Structure and Function of the Lower Limb - Essay Example

Running Head: STRUCTURE AND FUNCTION OF THE LOWER LIMB Structure and function of the lower limb of the of the Structure and function of the lower limb Introduction The muscles acting about the hip and knee may be categorized according to their function, that is, the relative limb displacements they produce when stimulated. Relative limb displacements are usually described anatomically, in terms of three independent rotations, e.g. at the hip we have flexion/extension, abduction/adduction and internal/external rotation. It is uncommon for a single muscle to produce a rotation about a single axis. Numerous attempts have been made to categorize muscle function using several methods, including (a) EMG studies (Wheatley and Jahkne, 2004; Basmajian, 2005) (b) electrical stimulation (Kaplan.2004), (c) anatomical inspection, and (d) various ana- lytical methods supported by extensive experimental data (Jensen and Davy, 2000; Storace and Wolf, 1999). Generally, these studies have been qualitative, limited to a single or small number of limb positions, or invasive in nature. Analytical methods of determining muscle function have the advantage that results can be obtained for individual muscles very quickly, for any number of possible limb positions. The major problem with analytical methods is the lack of data, and the difficulty of obtaining the data with which to formulate a model.The purpose of this investigation was to determine the primary, secondary and tertiary functions of the muscles crossing the hip and knee joints. Changes in the relative ranking of the primary, secondary and tertiary functions of each muscle were investigated for the different limb positions during normal gait. Methods The functions of each muscle, about a given joint, were determined by computing the moment arms relative to three perpendicular axes centered at the joint. The axes were defined so that a moment about each axis produced a rotation corresponding to one of the usual descriptions of limb rotation (flexion, abduction, etc.). The force which produced a unit moment about one of the three axes was then determined. Generally, this force also produced moments about the other two axes. The primary function of a muscle the intermediate moment, and the tertiary function to the direction of the least of the three moments. The changes in the functions of the muscles as the joint position changed were determined for muscles acting about the hip and knee joints during normal gait. The muscle force needed to produce a unit moment about one of the axes was computed from the moment arm of the muscle about each joint. The moment arm was determined assuming the muscle or a segment of a muscle acted in a straight line from its origin to insertion. Locations of origins and insertions The origins and insertions of thirty seven muscles crossing the joints of the lower limb were obtained using the averaged data of Brand et al. (2002). Muscle origins and insertions were located in coordinate systems fixed on the pelvis, femur and tibia. For each muscle, the origin was given in the coordinate system attached to the bone from which the muscle originated, and the insertion was given in the coordinate system attached to the bone to which the muscle inserted. Insertions on the patella were given in the tibia1 coordinate system. Since some muscles had origins or insertions spread over a large area (gluteus maximus, gluteus minimus, gluteus medius, adductor magnus, adductor brevis and gastrocnemius) their action was modeled by two or more muscle segments to account for the differing effects of the different parts of the muscle when acting asynchronously. Some other muscles could not be modeled using their true origin and insertion because, for certain joint positions, the straight line assumption led to anatomically incorrect muscle positions. In these cases, the origin (iliacus, psoas, obturator internus) or insertion (sartorius, gracilis, semitendinosus, tibialis posterior, flexor digitorum communis, flexor hallucis longus, tibialis anterior, extensor hallucis longus, extensor digitorum longus, peroneus tertius, peroneus brevis, peroneus longus) was modeled by an effective point in the vicinity of the joint where the estimated centroid of the muscle crossed the joint (Brand et al., 2002). Muscle moment arms Muscle moment arms were computed for thirty seven muscles crossing the joints of the lower limb of a human subject during normal walking. The moment arms were computed as the perpendicular from the joint center to the muscle line of action. The origins and insertions obtained from Brand et al. (2002) were given in coordinate systems defined by three bony landmarks on each of the pelvis, femur and tibia. These landmarks were not visible externally. Therefore, to predict the muscle origin and insertion data for the walking subject, it was necessary to relate these internal coordinate systems to external measurements (i.e. locate the bony landmarks in coordinate systems established by external measurements). The three dimensional positions (x, y and z coordinates with respect to a fixed laboratory system) of thirty one external points on the subject, for one complete gait cycle from right heel strike to right heel strike, were obtained from high speed motion picture film taken at 50 frames s- 1 (Simon et al., 2003; Lesh et al., 1999). Using these points, coordinate systems were defined on each of the pelvis, right thigh and right shank. The origin of the pelvic coordinate system was located at the right anterior superior iliac spine (ASIS) as shown in Fig. 1. The axes were defined as where Pi was the position (x, y and z coordinates) of the right ASIS, P2 was the position of the left ASIS, and P3 was the position of a point on the end of a stick attached to the sacrum, and pointing posteriorly out from the sacrum. The origin of the femoral coordinate system was located at the center of the right knee as shown in Fig. 1. Pelvic, femoral and tibia1 external coordinate systems. where F I was the position of the center of the right hip, F2 was the position of the center of the right knee, and F3 was the position of the center of the right ankle. The Xj axis pointed from the knee to the hip joint. The X[ axis was perpendicular to the plane formed by the Xl axis and the vector from the ankle to the knee. This vector pointed