Primary functions of the quadratus femoris and obturator externus muscles indicated from lengths and moment arms measured in mobilized cadavers

Clinical Biomechanics 30 (2015) 231–237

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Primary functions of the quadratus femoris and obturator externus muscles indicated from lengths and moment arms measured in mobilized cadavers Kjartan Vaarbakken a,⁎, Harald Steen a, Gunnar Samuelsen b, Hans A. Dahl c, Trygve B. Leergaard c, Britt Stuge a a b c

Department of Orthopaedics, Oslo University Hospital, PO Box 4956 Nydalen, N-0424 Oslo, Norway Ullevål and Tåsen Physical Therapy and Exercise Inc., Tåsen Senter, PO Box 22, Tåsen, N-0801 Oslo, Norway Department of Anatomy, Institute of Basic Medical Sciences, University of Oslo, PO Box 1105, Blindern, N-0317 Oslo, Norway

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Article history: Received 27 August 2014 Accepted 4 February 2015 Keywords: External hip rotators Human cadaver Length measurements Range of motion Function Moment arm Strength Stretch

a b s t r a c t Background: The small muscles of the pelvis and hip are often implicated in painful conditions. Although the quadratus femoris and obturator externus are usually described as external rotators of the hip, little is known about how they change their lengths and moment arms during human movement. Therefore, more precise measurements defining the positions and directions for their maximal strength and stretch are needed to better describe their functions and guide the clinical approach to pain. Methods: Repeated measurements of the muscle lengths and range of motion were obtained using wires simulating dissected muscles on human cadaver hips. The lengths were measured at every 15° of flexion with and without maximal range of ab/adduction, rotation, and combinations of the two motions. Measurements were obtained from normal hips (n = 3), and movement–lengthening relations were later differentiated into movement–moment arm relations. Findings: The quadratus femoris showed maximum lengthening by flexion, adduction or abduction, and internal rotation, with the largest moment arms observed for extension in the deduced force–length efficient range of 60–90° flexion. The obturator externus showed maximum lengthening by extension, abduction, and internal rotation, with the largest moment arms observed for flexion and adduction in the deduced force–length efficient range around the hip's neutral position. Interpretation: Our findings indicate that maximal strength of the quadratus femoris muscle will be delivered in a flexed position towards extension, while maximal strength of the obturator externus muscle will be delivered in an extended position towards flexion and adduction. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction MRI findings in athletes show that the quadratus femoris (QF) and obturator externus (OE) are amongst the most frequently injured muscles in the hip (Ansede et al., 2011) and that these injuries are regularly undiagnosed by clinicians (O'Brien and Bui-Mansfield, 2007). Most often, injuries of the QF and OE muscles are found in elite athletes of hamstring- and groin-risky sports such as tennis, soccer, badminton, and ice hockey (Ansede et al., 2011; O'Brien and Bui-Mansfield, 2007). These small pelvic–hip muscles can cause considerable disability and pain in the buttocks, groin, and hip (Kim et al., 2013; Tosun et al.,

⁎ Corresponding author at: Oslo University Hospital HF, Division of Surgery and Clinical Neuroscience, Kirkeveien 166, building 73, 2nd floor, N-0407 Oslo, Norway. E-mail addresses: [email protected] (K. Vaarbakken), [email protected] (H. Steen), [email protected] (G. Samuelsen), [email protected] (H.A. Dahl), [email protected] (T.B. Leergaard), [email protected] (B. Stuge).

http://dx.doi.org/10.1016/j.clinbiomech.2015.02.004 0268-0033/© 2015 Elsevier Ltd. All rights reserved.

