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Biomechanics of Musculoskeletal System andIts Biomimetic Implications: A Review

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Corresponding author: Lei RenE-mail:  lei.ren@manchester.ac.uk

Journal of Bionic Engineering 11 (2014) 159–175

Biomechanics of Musculoskeletal System and Its Biomimetic

Implications: A Review

Lei Ren1,2

, Zhihui Qian2, Luquan Ren

2 

1. School of Mechanical, Aerospace and Civil Engineering , University of Manchester , Manchester M 13 9 PL, UK  

2. Key Laboratory of Bionic Engineering  ( Ministry of Education, China), Jilin University, Changchun 130022, P . R. China 

Abstract 

Biological musculoskeletal system (MSK), composed of numerous bones, cartilages, skeletal muscles, tendons, ligaments

etc., provides form, support, movement and stability for human or animal body. As the result of million years of selection and

evolution, the biological MSK evolves to be a nearly perfect mechanical mechanism to support and transport the human or

animal body, and would provide enormously rich resources to inspire engineers to innovate new technology and methodology todevelop robots and mechanisms as effective and economical as the biological systems. This paper provides a general review of

the current status of musculoskeletal biomechanics studies using both experimental and computational methods. This includes

the use of the latest three-dimensional motion analysis systems, various medical imaging modalities, and also the advanced

rigid-body and continuum mechanics musculoskeletal modelling techniques. Afterwards, several representative biomimetic

studies based on ideas and concepts inspired from the structures and biomechanical functions of the biological MSK are dis-

cussed. Finally, the major challenges and also the future research directions in musculoskeletal biomechanics and its biomimetic

studies are proposed.

Keywords: musculoskeletal system, biomechanics, multi-scale, biomimetics, biologically inspired robots and mechanisms

Copyright © 2014, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved.

doi: 10.1016/S1672-6529(14)60033-0

1 Introduction

A musculoskeletal system (MSK) is a biological

system composed of bones, cartilages, skeletal muscles,

tendons, ligaments and other connective tissues (see

Fig. 1). The major function of the MSK is to provide

form, support, movement and stability for the human or

animal body. The MSK can be roughly considered to

have two constituent sub-systems: the skeletal system

and the muscular system.

The skeletal system consists of all the bones in the body and also the connecting tissues, e. g . cartilages and

ligaments. The skeletal system provides the fundamental

framework for body shape and load bearing, and also

 protects internal organs, e. g . brain, heart, lungs and liver

etc., from external impacts. In the skeletal system, bones

are connected to each other by joints, which provide

articulations in MSK. The most common type of joint is

synovial joint, which consists of fibrous connective

tissue capsule (ligaments) and the periosteum of the

connecting bones lubricated by synovial fluid inside of

the joint.

The muscular system is the prime mover of human

or animal body. For humans, there are approximately

Fig. 1  The musculoskeletal system of human body[1].

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 Journal of Bionic Engineering (2014) Vol.11 No.2 160

over 430 skeletal muscle groups accounting for up to

40% of body weight[2]

. The skeletal muscles are made up

of hundreds, or even thousands of muscle fibers, which

range in thickness from approximately 10 μm to 100 μm

and in length from about 1 cm to 30 cm[2]

. Skeletal

muscles are also arranged in layers over the bones, and

they are normally attached to bones through tendons so

that the forces generated by the contractile elements of

the muscle fibers can drive body motions.

As the result of million years of selection and evo-

lution, the biological MSK evolves to be a highly effi-

cient and economic mechanical mechanism to support

and transport the human or animal body with many ex-

traordinary characteristics compared to their man-made

counterparts. For example, cheetah is known as the

fastest living land quadrupedal animal, which can reach

to a speed of 29 m·s−1[3]

. Some special features of chee-

tahs’ MSK have been reported probably contributing to

attaining such a high speed. For example, their divergent

talar ridges may help to avoid limb interference in the

aerial phase of galloping. Their long hindlimb bones

may potentially assist them in making large stride length.

Moreover, their particularly large psoas muscles may

help them to rapidly protract the hindlimbs and also to

resist pitching moments around the hip during acceler-

ating[4]. Another example is horses, a representativeathletic ungulate land animal with excellent locomotor

capacity. Their third metacarpus bone has a small hole

where blood vessels enter the bone[5]

. As common

knowledge from mechanical engineering, holes nor-

mally weaken structures by increasing dramatically the

stresses near the holes as a result of stress concentration[5]

 

(see Fig. 2). However, the holes at the third metacarpus

 bones of horses do not appear to cause bone fractures

even for racing horses. This is probably due to an in-

creased compliance near the foramen[5]

. The sharp dis-

continuity in geometry due to the hole is softened by an

embedded compliant region[5]

. A reinforcing ring with

increased stiffness, together with the ring of lamellar

 bone along the foramen’s inner edges, might help to

reduce the possibility of cracking[5]

. The special con-

figuration of the hole helps to move the highest stresses

away from the foramen to regions with higher material

strength[5]

 (see Fig. 2).

