Lateral Ankle Sprain Project

Table of Contents

1. Objective ……………………………………………………………………………… page 3
2. Functional Anatomy……………………………………………………………… page 3 – 11

1. Function of the Ankle………………..……………………………………… page 3 – 4
2. Anatomy……………………………………………………..……………… page 4 – 5
   1. Bones………………………………………………………………… page 5 – 6
   2. Joints …………………………………..…………………………… page 6 – 8

• Ligaments ………………………………………….……………… page 8 – 10

1. Muscles ………………..………………………………………… page 10 – 11

1. Injury……………………………………………………………………………… page 11 – 15
   1. Definition ………………………………………………………………… page 11 – 13
   2. Mechanism Involved …………………………..………………………… page 13 – 14
   3. Causes/treatment/prevention ………………………..…………………… page 14 – 15
2. Solid Mechanics Analysis ……………………..………………………………… page 15 – 20
   1. Gait lab analysis ……………………………………………………….… page 15 – 16
   2. Normal vs. sprained ankle …………………..…………………………… page 16 – 20
3. Discussion ………………………………….…………………………………… page 20 –  33
   1. Forces/moments ……………………………….………………………… page 21 – 24
   2. Ligaments ……………………………..……………………………………… page 25

1. Calcaneofibular ligament ………..………………………………… page 25 – 29
2. Tibiocalcaneal ligament …………………………….……………… page 29 – 33

1. 1. Buckling ……………………………….………………………………… page 33 – 36
2. Conclusion…………………………..………………………………………………… page 36
3. Appendix …………………………………………………………….…………… page 37 – 42
   1. Figures …………………………………………………………….………page 37 – 41
   2. Tables  …………………………………………….…………………………… page 42
4. References ………………..……………………………………………………… page 43 – 46

1. Objective

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

 

1. Functional Anatomy

1. Function of the Ankle
   The ankle is a joint that form the kinetic linkage between the foot and the leg. Due to its location, the ankle plays a vital role in maintaining gait stability while bearing high compressive and shear forces (Brockett 2016). The ankle’s bony and ligamentous structures enable it to produce dorsiflexion, plantar flexion, inversion, eversion, and a limited degree of supination, and pronation (KenHub). Dorsiflexion is lifting the front of the foot, while plantar flexion is pointing the toes downwards (Learning). Inversion is when the soles of the feet face towards the body’s centerline, and eversion is when the soles of the feet face away from the body’s centerline (Swenson 2008).

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

1. Anatomy
   The ankle is a synovial hinge joint which is made up of the lower and upper ankle joint. Due to its complex structure, shown in figure 2, which consists of bones, joints, ligaments, and muscles, the ankle is able to support five times the body weight while walking on level surfaces (Blomberg 2016). The upper ankle consists of the fibula, tibia, and talus bone (KenHub). The lower ankle joint consists of the talus, calcaneus, and the navicular bone (KenHub). The ankle also contains three main joints, which are the talocalcaneal, tibiotalar, and talocalcaneonavicular joint (Brockett 2016).
   The numerous ligaments which support the ankle joint are categorized based on their anatomical locations. The ankle contains lateral ligaments, medial ligaments, and the ligaments of the tibiofibular syndesmosis (Galano 2010). The muscles which are part of the ankle are the twelve extrinsic muscles, which enhance motion of the ankle, foot, and leg (Hertel 2002).

            Figure 2: The Ankle Joint

1. Bones
   The ankle is made up of mainly three bones, which are the fibula, tibia, talus. Meanwhile, the calcaneus and navicular bone connect the ankle with the heel (KenHub). The upper ankle, which is responsible for enabling dorsiflexion and plantar flexion, consists of the fibula; the calf bone, tibia; shin bone, and the talus; ankle bone. The medial malleolus, which is the interior part of the tibia, the posterior malleolus, which is the posterior part of the tibia, the lateral malleolus, which is the end of the fibula, and the talus, articulate together to form the ankle, as illustrated in figure 3 (Crist 2013). The medial malleolus forms the inside ankle bone, and the posterior malleolus makes up the lateral ankle bone, along with the lateral malleolus, meet on top of the talus, and are encased in a fibrous membrane called the joint capsule to form the bony structure of the ankle joint (WebMD).

