Talus morphology and its functional implications on the ankle joint
A Thesis
Submitted to the Faculty
of
Drexel University
by
Damani .Y. Seale
in partial fulfillment of the
requirements for the degree
of
Master of Science in Mechanical Engineering and Mechanics
June 2011
ii
Acknowledgements
Thank you to my parents and siblings for your constant support and your continued implicit confidence in me and my abilities. To my parents, your accomplishments, despite the challenges you faced greatly inspire me and are the source for my own confidence in myself and my abilities.
Thank you to my advisor and mentor Dr. Sorin Siegler for the opportunity to work with you and learn from you over the past couple years. The opportunities you have provided me and your guidance throughout my time at the biomechanics lab have greatly improved my analytical and engineering skills.
Thank you to Dr. Jason Toy for your contributions to this work.
Thank you to the teachers and staff of Queen’s Royal College for your efforts which were largely responsible for my development.
Thank you to my friends for your support during this and every time. May we never change unless we choose to.
Dedicated to Safi and Kani.
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Table of Contents
List of Figures ...... iv List of Tables ...... iv Abstract ...... vi Chapter 1: Introduction ...... 1 1.1 Specific Aims ...... 1 1.2 Background and Significance ...... 2 1.2.1 Osteology ...... 2 1.2.2 Syndesmology ...... 10 1.2.3 Mechanics of the Ankle joint ...... 11 1.2.4 Limitations of Previous Studies ...... 16 Chapter 2: Methods ...... 17 2.1 Image Processing ...... 17 2.2 Morphological Measurements ...... 19 2.3 Anatomical Axes ...... 22 2.3.1 Intermalleolar axis ...... 22 2.3.2 Trochlear cone axis ...... 24 2.4 Anatomical Reference Planes ...... 25 2.5 Anatomical Axes Orientation ...... 30 2.6 Cone Skewness ...... 32 Chapter 3: Results ...... 34 3.1 Morphological measurements of Talus ...... 35 3.2 Anatomical Axis Orientation ...... 37 3.3 Square of Direction Cosines ...... 39 3.4 Cone Skewness ...... 41 Chapter 4: Discussion ...... 43 4.1 Trochlear Cone ...... 43 4.2 Axis of Rotation ...... 44 List of References ...... 49
iv
List of Tables
Table 1: Morpological Measurements of Talus ...... 35 Table 2 Angles between intermalleolar axis, trochlear cone axis and reference axes ...... 37 Table 3 Square of Direction Cosines...... 39 Table 4 Trochlear Cone Skweness...... 41
v
List of Figures
Figure 1: Distal Fibula ...... 2 Figure 2: Distal Tibia ...... 4 Figure 3: Tibial Plafond Conical Angle ...... 5 Figure 4: Talus ‐ General Features ...... 7 Figure 5: Talus ‐ Trochlear Surface Apical Angle Variation ...... 8 Figure 6: Trochlear Surface approximation as frustum of cone ...... 9 Figure 7: Anterior Talofibular Ligament ...... 10 Figure 8: Single axis of motion of the ankle joint ...... 12 Figure 9: Multiple axes of rotation of the ankle joint ...... 14 Figure 10: Thresholding process in Analyze 8.1...... 18 Figure 11: 3D volumetric talus model...... 20 Figure 12: Creation of the medial and lateral best fit circles...... 21 Figure 13: Intermalleolar axis ...... 23 Figure 14: Trochlear cone axis ...... 24 Figure 15: Coronal plane construction ...... 26 Figure 16: Transverse plane construction ...... 27 Figure 17: Anatomical Reference planes ...... 28 Figure 18: Anatomical Reference axes...... 29 Figure 19: Measurement of angle between intermalleolar axis and anatomical reference axis 1...... 31 Figure 20: Skewness of trochlear cones...... 33
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Abstract
Talus morphology and its functional implications on the ankle joint Damani Seale Sorin Siegler, PhD.
A clear understanding of the ankle joint has applications from the design of ankle braces to the design of ankle implants and total ankle replacements. Examination of the articular trochlear surface of the talus can be used to describe talar morphology and explain ankle joint kinematics.
A testing protocol was established to determine which of two anatomical axes; intermalleolar axis and trochlear cone axis; best approximates the axis of rotation of the ankle joint. Anatomical axes were located and oriented using anatomical landmarks obtained from CT images for the foot and ankle. An anatomical reference axis system was established to standardize the location and orientation of the anatomical axes. The talus geometry was approximated as the frustum of a cone, the axis of which potentially represented the axis of rotation of the ankle joint.
The results showed that the ankle joint is not accurately modeled as a single fixed axis of rotation joint.
The talus was best approximated as the frustum of a skewed cone. Due to the asymmetry, rotation about the skewed cone results in a constantly changing axis of rotation. Hence, the ankle joint was modeled as a single degree of freedom joint, the axis of rotation of which is constantly changing.
vii
1
Chapter 1: Introduction
1.1 Specific Aims
The objective of this research is to characterize the talus morphology, particularly that of the trochlear surface and determine the effect of this morphology on the talocrural ankle joint. Based on the literature, the following hypotheses was made and tested:
H1: The trochlear surface of the talus can be approximated as the surface of a cone, with apex
oriented medially, the axis of which is the axis of rotation of the talocrural joint.
H2: The axis of the trochlear cone serves as a more accurate approximation of the axis of
rotation of the talocrural joint than the commonly used intermalleolar axis.
This hypothesis was tested by examining magnetic resonance (MRI) images of the foot and ankle of 9 healthy individuals. Three dimensional models of the images were created and reverse engineering software was used to take measurements and define anatomical planes and axes. 2
1.2 Background and Significance
1.2.1 Osteology
The primary bones of the human ankle joint are the distal fibula, the distal tibia and the talus.
