Femur

The femur (/ˈfiːmər/, pl. femurs or femora /ˈfɛmərə/)[1][2] or thigh bone, is the proximal bone of the hindlimb in tetrapod vertebrates. The head of the femur articulates with the acetabulum in the pelvic bone forming the hip joint, while the distal part of the femur articulates with the tibia and kneecap forming the knee joint. By most measures the femur is the strongest bone in the body. The femur is also the longest bone in the human body.

Femur
Femur - anterior view2
Position of femur (shown in red)
Gray252
Left femur seen from behind.
Details
OriginsGastrocnemius, vastus lateralis, vastus medialis and vastus intermedius
InsertionsGluteus maximus, gluteus medius, gluteus minimus, iliopsoas, lateral rotator group, adductors of the hip
Articulationship: acetabulum of pelvis superiorly
knee: with the tibia and patella inferiorly
Identifiers
LatinOs femoris, os longissimum
MeSHD005269
TAA02.5.04.001
FMA9611
Anatomical terms of bone

Structure

The femur is the only bone in the upper leg. The two femurs converge medially toward the knees, where they articulate with the proximal ends of the tibiae. The angle of convergence of the femora is a major factor in determining the femoral-tibial angle. Human females have wider pelvic bones, causing their femora to converge more than in males. In the condition genu valgum (knock knee) the femurs converge so much that the knees touch one another. The opposite extreme is genu varum (bow-leggedness). In the general population of people without either genu valgum or genu varum, the femoral-tibial angle is about 175 degrees.[3]

The femur is the longest and, by most measures, the strongest bone in the human body. Its length on average is 26.74% of a person's height,[4] a ratio found in both men and women and most ethnic groups with only restricted variation, and is useful in anthropology because it offers a basis for a reasonable estimate of a subject's height from an incomplete skeleton.

The femur is categorised as a long bone and comprises a diaphysis (shaft or body) and two epiphyses (extremities) that articulate with adjacent bones in the hip and knee.[3]

Upper part

Gray243
The upper extremity of right femur viewed from behind and above, showing head, neck, and the greater and lesser trochanter

The upper or proximal extremity (close to the torso) contains the head, neck, the two trochanters and adjacent structures.[3]

The head of the femur, which articulates with the acetabulum of the pelvic bone, comprises two-thirds of a sphere. It has a small groove, or fovea, connected through the round ligament to the sides of the acetabular notch. The head of the femur is connected to the shaft through the neck or collum. The neck is 4–5 cm. long and the diameter is smallest front to back and compressed at its middle. The collum forms an angle with the shaft in about 130 degrees. This angle is highly variant. In the infant it is about 150 degrees and in old age reduced to 120 degrees on average. An abnormal increase in the angle is known as coxa valga and an abnormal reduction is called coxa vara. Both the head and neck of the femur is vastly embedded in the hip musculature and can not be directly palpated. In skinny people with the thigh laterally rotated, the head of the femur can be felt deep as a resistance profound (deep) for the femoral artery.[3]

The transition area between the head and neck is quite rough due to attachment of muscles and the hip joint capsule. Here the two trochanters, greater and lesser trochanter, are found. The greater trochanter is almost box-shaped and is the most lateral prominent of the femur. The highest point of the greater trochanter is located higher than the collum and reaches the midpoint of the hip joint. The greater trochanter can easily be felt. The trochanteric fossa is a deep depression bounded posteriorly by the intertrochanteric crest on medial surface of the greater trochanter. The lesser trochanter is a cone-shaped extension of the lowest part of the femur neck. The two trochanters are joined by the intertrochanteric crest on the back side and by the intertrochanteric line on the front.[3]

A slight ridge is sometimes seen commencing about the middle of the intertrochanteric crest, and reaching vertically downward for about 5 cm. along the back part of the body: it is called the linea quadrata (or quadrate line).