2012; Travell and Simons, 2009) with symptoms fitting the clinical diagnoses of low back pain (O'Neill et al., 2002), sacroiliac joint pain (Schwarzer et al., 1995), and hip joint pain (Khan et al., 2004). Rehabilitation programs addressing these disorders typically involve the stretching and strengthening of specific muscle groups. Diagnostic precision and therapeutic efficacy, however, depend on a thorough understanding of the muscle function in various anatomical positions. There is a lack of consensus regarding how the QF and the OE are maximally stretched (Dalmau-Carolà, 2010; Evjenth and Hamberg, 1993; Kim et al., 2013) or how specific movements change the lengths of these muscles. The movement–lengthening relation is of particular functional importance because the muscle contraction force greatly depends on the muscle length, as demonstrated in isolated animal fibers (Gordon et al., 1966; Hill, 1953) and whole muscle–tendons in living humans (Hof, 2003; Maganaris, 2003). Consequently, the hip positions used for testing the peak strength (force × moment arm) should be directed according to how the muscles change length between various positions because this relationship greatly affects the in vivo strength

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(Cibulka et al., 2010) and reflects the moment arms (An et al., 1984; Delp et al., 1999). Moment arms for the QF and OE beyond the anatomical position have previously been reported in three cadaver studies, including one empirical study (n = 4) (Delp et al., 1999) and two computer-simulations (n = 2) (Dostal et al., 1986; Pressel and Lengsfeld, 1998), indicating that these muscles can move the hip in all directions except internal rotation. Although the instantaneous moment arm equals the slope of the movement–lengthening curve (An et al., 1984; Delp et al., 1999), the moment arm data do not demonstrate muscle lengthening. The only available comprehensive measurements of the movement–lengthening relations of the QF and OE are from a cadaver pilot study published in Norway (n = 3) (Samuelsen et al., 1996). These researchers reported the QF as a primary muscle for extending the flexed hip, whereas they reported the OE as a primary flexor and adductor of the extended hip. Classically, these muscles are categorized as primary external rotators of the hip in the basic anatomical position (Neumann, 2010; Paulsen et al., 2011; Standring et al., 2008), although earlier reports indicated that the QF is outside its length–force efficient range and that the OE has a small external rotation moment arm (Dostal et al., 1986; Pressel and Lengsfeld, 1998; Samuelsen et al., 1996) in that position. Improved knowledge about the position and direction of maximal strength of the QF and OE is needed to better understand the primary function of these muscles. To shed light on the primary functions of the QF and OE (defined as their maximal strength and stretch directions and positions), we measured how relevant human movements lengthen these muscles in anatomically normal cadavers. We specifically addressed how the QF and OE are stretched and relaxed in response to extension–flexion (one-dimensional), ab/adduction during flexion and rotations during flexion (two-dimensional), and combined ab/adductions and rotations during flexion (three-dimensional). The movement–lengthening relations were later mathematically differentiated into movement–moment arm relations.

for the QF (Fig. 1A) and medial and lateral for the OE (Fig. 1B). At the QF insertion, additional eye screws were placed to allow for wire tightening and measurements to be made (against the screws) as the hips were moved to new positions. At the OE insertion, a hole for the wires was drilled through the femur before an aluminum eyelet was attached laterally in the femoral socket as a contact point for the caliper. Reference collar points of metal were then pinched onto the lateral part of the wires to denote the distance-to-screw or distance-to-hole values. To control the rotation of the hip, a 30-cm aluminum rod was inserted through the epicondyles (Fig. 1C and D). The left hips were used for piloting and sensitivity testing (Vaarbakken et al., 2014), and the right

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2. Methods The Norwegian Regional Committee for Medical and Health Research Ethics, Southeast Region approved the study (2011/2612). Three anatomically normal pelvis–hip specimens from Caucasian cadavers (one female aged 59 years and two males aged 68 and 70 years) were used. The methodological approach is explained in detail in Vaarbakken et al. (2014) but key methodological features are summarized below together with pertinent details regarding the QF and the OE muscles.

