allow a non-invasive measurement, • allow dynamic rather than static observation and measurement of joint motion and laxity, by permitting motion of the shoulder and simultaneous quantitative measurement, • require only one person to use the system and interpret the data with no additional skill set necessary, 2 • allow the "best practice" or optimal type of surgical procedure to be identified, • facilitate the identification of patients who would not benefit from surgery or for whom surgery would not be warranted because no significant improvement would likely result from the surgery, • facilitate the evaluation of surgeons and the evaluation of the outcomes of shoulder surgery. In the shoulder, some laxity allowing small amount of joint translation is required for normal joint function. Too little translation would limit the range of motion of the shoulder. If laxity is too large, excessive translation in the shoulder joint may cause the joint to dislocate, and the joint is then said to be unstable. Instability of the shoulder can come from various causes and can be characterized by its direction (direction in which the joint is susceptible to dislocate) and degree.. It is hypothesized that measuring the amplitude and direction of shoulder translations is therefore a good way to identify and characterize shoulder instabilities. The purpose of this thesis was to develop a method and apparatus to measure shoulder translations in a non-invasive and repeatable way, suitable for routine clinical use before and after surgery. It is hypothesized that such a system, if successfully implemented in a clinical environment and routinely used, would be an important improvement in shoulder patient outcomes and would be a step in responding to the general need for better patient outcome technology. This thesis was undertaken in collaboration with Western Clinical Devices Inc., a small growing medical devices company based in Vancouver and was funded by Western Clinical Devices Inc., IRIS/PRECARN and the BC Advanced Systems Institute. It is part of a project involving these parties and the University of British Columbia. Because shoulder surgery for recurrent dislocations represents one of the most complex and rapidly evolving areas, Western Clinical Devices Inc. identified the shoulder as being a promising target application for research on new technology for improved patient outcomes, and this thesis follows on previous work undertaken by these parties involving measurement of shoulder instability and function [2]. 3 1.2 Scope of the Thesis The purpose of this thesis was the development and the evaluation of a system to measure shoulder instabilities in a non-invasive and repeatable way. This includes the development and implementa-tion of a prototype system, its evaluation from laboratory and clinical testings and recommendations for future work. The specific objectives were: • reviewing and investigating current systems, apparatus and methods to evaluate shoulder instabilities; • understanding the mechanism of the shoulder joint, and normal and pathologic translation during certain movements and under certain conditions; • defining functional specifications for a system to measure shoulder translation; • developing, implementing and initially evaluating a mathematical and physical model of the shoulder with a view to developing a system for outcomes assessment; • developing and implementing a system that measures shoulder translations according to the said specifications, based on the developed model of the shoulder; • performing laboratory and clinical tests to evaluate and refine the system; • adapting the system for routine clinical use. 1.3 Contributions of the Research The main contributions of this work are: • the development of detailed functional specifications for a novel system to satisfy a previously unmet clinical need for quantitative assessment of shoulder dynamic function in connection with surgical patient outcome studies; 4 • the development, application and evaluation of a method to assess the performance and check the calibration of existing electro-magnetic sensors in a broad range of medical applications, including the specific application addressed in this thesis; • the identification of opportunities for improving the design of the existing electro-magnetic sensors both to overcome limitations encountered in the specific application addressed in this thesis and to facilitate their practical use in a broader range of related biomedical applications; • the development and implementation of a prototype system to measure shoulder instabilities by meeting denned functional specifications; • the evaluation of the prototype system in the laboratory on an artificial model of the shoulder and subsequently on normal and symptomatic patients with stable and unstable shoulders. • the identification of inherent limitations of the system, the identification of possible improve-ments in the system and specific recommendations for further work related to this application as well as the broader range of applications involving improved assessment of patient out-comes. 1.4 Thesis Overview Chapter 2 provides clinical and technical background. The clinical portion familiarizes the reader with shoulder anatomy and mechanisms, reviews current methods to assess shoulder instabilities and shows the need for a new method to measure shoulder instabilities. The specifications for a new method and apparatus to measure shoulder instabilities are defined. Studies on gleno-humeral* translations are presented. The technical part provides an overview of different types of commercially available position sensors and presents their advantages and disadvantages, which motivated the choice of electro-magnetic technology for integration in the system. Chapter 3 is dedicated to the study of Ascension Technology Corporation "Flock of Birds"™, the electro-magnetic sensor used in this work. The technology is explained and cautions for using it are given. A methodology to evaluate the different errors of the sensor is presented. The possibility 5 of modifying the system filters and calibrating the system to better suit the system to the shoulder translation application is investigated. A general methodology is presented to assess the perfor-mance and calibration of electro-magnetic sensors when used to track joints movements. Finally, directions towards modifying the electro-magnetic technology of the sensor are suggested to make the sensor more suitable to the application addressed in this thesis and for similar "applications. In Chapter 4, a simple model of the glenohumeral joint is presented. A n algorithm that determines shoulder translations from elbow position was developed and implemented. This chapter includes a presentation of the hypotheses used to build the model, the algorithm, a study on the propagation of errors in the algorithm and some simulations to validate the algorithm. Chapter 5 presents the evaluation of the system. The algorithm was combined with the position sensors to track the elbow and the acromion to form the overall system. The system was validated on an artificial model. The attachment of the sensors to the patient was studied and the errors associated with it were estimated. A clinical protocol was developed for use'on patients Finally, the system was evaluated on patients with stable shoulders and patients with unstable shoulders. Chapter 6 concludes this work. The results presented in Chapter 5 are discussed and the system is compared to the specifications defined in Chapter 2. Directions for future work are suggested to improve the system, so that it can be routinely used to assess shoulder instabilities. 6 Chapter 2 Background 2.1 Clinical Background 2.1.1 The Shoulder Mechanism and Causes of Instabilities The shoulder joint is one of the most complex joints of the body, and its complete mechanism is not fully understood yet. It is also the most mobile joint. It is composed of the following bones (see Figure 2.1): • the humerus; • the scapula; • the clavicle; • the sternum. The shoulder joint allows movement of the humerus with respect to the thorax. This mo-tion is composed of the individual motions occurring at the sternoclavicular, acromioclavicular, scapulothoracic, and glenohumeral joints. The most frequently injured and most thoroughly investigated joint of the shoulder complex is the glenohumeral (GH) joint. This very mobile joint is situated between the distal end of the scapula (glenoid*) and the humerus (see Figure 2.2). The humeral head is spherical while the glenoid is a shallow surface congruent to the humeral head. A circular band of fibrocartilage 7 Figure 2.1: The anatomy of the shoulder [4]. 8 called the glenoid labrum is attached to the glenoid fossa to deepen its concavity and facilitate the rotation of the humeral head. Because of its small articulating surface, the glenoid does not cover the humeral head and allows translations to occur. The glenoid's concavity actually provides little stabilization of the glenohumeral joint. Most of the stability of the shoulder is due to the combined action of muscles, ligaments, tendons sur-rounding the complex (see Figure 2.1), and the joint capsule: • Muscles are dynamic stabilizers. They are attached to the bones by tendons which participate actively in the stability of the joint. Stability is provided mainly by the tendons of the sub-scapularis (see Figure 2.2), supraspinatus, infraspinatus, and teres minor muscles. Together, they form the musculotendinous (rotator) cuff. • The joint capsule surrounds the joint. It is composed of fibrous layers and synovial fluid that "lubricates" the joint and has "negative" pressure. • The ligaments are shown in Figure 2.2. They are passive stabilizers and they reinforce the capsule of the joint. There is considerable individual variation in musculotendinous and capsuloligamentous anatomy and inherent "normal" shoulder laxity. Laxity is present in varying degrees in normal shoulders and is required for normal, unrestricted glenohumeral motion in all planes. Instability is a pathological condition that manifests itself as pain in association with excessive translation of the humeral head on the glenoid during active shoulder motion [5]. Glenohumeral instability is classified according to the timing of diagnosis and frequency of the event, the degree, the direction(s), the etiology of the first occurrence, and whether or not the individual can voluntarily produce the instability [6]. This classification is summarized in Table 2.1. Regarding the degree of instability, a dislocation of the glenohumeral joint is said to occur when there is a complete separation of the articular surfaces, and usually, the humeral head remains locked outside the joint. A subluxation may be defined as symptomatic excessive translation of the humeral head on the glenoid [6], but the humeral head does not pop out the glenoid. 9 Ligaments Coracoclavicular Acromioclavicular thoracoacromial Coracohumeral Bursae: Subacromial Supraspinatus m. Tendon of supraspinatus m. M«rjl*um/WtklfOp Figure 2.2: The shoulder joint. (a)An anterior view, (b)a coronally sectioned anterior view, (c)a posterior view, and (d)a lateral view with the humerus removed [3]. 10 CxASStfKATTON Of Gi£NOHUMERAl NSTA8JU7Y I. Tening/Frequency A . Acute 1. Primary 2. Recurrent B. Chronic H. Degree A . Dislocation B Subluxation NI. Direction A . Anterior B Posterior C. Inferior D. Bidirectional 1. Anterior-inferior 2. Posterior-inferior E. Multidirectional IV. Etiology A . Traumatic B. Atraumatic C Repetitive microtrauma (overuse) Tounoci A. Involuntary B. Voluntary 1. Positional 2. Muscular 3. Psychological disorder Table 2.1: Classification of glenohumeral instability [6]. 11 Shoulder instabilities may be due to various causes. Most instabilities occur after a shock (where the joint dislocates), or from repeated subluxations that are common in throwing athletes. A few instabilities can result from congenital laxity where the ligaments are naturally loose, or the glenoid labrum does not fit the shape of the humeral head or is non-existent. Dislocations and subluxations are usually associated with damage of one or several of the stabilizing parts of the shoulder complex and/or fracture of the humeral head and/or the glenoid. First dislocations are usually managed by immobilization of the shoulder followed by physiotherapy to "naturally" recon-struct the damaged tissues. If the tissues are still damaged, the stabilizing functions are not totally provided, exposing the shoulder to further dislocations. Shoulders with recurrent dislocations may be repaired by arthroscopic or open surgery. Surgery may or may not be prescribed depending on the activity of the patient and the benefit of a surgical procedure for the patient. A precise diagnosis is necessary to identify the damaged tissue and determine the extent of the damage. This information can be used to decide whether a surgical procedure is necessary or not, and if yes, what type of surgery is to be done. 2.1.2 Definitions of Anatomical Plans and Joint Movements To visualize and study the structure of the body and its movements, the body may be sectioned according to three planes of reference, as shown in Figure 2.3: • the midsagittal plane; • the coronal plane; and • the transverse plane. The three elementary movements of the shoulder joint are abduction/adduction, cross-body movement and rotation of the shoulder. • abduction of the shoulder is the elevation of the arm in the coronal plane. The opposite direction of movement is adduction. • cross-body movement is a motion of the shoulder in the transverse plane at shoulder height. Cross-body movement is composed of flexion and extension. Flexion is a movement from side 12 Coronal Plane Midsagittal Plane Transverse Plane Figure 2.3: Definition of anatomical planes. 13 to front and extension is a movement from front to side. • rotation of the shoulder is rotation of the arm around the same axis as the arm. In this thesis, because of difficulties associated with the mathematical model of the shoulder joint (see Chapter 4), translations during rotation of the shoulder were not studied. 2.1.3 Literature Review on Translations in Glenohumeral Joints A preliminary literature search has been done to attempt to determine how translations were related to instability, and in particular, what amount of translation is characteristic of an unstable shoulder. Many studies have been performed, but results are very controversial and depend on the type of studies: on cadavers or in vivo, static or dynamic models, passive or active motion, weight applied or no weight applied. Assessment of instability by measuring translation during clinical manipulation is also con-troversial. Hawkins et al. [12] showed that measurement of glenohumeral translation of patients under anesthesia with radiography gave a good insight on the nature of instability. Adler and Lohmann [13] also found that translation measurement with stress radiography was an effective method to assess shoulder instability. Normal shoulders are extremely stable with this method: the average anterior translation being 0.8 mm and the posterior translation 0.2 mm. However Lip-pitt et al. [14] suggested that assessment of the magnitude of glenohumeral translation in clinical laxity tests was not a specific test for the diagnosis of glenohumeral instability: they did not find significant difference in translation between healthy subjects and subjects with unstable shoulders. Younger et al. [2] used radiography to observe anterior translations of shoulders exposed to several anterior loads applied at different positions. They reported that no significant difference in the amount of translation in the previously anteriorly dislocated shoulders compared to the normal side in any position. The measurements were accurate within 4.5 mm. Only a few authors studied translations during abduction or cross-body movements. Some studies on cadavers showed the role of different muscles, ligaments and rotator cuff in shoulder stability by studying glenohumeral translations after selective cuttings [15]. Sharkey et al. [16] showed that the humeral head translates about 1.5 mm superiorly in normal shoulders during ac-14 tive elevation. Significant translation occurs when the rotator cuff is damaged. Combined and balanced action of the infraspinatus, teres minor, and subscapularis muscles, effectively limit su-perior translation and makes important contributions to glenohumeral stability. Karduna et al. [17] demonstrated the importance of muscles activity on shoulder stability by comparing gleno-humeral translations on the shoulder of a cadaver during passive movements and when simulating the activity of muscles (active motion). Little translation was found on active motion, in contrast to Wuelker et al. [18] who found significant translation during active elevation. However their model did not include muscle activities which have some influence on the amount of glenohumeral translation. Warner at al. [19] showed the importance of the superior glenohumeral ligament in the restraint of inferior translation. In vivo studies were performed by Poppen and Walker [20] and Howell et al.