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B) Estimation of MAL under different hip joint (cm)30-32).A) Measurement of three-dimensional reference 354pennation angles were measured with a protractor at the distal myotendinous junction as the angular deviation between the muscle fibers and tendon28). The FL and pennation angles were measured and averaged in three places (superficial, intermediate, and deep portions) on the iliopsoas and in three places (on the left, right, and distal sides of the origin tendon) on the rectus femoris.Based on these data, the PCSA was calculated using the following formula, with the density of mammalian muscles represented by ρ (ρ=1.056 g/cm3)29):PCSA (cm2) = M (g) × cos θ/ρ (g/cm3) × FL Measurement of muscle MAL in skeletal specimensThe 10 lower limbs were dissected, and the loca-tions of the origin and insertion of the iliopsoas (the psoas major and iliacus) and rectus femoris were marked on the skeleton. Then, the muscles were removed to prepare the skeleton specimens. The diameter of the femoral head was measured after opening the hip joint and removing the iliofemoral and pubofemoral ligaments covering the head. Three-dimensional reference values were obtained with two reflective markers for the origin and insertion of the muscle on the skeleton, and four reflective markers on the surface of the femoral head for the joint center of the hip joint.values in the hip extension position.The MAL in the hip extension position was calculated from the three-dimensional reference values of the reflective markers attached to the skeleton that were measured with four infrared cameras and an optical motion capture system (NaturalPoint, Inc., Corvallis, OR, USA). The origin of the psoas major was marked on the T12 for the superficial head and on the costal process of L1 for the deep head, and the insertion was marked on the lesser trochanter of the femur33). The origin and insertion of the iliacus were marked on top of the iliac crest and the lesser trochanter, respec-tively. The origin and insertion of the rectus femoris were marked on the ridge of the anterior inferior iliac spine and the tibial tuberosity, respectively. The center of the hip joint was determined from the four markers attached to the femoral head surface, and the offset distance in the direction of the ball center representing the radius was deter-mined by direct measurement.angles in the sagittal plane.The MAL of the muscles was calculated from the three-dimensional reference values of the reflection markers projected on the sagittal plane as the distance between the center of the hip joint and the vector of the muscle force by Skycom soft-ware (Optitrack Japan, Tokyo, Japan). The ilio-psoas did not take a straight course between the origin and the insertion in the hip extension posi-tions in various degrees up to 60°, but a curved course around the femoral head, so that the MAL was represented by the radius of the femoral head.The psoas major (PM) had two heads whose origins were represented by the T12 vertebral body for the superficial head (PM-I) and by the L1 transverse process for the deep head (PM-II). The iliacus (IL) had a broad origin region on the iliac fossa, and the origins were represented by four points on the iliac crest including the anterior supe-rior iliac spine (IL-I), the midpoint between the former and the apex of the iliac crest (IL-II), the apex of the iliac crest (IL-III), and the posterior superior iliac spine (IL-IV). The MAL was repre-sented by the radius of the femoral head for IL-I in joint angles up to 10°, IL-II up to 30°, PM-I up to 50°, and IL-III, IL-IV, and PM-II up to 60°, and by the length of the vertical line from the hip joint center to the vector from the origins to the inser-tion (lesser trochanter of the femur) in larger joint angles. We employed the mean value of the MAL of PM-I and PM-II for the PM, and of IL-I to IL-IV for the IL.For the rectus femoris, the MAL was repre-sented by the length of the vertical line from the hip joint center to the vector from the origin (infe-rior anterior iliac spine) to the insertion (tibial tuberosity) in all of the angle regions (Figure 1).Estimation of the relative contribution to the maximal hip flexion torqueTo estimate the relative contribution of the indi-vidual flexors to the maximal hip flexion torque, we calculated an indicator of maximal hip flexion