The human foot complex is another good example

of highly efficient mechanical mechanism from the

 biological world. The human foot is a complicated

structure comprising numerous bones, muscles, tendons,

ligaments, synovial joints and other tissues. It has been

found recently that such a small body component de-

livers multiple critical biomechanical functions in at-

tenuating ground impact, supporting body against grav-

ity, maintaining locomotor stability, generating and

transmitting propulsive power during locomotion[6–8]

.

The fascinating structure and characteristics of the

 biological MSK, which has been optimally selected after

million years’ evolution, would provide enormously rich

resources to inspire engineers to innovate new technol-

ogy and methodology to develop mechanisms and ma-chineries as effective and economical as the biological

systems. For example, legged locomotion, as a biologi-

cal transportation solution over rough terrain, has been

attracting intensive researches from mechanical engi-

neering and robotics field[9–13]

. This may greatly facili-

tate the development of legged robots with high agility,

stability and energy efficiency.

Δ  =1  . 5 MP  a 

 Fig. 2  The foramen in horse third metacarpus bone and its stress analysis[5].

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Ren et al .: Biomechanics of Musculoskeletal System and Its Biomimetic Implications: A Review 161 

This paper starts with a brief introduction of the

MSK and the biomechanics of its constituent compo-

nents. Afterwards, a general review of the current status

of the MSK biomechanics, including both experimental

and computational studies, is provided. Several repre-sentative biomimetic examples based on inspired ideas

from MSK biomechanics are discussed. Finally, the

major challenges and also the future research directions

in MSK biomechanics and its biomimetic studies are

 proposed.

2 Experimental studies of MSK biomechanics

2.1 Motion capture

In the past decades, motion capture technique has

 been increasingly used in recording the two-dimensional

(2D) or three-dimensional (3D) human/animal motion,

which is characterized by the time histories of segmental

or joint angles. Generally, optoelectronic motion analy-

sis systems are employed by using infrared camera ar-

rays to track the positions of active or passive markers

 placed on the body segments of interest[14–22]

 (see Fig. 3).

Although the optoelectronic motion capture technique

has now been widely used in human/animal movement

studies, the collected data normally suffer from some

technical problems, e. g . skin artifact (due to the relative

movement of skin mounted markers with respect to the

underlying bones)[16,23–25]

, light reflections and marker

occlusions[26]

. Markerless motion tracking method based

on computer vision provides a new promising motion

capture technique[27]

. Currently, the markerless systems

can work with large, obvious movements, while the

measure of more subtle movements still remains chal-

lenging.

To complement the motion capture, many biome-

chanics labs are also equipped with force sensing de-

vices to record the simultaneous kinematic and kinetic

data associated with human/animal motions. 3D force platforms are normally used to measure the ground re-

action forces and moments induced by human/animal

motions. Integrated with the simultaneous motion data,

 joint kinetic analysis can normally be conducted by

using the inverse dynamics method[17,28–30]

. Additionally,

 pressure plates are often employed to record the foot

 pressure distribution during human/animal motions[31 – 34]

.

In addition to multi-camera systems, portable motion

sensors are also used to capture human/animal body

motions, e. g . inertia sensors (i.e. accelerometers, gyro-

scopes etc.) and magnetometers etc.[35 – 38]

. This offers an

alternative way to measure the human/animal motions

outdoors without the constraints of the indoor equip-

ments[39,40]

.

2.2 Surface electromyography

Human or animal electromyography signals at dif-

ferent motor activities can be recorded using invasive or

non-invasive methods. Surface electromyography

(sEMG) is a non-invasive technique widely used for

detecting and recording muscle electrical activity that

occurs during muscle contraction and relaxation cycles

 by using surface electrodes. The sEMG signal is nor-

mally used in musculoskeletal biomechanics studies as

an indicator of the initiation of muscle activation, as an

estimator of the force produced by a contracting muscle,

or as an index of the fatigue occurring within a mus-

cle[28,41,42]

. In other words, sEMG signals may contain

information about whether a muscle is active or not, if a

muscle is more or less active, when it is on and/or off,

and also if it fatigues[43]

. However, raw sEMG data maycontain mixed electrical signals from multiple muscles

nearby the electrodes and/or noisy signals due to

movement artifact, so dedicated signal processing is

normally needed before useful information can be ob-

tained to interpret the muscle functions[28,44,45]

.

