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MATH
DUNK
The Knee
STEM Topic 9: VOCABULARY
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Allograft: Tissue taken from another person's body for transplantation.
Anterior Cruciate Ligament (ACL): One of the ligaments in the knee that provides stability and prevents excessive forward movement of the tibia.
Apex: The highest or lowest point of something.
Arthroscopic: A small camera inserted into a joint to visualize and treat the problem.
Articulations: The joints where two bones come together and allow movement.
Autograft: Using tissue from the patient's own body for a surgical repair.
Avascular: Lacking a blood supply.
Cartilage: A thin, elastic tissue that protects bones and allows smooth movement of joints.
Collateral ligaments: Ligaments that provide stability to the sides of a joint.
Complementary: The definition of "complementary" in this context refers to the angle that, when added to the given angle, would result in a sum of 90 degrees.
Cruciate ligaments: Ligaments that cross each other inside a joint and provide stability.
Dislocations: When a bone is forced out of its normal position in a joint.
External rotation: Turning or twisting a joint outward, away from the body.
Femur: The thigh bone, the longest and strongest bone in the human body.
Fibula: The smaller bone in the calf, located on the outer side of the leg.
Fractures: Breaks or cracks in a bone.
Graft: A piece of tissue used to replace a damaged or missing part of the body.
Hinge joint: A type of joint that allows movement in only one plane, like a door hinge.
Hypotenuse: This is the side opposite the right angle in a right-angled triangle.
Internal rotation: Turning or twisting a joint inward, toward the body.
Isometric exercises: Exercises that involve muscle contractions without movement of the joints.
Ligament: A band of tough, fibrous tissue that connects bones and supports joints.
Medial Collateral Ligament (MCL), which is a ligament located on the inner side of the knee.
Medial meniscus: A cartilage in the knee joint located on the inner side of the knee.
Medial: Relating to the middle or inner side of something.
Meniscectomy: Surgical removal of a damaged or torn meniscus.
Meniscus: A crescent-shaped fibrocartilaginous strip in the knee joint that provides stability and absorbs shock.
Non-operatively: Without the need for surgery.
Patella: The kneecap, a bone in the front of the knee joint.
Perimeter: The perimeter refers to the total distance around the edge of a shape, when that shape is round is also known as its circumference.
Popliteal: Relating to the back of the knee.
Quadriceps: A group of muscles at the front of the thigh.
Radius: This refers to the distance from the center of a circle (or a rounded shape) to any point on its circumference (perimeter).
Rupture: A complete tear or break in a tendon or ligament.
Scar tissue: Fibrous tissue that forms at the site of a wound or injury, often leading to reduced flexibility or movement.
Severity: The degree or extent of something, in this case, the seriousness of an injury.
Stressful: Involving or causing a lot of mental or physical pressure or strain.
Supplementary: In this situation refers to the angle that, when added to the given angle, would result in a sum of 180 degrees.
Taut: Tight or stretched.
Tendon: A fibrous cord that connects muscle to bone.
Terminal rotation: The final rotation that occurs at the end of a joint's range of motion.
Thigh: The upper part of the leg, between the hip and the knee.
Tibia: Also known as the shinbone, it is the larger and stronger bone in the leg below the knee.
Weight-bearing: Referring to exercises or activities that involve putting weight or pressure on a body part, such as the legs or feet.
The knee joint joins the thigh with the calf and consists of two articulations: one between the femur and tibia, and one between the femur and patella .It is the largest joint in the human body. It plays an essential role in movement related to carrying the body weight in the horizontal and vertical directions. The knee is a modified hinge joint, which permits flexing and extension as well as slight internal and external rotation. The knee joint is vulnerable to injury.
The knee permits flexion and extension about a virtual transverse (at right angle to the leg) axis, as well as a slight rotation about the axis of the lower leg in the flexed position. The knee joint is called "mobile" because the femur (thigh bone) and lateral meniscus (the pad on top of the tibia), move over the tibia (larger shinbone), during rotation, while the femur rolls and glides over both menisci during extension-flexing.
