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CHAPTER TWO
A Review of Computational
Musculoskeletal Analysis
of Human Lower Extremities
A. Alamdari, V.N. Krovi
The State University of New York at Buffalo, Buffalo, NY, United States
1. INTRODUCTION
In recent years, numerous computational tools have been developed
for kinematic and dynamic analyses of neuromusculoskeletal (NMS)
systems, building on an articulated-multibody systems framework. Such
NMS analysis tools allow monitoring of internal human variables such as
muscle fiber lengths, joint forces, reactions of muscles/tendons/joints,
metabolic power consumption, and mechanical work. Examples include
both commercial tools such as LifeMod, SIMM, and AnyBody (Anybody
Technology), as well as the more recent open-source tools such as OpenSim
to track human movements, compute muscle forces, and analyze normal and
pathological gaits [1–3]. This software includes all of the necessary compu-
tational components for deriving equations of motion for dynamical systems,
performing numerical integration, and solving constrained nonlinear
optimization problems.
Body anthropometry, soft-tissue properties, bone geometry, muscle
paths, and muscle-tendon architecture can be substantially dissimilar among
people, and consequently muscle and joint function can be different among
them [120,121]. Relatively few studies have used a subject-specific model
(personalized model) to simulate gait disorders resulting from conditions
such as cerebral palsy, stroke, and knee osteoarthritis [4]. Most studies, how-
ever, have used generic musculoskeletal models based on estimates derived
from average adult anatomy [5–7]. The value of employing subject-specific
musculoskeletal models for evaluation of muscle and joint functions depends
on the aim of the model. If orthopedic surgery is the main purpose, then
using the subject-specific model will be unavoidable. For example, making
small changes in the muscle’s moment arm might change the moment
Human Modeling for Bio-Inspired Robotics ©2017 Elsevier Inc.
All rights reserved. 37
generated by the muscle [8]. On the other hand, if the main purpose is to
study the muscle coordination of locomotion in a healthy person, then
scaled-generic models may suffice. To validate these musculoskeletal
models, computed-muscle forces are usually validated against electromyo-
gram (EMG) signals of muscle activities, or internal contact forces measured
from instrumented knee joint [9] or hip joint [10] replacements.
Our particular focus will be on computational modeling efforts focused
on improving understanding of physical interactions of the human lower
extremities with their physical environment (eg, walking, standing, bicy-
cling). Walking is the most fundamental human motion with great complex-
ities in terms of the central nervous system (CNS) for controlling,
intermittent contact, dynamic stability, and nonlinearity of the dynamic
system. There have been extensive experimental studies in the biomechanics
literature that give detailed descriptions of dynamic human walking [11,12].
Furthermore, adding dynamics constraints to kinematically computed
motion results in a realistic and smooth human motion in interactions with
the environment.
Such efforts have been devoted to the development and simulation of dif-
ferent models for human walking, ranging from real-time control of human-
oid robots with high degrees of freedom in the robotics field, to high-fidelity
NMS models in biomechanics, and pathological gait studies. Simulation of
human motion with high degrees of freedom is a challenging problem from
both analytical and computational perspectives. Significant literature focuses
on developing natural and human-like walking with increasing fidelity of
mechanical models and efficient numerical algorithms. This review paper will
trace these developments in computational modeling of human walking,
beginning with: (i) skeletal models in which all effects of muscles are modeled
merely as torques applied to joints (commonly seen for real-time control of
biped robots); transitioning to (ii) musculoskeletal models where muscle
groups are included in the multibody dynamic systems (applications in bio-
mechanics); and finally (iii) the NMS model in which human movements
are produced by the muscular and skeletal systems, coupled with the neural
excitations (more recent biomechanical applications).
On an allied front, there is significant interest in studying the interactions
of the human lower extremities with other articulated mechanical systems,
ranging from exercise equipment such as treadmills, bench-presses, and
bicycles to foot-pedal controlled complex machinery such as cranes. In addi-
tion to the innate variability of geometry, performance, and function across
individuals in a population (due to sex/age/race), significant variability is
also introduced by the diversity and adjustable features within such
38 A. Alamdari and V.N. Krovi
articulated mechanical equipment [13]. System-level interactions between
users and equipment make it difficult for designers to select the “best” set
of options/parameters to realize desired performance outcomes a priori
[14,15]. Hence, this creates a need for interactive simulation of personalized
musculoskeletal models coupled with articulated multibodies under a variety
of “what-if” scenarios to realize the optimal system-level motor perfor-
mance. To this end, we discuss various efforts at designing of virtual envi-
ronments, leveraging tools from musculoskeletal analysis, optimization, and
simulation-based design to permit designers to rapidly evaluate and system-
atically customize and match human-machine interactions.
The rest of the chapter is organized as follows. Sections 2 and 3focus on
human gait cycle and the biomechanics of human walking, while Section 4 is
a review of experimental kinematic approaches for studying human walking
including vision-based and nonvision-based techniques. Additionally, the
development of quantitative multibody dynamic systems consisting of skel-
etal, musculoskeletal, and NMS models based on optimization or control-
based methods is reviewed. Computational musculoskeletal interactions
with articulated systems are presented in Section 5 and, finally, Section 6
presents the concluding remarks.
2. HUMAN WALKING GAIT CYCLE
Human walking can be described as a cyclic pattern of body move-
ments which advances an individual’s position. Assuming that all walking
cycles are about the same, studying the walking process can be simplified
by investigating one walking cycle.
In general, each of these walking cycles is composed of two phases: the
single-support phase and the double-support phase. During the single-support
phase, one leg is on the ground and the other leg is experiencing a swinging
motion. The double-support phase starts once the swinging leg meets the
ground and ends when the support leg leaves the ground [12]. Walking is
generally distinguished from running in that only one foot at a time leaves
contact with the ground.
Assuming we start with the right leg, in the first walking step from the
vertical position of the human, the right leg is moved forward and placed on
the ground. The first steady walking step involves lifting the left leg with
single leg support of the right leg until the left leg is placed on the ground
again. The second steady walking step is similar to the first steady walking
step, but this step has single leg support of the left leg until the right leg is
39A Review of Computational Musculoskeletal Analysis
lifted and placed on the ground again. The successive repetitions of steady
walking steps result in a continued locomotion in the sagittal plane.
The gait cycle is the time interval between two successive occurrences of
one of the repetitive events of locomotion. The human gait cycle is split into
two separate regions representing the period of time when the foot is in con-
tact with the ground, the stance phase (shown with R: Stance, Fig. 1), and the
period of time when the limb is not in contact with the ground, the swing
phase (shown with R: Swing, Fig. 1). During the stance phase, the foot
contacts the ground, the mass of the body is supported, and then the body
is propelled forward during the later stages of stance. The stance phase itself
involves five events as illustrated in Fig. 1: (i) heel-strike (HS), (ii) foot-flat
(FF), (iii) midstance (MS), (iv) heel-off (HO), and (v) toe-off (TO) [11].
i. Heel-strike: The beginning instant of the gait cycle is represented as initial
contact of one foot with the ground, usually termed HS or foot-strike.
ii. Foot-flat: The instant that the rest of the foot comes down to contact the
ground and usually is where full body weight is being supported by the leg.
iii. Midstance is defined when the center of mass is directly above the ankle
joint center. This is also used as the instant when the hip joint center is
above the ankle joint.
iv. Heel-off occurs when the heel begins to lift off the ground in preparation
for the forward propulsion of the body.
v. Toe-off happens as the last event of contact during the stance phase.