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2.1. Radiographs Cadavers were screened by radiography, and only those with normal radiographs were included in the study. Bone configurations of the dissected specimens were subsequently characterized by CT imaging, where normality was demonstrated for all of the hips except for a borderline anterior offset ratio for hip 2 and a borderline anterior offset by alpha angle for hip 3 (Vaarbakken et al., 2014).

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2.2. Preparations Professional preparators embalmed the cadavers within one to three days post mortem. The specimens that were evaluated included the lower lumbar spine, pelvis and both lower extremities. The external rotators and hip capsules were exposed and isolated by the removal of all the surrounding soft tissues. The muscles were cut near their insertions to allow for natural movement of the hips and accurate placement of the muscle-simulating strings. To model the QF and OE, two brass wires per muscle were tied to eye screws placed at the periphery of the bony origins, superior and inferior

Fig. 1. Hip specimen, with muscle-strings, fixed in a custom-made frame equipped with an angle-dial for measuring flexion. (A) Posterolateral view of the superior and inferior string modeling the quadratus femoris. (B) Anterolateral view of the medial and lateral string modeling the obturator externus. (C) Superolateral view of the femur with the epicondylar rod fixed upon the flexion arm, right fixator-post, and removable frontal plate (for the spina iliaca anterior superior and pubic orientation). (D) Anterior view of the iliac fixator bolts (adjustable for width and depth), tuber ischii plate (adjustable for height), and string used for measuring ab/adduction.

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hips for reliability and the final measurements (see Sections 2.3 and 2.4 below). 2.3. Equipment and measurements The range of motion (ROM) was measured by two researchers (Vaarbakken et al., 2014) using a purpose-made fixation frame with a flexion-measuring arm and a 1° incremental goniometer (Steens Physical, Steens Inc., Moelv, NO; accuracy of ±0.03 mm/°). The pelvis was oriented in the fixation-and-measurement frame (by a frontal and a horizontal plate) before it was securely bolted. In the starting position, the femur was oriented at neutral flexion with neutral rotation and neutral adduction (Delp et al., 1999). In all positions, the flexion arm was the movement-base for additional ab/adduction and rotational movement as well as all combinations thereof. The entire measurement model, which consists of a prepared specimen in the custom-made frame, is shown in Fig. 1C and D. An accurate digital laser (Vaarbakken et al., 2014) was used to level the femur into the starting position. The muscle length was measured using inelastic brass wires and a caliper traceable to the International Organization for Standardization's (ISO) standard with an accuracy of ± 0.03 mm. The flexion arm's angle-dial was engineered using a machine with a traceable accuracy of ±0.03 mm/° (Vaarbakken et al., 2014). For each femoral position, muscle lengthening was calculated using the measured distances between the eyelet or screw and collar reference points. String lengths were measured at 15° increments of flexion from −15° to a maximum of 105°. When performing movements in two planes, each step of flexion was followed by maximum abduction and adduction and maximum internal and external rotations. Complex relations, or measurements for maximum muscle stretching and maximum muscle relaxing positions, were based on the most lengthening and shortening three-planar combinations of the two 2-planar results. These procedures were repeated at each step of flexion. The applied method of the measurement assumed the center of the femoral head as the point of rotation and the local frame of reference as fixed to the femur. In the zero position, the axes were defined as recommended by the International Society of Biomechanics (Wu and Cavanagh, 1995), whereas in the combined positions the axes were inferred from goniometric measurements (Snijders et al., 2006) using direct cadaver points, room lines, and frame lines as reference points. Flexion was measured by the frame's flexion arm with its angle-dial, whereas rotation and ab/adduction were independently measured by two researchers using a goniometer and the length was measured by one researcher using a caliper.