2.3 Medical imaging

Medical imaging domains, e. g . Computed Tomo-

graphy (CT), Magnetic Resonance Imaging (MRI), ul-

trasound, are very useful techniques to examine theanatomy, geometry and structure of a MSK. Among

Head

Humerus

Forearm+hand

Thigh

Shank 

Foot

Pelvis

gr  F gr 

gl

gl F 

 X 

Y 

 Z 

Torso

 Fig. 3 The three-dimensional whole body model with 13 seg-ments and 12 connecting joints. A specially designed marker

cluster system mounted on plastic plates was used to capture thesegmental motions[17].

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them, the ultrasound provides an economic noninvasive

imaging technique by transmitting high-frequency

sound waves through a body part. As a handy diagnostic

tool, ultrasound has been widely employed in muscu-

loskeletal biomechanics studies to investigate the in vivo 

muscle structure, muscle fiber movement, neuromus-

cular disorders etc.[46 – 49]

. Although superficial muscles

may be easily detected by ultrasound probes, it is diffi-

cult to identify individual small muscles when multiple

muscle groups are involved[50]

. Additionally, due to the

reflection or absorption of sound by superficial tissue

layers, it is still challenging for ultrasound to detect

deeper muscles especially in the pelvic region or around

the trunk. Since ultrasound has difficulty in penetrating

 bones, to examine the structure of bones, or a particular

musculoskeletal complex, e. g . certain joints or body

segments, other imaging modalities, such as CT and/or

MRI, are generally used.

3 Biomechanical MSK modelling

3.1 Rigid body modelling of MSK

Rigid body dynamics is typically used to simulate

human/animal motions by considering the body seg-

ments of interest as rigid bodies without any deforma-

tions. Over the past decades, numerous rigid body

models have been developed to simulate human/animalmovements or motions of particular body parts with

varying complexity from simple one-segment model

with 1 DOF to complex model with 10 segments and 23

DOFs[17,51 – 66]

  (see Fig. 4). In those models, the con-

necting joints are typically defined as frictionless

 ball-and-socket joints, hinge joints or universal joints.

Whilst the mechanical behaviour of muscles was nor-

mally represented using Hill-type models[56,66,67]

, where

the normalized muscle force of the contractile element is

the product of three independent experimentally meas-

ured factors describing the force-length property, the

force-velocity property and the dynamics of neural ac-

tivation[56,57]

. Model simulations can be applied in two

different ways, which are usually referred to as the

forward (direct) dynamics method, and the inverse dy-

namics method. In the forward dynamics method, the

motions of the segments are determined by integrating

the equations of motion based on predefined joint mo-

ment or muscle force/activation data[53,61,65,66,68,69]

. In the

inverse dynamics method, the joint forces and moments

are determined based on the measured joint or segment

motion data[17,28–30,66]

.

Biomechanical analysis based on rigid body models

can be applied to a wide range of problems, such as the

assessment of the effect of tendon transfer surgeries[69 – 71]

,

the investigation of multi-segment interaction[72,73]

, the

musculoskeletal performance during walking and

 jumping[65,68,74 – 76]

, the development of neural prosthe-

ses[77]

, the neural control principles of movement[78 – 80]

,

the effect of musculotendon loss or damage on theoverall joint moment capacity

[81], and the effect of load

carriage design on walking performance[82]

. Recently,

several software packages have been developed for rigid

 body musculoskeletal model construction, simulation

and analysis, e. g . SIMM[69]

, OpenSim[83]

, AnyBody[84]

,

MSMS[77]

  etc., which normally provide graphical user

interface for general users.

Despite the recent great progress and success, there

are still some major unsolved problems in rigid body

musculoskeletal modelling. Firstly, the anatomical jointsare typically simplified as ideal ball-and-socket or hinge

 joints to reduce computational load, which are not real-

istic representations of most biological joints. In addi-

tion, there are still a large amount of works needed to

improve the  in vivo  representation of musculotendon

mechanics and neural dynamics, especially on a sub-

 ject-specific basis. Finally, the development of predic-

tive musculoskeletal models, which are capable of pre-

dicting kinematic and kinetic variables during motions

with minimal measurement inputs, still remains as a very

challenging task [61,66,85]

.Fig. 4  A large-scale musculoskeletal model with 23 generalizedDoFs and 54 musculotendon actuators[61].