[21]. They mea-sured humeral head superior/inferior translations using radiography during abduction movement in normal and abnormal shoulders. The range of superior/inferior translation in normal subjects was less than 1.5 mm, and significant previous injury resulting in abnormal motions of the shoulder joint was associated with abnormal values of excursion of the humeral head. Howell et al. did similar work, but in the horizontal plane. They concluded that during cross-body movement, the humeral head of normal subjects was centered in the glenoid cavity throughout the horizontal plane of motion except when the arm was in maximum extension and external rotation. In this position, the humeral head rested approximately four millimeters posterior to the center of the glenoid. In patients with anterior instability, abnormal movement in the glenohumeral joint was observed, as anterior translation of the humeral head occured. According to the two last mentioned studies [20] [21], significant superior/inferior trans-lation can be detected during abduction of the arm if the shoulder is unstable, and significant anterior/posterior translation occurs during cross-body movements of the unstable shoulder. A system that would measure superior/inferior translation during abduction of the arm and ante-rior/posterior during cross-body movements would therefore be very useful in measuring outcomes for instability of the shoulder. 15 Invasive Requires add. person Precise Quantitative Manipulat ion No No No No Scoring Tests No No No No M R I No Yes No No Radiography . (Yes) Yes No No Surgical Intervention Yes No Yes No Objective Repeatable Cost Dynamic observation Manipulat ion No (Yes) Cheap No Scoring Tests Yes Yes Cheap No M R I Yes Yes Very Expensive No Radiography Yes Yes Expensive No Surgical Intervention Yes Not applic. Very Expensive No Table 2.2: Summary of characteristics of current methods to assess shoulder instabilities. 2.1.4 Current Methods to Assess Shoulder Instabilities and Specifications for a Novel Method and System Current medical practice for assessment of shoulder joint stability is manipulation of the shoulder. The clinician manually manipulates the relaxed shoulder and subjectively grades the degree of joint laxity based on an estimate of how far across the glenoid the humeral head can be made to translate in the anterior and posterior directions, as well as inferior direction. The severity of the injury and the improvement after treatment are subjectively measured. The usual outcome measurement tools are scoring tests, based on the improvement in the patient's Me, and on his or her ability to perform certain movements [7][8], and post-treatment manipulation to assess laxity. Imaging techniques such as Magnetic Resonance Imaging (MRI) may be used to examine soft tissues for assessment of tissue damage or abnormality and radiography may be used to observe bone damage and bone positions. Both are expensive and imprecise, they do not allow dynamic examination and manipulation of the shoulder by the clinician. Both require the presence of another person with a different skill set to operate the imaging system and interpret the image data. The only effective existing method to assess shoulder instability in manipulation of the shoulder during surgical intervention. The characteristics of the current techniques for assessment of shoulder instabilities are summarized in Table 2.2. Other techniques have been proposed, but are not in current clinical practice. Assessment 16 of anterior-posterior translation with a knee laxity tester is described by J0rgensen and Bak [10]. The tester applies a known force anteriorly and posteriorly on the humeral head and measures the displacement of the contact point. The results were repeatable, but the instrument could not fit all the patients, it measured translation only in one plane and did not measure translation dynamically. Bonutti et al. [11] have reported on their initial efforts at a kinematic cine-MRI which permits the shoulder to be evaluated in its dynamic state. This system is still at an experimental stage and is not routinely used. None of the existing methods provides a precise, quantitative, repeatable assessment of the instability. This shows the need for a novel system with suitable characteristics to more objec-tively and more precisely quantify shoulder instability. An effective system to measure shoulder instabilities should have the following characteristics: • It must be non-invasive, and safe for the patient and the clinician. • It must give a precise, quantitative, objective and repeatable measurement of the laxity. • It must be inexpensive, easy to use and to set and must fit any sized patient. • The tester must be able to operate the method/system and retrieve the information relative to the shoulder laxity without any additional skill set. • The shoulder must be assessed in its dynamic state, for a more complete assessment, since dislocation usually occurs during a movement. The precision required is one tenth of the translations expected to ensure detection of ab-normality. The glenoid has an oval shape (see Figure 2.2) whose small diameter is about 2 or 3 cm. Therefore the humeral head in order to dislocate must translate of about 2 cm. We expect to see translation of the order of 1 to 2 cm, therefore an accuracy of 1 or 2 mm is suitable to have a precise measurement. The goal of this work was to develop a system that will meet these functional specifications. We suggested to develop a system that measures glenohumeral translations within the required accuracy using elbow position. The following chapters will describe the system developed and its 17 evaluation, the last chapter will compare the characteristics of the system and the results of its evaluation with these specifications. Specific directions for future work will be recommended so that any unmet specifications can be met. 2.2 Technica l Background 2.2.1 Specifications for Position Sensors The system we developed uses the positions of the elbow with respect to the positions of the scapula to measure the translations of the shoulder. Therefore a position sensor is needed to track the elbow and the scapula. Following the general specifications defined in the previous section, specifications for the sensors are as follows: • The sensors must be precise and must produce repeatable measurements. As we set the necessary accuracy for the overall system to 1 or 2 mm, the sensor should have sub-millimetric accuracy. • They must be relatively inexpensive. • They must fit any sized patient. • The part to be placed on the body must be light and must not interfere with the movements of the patient and the clinician. • They should be easy to use and to set up so that the clinician can operate the system himself and without a tedious learning requirement. • They must be operated in any environment. 2.2.2 Review of Different Types of Position Sensors This section discusses commercially available position sensors and our selection of a suitable one for this work after analyzing the advantages and disadvantages of each technology. 18 Devices which measure the position (x, y and z coordinates), and the orientation (yaw, pitch and roll) are called tracking devices or 6-degree-of-freedom (6-DOF) devices (see Figure 2.4). These are mainly used in virtual reality systems to track heads and hands [22][23]. y z X Figure 2.4: 6-DOF in Position/Orientation The precision of the measurements depends upon the resolution and the accuracy of the tracking device. While the resolution is fixed for a given device, the accuracy usually decreases with the distance of the sensor from the source. The range of a tracking device is the maximum distance between sensor and source up to which the position and orientation can be measured with a specified accuracy. Interference, or sensitivity to environmental factors, can also limit the effectiveness of tracking devices, depending on the technology used, as will be discussed further. Most currently used tracking devices are active, in that the sensor or the source is attached to the target to be tracked. In passive tracking, the target is monitored from a distance by one or several cameras. Current tracking devices are based on five main technologies: • Mechanical, • Inertial, 19 Figure 2.5: ADL-1 (Shooting Star Technology, British Columbia, Canada)[23]. • Optical, • Acoustic, • Electro-magnetic. Each of these technologies is briefly described below. Mechanical Tracking Devices These devices measure position and orientation by using a direct mechanical connection between a reference point and the target. Typically, a light-weight arm connects a control box to a target, and encoders placed at the joints of the arm measure the change in position and. orientation with respect to the reference point. One device which fits this description is the A D L - 1 head tracker (see Figure 2.5). The main advantage of mechanical tracking devices is that their time lag is very short (less 20 than 5 ms), their update rate is fairly high (300 updates per second), and they are accurate. They are much less sensitive to their immediate environment than others technologies, and they tend to be low cost. Their main disadvantage is that the user's motion is constrained by the mechanical arm, which in our application would prevent the patient and the doctor from moving freely and they may not fit any sized patient because of the limited length of the mechanical arm. They also have a small working volume which prevents large ranges bf motion, and they may wear out after a period of time. Optical Tracking Devices There are many different optical technologies used in metrology. Implementations of optical tracking systems are diverse, using lasers, Infra-Red LEDs, video cameras, photo-diodes and combinations of these. Infra-Red (IR) LEDs systems are often used because IR is outside the visible spectrum and hence less confusing to the eye of users, and LEDs emit everywhere, unlike lasers. Basically, optical devices come in two variants: • one or several cameras are mounted on top of the object to be tracked, and a set of LEDs is placed above the head at fixed locations in the environment. An example is an optoelectronic ceiling tracker developed at the University of North Carolina [23]. • alternatively, the cameras are mounted on the ceiling, or a fixed frame, and a few LEDs are placed at fixed and known positions on the object to be tracked, such as a L E D array system developed at Honeywell [22]. Another commercially available optical system is the R t P M from Spatial Positioning Sys-tems, Inc.(Virginia, USA) , which uses lasers to locate an optical sensor [23]. The major advantage of these systems is that they are able to work over a large area, restricted by the intensity (and coherence) of the light sources and sensitivity of the detectors. They have in general high update rates, and sufficiently short lags. 21 However, since light is involved, optically tracking an object necessitates maintaining the line-of-sight from source to detector. Ambient light and infrared radiation also affect optical tracker performance. Other problems may include weight (e.g. wearing light sources or cameras may be impractical), cost and set-up time. Acoustic Tracking Devices Acoustic systems almost invariably use ultrasonic signals for the same reason that many optical trackers use Infra-Red light : to avoid annoyance of human users or interference with other sources of sounds. Ultrasonic devices use two main techniques: time-of-flight (TOF) tracking and phase coherence tracking. T O F tracking measures the amount of time that it takes for sound emitted by transmitters on the target to reach sensors located at fixed positions in the environment. From the speed of sound, distance can be then determined. In order to find position, only'one transmitter and three receivers are required,- while three transmitters and three receivers are necessary for full 6 D O F tracking. Examples of this method are a Logitech device and SAC GP-8-3D (Science Accessories Corp., Connecticut USA) [23]. -Phase coherence tracking works by measuring the difference in phase between the received signal and a reference signal. This phase difference is used to calculate changes in the position of the transmitter relative to the receiver, as long as the distance traveled by the target is less than the wavelength between updates. Unfortunately, errors accumulate with time and so the tracker needs to be corrected from time to time using an external source. The main advantage of acoustic devices is that the transducers used in this technique are readily available, allowing simple acoustic tracking devices to be constructed at low cost. One disadvantage is that the speed of sound in air varies with air temperature, pressure and humidity. Hence, calculations of distance may be incorrect due to environmental conditions unless steps are taken to account for these. Another common problem is that echoes of the sound signal will be reflected from acoustically "hard" surfaces (such as office walls), causing reception of "ghosts" pulses at the receiver and interference with other transmitted pulses. As with optical 22 tracking, an inherent limitation of using acoustic signals is that a line-of-sight must be maintained between transmitter and receiver if errors are to be avoided. Due to these effects, acoustic trackers are typically low in accuracy and limited in range. Electro-magnetic Tracking Devices Electro-magnetic tracking devices function by measuring the strength of the magnetic fields gener-ated by sending current through three small wire coils, oriented perpendicular to one another and embedded in a small unit (transmitter). Three corresponding coils are set in a receiver and the variations in the received signal can be used to calculate the relative position and orientation of the receiver and transmitter with 6-DOF. The magnetic field can be driven by either A . C . signals (Polhemus Inc, Vermont USA) or D.C. signals (Ascension "Bi rd" , Ascension Technology Corp., Vermont, USA) [23]. These devices are generally very flexible since the small size of the receiver allows it to be attached with minimum intrusion. Although the working volume is generally not very large (typically a few feet for maximum accuracy), it is usually possible to arrange various combinations of time-multiplexed transmitters and receivers to cover more space and track more objects. Unlike optical and acoustic devices, you do not need to keep a line of sight between the transmitter and the receiver. Unfortunately, electro-magnetic trackers are susceptible to several error sources. Firstly, electro-magnetic interference (EMI) from devices such as radios or video systems can cause er-roneous readings. Secondly, large objects made of ferrous metals can interfere with the electro-magnetic field, again causing inaccuracies. This problem has been partly solved by Ascension Technology because they use a D.C. signal and do not produce eddy currents in conducting metals (see Chapter 3). Conclusion Each approach has its advantages and drawbacks and none of them meets the specification defined in Subsection 2.2.1. Trade-off had to be made to choose a suitable sensor. Electro-magnetic trackers 23 were chosen because: • they are relatively cheap, easy to use and to set up and they can fit any sized patient, • they are light and allow free movements of the patient and the doctor, since they do not require a line-of-sight between the transmitter and the receiver. In addition, their possibility to be used in a medical environment to measure body joints motion has been demonstrated [24]. However, attention must be paid to the environment to avoid interferences with CRTs, other electric devices and nearby metallic objects. The repeatability and accuracy of the sensor is addressed in Chapter 3. The technology of the sensor is also described and suggestions are given in Chapter 3 for improving the design of the existing sensor both to overcome difficulties encountered in this application and to facilitate their practical use in a broader range of related biomedical applications. 