Figure 3: The Bones in the Ankle Joint

4. Joints
   The ankle joint consists of the talocalcaneal joint, which is also known as the subtalar joint, the tibiotalar joint, which is known as talocrural, and the talocalcaneonavicular joint, which is known as the transverse-tarsal joint.
   The subtalar joint is comprised of the two articulating surfaces of the talus and the calcaneus bone (Unit VIII). The two bones articulate at two surfaces, the anterior and posterior surfaces, where one surface is concave and the other is convex, as shown in figure 4. This setup provides stability to the joint, while allowing inversion and eversion at the joint. Even though the joint is capable of performing other motions, this joint is mainly responsible for inversion and eversion. The anterior subtalar joint is formed by the convex shape of the talus and the concave shape of the calcaneus. The posterior subtalar joint is formed by the concave shape of the talus and the convex shape of the calcaneus (Iagnocco 2017).

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

iii. Ligaments

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

8. Muscles
   The ankle joint is supported by the twelve extrinsic muscles, which originate from the leg and insert into the foot, hence connecting the two components together, as demonstrated in figure 8. The muscles provide the ankle with active stability, which allows the joint to contract when needed (TwinBoro). The main muscles of the ankle are the gastrocnemius, soleus, and the plantaris muscles, which contribute to plantar flexion and are found in the posterior section of the ankle joint (Brockett 2016). The anterior section, which consists of the tibialis anterior, , the extensor hallucis longus, the peroneus tertius, and the extensor digitorum longus are responsible for producing dorsiflexion (Brockett 2016). The lateral section is responsible for plantarflexion and eversion of the foot. Meanwhile, the deep posterior section produces plantarflexion and inversion of the foot (Brockett 2016).

Figure 8: The Muscles of the Ankle Joint

 

 

 

 

 

 

1. Injury 

 

1. 1. Definition

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 (Brostroem 1964). Rupture to the ATFL is followed by damage to the CFL and finally to the PTFL(Brostroem 1964).  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.).

 

1. 1. Mechanism involved

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.

 

1. 1. Causes/treatments/prevention

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.

 

 

1. Solid Mechanics Analysis

 

1. 1. Gait lab analysis

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

1. 1. Normal vs. sprained ankle

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 5^th 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

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Figure 14: The vertical force acting on the ankle

 

 

 

1. Discussion

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

 

1. 1. Forces/moments

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

Variable /Component	Average Linear acceleration (M/s^2)	Average Angular acceleration (Rad/s^2)	Average reaction force (N)
Z	1.003	1295	856
X	1.4	1295	174

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

1. Fax = max- Fx = -173.648 N
2. Faz= maz-Fz + mg = -30.2 N
3. M_sigma = Ia

Ma + (Fx*R) + (Fz*Q) – (Faz*L) – (Fax*N) =Ia

.. Ma = – (Fx*R) – (Fz*Q) + (Faz*L) + (Fax*N) +Ia = -79.22 N.m

Where:

 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 F_reaction/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 in Figure 18.

Figure 18 : FBD of the foot during walking at an instance (a=0)

sigmaF_y=0= F_{body weight} + F_{reaction force}

This hypothesis can be verified by Figure 18 shown previously which shows the maximum joint force obtained in the gait lab.

 

1. 1. Ligaments

 

1. 1. 1. Calcaneofibular ligament

The CFL ligament is the 2^nd 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 3^rd 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 3^rd 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.