Events of a gait cycle remarkably occur in similar sequences and are inde-
pendent of time. That is why the cycle is commonly described in terms
of percentage, rather than the time elapsed. Initial HS is designated as 0%
and the subsequent HS of the same foot as 100% (0–100%). During a normal
gait cycle, hip, knee, and ankle joints experience a range of motion [16].
Fig. 2A illustrates these ranges of movement during different speeds. Hip
Fig. 1 Human walking gait cycle, and stance and swing phases of the right leg.
40 A. Alamdari and V.N. Krovi
(
A
)
0 50 100
–15
–10
–5
0
5
10
15
20
25
% of gait cycle
Ankle range of motion (degree)
0 50 100
0
10
20
30
40
50
60
Knee range of motion (degree)
0 50 100
–10
0
10
20
30
40
50
Hip range of motion (degree)
0.5 m/s 1 m/s 1.5 m/s
% of gait cycle % of gait cycle
Fig. 2 (A) Range of motion of ankle, knee, and hip in a normal gait cycle [17], (B) ground
reaction forces in a normal gait cycle.
41A Review of Computational Musculoskeletal Analysis
movement can be categorized into two basic motions: first, hip extension,
which happens during the stance phase and has the primary role of stabili-
zation of the trunk, and, second, hip flexion, which happens during the
swing phase. During the stance phase, the knee is the basic determinant
of limb stability, and in the swing phase, knee flexibility is the primary factor
in the limb’s freedom to advance. At MS, total body weight is transferred
into the flexed knee. The range of motion of the ankle is not large, but it
is critical for progression and shock absorption during stance.
3. BIOMECHANICS OF NORMAL HUMAN WALKING
Normal human walking can be explained with a strategy similar to the
double pendulum. During forward motion, the leg that leaves the ground
swings forward from the hip. This sweep is the first pendulum. Then the
leg strikes the ground with the heel and rolls through to the toe in a motion
described as an inverted pendulum. The motion of the two legs is coordi-
nated so that one foot or the other is always in contact with the ground.
While walking, the center of mass of the body raises to its highest point
during the MS event when one leg passes the vertical, and then drops to its
lowest point as the legs spread apart. Essentially, the kinetic and potential
energy are constantly being exchanged.
To find the required moment/force at each joint during walking, an
inverse dynamic analysis must be implemented. Kinetic data and external
forces should be recorded during experimentation for this purpose.
Ground reaction force (GRF) is the main force acting on the body during
human movements. Since the body massisbeingmovedinallthreedirec-
tions, a 3D force vector consisting of a vertical component and two shear
components will act upon the contact area. These shear forces are usually
resolved into anterior-posterior and medial-lateral directions [12]. The
two shear forces are small compared to the vertical GRF. Herein, only
the vertical GRF is investigated, and the two shear components are not
discussed.
Fig. 2B shows a typical vertical GRF profile of a single walking step. The
vertical GRF at the moment of contact with the ground (HS) will be zero
and will rise sharply up to almost body weight in a fraction of a second. At
the instant of FF, the body mass is moving downwards and landing on the
leg. In order to decelerate this downward motion and at the same time
support the body weight, it will be necessary to apply a vertical force larger
42 A. Alamdari and V.N. Krovi
than body weight on the foot. This instant for the subject shows 120% body
weight being applied to the foot.
At MS the movement of the center of mass of the body is actually
upward. This movement creates an upward acceleration that allows a force
of less than a body weight to support the body. This subject shows 63% body
weight at MS. At HO, the body mass is accelerated forward and upward,
ready for the stance phase of the other leg. This means that more than body
weight will be required to support the body. Finally, TO is the instant where
contact with the ground is lost and the force returns to zero. The M-shaped
graph, or double peak graph, is typical for normal gait and shows the
fluctuation of force relative to body weight [12].
During stance phase, the forces applied to the foot are backwards as the
body lands and then forwards in late stance as the body lifts up and moves
more rapidly in the forward direction (shown with yellow (light gray in print
version) arrow in Fig. 1)[18]. We can assume the line of action of the resul-
tant force is passing through the position of whole-body center of mass.
4. QUANTITATIVE HUMAN WALKING MODELS
Gait analysis has been used for more than a century to provide quanti-
tative information on the kinematics and kinetics of human walking. Early gait
analysis efforts usually focused on experimental observations to study kinemat-
ics and kinetics. Studies involving human subjects may be associated with dis-
comfort or even injuries. Therefore, it is not always possible to use human
subjects for experimentation. One feasible way to proceed is to combine
the power of computational modeling with available noninvasive instruments
to determine information that is not readily attainable from an experiment.
Thus, these challenges illuminate the importance of articulated-multibody
system modeling. However, it is only in the past couple of decades that a more
complete understanding of muscles and joint function via high-fidelity com-
putational musculoskeletal models and analysis has emerged [18–20]. Herein,
a review of human walking modeling and simulation is presented.
One important challenge for clinicians is to understand the relationships
between the observed motion patterns and muscle behavior [21]. Unfortu-
nately, no fully satisfactory data analysis tools are currently available to per-
form patient data interpretation. Modeling tools have been previously
developed but are not entirely satisfactory because of a lack of integration
of the real underlying functional joint behavior [22]. In order to improve
our understanding about the relationships between muscle behavior and
43A Review of Computational Musculoskeletal Analysis
motion data, modeling tools must guarantee that the joint kinematics in the
model are correctly validated to ensure meaningful interpretation. Once a
proper generic model is available, properly adjusted, and validated, it could
then be used in further simulation to obtain clinically relevant muscle infor-
mation [22]. Sholukha et al. [23] presented a model-based method that
allows fusing accurate joint kinematic information with motion analysis data
collected using either marker-based stereophotogrammetry (ie, bone dis-
placement collected from reflective markers fixed on the subject’s skin) or
markerless single-camera hardware. They described a model-based approach
for human motion data reconstruction by a scalable method for combining
joint physiological kinematics with limb segment poses, and finally pres-
ented physiologically acceptable human kinematics.
4.1 Kinematics of Human Walking
To understand kinematics of human walking, it is necessary to track human
motion. The first set of tools developed for analyzing human movement in
computer simulation was based on forward and inverse kinematics [24].
These tools use empirical and biomechanical knowledge of human motion
in order to compute realistic motions. In forward kinematics the state vector
of an articulated human movement over time and interpolation techniques
are used to generate in-between positions to generate smooth motion.
Inverse kinematic algorithms can be used to solve some constraints such
as foot penetration to the ground. Most of the kinematic approaches used
for generating synthetic human locomotion rely on biomechanical knowl-
edge, and combine forward and inverse kinematics for computing motions
[25]. The kinematic techniques presented here rely on a certain understand-
ing of the basic walking motion mechanisms. One of the main advantages of
these models is the high-level parameter (eg, velocity, acceleration, step-
length) they provide leading to the generation of families of different gaits.
Another advantage is the low cost of such computations.
