Table of Contents
This research was conducted to analyze the biomechanics of a lateral ankle sprain through various means of experimental data and calculations. The data was found with the use of Gait analysis, calculations, and data provided from previous cases studies.
Collectively, the information allows for a better understanding of the mechanisms behind a lateral ankle sprain. By determining data such as the forces, shear stresses, static and dynamic loads, this data can be used to further explore the mechanisms of a lateral ankle sprain.
The topic of lateral ankle sprains is prevalent to not only the high-intensity athlete but also the common athlete or active individual. An ankle sprain is a troublesome injury that can be better prevented in many situations
Supination is when the foot rolls outwards from the centerline of the body, meanwhile pronation is when the foots rolls inwards (Learning), as illustrated in figure 1.
Figure 1: Supination and Pronation of the Foot
Figure 2: The Ankle Joint
Figure 3: The Bones in the Ankle Joint
Figure 4: The Subtalar Joint of the Ankle Joint
The talocrural joint is the only mortise and tenon joint in the body, which is comprised of the tibia and fibula of the leg and the talus (Brockett 2016). The distal ends of the fibula and tibia form a square shaped opening where the talus fits in, hence forming a mortise and tenon joint, as shown in figure 5. Due to the tight fit of the joint, the talocrural joint is a pure hinge joint. Hence, motion in only one plane can occur which is dorsiflexion and plantarflexion (Unit VIII). The anatomy of this joint in addition to its supporting ligaments enable it to maintain gait stability.
The transverse-tarsal joint combines the talus, calcaneus, and navicular. This joint absorbs the forefoot rotation, hence reducing the forces on the talocrural and subtalar joint (Chaitow 2011).
Figure 5: The Talocrural Joint
The ankle joint contains three compartments of ligaments which are grouped based on their anatomical location. The lateral ligaments are further divided into three different parts, which are the anterior talofibular, posterior talofibular, and calcaneofibular ligaments, as shown in figure 6 (Volker 2018). They are mainly responsible for preventing extreme inversion and internal rotational stress. The anterior talofibular ligament is responsible for restraining the movement of the talus with respect to the fibula and tibia, while resisting inversion and plantarflexion (O’Reilly). The posterior talofibular ligament resists posterior movement of the talus. Meanwhile, the calcaneofibular ligament is responsible for providing stability during dorsiflexion and preventing inversion of the calcaneus with respect to the fibula (O’Reilly).
Figure 6: The Lateral Ligaments of the Ankle Joint
The medial ligaments, which are also known as the deltoid ligaments, are grouped into two groups, superficial and deep, as shown in figure 7. They are responsible for stabilizing the ankle joint during eversion and preventing dislocation of the ankle joint. The superficial parts are the anterior, posterior tibiotalar ligament, and the tibionavicular ligament. The anterior tibiotalar ligament controls plantarflexion and eversion and the posterior tibiotalar controls dorsiflexion. Meanwhile, the deep part consists of the tibiocalcaneal ligament, which reinforces the ankle joint (O’Reilly).
Figure 7: The Medial Ligaments of the Ankle Joint
Figure 8: The Muscles of the Ankle Joint
Injury in a ligament that supports the ankle leads to an ankle sprain. A foot has lateral and medial ligaments that support the ankle joint from the outside against forces of inversion. The main reason for sustaining ankle sprains involves rotating the foot, causing partial or complete tears in the lateral ligaments supporting the bones and ankle joint from the outside part of the foot. One way this form of injury can occur is stepping on an uneven surface.
Lateral ankle sprains are one of the most common sports injuries; they are caused by torn or pulled ligaments. These ligaments lie on the lateral side of the ankle joint.Lateral ligaments are most often pulled or torn due to an inversion motion occurring at the ankle joint.The three lateral ligaments that are often injured are the Posterior Talofibular Ligament (PTFL), Anterior Talofibular Ligament (ATFL), and the Calcaneal Fibular Ligament (CFL). Lateral ankle sprains involve the tearing of fibers in one or more of these ligaments or total tear of the entire tissue, which can result in an unstable ankle joint prone to further damage to the bones.The ATFL, reported to be the weakest is first ligament injured (Brostroem1964). Rupture to the ATFL is followed by damage to the CFL and finally to the PTFL(Brostroem1964). Figure 9 shows the location of the lateral and medial ligaments of the ankle joint.