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The optimal ROM for clinical testing of the maximal muscle strength was assumed to be within 50% to 75% of the total lengthening distance. This assumption was based on isolated fiber force–length relations (Gordon et al., 1966) and positive associations between in vivo human abductor torque and abductor muscle lengthening (Neumann et al., 1988) with simultaneous reduction in the abduction moment arm length (Henderson et al., 2011). This rule also incorporated the reported moment arms of the QF and OE for various flexed positions (Delp et al., 1999; Dostal et al., 1986; Pressel and Lengsfeld, 1998). Movement–moment arm relations were developed using the slope of the muscle–tendon excursion versus joint angle method (An et al., 1984; Delp et al., 1999; Hughes et al., 1998; Payne et al., 2006). Polynomials of the third order were fitted to the extension–flexion lengthening data and polynomials of the second order to the ab/adduction and internal– external rotation lengthening data at each 15° of flexion. The equations were later differentiated and interpolated at 1° joint angles before key data were extracted (i.e., 0° positions for ab/adductions and rotations). To indicate the maximum strength positions and directions, we first calculated the force–length efficient range in the sagittal plane, followed by the direction and sizes of moment arms in the same plane, before the moment arms (in the force–length efficient flexional range) were compared between planes. Finally, we assigned the maximum strength direction(s) according to the one(s) with the largest moment arms in the force-efficient range. 3. Results In this paper, we present mathematically derived movement– moment arm relationships for all hips. The figures show movement– lengthening relations for one representative hip (hip 2), while similar data for all hips are available as online Supplementary Figs. (S. Figs. 1 to 3). 3.1. Reproducibility and validity Statistical control and concurrent validity in the anatomical position have been reported previously for all muscles and the calipers, respectively (Vaarbakken et al., 2014). In our earlier investigation (Vaarbakken et al., 2014), test–retest reliability of muscle lengthening showed similar curves, with low SEMs (from 1.4 to 1.8 mm) and moderate to high r values (from 0.72 to 0.98) for movements in one, two, and three planes. For angular movements in two and three planes, the reliability by the SEM ranged from 1.9 to 2.4° and r from 0.72 to 0.99 (Vaarbakken et al., 2014). 3.2. Flexion–extension

2.4. Reproducibility and validity Firstly, the reproducibility and concurrent validity of the lengthmeasurement setup were tested with various tensile forces on a wooden board with two ISO-traceable calipers from different producers. To further test reproducibility, 10 N tensions were used on all of the wires in each single specimen fixed in the frame in the anatomical position. Testing–retesting of the entire ROM and lengthening measurement model was assessed for flexion (one-dimensional, 1D), flexion and adduction (2D), and maximum lengthening at the combined positions (3D). This procedure was conducted on one protocol-specified representative muscle (Vaarbakken et al., 2014).

In the sagittal plane for all hips, we found that the QF was generally shortest in extension and lengthened by flexion (Fig. 2A). The ROM which lengthened the muscle from the middle to 75% (deduced as the force–length efficient range) spanned from approximately 60–90° and showed important extension moment arms (Fig. 2C). The peak strength (of the QF) is estimated in extension at 60–90° flexion. In contrast, for the OE most strings (4 out of 6) were deduced as force–length efficient in the range from about −5 to 30° flexion (Fig. 2B), which is where they showed important flexion moment arms (Fig. 2D). The peak strength (of the OE) is estimated in flexion at approximately −5 to 30° flexion. 3.3. Ab/adduction in flexion

2.5. Data analysis Statistical controls of the static-length models were assessed by the run-sequence y(i) versus i plots (Anon., 2013). The reproducibility of the entire ROM–lengthening model was calculated by the standard error of measurement (SEM) and Pearson product moment correlation r (Hopkins, 2000) of our test–retest measurements.

