MR Imaging of Disorders of the Achilles Tendon
The Achilles tendon is among the most frequently injured tendons of the body with a variety of types of traumatic and overuse conditions affecting it. These conditions are common, often come to clinical attention, and are frequently imaged. The pathophysiology of Achilles disorders is complex, and the nomenclature is irregularly applied; this leads to miscommunication between clinicians and radiologists and inconsistencies in the literature. Therefore, we review the anatomy, MR imaging findings, and pathologic findings in an attempt to develop a systematic nomenclature.
Gross Anatomy
The Achilles tendon originates in the mid leg and is formed by the junction of the two heads of the gastrocnemius muscles and the soleus muscle [1, 2]. The bulk of the Achilles is formed from the gastrocnemius muscle. The larger medial head originates almost entirely from just proximal to the medial femoral condyle, and the smaller lateral head arises from both the posterior and lateral surfaces of the lateral femoral condyle. At the junction of the proximal and mid calf, the two heads of the gastrocnemius muscles and their tendons approximate midline. The gastrocnemius tendon origin is gradual, occurring over approximately 3-4 cm. The fibers of the medial head originate slightly lower than those of the lateral head. The Achilles tendon is not formed until the soleus muscle inserts onto the gastrocnemius tendon, approximately 3-4 cm more distally [2].
The plantaris muscle originates from the lateral meniscus and the lateral femoral epicondyle in close association with the lateral head of the gastrocnemius muscle. The plantaris tendon then crosses obliquely between the soleus and gastrocnemius muscles and continues just medial to the Achilles. Various plantaris insertions are seen, but most fibers insert on the medial aspect of the superior calcaneal tuberosity or 1 cm anterior and medial to the Achilles on the calcaneus, a distinct insertion point separate from that of the Achilles. The Achilles-plantaris complex is termed the “triceps-surae complex” [3].
The Achilles tendon is enclosed almost completely within a paratendon. This paratendon has both visceral and parietal layers [4]. The paratendon is analogous to synovium in that it provides nutrition for the tendon, but because the Achilles tendon does not change its axis of motion, there is no need for the lubrication function of synovium.
Two layers of filmy fibrous tissue with fine internal mesotendal blood vessels make up the paratendon [5]. The interwoven fibers of the paratendon allow it to stretch up to several centimeters in length with tendon movement and provide some degree of tendon gliding [4].
Mesotendal vascular anastomoses provide tendon nourishment. However, 2-6 cm proximal to the calcaneal insertion, this blood supply is diminished [6]. This region of decreased vascularity is the usual region of Achilles rupture [7]. Proximal tears are uncommon because of the nutrition provided by the muscular branches from the gastronemius [8]. Distal tears are uncommon because the blood supply from the periosteal vessels is near the calcaneal insertion.
As the Achilles tendon descends, the fibers rotate laterally approximately 90°. Therefore, the gastrocnemius fibers insert laterally onto the posterior calcaneus, whereas the soleus fibers insert medially [9].
The insertion site of the Achilles onto the calcaneus is an enthesis and is intimately related to the only true anatomic bursa in the ankle, the retrocalcaneal bursa [10].
The retrocalcaneal bursa is horseshoe-shaped, filled with synovial fluid, and surrounded anteriorly by Kager's fat pad. The function of the retrocalcaneal bursa is to protect the distal Achilles tendon from frictional wear against the posterior calcaneus [11]. Posterior to the tendon lies an acquired bursa, termed the “retro-Achilles.” The enthesis itself is fibrocartilage directly intermeshing into the marrow of the calcaneus [10]. This direct meshing of tendon fibrils into marrow provides significant strength at the enthesis and makes it a rare site of tendon failure.
Tendon Ultrastructure
Approximately 15 cm in length, the Achilles is the strongest, largest, and thickest tendon in the human body. The Achilles is made of fascicles, with an interfascicular membrane separating the fascicles into bundles. Each bundle of fascicles is roughly shaped like a quarter of a pie. On a microstructural level, the fascicles are made of fibroblasts, which have a sinusoidal structure. This sinusoidal structure allows the Achilles to stretch considerably before tendon rupture. The fibroblasts are made of fibrils, the fibrils are made of microfibrils, and the microfibrils are made of tropocollagen [12]. The fibrils normally have an undulating pattern. This undulation decreases with aging, which leads to a decrease in the Achilles' elasticity [13]. In addition, the average diameter, density, and cellularity of the collagen fibrils also decrease with aging. The combination of cellular changes, ultrastructural changes, and a tenuous blood supply predisposes the aged Achilles to degeneration and injury.