Figure 9: Ligaments on the ankle joint
The severity of ankle injuries depends on the extent of stress placed on the ankle joint bones and ligaments. However, it is safe to assume that you have suffered a sprained ankle if you have sharp pain placing your weight on the affected foot. Ankle sprains impact the ankle’s ability to function or support a person. Repetitive ankle sprains may eventually cause chronic pain or arthritis(Biomechanical Analysis of an Ankle Sprain 2017). When the ankle is sprained, inflammation occurs. Blood vessels allow fluids to migrate into the soft tissue surrounding the joint causing swelling. White blood cells responsible for inflammation migrate to the area, and blood flow increases as well(Blumstein n.d.).
The main movements of the ankle joint are plantar and dorsiflexion, which are movements in the sagittal plane. The range of motion (ROM) of our ankle joint is not a fixed one due to many factors including geographical location, cultural predisposition, and extent of physical activity(Blumstein n.d.).
Lateral ankle sprains usually occur with inversion and plantar mechanisms. This mechanism involves the ankle rolling in such a way that the outer border of the foot contacts the ground. Many other movements can occur. Each mechanism can injure different ligaments.
Ankle braces are the most modern innovations to prevent ankle injuries. They increase the stability of the ankle by restricting ankle inversion and eversion. Research has shown that ankle braces have the potential to restrict inversion range of motion by 18% to 53% (Alves, Alday, Ketcha, &Lentell, 2002; Eils et al., 2002). This percentage can correspond to a range of approximately 14.9° to 20° restriction to inversion motion (Cordova, Ingersoll & Leblanc, 2002). Ankle inversion is not the only range of motion restricted by ankle bracing; ankle braces have also demonstrated an ability to modify sagittal plane ankle joint kinematics (Simpson, Craven, Theodorou, &DelRay, 1999). Research showed that plantar flexion was restricted between 8.6° to 15° and dorsiflexion was restricted between 7° and 14° when wearing an ankle brace.
Initial treatment for a sprained ankle is applying ice on the swollen area to reduce inflammation. The doctor may apply an ankle brace or a cast to reduce motion of the ankle. Crutches are usually used to reduce the weight put on the injured ankle. The most common medications used for ankle sprains are anti-inflammatory pain medications that control inflammation and reduce pain. Tylenol is a common alternative for pain reduction. Recovery from an ankle sprain can take anywhere from two to twelve weeks and in some cases even more. The time required to recover from an ankle sprain depends on the severity of the injury. Surgery might be required if any ligament is torn.
Ankle sprain prevention can be as simple as wearing the right shoes or as complicated as balance training for athletes. A person must keep their ankles strong and flexible to avoid injury. There are ankle strengthening exercises that aid in preventing a future injury. One must always wear stable shoes that give his/her ankle the proper support. Wearing ankle tape is recommended when playing a sport to offer extra support to the ankle. Wearing an ankle brace is a must if one has repeated sprains.
The team optimized the use of the gait lab in order to run some trials and obtain kinematic and kinetic data. An ankle sprain was simulated by purposefully spraining the left ankle while walking. This was not the most efficient way of obtaining data as it was painful to sprain the ankle. Using motive motion capture software, walking trials (with and without sprains) were recorded and then were taken to visual3D software for the motion analysis. The marker set that was applied to the left ankle was the “Rizzoli Left Foot” which allows the accurate tracking of the degrees of motion of the foot which is shown below in Figure 10. This marker set was chosen as it mainly focus on the foot rather than the entire lower body. This marker set allows the cameras in the gait lab to follow lateral motion of the ankle accurately.