The goal of this approach is to work directly on experimental data from
captured motions. Using optical technologies, it is possible to store the posi-
tions and orientations of markers located on the human body. A further
computation provides the link between the synthetic skeleton and the real
skeleton, in order to adapt data to the new morphology.
In general, there are different types of human movement tracking
systems including nonvision-based tracking systems and vision-based track-
ing systems (marker and markerless).
44 A. Alamdari and V.N. Krovi
4.1.1 Nonvision-Based Tracking System
Nonvision-based systems employ sensor technology attached to the human
body to collect human movement information. These sensors are com-
monly categorized as mechanical, inertial (eg, accelerometer and gyro-
scopes) [26], acousto-inertial, radio or microwave [27], and magnetic [28]
sensing. These systems do not suffer from the “line-of-sight” problem.
Skeletal movement can also be measured directly through stereo-
radiograph, bone pins [29], and X-ray fluoroscopic techniques [30]. While
these methods provide direct measurement of skeletal movement, they are
invasive or expose the human subject to radiation. Real-time magnetic
resonance imaging (MRI) provides noninvasive and harmless in vivo mea-
surement of bones, ligaments, and muscle positions [31]. However, all these
methods impede natural patterns of movement and care must be taken when
attempting to extrapolate these types of measurements to natural patterns of
locomotion.
4.1.2 Vision-Based Tracking System
These techniques use optical sensors, for example, cameras, to track human
movements, which are captured by placing identifiers on the human body.
Herein, we review two current systems for tracking of human movement:
(i) marker-based and (ii) markerless-based vision systems.
Marker-Based Tracking Systems
Marker-based vision systems have attracted the attention of researchers in
medical science and engineering. In this system, the movement of
the markers is used to determine the relative movement between two
adjacent segments with the goal of precisely defining the movement of
the joint. These systems are able to minimize the uncertainty of a subject’s
movements, due to the unique appearance of markers. This basic theory is
embedded in current, state-of-the-art optical motion trackers. Qualisys,
Vicon, Codamotion, and Polaris systems are examples of motion capture
systems. Qualisys (Qualisys Motion Capture Systems, Gothenburg, Sweden)
consists of several cameras, each emitting a beam of infrared light. Small
reflective markers are placed on an object to be tracked. Infrared light is
flashed and then picked up by the cameras. The system then computes a
3D position of the reflective target, by combining 2D data from several cam-
eras. A Vicon system is also used to calculate joint centers and segment
orientations by optimizing skeletal parameters from the trials. For example,
Davis et al. reported a study of using a Vicon system for gait analysis [32].
45A Review of Computational Musculoskeletal Analysis
Codamotion (Charnwood Dynamics Ltd) is another active visual tracking
system which is precalibrated for 3D measurement, without the need to
recalibrate. The Polaris system is also particularly useful when background
lighting varies and is unpredictable.
Markerless Vision Systems
Accurate measurement of 3D human body kinematics can be achieved using
the markerless motion capture (MMC) tracking system for a subject-specific
model. Eliminating the need for markers would also considerably reduce
patient preparation time and enable simple, time-efficient, and potentially
more meaningful assessments of human movement in research and clinical
practice. The feasibility of precisely measuring 3D human body kinematics
for the lower [33] and upper limbs using a MMC system is demonstrated in
literature [34]. For example, a recently described point cluster technique
employs an overabundance of markers placed on each segment to minimize
the effects of skin movement artifact [35].
4.2 Dynamics of Human Walking
Generally, there are two ways to enforce the equations of motion for gait sim-
ulation: forward dynamics and inverse dynamics. Forward dynamics calculates
the motion from given forces and joint torques and muscle excitations by inte-
grating equations of motion with specified initial conditions. In contrast,
inverse dynamics computes associated joint torques that lead to a prescribed
motion for the system. In this framework, the main question is to find the joint
torques and muscle forces that will result in the desired motion [122].
Broadly speaking, in the literature, human locomotion modeling is
divided into three categories as illustrated in Fig. 3: (i) skeletal models in
which all effects of muscles are modeled as simply as torques applied to joints,
(ii) musculoskeletal models where muscle groups are included in the system
dynamics, and (iii) NMS models in which human movements produced by
the muscular and skeletal systems are controlled by the CNS. Features of
various models are explained and their advantages and disadvantages are
discussed in detail.
4.2.1 Skeletal Modeling
The skeletal model has been used quite extensively in the robotics field, par-
ticularly in humanoid robots [36–38]. In this model, the muscle group at a
joint is lumped and represented by a joint torque. Therefore, skeletal models
are commonly used in biped walking simulation due to their simplicity and
46 A. Alamdari and V.N. Krovi
computational efficiency. The number of DOFs for these simplified
mechanical models is quite different. The simplified mechanical model
can be categorized as a planar or spatial model based on the geometry.
For a planar model, the gait motion is assumed to be in the sagittal plane
because of the complexity of studying the lateral motion [39–45]. On the
other hand, for a spatial model, both sagittal and lateral walking motions
are considered [46–50].
Several attempts have been made in the literature to develop realistic and
smooth human walking using a rigid-link multibody system such as the
inverted pendulum model [36,51], passive dynamic walking [52], zero-
moment-point (ZMP) method [37,53], optimization- [49], and control-
based [54] approaches.
Skeletal Modeling Using Inverted Pendulum Model
As we mentioned earlier, potential energy and kinetic energy are being
traded periodically during human walking. Therefore, the simple inverted
pendulum model can be used to simulate biped locomotion. This approach
uses a simple pendulum model with lumped body mass at the center of grav-
ity (COG). This model always has a closed-form analytical solution for the
trajectories of the COG of the model. However, it is difficult to generate
natural and smooth biped walking through this method. To resolve this
problem, an enhanced inverted pendulum model named the angular-
momentum-inducing inverted pendulum model was presented by Kudoh
Fig. 3 Classification of human modeling.
47A Review of Computational Musculoskeletal Analysis
and Komura [50] to generate continuous gait motion. The method can eas-
ily handle angular momentum around the COG. Using this method it is
possible to plan motion paths for biped robots without discontinuity in
the acceleration, even during switching from single-support phase to
double-support phase, and vice versa, in both sagittal and frontal planes.
To solve the continuity of motion, the gravity-compensated inverted
pendulum model was proposed to generate a natural human gait pattern
[55]. This model accommodates the effect of the free leg dynamics based
upon its predetermined trajectory. One mass was assigned to the free leg,
and another mass for the rest of the body. The mass for the free leg was
assumed to be concentrated at the foot. The trajectory of the COG was ana-
lytically obtained by solving the linear equations of the two-mass inverted
pendulum. This model was developed further by considering the dynamic
effect of the swinging leg as a two-mass inverted pendulum model and
multiple-mass inverted pendulum model. The mechanical model consisted
of 12 DOFs without a trunk, and the designed walking motion was con-
strained in the sagittal plane [43].