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Ren et al .: Biomechanics of Musculoskeletal System and Its Biomimetic Implications: A Review 163

3.2 Continuum mechanics modelling of MSK

Over the past decades, methods based on contin-

uum mechanics, e. g . Finite Element (FE) method,

 boundary element method etc., have been increasingly

used to investigate the mechanical behaviour of mus-culoskeletal structures by considering constituent com-

 ponents as deformable bodies. The FE method is a very

useful numerical tool to handle biological structures

normally with highly non-linear material properties,

irregular geometries and complicated boundary condi-

tions. Recently, the FE method has been widely used in

 biomechanical studies of MSK, covering a broad range

of topics, e. g . functions of musculoskeletal complexes,

mechanics of joints and skeletal muscle mechanics etc.

3.2.1 FE modelling of musculoskeletal complexes

The FE method has been particularly useful to in-

vestigate the mechanical behaviour of specific muscu-

loskeletal complexes of the human body, normally

comprising numerous bones, joints and soft tissues, e. g .

the spinal column or the ankle-foot complex. Substantial

FE studies have been conducted on the biomechanics of

cervical vertebrae, thoracic vertebrae and lumbar verte-

 brae. Some earliest works involves the modelling of the

cervical spine and the lumbar vertebral motions[86 – 90]

.

Saito et al . constructed a spine model to analyze the

 prevention of spinal column deformity with oversimpli-

fied representation of vertebral geometry and the in-

ter-vertebral joints, which may lead to an unrealistic

assessment of load sharing and stress distributions[91]

.

The model may be suitable for the study of gross re-

sponses of the whole column rather than the local

changes at the individual vertebrae level. Kleinberger

 presented a sophisticated model including head and

various spinal components for FE analysis[92]

. However,

the model lacked sound representations of the anatomi-cal structure of the spine probably because the major aim

of the study was for crash impact analyses rather than

medical applications. The three-segment lower cervical

spinal unit model constructed by Voo et al . had a rea-

sonable representation of the cervical anatomy based on

CT scans and cryomicrotome anatomical sections[93,94]

,

which could be extended to the construction of the entire

cervical column. Most of the FE studies of spinal col-

umn are based on static analysis[95 – 97]

. Although internal

stresses, strains and other biomechanical responses un-der complex loading conditions could be predicted, they

 provide very little information about the in vivo condi-

tion of the whole column during dynamic motions.

Whereas some FE models consisting of a series of

connected vertebrae could predict the dynamic re-

sponses of the spine to external loads

[98,99]

. Zhang et al .constructed a detailed cervical spine model (C0-C7)

[100].

The predicted biomechanical response of human neck

under physiological loadings, near vertex drop impact

and rear-end impact conditions, were analyzed and

compared with published measurement data, demon-

strating potential for future biomedical and traumatic

studies.

The human foot is a very complex structure com-

 prising numerous bones, joints and soft tissues, deliver-

ing a variety of biomechanical functions during human

motions. Over the past decades, a large number of studies

 based on FE method have been conducted to investigate

the biomechanical functions of the foot complex. Lem-

mon et al . used a 2D FE model to study the effect of

insoles on therapeutic footwear based on quasi-static

simulations[101]

. Patil et al .[102]

 conducted a stress distri-

 bution study on normal and neuropathic feet during gait

using a 2D model, which was constructed from a lateral

X-ray image. Wu[103]

 constructed a 2D FE model to study

the foot bone and muscle stresses resulting from plantar

fasciotomy and major plantar ligament injuries. Chu et

al .[104]

  conducted a static parametric analysis using an

asymmetric 3D FE foot model to investigate the an-

kle-foot orthosis effects by considering the foot complex

as a single segment. Jacob et al .[105]

 developed a 3D FE

model with the purpose being to investigate the contrib-

uting factors to disintegration of tarsal bones in Hansen’s

disease and diabetes. Gefen et al .[106]

 constructed a sub-

 ject-specific 3D foot model based on realistic bone ge-

ometry to investigate the biomechanical foot function

during gait. The stress distribution analysis was con-ducted at six representative instants of time during gait.

Gefen[107,108]

  also developed a 2D FE model to investi-

gate the foot biomechanics following surgical plantar

fascia release and also to evaluate the plantar stress dis-

tribution of a standing diabetic foot. Cheung et al .[109– 111]

 

developed a more complicated 3D foot model by using

realistic bone geometry and nonlinear material properties.

