The Femur

Anatomy > Gray's Anatomy of the Human Body > II. [Osteology]] > 6c. 3. The Femur

Henry Gray (1821–1865). Anatomy of the Human Body. 1918. 6c. 3. The Femur (Thigh Bone)

The femur (Figs. 244, 245), the longest and strongest bone in the skeleton, is almost perfectly cylindrical in the greater part of its extent. In the erect posture it is not vertical, being separated above from its fellow by a considerable interval, which corresponds to the breadth of the pelvis, but inclining gradually downward and medialward, so as to approach its fellow toward its lower part, for the purpose of bringing the knee-joint near the line of gravity of the body. The degree of this inclination varies in different persons, and is greater in the female than in the male, on account of the greater breadth of the pelvis. The femur, like other long bones, is divisible into a body and two extremities The Upper Extremity ([[proximal extremity Fig. 243)]]—The upper extremity presents for examination a head a neck a greater and a lesser trochanter The Head ([[caput femoris)]]—The head which is globular and forms rather more than a hemisphere, is directed upward, medialward, and a little forward, the greater part of its convexity being above and in front. Its surface is smooth, coated with cartilage in the fresh state, except over an ovoid depression, the fovea capitis femoris which is situated a little below and behind the center of the head, and gives attachment to the ligamentum teres. The Neck ([[collum femoris)]]—The neck is a flattened pyramidal process of bone, connecting the head with the body, and forming with the latter a wide angle opening medialward. The angle is widest in infancy, and becomes lessened during growth, so that at puberty it forms a gentle curve from the axis of the body of the bone. In the adult, the neck forms an angle of about 125° with the body, but this varies in inverse proportion to the development of the pelvis and the stature. In the female, in consequence of the increased width of the pelvis, the neck of the femur forms more nearly a right angle with the body than it does in the male. The angle decreases during the period of growth, but after full growth has been attained it does not usually undergo any change, even in old age; it varies considerably in different persons of the same age. It is smaller in short than in long bones, and when the pelvis is wide. In addition to projecting upward and medialward from the body of the femur, the neck also projects somewhat forward; the amount of this forward projection is extremely variable, but on an average is from 12° to 14°.

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FIG. 243– Upper extremity of right femur viewed from behind and above. (Picture From the Classic Gray's Anatomy) The neck is flattened from before backward, contracted in the middle, and broader laterally than medially. The vertical diameter of the lateral half is increased by the obliquity of the lower edge, which slopes downward to join the body at the level of the lesser trochanter, so that it measures one-third more than the antero-posterior diameter. The medial half is smaller and of a more circular shape. The anterior surface of the neck is perforated by numerous vascular foramina. Along the upper part of the line of junction of the anterior surface with the head is a shallow groove, best marked in elderly subjects; this groove lodges the orbicular fibers of the capsule of the hip-joint. The posterior surface is smooth, and is broader and more concave than the anterior: the posterior part of the capsule of the hip-joint is attached to it about 1 cm. above the intertrochanteric crest. The superior border is short and thick, and ends laterally at the greater trochanter; its surface is perforated by large foramina. The inferior border long and narrow, curves a little backward, to end at the lesser trochanter. The Trochanters—The trochanters are prominent processes which afford leverage to the muscles that rotate the thigh on its axis. They are two in number, the greater and the lesser.