Distal Fibula
The distal end of the fibula is separated into the distal fibular shaft and the lateral malleolus [1].
Figure 1: Distal Fibula (A) Medial View of left fibula. (B) Lateral view of fibula. (C) Posterior view of fibula. (D) Anterior view of fibula. (E) Medial view of tibia‐lateral malleolus. (F) Lateral view of distal fibula‐tibia. (G) Inferior view of distal tibia‐fibula. (1, articular surface; 2, anterior border; 3, posterosuperior tubercle; 4, insertion tubercle of posterior talofubilar ligament; 5, tip lateral malleolus; 6 digital fossa; 7, gluiding surface for peronei tendon 8, anterior tibial tubercle; 9, posterior tibial tubercle; 10, tibial plafond; 11, lateral malleolus; 12, medial malleolus.) [1]
3
Distal Fibular Shaft
The distal fibular shaft has two surfaces, medial and lateral, separated by an anterior‐posterior border.
The medial surface is separated into an anterior narrow segment and a broader posterior flat part. The lateral surface is also separated into anterior and posterior sections. Both of these sections continue downward to the respective anterior and posterior boarders of the lateral malleolus [1].
Lateral Malleolus
The lateral malleolus is pyramid shaped with three surfaces, lateral, medial and posterior. The lateral malleolus extends 1 cm further distally than the medial malleolus. The lateral surface of the lateral malleolus is smooth and convex. The medial surface is in contact with the incisura fibularis of the distal tibia. The anterosuperior aspect of the medial surface is a triangular surface. This surface is in continuity with the cartilage‐coated surface of the distal tibia that it is in contact with. The posterior surface tapers distally and usually contains a sulcus [1].
Distal Tibia
The distal tibia is formed by five surfaces: inferior, anterior, posterior, lateral and medial. The inferior surface of the tibia, the tibial plafond is an articular surface which corresponds to the talar dome. This surface is concave anterioposteriorly but is slightly convex transversely. A slightly elevated ridge dives the articular surface into a wider lateral and narrower inner segment. Geometrically, Sarrafian reports this surface to be a section of a frustum cone with a medial conical angle of 22° 4° [2]. 4
Figure 2: Distal Tibia – Genral Features (A) Anterior aspect of left distal tibia. (B) Posterior aspect of distal tibia. (C) Lateral aspect of distal tibia.(D) Medial aspect of distal tibia. (E) Lateral aspect of medial malleolus. (F) Inferior view of distal tibia. (1, medial malleolus; 2, sulcus for tibialis posterior tendon; 3, anterior colliculus; 4, intercolliculus groove; 5, posterior colliculus; 6, anterior tibial tubercle; 7, posterior tibial tubercle.) [1] 5
Figure 3: Tibial Plafond Conical Angle [2]
Regardless of the position of the talus relative to the tibia, the tibial plafond only covers two thirds of the talar dome. The tibial plafond makes an angle of 93° 3.2° with the long axis of the tibia [1].
The anterior surface of the distal tibia is in continuity with the lateral surface of the tibial shaft. The surface is narrow proximally and enlarges distally. The posterior surface is in continuity with the posterior surface of the tibial shaft. The proximal segment is smooth and slightly convex. The distal segment bears an oblique groove medially, directed downward and inward. The lateral surface is triangular, apex superiorly. The medial surface is smooth, directed obliquely downward and inward. It is larger proximally and narrows distally as it is prolonged by the medial malleolus. The medial malleolus is a strong process at an obtuse angle from the medial aspect of the distal tibia. Its base is large anteroposteriorly and flat and narrow transversely. It is formed by two segments separated by a groove. The anterior segment descends lower, usually 0.5 cm, than the posterior segment. The groove is large and measures 0.5 to 1 com in width. The lateral malleolus, the tibial plafond and the medial malleolus form a bony unit, considered to be a malleolar fork that covers and holds the talus on three sides [1]. 6
Talus
The talus is an intercalated none located between the ankle bi‐malleolar fork and the tarsus. It is moored with strong ligaments but has no tendinous attachments. The talus is formed by three parts: the body (corpus tali), the neck (collum) and the head (caput). The body has five surfaces: superior, lateral, medial, posterior and inferior [1].
7
Figure 4: Talus ‐ General Features
(A) Lateral aspect. (B) Medial aspect. (C) Superior aspect. (D) Inferior aspect. (E) Anterior aspect. (F) Posterior aspect. (1, articular surface ‐ facies malleolus lateralis; 2, cervical collar; 3, articular surface ‐ facies articularis navicularis; 4, 5, tubercles for insertions of anterior talofibular ligaments; 6, lateral process; 7, posterolateral tubercle; 8, oval surface for insertion of talotibial component of deltoid ligament; 9, articular surface ‐ facies malleolaris medialis; 10, talar neck; 11, posteromedial tubercle; 12, tubercle of insertion of deltoid ligament; 13, segment of talar neck located within talonavicular joint; 14, segment of talar neck located within talotibial joint; 15, extra‐articular segment of talar neck where a bursa may be found against which glides medial root of inferior extensor retinaculum; 16, sinus tarsi; 17, canalis tarsi; 18, anterior calcaneal articular surface of the talar head; 19, articular segment of talar head corresponding to superomedial and inferior calcaneonavicular ligaments; 20, middle calcaneal articular surface of talar neck; 21, posterior calcaneal articular surface of the talar body; 22, canal of the flexor hallucis longus tendon; 23, trochlear surface; 24, anteromedial extension of trochlear.) [1]
8
The superior surface, termed the trochlear surface, is pulley shaped and articulates with the distal inferior surface of the tibia. The groove or saddle point of the pulley is nearer to the medial border, making the lateral segment wider. The trochlear surface is convex anteroposteriorly with an average sagittal radius of convexity of 20m. The medial border of the trochlear surface is straight and slightly lower than the lateral. The lateral border is oblique, directed posteromedially and beveled in its posterior segment. Due to this, the trochlear surface is wedge shaped and is narrower posteriorly). The inferior surface of the talus forms the subtalar joint with the calcaneus [1].