24 Chapter 3 Electro-magnetic Position Sensors 3.1 In t roduct ion This chapter gives a general overview of the technology of commercially available electro-magnetic position sensors followed by a detailed study of the sensor we used. Characteristics pertaining to electro-magnetic sensors are defined and the different sources of possible measurement errors are explained. A method was developed to measure static and dynamic error of the sensor to assess the performance and to check the calibration of the sensor. This method is generalized to be used in a broader range of related medical applications. Finally, some suggestions are made to improve the existing sensor technology both to overcome limitations encountered in the specific application addressed in this thesis and to facilitate their practical use in a broader range or related medical applications. 3.2 E lect ro-magnet ic Sensors Technology The basic components of electro-magnetic sensors are shown diagrammatically in Figure 3.1. The main components of these systems are: • a transmitter (or source); • one or several receivers (or sensor(s)); 25 Field coupling 3-axis magnetic source. , 3-axis magnetic sensor Computer 7 Amplifying circuits Position and orientation measurement Figure 3.1: System diagram for the magnetic-field coupling technique [27] • some driving circuits and amplifying circuits gathered in an electronics unit; • a computer that collects data and controls the electronics unit. The transmitter and the receiver are each composed of three perpendicular coils or antennas which create a source-sensor magnetic field coupling. The magnetic field generated by the trans-mitter is driven, by either A C signals (technology used by Polhemus Inc.) or pulsed D C signals (technology used by Ascension Technology Corp.). A C signals may.be applied in a time divi-sion (signal is applied to each antenna one at a time), frequency division (signals have a different frequency for each antenna), or phase division format. DC signals, because of their nature (no frequency and no phase) can be applied only in a time division format, as shown in Figure 3.2 [25][26]. The sequence of signals is controlled by the computer. While a.given transmitter antenna is being provided with current, the magnetic field is measured by each antenna in the receiver giving three measurements. After the three antennas of the transmitter have been provided with current, a total of nine measurements of the fields are recorded by the receiver. The signal output from the receiver is the input to the signal processing electronics unit. The unit conditions and converts the analog receiver signals into a digital format that can be manipulated by the computer. Initially, 26 Source . X axis •Source Y axis Source Z axis • ^ ^ ^ \ ^ Measurement of the field by the 3 receiver antennas " Figure 3.2: Signal diagram illustrating the sequence of signals sent to the transmitter. the transmitter is shut off so that the receiver can measure the components of the Earth's magnetic field. This field is subtracted from subsequent measurements of the field by the receiver. Geometry is then used to compute the three position components and three orientation components of the receiver with respect to the transmitter. This information in then output to the user's computer host. Note that the system is over-determined, since 9 measurements of the field are taken in a cycle for only 6 unknowns. The position and the orientation of the receivers with respect to the transmitter are de-termined by measuring small changes in coordinates and updating the previous measurements via linear transformations [27]. The strength of the field is controlled by the computer and is a function of the'distance between the transmitter and the receiver closest to the transmitter. This is to pre-vent the electronics unit from being saturated when the receiver gets close to the transmitter and to ensure a strong enough field.to distinguish the signal from background noise when the receiver gets further away [28]. When the magnetic field fluctuates, eddy currents are created in nearby conductive metallic objects creating field distortions. If the field is stable, no interaction occurs. If the magnetic field is driven by an A C signal, the field fluctuates all the time and eddy currents are therefore always 27 present [29]. If the field is driven by a DC signal, eddy currents occur when the field is turned on, but then drop exponentially as the field stabilizes. Measurement can then be taken after a suitable delay when eddy currents have disappeared and' the field has stabilized (see Figure 3.2). Therefore, DC fields trackers tend to be less susceptible to immobile conductors in the environment. Note that if a nearby metallic object is moving or if the transmitter is moving, eddy currents occur even when the field delivered by the transmitter is stable, leading to wrong measurements. Also, the magnetic field is stronger near the source than further away and the field changes when the magnetic field is turned on. Therefore, if a large metallic object is present near the source, eddy currents are large and do not have time to dissipate before measurement of the field, which leads to distorted measurements. An example of metal distortion is given in Section 3.7. These distortions-can be attenuated if the measurement rate is decreased, as the eddy currents have more time to dissipate, but then the response of the system is slower-. There is a trade-off between static errors due to metallic environment and errors due to time-lag. 3.3 Def in i t ion of Terms and Character is t ics It is important to have a clear understanding of definitions pertaining to electro-magnetic sensors, as these definitions may not correspond to classic definitions used in other applications. Definitions of specifications and characteristics of electro-magnetic sensors are as follows: . 1. Accuracy is the fractional error in making a measurement. Accuracy is specified as "Static Accuracy" by all manufacturers of electro-magnetic six-degree-of-freedom instruments, spec-ified in statistical error terminology (RMS). Error terms are recorded in a statistically valid number of fixed and surveyed locations throughout a specified working volume, and RMS values are calculated for each coordinate. Accuracy is specified in a metallic clean environ-ment and within a certain range of temperature and distances [30]. One has to be aware of this definition used both by Polhemus and Ascension Technology which is different than the classic definition of accuracy, that is: the worst case error over the workspace!' The classic definition is usually the^one that the user needs. 28 2. Resolution is the smallest amount of the quantity measured that the instrument will detect. 3. Lag or Latency is the time difference between the start of a physical motion of the receiver and the start of the output of its correct measurement. The Ascension Technology definition includes time for the receiver to measure the transmitted field, compute a solution, filter the signal as necessary, and to settle to the correct measure of the angle [29]. Electro-magnetic sensor errors can be of different natures. One must assess these errors individually to identify the sources of-each error and possibly to adjust the parameters of the electro-magnetic system to reduce the error. The different sources of errors are: • Static errors are due mainly to metallic environment. Field distortions due to static metallic objects can be mapped and can be corrected by using look-up tables [33] or by a curve fit method (this method is used by both Ascension Technology and Polhemus). Both methods are possible if the transmitter is fixed in a given environment that will never change. Otherwise, one must map the environment or apply the curve-fit method each time the source is moved or the environment is changed. • Time-varying noise due to the environment and the system itself. Time varying .noise can be observed by looking at the data while the sensor is immobile. This noise depends on the distance between the transmitter and the receiver. The systems include various filters to minimize this noise. • Errors due to time lags. These errors depend on the speed and acceleration in the movement. They can be reduced by increasing the measurement rate and by modifying the internal filters of the system. There is a trade off between time lag and noise, as a smaller filter bandwidth leads to a greater delay in the system. • Aperture errors: The algorithm used to compute the position and orientation of the receiver considers the transmitter to be a point source. If the receiver is too close to the transmitter. This is known as the aperture problem. The receiver must be kept at a minimum distance from the transmitter to avoid this problem. 29 ' • Other errors occur because electro-magnetic sensors are sensitive to other factors such as temperature or atmospheric pressure. This will cause measurements to be different from one day to another, especially if the receiver is far away from the transmitter [34]. These errors are negligible compared with other sources of errors and are not discussed further. Considering the previously-mentioned characteristics of electro-magnetic sensors, special attention must be paid to the placement of the transmitter and the receivers. They should all be far away from metallic objects: Polhemus suggests to keep the distance between the system and any metallic object at least twice the distance between the transmitter and the receiver. The distance between the transmitter and the receivers should be between 22.5 and 64 cm [32] to avoid aperture. errors and to keep the time-varying noise to a reasonable level. If several receivers are used, the distance between the transmitter and each receiver should remain about the same to avoid larger, relative noise in the receiver placed further away [28] and to avoid incorrect measurements in the receiver furthest away due to distortions of the field by the closest receiver. 3 . 4 Overv iew of the " F l o c k of B i r d s " ™ The electro-magnetic system used in this work is the "Flock of Birds" from Ascension Technology Corporation. A l l the experiments were done at Simon Fraser University where the system was linked to a Silicon Graphics 6.2 system. The Flock of Birds is composed of: • one transmitter, • two receivers, • two electronics units (one for each receiver), • two power supplies. The computer is connected to the Flock of Birds via an RS-232 serial interface and the two Birds communicate between each other via an RS-485 serial interface called Fast Bird Bus (FBB) . The system measures the position and the orientation of the receivers with respect to the transmitter and can report the data in several formats: 30 • position only; • orientation-only; . • • position and orientation; • position and cosine matrices. The number of bits transmitted depends on the format ordered and influences the maximum rate at which the data can be transmitted. The manufacturer recommends using the minimum number of bits required to minimize time lag. Data can be read in three modes: • in point mode, the system transmits one data record only as the user requests it; • in continuous point mode, the data are recorded as they are received by the computer. The flow of data received by the computer depends on the Baud rate of the system. The drawback of this mode is that data are not transmitted regularly as the Baud rate and the measurement rate may be uncoordinated and the user does not have control over the flow rate. • in stream mode, data are reported according to a report rate ordered by the user. The maximum possible report rate depends on the Baud rate and the number of bytes of the output record. The report rate can be chosen between the max. output rate, max./2, max./8 or max./32. . The stream mode is the mode that would have been appropriate for our application. Un-fortunately, a malfunction either in the Flock of Birds system or in the SGI driver prevented us from using the stream mode. Therefore, the continuous point mode was used, but no linear data processing such as low-pass filtering could be done on the final sequence, since the sampling rate was not constant. The specifications of the Flock of Birds from Ascension Technology can be found in Appendix [31]. The accuracy specified by the manufacturer is 0.1" RMS averaged over the translational range of ± 36" in any direction. 31 Transmitter Receiver Arm Receiver Figure 3.3: Equipment set up to.test the accuracy of the electro-magnetic sensor To estimate the measurement errors in the.system, a plastic arm fixed on a plastic planar-surface was used. The arm described a perfect circular trajectory (the error was negligible). The positions of a receiver placed on the arm were recorded and a circle was fit to the recorded trajectory. The error is the distance between the trajectory and the fitted circle. This error was studied and minimized. . The system was placed on a wooden table and precautions were taken so that no metallic object was nearby. One receiver was placed on the planar surface and the other one was placed on the arm. The transmitter was placed about 40 cm higher so that the two receivers stayed within the manufacturer's optimal range and at about the same distance from the transmitter. The setup of the experiment is represented on Figure 3.3 3.5 E r ro rs w i t h the Defaul t F i l t e r Set t ing 3.5.1 Static Error To measure static error of the system, measurements were taken in point mode. The circular trajectory was followed three times back and forth and measurements were taken twice about every two cm on the trajectory. A circle was fit to the x-y measurements (horizontal plane) and the 32 Static error 0.08,— 1 : n 1 : 0.06- I I Angle (Radians) Figure 3.4: Static error. The semi-circle was traced three times back and forth and the measure-ments are taken in point mode. radius of this circle and the distance between sensor and center of the circle were compared: e = \\U-c\\ - R where e is the error, U is the x-y position given by the sensor, c is the center of the fitted circle and R is the radius of the fitting circle. The error was very small with a variance of 0.2 mm and a maximum of about 0.6 mm. The error is shown on Figure 3.4. 