Extended Position
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With the knee extended both the lateral and medial collateral ligaments, as well as the anterior part of the anterior cruciate ligament (ACL), are taut. During extension, the femoral condyles (the rounded ends of the femur) glide and roll into a position which causes the complete unfolding of the knee’s collateral ligaments. During the last 10° of extension, an obligatory terminal rotation is triggered in which the knee is rotated medially 5°.
Flexed Position
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In the flexed position, the collateral ligaments are relaxed while the cruciate ligaments (ACL & (PCL) are taut. Rotation is controlled by the twisted cruciate (crossed) ligaments; the two ligaments get twisted around each other during medial rotation of the tibia, which reduces the amount of rotation possible. Because of the opposing position of the cruciate ligaments at least a part of one of them is always tense and these ligaments control the joint as the collateral ligaments are relaxed.
Quadriceps Tendon
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The quadriceps tendon (tendons connects muscle to bone), also known as the patellar tendon, allows the quadriceps muscles to converge on the upper end of the patella on the front of the thigh, which continues as the patellar ligament. The quadriceps tendon works with the quadriceps to extend the leg.
Injuries are common to this tendon, with tears, either partial or complete, being the most common. If the quadriceps tendon is completely torn, surgery is required to regain function of the knee. Without the quadriceps tendon, the knee cannot extend. Often, when the tendon is completely torn, part of the kneecap bone will break off with the tendon as well.
Patella
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The patella, also known as the kneecap is a thick, circular-triangular bone which articulates with the femur (thigh bone) and covers and protects the front surface of the knee. The primary functional role of the patella is knee extension. The patella allows back and straightening movements of the leg through an arc that approaches 180 degrees.
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The patella is a roughly triangular in shape, with the point of the patella facing downwards. The apex is the lowest part of the patella. It makes the attachment to the patellar ligament.
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The kneecap is prone to injury because of its particularly exposed location, and fractures of the patella commonly occur as a consequence of direct trauma onto the knee. These fractures usually cause swelling and pain, bleeding into the joint, and an inability to extend the knee. Patella fractures are usually treated with surgery.
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Patellar dislocations occur with significant regularity, particular in young female athletes.
Patellar Ligament
The patellar ligament is a strong, flat, ligament (ligaments connect bone to bone). It originates on the lower part of the patella and ends on the upper part of the tibia. It can be injured in a patellar tendon rupture.
Warrior broadcaster, Kelenna Azubuike’s patella tendon rupture ended his NBA playing career.
It can be used as a tissue source in the repair of other ligaments. In the event of a torn anterior cruciate ligament (ACL), the patellar ligament can be used in the rehabilitation process. In this case, the middle one third of the patellar ligament is harvested and inserted through tunnels that are drilled into the femur and tibia. The portion of the patellar ligament is then drawn through these tunnels in the bone and will be affixed to the bone via screws. This patellar ligament method of reconstruction was traditionally the gold standard graft for ACL reconstruction, and is still one of the more preferred methods.
Femur
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The femur or thigh bone is by most measures the strongest bone in the body. The femur is also the longest bone in the body. Its length on average is 26.74% of a person's height.
The femur is the only bone in the thigh. The two femurs converge inward toward the knees, where they articulate with the end of the tibiae.
Medial Collateral Ligament
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The medial collateral ligament (MCL) is on the medial (inner) side of the knee joint in humans. Its primary function is to resist deforming forces on the knee that would push it toward the center line of the body. It is attached to the femur and the tibia.
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A MCL injury can be very painful and is caused by stress to a slightly bent knee, often when landing, bending or on high impact. MCL strains and tears are also fairly common in basketball and American football. Depending on the severity of the injury, it can take between 2 weeks to several months for the injury to fully heal.