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FIG. 244– Right femur. Anterior surface. (Picture From the Classic Gray's Anatomy) The Greater Trochanter (trochanter major; great trochanter) is a large, irregular, quadrilateral eminence, situated at the junction of the neck with the upper part of the body. It is directed a little lateralward and backward, and, in the adult, is about 1 cm. lower than the head. It has two surfaces and four borders. The lateral surface quadrilateral in form, is broad, rough, convex, and marked by a diagonal impression, which extends from the postero-superior to the antero-inferior angle, and serves for the insertion of the tendon of the Glutæus medius. Above the impression is a triangular surface, sometimes rough for part of the tendon of the same muscle, sometimes smooth for the interposition of a bursa between the tendon and the bone. Below and behind the diagonal impression is a smooth, triangular surface, over which the tendon of the Glutæus maximus plays, a bursa being interposed. The medial surface of much less extent than the lateral, presents at its base a deep depression, the trochanteric fossa (digital fossa), for the insertion of the tendon of the Obturator externus, and above and in front of this an impression for the insertion of the Obsturator internus and Gemelli. The superior border is free; it is thick and irregular, and marked near the center by an impression for the insertion of the Piriformis. The inferior border corresponds to the line of junction of the base of the trochanter with the lateral surface of the body; it is marked by a rough, prominent, slightly curved ridge, which gives origin to the upper part of the Vastus lateralis. The anterior border is prominent and somewhat irregular; it affords insertion at its lateral part to the Glutæus minimus. The posterior border is very prominent and appears as a free, rounded edge, which bounds the back part of the trochanteric fossa. The Lesser Trochanter (trochanter minor; small trochanter) is a conical eminence, which varies in size in different subjects; it projects from the lower and back part of the base of the neck. From its apex three well-marked borders extend; two of these are above—a medial continuous with the lower border of the neck, a lateral with the intertrochanteric crest; the inferior border is continuous with the middle division of the linea aspera. The summit of the trochanter is rough, and gives insertion to the tendon of the Psoas major. A prominence, of variable size, occurs at the junction of the upper part of the neck with the greater trochanter, and is called the tubercle of the femur it is the point of meeting of five muscles: the Glutæus minimus laterally, the Vastus lateralis below, and the tendon of the Obturator internus and two Gemelli above. Running obliquely downward and medialward from the tubercle is the intertrochanteric line (spiral line of the femur); it winds around the medial side of the body of the bone, below the lesser trochanter, and ends about 5 cm. below this eminence in the linea aspera. Its upper half is rough, and affords attachment to the iliofemoral ligament of the hip-joint; its lower half is less prominent, and gives origin to the upper part of the Vastus medialis. Running obliquely downward and medialward from the summit of the greater trochanter on the posterior surface of the neck is a prominent ridge, the intertrochanteric crest Its upper half forms the posterior border of the greater trochanter, and its lower half runs downward and medialward to the lesser trochanter. 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 and gives attachment to the Quadratus femoris and a few fibers of the Adductor magnus. Generally there is merely a slight thickening about the middle of the intertrochanteric crest, marking the attachment of the upper part of the Quadratus femoris.

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FIG. 245– Right femur. Posterior surface. (Picture From the Classic Gray's Anatomy) The Body or Shaft ([[corpus femoris)]]—The body, 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. The linea aspera (Fig. 245) is a prominent longitudinal ridge or crest, on the middle third of the bone, presenting a medial and a lateral lip, and a narrow rough, intermediate line. Above, the linea aspera is prolonged by three ridges. The lateral ridge is very rough, and runs almost vertically upward to the base of the greater trochanter. It is termed the gluteal tuberosity and gives attachment to part of the Glutæus maximus: its upper part is often elongated into a roughened crest, on which a more or less well-marked, rounded tubercle, the third trochanter is occasionally developed. The intermediate ridge or pectineal line is continued to the base of the lesser trochanter and gives attachment to the Pectineus; the medial ridge is lost in the intertrochanteric line; between these two a portion of the Iliacus is inserted. Below, the linea aspera is prolonged into two ridges, enclosing between them a triangular area, the popliteal surface upon which the popliteal artery rests. Of these two ridges, the lateral is the more prominent, and descends to the summit of the lateral condyle. The medial is less marked, especially at its upper part, where it is crossed by the femoral artery. It ends below at the summit of the medial condyle, in a small tubercle, the adductor tubercle which affords insertion to the tendon of the Adductor magnus. From the medial lip of the linea aspera and its prolongations above and below, the Vastus medialis arises; and from the lateral lip and its upward prolongation, the Vastus lateralis takes origin. The Adductor magnus is inserted into the linea aspera, and to its lateral prolongation above, and its medial prolongation below. Between the Vastus lateralis and the Adductor magnus two muscles are attached—viz., the Glutæus maximus inserted above, and the short head of the Biceps femoris arising below. Between the Adductor magnus and the Vastus medialis four muscles are inserted: the Iliacus and Pectineus above; the Adductor brevis and Adductor longus below. The linea aspera is perforated a little below its center by the nutrient canal, which is directed obliquely upward. The other two borders of the femur are only slightly marked: the lateral border extends from the antero-inferior angle of the greater trochanter to the anterior extremity of the lateral condyle; the medial border from the intertrochanteric line, at a point opposite the lesser trochanter, to the anterior extremity of the medial condyle. 13 The anterior surface includes that portion of the shaft which is situated between the lateral and medial borders. It is smooth, convex, broader above and below than in the center. From the upper three-fourths of this surface the Vastus intermedius arises; the lower fourth is separated from the muscle by the intervention of the synovial membrane of the knee-joint and a bursa; from the upper part of it the Articularis genu takes origin. The lateral surface includes the portion between the lateral border and the linea aspera; it is continuous above with the corresponding surface of the greater trochanter, below with that of the lateral condyle: from its upper three-fourths the Vastus intermedius takes origin. The medial surface includes the portion between the medial border and the linea aspera; it is continuous above with the lower border of the neck, below with the medial side of the medial condyle: it is covered by the Vastus medialis. 14