Figure 10 : Rizzoli Left Foot markerset
The first variable that was calculated was the normal angle of the ankle during the gait cycle (more specifically between heel plant and toe takeoff. This data was recorded by tracking the healthy walking data of a participant (myself) seven times. To obtain consistent normalized results, it was made sure that the targeted foot (left foot) was planted on the force plates on the fifth step. The walking trial was also initiated with a step using the left foot. The maximum ankle angle was around 93 degrees meanwhile the mean angle was around 90 degrees. This data was recorded to act as a control. The data is shown below in Figure 11.
Figure 11 : Normal Ankle Angle with reference to left shank
This second set of data illustrates ankle angle during the sprain. Seven trials were recorded, with the same constraints of having the 5th step on the force plates and initiating the gait cycle with the left foot. The only difference is actually spraining the ankle on the 5th step on the force plate. As shown in the graph, 2 trials were anomalies as spraining your ankle intentionally was quite hard to replicate and painful to achieve. Also, as shown in Figure 12 below, the maximum angle reached by the ankle around 113 degrees. This shows that once you sprain your ankle, the joint undergoes and extra 25 degrees of extension ( plantarflexion).
Figure 12 : Ankle Angle During Sprain
The reaction force from the ground was also obtained using visual3D analysis software as is shown below in Figure 12. The reaction force obtained here is the force applied from the ground (force plates) on the lateral side of the foot when it undergoes a lateral sprain. This reaction force was obtained to see whether the force fully transmits from the lateral side of the foot onto the ankle. The mean force applied onto the lateral side of the foot was around 825 N . This value correlates to the participant’s weight which was around 84 kg. This set of data also shows that the entire weight of the person is applied onto the lateral side of the foot when sprained.
Figure 13: The reaction force on the lateral side of the foot mid sprain
The set of data shown below in Figure 14 shows the force on the ankle joint due to sprain. In comparison to the previous data shown in Figure 12, this confirms that the force is transmitted efficiently all the way up to the ankle joint. This also means that once the ankle is sprain, the force applied on the ankle is equivalent to the force of the entire body weight. This also means the heavier the person is, the more susceptible the joint is to damage
Figure 14: The vertical force acting on the ankle
The extent of damage applied to the foot due to sprain depends on the grade of tear of the ligaments surrounding the ankle joint. Taken into account are the two major ligaments out of the eight surrounding the ankle joint. They have been chosen by taking into account function, importance in lateral sprain, superficiality and simplicity of calculation (due to limited data in literature). The two ligaments chosen are the deltoid ligament (medial side) and the calcaneofibular ligament (CFL) (lateral side). The deltoid ligament (or medial ligament of talocrural joint) is a strong triangular band, attached, above, to the apex and anterior and posterior borders of the medial malleolus. The deltoid ligament is composed of: 1. Anterior tibiotalar ligament 2. Tibiocalcaneal ligament 3. Posterior tibiotalar ligament 4. Tibionavicular ligament. It consists of two sets of fibers, superficial and deep (wiki). The ligament taken into account from the deltoid ligament is the Tibiocalcaneal ligament as it’s the most superficial (visible) and can be modelled as both flat or cylindrical due to its “flat oval” shape
Firstly, the forces and moments on the ankle joint will be addressed. To be able to achieve this, there are many variables to be taken into account which are shown in the Figure 15 below. Using the equations below the joint moment was able to be calculated. The distances required on the foot (gait lab participant) were measured, therefore allowing for the gait lab obtained values – such as ground reaction force, acceleration of the centre of segment and angular acceleration of the segment – to be used. From literature, the forces and moment on the ankle joint can be computed using the following equations and the schematic shown below in Figure 15.