Lateral Collateral Ligament
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The lateral (fibular) collateral ligament, (LCL) is a ligament located on the lateral (outer) side of the knee. The fibular collateral ligament stretches from the femur above, to the fibula (the smaller bone in the calf). The lateral collateral ligament is more flexible than its medial counterpart, and is therefore less susceptible to injury.
This pair of ligaments help stabilize the knee joint. Both (outside and inside) collateral ligaments are taut when the knee joint is in extension. When the knee is flexed, the origin and insertions of the ligaments are brought closer together which make them loose. Damage and rupture of these ligaments can be diagnosed by examining the knee's side to side stability.
The LCL is usually injured as a result of force pushing the knee from the medial (inner) side of the joint, causing stress on the outside. An example of this would be a direct blow to the inside of the knee. The LCL can also be injured by a noncontact injury, such as a hyperextension.
Symptoms of a sprain or tear of the LCL include pain, instability of the knee when walking, swelling and bruising at the site of trauma.
An LCL injury usually occurs simultaneously as the other ligaments of the knee are injured. An isolated LCL tear or sprain rarely requires surgery. If the injury is not severe, it is treated with rest and rehabilitation. Ice, electrical stimulation and elevation are all methods to reduce the pain and swelling felt in the initial stages after the injury takes place. Physical therapy focuses on regaining full range-of-motion, such as stretching and careful applications of pressure on the joint.
Tibia
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The tibia, also known as the shinbone, is the larger and stronger of the two bones in the leg below the knee and it connects the knee with the ankle bones. The tibia is found on the inner side of the calf next to the fibula. It is the second largest bone in the human body next to the femur.
The upper extremity of the tibia is expanded by the medial and lateral condyle (the rounded bulges at the upper end of the bone). The upper surfaces of the condyles meet with the femur to form the tibiofemoral joint. This is the weight bearing part of the knee joint.
Fibula
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The fibula is the leg bone located on the outside side of the tibia, with which it is connected above and below. It is the smaller of the two bones. Its upper end is placed toward the back of the head of the tibia, below the level of the knee joint, and excluded from the formation of this joint. The fibula does not carry any significant weight of the body. It extends past the lower end of the tibia and forms the outer part of the ankle providing stability to that joint.
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Cartilage
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Cartilage is a thin, elastic tissue that protects the bone and makes certain that the joint surfaces can slide easily over each other. Cartilage ensures supple knee movement. There are two types of joint cartilage in the knees: fibrous cartilage (the meniscus) and hyaline cartilage. Fibrous cartilage has tensile strength and can resist pressure. Hyaline cartilage covers the bone surfaces along which the joints move. Cartilage will wear over the years. Cartilage has a very limited capacity for self-restoration. After healing from an injury, the newly formed tissue will generally consist of a large part of fibrous cartilage of lesser quality than the original hyaline cartilage. As a result, new cracks and tears will form in the cartilage over time.
Meniscus
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A meniscus is a crescent-shaped fibrocartilaginous strip that partly divides a joint cavity. In humans they are present in the knee, wrist, jaw, shoulder joints.
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Generally, the term 'meniscus' is used to refer to the cartilage of the knee, either to the lateral or medial meniscus. Both are cartilaginous tissues that provide structural integrity to the knee when it undergoes tension (bearing weight) and torsion (twisting). The menisci are also known as "semi-lunar" cartilages — referring to their half-moon, crescent shape.
The menisci of the knee are pads which serve to disperse the body weight and the friction in the knee joint between the femur and the tibia. They sit between the thigh bone and the shin bone. While the ends of the thigh bone and the shin bone have a thin covering of soft hyaline cartilage. Hyaline (Articular) cartilage is glass-like translucent cartilage. It is found on many joint surfaces but contains no nerves or blood vessels. Though it is often found in close contact with menisci but, hyaline cartilage is not considered a part of it.