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FIG. 246– Lower extremity of right femur viewed from below. (Picture From the Classic Gray's Anatomy) The Lower Extremity ([[distal extremity), (Fig. 246)]]—The lower extremity, larger than the upper, 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 In front, the condyles are but slightly prominent, and are separated from one another by a smooth shallow articular depression called the patellar surface behind, they project considerably, and the interval between them forms a deep notch, the intercondyloid fossa 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. 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, already referred to, and behind it is a rough impression which gives origin to the medial head of the Gastrocnemius. The lateral epicondyle smaller and less prominent than the medial, gives attachment to the fibular collateral ligament of the knee-joint. Directly below it is a small depression from which a smooth well-marked groove curves obliquely upward and backward to the posterior extremity of the condyle. This groove is separated from the articular surface of the condyle by a prominent lip across which a second, shallower groove runs vertically downward from the depression. In the fresh state these grooves are covered with cartilage. The Popliteus arises from the depression; its tendon lies in the oblique groove when the knee is flexed and in the vertical groove when the knee is extended. Above and behind the lateral epicondyle is an area for the origin of the lateral head of the Gastrocnemius, above and to the medial side of which the Plantaris arises. 15 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. The lower and posterior parts of the articular surface constitute the tibial surfaces for articulation with the corresponding condyles of the tibia and menisci. These surfaces are separated from one another by the intercondyloid fossa and from the patellar surface by faint grooves which extend obliquely across the condyles. The lateral groove is the better marked; it runs lateralward and forward from the front part of the intercondyloid fossa, and expands to form a triangular depression. When the knee-joint is fully extended, the triangular depression rests upon the anterior portion of the lateral meniscus, and the medial part of the groove comes into contact with the medial margin of the lateral articular surface of the tibia in front of the lateral tubercle of the tibial intercondyloid eminence. The medial groove is less distinct than the lateral. It does not reach as far as the intercondyloid fossa and therefore exists only on the medial part of the condyle; it receives the anterior edge of the medial meniscus when the knee-joint is extended. Where the groove ceases laterally the patellar surface is seen to be continued backward as a semilunar area close to the anterior part of the intercondyloid fossa; this semilunar area articulates with the medial vertical facet of the patella in forced flexion of the knee-joint. The tibial surfaces of the condyles are convex from side to side and from before backward. Each presents a double curve, its posterior segment being an arc of a circle, its anterior, part of a cycloid. 61 16 The Architecture of the Femur—Koch 62 by mathematical analysis has “shown that in every part of the femur there is a remarkable adaptation of the inner structure of the bone to the machanical requirements due to the load on the femur-head. The various parts of the femur taken together form a single mechanical structure wonderfully well-adapted for the efficient, economical transmission of the loads from the acetabulum to the tibia; a structure in which every element contributes its modicum of strength in the manner required by theoretical mechanics for maximum efficiency.” “The internal structure is everywhere so formed as to provide in an efficient manner for all the internal stresses which occur due to the load on the femur-head. Throughout the femur, with the load on the femur-head, the bony material is arranged in the paths of the maximum internal stresses, which are thereby resisted with the greatest efficiency, and hence with maximum economy of material.” “The conclusion is inevitable that the inner structure and outer form of the femur are governed by the conditions of maximum stress to which the bone is subjected normally by the preponderant load on the femur-head; that is, by the body weight transmitted to the femur-head through the acetabulum.” “The femur obeys the mechanical laws that govern other elastic bodies under stress; the relation between the computed internal stresses due to the load on the femur-head, and the internal structure of the different portions of the femur is in very close agreement with the theoretical relations that should exist between stress and structure for maximum economy and efficiency; and, therefore, it is believed that the following laws of bone structure have been demonstrated for the femur: 17 “1. The inner structure and external form of human bone are closely adapted to the mechanical conditions existing at every point in the bone. 18 “2. The inner architecture of normal bone is determined by definite and exact requirements of mathematical and mechanical laws to produce a maximum of strength with a minimum of material.” 19 The Inner Architecture of the Upper Femur—“The spongy bone of the upper femur (to the lower limit of the lesser trochanter) is composed of two distinct systems of trabeculæ arranged in curved paths: one, which has its origin in the medial (inner) side of the shaft and curving upward in a fan-like radiation to the opposite side of the bone; the other, having origin in the lateral (outer) portion of the shaft and arching upward and medially to end in the upper surface of the greater trochanter, neck and head. These two systems intersect each other at right angles. 20 “A. Medial (Compressive) System of Trabeculæ—As the compact bone of the medial (inner) part of the shaft nears the head of the femur it gradually becomes thinner and finally reaches the articular surface of the head as a very thin layer. From a point at about the lower level of the lesser trochanter, 2 1/2 to 3 inches from the lower limit of the articular surface of the head, the trabeculæ branch off from the shaft in smooth curves, spreading radially to cross to the opposite side in two well-defined groups: a lower, or secondary group, and an upper, or principal group. 21