The model was used to investigate the effects of plantar

fascia stiffness and Achilles tendon loading, and also to

conduct the parametric design using different structuraland material properties of a foot orthosis. Recently, the

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foot plantar fascia mechanics, stress concentration in

 plantar soft tissues and also the load transfer mechanism

were analyzed using different 3D FE foot models[112 – 116]

.

However, it is noteworthy that almost all these studies are

static or quasi-static in nature. So far, very few foot

 biomechanics studies used dynamic FE analysis. Dai et

al .[117]

 used a 3D foot model to investigate the effect of

sock wearing on the plantar pressure under different

contact conditions from the foot-flat to the push-off

during the stance phase of gait based on dynamic FE

simulations. However, constant loads were assumed and

extra constraints were used to define the model, which

may lead to unrealistic motion of the foot complex. Very

recently, a fully dynamic foot model without any extra

constraints has been developed to simulate the dynamic

 behaviour of the human foot structure during stance

 phase of walking, which has demonstrated some advan-

tages over the traditional static or quasi-static FE mod-

els[118]

 (see Fig. 5).

3.2.2 FE modelling of musculoskeletal joints

The FE method has also been extensively used to

investigate the joint mechanics, especially the contact

stress and strain responses of different joint components.

Brown and Digioia[119]

 used a 2D FE model to analyze

the articular contact at hip joint, by representing the

cartilage using non-linear contact elements. An

axis-symmetric FE model of meniscus was proposed

with non-linear material properties, and the simulation

results suggested high radial strains in the regions where

lesions were most often observed[120]

. Eckstein[121]

 used

the FE model to analyze the stress distribution at elbow

 joint, and found that incongruity generates advantageous

mechanical stimuli in the joint tissues. The FE method

was also applied to the shoulder mechanism by using

truss, hinge and surface elements to construct the

model[122]

. Sophisticated FE models of the knee joint

were also reported to study the meniscus and the contact

condition between cartilage and meniscus[123 – 125]

. In

addition to cartilages, ligaments are also important

components of a musculoskeletal joint. Usually, 1D

element was employed to represent ligaments in FE

modelling of joints. The 1D representation requires only

few parameters to define the mechanical behaviour. This

approach was proved useful for predicting joint kine-

matics under the application of external loads[126]

. But it

has some shortcomings: (1) non-uniform 3D stresses and

strains cannot be predicted; (2) multiple sets of pa-

rameters and initial tensions routinely produce nearly

identical predictions of joint kinematics[127]

. Ligaments

t = 0 (s) t = 0.03 (s) t = 0.08 (s)

t = 0.27 (s)t = 0.23 (s)t = 0.19 (s)

t = 0.40 (s) t = 0.43 (s)

t = 0.45 (s)t = 0.44 (s)  

Fig. 5  The von Mises stress distribution predicted by a dynamic finite element foot model at 10 representative instants oftime over the whole stance phase of human walking [118].

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Ren et al .: Biomechanics of Musculoskeletal System and Its Biomimetic Implications: A Review 165 

are subjected to highly non-uniform deformations in vivo 

that result from a combination of tension, shear, bending,

and compression[128,129]

, and the regional contribution of

a ligament to joint stability changes with joint orienta-

tion

[130,131]

. Therefore, 3D FE modelling is desirable torepresent these mechanical characteristics

[132–134]. The

FE modelling of musculoskeletal joints offers a useful

tool to predict the spatial and temporal variations in joint

contact stresses and strains, which are difficult or im-

 possible to obtain experimentally.

3.2.3 FE modelling of skeletal muscles

As the prime mover of the MSK, skeletal muscles

demonstrate very complicated mechanical properties

coupled with neural excitations and muscle fibre con-

tractions[135,136]

. Currently, most of the mathematical

representations of muscle contraction mechanics are

 based on either Hill’s model or Huxley’s theory[137 – 140]

.

Hill’s model depicts the dynamics of a musculotendon

unit using a set of connected discrete mechanical ele-

ments. This could help stimulate some initial schemes

toward a simple FE model of skeletal muscles[141]

.

Some initial works on FE modelling of skeletal

muscles involved the representation of muscle-tendon

complex using a number of simple active 1D line ele-

ments, each of which is composed of motor and vis-

coelastic elements. Since the 1D line elements did not

have volumes and masses, the information about muscle

tissue stresses and inertia effects could not be obtained.

Moreover, the muscle moment arms were assumed to be

equivalent for all fibres within a muscle compartment.