Where,

P is is 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

1. 1. 1. Tibiocalcaneal ligament

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 = F_Z (Reaction force of the ground)/A_{of attachment}

                                      = (9.81 x 84kg)/(52.1 x 10^-5)= 1.5 MPa

Shear Stress = F_y (Horizontal component of reaction force from gait lab)/ A_{of attachment}

                                      = (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 = F_Z (Reaction force of the ground)/A_{of attachment}

                                      = (9.81 x 84kg)/(29.4 x 10^-5)= 2.8 MPa

Shear Stress = F_y (Horizontal component of reaction force from gait lab)/ A_{of attachment}

                                      = (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.

 

 

 

1. 1. Buckling

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
Inversion	40 degrees
Eversion	10 degrees

If a motion cannot fully be executed, further investigation should commence to determine the magnitude of the injury (Singh et.al., 2014).

1. Conclusion

 

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.

 

 

 

 

 

 

 

 

 

 

 

 

 

1. Appendix
   1. Figures

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. Tables

Table 1:  Gait lab obtained variables

Variable /Component	Average Linear acceleration (M/s^2)	Average Angular acceleration (Rad/s^2)	Average reaction force (N)
Z	1.003	1295	856
X	1.4	1295	174

 

Table 2: Dimensions of CFL

 

Table 3: Range of motion of ankle movements affected by inversion fracture

MOTION	NORMAL MOVEMENT RANGE
Dorsiflexion	10 – 15 degrees
Plantarflexion	50 – 70 degrees
Inversion	40 degrees
Eversion	10 degrees

 

 

 

 

 

1. References

Alves J. W., Alday, R. V., Ketcham D. L., & Lentell, G. L. (1992) A comparison of the passive support provided by various ankle braces. Journal of Orthopeadic & Sports Physical Therapy 1, 10–18.

Ankle Fractures. (n.d.). Retrieved from https://www.webmd.com/fitness-exercise/ankle-fracture#1

Ankle – Bones, Ligaments, Muscles & Conditions. (n.d.). Retrieved from https://twinboro.com/body/ankle/ankle-conditions-new-jersey.html

Biomechanical Analysis of an Ankle Sprain. (2017). Retrieved from https://www.trainingcor.com/biomechanical-analysis-of-an-ankle-sprain/

Blomberg, J. (2016). Ankle Ligaments. Retrieved from https://www.orthobullets.com/foot-and-ankle/7005/ankle-ligaments

Blumstein, H. A. (n.d.). Ankle Sprain. Retrieved from https://www.webmd.com/pain-management/ankle-sprain#1

Brockett, C. L., & Chapman, G. J. (2016). Biomechanics of the ankle. Orthopaedics and trauma, 30(3), 232-238.

Brostroem L. (1964), Sprained ankles. I. Anatomic lesions on recent sprains. Acta Chir Scand., 128:483–495.

Campbell, K. J., Michalski, M. P., Wilson, K. J., Goldsmith, M. T., Wijdicks, C. A., Laprade, R. F., & Clanton, T. O. (2014). The Ligament Anatomy of the Deltoid Complex of the Ankle: A Qualitative and Quantitative Anatomical Study. The Journal of Bone and Joint Surgery-American Volume,96(8). doi:10.2106/jbjs.m.00870

Chaitow, L. (2011) Transverse tarsal joint. Retrieved from https://www.sciencedirect.com/topics/veterinary-science-and-veterinary-medicine/transverse-tarsal-joint

Cordova. M. L., Ingersoll, C. D., & LeBlanc, M. J. (2002). Influence of ankle support on joint range of motion before and after exercise: a meta-analysis. Journal of Orthopaedic & Sports Physical Therapy, 30(4), 170-182.