In the deduced force–length efficient flexional range (60 to 90°) of the QF, both strings showed minor lengthening due to ab/adduction (Fig. 3A). The superior string showed small adductor and abductor moment arms and the inferior string showed small adductor moment arms (Fig. 3C) when compared to the larger extension moment arms. The peak strength (of the QF) is estimated not to be in abduction or

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and the peak stretch is by extension and abduction. The OE's ab/ adduction–lengthening relations are presented in Fig. 3B (hip 2), the ab/ adduction–moment arm relations in Fig. 3D, and the lengthening of all hips in Supplementary Fig. 1C. 3.4. Rotations in flexion

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Through the deduced force–length efficient range of flexion, both the QF strings showed a gradual decrease in extra lengthening due to internal rotation when compared to flexion alone. During flexion, the superior string showed small and gradually declining external rotation moment arms. The QF's external rotation moment arms, however positive, were clearly smaller than the extension moment arms in the force– length efficient range. The peak strength (of the QF) is estimated not to be in external rotation (as compared to extension). Through the deduced force–length efficient flexional range, it appears that both OE strings were somewhat more lengthened by internal rotation than by extension alone. The external rotation moment arms, however, were small compared to both the adduction and the flexion moment arms in this range. The peak strength (of the OE) is estimated not to be in external rotation (as compared to combined flexion and adduction). Finally, we found that the QF was mostly lengthened at full flexion, for which internal rotation added very little extra length. For the lateral OE string, the greatest lengthening occurred by internal rotation combined with flexion between 45 and 80°, whereas the medial OE string was lengthened more than twofold from full extension by the addition of internal rotation. The rotation–lengthening relations of the QF and OE are shown for hip 2 in Fig. 4A and B, respectively, and for all hips in Supplementary Fig. 2. The rotation–moment arm relations are shown in Fig. 4C and D. 3.5. Complex curves For stretching, the superior string of the QF was maximally lengthened by flexion, adduction, and internal rotation, and the inferior string by flexion, abduction, and internal rotation. The maximal lengthening of the OE was by extension, abduction, and internal rotation. The complex stretching and relaxation movement relationships are shown in Fig. 5 (hip 2) and Supplementary Fig. 3 (three hips). None of the complex curves added much more to the determination of the peak strength positions and directions other than by theoretically combining the two-planed curves. 4. Discussion

Fig. 2. Flexion curves. Lengthening due to hip flexion for the quadratus femoris (A) and for the obturator externus (B) in all three hips. The vertical bars in (B) show where, in the flexional range, the lateral OE changed from being shortened to lengthened. Solid arrows indicate the deduced length–force efficient ranges. Notes for (A) and (B): H1 = hip number one, s = superior string, i = inferior string, l = lateral string, m = medial string, and negative flexion = extension (°). (C) and (D) show flexion or extension moment arms due to flexion movement in the three hips for the quadratus femoris and obturator externus, respectively. Notes: ma = moment arm, E = extension, F = flexion, E+ = extension moment arms are denoted with positive values for the QF in (C), and F+ = flexion moment arms denoted with positive values for the OE in (D).

adduction (as compared to extension), and the peak stretch directions are flexion and adduction for the superior string and flexion and abduction for the inferior string. We further measured that both OE strings were lengthened approximately two times more by extension and abduction than by pure extension. They were mostly shortened by flexion and adduction and had the largest moment arms for adduction in the deduced force–length efficient range of − 5 to 30° flexion. The peak strength (of the OE) is estimated in flexion and adduction at slight extension and abduction,

Although the QF and OE are defined as external rotators of the hip (in the anatomical position), our findings indicate that they contribute minimally to external rotation in their maximum strength positions. Our findings indicate that the maximal strength of the QF will be delivered in a flexed position towards extension and that the maximal strength of the OE will be delivered in an extended position towards flexion and adduction. Our measurements therefore indicate that the QF is a primary extensor of the flexed hip, whereas the OE is a primary flexor and adductor of the extended hip. The measurement setup employed in this study has previously documented reliable kinematics and lengths, in addition to concurrently valid lengths (Vaarbakken et al., 2014). However, the concurrent validity of the kinematics was unexamined and the old and embalmed hips were somewhat stiff in the combined positions, while the sequence of the complex motions was not applied randomly, and the sample size was small. Our removal of the adjacent deep muscles, however, is not considered to be a limitation on basis of anatomical configuration (Standring et al., 2008). Although our implementation of the muscle–tendon elongation versus joint angle method for moment arms was relatively basic for ab/adduction and rotation, our findings are consistent with earlier,