About the junction of the upper one-third and lower two-thirds on the intertrochanteric crest is the quadrate tubercle located. The size of the tubercle varies and it is not always located on the intertrochanteric crest and that also adjacent areas can be part of the quadrate tubercle, such as the posterior surface of the greater trochanter or the neck of the femur. In a small anatomical study it was shown that the epiphyseal line passes directly through the quadrate tubercle.[5]

Body

The body of the femur (or shaft) is long, slender and almost cylindrical in form. It is a little broader above than in the center, broadest and somewhat flattened from before backward below. It is slightly arched, so as to be convex in front, and concave behind, where it is strengthened by a prominent longitudinal ridge, the linea aspera which diverges proximal and distal as the medial and lateral ridge. Proximal the lateral ridge of the linea aspera becomes the gluteal tuberosity while the medial ridge continues as the pectineal line. Besides the linea aspera the shaft has two other bordes; a lateral and medial border. These three bordes separates the shaft into three surfaces: One anterior, one medial and one lateral. Due to the vast musculature of the thigh the shaft can not be palpated.[3]

The third trochanter is a bony projection occasionally present on the proximal femur near the superior border of the gluteal tuberosity. When present, it is oblong, rounded, or conical in shape and sometimes continuous with the gluteal ridge.[6] A structure of minor importance in humans, the incidence of the third trochanter varies from 17–72% between ethnic groups and it is frequently reported as more common in females than in males.[7]

Lower part

Gray246
Lower extremity of right femur viewed from below.
Gray348
Left knee joint from behind, showing interior ligaments.

The lower extremity of the femur (or distal extremity) is larger than the upper extremity. It is somewhat cuboid in form, but its transverse diameter is greater than its antero-posterior (front to back). It consists of two oblong eminences known as the condyles.[3]

Anteriorly, the condyles are slightly prominent and are separated by a smooth shallow articular depression called the patellar surface. Posteriorly, they project considerably and a deep notch, the Intercondylar fossa of femur, is present between them. The lateral condyle is the more prominent and is the broader both in its antero-posterior and transverse diameters. The medial condyle is the longer and, when the femur is held with its body perpendicular, projects to a lower level. When, however, the femur is in its natural oblique position the lower surfaces of the two condyles lie practically in the same horizontal plane. The condyles are not quite parallel with one another; the long axis of the lateral is almost directly antero-posterior, but that of the medial runs backward and medialward. Their opposed surfaces are small, rough, and concave, and form the walls of the intercondyloid fossa. This fossa is limited above by a ridge, the intercondyloid line, and below by the central part of the posterior margin of the patellar surface. The posterior cruciate ligament of the knee joint is attached to the lower and front part of the medial wall of the fossa and the anterior cruciate ligament to an impression on the upper and back part of its lateral wall.[3]

The articular surface of the lower end of the femur occupies the anterior, inferior, and posterior surfaces of the condyles. Its front part is named the patellar surface and articulates with the patella; it presents a median groove which extends downward to the intercondyloid fossa and two convexities, the lateral of which is broader, more prominent, and extends farther upward than the medial.[3]

Each condyle is surmounted by an elevation, the epicondyle. The medial epicondyle is a large convex eminence to which the tibial collateral ligament of the knee-joint is attached. At its upper part is the adductor tubercle and behind it is a rough impression which gives origin to the medial head of the gastrocnemius. The lateral epicondyle which is smaller and less prominent than the medial, gives attachment to the fibular collateral ligament of the knee-joint.[3]

Development

The femur develops from the limb buds as a result of interactions between the ectoderm and the underlying mesoderm, formation occurs roughly around the fourth week of development.[8]

By the sixth week of development, the first hyaline cartilage model of the femur is formed by chondrocytes. Endochondral ossification begins by the end of the embryonic period and primary ossification centers are present in all long bones of the limbs, including the femur, by the 12th week of development. The hindlimb development lags behind forelimb development by 1–2 days.

Function

As the femur is the only bone in the thigh, it serves as an attachment point for all the muscles that exert their force over the hip and knee joints. Some biarticular muscles – which cross two joints, like the gastrocnemius and plantaris muscles – also originate from the femur. In all, 23 individual muscles either originate from or insert onto the femur.

In cross-section, the thigh is divided up into three separate fascial compartments divided by fascia, each containing muscles. These compartments use the femur as an axis, and are separated by tough connective tissue membranes (or septa). Each of these compartments has its own blood and nerve supply, and contains a different group of muscles. These compartments are named the anterior, medial and posterior fascial compartments.