3.5.2 Error Due to the Time-Varying Noise and to the Interaction between the Receivers To measure the time-varying noise and the interaction of the two receivers with each other, the position given by the sensor was compared to the circle determined during the static experiment. The experiment was done in continuous mode for a slow movement (half a circle was traced in 33 Error of a Slow Movement for Semi-Circle Angle(radians)of semi-circle Figure 3.5: Error during a slow movement. The time-varying noise had an amplitude of about 0.5 mm and the error due to the interaction of the receiver closest to the transmitter on the receiver furthest from the transmitter was up to about 1 mm. about 5 seconds), such that the time lag was negligible. The time-varying noise had an amplitude of about 0.5 mm (see Figure 3.5). The maximum error due to the interaction between the two receivers was about 1 mm. The error was largest when the receiver on the arm is the furthest away from the fixed receiver and from the transmitter. This demonstrates the importance of keeping the two receivers in the same range. 3.5.3 Errors Due to Time-Lag At a human-like speed (half a circle was described in 2 to 3 seconds), the error was larger (see Figure 3.6). Errors were up to 1.5 mm. If the speed of the movement was increased, there was a "figure-eight"-like characteristic to the error curve, which was due to time-lag in the measurements. Indeed, the error was larger during acceleration phases and the recorded trajectory tended to look 34 Error of Dynamical Tests with Default Filters 0.251 1 1 1 r 1 1 U - 2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Angle(radians) Figure 3.6: Error during a movement whose speed is similar to that of a human arm during abduction movement. ' like the trajectory shown on Figure 3.7. Figure 3.8 gives an example of error due to timeTag when fitting a circle to the trajectory. The gap between the trajectory traced in one direction and the trajectory traced in the other direction was up to 1.5 mm. 3.6 Mod i f i ca t i on of the Sys tem Sett ing The system uses three internal niters to attenuate time-varying noise. They can be turned on or off by the user (see Appendix). These filters are: • an A C wide notch filter; • an A C narrow notch filter, that can be used instead of the A C wide notch filter to attenuate the filtering, but increase the dynamic response; .. 35 Real Trajectory (semi-circle) Recorded Trajectory Acceleration Phases Figure 3.7: "Figure-eight"-like shape trajectory when the speed of the movement increases. "figure-eight"-like characteristics 0.151 1 1 : — i 1 3.5 Angle(radians) Figure 3.8: An example of "figure-eight"-like shape of the measurement error when fitting a circle to the trajectory of the receiver. 36 • an adaptive DC filter, whose parameters can be modified by the user. When the system is turned on, the default filters are the A C wide notch filter and the DC adaptive filter. This setting was chosen by the manufacturer for having a good trade-off between time-varying noise level and time-lag in an ordinary environment (with no metal close by). This filter setting can be modified according to the acceptable level of noise and the acceptable time lag. The influence of these different filters on the measurement errors were studied. When the " A C wide filter" was turned off and the " A C narrow filter" was turned on, the amount of noise was much higher and there was no improvement in the result. The " D C filter" was then modified. The " D C filter" uses two parameters: -• a is the adaptive parameter of the filter and it is a function of the measured dynamic energy (motion and noise), the present filtering state, and the distance between the transmitter and-the receivers, and varies between a m i n and amax that can be adjusted by the user; • Vm is proportional to the expected sum of the variance of the noise. Vm is used by the system to distinguish motion from background noise and is different for different ranges. Vm values can be adjusted by the user. The Vm values are given in Table 3.1. The table entries correspond to distance ranges from trans-mitter. The Vm values have an effect on the system lag. As one increases the Vm values, one increases the low-pass character of the filter and the system responds slower tothe movement. The optimum values of Vm, a m i n and amax are dependent on the environment and application. Following instructions from the manufacturer (see Appendix), Vm values were increased to decrease the noise. The default values for Vm are given in Table 3.1. To adjust Vm values, continuous values were read from the Bird while the receiver was immobile. If the values output were too noisy, the value used in the Vm table was doubled. This step was repeated as needed until values were quiet while receiver was at rest. This operation was done at several positions in working ranges only (between 15 and 30 inches) and the corresponding Vm values were modified. The new Vm table is given in Table 3.2. 37 Distance Range Vm values 0 to 12 inches 2 12 to 15 inches . 6 15 to 19 inches 26 19 to 24 inches 99 24 to 30 inches 396 30 to 38 inches 1615 38 and above 6440 Table 3.1: Table of default Vm values. The table entries correspond to the distances range from the transmitter. Distance Range Vm values 0 to 12 inches 2 12 to 15 inches 6 15 to 19 inches 40 19 to 24 inches 180 24 to 30 inches 1000 30 to 38 inches 1615 38 and above • 6440 Table 3.2: New Vm values. The error with the DC filter modified is represented on Figure 3.9. The time-varying noise was decreased, but larger time-lag errors occurred. The resulting error was not improved with respect to the error during the dynamic test with default filters. The default D C filter characteristics and the wide A C filter were therefore used. We also tried to increase the measurement rate, to reduce the time lag, but this added more time-varying noise in the result than with the default configuration. 3.7 Influence of Me ta l l i c Env i ronment The environment these experiments were done in was metallically clean and did not produce static distortions. However, to illustrate the effect of metallic objects on the field, different metallic objects were placed around the apparatus and observed the distortion of the measurements. The positions given by the sensor were compared as a pair of metallic scissors was placed on the table near the receivers, the metallic head of desk lamp was paced on the table near the receivers and 38 Error when Vm modified 0.251 • 1 1 1 -Angle(radians) Figure 3.9: Error during a dynamic movement when the Vm values of the DC filter have been modified 39 the head of lamp was brought to a few centimeters from the transmitter. When the scissors or the head of the lamp were placed on the table. The distortion was up to 4 mm (see Figure 3.10). However, when the head of the lamp was placed at approximately 10 cm from the transmitter, much larger distortion was observed (see Figure 3.11). Errors in the measurement of the position of the sensor were up-to 3 cm. This demonstrates that even if DC fields produce less metal interactions than A C fields, the environment must be as clear as possible of metallic objects. 3.8 Resu l t s , Poss ib i l i ty of Ca l i b ra t i on and Ex tens ion to a B roader Range of Re la ted M e d i c a l App l i ca t ions In the environment of these experiments',, errors due to the metallic environment (static error) were found to be negligible and did not require any mapping and calibration. In our set-up, the error due to the interaction of the receiver closest to the transmitter on the receiver furthest away was up to 1 mm (see Figure 3.5) even though we tried to keep the distances between each receiver and the transmitter about the same. The dynamic error had an amplitude of up to 1.5 mm with the default filter setting (see Figure 3.6 and increased as we replaced the A C wide notch filter by the A C narrow notch filter. The time lag increased as we increased the Vm values in the DC filter. To minimize noise and time lag, the ideal set up would have been to allow the recording "of noisy data and filter them afterwards. Unfortunately, because the stream mode could not be used, no linear low-pass filtering was possible afterwards to suppress the time-varying noise. The possibility of correcting for the time-lag was investigated. We considered using the rotational arm used in the previous experiments, placing it in the same area as where the testing on the patient would occur, placing the receiver on the arm such that the receiver described a circle of radius equal to the length of the patient's humerus, and recording data while moving the rotational arm at the same speed as a human would move. By fitting a circle to these data, it was possible to measure the error with respect to the angle on the circle and the direction of 40 Error when no metallic object is nearby E o -1.5 -1.5 -0.5 0 0.5 Error caused by some scissors placed on the table -0.5 0 0.5 Errors caused by the head of a light placed on the table Angle (radians) Figure 3.10: Errors introduced by metallic objects (a pair of scissors and the head of a desk lamp) placed on the experimental table) 41 Comparison of trajectories 0 1 1 1 : 1 1 ' vs . v\ \\ \\ \\ I i ij '/ "Clean" environment "Dirty" environment ^ y' i i I I i - 2 0 0 20 40 60 80 Error when the head of lamp is near the transmitter 4r-—; —i '• : 1 1 : -i ;— _2} i I i i i i -1 .5 -1 -0 .5 0 0.5 1 1.5 Angle(radians) Figure 3.11: Influence of a large metallic object (the head of a desk lamp) on the measurements. The first graph shows the trajectory given by the sensor when no metallic object is nearby ("clean" environment) and when the head of the lamp is at a few centimeters from the transmitter ("dirty" environment). The second graph shows the error as a function of the angle on the circle. 42 the movement. These errors could be stored in a look-up table and subtract the error from, the elbow trajectory. However, compensating for. the time lag after recording was a tedious task. It. also assumes that the movement of the patient's arm.has the same speed as the calibrating circular trajectory and that the radii of the circles are the same, which is difficult to achieve. . ' It was finally decided not to Calibrate the device and to use the default setting, which pro-vided a good trade off between noise and time lag. Errors could probably be attenuated if the stream mode was working (it worked on PCs). The initial filtering and measurement rate could be modified to optimize the time lag. Finally applying a low pass filter on the data after recording would suppress the noise. A l l the steps we described can be performed to check the performance and the calibration of these electro-magnetic sensors and to adjust their parameters In a broader range of medical applications. These steps are gathered to form the following "recipe"for good results: • Remove as many metallic objects and electrical apparatus possible from the working environ-' ment. ' • . > ' . . • ' ' • ' • • Check the static accuracy by moving point-by-point the sensor on a known trajectory and compare the positions measured by the sensor.to the trajectory. ' ' ' " ' • • , ' . • If the static accuracy is poor, the two possible causes are: - metallic objects and/or electrical apparatus are too close to the transmitter: clean up as much as possible. If using D C fields, reduce the sampling rate. If the environment and the transmitter are immobile, it is possible to map the environment and'create a look-up table or use a curve fit method (these methods have not been tested in this application); - if no metallic object is around the system, the calibration of the system is wrong, call the manufacturer! • • Observe the time-varying noise due to surrounding electrical devices and to the electro-magnetic system itself by examining measurements given by the sensor when it is immobile. 43 If the level of noise is not acceptable, adjust the sampling rate and the filter settings as described in Ascension Technology technical note (see Appendix). If using two receivers, look at the interaction between the receivers by placing the two receivers according to the application. For instance, if one receiver is to move significantly less than the other one, fix one receiver and describe a known curve with the other one. Compare the measurement given by the receiver to the known trajectory and check that the measurements given by the immobile receiver are constant. If the receivers are to be placed on an arm for instance and the distance between the-receiver does not vary significantly, place the two receivers on a non-metalhc board. Move the board and observe the distance between the two receivers given by the system. This distance should stay constant if there is no error. In any case, in any application, you should keep about the same distance between the transmitter and each receiver. Do the same kind of test if using more than two receivers. Estimate the dynamic error (error due to time lag) by using a known trajectory that has the same characteristics as the trajectory of the target to track. These characteristics are: - roughly the same geometry; for instance, we used a circular trajectory, which is close to the trajectory of the elbow, - roughly the same acceleration; this would for instance be important if the sensor is to be used on the arm of a throwing athlete, - roughly the same speed, - about the same distance between the transmitter and the receiver. Adjust the internal filters and the sampling rate for the best trade-off between time-varying noise and time-lag errors. If you do not need real time measurement, use the. stream mode and decrease the bandwidth of the filters to have a better dynamic response and low-pass filter your sequence afterwards to eliminate the time varying noise. If one uses eiectro-magnetic sensors to track a movement, it is imperative that one measures dynamic error, as the static error is not representative of the real error during the movement. 4 4 One must not use the specifications given by the manufacturer as a reference for accuracy, as the definition of the manufacturer for accuracy is not the maximal error, but an averaged error, it is also a static accuracy, and- is measured in an environment clean of metallic objects. If one uses electro-magnetic sensor in an overall system, it is invalid to claim the accuracy of the overall system if the accuracy of the sensor is not defined or if the technique to measure this accuracy is not defined. We suggest that the "recipe" described above be followed for any related medical application or for body joints tracking. 3.9 Poss ib le Improvements to the Sensor The errors of the sensor we worked with had errors up to about ±1.5 mm. This is greater than the. accuracy we specified in Chapter 2. Therefore the specifications of the overall system will not be met either. For future work, in order to meet the specifications or to facilitate the use of electro-magnetic sensors in other related medical applications, we suggest the following directions to improve the design of the sensor. D C field electro-magnetic sensors are less susceptible to metal than A C field sensors. How-ever, because they use time division signals, if the receiver moves between the time where the signal is sent to the first transmitter antenna and the time where the signal is sent to the third transmit-ter antenna, the measurement is wrong and may be the cause of time-lag errors. Our application however does not need real time measurement and neither do many other medical applications studying body joints movements. It is then possible for these applications to measure the fields during the motion, to re-sample the fields afterwards so that we get estimates of the three fields at the same time, and to process the field measurements afterwards and compute the position and orientation of the receiver. This eliminates time-lag errors and allows a more precise signal processing to attenuate time varying noise. Our application uses the relative position of two receivers placed on the body. Many other medical applications use the movement of a joint relative to a reference point on the body. If the 45 transmitter is smaller (i.e. the size of a receiver), it, is possible to place the transmitter directly on the body, and use only one receiver. This would require less equipment and would avoid interactions between the receivers as described in Section 3.3. Polhemus has already developed such a system called the Short Ranger transmitter [35]. The drawback of this system is that because the size of the transmitter coils is significantly reduced, so is the intensity of the field. Therefore, the distance between the transmitter and the receiver has to be less than about 30 cm. There is a trade-off between the size of the transmitter and the maximum range. However, as mentioned in Section 3.2, the system is over-determined since it takes 9 measurements in a cycle for only 6 unknowns. If there were only two coils in the transmitter, 6 measurements of the fields would take place in a cycle and would be enough to determine the 3 position components and the 3 orientation components. Using two coils instead of three would reduce the size of the transmitter without affecting the range between the transmitter and the receiver. In addition, if the position only or the orientation only are used, the system is reduced to three unknowns and only one coil in the transmitter is necessary to determine the unknowns. However, this may decrease the accuracy of the measurements. It may be better to keep the extra data to get a higher signal-noise ratio. These modifications in the design of the electro-magnetic sensor should allow sensor require-ments to be met. A smaller transmitter and a more precise system should allow electro-magnetic sensors to.be used more often-in related medical applications, especially in the study of body joints motion. 