The length and width of the talus was measured for 100 dry tali. The average length was 48mm, with a maximum of 60mm and a minimum of 40mm. The average width was 37mm with a maximum of 45mm and a minimum of 30 mm [1].
The morphology of the trochlear surface allows for its approximation as the frustum of a cone whose apex is directed medially. The apical angle varies widely among individuals with an average of 24° 6° with a range of 0°, representing a cylinder to 38° [3].
Figure 5: Talus ‐ Trochlear Surface Apical Angle Variation [3]. 9
The lateral facet of the talus corresponds to the base of the cone, making a 90° angle between this facet and the cone axis. However, due to the wedge shape of the talus, the medial facet makes an oblique angle with the cone axis. As a result, this facet corresponds to an elliptical section of the cone [3].
Figure 6: Trochlear Surface approximation as frustum of cone. The lateral facet serves as the base of the cone. The medial cross‐section of the medial facet with the cone creates an elliptical section [3].
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1.2.2 Syndesmology
The tibiofibular complex is a system of bones and ligaments which firmly attach the tibia and fibula. This complex embraces the talus on which it articulates. The three ligaments of the complex are the anterior tibiofibular ligament, the posterior tibiofibular ligament and the interosseous ligament [1].
The lateral malleolus of the distal fibula is connected to the talus by the anterior talofibular ligament and the posterior talofibular ligament. The calcaneofibular ligament spans from the fibula, over the talus, and connects to the calcaneus. These three ligaments comprise the lateral collateral ligament. The medial malleolus of the tibia is connected to the talus and the calcaneus by the deltoid ligament [2]. The deltoid ligament is divided into two layers, superficial and deep, each being formed by multiple fascicles
[1]. The effect of the ligaments on ankle joint kinematics is not a focus of this study but knowledge of the ligaments of the ankle joint allow for a full understanding of the articulation of the bones of the ankle joint.
Figure 7: Anterior Talofibular Ligament. (1, anterior talofibular ligament, main component; 2, anterior talofibular ligament, accessory component; 3, anterior tibiofibular ligament; 4, cervical ligament.) [1]. 11
1.2.3 Mechanics of the Ankle joint
The study of the biomechanics of the foot‐ankle complex is of great interest as it is central to the design of commercial ankle implant and ankle replacement products. Several areas of the mechanics of the foot‐ankle complex have been studied via several approaches. The focus of the current study is the tibiotalar joint, also termed the talocrural joint or simply the ankle joint. When focused on the ankle joint, the number of studies remains large but the number of approaches can be can be covered by two groups; studies which aim to determine the location and orientation of the axis of rotation of the ankle joint, and studies which assume the location and orientation of the axis of rotation of the ankle joint and seek to determine kinematic and kinetic parameters with reference to the axis of rotation. In these studies, there are three classes of ankle joint models, whether determined or assumed. In general, the ankle is modeled as a one degree of freedom joint; the distinction lies in the nature of the axis of rotation.
Axis of rotation of the Ankle Joint
The first class models the ankle as a single degree of freedom joint with a single fixed axis of rotation.
Inman suggested that the trochlear surface was such that it could be approximated as the frustum of a cone whose apex is directed medially, the major axis of which serves as the axis of rotation of the ankle joint [3]. Inman found the single fixed axis of rotation of the ankle joint to pass through the distal tips of the medial and lateral malleoli [3]. Consequently, the axis of rotation of the ankle joint has long been approximated as the intermalleolar axis. Clinically, this axis is located by palpation. 12
Figure 8: Single axis of motion of the ankle joint [3].
Subsequent studies, aimed at finding dynamic parameters with reference to a fixed axis of rotation of the ankle joint are often based on Inman’s single axis model [4‐12]. Arebald et al measured lower leg kinematics in three dimensions relative to a single axis of rotation fixed to the lower leg using motion capture equipment and software [4]. Caputo et al compared instable and stable ankle joint kinematics in a similar manner using motion capture and an ankle joint axis fixed to the distal tibia [5]. Dul et al created an analytical kinematic model of the foot‐ankle complex by modeling both joints as single axis hinge joints [6].
A kinematic study conducted by Singh et al corroborated Inman’s single axis hinge model. The study involved the insertion of a rod into the foot‐ankle complex. The rod was considered to be representative of the axis of rotation of the ankle joint when sagittal plane rotation of the lower leg resulted in a screw like rotation of the rod, rather than translation of the rod. Investigators determined a single orientation of the inserted rod that best met the criterion and concluded that the ankle joint could be modeled as a single axis hinge joint [10].Other studies, aiming to locate and orient the axis of rotation of the ankle joint, used a subject specific method to determine the axis [7, 11]. van der Bogert used a twelve 13
parameter analytical model of the foot‐ankle complex was created. The analytical model constrained the ankle joint to a single axis but the location and orientation were not fixed. Experimental kinematic data collected with motion capture equipment was fit to the model, via optimization to determine the values of the twelve variable parameters. These parameters were used to locate and orient the axis of rotation. The findings were in agreement with the orientation of Inman’s axis [11].