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FIG. 247– Frontal longitudinal midsection of upper femur. (Picture From the Classic Gray's Anatomy) “a. The Secondary Compressive Group—This group of trabeculæ leaves the inner border of the shaft beginning at about the level of the lesser trochanter, and for a distance of almost 2 inches along the curving shaft, with which the separate trabeculæ make an angle of about 45 degrees. They curve outwardly and upwardly to cross in radiating smooth curves to the opposite side. The lower filaments end in the region of the greater trochanter: the adjacent filaments above these pursue a more nearly vertical course and end in the upper portion of the neck of the femur. The trabeculæ of this group are thin and with wide spaces between them. As they traverse the space between the medial and lateral surfaces of the bone they cross at right angles the system of curved trabeculæ which arise from the lateral (outer) portion of the shaft. (Figs. 247 and 249.) 22 “b. The Principal Compressive Group—This group of trabeculæ (Figs. 247 and 249.) springs from the medial portion of the shaft just above the group above-described, and spreads upward and in slightly radial smooth curved lines to reach the upper portion of the articular surface of the head of the femur. These trabeculæ are placed very closely together and are the thickest ones seen in the upper femur. They are a prolongation of the shaft from which they spring in straight lines which gradually curve to meet at right-angles the articular surface. There is no change as they cross the epiphyseal line. They also intersect at right-angles the system of lines which rise from the lateral side of the femur. 23