46 Chapter 4 Mathematical Model of the Shoulder and Algorithm 4.1 In t roduct ion The system we developed uses the electro-magnetic sensors described in Chapter 3 to track the positions of the elbow and the scapula. The trajectory of the scapula is subtracted from the trajectory of the elbow and the resulting trajectory is used to determine the translations of the humeral head on the glenoid. In this chapter, we present the algorithm developed to determine the translations of the humeral head on the glenoid from the position of the elbow with respect to the scapula. In Section 4.2, a model of the glenohumeral joint is presented. The humeral head is modeled as a sphere and the glenoid is modeled as a planar surface. From this model, an algorithm was developed (see Section 4.3). The algorithm was validated on simulations (see Section 4.4). The source of possible errors are identified and their propagation in the algorithm is studied in Section 4.5. 47 Figure 4.1: Simplified model of the glenohumeral joint. The humeral head is modeled as a sphere and the glenoid is modeled as a small planar surface. 4.2 M o d e l of the G lenohumera l Jo int and In t roduct ion to the A l -gor i thm. A simplified model of the glenohumeral joint was developed from geometrical properties of the humeral head and of the glenoid [36] : • the articulating surface of the humeral head is essentially spherical, therefore the humeral head was modeled as a sphere; • the glenoid is almost congruent to the humeral head, but of very small dimension to allow the large mobility that characterizes the glenohumeral joint. Because the translations are small compared with the surface of the humeral head, the glenoid was modeled as a small planar surface (see Figure 4.1). Initially, an algorithm was built to measure the positions.of the humeral head on the glenoid from the elbow positions in three-dimensions. This algorithm was using the orientation of the 48 Glenoid segment Figure 4.2: 2D representation of the humeral head and the glenoid. The humeral head is a disk and the glenoid is a segment of a straight line that makes an angle 6 with the vertical line. glenoid and the distance between the elbow sensor and the center of the humeral head R. However, a parameter was missing to be able to determine the position of the humeral head. To replace this missing parameter, an additional hypothesis was introduced. It was hypothesized that the translations were in the same direction as the projection of the humerus on the glenoid plane. However this hypothesis could not be justified by any previous work. For this reason, a simpler model was developed: the translations of the humeral head on the glenoid were measured in two-dimensions only. The algorithm we developed determines su-perior/inferior translations during abduction movement and inferior/posterior translations during cross-body movement. Since we work in 2D, the humeral head was modeled as a circle and the glenoid as a segment of straight line which makes an angle 8 with the vertical for abduction move-ment and with the axis perpendicular to the body for cross-body movement (see Figure 4.2). The "elbow trajectory" is described as the elbow trajectory relative to the scapula. From now on, the reference frame is a frame fix with respect to the glenoid. The model uses two parameters: • the distance R between the receiver placed on the elbow of the patient and the center of the humeral head, and • the angle 6 of the glenoid. 49 4 . 3 A l g o r i t h m The algorithm consists of taking the intersections between the glenoid segment and.the circle of radius R and with the elbow at the center. A reference point C was used. We define this point the humeral head position when the humerus is exactly perpendicular to the glenoid. At a given elbow position, the humeral head position is the one of the two intersections that is closest to the reference point C. Given 6, T and N are the unit tangential vector and unit normal vector given with respect to the initial frame (/, J) (Figure 4.3): . . . f = sin 61- cos 6» J , (4.1) N = cos 6io + sin 6jo. . If O is the origin of the coordinate system, k a time sample and U{k) is a point on the elbow trajectory, then it is possible to decompose the vector OU(k) in terms of its normal and tangential components: OU{k) = (OU(k).N)N+ (OU(k).T)T. The reference point C is the position of the humeral head when the humerus is exactly perpendicular to the glenoid. At this position, the distance between C and the elbow is exactly R and the corresponding elbow position'has the largest normal component i.e. at the elbow position shown in Figure 4.4. The corresponding elbow position UM is given by: OUM-N = max \OU(k).N ke[i--n] 1 From there, we can determine the reference point C: Ot = OU^i - RN. It is now possible for each elbow position U(k) to determine the translations Hi(k) and H2(k) between the circle of radius R and center U(k) and the glenoid segment (see Figure 4.5): 50 51 52 ( Glenoid -Humeral head position -Humerus Elbow position U(k) Figure 4.5: We can determine the intersection Hi and H2 between the circle of center1 U(k) and of radius R and the glenoid segment. 53 CH2{k) = (cu{k).f + \JR2 - (c77(^.iv)2j f. If CU(k).T is positive, then the intersection closest to C is Hi(k). If CU(k).T is negative, then the intersection closest to C is H2(k). Therefore, the humeral head position H which is the point of intersection closest to C is given by: cm = (cm.f * (i - 1 F | JR* - (cm^y)) * ?• 4 . 4 S i m u l a t i o n s To verify the algorithm, we simulated an elbow trajectory, estimated the translations and compared them with the actual translation. The model of the elbow trajectory is: xk - 35 * cos(0.05 + ^ f 1 ^ ) + 1.5 -yk = 35 * sin(0.05 + i ^ f i ^ ) f o r k = 0,.., N - 1. These equations simulate an elbow trajectory where the parameter R is 35 cm, the glenoid has an angle 0=0 degree, and the total amount of translation is 3 cm. The trajectory is shown on Figure 4.6. The translations estimated from this trajectory are shown on Figure 4.7. There is a slight gap of about 0.6 mm between the simulated and the actual translations, because of a slight error in the estimation of the reference point C The C coordinates were estimated as [0.0573 -0.0000], instead of [0 0]. Since this 0.6 mm error is constant during the whole trajectory, it does not affect the shape of the translation curve and the total amount of translation. In fact, to have a more precise estimate of C, we interpolate the curve around the point on the elbow trajectory where the normal component is largest using splines. 54 Simulated elbow trajectory Figure 4.6: Simulated elbow trajectory, where the parameter R is 35 cm, the angle 6 is 0 degree, and the total amount of translation is 3 cm. 55 Translation from simulated trajectory 1.5r 0.5 E 3 Of (/> ' c g as I— -1h -1 .5h Translation curve obtained from the algorithm Real translations 0.5 1 1.5 2 2.5 Angle of Abduction or cross-body movement 3.5 Figure 4.7: Translation from the simulated trajectory. 56 4 . 5 S tudy of the Er ro rs and of their P ropaga t ion on the M o d e l Errors can occur from a bad estimate of either of the parameters R or 6, or from errors in the 'initial trajectory.. Errors in the trajectory can.be errors due to sensor errors, due to the sensing itself (bad attachment of the sensor, bone-tissue movement),-or due to rotation of the scapula that, was neglected. The purpose of the following section is studying the propagation of these errors in the model. An analysis of the error propagation is first presented and the.results are then simulated. 4.5.1 Propagation of error in estimation of R R is estimated by fitting a circle to the elbow trajectory. The estimation of R can be inaccurate because the differential elbow trajectory of a normal limb is not exactly circular. By studying the difference between the fitting circle and the actual elbow trajectory, we can estimate the error in . R,AR. By differentiating Equations (4.2), we get: . ; „ ,-RAR + UNAUN . An = sign(UT) , = , but Al'\ AR and then, ' • Ah = sign(UT) ~ R + U N AR,. ' . ' ... ^ R 2 - U N 2 •• • , where h = \CH{^]1 UN = CU(k).N, UT = CU(k).f. •"• The behavior of the error can be studied in two extreme cases: when the humerus is per-pendicular to the glenoid '(UN —• R) o r when the humerus if far away from this position (UN.-+' 0). Then we get: . lim Ah = 0, • lim Ah =-sign(UT)AR. -The maximum error due to the estimation of the parameter R is then equal to the error AR itself (see Figure 4.8). 57 1.5h 0.5 c o j2 -0.5 CO -1.5 -2.5 Influence of errors in estimation of R on the calculation of translations True translations (R = 35 cm) R = 34.5 cm R = 35.5 cm 0.5 1.5 2 Angle (radians) 2.5 3.5 Figure 4.8: Propagation of errors in estimation of R in the calculation of translations from the simulated elbow trajectory. 58 Figure 4.9: Influence of the actual circular shape of the glenoid and the rotation of the scapula during the movement. 4.5.2 Propagation of Errors in Estimation of 9 (Glenoid angle) We assumed that the glenoid is flat, but in fact it has a concave shape. Furthermore, because the scapula rotates during an abduction movement, the slope varies during the movement. It is then important to analyze the effect of errors in 6 on the estimate of the translations. We assume that the reference frame is attached to the reference point C. Then, the reference point C is fix during the totality of the movement. If at a given time, the actual position of the glenoid is as shown on Figure 4.9. We define the translation as the distance between the reference point C and the humeral head position. By differentiating Equations (4.1) with respect to 0, we get: 59 A T = (cos0/ + sm6J)A6 = NA9, AN = ( - s inf l /+ cos Of) Ad = -TAB. Therefore, AUT = UAT = UNA6, AUN = UAN = -UTA8. By differentiating Equations (4.2), we get: Ah = A/7T + sign(UT) \JR2 - UN2 AUN.UN = UN 1 — sign^Ur) \/R2 - UN2 UT glenoid, the error is small. When the humerus is perpendicular to the glenoid, since the trajectory is almost circular, I , U r =1 ~ 1. Then the error is close to 0. Figure 4.10 shows how an error in estimating 9 propagates in the model. The curves are shifted with respect to the one with the true 9 value, because the estimate of C is affected by 9. The general shape of the curve however is not significantly changed. The same type of curve would be obtained if 8 changed during the movement, assuming that the reference point C is fixed during the movement. Since a bad estimate of 9 does not significantly affect the shape of the translation curve, the fact that we consider the glenoid flat instead of spherical and that the orientation of the glenoid changes during the movement does not significantly affect the shape of the result and the estimate of glenohumeral translation. 4.5.3 Propagation of Sensor and Sensing Errors Errors in the elbow trajectory can either come from sensor errors as described in the previous chapter, from sensing errors : displacement of the sensor with respect to the bones, sensor errors 60 Influence of errors in the estimation of Gin the calculation of translations. 1.5 E ° - 5 CO c 1 0 co c CO ^-0.5 -1.5 Real translations A6 = 10° A0 = -1O° 0.5 1.5 2 Angle(radians) 3.5 Figure 4.10: Propagation of errors in the estimation of m in the model. Here, the error is mainly due to a bad calculation of the reference point C : C = [-0.2986 - 0.0298] for AO = 10 degrees and C = [0.4130 - 0.0320] for AO = -10 degrees. 61 described in Chapter 3 or errors due to the rotation of the scapula. By differentiating Equation (4.2), we obtain: Ah = AUT + sign(UT)-^tE^=. (4.3) yjR2 - UN2 Studying the behavior at the two extreme positions where the humerus is perpendicular to the glenoid (UN —• R) o r f a r away from this position (\UN\ —* 0), we get: lim Ah = AUT-If \UN\ -> R (\R2 - (UN)2\ < \AUN\), the expression 4.3 is not valid. We need to directly use Equation 4.2: h + Ah = UT + AUT - sign(UT)\J'R2 - UN2 - (WNAUN + (AUN)2-Since \UN + AUN\ < R (see computation of C in Section 4.3), and R2 — (UN)2 <C \AUN\, then UN and AUN have opposite sign (UNAUN < 0). Then, h + Ah ~ UT + At7 T - sign(UT)\j2R\AUNl Ah ~ AUT- sign(UT)y/2R\AUN\. This implies that relatively large errors will occur at the position where the humerus is perpendicular to the glenoid (around the reference point C). It is also possible to displace this point by modifying 8, as 6 does not have significant influence on the shape of translation. 9 has some influence on the calculation of C, which moves the unstable point on the translation curve. Figure 4.11 presents the translation curve after a normally distributed random noise of variance 0.5 mm was added to the previous trajectory. 0.5 mm corresponds to the time-varying noise in the sensor that was found in Chapter 3. A bad estimate of C (C = [-1.3972 0.0677] versus [0 0]) causes the curve to be shifted and leads to an instability where the humerus is perpendicular to the glenoid. If C is accurately estimated, there is no discontinuity in the translation curve, but 62 Propagation of trajectory errors in the algorithm. 3(— 1 1 1 1 1 21 i i i i i i I 0 0.5 1 1.5 2 2.5 3 3.5 Angle(radians) Translations before noise being added Translations from noisy trajectory Unstable point displaced by changing 0, 9 = 20 ° Figure 4.11: Propagation of trajectory errors in the model. Large errors occur around the position where the humerus is perpendicular to the glenoid. The unstable point can be moved by changing 9. 63 Translation with correct estimate of C. 1.5 0.5 E CO c 1 0 CO c ^ - 0 . 5 -1.5 Before noise being added After Noise being added 0.5 1 1.5 Angle(radians) 2.5 Figure 4.12: Propagation of measurement errors through the algorithm if the reference point C accurate. 64 Computation of the translations with two different values of 0. 1.5 CO (S) | - 0 . 5 i -1 -1.5 " V ; / - . I M ! i ! i ! ! 1 I j I tl A 9 = 1 0 ° A 0 = -1O< ' A - V , .-T / ' 0 0.5 1 1.5 2 Angle(radians) 2.5 Translation curve after averaging the two previous curves. 2 - 1 . 5 h o l I I 1 1 1 1 1 0 0.5 1 1.5 2 2.5 3 Angle(radians) Figure 4.13: Attenuation of large errors at the unstable point by computing the translations with two different values oW and averaging. 