This single axis of rotation was contradicted by a study by Barnett and Napier which found the ankle to have two distinct axes of rotation [13]. This is characteristic of the second class of ankle models; single degree of freedom hinge joints with two separate axes of rotation, one each for dorsiflexion and plantarflexion. Barnet and Napier studied the anatomy of the talus in order to determine the axis of rotation of the ankle joint among other things. They approximated the medial and lateral facets as circles with different radii. The medial facet was found to be best approximated by two separate circles of different radii. Each circle is prominent in either dorsiflexion or plantarflexion as it is then engaged with the distal tibia. The circle approximating the anterior portion of the medial facet, which is engaged in dorsiflexion was found to have a smaller radius than the lateral radius. The effective axis of rotation of the ankle joint in dorsiflexion, the line connecting the centers of both circles, pointed downward laterally. However the posterior section of the medial facet, which is engaged in plantarflexion, was approximated by a circle of radius larger than that of the lateral facet. Hence, the plantarflexion axis of rotation points upward laterally. The axis changeover was found to occur around the neutral position
[13]. 14
Figure 9: Multiple axes of rotation of the ankle joint [1].
Hicks corroborated this in a kinematic study which used the method of least translation of a screw axis to determine the axis of rotation of the ankle joint. Two distinct axes of rotations in agreement with the findings of Barnet and Napier were reported [13, 14].
A subsequent kinematic study by Lundberg et al aimed to determine the axis of rotation of the ankle joint had similar findings. Investigators used roentgen stereography markers to capture the orientation of the foot and ankle bones after incremental sagittal plane rotations. A helical axis of rotation was then fit to the data to locate and orient two axes of rotation of the ankle joint [15].
Sammarco et al [16] found the ankle joint to have not two axis, but to have a continuously changing axis of rotation. This is characteristic of the third class of ankle joint models. In this study, investigators took
X‐ray exposures of various sagittal plane rotational displacements to determine the relative motion of the bones of the ankle joint which were tracked with roentgen stereography markers. The method of instant center of rotation was used to determine that the axis of rotation of the joint was continuously changing throughout the range of sagittal plane motion [16]. Subsequent studies have had similar findings [17, 18]. Leardini et al studied the effect of the morphology of the articulating surfaces and 15
ligaments of the ankle joint on the kinematics of the joint. This was achieved by fixing the shank, and applying a small force to cause sagittal plane rotation. The force was then removed and the ankle was allowed to passively (under its own weight) return to the neutral position. The argument is that since the motion is passive, the motion depends exclusively on the interactions between the articulating surfaces and the ligaments. Further, the interactions of the articulating surfaces owe to the morphology of the respective surfaces. A helical axis approach was used to determine that the axis of rotation is continuously changing as reported by Sammarco et al [16, 17].
Coupling of rotations at the ankle joint
An oversight of many ankle studies is the characterization of the motion at the ankle joint as purely sagittal [3‐7, 10, 14, 19‐22]. It was widely accepted that the ankle joint was responsible for sagittal plane motion while the subtalar joint was responsible for coronal and transverse plane rotations. However,
Siegler et al studied the kinematics of the ankle and subtalar joints and found this not to be the case
[23]. In a novel approach, the contribution of each joint to each of the three rotations of the ankle was separated. Using an anatomical reference system similar to that established by Grood and Suntay for the knee, the magnitude of rotations at each joint was measured [23‐25]. It was determined that though minimal (less than 10 percent of the entire range of motion), the ankle joint did contribute to coronal and transverse plane rotations [23]. It was also determined that not only did the ankle joint contribute to non‐sagittal rotations, but sagittal plane rotation of the passive ankle was coupled with non‐sagittal rotations. The coupling was such that in plantarflexion, the passive ankle also inverted and rotated interlay. In dorsiflexion, the ankle tends to rotation externally and this is also accompanied by eversion
[23].
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1.2.4 Limitations of Previous Studies
Leardini et al [17] argued convincingly that the kinematics of the ankle joint is determined by the morphology of the articulating surfaces and the ligaments at the joint. However, rather than conducting a morphological study to establish a causal relationship between the morphology and the kinematics, investigators studied the kinematics and then attempted explain them with the morphology [17]. Inman and Barnet and Napier did conduct morphological studies and sought to establish a causal relationship between the morphology and the kinematics [3, 13]. However, both were limited by the technology available at the time. Advances in image processing and solid modeling technologies now allow for more sophisticated and perhaps more accurate methods of analysis. Utilizing image processing software, several investigators have created solid models of bones of the foot and ankle [19, 26‐29]. Roche et al then used solid modeling and editing software to make morphological measurements of best fit circles approximation sagittal slices of the trochlear surface and the corresponding tibial plafond articular surface [28]. However, no attempt was made to connect morphology and kinematics.
The current study aims to establish a cause relationship between the talus morphology and ankle joint kinematics. The findings of Inman and Barnet and Napier will be re‐visited utilizing modern image processing and solid modeling and editing tools. The results are expected to locate and orient the true anatomical axis or axes of rotation of the ankle joint and elucidate the phenomenon of sagittal, coronal and transverse rotation coupling at the ankle joint. These findings should refine design criteria for ankle implant and total ankle replacement products.