Functional Anatomy
The gastrocnemius, soleus, and plantaris muscles act to flex the foot [14]. The gastrocnemius is also a knee flexor. The gastrocnemius muscle is active in walking, jumping, and running, and therefore it is composed predominantly of type II fibers [15]. Because the soleus muscle has more of a stabilization effect on the foot for standing, it consists primarily of type I fibers [16]. Consequently, muscle fiber atrophy of the soleus occurs more rapidly than does that of the gastrocnemius [17], making the soleus muscle a more sensitive indicator of atrophy as a result of complete tears or denervation.
Normal MR Appearance
The normal average thickness of the Achilles tendon is 6 mm. The Achilles tendon is thicker in tall patients, in men, and in the elderly [18]. Achilles size is also directly related to lean body mass and is somewhat related to total body mass.
On sagittal images, the anterior and posterior margins of the Achilles tendon should be parallel below the soleus insertion (Fig. 1A,1B). On axial images, the anterior margin of the Achilles is concave for most of its course. Somewhat proximally, just above the soleus insertion, the margin may be straight or convex; at the soleus insertion, the margin is typically convex and may be focally bulbous. On coronal images, both sides of the Achilles are fairly straight and the tendon widens as it extends distally at the lesion.
The normal retrocalcaneal bursa is visible on MR imaging but should measure less than 6 mm superior to inferior, 3 mm medial to lateral, and 2 mm anterior to posterior [19]. Subcutaneous fat should be seen between the Achilles and the skin. Focal absence of fat may represent a skin callus, a blister (if it has high signal on T2-weighted images and bows the skin out), or retro-Achilles bursitis (if it has high signal and is without mass effect on the skin). Fat should also be normally seen anterior to the tendon in Kager's fat pad. Occasionally, vessels within Kager's fat pad can mimic edema, although their tubular morphology should allow differentiation.
The Achilles tendon is usually dark on all imaging sequences. However, the normal fascicular anatomy of the Achilles tendon may be visible as a single line and can mimic an interstitial tear [20]. This fascicular signal is usually not present or fades on T2-weighted images. Small punctate areas of high signal, seen distally in the Achilles tendon on axial images, are interfascicular membranes (Figs. 2 and 3). Lastly, some fraction of distal internal signal may represent the “magic angle” artifact. This phenomenon occurs in the Achilles tendon even though it does not grossly change its axis, because the fibers twist internally. This artifact is not present on T2-weighted images [21].
Epidemiology
True rupture of the Achilles tendon was first described by Ambroise Pare in 1575 and first reported in the medical literature in 1633. Achilles tendon rupture was a rarely reported injury until the 1950s [22]. Before 1929, fewer than 70 cases were reported in the world literature. During the 1970s, the reported incidence increased by up to 50% a year in developed countries [23].
Achilles tendon tears are most common in developed countries, but the prevalence varies among developed countries. The highest rates are seen in Germany, Austria, Sweden, Denmark, and Switzerland. Lower rates occur in France, Spain, the United Kingdom, and the United States [23]. However, some industrialized nations, such as The Netherlands, Japan, and Korea, have an extremely low incidence of Achilles tears, and in the third world, the incidence of Achilles tears is even lower [24]. Currently, the incidence in industrialized nations is approximately seven cases per 100,000 inhabitants per year [24].
Achilles tendon rupture occurs in younger patients, with a mean age of 36 years, as compared with ruptures of other tendons, but Achilles rupture almost never occurs in patients before the onset of adolescence [25]. Of all the tendons in the foot and ankle, the Achilles tendon is the only one for which disorders have a male predominance [26]. Achilles tendon disorders are also more common on the left than on the right side for unknown reasons [27]. Because Achilles tendon disorders are activity-related disorders, incidence peaks during the summer [28].
A significant relationship between leisure athletic activities and tendon injuries exists [27]. The sedentary lifestyle of modern whitecollar workers results in decreased blood flow and nutrition to the Achilles tendon [29]. This situation is compounded by the effects of aging on the vascular supply. Recreational physical activities that intermittently stress the ischemic Achilles tendon, without giving it time to adapt, may lead to “spontaneous” Achilles tendon rupture [29].