65 only large errors around the position where the humerus is perpendicular to the glenoid (see Figure 4.12). Figure 4.11 shows that the unstable point can be moved by changing the value of 0. Since a variation of 6 modifies the position of the reference point C, but not the general shape of the curve, it is possible to minimize the large errors around the unstable point by: • computing the translations with two different values of 0, • centering the two curves to eliminate the curve shifting, • flattening the data to eliminate the large errors around C , • combining the two curves. An example is given by Figure 4.13. This method attenuates the large errors when the humerus is perpendicular to the glenoid but does not affect the general shape of the curve. This method was used when working with actual elbow position data (see Chapter 5). 4 .6 S u m m a r y A model of the glenohumeral joint was developed based on the geometrical properties of the bones. The humeral head was modeled as a sphere and the glenoid was modeled as a small planar surface (see Section 4.2). From this model, an algorithm was developed to measure the translations of the humeral head on the glenoid from elbow positions relative to scapula positions (see Section 4.3). This algorithm measures superior/inferior translations during abduction movements and anterior/posterior translations during cross-body movements. The algorithm was validated using simulations. The different sources of possible errors were listed and the propagation of these errors was studied and evaluated on simulations (see Section 4.5). A n error in the estimation of the distance R between the elbow sensor and the center of the humeral head does not affect the translation curve when the humerus is perpendicular to the glenoid, but the error in the curve tends to reach the error in R as the humerus gets further from that position. The angle 6 corresponding to the orientation of the glenoid has no significant influence 66 on the general shape of the curve, but it affects the estimate of the reference point C. Errors in the trajectory lead to large errors that tend towards infinity in the computation of translations when the humerus is perpendicular to the glenoid. It is possible to move this position by using a different 6. Large errors around the unstable points can therefore be attenuated by computing the translations with two different values of 6 and averaging the two curves. 67 Chapter 5 Evaluation of the Model and Clinical Application 5.1 I n t r o d u c t i o n In this chapter, the algorithm developed in Chapter 4 is used with the Flock of Birds system described in Chapter 3. An artificial model of the glenohumeral joint was built based on the simplified model from Chapter 4. The model was made of plastic and wood so that no metallic interference would disturb the sensor. We evaluated the algorithm on the physical model in Section 5.2. The system was then tested on patients. Subsection 5.3.1 justifies the placement of the sensors on the body. Special attention is paid to movements between bones and skin. Subsection 5.3.2 describes the positions of the patient and the tester. We applied the sensors on the arm of a patient with stable shoulders to study the repeatability of the system during five series of five abductions/adductions (see Section 5.4). The system was evaluated on a patient with an unstable shoulder during abduction and cross-body movements (see Section 5.5). The protocol was then refined and the system was re-tested. In particular we introduced the application of force against the movements, to try and force the humeral head to translate more. The system was tested again on a patient with a stable limb, the patient with an unstable shoulder previously tested and another patient with an unstable shoulder (see Section 5.6). The results are 68 Ligaments model .Sensor Humerus model Humeral head model .Glenoid model Figure 5.1: Artificial model of the glenohumeral joint then discussed in Section 5.7. In particular, the influence of the rotation of the scapula is studied in more detail. 5.2 Eva lua t ion on an Ar t i f i c i a l M o d e l An artificial model of the shoulder joint was created according to Chapter 4 to evaluate the per-formance of the algorithm. The model was composed of a wooden stick modeling the humerus terminated by a plastic ball modeling the humeral head. It is held on a flat piece of plastic mod-eling the glenoid by rubber bands attached from the wooden stick to the flat plastic piece. No metallic part was present in the model to avoid disturbing the sensor measurements. The artificial model is shown on Figure 5.1. We then applied the algorithm to the physical model. We placed both electro-magnetic sensors on the wooden stick and determined mathematicaUy the position of the humeral head from the position of the two sensors. Let sensor 1 be the sensor further away from the "humeral head" and sensor 2 be the closest. By measuring the distance R between the sensor 1 and the center of the ball and knowing the position of the two sensors, it is possible to calculate the position of the center of the ball at any time: 69 Validation of the Algorithm on the Artificial Model 2 1 1 1 1 1 1 Time (samples) Figure 5.2: Validation of the algorithm on the artificial model. The parameters are R=29.6 cm and 9 = 0 degree. The plain line is the translation curve estimated from the algorithm and the dashed line is the translation curve determined from Equation 5.1. UiH = " U{lJ2 (5.1) \\VxU2\\ where U\ is the position of sensor 1, U2 is the position of sensor 2 and H is the position of the center of the ball. We applied the algorithm to the trajectory of sensor 1, with the parameters R as measured before and 9=0 degree. We compared the estimated translations to that of Equation 5.1. The results are shown in Figure 5.2. The discontinuities from each passage correspond to the large errors mentioned in Chapter 3 around the position where the humerus is perpendicular to the glenoid. Apart from these points of discontinuity, the results are good. The accuracy is within 1 mm except when the humerus is far from being perpendicular to the glenoid. There, the error can reach 3 mm. This error may be due to a slight error in the estimation of R or due to sensor errors. However, the results confirmed that the algorithm and sensor were working properly. 70 5.3 C l i n i c a l S e t - u p The system was then tested on patients. In Subsection 5.3.1 the placement of the sensors on the body is studied and validated and the position of the patient and the tester is described in Subsection 5.3.2. 5.3.1 Placement of the Sensors The elbow was tracked by a sensor placed on the bony point of the distal humeral head outside the arm (lateral epicondyle) (see Figure 5.3). The sensor was fixed with surgical tape and an elbow fixture maintained the elbow at 90 degrees. This elbow fixture was specially designed to maintain the elbow at 90 degrees and to prevent any movement in the joint. This way, the sensor stayed in position on the epicondyle. Movements between the sensor and the bone were not discernible. Since the trajectory of the elbow must be recorded with respect to the position of the scapula, we investigated the possibility of immobilizing the scapula. One suggestion was to use "bean bags", a sort of a sack that can be shaped around the shoulder while the patient lies on his/her back. However, this would have considerably limited the movements of the patient and immobilization of the scapula would not be guaranteed to get the 1-2 mm accuracy in the computation of translations. We then decided to track the acromion of the scapula (see Figure 2.2) with one of the electro-magnetic sensors. Because there is no muscle covering the spine of the scapula (see Figure 2.2), it is possible to sense its extremity (acromion). In addition, the acromion is close to the glenoid (about 5 cm), therefore the relative position of the glenoid with respect to the acromion stays approximately the same during the movement. To avoid bone-skin movements while sensing the acromion, the sensor was not directly placed on the acromion, but was attached to the two fingers of the tester (see Figure 5.3) who palpated the acromion. The position of the receiver, because it is not directly placed on the acromion, does not actually give the position of the acromion. The sensor moves with respect to the position of the acromion if the tester's fingers rotate on the acromion (see Figure 5.4). Therefore, both position and orientation of the sensor are recorded and 2.5 cm in the direction perpendicular to the sensor are subtracted from its position(see Figure 5.4). 2.5 cm was chosen as the thickness of the fingers 71 Elbow fixture Acromion sensing Elbow sensing b) Elastic Band Sensor Fixture Figure 5.3: Placement of the sensors. a)The elbow fixture maintains the elbow at 90 degrees, one receiver is placed on the bony point of the humerus by the elbow, the second receiver is fixed to the tester's fingers who senses the acromion of the patient; b)Fixation of the acromion sensor on the tester's fingers. Figure 5.4: To correct for possible rotation of the tester's fingers while sensing the acromion, the orientation of the receiver is also measured and we subtract 2.5 cm following the z-vector from the position of the sensor to get the position of the acromion. plus the thickness of the fixture holding the sensor plus half of the receiver thickness. For instance, Figure 5.5 shows the x-y position (horizontal) coordinates as defined in Figure 5.10 of the sensor placed on the fingers of the tester who palpates an immobile knob placed on the table. The position of the sensor fluctuates within 1 cm. In Figure 5.6, we subtracted 2.5 cm from the position in the direction perpendicular to the receiver. The movements of the fingers of the tester on the knob (Figure 5.5) are corrected to within 2 mm (Figure 5.6). As the thickness of the tester's fingers may vary or the pressure on the acromion may be different from one tester to another, the distance between the receiver and the acromion may be different than 2.5 cm. The error due to these variations was studied. Let <j> be the angle between the direction perpendicular to the receiver and the direction perpendicular to the motion of the arm and A/ the error in the estimation of the distance between the receiver and the acromion. Since we Sensor Position Orientation perpendicular to the sensor Acromion Position 72 73 Position of the knob estimated by subtracting 2.5 cm perpendicularity to the sensor. 321 1 1 1 1 1 :—i 1 1 1 31.5h x 31 30.51 _i J i i_ 10 20 30 40 50 60 70 80 90 100 -11.5 E o -12.5 -13 90 100 Figure 5.6: Position of the knob determined by subtracting from the sensor position 2.5 cm in the direction perpendicular to the sensor. Line perpendicular the motion plane Figure 5.7: Error in the estimation of the position of the acromion due to the variation Al between the position of the sensor and the position of the acromion. 74 consider only the two-dimensions of the motion plane (patient's plane during abduction/adduction movement and horizontal plane during cross-body movement), the error in the estimate of the position of the acromion is: e = sin (f> * Al. If during the whole movement, the angle (f> varies between fa and fa, then the maximum relative error is: E = |(sin fa — sin fa)Al\ = |(sin 7 cos A(j> + cos 7 sin A<f> — [sin 7 cos A(j> — cos7 sin A<f>])Al\ = |2 cos7 sin A<pAl\, where 7 = ^ a n d A(j> = <^2~^'1. For instance, if A / = 3 mm and A<f> = 20 degrees, the maximum error is 1 mm. To validate the sensing of the acromion, a tester tracked a mobile knob. The same apparatus as in Chapter 3 was used: a knob was placed on the plastic arm anchored to the plastic board, such that the knob describes a circular trajectory. A tester sensed the knob with the sensor attached to his fingers. Both position and orientation matrices were recorded and the obtained trajectory was compared to the fitting circle. We found that the measurements were more precise after several trials, which implies that some training in sensing the acromion may be useful to get good results. Figure 5.8 shows the error in the sensing. The variance of the error was 0.7 mm and the maximum error 2 mm. A second test is shown on Figure 5.9 where the variance of the error dropped to 0.4 mm and the maximum error was about 1 mm. We concluded that if the tester is experienced in sensing the acromion, we expect errors smaller than 1 mm in the tracking the acromion. 5.3.2 Position of the Patient and the Tester During the tests, the patient was sitting and the tester was standing in front of the patient. The transmitter was placed about 40 cm behind the patient at about the same height as the shoulder 75 Sensing of a knob on a circle o U J -0.2 h -0.6 -10 -5 0 5 Difference between obtained trajectory and fitting circle -0.4 -0.2 0 0.2 Angle (radians) Figure 5.8: Tracking of a knob on a circular trajectory. The variance of the error was 0.07 cm. 76 Tracking of a knob over a circular trajectory 24 -i i i - i --10 -5 0 5 Difference between the trajectory and the fitting circle 0.4 | 1 1 r 1 1 1 1 i i Angle (radians) Figure 5.9: Second tracking of a knob on a circular trajectory. The variance of the error was then 0.04 cm 77 Figure 5.10: Placement of the apparatus of the experiments. The patient is sitting, the tester is standing in front of the patient, the transmitter is placed behind the patient. (see Figure 5.10). Abduction movements were performed from 0 to about 90 degrees of abduction and cross-body movements were performed from 0 to about 90 degrees of flexion. This range may be less if the patient cannot tolerate such a range of motion. 5 . 4 In i t ia l S tudy of the Repeatab i l i t y of the Sys tem To study the repeatability of the system, we performed five series of abduction/adduction move-ments on the left arm of a normal patient. The placement of the sensors was according to Subsection 5.3.1. The distance -R between the elbow sensor and the humeral head was estimated by fitting a circle to the elbow trajectories. For each series of measurements, five abduction/adduction move-ments were performed on the shoulder passively (the tester moved the arm of the patient). In each series, we determined the averaged elbow trajectory during abduction by interpolating the the 78 five abduction trajectories at regular intervals of angle of abduction and by averaging the interpo-lated data. We did the same thing for the trajectories during adduction. Figure 5.11 shows the translations for the five series. The five translation curves computed from the averaged trajectories are shown together on Figure 5.12 to inspect the repeatability. The maximum amount of estimated translation was 7 mm and most translations were within 3 mm. This graph shows that the system is not repeatable within 2 mm as required (see Chapter 2). These errors may be due to some changes of patient's posture from one series to another, which may lead to different orientations of the scapula. Also, the acromion of this patient was particularly difficult to sense because of tissues covering it. Even though the results were not repeatable within the required accuracy, they were repeatable in the sense that all the graphs showed flat translation curves that are characteristic of normal shoulders. 5.5 Initial Testings on a Patient with an Unstable Shoulder We applied the system on a patient who had dislocated her left arm several times. Two series of five passive abductions/adductions and cross-body movements were done on each arm. On Figure 5.13, the dashed fines shows the translations computed from the five movements, the plain fine shows the translations computed from the averaged trajectory during abduction or flexion for cross-body movements. The broken line shows the translations computed from the averaged trajectory during adduction or extension for cross-body movements. During abduction/adduction, the positive values of translations are superior translations and the negative values are inferior translations. During cross-body movements, positive values are anterior translations and negative values are posterior translations. In Figure 5.14, the translation curves computed from the averaged trajectories are detailed. The patterns of translations were only slightly different on the left side and the right side and translations were small (within 1 cm) for all the series of testing. We decided then to introduce forces applied against the movement (see Section 5.6), as it was expected to produce more translation in the joint. 