Skeletal Modeling Using Passive Dynamic Walking
The idea of passive dynamics walking is that a skeletal model can only be
driven by gravity to walk down a slope automatically with no actuation
and control. They can walk downhill with human-like gaits. This concept
was first proposed by McGeer, and studied a compass-like structure to per-
form a passive sagittal walking down a slope by gravity-induced motion
without any actuation and control [56,57]. The leg swings naturally as a
pendulum, and conservation of angular momentum governs the contact
of the swing foot with the ground. Therefore, the model is simple and
energy-efficient. Passive dynamics walking has progressed from 2D sagittal
models to 3D spatial models. In addition, some form of actuation and control
is added to the model to extend the passive dynamics walking on level gro-
und [52]. Small active power sources are introduced to substitute for gravity
to extend the passive dynamics walking to level ground. Kuo [58] extended
the planar passive dynamics walking to a 3D biped motion allowing for
tilting side to side. Collins et al. [59] built the first 3D passive dynamics walk-
ing machine with knees. The model has a four-link sagittal model with a
knee joint, curved feet, a compliant heel, and mechanically constrained arms
to achieve a harmonious and stable gait. Furthermore, the 3D passive
dynamics walking model was recently used to study arm swing in human
walking [60].
48 A. Alamdari and V.N. Krovi
Skeletal Modeling Using ZMP Method
Another method to develop realistic and natural human walking using a
rigid-link multibody dynamic system is ZMP trajectory generation. This
method is a fast and efficient anthropomorphic gait simulation method.
ZMP is a significant dynamic equilibrium criterion and plays a major role
in stability analysis of dynamic human walking [53]. Zero-moment point
is a concept related to dynamics and control of humanoid robots. It specifies
the point with respect to which the dynamic reaction force at the contact of
the foot with the ground does not produce any moment in the horizontal
direction on the sagittal plane, that is, the point where the total of horizontal
inertia and gravity forces equals zero. The concept assumes the contact area is
planar and has sufficiently high friction to keep the feet from sliding. The
history of ZMP and clarification of some basic concepts was first reviewed
in Ref. [61]. Kajita et al. [38] combined the inverted pendulum model with
the ZMP-based method to plan walking motion for a biped robot. The mul-
tibody dynamics of the robot was represented by a 3D inverted pendulum
model from which the ZMP was calculated efficiently. Hirai et al. [62] pres-
ented the development of a Honda humanoid robot that had 26 DOFs: 12
DOFs in 2 legs and 14 DOFs in 2 arms. The general procedure for the ZMP
method was to first plan a desired ZMP trajectory and then derive the hip or
torso motion required to achieve that ZMP trajectory. In this process, the
whole-body walking motion was decoupled into three parts: (i) GRF
control, (ii) ZMP control, and (iii) foot landing position control.
In ZMP, the basic idea is to enforce the mechanism tracing the pre-
scribed ZMP locations. The key point of this approach is that the dynamics
equations are used only to formulate the balance ZMP constraint rather than
generation of the entire motion trajectory directly.
Skeletal Modeling Using Optimization-Based Approaches
In biped walking simulation using optimization approaches, it is ideal to opti-
mize the entire walking motion including all physical details with accurate
human models. However, such a detailed and accurate model needs powerful
computational resources. Therefore, the mathematical gait models used in the
literature are generally simplified. Chow and Jacobson [63] first used an opti-
mal programming for gait motion simulation; then, a more complicated 3D
skeletal model was successfully developed for gait simulation with
optimization-based approaches [47,49].
The complex walking motion includes seven phases in a complete gait
cycle [12]. For optimization-based simulation, the gait cycle is simplified so
49A Review of Computational Musculoskeletal Analysis
that it only covers a partial gait motion. In the literature, a simplified gait
cycle for skeletal modeling based on an optimization method has been
generally separated into four groups: (1) single-support swing motion
[63]; (2) single-support with instantaneous double-support [40,48]; (3)
single-support and double-support—a step [41,49]; and (4) complete gait
cycle [64].
In general, there are two approaches for gait optimization of a skeletal
model: forward dynamics optimization and inverse dynamics optimization
[123]. For a forward dynamics optimization problem, forces and torques are
the design variables. The optimal gait is calculated by minimizing a human
performance measure or muscle activities subject to physical constraints.
During optimization iterations, motion is obtained by integrating the equa-
tions of motion with initial conditions. The main problem for forward
dynamics optimization is the high computational cost of integration of equa-
tions of motion [39,65]. The benefit of this method is that the forces are
optimized directly and the motion is generated from equations of motion
during optimization.
For inverse dynamics optimization of a skeletal model, the design vari-
ables are the joint angle profiles. The optimization problem is solved for
optimal gait motion. During an optimization iteration, the forces are directly
calculated from equations of motion so that their numerical integration is
avoided. The inverse dynamics optimization is computationally efficient
because the equations of motion are not integrated in the solution process
[40,47,66,67]. Therefore, inverse dynamics is better to be used in the opti-
mization process instead of forward dynamics to avoid integration of the
equations of motion [68].
In optimization problems, one needs to decide which physical quantities
should be treated as unknowns (design variables), which objective functions
should be used to drive the human motion, and which constraints should be
imposed for a specific task. Therefore, different formulations result in var-
ious optimization problems, and their solution procedures and numerical
performance are quite different. The following performance measures are
commonly used in the literature for skeletal models to simulate walking
motion: mechanical energy, dynamic effort, jerk, stability, and maximum
absolute value of joint torque. The constraints associated with human walk-
ing simulation are categorized as: (i) physical constraints such as joint angle
limits, joint torque limits and (ii) characteristic constraints such as continuity
and unilateral contact constraints. The hip, knee, and ankle are constrained
to follow measured data [69].
50 A. Alamdari and V.N. Krovi
A complete gait cycle in the sagittal plane on level ground by using the
inverse dynamics optimization method was simulated in Ref. [44]. Walking
was formulated as an optimal motor task subject to multiple constraints with
minimization of mechanical energy expenditure over a complete gait cycle
being the performance criterion. The mechanical model has a seven-
segment linkage, and Fourier series approximated joint profiles.
In Ref. [67], an eight-segment 3D model was used to simulate normal
walking for the gait cycle. The hip, knee, and ankle extension/flexion
motions were measured from experiments and treated as constraints. This
input movement was reconstructed to a kinematically and dynamically con-
sistent 3D movement. In another study, a seven-link planar biped robot for
single-support in the sagittal plane was solved for optimal gait motion [39].
The optimization problem of gait simulation was treated as a continuous
problem and solved by optimal control methods. The method was based
on the implementation of the Pontryagin maximum principle used as a
mathematical optimization tool. It applied to mechanical systems with kine-
matic tree-like topology such as serial robots, walking machines, and artic-
ulated biosystems. In this process, the optimal control equations needed to
be derived. The algorithm was not efficient when a large-DOF mechanical
model was used. This study was extended to a nine DOFs model that moved
in the sagittal plane; then an optimization method was used for cyclic, sym-
metric gait motion of a skeletal model to minimize the actuating torques
[45]. Bessonnet et al. [46] extended their 2D model to a 3D skeletal model
with 13 DOFs. The optimal control problem was formulated as a nonlinear
programming problem where the dynamic effort was considered as a human
performance measure to be minimized. In the parameter optimization prob-
lem which was used, ordinary differential equations were discretized into
algebraic equations, and the time-dependent constraints were simply
imposed at time grid points.
Xiang et al. [49] presented a new methodology to simulate one-step spa-
tial digital human walking motion using a 55-DOFs skeletal model. The
proposed methodology was based on an optimization formulation that min-
imizes the dynamic effort of people during walking. The formulation con-
sidered symmetric and periodic normal walking and GRFs. Recursive
Lagrangian dynamics and analytical gradients for all the constraints and
the objective function were incorporated in the optimization formulation.