The specific causative activity varies among countries according to the popularity of sporting events in the country involved. In the United States, running sports, particularly those that involve pivot motion, are the most common causative sport, with jogging as the leading cause of Achilles disorders [28]. However, in Germany, soccer is the leading cause [27].
MR Imaging and Pathologic Anatomy
“Achilles tendonosis” is a preferable term to “Achilles tendonitis” because this disorder is manifested as intratendinous degeneration without a significant inflammatory response [18]. The Achilles tendon is protected against inflammatory processes because no true synovial sheath is present. However, because of the intimate association between the distal Achilles tendon and the retrocalcaneal bursa, the Achilles tendon is secondarily affected by inflammatory processes involving the retrocalcaneal bursa [10]. In addition, involvement of the Achilles paratendon has been noted to be reasonably frequent in systemic inflammatory diseases, such as rheumatoid arthritis [30]. This manifestation of rheumatoid arthritis has not been widely recognized previously because this inflammation, similar to that of many wrist tendons, is often clinically occult [31].
Most imaging findings represent the pathologic processes of tendon degeneration and repair [32]. Grossly, the degenerated tendon appears nodular and yellow and loses its usual glistening luster, often appearing edematous or fibrillated [33].
On a microscopic level, four predominant types of tendon degeneration are seen including fibromatosis or hypoxic, lipoid, osseous or calcific, and myxoid [34]. Although only the former two frequently lead to macroscopic tears, all pathologic changes may be the result of microscopic tears [35]. These microscopic tears evolve and coalesce to form the spectrum of Achilles disorders that is seen on imaging. It is the coalescence of these microtears that leads to the development of focal mycoid regions and interstitial tears along the long axis of the tendon. Therefore, tears on a microscopic level begin the cascade of tendon disorders, and tears on a macroscopic level end it [35].
Fibromatous degeneration is also termed “hypoxic degenerative tendonopathy” and is the most frequently seen degenerative finding in ruptured Achilles tendons [36]. These hypoxic changes are likely caused by ischemia because of the relative hypovascularity of the critical zone of the Achilles tendon [37]. This hypovascularity results in anoxic injury to tenocytes and collagen fibers [34]. Hypoxic degenerative tendonopathy leads to a thickened dysmorphic Achilles tendon [36] (Figs. 4A,4B and 5). This type of degeneration usually occurs after multiple symptomatic episodes [37] and usually lacks internal signal on MR imaging. A similar MR appearance can be seen in rheumatoid arthritis (Fig. 6) and gout (Fig. 7) and after tendon repair.
The second most common type of degeneration is mucoid. Most patients with mucoid degeneration also have some degree of hypoxic degeneration [33]. This is the most common degeneration to occur asymptomatically. In mucoid degeneration, large mucoid patches and vacuoles are seen between the thinned degenerated tendon fibers [35]. Interrupted signal on T2-weighted images is the best marker for mucoid deposits (Figs. 8A,8B,9,10). Grossly, these tendons appear enlarged, and enlargement may also be seen on MR imaging. It is the coalescence of vacuoles and lacunae that is the beginning of an interstitial tear. Patients with mucoid degeneration may have a tear at first clinical presentation because earlier episodes were asymptomatic.
Tenolipomatosis is the most age-dependent type of tendon degeneration. Tenolipomatosis occurs with fatty deposits between normal tenocytes [38]. Because the tenocytes are normal, lipoid degeneration does not seem to affect the structural properties of the Achilles [39] and does not predispose the tendon to tear [40]. This disorder, like hypoxic degeneration, is often clinically silent and is related to, but distinct from, tendinous xanthoma. Xanthomas are the result of lipomatosis seen in inherited metabolic diseases such as type 2 and type 3 hyperpoproteinemias and cerebrotendinous xanthomatosis [41]. Although severe forms of these metabolic disorders are rare, one diagnostic criterion for familial hyperlipoproteinemia is focal thickening of the Achilles tendon on imaging [42]. Xanthomas can mimic hypoxic Achilles tendonitis or various rheumatologic conditions, with diffuse tendon thickening and, often, quite subtle internal signal.