79 Figure 5.11: Algorithm applied to 5 series of abduction on a normal left shoulder. i2 = 31.7cm. The dashed lines represent the translations from all the trajectories. The plain line is the translation curve from the averaged elbow trajectory during abduction and the broken line is the translation curve during adduction. A l l the curves are normalized so that the mean is 0. The x-axis is the angle of abduction in radians. It is 0 when the arm is vertical and w/2 when the arm is horizontal. Translations are superior when the value is positive and inferior when the value is negative. 80 Figure 5.12: The translation curves of the averaged trajectory are plot on the same graph for comparison. 81 2 Left Abduction 1 Right Abduction 1 2, • • 0.5 1 1.5 Left Cross-body 1 0.5 1 1.5 Right Cross-body 1 Figure 5.13: Translations from a patient with an unstable shoulder. The dashed line is the trans-lation curve computed from all the trajectories. The plain line is the translation curve computed from the averaged elbow trajectory during abduction. The broken line is the translation curve computed from the averaged elbow trajectory during adduction. All the curves are normalized so that the mean is 0. 82 Left Abduction 1 Right Abduction 1 0.5 1 1.5 Left Abduction 2 0.5 1 1.5 Left Cross-body 1 1 0.5 0 -0.5 -1 1 0.5 0 -0.5 -1 V . _ . \ - ^ • / J \ l i t / ' V \ • / / • / 0 0.5 1 Left Cross-body 2 1.5 .y' \ \ / K r * ' ^ /".V / / \ "''\ / . J i 0 0.5 1 1.5 0.5 1 1.5 Right Abduction 2 1 0.5 0 -0.5 -1 • N • ~" •1 0.5 1 1.5 Right Cross-body 1 0.5 1 Right Cross-body 2 Figure 5.14: Same as Figure 5.13 with only the translations computed from the averaged trajecto-ries. 83 5.6 Introduction of Forces Applied Against the Movement To observe more translation in the joint and to see more difference between the stable and the un-stable side of a patient, we introduced constrained movements. The patient's movements were con-strained by the tester who applied some force against the movement. The force was not measured, but the tester applied an equivalent force on the two limbs as hard as the patient could tolerate without pain or apprehension. In some future work, the force should be applied repeatably. For instance, a known weight could be attached to the arm of the patient during abduction/adduction. During abduction movement, the tester pushes down on the forearm while the patient elevates his arm and pushes up while the patient depresses his arm. During cross-body, the patient pushes the tester's hand with his wrist during flexion and the tester pulls the patient's wrist during extension. Figure 5.15 shows where the forces are applied for the different movements. Forces are not applied at the elbow to avoid bone-tissue movements at the elbow, so that the sensor remains in place on the elbow. The system was applied on the patient with an unstable shoulder previously tested, on a patient with normal shoulders and a patient who dislocated his shoulder many times. The results are shown in the Appendix in the same format as Figures 5.13 and 5.14. Only the most significant results are shown in this section. Because of the movement of the scapula (see Section 5.7), the numerical values of the translations are unlikely to be accurate. Therefore, only the shapes of the curves are discussed. For the patient with an unstable shoulder previously tested, more translations occured dur-ing constrained abduction on both sides than during the non-constrained movements. During constrained abduction/adduction, on the left side (unstable side) translations were superior dur-ing abduction and inferior during adduction, on the right side, translations were superior during abduction and not significant during adduction. For the normal patient, significant translation occurred during constrained abduction/adduction movements. The patterns were the same on both shoulders. Translations were superior during ab-duction and superior again during adduction (see Figure 5.16). The most significant results were during constrained movements on the patient who dislo-84 Constrained Left Abduction 1 Constrained Right Abduction 1 I 1 03 C •B o 03 | - 1 - 2 0.5 1 1.5 Constrained Left Abduction 2 fen/'..-'-' 0.5 1 1.5 2 1 0 -1 - 2 0.5 1 1.5 Constrained Right Abduction 2 Angle (radians) Figure 5.16: Translations in constrained abduction/adduction for a patient with normal shoulders. 86 "0 0.5 1 1.5 Constrained Left Cross-body 2 2 1 0 -1 - 2 ^ " • • • • • • • • • • ^ ; . / . - i r - ' - . - . . 0 0.5 1.5 "0 0.5 1 1.5 Constrained Right Cross-body 2 Figure 5.17: Translations during constrained movements on the patient with severe instability on the left shoulder. 87 I I I I I I 1 1 0 10 20 30 0 10 20 30 x (cm) x (cm) Figure 5.18: Comparison of left and right elbow trajectories during constrained abduc-tion/adduction on the patient with severe instability on the left shoulder. 88 cated his left arm many times. The patterns were different between the left and the right side (see Figure 5.17). During abduction, much more significant superior translation occurred on the left side than on the right side, during adduction, slight superior translation occurred on the left side, where no significant translation occurred on the right side. During cross-body movements, some anterior translation occurred during flexion on the left side. The difference between the left and right side during abduction/adduction was so obvious that it could easily be seen directly on the elbow trajectory (see Figure 5.18). The trajectory of the elbow is not the same during abduction and adduction. Note that the range of motion is also larger on the right side than on the left side. 5.7 Analysis of Results and Discussion The system showed that the patterns of the translation curves were the same on both side for the normal patient and were significantly different for the patient with severe left instability. However, the amount of translation estimated is too large to be realistic. For instance, on the normal subject, the total range of translation estimated during constrained abduction movement is 3.5 cm! This is physically impossible, since it is larger than the size of the glenoid. Rather than glenohumeral translation, the curve we observe is translation in the whole shoulder joint with respect to the acromion. This includes the rotation of the scapula. The difference of shape between constrained abduction and adduction is probably a consequence of a different pattern in the rotation of the scapula due to the force applied by the tester. We studied the influence of the rotation of the scapula on the elbow trajectory. Let I be the distance between the acromion and the glenoid, and 0 the angle of rotation of the scapula (see Figure 5.19). If u is the vector between the initial position of the glenoid and its position after rotation, we get: u = 2/sin0/2(cos0/2z*-r-sin0/2j) = /(sin©if + (1 - cos©)/) For instance if / = 4 cm and 0 = 30 degrees, then u = 2i + 0.54j and \u\ = 2.07 cm. This leads to 89 Acromion Figure 5.19: Influence of the rotation on the displacement of the glenoid, large errors in the elbow trajectories and to large errors in the final results as well. 5.8 Conclusion To determine glenohumeral translations accurately, it is extremely important to measure the rota-tion of the scapula and to accurately know the position of the center of the glenoid with respect to the bony points that are tracked. For instance, we suggest that the scapula be tracked from three points: the acromion, another point on the spine and the inferior extremity of the scapula triangle. We suggest that a radiograph is taken to identify the position of the glenoid center with, respect to the acromion and the inferior extremity. Another solution would be to immobilize the scapula. Bean bags were suggested, but these would not assure a total immobilization. The system as it stands now gives interesting information on the movement by comparing stable and unstable side of the patient especially during constrained movements, but does not give useful quantitative information. .More work is necessary towards tracking the whole scapula or immobilizing it to obtain accurate translations. 90 Chapter 6 Conclusions 6.1 Motivation The only precise method to currently assess shoulder instability is by invasively manipulating and observing the shoulder during surgery. One method currently used to assess shoulder instabilities is the external manipulation of the shoulder by the clinician to see how far across the glenoid the humeral head translates. This method is subjective and non-precise. Magnetic Resonance Imaging (MRI) and radiography are also used to assess shoulder instabilities. M R I typically is used to observe soft tissue damage and radiography is used to observe bone damage and position. They do not give information on the dynamic function of the joint and they require two persons with different skill sets to operate the imaging system and interpret the data. Based on these observations, the need for a novel method to measure shoulder instability for improved patient outcomes was recognized. Excessive translations of the humeral head on the glenoid are directly related to shoulder instabilities. Measuring glenohumeral translations allows the tester to determine the degree and direction of the instability. The overaU purpose of this thesis was to develop a methodology and apparatus to measure glenohumeral translations. 6.2 Contributions The main contributions of this work are: 91 • The development of detailed functional specifications for a novel system to measure shoulder instabilities to satisfy specific needs unmet by current methods that assess shoulder instabil-ities. • The development, implementation and validation of a method to measure the errors inherent to electro-magnetic sensors and to assess the performance and calibration of electro-magnetic sensors when used in medical applications. • The identification of inherent limitations in the electro-magnetic sensor and some suggestions to improve the technology of the sensor to meet the specifications that were defined but unmet and to facilitate use of electro-magnetic sensors in a broader range of related medical applications. • The development of a mathematical model of the glenohumeral joint and the development, implementation and validation of an algorithm that estimates the superior/inferior transla-tions of the humeral head on the glenoid during abduction/adduction movement and ante-rior/posterior translations during cross-body movement, as a function of elbow position with respect to the scapula. • The evaluation of the system on patients with stable and unstable shoulders. • The identification of inherent limitations of the system, some specific recommendations for future work to improve the system so that it meets the specifications defined, but unmet, and some suggestions related to a broader range of applications involving assessment of patient outcomes. 6.3 Conclusions In Chapter 2, from a literature search on existing technology, we recognized the need for the development of a novel system to satisfy a previously unmet clinical need for quantitative assessment of shoulder dynamic function. We defined the following specifications: the system must be safe for the patient and the tester, non-invasive, objective, quantitative, adaptable to any sized patient and 92 any environment, inexpensive, easy to use and to set up such that a non-technical person could interpret the results, and it should be precise and repeatable within 2 mm. The system uses a position sensor which must have the same specifications as the overall system. It should also be light and have a sub-millimeter accuracy to satisfy the overall 2 mm requirement. After evaluation of commercially existing position sensors (Section 2.2), it was con-cluded that electro-magnetic position sensors were the best suited for the application. However, they are sensitive to the metallic and the electrical environment and have errors associated with time-lag of measurement which may be important. From a literature search and from experiments, it was found that there are several sources of measurement errors in electro-magnetic sensors. The errors can be due to: metallic environment (static errors) that distorts the field, time-varying noise, time-lag because of excessive low-pass filtering during dynamic measurements, the "aperture problem" (when the receivers are too close to the transmitter) and interaction between receivers if several receivers are used (Section 3.3). Because the manufacturer's definition of accuracy was not applicable to our experiments (Section 3.3), we concluded the necessity to measure each error individually and a methodology was devel-oped to assess the performance of electro-magnetic sensors in related medical applications (Section 3.8). By applying this methodology to the sensor we used in the shoulder application (Section 3.5), we found that the static error due to metallic distortions was negligible, the error due to time-varying noise had an error of ± 0.5 mm and the error due to time-lag and interactions between the two receivers produced a maximum error magnitude of 2 mm. We also found that the default settings of the electro-magnetic sensor gave the best trade-off between time-lag errors and time-varying noise (Section 3.6). Some suggestions about modifying the sensor technology were made so that it could meet the specified requirements and become more useful to medical applications (Section 3.9): a smaller transmitter could replace one receiver and the computation of positions could take place after the motion and complete recording of the magnetic fields. 93 A simple model of the shoulder was developed in Chapter 4. The humeral head was mod-eled as a sphere while the glenoid was modeled as a planar surface (Section 4.2). Based on this model, an algorithm that measures superior/inferior translations during abduction* movement and anterior/posterior translations during cross-body* movement was developed (Section 4.3) from the positions of the elbow with respect to the scapula. After identifying the different possible errors in the parameters used by the algorithm and after studying mathematically and from simulations the propagation of these errors on the algo-rithm, we concluded that small errors in the elbow trajectory led to large errors when the humerus is perpendicular to the glenoid (Section 4.5). However, it was possible to discard large errors around this position (Subsection 4.5.3). When the system was evaluated on an artificial model (Section 5.2) the error in estimating the translations was smaller than 1 mm except where the humerus was perpendicular to the glenoid (unstable point) and far from that position where the error was up to 3 mm, most likely because of a slight error in the estimate of R or because of sensor errors. Despite these errors, the evaluation on the artificial model showed that the algorithm and the electro-magnetic sensor were working properly. The system was then tested on patients. The effectiveness in tracking the elbow and the acromion with the electro-magnetic sensors was evaluated from experiments (Subsection 5.3.1) the error magnitude was smaller than 2 mm. After testing the system on a normal patient, we found that the results were repeatable within 7 mm (Section 5.4), which is larger than the required accuracy of 2 mm. On a patient with an unstable shoulder, no significant translation was detected (smaller than 0.5 cm) and no significant difference between the two limbs was found (Section 5.5). We then introduced forces applied against the movement, as more translation on the unstable side was expected during constrained movements (Section 5.6). When the system with the revised protocol was tested on a patient with severe shoulder instability, significant difference in the patterns of the translation curves between 94 the two limbs was observed. Translations on the unstable side were much larger than on the stable side. On the normal patient, translations were detected during abduction/adduction with the same pattern for both sides. No significant translation was noted on the patient with unstable shoulder who was tested initially. Even though some conclusions could be made from comparing the patterns of the translation curves between the left and right side, quantitative values of translation could not be estimated mainly because of the rotation of the scapula which led to large errors in the results. We concluded that there is a need to measure the rotation of the scapula during the movement and determine the position of the center of the glenoid from radiography, or alternatively to immobilize the scapula. The developed system is safe for the patient and the tester, it is non invasive, objective, relatively inexpensive (around US$ 5,000 if a computer is already available), easy to use and to set up and the tester is able to interpret the results. However, even though it is adaptable to any sized patient, the acromion is more easily tracked on skinnier patients, because less tissue covers the acromion. Larger errors are expected on "larger" patients. We found that the system does not give accurate enough results to compete with clinical manipulation of the shoulder that is the current practice to assess shoulder instabilities. Large errors are mainly due to the rotation of the scapula that was neglected in the development of the model. As the system stands now, it gives useful information on the stability of shoulders by com-paring the unstable side to the normal side, but the quantitative values of translations should not be taken as being the values of glenohumeral translations. The system is useful in supplementing the manipulation of the shoulder by the clinician, but should not be used alone. Some future work is suggested below to aUow the system to be routinely used and give all the information necessary for a more precise diagnosis and to replace the subjective method of shoulder manipulation. 