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FIG. 248– Diagram of the lines of stress in the upper femur, based upon the mathematical analysis of the right femur. These result from the combination of the different kinds of stresses at each point in the femur. (After Koch.) (Picture From the Classic Gray's Anatomy) “This system of principal and secondary compressive trabeculæ corresponds in position and in curvature with the lines of maximum compressive stress, which were traced out in the mathematical analysis of this portion of the femur. (Figs. 247 and 250.) 24 “B. Lateral (Tensile) System of Trabeculæ—As the compact bone of the outer portion of the shaft approaches the greater trochanter it gradually decreases in thickness. Beginning at a point about 1 inch below the level of the lower border of the greater trochanter, numerous thin trabeculæ are given off from the outer portion of the shaft. These trabeculæ lie in three distinct groups. 25 “c. The Greater Trochanter Group—These trabeculæ rise from the outer part of the shaft just below the greater trochanter and rise in thin, curving lines to cross the region of the greater trochanter and end in its upper surface. Some of these filaments are poorly defined. This group intersects the trabeculæ of group ('a') which rise from the opposite side. The trabeculæ of this group evidently carry small stresses, as is shown by their slenderness. 26

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FIG. 249– Frontal longitudinal midsection of left femur. Taken from the same subject as the one that was analyzed and shown in Figs. 248 and 250. 4/9 of natural size. (After Koch.) (Picture From the Classic Gray's Anatomy)

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FIG. 250– Diagram of the computed lines of maximum stress in the normal femur. The section numbers 2, 4, 6, 8, etc., show the positions of the transverse sections analyzed. The amounts of the maximum tensile and compressive stress at the various sections are given for a load of 100 pounds on the femur-head. For the standing position (“at attention”) these stresses are multiplied by 0.6, for walking by 1.6 and for running by 3.2. (After Koch.) (Picture From the Classic Gray's Anatomy) “d. The Principal Tensile Group—This group springs from the outer part of the shaft immediately below group c and curves convexly upward and inward in nearly parallel lines across the neck of the femur and ends in the inferior portion of the head. These trabeculæ are somewhat thinner and more, widely spaced than those of the principal compressive group ('b'). All the trabeculæ of this group cross those of groups ('a') and ('b') at right angles. This group is the most important of the lateral system (tensile) and, as will be shown later, the greatest tensile stresses of the upper femur are carried by the trabeculæ of this group. 27 “e. The Secondary Tensile Group—This group consists of the trabeculæ which spring from the outer side of the shaft and lie below those of the preceding group. They curve upward and medially across the axis of the femur and end more or less irregularly after crossing the midline, but a number of these filaments end in the medial portion of the shaft and neck. They cross at right angles the trabeculæ of group ('a'). 28