Calcifying tendonopathy is rare in the Achilles tendon, seen in only 3% of ruptured tendons [43]. This dystrophic calcification may progress to Achilles ossification [41] (Fig. 11). On a macroscopic level in the Achilles, tendon ossification occurs more frequently than tendon calcification and is relatively more common than in other tendons in the body [42]. Therefore, not only is ossification distinct from calcification because of the presence of cortical bone and trabeculae, but it may represent a different degenerative pathway than calcification.
The first symptomatic stage of Achilles disorders is paratendonitis, which is often mistakenly termed “tendonitis” [44] (Figs. 3 and 12). This stage is analogous to synovitis in sheathed tendons. On T2-weighted MR sequences, paratendonitis appears as partially circumferential high signal around the Achilles tendon. Fat suppression is usually necessary to visualize this high signal. The high signal is not as bright as synovial fluid because the paratendon is not made of a synovial membrane. The external margins of the signal are typically slightly ill defined, and the high signal predominates posteriorly and extends medially up to three quarters around the tendon. In isolated paratendonitis, the tendon itself is normal. True acute tendonitis is an infrequent entity and is an even less frequent entity to be imaged. Most clinical cases of tendonitis are either paratendonitis or an exacerbation of hypoxic tendonosis. True tendonitis, if imaged, occasionally appears as edema not only in the paratendon but also in Kager's fat pad anterior to the Achilles tendon [45] (Fig. 13).
The spectrum of tears ranges from microtears to interstitial tears (parallel to the long axis of the Achilles), to partial tears, and eventually to complete tears [46]. This abrupt demarcation between tears and “nontears” is misleading because there is a junctional entity, mucoid degeneration [35]. In mucoid degeneration, the vacuoles may coalesce into an interstitial tear [36]; also, in tendonosis perhaps the inciting event is a microtear [47]. Lastly, many cases of tendonosis are treated identically to cases of interstitial tears with débridement of the degenerative center of the tendon and oversewing of the preserved peripheral aspects of the tendon [48].
Almost all tears, interstitial (Figs. 14 and 15), partial (Figs. 16 and 17), or complete (Figs. 18 and 19) show high signal on T2-weighted imaging [49]. Tendon-end retraction can also be seen occasionally in acute tears [50]. Because one of the treatments for an Achilles tendon tear is casting in plantar flexion, sagittal images can be obtained after casting. If the tendon edges are not opposed in this position, the treatment will be unsuccessful [48].
Achilles tendon tears can also occur abruptly without a definite history of overuse [45]. In some patients, MR images show evidence of mucoid (silent) degeneration but not of interstitial tear, and in a smaller number of these patients, MR images show chronic tendonosis related to hypoxic degeneration [51] or no evidence of degeneration at all.
With chronic Achilles tendon tears not only are the tendon edges retracted from each other, but there is ongoing atrophy of the Achilles tendon fibers and, to a greater and more mechanically important degree, of muscle [52]. Muscle atrophy can be classified either as acute or subacute and potentially reversible or as remote and irreversible [53]. Acute atrophy manifests as diffuse edema throughout the muscle belly [54] (Fig. 20). A patient with acute atrophy has the best prognosis after surgery. Irreversible atrophy appears as a fatty infiltrated or fatty marbled muscle [55]. A small muscle may have undergone either reversible or irreversible atrophy [56].
In disorders of the Achilles, atrophy occurs first in the soleus because of the predominance of slow-twitch fibers. Because the soleus muscle is part of the Achilles tendon, soleus atrophy can be thought of as a predictor of a dysfunctional myotendinous unit. Therefore, when imaging the Achilles tendon, sagittal images should include at least 3 cm of the distal soleus belly to reveal whether soleus fatty infiltration is present. Occasionally, gastrocnemius muscle atrophy can be seen, but atropy of this muscle is rare even in remote Achilles tendon tears.
Nomenclature
One difficulty in interpreting images of Achilles tendon disorders is the inconsistent use of nomenclature in imaging and clinical articles. Clinically, there is an abrupt demarcation between tendon disorders in which the tendon is overtly torn versus those in which it is not [57]. This demarcation, although useful in triaging patients for surgery, is arbitrary and inaccurate. Mucoid degeneration can mimic a tear clinically, and silent Achilles disorders frequently have microscopic tears. We describe some commonly used clinical terms and their meanings in an attempt to develop a systematic nomenclature (Table 1).