The predicted walking motion was verified with six walking determinants
obtained from motion capture experiments. The formulation also showed
high-fidelity in predicting joint torques and GRFs.
51A Review of Computational Musculoskeletal Analysis
Skeletal Modeling Using Control Algorithm
Biped locomotion modeling with tracking control is another approach pres-
ented in the biped walking literature. Tracking control chooses a proper
input force/torque to drive the biped to follow a desired preplanned motion.
The key issue is to obtain the desired walking trajectories before utilizing the
tracking control. This can be achieved by (i) generation of the desired walk-
ing trajectory by a motion capture method which constructs a database from
human motion experimentation [70] and (ii) synthesizing desired walking
trajectories using an inverted pendulum model or ZMP-based methods.
Various control algorithms have been implemented in the literature such
as feedback control [55] and intelligent control techniques [54] (neural net-
work [71], fuzzy logic [72], genetic algorithms [73]) and their hybrid forms
(neuro-fuzzy networks [74], neuro-genetic and fuzzy-genetic algorithms) in
the area of humanoid robotic systems.
Optimal control drives the model from the initial state to the final state
while minimizing a cost function. The standard optimal control problem is
to find the control history τ(t) that minimizes the performance measure in
the time interval. The optimal control of biped walking is equivalent to the
continuous forward optimization problem in which the continuous input
joint torques are treated as unknowns in the formulation [45,63].
4.2.2 Musculoskeletal Modeling
The musculoskeletal model has been used quite extensively in the biome-
chanics field. Many human walking features cannot be represented by the
rigid-link mechanical model (skeletal model). Biomechanics gait analysis
using a musculoskeletal model can give more details about the physiology
of human walking. In contrast to the skeletal model, the musculoskeletal
model aims to predict the motion and forces at the muscle level. This is cru-
cial for pathological studies, and it deepens our understanding of muscle
excitation during the walking motion [5,18,75].
Muscle contraction dynamics govern the transformation of muscle activa-
tion, to muscle force. Once the muscle begins to apply force, the tendon (in
series with the muscle) transfers force from the muscle to the bone. This force
is named the musculo-tendon force. The joint moment is the sum of the
musculo-tendon forces multiplied by their corresponding moment arms.
The force in each musculo-tendonous unit contributes in the total moment
about the joint. The musculoskeletal geometry determines the moment arms
of the muscles (muscle force is dependent on muscle length, ie, the classic mus-
cle “length-tension curve”). It is important to note that the moment arms of
muscles are not constant values, but change as a function of joint angles [20,76].
52 A. Alamdari and V.N. Krovi
Musculoskeletal modeling has been applied to a broad range of problems
in movement science, including: (a) understanding how geometry and
muscle-tendon properties independently affect a muscle’s ability to develop
moment about a joint [8,77]; (b) evaluating a muscle’s capacity to accelerate
the body joints in various tasks such as walking, jumping, and cycling [6];
and (c) analyzing how orthopedic surgical procedures, such as muscle-
tendon transfers, alter the lengths and moment arms of muscles [78]. For
example, Riewald et al. [78] used musculoskeletal modeling, neuromuscular
control, and forward dynamic simulation to investigate the role of rectus
femoris tendon transfer surgery on balance recovery after support-surface
perturbations for children with cerebral palsy. However, the most common
use of modeling has been in the determination of muscle and joint loading
[18,20]. Accurate knowledge of muscle forces could improve the diagnosis
and treatment of patients with movement disabilities.
The ability to predict patient-specific joint contact and muscle forces
accurately could improve the treatment of walking disorders. Muscle syn-
ergy analysis, which decomposes a large number of muscle EMG signals into
a small number of synergy control signals, could reduce the dimensionality
and thus redundancy of the muscle and contact force prediction process. In
Ref. [79], authors investigated whether use of subject-specific synergy con-
trols can improve optimization prediction of knee contact forces during
walking. In an optimization problem, the sum of squares of muscle excita-
tions was minimized to investigate how synergy controls affect knee contact
force predictions.
Alternatively, inverse dynamics approaches begin by measuring the posi-
tion of markers and the external forces acting on the body. In gait analysis,
for example, the position of markers attached to the participants’ limbs can
be recorded using a camera-based video system and the external forces
recorded using a force platform. The tracking targets on adjacent limb seg-
ments are used to calculate relative position and orientation of the segments,
and from these, the joint angles are calculated. These data are differentiated
to obtain velocities and accelerations. The accelerations and the information
about other forces exerted on the body (eg, the recordings from a force plate)
can be input to the equations of motion to compute the corresponding joint
reaction forces and moments. If the musculoskeletal geometry is included,
muscle forces can then be estimated from the joint moments. However,
inverse dynamics has important limitations: (i) it is difficult to measure
and estimate inertia and mass of each segment, (ii) differentiating displace-
ment data is ill conditioned and sensitive to noises, (iii) co-contraction of
muscles is very common and the resultant joint reaction forces and moments
53A Review of Computational Musculoskeletal Analysis
are net values, (iv) there are multiple muscles spanning each joint, and the
transformation from joint moment to muscle forces yields many possible
solutions and cannot be readily determined, and (v) there is no verified
model which gives inverse transformation from muscle forces to muscle
excitation.
One sensible way to proceed is to combine the power of computational
modeling with available measurements to determine information that is not
readily obtainable from an experiment. Muscle and joint function can be
determined when the following information is available: (i) accurate mea-
surements of the forces applied to the body by the ground, (ii) accurate
measurements of body segmental motion, and (iii) accurate knowledge of
muscle and joint contact loading. In gait analysis experiments, force plat-
forms are used to measure GRFs, while video-based motion capture tech-
niques are applied to monitor the 3D positions and orientations of the body
segments. X-ray fluoroscopy [30] and MRI [80] are also used to record
dynamic joint motion in vivo.
The synthesis of human movement involves accurate reconstruction of
movement sequences, modeling of musculoskeletal kinematics, dynamics
and actuation, and characterization of reliable performance criteria. Task-
based methods used in robotics can provide novel musculoskeletal modeling
methods and accurate performance predictions. Khatib et al. [81] presented a
new method for the real-time reconstruction of human motion trajectories
using direct marker tracking with new human performance measure, and a
task-driven muscular effort minimization criterion. Dynamic motion recon-
struction through the control of a simulated human model was able to follow
the captured marker trajectories in real time.
The musculoskeletal model is mechanically redundant as several muscles
span each joint and many combinations of muscle forces can produce a net
joint moment. For example, more than 15 muscles control 3 degrees of free-
dom at the hip [18]. Also, biarticular muscles cross two joints and so con-
tribute to the net moments exerted about both joints simultaneously. It is
therefore not possible to discern the actions of individual muscles from cal-
culations of net joint moments alone.
This musculoskeletal redundancy allows for an infinite number of com-
binations of muscle activation patterns for performing a task. Typically, the
redundancy resolution is resolved by assuming some optimization criterion,
for example, minimizing muscle tension/stress [82], to determine a unique
solution for muscle activation pattern among an infinite number of solutions
that satisfy biomechanical constraints such as joint torques, joint contact
54 A. Alamdari and V.N. Krovi
forces [79], and joint impedance [83]. The most typical biomechanical con-
straints on muscle activation patterns are based on experimentally measured
kinematics (eg, joint angles) and kinetics (eg, GRFs), and finally defining
single or multiple optimization criteria. Such inverse approaches identify
optimal solutions that may capture major features of experimentally mea-
sured muscle activation patterns [75].