Muscle attachments

Femur front
Muscle attachments
(seen from the front)
Femur back
Muscle attachments
(seen from the back)
Muscle Direction Attachment[9]
Iliacus muscle Insertion Lesser trochanter
Psoas major muscle Insertion Lesser trochanter
Gluteus maximus muscle Insertion Gluteal tuberosity
Gluteus medius muscle Insertion Lateral surface of greater trochanter
Gluteus minimus muscle Insertion Forefront of greater trochanter
Piriformis muscle Insertion Superior boundary of greater trochanter
Gemellus superior muscle Insertion Upper edge of Obturator internus's tendon (indirectly greater trochanter)
Obturator internus muscle Insertion Medial surface of greater trochanter
Gemellus inferior muscle Insertion Lower edge of Obturator internus's tendon (indirectly greater trochanter)
Quadratus femoris muscle Insertion Intertrochanteric crest
Obturator externus muscle Insertion Trochanteric fossa
Pectineus muscle Insertion Pectineal line
Adductor longus muscle Insertion Medial ridge of linea aspera
Adductor brevis muscle Insertion Medial ridge of linea aspera
Adductor magnus muscle Insertion Medial ridge of linea aspera and the adductor tubercle
Vastus lateralis muscle Origin Greater trochanter and lateral ridge of linea aspera
Vastus intermedius muscle Origin Front and lateral surface of femur
Vastus medialis muscle Origin Distal part of intertrochanteric line and medial ridge of linea aspera
Short head of biceps femoris Origin Lateral ridge of linea aspera
Popliteus muscle Origin Under the lateral epicondyle
Articularis genu muscle Origin Lower 1/4 of anterior femur deep to vastus intermedius
Gastrocnemius muscle Origin Behind the adductor tubercle, over the lateral epicondyle and the popliteal facies
Plantaris muscle Origin Over the lateral condyle

Clinical significance

Fractures

A femoral fracture that involves the femoral head, femoral neck or the shaft of the femur immediately below the lesser trochanter may be classified as a hip fracture, especially when associated with osteoporosis. Femur fractures can be managed in a pre-hospital setting with the use of a traction splint.

Other animals

Identification-Classification-and-Growth-of-Moa-Chicks-(Aves-Dinornithiformes)-from-the-Genus-pone.0099929.g002
Femora of Moa chicks.

In primitive tetrapods, the main points of muscle attachment along the femur are the internal trochanter and third trochanter, and a ridge along the ventral surface of the femoral shaft referred to as the adductor crest. The neck of the femur is generally minimal or absent in the most primitive forms, reflecting a simple attachment to the acetabulum. The greater trochanter was present in the extinct archosaurs, as well as in modern birds and mammals, being associated with the loss of the primitive sprawling gait. The lesser trochanter is a unique development of mammals, which lack both the internal and fourth trochanters. The adductor crest is also often absent in mammals or alternatively reduced to a series of creases along the surface of the bone.[10]

Some species of whales,[11] snakes, and other non-walking vertebrates have vestigial femurs.

One of the earliest known vertebrates to have a femur is the eusthenopteron, a prehistoric lobe-finned fish from the Late Devonian period.

Structures analogous to the third trochanter are present in mammals, including some primates.[7]

Invertebrates

In invertebrate zoology the name femur appears in arthropodology. The usage is not homologous with that of vertebrate anatomy; the term "femur" simply has been adopted by analogy and refers, where applicable, to the most proximal of (usually) the two longest jointed segments of the legs of the arthropoda. The two basal segments preceding the femur are the coxa and trochanter. This convention is not followed in carcinology but it applies in arachnology and entomology. In myriapodology another segment, the prefemur, connects the trochanter and femur.

Additional images

Femur - animation9

Position of femur (shown in red). Pelvis and patella are shown as semi-transparent.

Fumur Posterior annoted

View from behind.

Fumur Anterior annoted

View from the front.

Human femur.stl

3D image

Long Bone (Femur)

Long Bone (Femur)

Slide2DADE

Muscles of thigh. Lateral view.

Slide2EA

Muscles of thigh. Cross section.