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Chapter 2: Methods
2.1 Image Processing
Twenty two models of the bones of the lower leg are developed using magnetic resonance image (MRI) and X‐ray computed tomography (CT) from eighteen health subjects between ages of 18 and 35, and 4 cadaveric legs (average age 71.5 years) using Biomedical Imaging Resource Analyze 8.1 image processing software. The Digital Imaging and Communications in Medicine (DICOM) files were imported into
Analyze 8.1, and the set of slices which cover the entire distal tibia, distal fibula and talus was loaded into the Analyze 8.1 workspace. Using the Analyze 8.1 Volume Render tool, the software created a three dimensional model of the lower leg based on the two dimensional image data. This model included both soft tissue and bone material. In order to separate the bone from the soft tissue, the Analyze 8.1
Threshold told is used to accurately delineate the boundaries of the bones thereby separating the image data for bones from that of soft tissue [30]. The Analyze 8.1 Object Separator tool was used to separate the bones being studied from each other and from the other bones of the foot. The Analyze 8.1 Surface
Extractor tool was then used to create a solid surface model of each of these models and these models were saved as .stl files. 18
Figure 10: Thresholding process in Analyze 8.1. Clockwise from top left; volume rendering of left foot and ankle including soft tissue and bones, volume rendering of left foot and ankle including only bones, volume rendering three segmented bones of the left foot and ankle, talus(yellow), tibia(red) and fibula(green).
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2.2 Morphological Measurements
The .stl files of the talus bone models are then imported into Geomagic Inc Geomagic Qualify 10 computer aided design software. This software is capable of performing 2D and 3D measurements of
CAD models and these capabilities are used in order to make morphological measurements of individual bones as well as combinations of bones. Before the morphological measurements are taken, a local smoothing function is applied to remove rough contours caused by noise in the image data processed in
Analyze 8.1.
The medial and lateral talus dome radii will be measured. These are the radii of circles which approximate the sagittal curvature of the medial and lateral talus shoulders respectively. Using the
Geomagic Qualify 10 Section Though Object tool, a sagittal slice was constructed using three points along the shoulder. The cross section of the talus of this plane was then computed. A circle was then fit to the cross section of the talar dome. The radius and angle of opening of the best fit circle were both calculated. These methods were performed for both the medial and lateral shoulders of the talus.
20
Figure 11: 3D volumetric talus model. Clockwise from top left; isometric view, front view, medial view and lateral view.
21
Figure 12: Creation of the medial and lateral best fit circles. Clockwise from top left; solid isometric view of best fit circles, hollow isometric view of best fit circles, medial cross‐section, lateral cross section.
22
2.3 Anatomical Axes
2.3.1 Intermalleolar axis
Surface models of the distal tibia, distal fibula and talus were imported into Geomagic Qualify 10 and a local smoothing function is applied to remove rough contours caused by noise in the image data processed in Analyze 8.1.The lateral and medial malleoli, the distal tips of the respective malleoli, were located. The intermalleolar axis, the line joining the malleoli, was drawn. 23
Figure 13: Intermalleolar axis 24
2.3.2 Trochlear cone axis
The axis of the trochlear cone, a cone drawn to approximate the trochlear surface, was then drawn as the line joining the centers of the lateral and medial shoulder circles.
Figure 14: Trochlear cone axis 25
2.4 Anatomical Reference Planes
In order to standardize measurements across subjects, subject‐specific anatomical reference planes were created. The transverse, sagittal and coronal planes were created using subject‐specific anatomical references. The anatomical references used were the malleoli, and the centroids of the superior surfaces of both the tibia and the fibula. To construct the anatomical planes, an origin point was first chosen as the midpoint of the intermalleolar axis. The normal to the transverse plane was then drawn as the line joining the origin and the centroid of the tibia on its superior surface. Anatomically, this axis represents the shank axis or the long axis of the tibia. The transverse plane was then drawn as the plane perpendicular to this axis, passing through the origin. The coronal plane was then drawn as the plane in which the origin as well as the centroids of both the tibia and the fibula lie. Lastly, the sagittal plane was drawn as the plane passing through the origin, that is perpendicular to both the transverse and coronal planes. Anatomical reference axes, the normals to the anatomical reference planes were then named.
Axis 1, was the line normal to the transverse plane, Axis 2, normal to the coronal plane and Axis 3, normal to the sagittal plane. Under this convention, Axis 1 is the axis about which internal/external rotation of the ankle occurs. Axis 2 is the axis about which inversion/eversion occurs. Axis 3 is the axis about which dorsiflexion/plantarflexion occurs. 26
Figure 15: Coronal plane construction
27
Figure 16: Transverse plane construction
28
Figure 17: Anatomical Reference planes
29
Figure 18: Anatomical Reference axes. Axis 1 normal to transverse plane, axis 2 normal to coronal plane, axis 3 normal to sagittal plane.
30
2.5 Anatomical Axes Orientation
The anatomical reference axis and planes were used to determine the orientation of the intermalleolar and trochlear cone axis. The orientation was characterized by the angles between the anatomical axes
(intermalleolar and trochlear cone axes) and the anatomical reference axis. The angle between the anatomical axis and each of the three reference axis is measured. The direction cosines and the square of the direction cosines are computed. Since the anatomical reference axes are orthogonal, as a rule, the square of the direction cosines of the measured angles sum to one.
31
Figure 19: Measurement of angle between intermalleolar axis and anatomical reference axis 1.
32
2.6 Cone Skewness
Using the medial facet as the base of the cone, the axis of a regular cone, line through the base circle center, normal to the plane in which the base lies should contain both the medial and lateral circle centers. Therefore, for a regular cone, the vertical and horizontal distances should be zero. However, for a skewed cone, there axis of a regular cone of same base will not contain both circle centers. The degree skewness of the cone was characterized by two measurements, the vertical and horizontal distances of the centers of the medial and lateral trochlear cone best fit circles projected on a plane parallel to the medial facet.