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FIG. 251– Intensity of the maximum tensile and compressive stresses in the upper femur. Computed for the load of 100 pounds on the right femur. Corresponds to the upper part of Fig. 250. (After Koch.) (Picture From the Classic Gray's Anatomy) “In general, the trabeculæ of the tensile system are lighter in structure than those of the compressive system in corresponding positions. The significance of the difference in thickness of these two systems is that the thickness of the trabeculæ varies with the intensity of the stresses at any given point. Comparison of Fig. 247 with Fig. 251 will show that the trabeculæ of the compressive system carry heavier stresses than those of the tensile system in corresponding positions. For example, the maximum tensile stress at section 8 (Fig. 251) in the outermost fiber is 771 pounds per square inch, and at the corresponding point on the compressive side the compressive stress is 954 pounds per square inch. Similar comparisons may be made at other points, which confirm the conclusion that the thickness and closeness of spacing of the trabeculæ varies in proportion to the intensity of the stresses carried by them. 29 “It will be seen that the trabeculæ lie exactly in the paths of the maximum tensile and compressive stresses (compare Figs. 247, 248 and 251), and hence these trabeculæ carry these stresses in the most economical manner. This is in accordance with the well-recognized principle of mechanics that the most direct manner of transmitting stress is in the direction in which the stress acts. 30 “Fig. 249 shows a longitudinal frontal section through the left femur, which is the mate of the right femur on which the mathematical analysis was made. In this midsection the system of tensile trabeculæ, which rises from the lateral (outer) part of the shaft and crosses over the central area to end in the medial portion of the shaft, neck and head, is clearly shown. This figure also shows the compressive system of trabeculæ which rises on the medial portion of the shaft and crosses the central area to end in the head, neck and greater trochanter. By comparing the position of these two systems of trabeculæ shown in Fig. 249 with the lines of maximum and minimum stresses shown in Figs. 248 and 250 it is seen that the tensile system of trabeculæ corresponds exactly with the position of the lines of maximum and minimum tensile stresses which were determined by mathematical analysis. In a similar manner, the compressive system of trabeculæ in Fig. 249 corresponds exactly with the lines of maximum and minimum compressive stresses computed by mathematical analysis. 31 “The amount of vertical shear varies almost uniformly from a maximum of 90 pounds (90 percent. of the load on the femur-head) midway between sections 4 and 6, to a minimum of —5.7 pounds at section 18” (Fig. 251). There is a gradual diminution of the spongy bone from section 6 to section 18 parallel with the diminished intensities of the vertical shear. 32 1. The trabeculæ of the upper femur, as shown in frontal sections, are arranged in two general systems, compressive and tensile, which correspond in position with the lines of maximum and minimum stresses in the femur determined by the mathematical analysis of the femur as a mechanical structure. 33 2. The thickness and spacing of the trabeculæ vary with the intensity of the maximum stresses at various points in the upper femur, being thickest and most closely spaced in the regions where the greatest stresses occur. 34 3. The amount of bony material in the spongy bone of the upper femur varies in proportion to the intensity of the shearing force at the various sections. 35 4. The arrangement of the trabeculæ in the positions of maximum stresses is such that the greatest strength is secured with a minimum of material. 36 Significance of the Inner Architecture of the Shaft—1. Economy for resisting shear. The shearing stresses are at a minimum in the shaft. “It is clear that a minimum amount of material will be required to resist the shearing stresses.” As horizontal and vertical shearing stresses are most efficiently resisted by material placed near the neutral plane, in this region a minimum amount of material will be needed near the neutral axis. In the shaft there is very little if any material in the central space, practically the only material near the neutral plane being in the compact bone, but lying at a distance from the neutral axis. This conforms to the requirement of mechanics for economy, as a minimum of material is provided for resisting shearing stresses where these stresses are a minimum. 37 2. Economy for resisting bending moment. “The bending moment increases from a minimum at section 4 to a maximum between sections 16 and 18, then gradually decreases almost uniformly to 0 near section 75.” “To resist bending moment stresses most effectively the material should be as far from the neutral axis as possible.” It is evident that the hollow shaft of the femur is an efficient structure for resisting bending moment stresses, all of the material in the shaft being relatively at a considerable distance from the neutral axis. It is evident that the hollow shaft provides efficiently for resisting bending moment not only due to the load on the femur-head, but from any other loads tending to produce bending in other planes. 38 3. Economy for resisting axial stress. 39 The inner architecture of the shaft is adapted to resist in the most efficient manner the combined action of the minimal shearing forces and the axial and maximum bending stresses. 40 The structure of the shaft is such as to secure great strength with a relatively small amount of material. 41 The Distal Portion of the Femur—In frontal section (Fig. 249) in the distal 6 inches of the femur “there are to be seen two main systems of trabeculæ, a longitudinal and a transverse system. The trabeculæ of the former rise from the inner wall of the shaft and continue in perfectly straight lines parallel to the axis of the shaft and proceed to the epiphyseal line, whence they continue in more or less curved lines to meet the articular surface of the knee-joint at right angles at every point. Near the center there are a few thin, delicate, longitudinal trabeculæ which spring from the longitudinal trabeculæ just described, to which they are joined by fine transverse filaments that lie in planes parallel to the sagittal plane. 42 “The trabeculæ of the transverse system are somewhat lighter in structure than those of the longitudinal system, and consist of numerous trabeculæ at right angles to the latter. 43 “As the distal end of the femur is approached the shaft gradually becomes thinner until the articular surface is reached, where there remains only a thin shell of compact bone. With the gradual thinning of the compact bone of the shaft, there is a simultaneous increase in the amount of the spongy bone, and a gradual flaring of the femur which gives this portion of the bone a gradually increasing gross area of cross-section. 44 “There is a marked thickening of the shell of bone in the region of the intercondyloid fossa where the anterior and posterior crucial ligaments are attached. This thickened area is about 0.4 inch in diameter and consists of compact bone from which a number of thick trabeculæ pass at right angles to the main longitudinal system. The inner structure of the bone is here evidently adapted to the efficient distribution of the stresses arising from this ligamentary attachment. 45