Figure 15: Schematic of foot (Fukashiro, Komi, Järvinen, Miyashita 1993)
Table 1: Gait lab obtained variables
|Average Linear acceleration
|Average Angular acceleration (Rad/s^2)||Average reaction force
Using the gait lab values illustrated above in Table 1, we could simply plug in the values for the joint reaction forces, segment angular acceleration, linear acceleration, and the mass of the segment, which is approximately 2% of the body mass(Nieddu, Boatto, Pirisi, Dessi 2010). N= 4cm, R=6 cm, Q=7 cm, L=6 cm. Due to the complexity of the shape of the foot, the foot has been modelled as a right angle triangle in order to estimate the polar mass moment of inertia as shown below in Figure 16.
Figure 16: Modelling foot as right angle
Where I= (bh^3)/(36), b=25.1 cm , h= 8 cm
Ma + (Fx*R) + (Fz*Q) – (Faz*L) – (Fax*N) =Ia
.. Ma = – (Fx*R) – (Fz*Q) + (Faz*L) + (Fax*N) +Ia = -79.22 N.m
Fax, Faz = joint reaction force
Ma = moment of the joint
Fx, Fz = ground reaction force
ax, az = acceleration of the centre of segment
m = segment mass
g = gravity due to acceleration
I = inertia moment of the segment
a= angular acceleration of the segment
L,N,Q,R = distance.
The value of the of joint moment was calculated to be -79.22 Nm, which shows a standard deviation of 3.97 from the joint moment value obtained in the gait lab, which is shown below in Figure 17. The mean value obtained for the gait lab is -73.6 N.m.
Figure 17: Gait lab values of ankle joint moment
As for the forces on the ankle joint at the instance of spraining (stationary), this can be easily calculated using the sum of forces on the Z direction of the ankle. The ankle joint forces changes with % gait cycle, thus we will study the instance when the force is maximum, which occurs midsprain. One would assume that the vertical force on the ankle joint would be Freaction/2 as we have two feet that support the force equally, but when a sprain occurs while walking, only one foot is in contact with the ground , leaving the sprained foot the only support of the body, therefore carrying the entire body weight. This can be shown in a FBD shown below inFigure 18.
Figure 18 : FBD of the foot during walking at an instance (a=0)
sigmaFy=0= Fbody weight + Freaction force
This hypothesis can be verified by Figure 18 shown previously which shows the maximum joint force obtained in the gait lab.
The CFL ligament is the 2nd most ruptured ligament in the ankle joint as it plays a large role in the stability of the ankle. The CFL can be modeled as either cylindrical or flat due to its “oval flat” shape. Due to its small size, Literature has shown using Magnetic resonance imaging (MRI) the rectangular dimensions of the CFL ligament were obtained and shown below in the table
Table 2: Dimensions of CFL
Being on the lateral side of the ankle, The CFL stretches as the ankle sprains laterally, causing stress and strain on then ligament. For a 3rd degree rupture to occur, the ankle ligaments must stretch to approximately 12-15% of its initial length. The strain on the CFL ligament can be calculated using the following equation.
Where, deltaL is the change in length of the ligament
And L is the original length of the Ligament.
Applying the values from literature regarding the length of the CFL ligament due to ankle sprain, a 3rd degree rupture occurs when 12.5% strain is applied
Strain = (24.9-21.59)/(21.59) = 12.5%
The ligament also undergoes torsion due to the sprain. But while calculating Torsion, the ligament must be modelled as a shaft/cylinder rather than rectangle. Torsion can be calculated using the equation below.
Where T is the Torque applied to the ligament, which can be obtained from the gait lab. Meanwhile r is the radius of the modelled shaft and J is the polar moment of inertia.
In order to find r, we calculate the volume of the ligament using the dimensions shown above in table x. Once we obtain the volume of the ligament, we can apply the equation for a volume of a cylinder which then allows us to calculate the radius of the cylinder. The calculation is shown below in Figure 19.
Figure 19: Modelling CFL to a cylinder
Once the radius is found, the polar moment of inertia can be calculated using the equation below.
The applied torque was found from the gait lab to be 5.3 Nm, meanwhile the radius and polar moment of inertia were found to be 4.28 mm and 2.635×10^-10 m^4 respectively.