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Fig. 3. Ab/adduction curves. Lengthening due to flexion and adduction, pure flexion, and flexion and abduction for the quadratus femoris (A) and obturator externus (B) in hip 2. The solid arrows allude to the adduction function, the broken arrow to abduction function, and all arrows delimit the length–force efficient range. The vertical bar to the left in (A) marks where, in flexion, the lengthening due to adduction was higher than that due to abduction as well as the lower limit of the deduced length–force efficient range. Notes for (A) and (B): F = flexion, AB = abduction, and AD = adduction. (C) and (D) show abduction or adduction moment arms during flexion in three hips for the quadratus femoris and obturator externus, respectively. Notes: AD+ = adduction moment arms denoted with positive values and AB− = abduction moment arms denoted with negative values.

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Fig. 4. Rotational curves. Lengthening due to flexion and internal rotation, pure flexion, and flexion and external rotation for quadratus femoris (A) and obturator externus (B) in hip 2. The arrows mark the upper and lower limits of the deduced length–force efficient range of flexion for concentric external rotation function. Notes for (A) and (B): F = flexion, IR = internal rotation, and ER = external rotation. (C) and (D) show the internal or external rotation moment arms during flexion in three hips for the quadriceps femoris and obturator externus, respectively. Notes: ER+ = the external rotation moment arm denoted with positive values, IR− = the internal moment arm denoted with negative values, and ER = external rotation moment arms in (D).

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Fig. 5. Lengthening due to complex elongating-positions, pure flexion, and complex shortening-positions for (A) the quadratus femoris and (B) obturator externus in hip 2. At each 15° of flexion, three-dimensional positions for maximal stretch and maximal relaxation were graphed together with flexion. Note that motions in all three directions were not always possible to perform because the range of the last motion performed depended on the remaining capsular laxity having performed the two foregoing motions. F = flexion, AD = adduction, AB = abduction, IR = internal rotation, ER = external rotation, and na = not applicable or possible.

high-resolution data for rotation (Delp et al., 1999). A known limitation of this moment arm method, however, is that it does not graph the line of action (An et al., 1984). The force–length efficient range of a muscle is influenced by several other factors besides the movement–length relationship (Hof, 2003; Lieber and Ward, 2011; Maganaris et al., 2006). The most important of these factors is the muscle tendon slack length to muscle fiber length ratio (Anderson and Pandy, 1999; Redl et al., 2007). This ratio is low for both the QF and OE (Delp, 2014; Friederich and Brand, 1990), which makes them more force–length efficient in a confined middle to 75% lengthened range compared to muscles with high ratios (Anderson and Pandy, 1999; Maganaris, 2003). Our movement–lengthening relationships were highly similar to those of Samuelsen et al. (1996), although they reported further lengthening of the QF at 120° of flexion than that found in our study. This dissimilarity might be explained by differences in the specimen mobility. For the OE in the sagittal plane, Samuelsen et al. (1996) only reported lengthening due to extension, whereas Lee et al. (2012) reported lengthening due to both extension and flexion. The one medial string of Samuelsen et al. (1996) was in agreement with our medial strings in both the model and results, whereas the lack of agreement with the medial strings of Lee et al. (2012) might be explained by differences in anatomical models. The latter researchers did, however, report a few combined positions that concur with our OE-lengthening findings. Prior moment arm data are also in agreement with our findings for both muscles in extension–flexion, ab/adduction, and internal–external rotation (Delp et al., 1999; Dostal et al., 1986; Pressel and Lengsfeld, 1998). Until now, only Delp et al. (1999) explicitly quantified their findings beyond the anatomical starting position. A limitation in all these studies, ours included, is the lack of reporting changes in moment arms through the ranges of ab/adduction and internal–external rotation at various degrees of flexion. Muscle activation and movement data have not previously been reported for the QF. Although unstudied at this point, the QF possibly activates as an extensor and external rotator in synergy with the gluteus maximus during one-legged squatting (Reiman et al., 2012). For the OE, however, Stern and Larson (1993) found that activation peaked during flexion and adduction of the straight hip as performed in arm-suspended activities, bipedal upright walking, and vertical climbing in apes of four different species. These findings (Stern and Larson, 1993) do not support the obturators functioning as “adjusting ligaments”, “postural muscles” (Standring et al., 2008) or “dynamic stabilizers” (Retchford et al., 2013). Although Stern and Larson's activation data (Stern and Larson, 1993) are from non-human primates, they support our indicated primary function of the OE as a locomotion-important flexing adductor.