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FIG. 252– Plan of ossification of the femur. From five centers. (Picture From the Classic Gray's Anatomy) “Near the distal end of the femur the longitudinal trabeculæ gradually assume curved paths and end perpendicularly to the articular surface at every point. Such a structure is in accordance with the principles of mechanics, as stresses can be communicated through a frictionless joint only in a direction perpendicular to the joint surface at every point. 46 “With practically no increase in the amount of bony material used, there is a greatly increased stability produced by the expansion of the lower femur from a hollow shaft of compact bone to a structure of much larger cross-section almost entirely composed of spongy bone. 47

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FIG. 253– Epiphysial lines of femur in a young adult. Anterior aspect. The lines of attachment of the articular capsules are in blue. (Picture From the Classic Gray's Anatomy)

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FIG. 254– Epiphysial lines of femur in a young adult. Posterior aspect. The lines of attachment of the articular capsules are in blue. (Picture From the Classic Gray's Anatomy) “Significance of the Inner Architecture of the Distal Part of the Femur—The function of the lower end of the femur is to transmit through a hinged joint the loads carried by the femur. For stability the width of the bearing on which the hinge action occurs should be relatively large. For economy of material the expansion of the end bearing should be as lightly constructed as is consistent with proper strength. In accordance with the principles of mechanics… …, the most efficient manner in which stresses are transmitted is by the arrangement of the resisting material in lines parallel to the direction in which the stresses occur and in the paths taken by the stresses. Theoretically the most efficient manner to attain these objects would be to prolong the innermost filaments of the bone as straight lines parallel to the longitudinal axis of the bone, and gradually to flare the outer shell of compact bone outward, and continuing to give off filaments of bone parallel to the longitudinal axis as the distal end of the femur is approached. These filaments should be well-braced transversely and each should carry its proportionate part of the total load, parallel to the longitudinal axis, transmitting it eventually to the articular surface, and in a direction perpendicular to that surface.” 48 Referring to Fig. 249, it is seen that the large expansion of the bone is produced by the gradual transition of the hollow shaft of compact bone to cancellated bone, resulting in the production of a much larger volume. The trabeculæ are given off from the shaft in lines parallel to the longitudinal axis, and are braced transversely by two series of trabeculæ at right angles to each other, in the same manner as required theoretically for economy. 49 Although the action of the muscles exerts an appreciable effect on the stresses in the femur, it is relatively small and very complex to analyze and has not been considered in the above analysis. 50 Ossification (Figs. 252, 253, 254)—The femur is ossified from five centers: one for the body, one for the head, one for each trochanter, and one for the lower extremity. Of all the long bones, except the clavicle, it is the first to show traces of ossification; this commences in the middle of the body, at about the seventh week of fetal life, and rapidly extends upward and downward. The centers in the epiphyses appear in the following order: in the lower end of the bone, at the ninth month of fetal life (from this center the condyles and epicondyles are formed); in the head, at the end of the first year after birth; in the greater trochanter, during the fourth year; and in the lesser trochanter, between the thirteenth and fourteenth years. The order in which the epiphyses are joined to the body is the reverse of that of their appearance; they are not united until after puberty, the lesser trochanter being first joined, then the greater, then the head, and, lastly, the inferior extremity, which is not united until the twentieth year. 51 Note 61 A cycloid is a curve traced by a point in the circumference of a wheel when the wheel is rolled along in a straight line. Note 62 The Laws of Bone Architecture. Am. Jour. of Anat., 21, 1917. The following paragraphs are taken almost verbatum from Koch’s article in which we have the first correct mathematical analysis of the femur in support of the theory of the functional form of bone proposed by Wolff and also by Roux.

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