A Whole-Body Musculoskeletal Model of the Mouse

Abstract

Neural control of movement cannot be fully understood without careful consideration of interactions between the neural and biomechanical components. Recent advancements in mouse molecular genetics allow for the identification and manipulation of constituent elements underlying the neural control of movement. To complement experimental studies and investigate the mechanisms by which the neural circuitry interacts with the body and the environment, computational studies modeling motor behaviors in mice need to incorporate a model of the mouse musculoskeletal system. Here, we present the first fully articulated musculoskeletal model of the mouse. The mouse skeletal system has been developed from anatomical references and includes the sets of bones in all body compartments, including four limbs, spine, head and tail. Joints between all bones allow for simulation of full 3D mouse kinematics and kinetics. Hindlimb and forelimb musculature has been implemented using Hill-type muscle models. We analyzed the mouse whole-body model and described the moment-arms for different hindlimb and forelimb muscles, the moments applied by these muscles on the joints, and their involvement in limb movements at different limb/body configurations. The model represents a necessary step for the subsequent development of a comprehensive neuro-biomechanical model of freely behaving mice; this will close the loop between the neural control and the physical interactions between the body and the environment.

Keywords: Mouse; biomechanical; biomechanics; moment-arms; musculoskeletal; neuromechanical; open-source model.

FIGURE 1.

Components of a closed-loop neuromechanical simulation. Movements in animals arise due to complex interactions between the nervous system, the musculoskeletal system and the environment. A neuromechanical model includes the neural and biomechanical components along with their interactions. Neural models (spinal and brain circuits) produce the necessary instruction signals (motoneuron activations) for a specific movement. Muscle models respond to the neural signals by producing forces that act on the skeletal model and cause movements. The skeletal model and the body interact with the environment to produce reaction forces. The sensory organ models encode the state of the movement (somatosensory afferent feedback signals) and transmit this information back to the nervous system which then adapts the instruction signals to sensed perturbations or external forces.

FIGURE 2.

Representation of skeletal model poses. (A) The skeletal model of the mouse in zero-pose, i.e., when all the joint angles are set to zero. The zero-pose need not necessarily fall into the range-of-motion for a given joint. For example, the knee joint is defined to operate between −145.0 and −45.0 with respect to the zero position. (B) An example of the mouse in a sitting posture that is defined relative to the zero-pose.

FIGURE 3.

Hill-type muscle model describing the force generation by the muscles. The contractile element (CE) or the active element produces active contraction forces. The parallel element (PE) prevents the muscle from over stretching the muscle-tendon unit during normal operation. The series element (SE) represents the series elasticity of the muscle, including the muscle-tendon. Contractile element length or fiber-length ($l_m$) is the length of muscles fibers. Pennate muscles are defined by the pennation angle α_o. Series tendon-length ($l_t$) is the length of series element. The total length of the muscle ($l_{mt}$) is defined as $l_{mt}=l_m\cos (\alpha )+l_t$.

FIGURE 4.

Polyline approximation of muscle paths. (A) and (B) show an example of an extensor muscle around the knee joint. Coordinates P_o(origin) through P_I(insertion) define the polyline muscle path. Coordinates P_O through P_WO(waypoint) are attached to the femur and coordinates P_WI(waypoint) through P_I are attached to the tibia. Thus, P_WO − P_WI is the only segment of the polyline that changes the muscle length when the joint is flexed or extended.

FIGURE 5.

Lateral view of the musculoskeletal system of the mouse. (A) right hindlimb showing the attachment of 42 muscle-tendon units and (B) right forelimb showing the attachment of 17 muscle-tendon units. For all computations in this paper, the pose of the limbs shown in (A) and (B) are used unless mentioned otherwise.

FIGURE 6.

Comparison of moment-arms from [31] (dotted lines) and current model (solid lines) for muscles (A) pectineus (PECT) and biceps femoris anterior (BFA) over hip flexion-extension range-of-motion (RoM) (B) semimembranosus (SM) and vastus intermedius (VI) over knee flexion-extension RoM (C) medial gastrocnemius (MG) and tibialis anterior (TA) over ankle flexion-extension RoM. The moment-arms are normalized by the respective thigh length (thigh_charles = 16.25 mm and thigh_current = 24.5 mm).

FIGURE 7.

Maximum moment arms (A, C) and moments (B, D) for each muscle and joint function. Grey boxes indicate joint functions for joints the muscle spans but has zero influence over. For example, a pure hip flexor muscle is considered to be spanning over both hip flexion and extension joints, but the corresponding hip extension will be in grey to indicate that the muscle has no influence on hip extension. The moment-arms and moments are normalized by the muscle which has the maximum influence in the group. $ϵ$ indicates a very low non-zero positive value.

FIGURE 8.

(A) Range of normalized muscle-fiber length (muscle-fiber length ($l_m$) normalized by optimal fiber length ($l_m^o$); ${\tilde{l}}_m=l_m/l_m^o$ for each muscle in the forelimb and the hindlimb. The range of ${\tilde{l}}_m$ is computed considering the range-of-motion of all the degrees-of-freedom the muscle spans. (B) Hill-type muscle force-length relationship showing the normalized force produced by muscle contraction (active force), by series and parallel elastic forces, and the sum of both (total force) across the ${\tilde{l}}_m$. At ${\tilde{l}}_m=1.0$ the muscle produces maximum active force in the force length curve.

FIGURE 9.

Sensitivity of joint moment-arms to changes in muscle attachment points and of joint moments to changes in muscle parameters. Analysis of muscle attachments and muscle parameters was done independently but is shown together in the figure. The colors indicate the first-order indices from the Sobol analysis. A first-order index value of 0.0 indicates that the parameter under observation has no contribution to the output’s (moment-arm/moment) variance and value of 1.0 indicates that the parameter is responsible for the total output’s variance. Analyzed DoF pairs are: Hip abduction-adduction (HA), flexion-extension (HF), internal-external rotation (HR), Knee flexion-extension (KF), Ankle abduction-adduction (AA), flexion-extension (AF), inversion-eversion (AI). Shoulder abduction-adduction (SA), flexion-extension (SF), internal-external rotation (SR), Elbow flexion-extension (EF), pronation-supination (ES), Wrist abduction-adduction (WA), flexion-extension (WF).

FIGURE 10.

(A-D) Variation of gracilis anterior moment-arms for the variation of the 3D position of the attachment points P_WO (attachment point in the parent bone of the joint) and P_WI (attachment point in the child bone of the joint) within the range of 0.5 mm for hip flexion-extension (HF), hip abduction-adduction (HA), internal and external rotation (HR) and knee flexion-extension (KF). (E-H) Variation of Gracilis anterior moments for the variation of the muscle parameters (maximum isometric force ($F_m^0$), muscle fiber length ($l_m$), tendon slack length ($l_t$) within the range of 10% of their default values for HF, HA, HR and KF.

FIGURE 11.

(A) Moment and (B) moment-arm of hip flexor muscles adductor brevis (AB), gemellus (GEM), iliacus (ILI), obturator externus (OE), obturator internus (OI), pectinus (PECT), psoas major (PMA), psoas minor (PMI), rectus femoris (RF). (C) Moment and (D) moment-arm of elbow flexor muscles anconeus (AN), brachialis (BRA), extensor carpi radialis longus (ECRL), extensor carpi ulnaris (ECU), triceps brachii lateral head (TBL), triceps brachii medial head (TBM), triceps brachii long head (TBO).