6.4 Suggestions for Future W o r k The main limitation of the system as it stands now is that position of the glenoid is estimated from the position of the acromion, and the rotation of the scapula is not taken into account. One 95 way to overcome this problem is to track the whole scapula by tracking several points, for instance tracking two points on the spine and the lower extremity and to determine the position of the glenoid with respects to these points from radiography. It may also be possible to immobilize the scapula. The use of bean bags was suggested, but it was concluded that they would not guarantee an immobilization within the required accuracy. Future work may include the development of a more effective method to immobilize the scapula. The distance R between the sensor on the elbow and the center of the humeral head could be better estimated with radiography and therefore reduce the error associated with it. A n improved sensor could be used to eliminate the use of two receivers, if the transmitter was smaller and lighter, it could be placed on the body and only one receiver would be required. As discussed in Chapter 3, new technology could be developed where the positions of the sensors would be processed after the motion. This technology would eliminate errors due to time-lag and would allow a more sophisticated data processing to reduce time varying noise. The system developed uses a two-dimensional model. For example, we do not measure anterior/posterior translation during abduction. Therefore, the results do not measure the full characteristics of the instability. In some future work, one may develop a 3D model, using some other types of movements. If a better fixture is applied to the elbow preventing any movement between the bone and the sensor, orientation of the sensor could also be used to determine gleno-humeral translations. If these suggestions are applied to the present system, the system should totally meet the initial specifications we defined and would represent a significant improvement in term of shoulder patient outcome. The clinician would be able to assess the shoulder of the patient quickly, quanti-tatively, with total safety for the patient and for himself/herself. He/she would be able to assess the shoulder repeatedly before and after surgery. The patient would then avoid having surgery to completely characterize his/her shoulder instability. This system, when improved, could be adapted to measure instabilities in other joints such as the knee or the hip. 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'; 0 0.5 1 1.5 Figure 6.3: Translation on constrained movements on the same patient as Figures 6.1 and 6.2. 103 Constrained Left Abduction 1 Constrained Right Abduction 1 0.5 1 1.5 Constrained Left Abduction 2 0.5 1 1.5 Constrained Left Cross-body 1 0 0.5 1 1.5 Constrained Left Cross-body 2 1 0.5 0 -0.5 -1 1 0.5 0 -0.5 -1 . II 1 ^ • V 0.5 1 1.5 Constrained Right Abduction 2 N /v. r 0.5 1 1.5 Constrained Right Cross-body 1 0 0.5 1 1.5 Figure 6.4: Same as Figure 6.3 but for averaged trajectories only. 104 105 106 Constrained Left Abduction 1 Constrained Right Abduction 1 • - \ v -0.5 1 1.5 0.5 1 1.5 Constrained Left Abduction 2 2 Constrained Right Abduction 2 1 0 -1 - 2 0.5 1 1.5 0.5 1 1.5 Constrained Left Cross-body 1 2 Constrained Right Cross-body 1 ' "v.'.';..; ' 1 .••.;:'v"..-S.v • • • • • • . . . • ' ~" •• • ••/" ' 0 -1 -O 0 0.5 1 1.5 Constrained Left Cross-body 2 "0 0.5 1 1.5 Constrained Right Cross-body 2 5 » 0.5 1.5 Figure 6.7: Constrained movement with same patient as in Figures 6.5 and 6.6 107 Constrained Left Abduction 1 Constrained Right Abduction 1 0.5 1 1.5 Constrained Left Abduction 2 0.5 1 1.5 Constrained Left Cross-body 1 0 0.5 1 1.5 Constrained Left Cross-body 2 1 0.5 0 -0.5 -1 / 11 V / v. J s 0.5 1 1.5 Constrained Right Abduction 2 0.5 1 1.5 Constrained Right Cross-body 1 0 0.5 1 1.5 Constrained Right Cross-body 2 0.5 1.5 1 0.5 0 -0.5 -1 A . -A Jr. <~./' yv/v v . / • / • 0.5 1.5 Figure 6.8: Same as Figure 6.7 but on averaged trajectories only. 108 109 110 - 2 l 0 0.5 1 1.5 Constrained Left Cross-body 2 2 1 0 -1 - 2 -. • I.: ' 0 0.5 1.5 - 2 L I 2 1 0 -1 - 2 0 0.5 1 1.5 Constrained Right Cross-body 2 0.5 1.5 Figure 6.11: Translations on constrained movements with same patient as in Figures 6.9 and 6.10. Ill Constrained Left Abduction'1 11 • • 1 1 i Constrained Right Abduction 1 0.5 1 1.5 Constrained Left Abduction 2 0.5 1 1.5 Constrained Left Cross -body 1 1 0.5 0 -0.5 -1 1 7 T ./ .'•1 j r.r> /V \J\h \ 1 i / hi 1. ft 1 0 0.5 1 1.5 Constrained Left Cross -body 2 1 0.5 0 -0.5 -1 1 0.5 0 -0.5 -1 A" • J j >/ / <\ v 0.5 1 1.5 Constrained Right Abduction 2 i J 0.5 1 1.5 Constrained Right C r o s s - b o d y 1 0 0.5 1 1.5 Constrained Right C r o s s - b o d y 2 1 0.5 0 -0.5 -1 A i " \ • /•' \ 0 0.5 1.5 Figure 6.12: Same as Figure 6.11 but on averaged trajectories only. 112 Nov-05-96 12:27P a s c a n s l o n B02 860 6439 P.02 Flock/Bird Filter Equations The Flock of Birds and the Bird use 3 internal, user-selectable filters. They are: 1. AC Wide Notch - NOTCHl * (SR^ + SR f J J) + NOTCH2 * (SR I4J + SR^) + NOTCH3 * (SR i4J + SR^) Vi J 2. AC Narrow Notch Sly « (SR^ + SR. J 12 3. DC (infinite impulse filter) Sfu = Alpha * (Sly-Sty + Sfu with Alpha adaptive Where Slj is the 3x3 matrix of new sensor voltages. The above filters can be applied to the outputs x,y,z,\M>4 with the same effectivity. The AC Wide and Narrow Notch filters can be turned on/off by user. The DC filler may be turned off or adjusted using the Vm, Alphajnin, and Alpha_max tables. The table entries correspond to distance ranges from transmitter (see Flock of Birds or Extended Range Transmitter user manual for distance ranges). Alpha in the DC filter ranges from Alphajnin to Alphajnax as a function of attasured-dynamic energy (motion and noise), present Sharing SUM, and distance from transmitter. Vm value is proportional to the expected sum of the variances of the noise. V » is used in -the system to distinguish motion from background noise. Valid Vm values are from 1 ( no noise) to 32767 (for very noisy). Vm values have an effect on system lag. The higher the Vm value, the slower the system will respond to movement. As Alpha is reduced towards zero, the new measured values are weighted more. The result is movement/noise has little effect on the calculated value. If Vm is set properly, Alpha should Nov-05-96 12:27P a s c e n s i o n 802 860 6439 P.03 be at Alpha_min when the receiver is at rest. As the value of Alpha expands towards one, the new measured values arc less weighted. The result is movement/noise that highly effects the calculated value, to make for a very reactive system. If Vm is set properly, Alpha should be at Alpha_max during rapid motion. The correct values of Vm, Alpha_min, and Alphajnax are dependent on your environment and application. The values have been set to default values when the system is reset, and these values are set for a 'normal' noise environment. You noise level may be different. To set Vm table values. 1. Place the receiver at the desired distance from the transmitter, in the area it will be operating. 2. Make sure the DC filter is active (the system defaults DC filter ON). Reset system or use CHANGE VALUE, FILTER ON/OFF STATUS command. 3. Drop the Vm table value for that range to 1 using the CHANGE VALUE, DC CONSTANT TABLE Vm command. 4. Read continuous POSITION/ANGLES from Bird. If the values output are too noisy, double the value used in the Vm table. Repeat this step as needed until values are quiet while receiver is at rest. 5. If the values output from the bird are quiet while the receiver is still, briefly move the receiver rapidly in your hand. Place the receiver back down so it's once again still. 6. If the values after the motion from the receiver are continuously changing you will have to increase the value in the Vm table by multiply value by 1.5. Repeat as needed until system returns constant values after moving the receiver rapidly. The Vm table value is correct if; a. While the receiver is still the position/orientation values settle rapidly to a constant or near constant value, (if not, Vm value is to small) b. When the receiver is moved, the position/orientation values respond quickly and when the receiver is still the values fail to return to a near constant value. (Vm value is still too small) c. When the receiver is moved, the output values respond slowly. (Vm value too large). A major cause of noise in the system may come from operation in close range with a CRT. If this is your situation we suggest using the CRT sync feature which will eliminate the CRT as a source of noise. I n **U«ioa «ad Op«r»tio€i Quid. Application Sous Application Note #5 Configuring The Bird For Minimum Lag 1. Use the highest baud rate possible for collecting data from The Bird. This means that if you have a PC compatible computer then you should use 115.2K baud when using its RS232 port If you are using the Bird's RS485 interface then you should collect data at a rate of 250K baud. 2. If you have multiple Birds in a flock configuration then you should use individual RS232 or RS485 ports to each Bird. If you used a single port to collect data from multiple Birds then the maximum data rate is reduced by a factor of two each time you double the number of Birds on this port 3. Use STREAM mode not POINT mode for collecting data. STREAM mode gives you data every Bird measurement cycle as soon as it has been computed. If you used POINT mode then the data request would come at some random point in the Bird's measurement cycle resulting in a random variation of up to 10 milliseconds in the 'age' of the Bird measured data. 4. Select an output format that transmits the minimum amount of data required. For example, if you only want to measure angles, then select ANGLE mode and not POSITION/ANGLE mode. 5. Unlock the outputs if you are going to be making sudden movements by setting the CHANGE VALUE, SUDDEN OUTPUT CHANGE LOCK command to zero. 6. Minimize the number of filters applied to the Bird data. To detennine which filters you can remove: 1) Set the Bird's receiver at the maximum distance from the transmitter that you will be using in your application. 2) Use the CHANGE VALUE, FILTER ON/OFF STATUS command to remove one filter at a time. Observe the noise on the outputs of your measurements as you remove each filter. If the amount of noise is acceptable then leave the selected filter out. The DC filter will have the largest impact on noise and usually cannot be eliminated unless you are going to be running with the receiver close to the transmitter or you are going to filter your own data. 115" Tmtillifinii lad Opwitioo Guide Application Sous 7. Minimize the amount of steady state filtering applied by the DC filter. Use the CHANGE VALUE, DC FILTER CONSTANT TABLE ALPHA_MIN command and increase ALPHA_MIN until the noise level is unsatisfactory. The closer the receiver is to the transmitter the larger ALFHA_MIN can be. 8. Run the Bird at a higher measurement rate. Use die CHANGE VALUE, BIRD MEASUREMENT RATE command and increase the Bird's measurement rate from its default speed of approximately 103 measurements/second. You can increase the speed up to a maximum of approximately 140 measurements/seconds. As you increase die speed you will note that die amount of noise in the Bird measurements may be higher or less than the amount of noise at the power-up default speed. The noise can increase or decrease rapidly with a speed change of just a few cycles/sec and then increase or decrease again as you continue to change the speed. 9. Reduce the amount of noise that the Bird thinks is in the local environment by using the CHANGE VALUE, DC FILTER TABLE Vm command. Set the receiver at various distances from the transmitter and reduce the Vm value for this range until the noise is unacceptable. The biggest gain in dynamic performance, other than elimination of the DC filter, comes from reducing Vm. 10. Reduce the amount of filtering during the steady state part of fast movements by using the CHANGE VALUE, DC FILTER CONSTANT TABLE ALPHA_MAX. Set AL?HA_MAX as close to 0.999 as possible. The larger alphajnax is, the less lag there will be during fast motions. But note, the larger alphajnax is, the larger the noise will be during the movement. At Ascension when we want a 'snappy* response with good noise characteristics we use all system defaults except for the following overrides: a) . Stream mode b) . Sudden output change lock - 0 c) . DC filter ON, AC narrow notch filter ON, AC wide notch OFF d) . Vm table - 2,2,2,10,10,40,200 Where most of the 'snap' comes from the Vm table. Installation and Operation Guide Appendix III - Bird Specifications APPENDIX HI - BIRD SPECIFICATIONS Physical: Transmitter: Receiver: Enclosure: Technical: Positional range: Angular range: Static positional accuracy: Positional resolution: Static angular accuracy: Angular resolution: Update rate: Outputs: Interface: Format: Modes: Electrical: Power requirements: Environment: 3.75-inch cube (mounted inside enclosure or external) with 10'cable. 1.0" x 1.0" x 0.8" cube (or optional 3-button mouse) with 10' or optional 25 'cable 9.5" x 11.5" x 4.4" ± 36" in any direction ± 180° Azimuth & Roll ± 90° Elevation 0.1" RMS averaged over the translational range 0.03" @ 12" 0.5° RMS averaged over the translational range 0.1° R M S ® 12" 100 measurements/sec X,Y,Z positional coordinates and orientation angles, rotation matrix, or quaternions RS232: 2,400 to 115,200 baud RS485: 57,600 to 312,500 baud Binary Point or Stream (RS232 only) +5 VDC @ 2.45 amps avg., 3.85 amps peak + 12 VDC @ 0.53 amps avg., 0.63 amps peak -12 VDC @ 0.34 amps avg., 0.46 amps peak All specifications are valid at 30 deg C ± 10 deg in an environment void of large metal objects and electromagnetic frequencies, other than the power line. 117: 

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