Musculoskeletal Modeling Using Optimization Methods
Progress in using musculoskeletal models in the recent decade has been
accelerated because of the enormous increases in computing power and
the availability of more efficient and robust algorithms for modeling and
numerical simulation. Computation approaches such as optimization
methods have been widely used to simulate and analyze human motions.
With the development of optimization techniques these methods have
become more attractive. The methods can handle large-scale models and
can optimize any human-related performance measure simultaneously.
More design variables can be included in the optimization formulation so
more natural human walking simulation can be achieved. For human walk-
ing simulations, the methods can produce optimal motions and joint force
profiles subjected to all the necessary constraints [69].
As mentioned earlier, in forward dynamics optimization of a musculoskel-
etal model, muscle forces are the design variables for the optimization prob-
lem. During optimization iterations, motion is obtained by integrating the
equations of motion with initial conditions. The benefit of this method is that
the forces are optimized directly and the motion is generated from equations
of motion during optimization [5,84].
Musculoskeletal modeling of human motion using optimization is usually a
large-scale nonlinear programming problem. In recent years, there has been
much progress in research on simulation of human walking, especially in uti-
lizing optimization techniques for large-scale musculoskeletal systems
[5,84,85]. Human locomotion is so efficient and the CNS tries to minimize
the metabolic cost, that is, the energy expended per unit distance traveled.
In Ref. [86], mechanics and energetics predictions in forward dynamics simu-
lations of human walking using different Hill-type muscle energy models are
compared. The following performance measures are commonly used in the
literature for musculoskeletal models to simulate walking motion: dynamic
effort, mechanical energy, muscle activation, fatigue, and metabolic energy.
In reality, human motion may be governed by multiple performance measures,
and multiobjective optimization methods can be used for gait simulation.
55A Review of Computational Musculoskeletal Analysis
In clinical studies, muscle forces are the main concerns instead of the net
joint torques. In optimization problems, muscle forces can be included in the
formulation in two ways: (i) a static optimization in which one can partition
the joint torques into each muscle group using the equilibrium equation at
each joint [75,84] and (ii) a dynamic optimization formulation in which the
muscle forces can be treated as design variables for dynamic motion predic-
tion, then the equilibrium equations between the muscles forces and the net
joint torques are simply imposed as equality constraints in the optimization
formulation [5,18,84], though it requires more computational effort. How-
ever, the performance measures evaluated over time, such as total muscular
effort [81] or metabolic energy consumption [84], can be considered in the
second formulation but not in the static optimization.
Computer modeling and simulation of human movement using the for-
ward dynamics optimization method with a musculoskeletal model were
reviewed in Refs. [6,18]. Muscle modeling and computational issues were
presented in detail. Also, the forward dynamic optimization approach was
illustrated by simulating human jumping, walking, and pedaling motions.
A 3D musculoskeletal model with 23 degree-of-freedom mechanical link-
age and 54 muscles was developed by Anderson and Pandy [84]fornormal
symmetric walking on level ground using the forward dynamics optimization
method. Muscle forces were treated as design variables, and metabolic energy
expenditure per unit distance was considered as a human performance mea-
sure to be minimized. Muscle metabolic energy was calculated by summing
five terms: the resting heat, activation heat, maintenance heat, shortening heat,
and the mechanical work done by all the muscles in the model. Then, the
model was used to analyze human walking, and many insights on muscle func-
tions for normal and pathological gait were obtained in Ref. [87].
As discussed earlier, musculo-tendon forces and joint reaction forces are
typically estimated using a two-step method: first computing the musculo-
tendon forces by a static optimization procedure and then deducing the joint
reaction forces from the force equilibrium. However, this method does not
allow studying the interactions between musculo-tendon forces and joint
reaction forces in establishing this equilibrium. So, the joint reaction forces
are usually overestimated. Moissenet et al. [88] introduces a new 3D lower-
limb musculoskeletal model based on a one-step static optimization proce-
dure allowing simultaneous musculo-tendon, joint contact, ligament, and
bone forces estimation during gait.
Neptune et al. [5] proposed a method which used muscle-actuated for-
ward dynamics optimization to drive the model to follow the measured joint
56 A. Alamdari and V.N. Krovi
angle profiles and GRFs. The simulation analysis showed that a simple
neural control strategy involving five muscle activation modules was suffi-
cient to perform the basic subtasks of walking (ie, body support, forward
propulsion, and leg swing). The musculoskeletal model in the sagittal plane
consisted of 7 rigid segments driven by 13 muscle groups. A complete gait
cycle from right HS to the subsequent right HS was simulated. The differ-
ence of kinematics and GRF between simulation and experiment was
minimized, and the muscle actuations were treated as design variables in
the optimization formulation.
The effects of different performance criteria on predicted gait patterns
using a 2D musculoskeletal model was studied in Ref. [89]. In this study
the mechanical model consisted of seven rigid segments with nine DOFs
to simulate single step walking and generate cyclic motion. Eight muscle
groups were included in each lower extremity. In the optimization problem
state variables, controls, and muscle activations were all treated as design var-
iables. The objective of this paper was to shed some light on the effects of the
cost function choice on the predicted kinematics and muscle recruitment
patterns of gait. A series of predictive simulations of gait are performed
utilizing a family of cost functions representative of a large range of perfor-
mance criteria traditionally adopted in the literature. It was found that a
fatigue-like cost function predicted a more realistic normal gait.
Optimization-based approaches determine the optimal solution among the
infinite number of solutions for muscle forces by defining biomechanical con-
straints. However, deviation from the optimal patterns for muscle activation
may also satisfy these constraints. Characterizing all these viable deviations in
muscle activity from an optimal solution would facilitate interpretation of
experimental variations in muscle activation patterns. In addition, it would
facilitate interpretation of how those biomechanical constraints affect not just
the optimal solutions, but the set of all possible solutions. A few attempts to
define feasible muscle activation ranges for a given movement have been made
previously [90–92].
Musculoskeletal Modeling Using Control-Based Approaches
In musculoskeletal modeling based on the control-based approaches, there
are two main issues: (a) experimental data collection and (b) appropriate
controller use to track measured trajectories. In general, there are many
factors that should be considered to accomplish proper experiments on
human subjects: (i) suitable subjects should be recruited, (ii) experimental
protocol should be set up, (iii) instruments should be calibrated, noise should
57A Review of Computational Musculoskeletal Analysis
be filtered, and errors should be quantified, (iv) experience and skills are
required to perform good experiments on human subjects, (v) appropriate
controllers need to be selected and designed to provide feedback on joint
torques, (vi) the nonlinear dynamics system should be simplified, and finally
(vii) the controllability and stability of the controller should be considered
and tested. Once the controller is tuned and validated, the control-based
method can be used to obtain joint torques and muscle forces based on
the measured experimental data [75].