Crist, B. (2013). Our knowledge of orthopaedics. Your best health. (n.d.). Retrieved from https://orthoinfo.aaos.org/en/diseases–conditions/ankle-fractures-broken-ankle/

Fukashiro, S., Komi, P., Järvinen, M., & Miyashita, M. (1993). Comparison between the directly measured achilles tendon force and the tendon force calculated from the ankle joint moment during vertical jumps. Clinical Biomechanics, 8(1), 25-30. doi:10.1016/s0268-0033(05)80006-3

Figure 2f from: Irimia R, Gottschling M (2016) Taxonomic revision of Rochefortia Sw. (Ehretiaceae, Boraginales). Biodiversity Data Journal 4: E7720. https://doi.org/10.3897/BDJ.4.e7720. (n.d.). doi:10.3897/bdj.4.e7720.figure2f

Golanó, P., Vega, J., de Leeuw, P. A., Malagelada, F., Manzanares, M. C., Götzens, V., & van Dijk, C. N. (2010). Anatomy of the ankle ligaments: a pictorial essay. Knee surgery, sports traumatology, arthroscopy : official journal of the ESSKA, 18(5), 557-69.

Hertel, J. (2002). Functional Anatomy, Pathomechanics, and Pathophysiology of Lateral Ankle Instability. Journal of athletic training, 37(4), 364-375.

Iagnocco, A. (2017, June 01). SP0039 How to evaluate the subtalar joint. Retrieved from https://ard.bmj.com/content/76/Suppl_2/10.3

Kenhub. Ankle Joint. Retrieved from https://www.kenhub.com/en/library/anatomy/the-ankle-joint

Learning, L. (n.d.). Anatomy and Physiology. Retrieved from https://courses.lumenlearning.com/nemcc-ap/chapter/types-of-body-movements/#m46398-fs-id2345326

Nieddu, M., Boatto, G., Pirisi, M. A., & Dessì, G. (2010). Determination of four thiophenethylamine designer drugs (2C-T-4, 2C-T-8, 2C-T-13, 2C-T-17) in human urine by capillary electrophoresis/mass spectrometry. Rapid Communications in Mass Spectrometry, 24(16), 2357-2362. doi:10.1002/rcm.4656

Omelchenko, T. (2014). Ankle fractures and rapidly progressing osteoarthrosis of the ankle joint: Prevention and treatment. ORTHOPAEDICS, TRAUMATOLOGY and PROSTHETICS, 0(4), 35. doi:10.15674/0030-59872013435-40

O’Reilly, N. (n.d.). Ankle Joint. Retrieved from https://www.physio-pedia.com/Ankle_Joint

Swenson, R. (2008). Chapter 17: The ankle and foot. Retrieved from https://www.dartmouth.edu/~humananatomy/part_3/chapter_17.html

Singh, R., Kamal, T., Roulohamin, N., Maoharan, G., Ahmed, B., & Theobald, P. (2014). Ankle Fractures: A Literature Review of Current Treatment Methods. Open Journal of Orthopedics,04(11), 292-303. doi:10.4236/ojo.2014.411046

Simpson, K.J., Craven, S., Theodorou, C., & DelRay, P. (1999). A comparison of the sport stirrup, malleoloc, and swede-o ankle orthoses for the foot-ankle kinematics of a rapid lateral movement. International Journal of Sports Medicine, 20, 396-402.

UNIT VIII – The Foot and Ankle. (n.d.). Retrieved from https://courses.vcu.edu/DANC291-003/unit_8.htm

Volker, J. H. (2018, September 26). Easy Notes On 【Ankle Joint (Talocrural Joint)】Learn in Just 4 Minutes! Retrieved from https://www.earthslab.com/anatomy/ankle-joint-talocrural-joint/?rm=true

Wenny, R., Duscher, D., Meytap, E., Weninger, P., & Hirtler, L. (2014, May 06). Dimensions and attachments of the ankle ligaments: Evaluation for ligament reconstruction. Retrieved from https://link.springer.com/article/10.1007/s12565-014-0238-

Yıldız, S., & Yalcın, B. (2013, January 05). The anterior talofibular and calcaneofibular ligaments: An anatomic study. Retrieved from https://link.springer.com/article/10.1007/s00276-012-1071-3