Recent reports on the diagnosis and treatment of pain originating from the QF and OE lend further support to our findings. For example, patients diagnosed by MRI with ischiofemoral impingement of the QF typically complain of pain during passive extension, adduction, and external rotation (Tosun et al., 2012). These movements can, according to our results, maximally shorten the QF and thus cause impingement by widening the muscle into a decreasing space (between the lateral ischium, trochanter minor, and the sciatic nerve). Furthermore, patients with QF pathology on MRI (e.g., tendinopathy, tendinitis, or tendon tear) frequently complain of pain during passive stretching in flexion and combined flexion, abduction, and internal rotation (Blankenbaker and Tuite, 2013; Kassarjian et al., 2011; Tosun et al., 2012). These combined movements concur nicely with those of our inferior QF-string. In addition, the OE has recently been identified as an important pain muscle. For example, in a case series, 23 patients with chronic pelvic pain who initially presented with anterolateral pelvic–hip pain on pain drawings and pressure pain on specific OE-palpation, reported a greater than 50% pain reduction, in addition to an improved walking ability, after intra-muscular and image-controlled anesthetic injections of the OE (Kim et al., 2013). High OE demands during walking concur well with the previously cited EMG-data and our strength indication. Clinicians should, however, be aware that the OE and QF are easily mixed by radiologists (O'Brien and Bui-Mansfield, 2007). Our findings may have clinical implications regarding the development of specific length strengthening exercises (Brughelli and Cronin, 2007) for the QF and OE muscles. The principle of length strengthening is to load the muscle eccentrically through its middle to upper lengths, thus inducing high forces through both active and passive tissues at large lengths. This approach is reported to increase muscle hypertrophy and lengthening (Bloomquist et al., 2013; Brughelli and Cronin, 2007; Hartmann et al., 2012) and decrease injury time in athletes (Askling et al., 2013, 2014) significantly more than exercises at inner and middle length. For the QF, one might initially eccentrically and slowly flex both hips from an easily inclined quadruple position, and progress by slowly climbing down from a high bench by eccentrically lowering the vertical body via further flexion of a weight-bearing hip over the benched knee. Similar exercises are partially supported by a trial of patients with hip disability (Vaarbakken and Ljunggren, 2007), but more clinical research on this topic is needed. 5. Conclusions This cadaver study indicates that maximal strength of the QF will be delivered in a flexed position towards extension with a corresponding important influence on squatting and climbing. Maximal strength of the OE will likely be delivered from an extended position towards

