Muscle moment arms and sensitivity analysis of a mouse hindlimb musculoskeletal model

Abstract

Musculoskeletal modelling has become a valuable tool with which to understand how neural, muscular, skeletal and other tissues are integrated to produce movement. Most musculoskeletal modelling work has to date focused on humans or their close relatives, with few examples of quadrupedal animal limb models. A musculoskeletal model of the mouse hindlimb could have broad utility for questions in medicine, genetics, locomotion and neuroscience. This is due to this species' position as a premier model of human disease, having an array of genetic tools for manipulation of the animal in vivo, and being a small quadruped, a category for which few models exist. Here, the methods used to develop the first three-dimensional (3D) model of a mouse hindlimb and pelvis are described. The model, which represents bones, joints and 39 musculotendon units, was created through a combination of previously gathered muscle architecture data from microdissections, contrast-enhanced micro-computed tomography (CT) scanning and digital segmentation. The model allowed muscle moment arms as well as muscle forces to be estimated for each musculotendon unit throughout a range of joint rotations. Moment arm analysis supported the reliability of musculotendon unit placement within the model, and comparison to a previously published rat hindlimb model further supported the model's reliability. A sensitivity analysis performed on both the force-generating parameters and muscle's attachment points of the model indicated that the maximal isometric muscle moment is generally most sensitive to changes in either tendon slack length or the coordinates of insertion, although the degree to which the moment is affected depends on several factors. This model represents the first step in the creation of a fully dynamic 3D computer model of the mouse hindlimb and pelvis that has application to neuromuscular disease, comparative biomechanics and the neuromechanical basis of movement. Capturing the morphology and dynamics of the limb, it enables future dissection of the complex interactions between the nervous and musculoskeletal systems as well as the environment.

Keywords: biomechanics; muscle architecture; muscle force; musculoskeletal anatomy; rodent.

Figure 1

Musculoskeletal model of a mouse's right hindlimb and pelvis developed in the biomechanics software framework. Oblique craniolateral view (a) shows the rotational centres of the hip, knee and ankle joints, which were modelled with three, one and three rotational degrees of freedom, respectively. The x, y and z axes, labelled 1, 2 and 3, respectively, for each joint are oriented the same (at 0 ° joint angle), which is the reference position or pose. Lateral view (b) shows how the 44 musculotendon units were incorporated into the model (see Fig. 2 for more details).

Figure 2

(a) A generic Hill‐type muscle model used to estimate muscle contractile dynamics in the musculoskeletal model. It consists of a contractile element (CE) connected in parallel to a passive elastic element (PE), which together represent the muscle fibres and their mechanical properties. Muscle force (F _m) depends primarily on fibre length and activation level. The contractile element is in series with a series elastic element (SEE), which represents the elastic properties of the entire tendon. Tendon force (F _t) is equal to F _m*cosα, where α represents fibre pennation angle. The entire musculotendon unit length (L _mt) is equal to L _t+ L _m*cosα, where L _m represents muscle length. Adapted from Delp et al. (1990) and O'Neill et al. (2013). (b) A realistic representation of a typical unipennate muscle, with an external tendon (L _t) and a large internal tendon (L _{t internal}), to which many muscle fibres attach. These variables together represent L _ts in the model. See Table 9 for a comparison between L _t and L _ts.

Figure 3

Select musculotendon units of the mouse hindlimb and pelvis musculoskeletal model. (a) Various hip extensors in a lateral view. (b) A craniomedial view, showing hip flexors, adductors and knee extensors. (c) A caudolateral view, showing ankle plantarflexors, ankle everters (except PB), as well as POP, a knee flexor. (d) A craniolateral view, showing ankle dorsiflexors, PB and PAT. For abbreviations, see Tables 3 and 4.

Figure 4

Positions and names of several wrapping objects placed into the musculoskeletal model. Depending on the anatomical landmark being modelled by the object, wrapping objects were shaped as either a semi‐torus or semi‐cylinder. Green points represent areas of the muscles that are being acted on by the wrapping object. Select wrapping objects in the medial hip (a), lateral thigh (b), posterior leg (c) and distal femoral (d) regions are shown. For muscle abbreviations, see Tables 3, 4, 5, 6.

Figure 5

Moment arms of musculotendon units acting around the hip joint through medial–lateral rotation (a), adduction–abduction (b) and flexion–extension (c and d) in the mouse musculoskeletal model.

Figure 6

Moment arms of musculotendon units acting around the knee joint through extension–flexion (a and b) in the mouse musculoskeletal model.

Figure 7

Moment arms of musculotendon units acting around the ankle joint through dorsiflexion–plantarflexion (a and b) and inversion–eversion (c) in the mouse musculoskeletal model.

Figure 8

Comparison between moment arms of the Biceps femoris (anterior) (a), Pectineus (b), Semimembranosus (c) and Vastus intermedius (d) muscles within the mouse and rat (Johnson et al. 2008) hindlimb musculoskeletal models, scaled to respective thigh lengths. Mouse thigh length: 16.25 mm; rat thigh length: 35.00 mm.

Figure 9

Comparison between moment arms of the Extensor digitorum longus (a), medial Gastrocnemius (b) and Tibialis anterior (c) muscles within the mouse and rat (Johnson et al. 2008) hindlimb musculoskeletal models, scaled to respective leg lengths. Mouse leg length: 17.56 mm; rat leg length: 39.57 mm.

Figure 10

Sensitivity analysis of the Gluteus maximus (dorsal) (a), Psoas major (b), Semitendinosus (c, d), Rectus femoris (e), Tibialis anterior (f) and lateral Gastrocnemius (g) muscles. Here, maximum isometric force (F _max), muscle fibre length (L _f), tendon slack length (L _ts) and fibre pennation angle were increased by 5% in turn to test the effect on maximal muscle moment.

Figure 11

Sensitivity analysis of the Gluteus maximus (dorsal) (a), Psoas major (b), Rectus femoris (c, d), Semitendinosus (e, f), Tibialis anterior (g) and lateral Gastrocnemius (h) muscles. Here, the coordinates of origin and insertion were changed ± 0.5 mm in turn to test the effect on maximal muscle moment.