The menisci are nourished by small blood vessels but have a large area in the center with no direct blood supply (avascular). This presents a problem when there is an injury to the meniscus, as areas without good blood supply tend not to heal.
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The menisci are made of tough fibrocartilage and conform to the surfaces of the bones they rest on. One meniscus rests on the inside of tibia; this is the medial meniscus. The other meniscus rests on the outer edge tibia; this is the lateral meniscus
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In sports and orthopedics, people will sometimes speak of "torn cartilage" and actually be referring to an injury to one of the menisci. Menisci can be torn during everyday activities such as walking or squatting. They can also be torn by traumatic force encountered in sports. The traumatic action is most often a twisting movement at the knee while the leg is bent. Tears can lead to pain and/or swelling of the knee joint. Especially acute injuries (typically in younger, more active patients) can lead to displaced tears which can cause mechanical symptoms such as clicking, catching, or locking during motion of the knee. The joint will be in pain when in use, but when there is no load, the pain goes away.
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Menisci can be torn during innocuous activities such as walking or squatting. A tear of the meniscus commonly follows a trauma which involves rotation of the knee while it was slightly bent. These maneuvers also exacerbate the pain after the injury; for example, getting out of a car is often reported as painful.
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A force applied to a flexed knee with the foot planted and the femur rotated externally can result in a lateral meniscus tear. A force applied to the flexed knee when the foot is planted and the femur rotated internally result in a tear of the medial meniscus.
The menisci hold 30–50% of the body load in standing position. Some sports where a meniscus tear is common are basketball, American football, and soccer.
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There are ways of diminishing the possibility of a meniscus tear:
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1. Wearing the correct footwear for the sport and surface that the activity is taking place on. The proper footwear is imperative when engaging in physical activity because one off-balanced step could mean a meniscus tears.
2. Strengthen and stretch the major leg muscles. Those muscles include the hamstrings, quadriceps, and calf muscles. One popular exercise used to strengthen the hamstrings is the leg curl. It is also important to properly stretch the hamstrings; doing standing toe touches can do this. Seated leg extensions strengthen the quadriceps and doing the quadriceps stretch will help loosen the muscles. Toe raises are used to strengthen and stretch the calves. Adequate muscle mass and strength may also aid in maintaining healthy knees. The use of the parallel squat increases much needed stability in the knee if executed properly. Execution of the parallel squat will develop the lower body muscles that will strengthen the hips, knees, and ankles.
If the tear is not serious, physical therapy, compression, elevation and icing the knee can heal the meniscus. More serious tears may require surgical procedures.
A tear of the medial meniscus can occur as part of the unhappy triad, together with a tear of the anterior cruciate ligament (ACL) and the medial collateral ligament (MCL).
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If the injury to the meniscus is isolated, then the knee would be relatively stable. However, if another injury such as an anterior cruciate ligament injury (torn ACL) was coupled with a torn meniscus, then an arthroscopy would be performed. Arthroscopy is a surgical technique in which a joint is operated on using a tiny camera as opposed to open surgery on the joint is frequently used to repair a meniscus tear.
Golden State top draft pick (2020) James Wiseman is still (2/22) recovering from suffering a torn meniscus.
A meniscal repair has a higher success rate if there is an adequate blood supply to the peripheral rim. The interior of the meniscus is avascular, but the blood supply can penetrate up to about 6 millimeters or a quarter inch.
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After a successful surgery for treating the destroyed part of the meniscus, patients must follow a rehabilitation program to have the best result. The rehabilitation procedure following a meniscus surgery depends on whether the entire meniscus was removed or repaired.
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If the destroyed part of the meniscus was removed, patients can usually start walking using a crutch a day or two after surgery. Although each case is different, patients return to their normal activities on average after a few weeks (2 or 3). Still, a completely normal walk will resume gradually, and it's not unusual to take 2–3 months for the recovery to reach a level where a patient will walk totally smoothly. Many meniscectomy patients don't ever feel a 100% functional recovery, but even years after the procedure they sometimes feel tugging or tension in a part of their knee.