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flexion and adduction with an important influence on initiating swing during locomotion. Our findings suggest that the QF is an extensor of the flexed hip, whereas the OE is a flexor and adductor of the extended hip. Maximum stretch of the QF is by flexion, abduction or adduction, and internal rotation, whereas the maximum stretch of the OE is by extension, abduction, and internal rotation. These findings may improve the diagnostics and exercise progressions for these frequently injured pelvic–hip muscles. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.clinbiomech.2015.02.004. Conflict of interest statement All authors hereby declare not to have any financial and personal relationships with other people or organisations that could inappropriately influence (bias) this work. Acknowledgments We thank Espen Petersheim and Gunnar Ljunggren for their expert assistance with embalming and preparing the specimens, Knut Rekdahl and his crew at the Mechanical Workshop at the Institute of Basic Medical Sciences for the expert assistance with design and construction of the custom measurement frame, Kathrine Lamark and Mette Karen Henning for the assistance with acquisition of hip X-ray and CT images, and Ragnhild Beate Gunderson for the specialist radiological interpretation of the X-ray and CT images. We also thank Espen Petersheim for the valuable assistance with photography and image processing. This work was funded by grants from the Norwegian Fund for Post-Graduate Training in Physiotherapy and the Foundation for the Promotion of Sports Medicine and Sports Physiotherapy in Norway. References An, K.N., Takahashi, K., Harrigan, T.P., Chao, E.Y., 1984. Determination of muscle orientations and moment arms. J. Biomech. Eng. 106, 280–282. Anderson, F.C., Pandy, M.G., 1999. A dynamic optimization solution for vertical jumping in three dimensions. Comput. Methods Biomech. Biomed. Engin. 2, 201–231. Ansede, G., English, B., Healy, J.C., 2011. Groin pain: clinical assessment and the role of MR imaging. Semin. Musculoskelet. Radiol. 15, 3–13. Askling, C.M., Tengvar, M., Thorstensson, A., 2013. Acute hamstring injuries in Swedish elite football: a prospective randomised controlled clinical trial comparing two rehabilitation protocols. Br. J. Sports Med. 47, 953–959. Askling, C.M., Tengvar, M., Tarassova, O., Thorstensson, A., 2014. Acute hamstring injuries in Swedish elite sprinters and jumpers: a prospective randomised controlled clinical trial comparing two rehabilitation protocols. Br. J. Sports Med. 48, 532–539. Blankenbaker, D.G., Tuite, M.J., 2013. Non-femoroacetabular impingement. Semin. Musculoskelet. Radiol. 17, 279–285. Bloomquist, K., Langberg, H., Karlsen, S., et al., 2013. Effect of range of motion in heavy load squatting on muscle and tendon adaptations. Eur. J. Appl. Physiol. 113, 2133–2142. Brughelli, M., Cronin, J., 2007. Altering the length–tension relationship with eccentric exercise: implications for performance and injury. Sports Med. 37, 807–826. Cibulka, M.T., Strube, M.J., Meier, D., Selsor, M., Wheatley, C., Wilson, N.G., Irrgang, J.J., 2010. Symmetrical and asymmetrical hip rotation and its relationship to hip rotator muscle strength. Clin. Biomech. 25, 56–62. Dalmau-Carolà, J., 2010. Myofascial pain syndrome affecting the quadratus femoris. Pain Pract. 10, 257–260. Delp, S.L., 2014. Musculotendon parameters for lower limb muscles. http://isbweb.org/ data/delp/Muscle_parameter_table.txt. Delp, S.L., Hess, W.E., Hungerford, D.S., Jones, L.C., 1999. Variation of rotation moment arms with hip flexion. J. Biomech. 32, 493–501. Dostal, W.F., Soderberg, G.L., Andrews, J.G., 1986. Actions of hip muscles. Phys. Ther. 66, 351–361. Evjenth, O., Hamberg, J., 1993. Muscle Stretching in Manual Therapy: A Clinical Manual. Alfta Rehab, Alfta, Sweden. Friederich, J.A., Brand, R.A., 1990. Muscle fiber architecture in the human lower limb. J. Biomech. 23, 91–95. Gordon, A.M., Huxley, A.F., Julian, F.J., 1966. The variation in isometric tension with sarcomere length in vertebrate muscle fibres. J. Physiol. 184, 170–192.

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