Blausen 0401 Femur DistributionofForces

Distribution forces of the femur

References

  1. ^ "Femora". Merriam-Webster Dictionary.
  2. ^ "Femora". Dictionary.com Unabridged. Random House.
  3. ^ a b c d e f g h i j Bojsen-Møller, Finn; Simonsen, Erik B.; Tranum-Jensen, Jørgen (2001). Bevægeapparatets anatomi [Anatomy of the Locomotive Apparatus] (in Danish) (12th ed.). pp. 239–241. ISBN 978-87-628-0307-7.
  4. ^ Feldesman, M.R., J.G. Kleckner, and J.K. Lundy. (November 1990). "The femur/stature ratio and estimates of stature in mid-and late-pleistocene fossil hominids". American Journal of Physical Anthropology. 83 (3): 359–372. doi:10.1002/ajpa.1330830309. PMID 2252082.
  5. ^ Sunderland S (January 1938). "The Quadrate Tubercle of the Femur". J. Anat. 72 (Pt 2): 309–12. PMC 1252427. PMID 17104699.
  6. ^ Lozanoff, Scott; Sciulli, Paul W; Schneider, Kim N (December 1985). "Third trochanter incidence and metric trait covariation in the human femur". J Anat. 143: 149–159. PMC 1166433. PMID 3870721.
  7. ^ a b Bolanowski, Wojciech; Śmiszkiewicz-Skwarska, Alicja; Polguj, Michał; Jędrzejewski, Kazimierz S (2005). "The occurrence of the third trochanter and its correlation to certain anthropometric parameters of the human femur" (PDF). Folia Morphol. 64 (3): 168–175.
  8. ^ Gilbert, Scott F. "Developmental Biology". 9th ed., 2010
  9. ^ Bojsen-Møller, Finn; Simonsen, Erik B.; Tranum-Jensen, Jørgen (2001). Bevægeapparatets anatomi [Anatomy of the Locomotive Apparatus] (in Danish) (12th ed.). pp. 364–367. ISBN 978-87-628-0307-7.
  10. ^ Romer, Alfred Sherwood; Parsons, Thomas S. (1977). The Vertebrate Body. Philadelphia, PA: Holt-Saunders International. pp. 204–205. ISBN 0-03-910284-X.
  11. ^ Struthers, John (January 1881). "The Bones, Articulations, and Muscles of the Rudimentary Hind-Limb of the Greenland Right-Whale (Balaena mysticetus)". Journal of Anatomy and Physiology. Anatomical Society of Great Britain and Ireland. 15 (Pt 2): i1–176. PMC 1310010. PMID 17231384.

External links

  • Media related to Femur at Wikimedia Commons
  • The dictionary definition of Femur at Wiktionary
  • The dictionary definition of thighbone at Wiktionary
Adductor tubercle of femur

The adductor tubercle is a tubercle on the Lower extremity of the femur (thigh bone).

The medial lips of the linea aspera ends below at the summit of the medial condyle, in a small tubercle, the adductor tubercle, which affords insertion to the tendon of the vertical fibers of adductor magnus.

Arthropod leg

The arthropod leg is a form of jointed appendage of arthropods, usually used for walking. Many of the terms used for arthropod leg segments (called podomeres) are of Latin origin, and may be confused with terms for bones: coxa (meaning hip, plural coxae), trochanter (compare trochanter), femur (plural femora), tibia (plural tibiae), tarsus (plural tarsi), ischium (plural ischia), metatarsus, carpus, dactylus (meaning finger), patella (plural patellae).

Homologies of leg segments between groups are difficult to prove and are the source of much argument. Some authors posit up to eleven segments per leg for the most recent common ancestor of extant arthropods but modern arthropods have eight or fewer. It has been argued that the ancestral leg need not have been so complex, and that other events, such as successive loss of function of a Hox-gene, could result in parallel gains of leg segments.

Body of femur

The body of the femur (or shaft), almost cylindrical in form, is a little broader above than in the center, broadest and somewhat flattened from before backward below. It is slightly arched, so as to be convex in front, and concave behind, where it is strengthened by a prominent longitudinal ridge, the linea aspera.

It presents for examination three borders, separating three surfaces.

Of the borders, one, the linea aspera, is posterior, one is medial, and the other, lateral.

Femoral fracture

A femoral fracture is a bone fracture that involves the femur. They are typically sustained in high-impact trauma, such as car crashes, due to the large amount of force needed to break the bone. Fractures of the diaphysis, or middle of the femur, are managed differently from those at the head, neck, and trochanter (see hip fractures).

Femoral head

The femoral head (femur head or head of the femur) is the highest part of the thigh bone (femur). It is supported by the femoral neck.