Anterior Cruciate Ligament
The anterior cruciate ligament (ACL) is one of a pair of cruciate ligaments (the other being the posterior cruciate ligament) in the knee. They are named cruciate because they are arranged in a crossed formation. The ACL provides 85% of the restraining force to a forward tibial displacement at 30 degrees and 90 degrees of knee flex.
The ACL originates from deep within the notch of the femur. Its proximal fibers fan out along the medial wall of the lateral femoral condyle. There are two bundles of the ACL—the anteromedial and the posterolateral, named according to where the bundles insert into the tibial plateau. (the tibia plateau is a critical weight-bearing region on the top end of the tibia). The ACL attaches in front of the tibia, being blended with the lateral meniscus. These attachments allow the ACL to resist anterior translation and medial rotation of the tibia, in relation to the femur.
ACL tears are among the most common knee injuries, with over 100,000 tears in the US occurring annually. Most ACL tears are a result of landing or planting in cutting or pivoting sports, with or without contact. Most serious athletes will require an ACL reconstruction if they have a complete tear and want to return to sports, because the ACL is crucial for stabilizing the knee when turning or planting.
Klay Thompson tears his ACL.
Anterior cruciate ligament surgery is a complex operation that requires expertise in the field of orthopedic medicine. Reconstruction is most commonly done by autograft, meaning the tissue used for the repair is from the patient’s body. The two most common sources for tissue are the patellar tendon and the hamstrings tendon. The surgery is arthroscopic, meaning that a tiny camera is inserted through a small surgical cut. The camera sends video a so that the surgeon can see any damage to the ligaments. In the event of an autograft (use of the patient’s own tissue), the surgeon will make a larger cut to get the needed tissue. The surgeon will make holes in the patient’s bones to run the tissue through, and the tissue serves as the patient’s new ACL.
Recovery time ranges between one and two years or longer. A week or so after the occurrence of the injury, the athlete is usually deceived by the fact that he/she is walking normally and not feeling much pain. This is dangerous as some athletes start resuming some of their activities such as jogging which, with a wrong move or twist, could damage the bones. It is important for the injured athlete to understand the significance of each step of an ACL injury to avoid complications and ensure a proper recovery.
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Tearing the anterior cruciate ligament can sometimes be part of a knee injury known as “the terrible triad”. This consists of the simultaneous tearing of the ACL, MCL and the medial meniscus.
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Rehabilitation is crucial to any ACL surgery; complete recovery and return to sports or other activities typically takes six to nine months. Revision ACL surgery will often take nine months to more than a year. During this time, the physical therapist should guide the patient through the rehabilitation process. The early rehab, usually lasting around six weeks, focuses on maintaining full knee motion and preventing scar tissue. The second phase of rehab is directed toward regaining knee strength. Finally, activity-specific rehabilitation is administered. The rehabilitation program can also be composed of aggressive motions and weight-bearing exercises.
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The ACL can be treated non-operatively with strengthening and rehabilitation and occasionally injections when the ACL is not completely torn and the knee is still stable or if the patient is not doing activities requiring cutting and pivoting or similar actions. The mainstay of ACL non-operative treatment is strengthening of the muscles around the knee, especially the hamstrings.
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If the doctor recommends surgery for ACL, he or she may prescribe "prehab" before operating, as many studies have shown that inducing good motion before the surgery will benefit the patient during recovery.
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Women have been known to suffer ACL injuries more frequently than men; current research gives some explanations for this. The joint through which the anterior cruciate ligament passes, along with the actual size of the anterior cruciate ligament, is significantly smaller in women than in men. This makes it more susceptible to damage. Along with these aspects, women tend to not activate their hamstring muscles as much as their male counterparts during certain cutting movements causing less stability in the knee joint.