Torsion = ((5.3)(4.28×10^-3))/( 2.635×10^-10) = 86.070570 N/mm^2
The third variable we look into finding is the stress that acts due to the axial and shear force applied onto the CFL. The CFL calcaneal attachment has a cross sectional area of 1.23 +- 0.24cm^2 which was obtained from literature. (Wenny, Duscher, Meytap, Weninger, Hirtler 2014). The forces were fairly tricky to find as the ligament comes in on angle and is not vertically erect. From literature, the angle between the CFL and Fibula was found to be was approximately 137 meanwhile the angle between the CFL and the ATFL was approximately 106 degrees which was obtained (Yildiz, Yalcin 2013). The Figure 20 below illustrates the angles.
Figure 20 : Angles between CFL,Fibula, and ATFL (Yildiz, 2013)
Since the maximum reaction force of the ground is vertical, a new set of axis must be set on the CFL ligament in order to obtain axial and shear forces. Using trigonometry, The axial and shear forces were obtained as shown below in Figure 21.
Figure 21: Computing axial and shear forces applied onto CFL
It was found that the shear force is equal to Fz (9.81x 84 kg) multiplied by the sine of 43 meanwhile the axial force is equal to Fz multiplied by the cosine of 43. Both axial and shear stress can be computed using the equation below.
P isis the axial/shear force
A is the cross sectional area the force is acting on.
The cross sectional area where the force is applied on the CFL ligament is 1.23 cm^2 (as mentioned above). Therefore we simply plug in the values and obtain the axial and shear stress as shown below.
Axial Stress = (824sin(43))/0.000123) = 4.56 MPa
Shear Stress = (824cos(43)/0.000123) = 4.9 MPa
The second ligament taken into account is the tibiocalcanleal ligament which is one of the four ligaments that make up the deltoid ligament as shown in the figure 22 below. The tibiocalcaneal ligament runs between the medial malleolus (the part of the tibia that sticks out on the inside of the ankle) to the sustentaculum tali of the calcaneus, a part of the heel bone near the bottom of the ankle as shown below in Figure 22.The Tibiocalcaneal ligament was chosen because it enables us to study the medial side of the ankle, it is the most superficial ligament of the deltoid ligament, and is almost vertical (simplicity). The damage that occurs due to a lateral sprain mainly affects the lateral ligaments of the ankle rather than the medial. This ligament under goes “negative” strain by compressing when a lateral sprain occurs.
Figure 22 : Deltoid ligament showing Tibiocalcaneal ligament (Campbell, 2014)
The Tibiocalcaneal ligament is approximately a vertical ligament (assumption) therefore the forces applied onto the ligament correlate with the forces applied on the joint. We will examine the axial and shear stresses applied onto the ligaments from both sites of attachment. The cross sectional areas of the sites of attachments were found from literature and are shown below in Figure 23.
Figure 23 : Dimensions of site of attachments of Deltoid ligament (Campbell, 2014)
The first site attachment studied is the calcaneus (lower site). Using the stress equation mentioned above, the axial and shear stress of the ligaments can be calculated by the use of values from the gait lab shown below in Figure 24.
Figure 24 : Horizontal and vertical reaction forces on ankle Joint
Axial Stress = FZ (Reaction force of the ground)/Aofattachment
= (9.81 x 84kg)/(52.1 x 10^-5)= 1.5 MPa
Shear Stress = Fy(Horizontal component of reaction force from gait lab)/ Aofattachment
= (174)/(52.1 x 10^-5)= 0.33 MPa
The malleolus site also undergoes Axial and shear stresses. The forces applied onto the site of attachment are the same forces that act on the on the calcaneal site as shown below in the FBD
Figure 25 :FBD of Tibiocalcaneal ligament
Therefore using the values obtained from the table above and using equations above, the axial and shear stresses can be calculated by
Axial Stress = FZ (Reaction force of the ground)/Aofattachment
= (9.81 x 84kg)/(29.4 x 10^-5)= 2.8 MPa
Shear Stress = Fy(Horizontal component of reaction force from gait lab)/ Aofattachment
= (174)/(29.4 x 10^-5)= 0.59 MPa
As calculated above, malleolus site undergoes approximately double the axial and shear stress as the area is almost half of the area in the calcaneal site.