Femur neck

The femur neck (femoral neck or neck of the femur) is a flattened pyramidal process of bone, connecting the femoral head with the femoral shaft, and forming with the latter a wide angle opening medialward.

Greater trochanter

The greater trochanter (great trochanter) of the femur is a large, irregular, quadrilateral eminence and a part of the skeletal system.

It is directed lateral and medially and slightly posterior. In the adult it is about 1 cm lower than the head. Because the pelvic outlet in the female is larger than in the male, there is a greater distance between the greater trochanters in the female.

It has two surfaces and four borders. It is a traction epiphysis.

Hip

In vertebrate anatomy, hip (or "coxa" in medical terminology) refers to either an anatomical region or a joint.

The hip region is located lateral and anterior to the gluteal region (i.e., the buttock), inferior to the iliac crest, and overlying the greater trochanter of the femur, or "thigh bone". In adults, three of the bones of the pelvis have fused into the hip bone or acetabulum which forms part of the hip region.

The hip joint, scientifically referred to as the acetabulofemoral joint (art. coxae), is the joint between the femur and acetabulum of the pelvis and its primary function is to support the weight of the body in both static (e.g. standing) and dynamic (e.g. walking or running) postures. The hip joints have very important roles in retaining balance, and for maintaining the pelvic inclination angle.

Pain of the hip may be the result of numerous causes, including nervous, osteoarthritic, infectious, trauma-related, and genetic.

Intercondylar fossa of femur

The intercondylar fossa of femur (intercondyloid fossa of femur, intercondylar notch of femur) is a deep notch between the rear surfaces of the medial and lateral epicondyle of the femur, two protrusions on the distal end of the femur (thigh bone) that joins the knee. On the front of the femur, the condyles are but much less prominent and are separated from one another by a smooth shallow articular depression called the patellar surface because it articulates with the posterior surface of the patella (kneecap).

The intercondylar fossa of femur and/or the patellar surface may also be referred to as the patellar groove, patellar sulcus, patellofemoral groove, femoropatellar groove, femoral groove, femoral sulcus, trochlear groove of femur, trochlear sulcus of femur, trochlear surface of femur, or trochlea of femur.

On a lateral radiograph, it is evident as Blumensaat's line.

Knee

In humans and other primates, the knee joins the thigh with the leg and consists of two joints: one between the femur and tibia (tibiofemoral joint), and one between the femur and patella (patellofemoral joint). It is the largest joint in the human body. The knee is a modified hinge joint, which permits flexion and extension as well as slight internal and external rotation. The knee is vulnerable to injury and to the development of osteoarthritis.

It is often termed a compound joint having tibiofemoral and patellofemoral components. (The fibular collateral ligament is often considered with tibiofemoral components.)

Lateral condyle of femur

The lateral condyle is one of the two projections on the lower extremity of the femur. The other one is the medial condyle. The lateral condyle is the more prominent and is broader both in its front-to-back and transverse diameters.

Lesser trochanter

The lesser trochanter (small trochanter) of the femur is a conical eminence, which varies in size in different subjects.

Ligament of head of femur

In human anatomy, the ligament of the head of the femur (round ligament of the femur, ligamentum teres femoris, or the foveal ligament) is a ligament located in the hip. It is triangular in shape and somewhat flattened. The ligament is implanted by its apex into the antero-superior part of the fovea capitis femoris and its base is attached by two bands, one into either side of the acetabular notch, and between these bony attachments it blends with the transverse ligament.It is ensheathed by the synovial membrane, and varies greatly in strength in different subjects; occasionally only the synovial fold exists, and in rare cases even this is absent.The ligament of the head of the femur contains within it the acetabular branch of the obturator artery.

Lower extremity of femur

The lower extremity of femur (or distal extremity) is the lower end of the thigh bone in human and other animals, closer to the knee. It is larger than the upper extremity of femur, is somewhat cuboid in form, but its transverse diameter is greater than its antero-posterior; it consists of two oblong eminences known as the condyles.

Medial condyle of femur

The medial condyle is one of the two projections on the lower extremity of femur, the other being the lateral condyle.