The vertical measurement is measured along an inferior‐superior direction and the horizontal measurement is measured along a posterior‐anterior direction. In order to do this geometrically, a medial plane is considered to be the plane in which the medial trochlear facet best fit circle lies.
Alternatively, the lateral plane is considered to be the plane in which the lateral trochlear facet best fit circle lies. A plane, parallel to the medial plane is constructed to pass through the center of the lateral trochlear facet best fit circle. The center of the medial trochlear facet best fit circle is projected onto this parallel medial plane so that this plane contains this projected point as well as a point locating the center of the lateral circle. The vertical and horizontal measurements are then taken in this plane. These measurements are obtained most expediently by creating two parallel transverse planes, the distance between which represents the vertical distance between the circle centers. Similarly, two parallel coronal planes are constructed, the distance between which represents the horizontal distance between the circle centers. 33
Figure 20: Skewness of trochlear cone. The magnitude of the vector (red) shown represents the distance between both circle projections projected on a plane parallel to the medial facet. This vector is broken into vertical (inferosuperior) and horizontal (anteroposterior) components.
34
Chapter 3: Results
Presented are data providing a quantitative description of talus morphology. 35
3.1 Morphological measurements of Talus
Table 1: Morpological Measurements of Talus. Measurements were made of a sagittal cross‐section of the talus. The radius reported is the radius of a best fit circle fitted to approximate the curvature of the talar dome. The medial best fit radius is compared to the lateral best fit radius. The angle measurement reported is the angle of opening of the talar dome. It carves out a wedge of the talar dome over which the best fit circle was drawn. Radii measured in millimeters and angles measured in degrees.
Subject
Section cad3R cad4L cad5L cad6R SahaR AD1L BR1R BS1R CJ2L CK1R DD1R
Medial 21.4 23.0 25.7 20.6 18.0 25.7 26.2 32.8 28.8 25.4 25.8
Lateral 17.4 21.7 17.9 18.1 17.4 19.4 21.6 27.2 24.9 19.9 24.2 Radius Plane
Medial 87.7 88.3 87.1 101.9 118.7 79.1 90.0 92.1 85.4 90.1 136.1
Sagittal
Angle Lateral 123.4 96.4 80.3 97.8 113.6 100.4 109.5 103.6 90.9 105.5 108.0
36
Table 1 continued
Subject
EB1L GR2L KM1L LC1L PJ1R SB1R SK1R SS3L TD1L WH1R 18151L
Medial 21.6 31.0 36.0 22.3 31.0 27.3 23.8 24.3 23.4 32.8 18.0
Lateral 22.3 22.8 23.8 23.9 27.2 24.0 22.1 22.0 18.8 21.6 20.2 Radius
Plane
Medial 103.5 87.1 74.4 85.8 98.5 87.2 120.9 90.8 99.2 66.5 106.3
Sagittal
Angle Lateral 93.6 93.6 89.5 74.9 97.7 85.0 108.2 106.9 109.7 87.8 86.8
37
3.2 Anatomical Axis Orientation
Table 2 Angles between intermalleolar axis, trochlear cone axis and reference axes. Reported are the angles between the intermalleolar axis and each of the three anatomical reference axes as well as the angle between the trochlear cone axis and each of the three anatomical reference axes. All angles measured in degrees.
Subject Intermalleolar Intermalleolar Intermalleolar Cone axis Cone axis Cone axis
axis and axis 1 axis and axis 2 axis and axis 3 and axis 1 and axis 2 and axis 3
BS1R 75.3 84.6 15.7 80.8 76.6 16.4
CJ2L 70.8 83 20.5 86.3 65.9 24.4
CK1R 75.6 78.2 18.7 79 58.3 34
H1R 69.8 84 21.1 88.1 73.6 16.5
KM1L 75.6 78.2 18.7 58.9 71.7 37.2
LC1L 75.3 85 15.6 83.1 68.7 22.5
SB1R 74.2 81.2 18.2 90 64.1 25.9
SS3L 69.0 87.4 21.1 81.9 80.8 12.3
TD1L 81.4 81.2 12.4 77 58 35.1 cad3R 75.4 75.6 20.7 79.9 64.3 27.9 cad4L 74.0 82.3 17.8 83.3 74.6 16.8 cad4R 77.6 85.5 13.2 86.9 70.4 19.8 38
cad5L 72.7 83 18.7 77.2 77.5 18 cad5R 75.8 81.7 16.5 74.6 76 21.1 cad6R 78.3 78.2 16.7 78.6 66.1 26.8 39
3.3 Square of Direction Cosines
Table 3 Square of Direction Cosines. Reported are the squares of the direction cosines of angles between intermalleolar axis and anatomical reference axes and trochlear cone axis and anatomical reference axes.