When the torsional forces are higher than the allowable force, the common lateral sprain can become a fracture. The fracture is the buckling of ligaments. The ligament affected is the medial collateral (deltoid) ligament, which has a triangular shape, thus being difficult to fracture. The fractures, commonly referred to as joint fractures, are difficult to differentiate between ankle fractures and ligamentous injury due to their similar nature. This injury frequently occurs due to the fact that, “The ankle joint is subjected to enormous forces across a relatively small surface area of contact, with up to 1.5 times body weight with gait and greater than 5.5 times bodyweight with more strenuous activity.” (Singh et.al., 2014). Figure 26, depicts the lateral ligament elements that can be affected in a buckling of the ankle.
Figure 26: The internal composition of lateral ligaments of the ankle
As previously stated, inversion sprains often cause damage to the lateral ligaments, and a fracture from similar mechanism of injury affects the lateral ligaments and bones as well. A study by Singh et. Al, stated that, “fractures involving approximately 25% of the articular surface will result inposterior instability” (Singh et.al., 2014).
Lauge-Hanson classified ankle injuries into 4 categories, one of which as an Inversion, also denoted to as supination lateralrotation. This respectively refers to the position of the foot at the time of injury and the deforming force applied to the ankle structures.
Figure 27: Lauge-Hanson classifications of ankle injuries
As seen above, supination-external rotation can cause a fracture to the distal tibia, posterior malleolus or medial malleolus depending on the stage and mechanism of injury.
The structures will buckle in the following order; anterior tibiofibular ligament, spiral fibular ligament, posterior malleolus fracture then the medial malleolus fracture/or deltoid ligament rupture. To determine the extent of the injury, the following motions must be assessed and bilaterally compared to their normality.
Table 3: Range of motion of ankle movements affected by inversion fracture
|MOTION||NORMAL MOVEMENT RANGE|
|Dorsiflexion||10 – 15 degrees|
|Plantarflexion||50 – 70 degrees|
If a motion cannot fully be executed, further investigation should commence to determine the magnitude of the injury (Singh et.al., 2014).
Through physical and research data, the topic of lateral ankle sprains was deeply investigated and explored from a biomechanical view. The injury was examined as well as the prevention and treatment. In addition, mechanical calculations were found and performed with the assistance of gait lab analysis and medical research papers.
Figure 1: Supination and Pronation of the Foot Figure 2: The Ankle Joint
Figure 3: The Bones in the Ankle Joint Figure 4: The Subtalar Joint of the Ankle Joint
Figure 5: The Talocrural Joint Figure 6: The Lateral Ligaments of the Ankle Joint
Figure 7: The Medial Ligaments of the Ankle Joint Figure 8: The Muscles of the Ankle Joint
Figure 9: Ligaments on the ankle joint Figure 10 : Rizzoli Left Foot markerset
Figure 11 : Normal Ankle Angle with reference to left shank Figure 12 : Ankle Angle During Sprain
Figure 13: The reaction force on the lateral side Figure 14: The vertical force acting on the ankle
of the foot mid sprain
. Figure 15: Schematic of foot Figure 16: Modelling foot as right angle
Figure 17: Gait lab values of ankle joint moment Figure 20 : Angles between CFL,Fibula, and ATFL
Figure 22 : Deltoid ligament showing Figure 23 : Dimensions of site of attachments
Tibiocalcaneal ligament of Deltoid ligament
Figure 24 : Horizontal and vertical reaction Figure 26: The internal composition of lateral
forces on ankle Joint ligaments of the ankle
Figure 27: Lauge-Hanson classifications of ankle injuries
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