The medial condyle is larger than the lateral (outer) condyle due to more weight bearing caused by the centre of mass being medial to the knee. On the posterior surface of the condyle the linea aspera (a ridge with two lips: medial and lateral; running down the posterior shaft of the femur) turns into the medial and lateral supracondylar ridges, respectively. The outermost protrusion on the medial surface of the medial condyle is referred to as the "medial epicondyle" and can be palpated by running fingers medially from the patella with the knee in flexion.

It is important to take into consideration the difference in the length of the condyles in a cross section to better understand the geometry of the knee. The medial femoral condyle has an extra segment which is the cause for the passive rotation of the knee joint.

Popliteus muscle

The popliteus muscle in the leg is used for unlocking the knees when walking, by laterally rotating the femur on the tibia during the closed chain portion of the gait cycle (one with the foot in contact with the ground). In open chain movements (when the involved limb is not in contact with the ground), the popliteus muscle medially rotates the tibia on the femur. It is also used when sitting down and standing up. It is the only muscle in the posterior (back) compartment of the lower leg that acts just on the knee and not on the ankle. The gastrocnemius muscle acts on both joints.

Quadriceps femoris muscle

The quadriceps femoris (, also called the quadriceps extensor, quadriceps or quads) is a large muscle group that includes the four prevailing muscles on the front of the thigh.

It is the great extensor muscle of the knee, forming a large fleshy mass which covers the front and sides of the femur. The name derives from Latin four-headed muscle of the femur.

Thigh

In human anatomy, the thigh is the area between the hip (pelvis) and the knee. Anatomically, it is part of the lower limb.The single bone in the thigh is called the femur. This bone is very thick and strong (due to the high proportion of bone tissue), and forms a ball and socket joint at the hip, and a modified hinge joint at the knee.

Upper extremity of femur

The upper extremity, proximal extremity or superior epiphysis of the femur is the part of the femur closest to the pelvic bone and the trunk. It contains the following structures:

Femur head including the fovea

Femur neck

Greater trochanter

Lesser trochanter

Intertrochanteric line

Intertrochanteric crest

Trochanteric fossa

Linea quadrata

Quadrate tubercleThe head of femur, which articulates with the acetabulum of the pelvic bone, composes two-thirds of a sphere. It has a small groove or fovea, connected through the round ligament to the sides of the acetabular notch. The head of the femur is connected to the shaft through the neck or collum. The neck is 4–5 cm. long and the diameter is smallest front to back and compressed at its middle. The collum forms an angle with the shaft in about 130 degrees. This angle is highly variant. In the infant it is about 150 degrees and in old age reduced to 120 degrees in average. An abnormal increase in the angle is known as coxa valga and an abnormal reduction is called coxa vara. Both the head and neck of the femur is vastly embedded in the hip musculature and can not be directly palpated. In skinny people with the thigh laterally rotated the head of the femur can be felt deep as a resistance profound (deep) for the femoral artery.In the transition area between the head and neck is quite rough due to attachment of muscles and the hip joint capsule. Here the two trochanters, greater and lesser trochanter, is found. The greater trochanter is almost box-shaped and is the most lateral prominent of the femur. The highest point of the greater trochanter is located higher than the collum and reaches the midpoint of the hip joint. The greater trochanter can easily be felt. The trochanteric fossa is a deep depression bounded posteriorly by the intertrochanteric crest on medial surface of the greater trochanter. Anterior and superior to the trochanteric fossa is a shallower depression known as the Unnamed Fossa. The Unnamed Fossa is the insertion point of the Superior Gemellus, Obturator Internus and Inferior Gemellus, which all act as lateral rotaters of the thigh.

The lesser trochanter is a cone-shaped extension of the lowest part of the femur neck. The two trochanters are joined by the intertrochanteric crest on the back side and by the intertrochanteric line on the front.A slight ridge is sometimes seen commencing about the middle of the intertrochanteric crest, and reaching vertically downward for about 5 cm. along the back part of the body: it is called the linea quadrata (or quadrate line).

About the junction of the upper one-third and lower two-thirds on the intertrochanteric crest is the quadrate tubercle located. The size of the tubercle varies and it is not always located on the intertrochanteric crest and that also adjacent areas can be part of the quadrate tubercel, such as the posterior surfare of the greater trochanter or the neck of the femur. In a small anatomical study it was shown that the epiphysial line passes directly through the quadrate tubercle.

This page is based on a Wikipedia article written by authors (here).
Text is available under the CC BY-SA 3.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.