This limits the ability of the model to accurately repre-

sent the actual paths of muscles with complex geometry

and also the stress response of the active part and passive

 part individually. A 3D FE muscle model has the poten-

tial to represent the complex muscular structures andimprove our understanding of the musculotendon me-

chanics[58]

. Since a skeletal muscle consists of contrac-

tile muscle fibres arranged within a passive matrix of

connective tissues[142]

, a number of FE models have been

developed to describe the active behaviours of skeletal

muscles. Tsui et al .[143]

  constructed a 3D active FE

muscle model by using a user-defined muscle behaviour.

The simulation results of isometric force-length rela-

tionship and force-shortening contraction demonstrated

the potential of the model for studying muscle damageand fatigue. Tang et al .

[140] developed a 3D FE model of

skeletal muscles by integrating a modified Hill’s muscle

model with a muscle fatigue formula, but neglected the

different fibre types inside of the muscle. Based on the

two-state Huxley model, Oomens et al .[144]

 constructed a

3D muscle model to estimate the inhomogeneous straindistribution in a skeletal muscle. A good agreement

 between the measurement data and the simulation result

showed the proposed model could be employed as a tool

for studies on damage and adaptation of skeletal muscles.

Different from the mechanical properties during active

conditions, the passive muscle behaviour was normally

represented by non-linear hyperelastic or viscoelastic

constitutive relationship in the FE modelling of the

skeletal muscle[140,145,146]

 (see Fig. 6).

Due to the highly anisotropic, nonlinear material

 property, and also the complex geometry (multiple layers

of soft tissue) and boundary conditions, 3D FE modelling

of stress-strain behaviour of skeletal muscles is normally

complicated and computationally demanding. The tradi-

tional solutions for FE simulations based on standard

Extended

Flexed 

Fig. 6 The reconstructed 3D muscle models of gluteus maximus,

gluteus medius, iliacus, psoas by segmentation of MR images[146].

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 Journal of Bionic Engineering (2014) Vol.11 No.2 166

non-linear FE formulations are time-consuming even for

one or two muscles[147]

. Blemker et al .[148]

 developed a

quasi-static invertible FE algorithm to reduce the com-

 putational load, which provided two major improve-

ments over the traditional methods: (1) elements are

allowed to invert by computing robust FE forces with a

invertible framework; (2) the stiffness matrix is positive

semi-definite.

 Nowadays, mathematical models representing the

mechanical behaviours for muscle-tendon complexes

used for studying the dynamics of the human MSK are

dominated by various Hill-type models[149 – 151]

. The de-

velopment of bio-realistic and computationally efficient

FE models of the muscular system for assessing the

dynamic functions of biological MSK is still at its very

early stage.

4 Biomimetic studies inspired by MSK bio-

mechanics

4.1 Bioinspired quadrupedal robot - BigDog

BigDog is a dynamically stable quadrupedal robot

developed by Boston Dynamics[152]

, with aim being to

 provide load carriage service to accompany soldiers in

harsh rough terrains, which are impossible for conven-

tional vehicles with wheels or treads. The size of the

robot is of a large dog or a small mule, about 1.1 m long

and 1 m tall, and weighs 109 kg. The robot has four legs

that are articulated like a typical quadrupedal animal,

with compliant elements to absorb shock and store en-

ergy during moving. It is capable of performing a variety

of locomotion behaviours, such as walking, running,

climbing, jumping and carrying heavy loads in

rough-terrain conditions[152]

.

Ideas and concepts inspired from quadrupedal

animals have been used in the structure and actuation

design, sensor and motion control of the BigDog robot.The single leg structure, in terms of joint configuration,

standing posture and actuator position, is very similar to

the leg of a typical quadrupedal animal (see Fig. 7).

Going distally from hip joint to metatarsal joint, the leg

actuation of a typical quadrupedal animal becomes less

strong, and contains more compliance. In addition, the

forelimb and hindlimb configuration of the BigDog uses

similar design principle of the four-legged configuration

in horses, dogs and goats[153,154]

. As the compliant

components of animals’ MSK play important role duringdynamic moving, such as running, jumping and gallop-

ing[155]

, spring components are integrated into the leg of

the BigDog to attenuate the ground impact during dy-

namic moving (see Fig. 7). When moving on the ground,

the joint position, joint force, ground contact, ground

load and external obstacles of the robot are monitored by

using onboard sensors to ensure its dynamic balance and

stability. The robot could also behave like quadrupedal

animals to adapt to the local terrain variation by adjust-

ing its body height and attitude, and also foot placements.