Clinical Findings | Histologic Findings | MR Imaging Findings |
---|---|---|
Tendonitis | Paratendonitis | Partially circumferential high signal |
Acute tendonitis | Paratendonitis | Partially circumferential high signal |
Hypoxic degeneration | Thick black tendon | |
Rarely true tendonitis | Edema of Kager's fat pad | |
Insertional tendonitis | Microscopic tear | Multiple thin distal longitudinal lines on T2-weighted images |
Ca++ and ossification | Intratendon ossification | |
Enthesopathy | Posterior calcaneal enthesophytes | |
Chronic tendonitis or tendonosis | Hypoxic degeneration | Thickened tendon with flat or convex anterior margin and little internal signal |
Silent tendonitis | Mucoid degeneration | Intratendon signal that becomes more focal on T2-weighted images but has interrupted appearance on sagittal images |
Spontaneous Achilles tear | Interstitial tears (coalescent mucoid vacuoles) | Longitudinal |
Noninterrupted high signal on T2-weighted images | ||
Chronic tear | Hypoxic degeneration and tear | Horizontal disruption with a thickened tendon |
Associated Osseous Injuries and Abnormalities
The most common associated osseous abnormality in Achilles disorders is an enthesophyte at the insertion of the Achilles into the calcaneus. This enthesophyte usually maintains normal marrow signal on MR images. Occasionally, these enthesophytes show evidence of marrow edema on MR imaging (Fig. 21A,21B). In this situation, the enthesophyte may be acutely symptomatic. These edematous spurs are the types of enthesophytes that respond best to focal surgical resection. Rarely, an enthesophyte can also cause pain as the spur grows past the protective margin of the retrocalcaneal bursa.
Tendon ossification predominates distally in the tendon, appearing as focal fatty marrow. This calcification is related to insertional enthesopathy [58]. However, true Achilles enthesopathy occurs at the edge of rather than within the tendon. This dystrophic ossification may have the appearance of a broken enthesophyte, although enthesophytes are not related to the Achilles disorders. Distal ossification appearing as a broken enthesophyte is thought to be the result of partial insertion tears [59]. Whether ossification also increases the risk of Achilles tears or is merely the result of prior partial tears is unclear. Although proximal ossification may present as a mass, most patients provide a history of repetitive running-related tendonitis [60].
Somewhat more common than proximal ossification is marrow edema around the enthesophyte in response to inflammatory retrocalcaneal bursitis or as a degenerative cystic phenomenon [61] (Fig. 22A,22B). The marrow edema caused by retrocalcaneal bursitis is seen at the calcaneal margin of an enlarged bursa. The degenerative edema is often cystic or has a cyst within it, is located at the inferiormost aspect of the Achilles insertion, and is well defined.
In addition, calcaneal edema can also be a response to altered mechanics [62]. This reactive marrow edema, although seen in several ankle tendon disorders, is less commonly related to Achilles disorders (Fig. 23). If present, this calcaneal response to altered mechanics is seen anterior to the Achilles insertion.
An associated osseous injury to the calcaneus occurs in Achilles disorders as well [63]. This microavulsion injury is similar to changes seen in the elbow with epicondylitis or in the knee with medial collateral ligament tears [58, 64], but this injury may occur in Achilles disorders other than tears. It is often difficult to differentiate the types of calcaneal marrow edema (Fig. 23).
Another consideration in the differential diagnosis of calcaneal marrow edema is stress fracture [65]. Typically, stress fractures occur several millimeters anterior to the posterior aspect of the calcaneus, do not occur posterior at the Achilles insertion, and are vertically oriented.
One final differential diagnosis to consider is residual red marrow. Residual red marrow may be bright, closely mimicking marrow edema, on fat-suppressed T2-weighted or short tau inversion recovery images [66]. Residual red marrow in the calcaneus occurs in children and adolescents but rarely persists in adults. Residual red marrow has a typical location superiorly—just posterior to the posterior facet of the calcaneus—and does not closely approach the Achilles insertion. Most important, this entity is usually multifocal in the foot. If necessary, in-phase and out-of-phase imaging can confirm the diagnosis of red marrow.