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Posterior Cruciate Ligament
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The posterior cruciate ligament (or PCL) along with the anterior cruciate ligament (ACL), lie deep within the knee joint. The PCL gets its name by attaching to the posterior portion of the tibia.
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The PCL is located within the knee joint where it stabilizes the articulating bones, particularly the femur and the tibia, during movement. It originates from the femur and then stretches downward toward the rear of the tibia. The function of the PCL is to prevent the femur from sliding off the top of the tibia and to prevent the tibia from displacing posterior to the femur.
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Common causes of injuries are direct blows to the flexed knee, such as the knee hitting the dashboard in a car accident or falling hard on the knee, both instances displacing the tibia posterior to the femur.
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Those persons suspected to have a posterior cruciate ligament injury should always be evaluated for other knee injuries that often occur in combination with PCL injuries. These include cartilage/meniscus injuries, bone bruises, ACL tears, fractures, posterolateral injuries and collateral ligament injuries.
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The PCL functions to prevent movement of the tibia in the backwards direction and to prevent the tilting or shifting of the patella. However, the laxity (looseness) of the two sections makes the PCL susceptible to injury during hyperflexion, hyperextension. Because ligaments are somewhat elastic they can handle higher amounts of stress only when the load is increased slowly. When hyperflexion and hyperextension occur suddenly in combination without time for the elastic behavior to compensate, the PCL deforms or tears. In the third and most common mechanism, the dashboard injury (when the knee hits it in a car crash), the knee experiences impact in a posterior direction during knee flexion toward the space above the tibia. This occurs in while the knee is bent.
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Surgery is usually required in complete tears of the ligament. Surgery usually takes place after a few weeks, in order to allow swelling to decrease and regular motion to return to the knee. A procedure called ligament reconstruction is used to replace the torn PCL with a new ligament, which is usually a graft taken from the hamstring or Achilles tendon from a cadaver. An arthroscope allows a complete evaluation of the entire knee joint, including the knee cap (patella), the cartilage surfaces, the meniscus, the ligaments (ACL & PCL), and the joint lining. Then, the new ligament is attached to the bone of the thigh and lower leg with screws to hold it in place. Surgery to repair the posterior cruciate ligament is controversial due to its placement and technical difficulty.
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It is possible for the PCL to heal on its own without surgery. PCL injuries that are diagnosed in these categories can have their recovery times reduced by performing rehabilitative exercises. Implementing an exercise program that emphasizes lunges, 1-leg squats, and trunk stabilization) has proven to be an effective way to recover from the PCL injury.
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SHAUN LIVINGSTON
(when it all goes horribly wrong)
In a game against the Charlotte Bobcats on February 26, 2007, Shaun Livingston suffered a debilitating knee injury, dislocating his left kneecap after landing awkwardly following a missed layup, resulting in the left leg snapping laterally. Livingston injured almost every part of his knee, tearing the anterior cruciate ligament (ACL), the posterior cruciate ligament (PCL), and the lateral meniscus, badly spraining his medial collateral ligament (MCL), and dislocating his patella and his tibio-fibular joint.
He faced the possibility of amputation if any damage was done to a major artery (Popliteal) in his knee. Luckily medical doctors didn’t see any issue with his artery.
On March 13, 2007 Dr. James Andrew and Dr. William Clancy performed successful surgery on Shaun Livingston’s left knee. Dr. Clancy who is considered the “father of ACL reconstructive surgeries” repaired his ACL, PCL, and MCL. These two surgeons used a patella tendon graft to replace his torn ACL.
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ACL Reconstruction
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Anterior cruciate ligament reconstruction (ACL reconstruction) is a surgical tissue graft replacement of the anterior cruciate ligament, located in the knee, to restore its function after an injury.
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Grafts are inserted through a tunnel that is drilled through the shin bone (tibia) and thigh bone (femur). The graft is then pulled through the tunnel and fixated with screws.
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Sources of replacement material for ACL reconstruction are commonly used:
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Autografts (tissue from the patient's body)
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Allografts (tissue from another body).