laterally out from the body. The X{ axis was perpendicular to the X{ and Xl axes and was in a forward direction when the femur was vertical. The origin of the tibia1 coordinate system was located at the ankle as shown in Fig. 1. The axes were defined as where T1 was the position of the right knee and T2 was the position of the right ankle. The X; axis pointed from the ankle to the knee. The Xi axis pointed in the same direction as the X{ axis of the femoral system, laterally out from the body. The Xi axis was perpendicular to the above two, and pointed in the forward direction when the tibia was vertical. Once the external coordinate systems were defined, the relationship between these systems and the internal coordinate systems used by Brand et al. were obtained. This was done by determining the positions, in the external coordinate systems, of the points used by Brand et aI. to define their internal coordinate systems. In most cases, these points coincided with or could be computed directly from the measured position of points on the walking subject. For example, two of the points used by Brand et al. to define their pelvic coordinate system were the right ASIS and the midpoint between the left and right ASIS. Since there were markers on the left and right ASIS of the walking subject, the relationship between these points used by Brand et al. and the corresponding points on the walking subject were directly obtained. For points which could not be computed directly from positions of points on the walking subject (the mid-point between the pubic tubercles, the lateral epicondyle, the lateral malleolus and the tibia1 tuberosity) their locations in the external coordinate systems were obtained by measuring and scaling the points on a human skeleton. For example, to determine the location of the mid-point between the pubic tubercles in the pelvic external coordinate system, measurements were made on a human skeleton of the location of this point in a coordinate system defined by the two ASH and the right hip of the skeleton. It was assumed that in the experimental subject the relative location was the same as in the skeleton, and the location was then transformed to the pelvic external coordinate system. Once the locations of the bony landmarks used by Brand et al. were determined in the external coordinate systems, the coordinates of all muscle origins and insertions were transformed from the internal coordinate systems to the external coordinate systems. In addition, the locations of the joint centers were determined in the external systems. The position of the center of the knee was estimated on each film frame when the film was digitized. The position of the center of the hip was calculated using the position of the pelvis (based on the right and left ASKS and sacral stick positions) and a known relationship between hip position and ASIS position (Tylkowski et al., 2002). No attempt was made to account for the variation in the position of the instantaneous center of rotation of the joints. To calculate the muscle moment arms, it was necessary to transform all of the muscle origins, insertions and joint centers to a single coordinate system, and the fixed laboratory system was chosen for this purpose. At each time increment in the experimental gait data, the transformation matrices between the external systems and the fixed lab system were determined. The muscle moment arm was then calculated as the perpendicular from the joint center to the assumed line of action of the muscle. The moment arm for each muscle and joint combination was then transformed back into the external coordinate system. The moment arms of muscles acting about the hip joint were transformed to the femoral external coordinate system. The moment arms of muscles acting about the knee joint were transformed to the tibia1 external coordinate system. The literature was reviewed to determine the most commonly accepted primary function of each muscle in the standard anatomical position. The axis of the external coordinate system corresponding to this function was assumed to be the major functional axis of the muscle. For example, the primary function of the rectus femoris about the hip is Aexion. This corresponds to a positive moment about the X, axis of the femoral coordinate system. Based on the calculated moment arm, the force necessary to produce a unit moment about the major functional axis was calculated for each muscle at every joint position in the gait cycle where R was the magnitude of the moment arm vector, F, was the muscle force necessary to produce a unit moment, r was a unit vector in the direction of the moment arm, f was a unit vector in the direction of the muscle force, and j was a vector in the direction of the major functional axis in the external coordinate system. The relative magnitudes of F, for different limb positions was a measure of change in the effectiveness of the muscle, in terms of mechanical advantage, in performing what is commonly considered to be its primary function. For every joint position, themoment produced by FM about the other two axes was then determined from RF,(r x f). The function of the muscle was defined by the relative magnitudes of the three moments. A muscle was classified as a primary flexor or extensor if its moment arm had its largest component in the X, direction. A muscle was classified as a primary abductor or adductor if its moment arm had its largest component in the X, direction. It was classified as a primary internal/external rotator if its moment arm had its largest component in the X, direction. Some of the results predicted by the model for muscles acting about the hip were checked qualitatively by electrically stimulating the muscles of a paraplegic subject involved in the functional electrical stimulation project at the Veterans Administration Medical Center, Cleveland, OH (Marsolais et al., 2001). The subject, with complete absence of motor function at the T8/9 level stood with the aid of a long leg brace on one leg while the other leg was allowed to hang freely. To avoid contamination of the response caused by a two joint muscle, the knee of the freely hanging limb was also locked with a long leg brace. The subject had implanted electrodes in the major muscles crossing the hip, knee and ankle joints (Marsolais and Kobetic, 2005). Results The amount of force necessary to produce a unit primary