Based on those bio-inspired ideas and concepts, the

BigDog exhibits excellent locomotion performance, e. g .

it can climb slopes up to 35 degrees, walk across rubbles,

climb muddy hiking trails, walk in snow and water etc.

So, the BigDog has been considered as one of the most

advanced quadrupedal robots moving on rough ter-

rains[152]

.

4.2 Efficient human-like robot with compliant legs

Over the past decades, many bipedal robots

have been developed to mimic human locomo-

tion[10,12,13,156 – 163]

. Most of those walkers used precise

control to regulate the angle values of each individual joint at each instant of time during locomotion. This

requires actuators with high precision and frequency

response, a precise environment model and also high

energy cost[10,12,13]

. Recently, the concept of passive

dynamic waking, which needs less actuators and active

control than mainstream robots, was proposed as a new

design and control paradigm[159 – 162,164]

. It has been

demonstrated that periodic stable walking can be

achieved with high energy efficiency and little control

 by integrating simple actuations into passive dynamicwalkers

[160].

Fig. 7  The bio-inspired back leg of the BigDog robot compared

to the hindlimb of a typical quadrupedal animal[152].

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Ren et al .: Biomechanics of Musculoskeletal System and Its Biomimetic Implications: A Review 167

A recently developed bipedal robot based on the

 passive dynamic walking concept, used minimum con-

trol to drive two elastic legs inspired from the structure

of the human leg MSK [164]

. The robot consists of seven

 body segments, two servomotors at the hip joints, four passive joints at knee and ankle joints, and totally eight

linear springs (see Fig. 8). The spring components were

used to mimic the passive mechanical function of the

major musculotendon units in human legs. A unique

feature of the robot is that it has six springs spanning

over two joints to mimic the major biarticular muscles in

the leg. The experimental study showed that this

 bio-inspired bipedal robot could produce human-like

walking gait by using extremely simple control without

sensory feedback [165]

. This is a good example for de-

velopment of bipedal robots with higher energy effi-

ciency and more natural walking pattern based on ideas

inspired from the biological structure of the MSK.

Hip motor 

Springs

Passive joints

Rubber 

(a) (b)

(c)

 Fig. 8  The human-like bipedal robot with compliant legs[165]. (a)

 bipedal robot model, only one leg is shown; (b) schematic of therobot design; (c) the physical robot platform.

5 Challenges and future directions

The last decade has seen great progress and ad-

vance in the human/animal movement studies, which

aim for understanding the biomechanical functions ofthe biological MSK using both experimental and com-

 putational approaches. However, due to the great com-

 plexity of the biological MSK, there still remain many

unsolved problems and grand challenges in muscu-

loskeletal biomechanics. Skin artefact has been the ma-

 jor barrier for 3D motion analysis systems to become a

useful clinical diagnostic tool. X-ray based video sys-

tems (e. g . fluoroscopic systems) may be helpful to re-

duce the skin artefact during motion capture[166 – 168]

, but

the effect of radiation and the limited measuring volume

 prevent it from being useful in general cases. Assess-

ment of individual muscle forces  in vivo  during hu-

man/animal motions has been proven to be a grand

challenge in musculoskeletal biomechanics field[169 – 171]

.

Due to the limitation of the current measuring tech-

niques and ethical reasons, the direct measurement of the 

in vivo musculotendon forces is almost impossible. So,

rigid body musculoskeletal modelling technique is

normally used together with optimisation algorithms to

estimate the muscle forces that can reproduce measured

 joint motions. However, the determination of the sub-

 ject-specific muscle parameters, musculoskeletal ge-

ometry and the rigorous experimental validation of the

calculated results still remain big challenges[172]

. In ad-

dition, development of predictive musculoskeletal

models, which are capable of predicting body kinemat-

ics and kinetics during various movements with mini-

mum measurement inputs[61,66,85]

, will be one of the

major future research directions due to their great po-

tential in clinical diagnosis, rehabilitation engineering

and surgical planning.In musculoskeletal biomechanics studies, compu-

tational FE modelling provides a unique tool to assess

the internal stress/strain conditions of the biological

MSK, which is normally not measurable in vivo. Prop-

erly conducted FE studies could help to investigate the

fundamental biomechanical mechanisms of the MSK, to

improve our understanding of the associated muscu-

loskeletal disorders, and hence to provide sound scien-

tific basis to facilitate clinical diagnosis and surgical

treatments. One of the challenging works in FE model-

ling of MSK is to provide accurate definitions of the in

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vivo material properties of the soft tissues and hard tis-

sues in MSK. For example, the definition of the consti-

tutive equation of cancellous bones is still a subject of

debate, in particular those relating to post-elastic be-

haviour [173 – 175]

, and the failure criteria[176,177]

. Similarly,

there are also lacks of accurate definitions for the in vivo 

material properties for the soft tissues (e. g . cartilages,

ligaments, tendons and muscles etc.).