Subject Intermalleolar Intermalleolar Intermalleolar Cone axis Cone axis Cone axis
axis and axis 1 axis and axis 2 axis and axis 3 and axis 1 and axis 2 and axis 3
BS1R 0.064393 0.008856 0.926775 0.025562 0.053707 0.920283
CJ2L 0.108153 0.014852 0.877355 0.004164 0.166734 0.829345
CK1R 0.061847 0.041819 0.897207 0.036408 0.27612 0.687303
H1R 0.119231 0.010926 0.870402 0.001099 0.079717 0.919335
KM1L 0.061847 0.041819 0.897207 0.266807 0.098591 0.63446
LC1L 0.064393 0.007596 0.927682 0.014433 0.131951 0.853553
SB1R 0.074137 0.023405 0.902447 3.22E‐18 0.190796 0.809204
SS3L 0.128428 0.002058 0.870402 0.019853 0.025562 0.954618
TD1L 0.022361 0.023405 0.953889 0.050603 0.280814 0.669369 cad3R 0.063539 0.061847 0.875056 0.030753 0.18806 0.781042 cad4L 0.075976 0.017952 0.90655 0.013612 0.07052 0.916461 cad4R 0.046111 0.006156 0.947856 0.002925 0.112528 0.885257 40
cad5L 0.088432 0.014852 0.897207 0.049084 0.046846 0.904508 cad5R 0.060176 0.020839 0.919335 0.07052 0.058526 0.870402 cad6R 0.041123 0.041819 0.917424 0.039068 0.16414 0.796709 41
3.4 Cone Skewness
Table 4 Trochlear Cone Skweness. Reported are the vertical and horizontal distances that characterize the skewness of the trochlear cone. Also reported is the fraction (presented as a percentage) of the width of the wedge of the cone. The wedge width is presented for reference. Distances measured in millimeters. Measured from the medial circle center projection to the lateral circle center projection, the positive vertical distance is inferosuperior (upward) and the positive horizontal direction is anteroposterior (backward).
Subject Vertical distance/W Horizontal distance/W Vertical Distance (%) Horizontal Distance (%) Wedge width (W) BS1R 6.70 21.75 3.00 9.74 30.8 CJ2L 5.40 20.45 1.40 5.30 26.4 CK1R 6.00 26.67 2.00 8.89 22.5 H1R 12.90 35.54 3.00 8.26 36.3 KM1L 10.50 43.93 1.70 7.11 23.9 LC1L 1.40 6.22 3.00 13.33 22.5 SB1R 8.50 28.72 2.10 7.09 29.6 SS3L 3.10 11.23 5.40 19.57 27.6 TD1L 4.70 20.80 0.60 2.65 22.6 cad3R 10.50 42.17 3.40 13.65 24.9 cad4L 9.70 25.80 5.30 14.10 37.6 cad4R 1.40 6.19 0.00 0.00 22.6 42
cad5L 5.90 22.61 8.40 32.18 26.1 cad5R 9.20 38.66 1.30 5.46 23.8 cad6R 2.80 14.29 1.50 7.65 19.6 43
Chapter 4: Discussion
4.1 Trochlear Cone
To verify Inman’s approximation of the trochlear surface as the frustum of a cone, morphological measurements of the medial and lateral talar dome radii of curvature were performed. Inman found the lateral radius to be larger than the medial radius so that the cone’s apex would occur medially [3]. The current study found the medial radius to be consistently larger than the lateral radius, 25.7 4.7 mm and 21.7 2.4 mm respectively. A t‐test analysis of the data sets for the medial and lateral radii for the twenty two subjects tested indicated the medial measurement was significantly different than the lateral measurement (p=0.002). The findings of the current study contradict those of Inman and indicate that the trochlear surface is more accurately approximated as the frustum of a cone with the apex occurring laterally. This finding is not immediately obvious but is revealed through the methods used in the current study. The reason for the non‐obvious nature of the finding is due to another finding of the current study concerning the skewness of the cone.
The line joining the centers of the medial and lateral best fit circles is considered to be the axis of the skewed cone. The line normal to the medial facet through the center of the medial best fit circle is considered to be the axis of the normal cone. Therefore, the angle between these two axes characterizes the degree of skewness of the skewed cone, relative to the normal cone of same base.
However, the angle is ambiguous and does not give a unique description of the skewness of the cone. In order to give a unique description, the skewness is characterized in terms of the horizontal and vertical parameters outlined in the Methods section and reported in Table 4.
The vertical and horizontal measurements characterizing cone skewness were 6.6 3.6 mm and 2.8
2.2 mm respectively. It should be noted that the positive direction for the vertical distance 44
measurement is inferosuperior (upward) and for anteroposterior (backward) for the horizontal distance measurement. This clarifies that the lateral circle center occurs superior to the medial circle center. This is a key finding as it explains that despite the finding that the medial radius is larger than the lateral radius, the trochlear medial trochlear surface is inferior to the lateral trochlear surface. Visually, this gives the impression that the lateral radius is larger than the medial radius as found by Inman [3].
To provide context, these are normalized with respect to the width of the wedge of the cone approximating the trochlear surface. The width measured is the distance between the medial and lateral facets. This distance was chosen as the normalizing parameter because it serves as an appropriate reference in characterizing the skewness of the cone. Two parameters are required to sufficiently describe the skewness of the cone or wedge, one distance measurement along the axis of the normal cone and one distance perpendicular to this measurement. The cone or wedge width provides the distance along the axis of the normal cone and the second parameter is the hypotenuse of the triangle formed by the vertical and horizontal distances. The measure of skewness is then derived as the ratio of the hypotenuse and the cone width. The average measurement of skewness was 0.28 0.11.
4.2 Axis of Rotation
Two anatomical axes, the intermalleolar axis and the trochlear cone axis were located and oriented relative to anatomical reference planes and axes. The ability to standardize the reference axis used to describe location and orientation of the anatomical axes was paramount to this study. The preferred method to establish anatomical references at the ankle joint is the one developed by Wu et al [25].
However, due to truncation of the tibia in the CT images obtained, its use was not possible. Instead, a novel method to establish anatomical reference system to characterize ankle joint rotation was 45
developed. This reference system uses similar analytical landmarks to those used in the reference system developed by Wu et al [25] including the location of the malleolar tips and the long axis of the tibia, however, the method of obtaining these parameters differed. However, since this is a comparative study, importance was placed on standardizing the method across all subjects rather than trying to replicate what has been done in the past. The goal of comparing the location and orientation of anatomical axis (intermalleolar and trochlear cone) was accomplished.