Insertional Tendonitis
Insertional Achilles tendonitis is an important subtype of injury that is common in runners and frequently leads to the development of an enthesophyte. Insertional Achilles tendonitis may be the only true form of acute Achilles tendonitis. On MR imaging, the Achilles is thickened distally with vaguely seen ill-defined longitudinal high signal (Figs. 24A,24B,25,26). This signal may be fairly intense and can mimic a partial tear, albeit fairly distally.
Atypical Achilles Tears
Although most Achilles tears occurs 2-6 cm from the insertion, Achilles tears can be seen in two other locations: distally and proximally. Distal tears occur as a result either of severe end-stage “pump-bump,” with attritional tendon tearing caused by shoe friction, or of inappropriately treated or severe insertional tendonitis.
More common than an insertional tear, a proximal Achilles tear is, in reality, a musculotendinous junction injury. This strain injury is listed in the differential diagnosis for “tennis leg” [67]. Proximal Achilles tears typically involve the medial head of the gastrocnemius, are twice as common in males as in females, usually involve the dominant leg, and occur in patients ranging in age from 23 to 57 years [68] (Figs. 27,28,29). The most common risk factor is participation in sports such as football, tennis, and squash [69]. Like all muscle strain injuries, the muscles at highest risk are those that cross two joints, function eccentrically, and have a high percentage of fast-twitch fibers [56], which is the reason the gastrocnemius is affected but the soleus is not.
On axial images, myotendinous junction tears are manifested as focal fluid at the musculotendinous junction of the Achilles tendon. Fluid follows the distal margins of the muscle belly. On coronal images, tears have a U appearance because the fluid dissects down along the fascial plane of a distal muscle belly of the gastrocnemius. The tear may be complete with focal absence of the tendon at a specific level or, more commonly, the tear is partial. Incomplete tear or edema from muscle strain occurs focally in the center of the muscle.
Adjacent edema can be seen in the muscle as a component of the strain injury or as a manifestation of acute atrophy. Although the medial head of the gastrocnemius is usually involved, the resulting atrophy can affect both heads because they act in concert [69].
In these circumstances, whether an adjacent hematoma (Fig. 29) is present should be noted. A hematoma is a frequent sequela of muscle injury. Clinically, hematomas are evacuated [70]. Complete myotendinous junction tears are also treated surgically, but partial proximal myelotendinous junction tears are treated conservatively [68].
Plantar Muscle Injury
The symptoms of a ruptured plantaris tendon have been described with specific sports (e.g., “tennis leg”). The tendon can tear when forcefully contracted, resulting in the patient feeling a “pop” in the calf [71]. Sudden dorsiflexion of the ankle with the knee in extension has been implicated as the mechanism for this injury. The symptoms consist of calf pain followed by medial swelling. Clinically, this condition needs to be differentiated from Achilles tendon injuries and medial gastrocnemius muscle injuries. Clinically, the torn plantaris is considered a less severe injury than gastrocnemius muscle tears and is conservatively treated with ice, rest, and antiinflammatory medications [72].
Haglund's Disease
Haglund's disease is frequently associated with “pump”-style shoes. More important than the shoe style is the presence of a stiff-heel counter, which compresses the retro-Achilles bursa against the posterior lateral calcaneal prominence [73]. The calcaneal tuberosity may focally enlarge in response to chronic irritation [74]. This enlargement further irritates the retro-Achilles bursa and the Achilles tendon, which increases the irritation that causes further enlargement of the tuberosity. This results in a cycle of injury, response to injury, and reinjury [75].
In patients with Haglund's disease, MR images reveal excessive fluid in the retrocalcaneal bursa, fluid in the retro-Achilles bursa, and an enlarged calcaneal tuberosity (Figs. 33A,33B and 34).
The diagnosis of an enlarged calcaneal tuberosity (or of a bursal projection) is made by drawing parallel pitch lines on the upper and lower aspects on the calcaneus on sagittal images. The lower parallel pitch line is tangent to the anterior tubercle and the medial tuberosity of the calcaneus. The upper line is drawn parallel to the lower pitch line at the level of the posterior lip of the subtalar articular facet. In Haglund's disease, a portion of the tuberosity is seen above the upper pitch line [76] (Fig. 34).
Conclusion
MR imaging can provide important information about the pathologic state of the Achilles tendon, and these imaging findings can provide information that is useful in patient treatment.
Footnote
Address correspondence to M. E. Schweitzer.
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Submitted: May 3, 1999
Accepted: February 24, 2000
First published: November 23, 2012
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