moment was a function of the joint position. The relative magnitudes of primary, secondary and tertiary moments produced by each muscle was also a function of the relative limb positions. In some cases, the magnitude of a secondary moment exceeded the magnitude of the primary moment for certain positions of the limbs. The effectiveness of a muscle in producing moments about the three orthogonal axes at a joint was proportional to the relative magnitudes of the moment arms, and was simply a measure of the relative mechanical advantage of the muscles in the three directions. The gluteus medius muscle is considered to be one of the primary abductors of the thigh. This muscle was separated into three different segments by Brand et al. (2002), with three separate origins and a common insertion. The model predicted that both the anterior and middle segments of this muscle were abductors of the thigh. However, the anterior gluteus medius produced an internal rotation moment whose magnitude exceeded the (unit) abduction moment at the beginning and end of the gait cycle when the hip was in flexion. The anterior and middle gluteus medius produced an extension moment that exceeded the (unit) abduction moment from mid to late stance, and at the end of the gait cycle prior to right heel strike. In addition, the model predicted that the middle part of the gluteus medius has a significant external rotation moment arm at the hip when the hip is extended prior to toe-off. The posterior part of this muscle was primarily an extensor and an external rotator of the hip, although it had a significant hip abduction moment arm. For the gluteus maximus, the model predicted that the superior and middle parts of this muscle were primarily extensors of the thigh, and the inferior part was primarily an adductor. In terms of mechanical advantage, the superior and middle gluteus maximus were most effective as extensors when the hip was extended to moderately flexed (30-60% of the gait cycle), requiring less force to produce the unit extension moment in this region. The superior part of this muscle was also relatively effective as an abductor of the hip, and in mid-swing produced a greater abduction moment than the (unit) extension moment. During late stance, it was relatively effective as an external rotator of the hip. The middle part of the gluteus maximus was also relatively effective as an external rotator of the hip for all of the gait cycle, and an adductor during stance. The inferior part of the muscle was an effective extensor throughout the cycle, but especially during late stance and early swing when it produced a greater extension moment than the (unit) adduction moment. The adductor magnus, which was modeled by three separate segments, was found to be an extensor as well as an adductor. As an extensor, the posterior part of this muscle was found to be most effective when the thigh was flexed. The rectus femoris and the sartorius showed very similar functions about the hip joint. The model predicted that both were mainly flexors of the hip, but also had a significant abduction moment arm. The sartorius was found to be especially effective in abduction; at times in the gait cycle producing a larger abduction moment than the (unit) flexion moment. When the thigh was extended prior to toe-off, the sartorius became very ineffective as a @exor, requiring a large force to produce the unit flexion moment. This increase in force also increased the abduction component. The function of the sartorius was studied qualitatively for one position of the hip joint by electrically stimulating the muscle of a paraplegic subject. It was observed that, in addition to flexion and abduction, the muscle contributed a significant amount of external rotation, which is a well accepted function of this muscle (Wheatley and Jahkne, 2004). The model predicted that the tensor fasciae latae was a flexor and abductor of the thigh for most of the gait cycle. When the hip was extended, however, it become a very poor hip flexor. Testing of this muscle in a paraplegic patient showed the muscle to be a relatively strong abductor, agreeing with the results of the model and the commonly accepted functions of of the tensor fasciae latae. The model predicted that the gracilis was a hip adductor for all positions of the thigh during gait, and a relatively effective hip flexor for most of the cycle. During mid to late stance the muscle produced about the same amount of flexion as the (unit) adduction moment. The semi membranosus was found to be an extensor of the hip, with the capability of producing some adduction at certain times in the cycle. As a hip extensor, the semimembranosus became very ineffective when the hip was in an extended position, which is the point at which the gluteus maximus became more effective as an extensor. About the knee, the semimembranosus was found to produce flexion, adduction and a small amount of internal rotation. As a flexor, it became slightly more effective when the knee was in a flexed position. It was found that for knee extensors, the model was very sensitive to small errors in defining the tibia1 internal system in external coordinates. Using the insertion data of Brand et al. for the quadriceps group resulted in the straight line from origin to insertion crossing behind the knee during knee flexion. To get some qualitative results for this group of muscles, two methods were used to alleviate this problem. The first method was to increase the X, coordinate of the insertions until the problem no longer occured. The second method was to use the patellar pulley model of Brand et al. (2002). Both methods predicted qualitatively very similar results. Using both methods, the model predicted that all muscles of the quadriceps group were primarily knee extensors. When the knee flexion angle increased, the vastus medialis produced an internal rotation moment and the vastus lateralis produced an external rotation moment on the shank. The vastus intermedius and the rectus femoris had very little rotation moment arm components at the knee. In terms of the amount of force necessary to produce a unit extension moment, all muscles of the quadriceps group were less effective when the knee was in a flexed position than when in an extended position. References View Within Article Abbot, B. C. and Wilkie, D. R. 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