Control methods can also be built into the optimization problem to
compute muscle forces such as the computed-muscle-control method
developed by Thelen and Anderson [75]. The objective of this study was
to develop an efficient methodology for generating muscle-actuated simu-
lations of human walking that closely reproduce experimental measures of
kinematics and GRFs. In this method, forward dynamics and feedback con-
trol were employed to obtain the joint actuation torques, which drive the
kinematic trajectories of the model toward a set of desired trajectories
obtained from experiments. Then, the muscle forces were computed by
using a static optimization algorithm. This method is more efficient and
stable than the dynamic muscle optimization algorithm using a forward
dynamics optimization approach.
Optimal control also drives the model from the initial state to the final
state while minimizing a cost function. Optimal control of a musculoskeletal
model is equivalent to the continuous forward optimization problem in
which the continuous input joint torques are treated as unknowns in the
formulation [7].
4.2.3 NMS Modeling
NMS modeling deals with the modeling of human movements generated by
the muscular and skeletal systems while it is controlled by the CNS. This
model is important for different purposes including: (i) studying how the
nervous system controls limb movements in both unimpaired people and
those with pathologies such as spasticity caused by stroke or cerebral palsy
[93,94], (ii) studying functional electrical stimulation of paralyzed muscles,
and (iii) designing prototypes of myoelectrically controlled limbs.
The human CNS system is quite complicated as it determines human
behavior. As we reviewed earlier, both optimization algorithms and the
control-based approaches can be used to accurately approximate the CNS
so as to predict and analyze human movement. In optimization methods,
the CNS is considered as one of the several human performance measures,
58 A. Alamdari and V.N. Krovi
and information from experiments assist as constraints. Thus, it can mimic
the entire CNS behavior system. The weakness of the method is that having
completely smooth, natural, and repeated motion is difficult to obtain
because the objective function only represents a partial CNS unless more
constraints are used to drive the motion [69]. Therefore, the optimization
algorithms are good at answering how people behave if some conditions
are changed by solving an optimization problem with different inputs.
In contrast, the control-based methods first duplicate complete human
motion from experiments, and then a controller is used to represent the
CNS to drive the model through the measured trajectories. The beauty of
the method is that the CNS is better approximated to re-create the recorded
human motion. Therefore, natural and subject-specific motions can be accu-
rately tracked and simulated. It is suitable to study pathological gait and asso-
ciated muscle forces to reveal the physical insights behind the motion. Thus,
the control-based method is good at answering why people behave the way
they do by tracking the corresponding experimental data [93,95].
Buchanan et al. [96] provided an overview of forward dynamic NMS
modeling in which the estimation of muscle forces and joint moments,
and movements from measurement of neural command, are discussed in
detail. In the first step of their four-step process (as illustrated in Fig. 4), mus-
cle activation dynamics governs the transformation from the neural com-
mand to a measure of muscle activation—a time-varying parameter
between 0 and 1. The neural command can be taken from EMGs in which
the magnitudes of the EMG signals will be changed when the neural
command calls for increased or decreased muscular effort. In the second step,
muscle contraction dynamics characterize how muscle activations are
transformed into muscle forces. The third step requires a model of the mus-
culoskeletal geometry to transform muscle forces to joint moments. Finally,
the equations of motion allow joint moments to be transformed into limb
acceleration and joint movement.
Fig. 4 NMS model for studying human movement.
59A Review of Computational Musculoskeletal Analysis
However, the forward dynamics approach has some limitations,including:
(i) estimation of muscle activation from EMG signals is difficult; (ii) the trans-
formation from muscle activation to muscle force is not completely understood
(although one way for direct determination of muscle forces from EMGs is
using optimization), as there is no known correlation between the level of a
measured EMG signal and the amount of force that the muscle might be pro-
ducing during a dynamic contraction; and (iii) determination of the muscle-
tendon moment arms and lines of action are still challenging problems.
A neuromusculoskeletal tracking (NMT) method was developed by Seth
and Pandy [95] to estimate muscle forces from observed motion data. This
NMT method consisted of two phases: (i) skeletal motion tracking control
and (ii) optimal neuromuscular tracking control. In the first stage, the skel-
etal motion tracker calculates the joint torques needed to actuate a skeletal
model and track observed segment angles and ground forces in a forward
simulation of the motor task. In the second stage, an optimal neuromuscular
tracker was used to determine the optimal muscle excitations and muscle
forces by tracking the joint torques obtained in the first stage. The proposed
NMT approach was compared with conventional approaches such as inverse
dynamics analysis and forward dynamics optimization. It was concluded that
NMT gave more accurate and more efficient simulation than the inverse and
forward dynamics method. It requires three orders-of-magnitude less CPU
time than parameter optimization. The speed and accuracy of this method
make it a proper tool for estimating muscle forces using experimentally
obtained kinematics and ground force data.
5. COMPUTATIONAL MUSCULOSKELETAL ANALYSIS
INTERACTION WITH ARTICULATED SYSTEMS
In the biomechanics field, many computational tools have been devel-
oped for kinematic and dynamic analysis of musculoskeletal systems, building
on an articulated-multibody systems framework [124]. Constrained muscu-
loskeletal models can be constructed modularly by placing constraints on ana-
tomical components. Such musculoskeletal analysis tools allow monitoring of
internal human variables such as muscle lengths, forces, reactions of muscles/
tendons/joints, metabolic power consumption, and mechanical work.
Examples include both commercial tools such as LifeMod, SIMM, and
AnyBody, as well as open-source software such as OpenSim to follow
human movements, compute muscle-tendon forces, and analyze the normal
and pathological gaits [1–3]. Among these software packages, the AnyBody
60 A. Alamdari and V.N. Krovi
modeling system offers a convenient tool for modeling and analyzing various
musculoskeletal systems [97]. The AnyBody musculoskeletal model is
established as a constrained articulated-multibody system with rigid skeletal
bones connected with multiple muscles which actuate the system. The
governing equations of motion can be obtained as the constrained dynamic
equations of this articulated-multibody system. The indeterminacy in
muscle-tendon force distribution is resolved by employing optimization
approaches. In AnyBody, redundancy resolution takes the form of minimi-
zation of the maximal muscle activity subject to equality constraints and
nonnegative muscle force constraints. For example, in Ref. [3], a biomedical
model of a thumb is developed by real CT scans of four bony sections, and
actuated by nine realistic muscle-tendons in AnyBody, and then the inde-
terminacy problem is solved by optimization-based approaches.
A graphical user interface (GUI) is also developed to facilitate user inter-
action with AnyBody settings (eg, using radio buttons and sliders) allowing
performance of parametric studies by manually varying the appropriate
design variables [15]. The optimization process, data manipulation, and
interfacing to AnyBody are handled using MATLAB, and the results of
the optimization are displayed back within the GUI (see Figs. 5 and 6).
Contrary to AnyBody, OpenSim uses a forward dynamics approach in
solving the musculoskeletal question. OpenSim is open-source software,
which includes all computational components for deriving equations of
motion for articulated-multibody systems, performing numerical integration,
and solving constrained nonlinear optimization problems. This software also
offers accessibility to control algorithms such as computed-muscle control,
actuators, and analyses (eg, muscle-induced accelerations). OpenSim inte-
grates all these components into a modeling and simulation platform. Users
can extend OpenSim by writing their own plug-ins for analysis or control,
or to represent NMS elements [99].