An accessory hamstring or part of the patellar ligament are the most common donor tissues used in autografts. Because the tissue used in an autograft is the patient's own, the risk of rejection is minimal.
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The patellar tendon connects the patella (kneecap) to the tibia (shin). The graft is normally taken from the injured knee, but in some circumstances, such as a second operation, the other knee may be used. The middle third of the tendon is used, with bone fragments removed on each end. The graft is then threaded through holes drilled in the tibia and femur, and screwed into place.
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Surgeons have historically regarded patellar tendon grafts as the "gold standard" for knee stability, but the procedure has a slightly higher complication rate, including knee pain when lunging.
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Initial physical therapy consists of range of motion (ROM) exercises, often with the guidance of a physical therapist. Range of motion exercises are used to regain the flexibility of the ligament, prevent or break down scar tissue from forming and reduce loss of muscle tone. Range of motion exercise examples include: quadriceps contractions and straight leg raises. In some cases, a continuous passive motion (CPM) device is used immediately after surgery to help with flexibility. The preferred method of preventing muscle loss is isometric exercises that put zero strain on the knee. Knee extension within two weeks is important with many rehab guidelines.
Livingston Rehabilitation (2007)
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Approximately six weeks is required for the bone to attach to the graft. However, the patient can typically walk on their own, and perform simple physical tasks prior to this with caution, relying on the surgical fixation of the graft until true healing (graft attachment to bone) has taken place. At this stage, the first round of physical therapy can begin. This usually consists of careful exercises to regain flexibility and small amounts of strength. One of the more important benchmarks in recovery is the twelve weeks post-surgery period. After this, the patient can typically begin a more aggressive regimen of exercises involving stress on the knee, and increasing resistance. Jogging may be incorporated as well.
After four months, more intense activities such as running are possible without risk. After five months, light ball work may commence as the ligament is nearly regenerated. After six months, the reconstructed ACL is generally at full strength (ligament tissue has fully regrown), and the patient may return to activities involving cutting and twisting if a brace is worn. Recovery varies highly from case to case, and sometimes resumption of stressful activities may take a year or longer.
Livingston (2009-10)
STEM Topic 9: Problem Set
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A knee brace costs $50 and has a 20% discount. What is the final price of the knee brace?
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If a person's knee is 15 cm in length and the person's leg is 90 cm in length, what percent of the leg is made up of the knee?
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A doctor orders an x-ray of a patient's knee that is 10 cm by 12 cm. What is the area of the x-ray?
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If the angle of the knee is 90 degrees, what is the value of the complementary angle?
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A person's knee bends at an angle of 120 degrees. What is the measure of the supplementary angle?
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If a person's knee can extend to an angle of 180 degrees, what is the measure of the angle formed by the knee and the ground?
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If a person's knee can bend at an angle of 45 degrees, what is the ratio of the length of the adjacent side to the length of the hypotenuse of the triangle formed by the knee and the ground?
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If a person's knee can extend to an angle of 150 degrees, what is the measure of the angle formed by the knee and the ground?
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If a person's knee joint can rotate 120 degrees, what is the measure of the angle if the person's knee is rotated halfway?
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A person's knee has a range of motion of 135 degrees. If the knee is currently at a 90 degree angle, how many degrees does the person have left to flex their knee?
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If the knee of a person measures 14 inches in circumference, what is the diameter of the knee?
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If a person's knee has a circumference of 16 inches, what is the radius of the knee?
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A doctor measures the circumference of a patient's knee to be 36 cm. What is the diameter of the knee?
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A person's knee (assume a perfect circle), has a circumference of 24 cm. What is the radius of the knee?
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A person's knee has a surface area of 30 square centimeters. If, for purposes of calculation, the knee is considered round, what is the perimeter of the knee?
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If a person's knee is at a 45 degree angle and the person's leg is 30 cm long, how far away is the foot from the knee?