Another challenging work in FE modelling of MSK

is to provide bio-realistic representations of the anatomy,

structure and function of the human MSK at different

levels/scales (e. g . organ level, tissue level and cell level).

As we know, mechanical loadings at macro level have

effect on behaviours at micro level, conversely me-

chanical properties at micro level influence system re-

sponses at macro level[178]. For example, diabetic foot

ulceration may have a biomechanical etiology[179]

. For

 patients with diabetes, some common daily activities,

e. g . walking, may be harmful because diabetes may

affect the biological functions of MSK at various levels.

Dysfunctions at different levels manifest themselves in

terms of loss of sensation[180]

, changes in control of

movement[181]

, and alteration of tissues[182]

 and also cell

 properties[183]

. It is unclear how do mechanical loads at

macro level (e. g . ground reaction forces) response to

cellular deformations that may cause cell damage oreven ulceration. Mechanical loadings at macro level (e. g .

increased foot contact pressures), redistribution of stress

due to changes in tissue composition (e. g . muscular

atrophy[184]

, cell distribution within tissues, increased

mechanical loading of cells or their decreased damage

resistance may all have contributions to the development

of ulceration. Therefore, a multi-scale modelling

framework is needed to identify the pathways to cell

damage from the mechanical loadings at organ level

through to the deformations at cell level.Multi-scale modelling has been used in basic sci-

ence and engineering areas e. g . mathematics, material

science, chemistry and fluid dynamics etc. for many

years. When applied to MSK biomechanics, the

multi-scale modelling approach is normally based on an

integrated hierarchical structure at multiple body levels,

where the mechanical outputs of macro level models are

transmitted to micro level models with detailed repre-

sentations of MSK at tissue and cell level[185]

. Normally,

rigid body dynamics is used to simulate the mechanical

 behaviour of MSK at body level, and continuum me-

chanics is employed to represent the stress-strain inter-

 play at organ level, whereas for simulations at tissue and

cell levels specialized algorithms and solvers are nor-

mally needed[178,185]

. Therefore, multi-scale MSK

simulations are computationally intensive, and require

intricate representations and also effective simulation

strategies/approaches to describe the complex interac-

tions among multiple levels.

After multi-scale MSK simulations are conducted

to address specific research problems or particular

clinical questions, the next challenging stage is to in-

terpret and validate the simulation results. It is a very

daunting and time consuming task to interpret the com-

 plicated calculation outcomes obtained or to extract

clinically meaningful information from the huge amount

of database generated by the multi-scale simulations.

Moreover, the lack of  in vivo subject-specific data (e. g .

muscle forces, mechanical properties of hard and soft

tissues etc.) and the complexity associated with ex-

 perimental measurements make the validation of the

simulation results even more challenging[178]

. Although

 parameter sensitivity studies coupled with statistical

 populations of   in vivo and primarily in vitro data may

 provide some initial verifications, the limitation of the

current measuring techniques make a thorough sub-

 ject-specific in vivo validation impossible. Furthermore,the highly demanding nature of clinical problems need

the future multi-scale MSK models to be easy-to-use,

robust and also with timely solutions.

It is evident that, for multi-scale modelling of hu-

man/animal MSK, from its solution formulation to ex-

 perimental validation and clinical application, the in-

herent challenges are hard to be handled based on the

current capacity of experimental and computational

 biomechanics. To tackle them effectively, some syner-

getic efforts are necessary not only by coordinating allworks involved in a coherent way, but also by increasing

and encouraging the level of resources sharing and ex-

change in biomechanics community, e. g . data and model

sharing (including those developed by commercial

software packages and self-coded models), format

standardization, and dissemination of solution databases

with model distribution.

Acknowledgements

This work was supported by the International

Cooperation Project of National Natural Science

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Ren et al .: Biomechanics of Musculoskeletal System and Its Biomimetic Implications: A Review 169

Foundation of China (No. 50920105504), the UK En-

gineering and Physical Sciences Research Council Grant

(No. EP/I033602/1), the Project of National Natural

Science Foundation of China (No. 51105167) and the

scientific and technological development planning pro- ject of Jilin Province, China (No. 20130522187JH).

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