The one limitation is that the comparison of findings made in this study to previous work is predicated on the use of an identical reference system. However, considering the great variability in the reference systems as well as the lack of use of anatomical reference systems to characterize used to characterize ankle joint motion, this limitation does not invalidate the current study [4, 13‐15, 25, 26]. Comparisons to previous work will be made where appropriate and the limitation what should be concluded from the comparisons is noted.
Table 3 describes the orientation of both the intermalleolar axis and the trochlear cone axis. Since the anatomical reference axes are orthogonal, the direction cosines, the cosines of the angles made between a vector, say the intermalleolar axis or trochlear cone axis and each of the anatomical reference axes, when squared, sum to one. This property of orthogonal reference planes was used to characterize and predict the coupled nature of ankle joint rotations. The ratio of the direction cosine of an anatomical axis and a particular anatomical reference axis (reported in Table 3) and the number one
(sum of direction cosines), represents the fraction of rotation that occurs about that particular reference axis if the axis of rotation of the joint is considered to be the anatomical axis.
On average, if the intermalleolar axis is considered to be the axis of rotation of the ankle joint, the current model predicts that 90.5 2.6 % of motion is sagittal plane motion, 2.3 1.7% of motion is coronal plane motion is 7.2 2.9% of motion is transverse plane motion. Alternately, when the axis of 46
rotation of the ankle joint is assumed to be the trochlear cone axis, 82.9 9.9 % of motion is sagittal plane motion, 13.0 8.0% of motion is coronal plane motion is 4.2 6.6% of motion is transverse plane motion. Both results seem reasonable when compared to previous findings indicating that the majority of motion at the ankle joint is sagittal plane motion [3‐7, 10, 14, 19‐22], though the intermalleolar axis model predicts a greater majority of sagittal plane motion. Therefore, tasked with determining which axis model best predicts ankle motion; the study of joint coupling does not suffice since both models are corroborated by the literature.
To determine which model best predicts ankle motion, thereby determining which axis is a more accurate representation of the axis of rotation of the ankle joint, the orientation of both axes will be compared to the axis of rotation determined by kinematic studies. In a converse approach, kinematics studies determine the axis of rotation of the ankle joint based on kinematic data [11, 14‐17]. However, there are contradictions even in this small group of studies. van der Bogert determined that the axis of rotation was similar to Inman’s [11]. This would support the intermalleolar axis model developed in the current study. However, a limitation of van der Bogert’s study was constraining the ankle joint to have a single fixed joint. The study was more advanced than other kinematic studies which constrain the ankle joint to a fixed pre‐determined joint (usually based on Inman’s joint) in that it used kinematic data to establish the orientation of the axis [4, 5, 10]. But by constraining the joint to have a fixed axis of rotation the method determines an average axis of rotation for the entire range of motion.
Studies by Lunberg and Hicks reported that averaging the axis of rotation over the entire range of sagittal motion hid a more complex kinematic pattern [14, 15]. Both studies found that ankle motion was more accurately modeled as rotation about two distinct axes of rotation. It was determined that rotation occurred about one axis during dorsiflexion and another during plantarflexion [14, 15]. The orientation of the dorsiflexion axis, sloped downward mediolaterally matches the intermalleolar axis 47
model established in the current study as well as Inman’s single axis of rotation model [3, 14, 15].
However, the plantarflexion axis orientation, sloping upward mediolaterally, matches the trochlear cone axis model established in the current study. An anatomical study conducted by Barnet and Napier supports this double axis model [13]. This suggests that neither axis model established in the current study accurately predicts ankle motion. Rather, both single axis models should be combined into a double axis model in which the intermalleolar axis model is used to model dorsiflexion and the trochlear cone model is used to model plantarflexion. However, the current study aims to determine a causal relationship between anatomy and kinematics. Combining both models to match the literature is convenient, but has no anatomical basis.
Through distinct approaches, Sammarco and Leardini concluded that neither a single axis nor a double axis model of the ankle joint accurately describes and predicts ankle motion. They determined that the ankle joint is most accurately described as a one degree of freedom joint, with the axis about which the rotation occurs constantly changing [16, 17]. Based on the findings of this study, there is no immediately obvious interpretation of the morphology that supports an instantaneously changing axis of rotation.
However, the current study is limited by the method in determining the axis of rotation of the trochlear cone. The trochlear cone axis was constructed by replicating a method used by Barnet and Hicks which considers the line joining the centers of the medial and lateral best fit circles as the axis of the cone, hence the axis of rotation of articulation along the surface of the cone [13]. This method is only appropriate for a normal cone. Due to the symmetric nature of a normal cone, the axis of the cone serves as the axis of rotation for articulations on the surface of the cone. It should be noted that this is based on full congruency of the articulating surfaces.
However, the current study showed that the trochlear surface is best articulated by a skewed cone. The average measurement of trochlear cone skewness was 0.28 0.11. This is significant as means that the 48
cone is considerably asymmetric. Due to this asymmetry, the line joining the medial and lateral best fit circle centers, considered to be the axis of the skewed cone, is not the axis of rotation for articulation on the cone surface. Geometrically, this asymmetry causes the axis of rotation for articulation along the surface of a skewed cone to be constantly changing. With this in mind, the current study has established a causal link between talus morphology and ankle joint kinematics. Due to the skewed nature of the cone approximating the trochlear surface, the ankle joint behaves as a single degree of freedom joint, the axis of rotation of which is constantly changing.
49
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