Simbody is an application programming interface which serves as the
dynamics engine behind OpenSim. It can incorporate robust, high-
performance, minimal coordinate multibody dynamics into a broad range
of domain-specific end-user applications. Simbody provides a diverse set
of tools to handle the modeling and computational aspects of multibody
dynamics, to ensure correct and efficient deployment. Simbody also includes
contact modeling, numerical integration and differentiation, constraint
stabilization and redundancy handling, etc. [100].
The rapid model-based design, control systems, and powerful numerical
method strengths ofMATLAB/Simulinkcan be combined with the simulation
61A Review of Computational Musculoskeletal Analysis
Fig. 5 Parametric bicep curl study on a simplified upper-arm/shoulder musculoskeletal
model with the graphical user interface [15].
Fig. 6 Performing a bicycling motion study on the lower extremity/hip musculoskeletal
model [98].
and human movement dynamics strengths of OpenSim by developing a new
interface between the two software tools. In Ref. [101], OpenSim is integrated
with Simulink using the MATLAB S-function mechanism, and the interface is
demonstrated using both open-loop and closed-loop control systems.
Exoskeletons are a new class of articulated-multibody systems used for
motion assistance for the elderly or disabled individuals and their perfor-
mance is realized while in intimate contact with individual musculoskeletal
systems. They are also intended to improve rehabilitation for people with
disabilities caused by strokes [14], muscle disease, spinal cord injuries
[102], etc. The state of the art for lower-limb exoskeletons presented by
Dollar and Herr [14] showed that having knowledge of the biomechanics
of walking is important to build an exoskeleton that can interact with the
user with minimal chances of harm. Alamdari et al. [103] comprehensively
surveyed the clinic- and home-based rehabilitation devices for upper and
lower limbs therapy to recognize the situations which need human-robot
interaction to be considered. For training patients under rehabilitation with
an exoskeleton, physical human-robot interaction is a major concern for a
safe and comfortable usage. For example, in Refs. [104,105] as shown in
Fig. 7A, a cable-driven end-effector-based exoskeleton named PACER is
directly coordinated with a human arm, and in Refs. [102,106] as shown
in Fig. 7B, a cable-driven exoskeleton named ROPES is in intimate contact
with human lower limbs. For modeling, analyzing and deep understanding
of human-robot interaction, the musculoskeletal model of the human body
(
A
)(
B
)
Fig. 7 (A) Parallel articulated-cable exercise robot (PACER): home-based cable-driven
mechanism for upper extremities rehabilitative exercises [104,105], (B) robotic physical
exercise and system (ROPES): a cable- driven robotic rehabilitation system for lower
extremity [102,106] which is driven by seven motors installed on the frame labeled 1–7.
63A Review of Computational Musculoskeletal Analysis
as well as multibody dynamics of the exoskeleton need to be integrated and
modeled [15,125] Therefore, the model is able to estimate the muscle activ-
ities in cooperative motions and enables the design analysis and optimization
of robotic exoskeletons.
Safety is one of the top priorities when designing any kind of exoskeleton
[107], as they interact closely with humans. In the past, one safe way to
design and test an exoskeleton was to build two robots prior to their usage;
if there is an unwanted dangerous torque on the master robot, then no
human would get harmed [108]. The other criteria when designing exoskel-
etons are the range of motion and magnitude of effort [109]. These two
criteria define the difficulties faced when matching to human biomechanics.
It is difficult to detect the axis of the human joints, to mimic all degrees of
freedom, and to avoid the relative motion between the exoskeleton and the
human due to nonoptimal fixation during exercise.
Nowadays, exoskeleton testing can be accomplished virtually using mul-
tibody modeling [110]. Multibody dynamic modeling can be seen as a pow-
erful tool to design exoskeletons by simulating both the musculoskeletal
system and exoskeleton dynamics, enabling the prediction, in a noninvasive
way, of the efforts performed by the exoskeletons and forces applied to the
human body [111]. Virtually designing the exoskeleton directly on a human
musculoskeletal model helps to constrain the exoskeleton kinematics to the
human kinematics. Ferrati et al. [112] analyzed an existing exoskeleton by
reproducing it virtually and constraining it to a human musculoskeletal
model. This means that the rehabilitation can be virtually quantified, and
therefore several designs can be tested according to the injury. To virtually
prototype exoskeletons on human musculoskeletal models opens the possi-
bilities of custom exoskeletons for rehabilitation. Agarwal et al. [113] argued
that virtually designing an exoskeleton model directly on a musculoskeletal
model allows the introduction of biomechanical, morphological, and con-
troller measures to quantify the performance of the device.
It is important to know how much force the exoskeleton generates
before manufacturing the real exoskeleton. One sensible way to predict
the force is using a virtual prototyping environment during the design stage.
In Ref. [114], a combined human-exoskeleton model is generated, and
dynamic analysis is performed under different constraints using AnyBody
software to predict the effect of connecting the user to the exoskeleton. This
dynamic analysis makes it possible to calculate the human joint torque and
the interaction force for the musculoskeletal model and the exoskeleton. To
accomplish this, the musculoskeletal model generated by AnyBody software
64 A. Alamdari and V.N. Krovi
is scaled with human subject data collected using motion capture data, and
the designed exoskeleton is converted into an STL model in SolidWorks and
merged with the musculoskeletal model in AnyBody software.
In Ref. [115], an integrated musculoskeletal-exoskeleton system is pro-
posed forthe optimal design ofexoskeletons. Thehuman-robot interactionsys-
tem is implemented in AnyBody, and kinematic and dynamic simulation of the
system isconducted in this software fora cooperative motion of the exoskeleton
and human arm for lifting a payload. The design parameters of the cable-driven
exoskeleton are formulated as an optimization problem. The activities of three
selected muscles of the upper limbs are displayed, which are considered as the
major extensor and flexors of arm motion. The muscle activity is evaluated by
taking the mean activity of major muscles. These individual muscle forces and
elbow flexion moments can serveas performance measures. Such performance
measuresallow the designer to directly evaluate the effectiveness of theexoskel-
eton design. These measures areconsidered for analysis because of the following
reasons: (i) individual muscle forces show which muscles play a significant role
in performing the given experiment andhence how modifications in designcan
relieve them; and (ii) elbow flexion moment signifies the load carried by the
human elbow joint, and thus gives an idea of the external load acting on the
joint [15].
The effects of backrest inclination of a seated person in an adjustable car
seat, and also the effects of vertical vibration frequency of the suspension sys-
tem on the muscle activity in the dynamic environment are assessed using the
musculoskeletal model in AnyBody software [116]. This study shows that the
vibration frequency significantly affects the muscle activity of the lumbar area,
and likewise, the inclination degree of the backrest significantly affects the
muscle activities of the right leg and the abdomen. The combination of vibra-
tion and forward inclination of the backrest can be used to maximize the mus-
cle activity of the leg, similar to the abdomen and lumbar muscles. Similarly,
Rasmussen et al. [117], Grujicic et al. [118] used a detailed musculoskeletal
computer model to examine the influence of car seat design/adjustments
and the consequences of variations in the seat pan angle, friction coefficient
of the seat surface on spinal joint forces, soft tissue contact normal and shear
stresses and muscular activity. Ma et al. [119] analyzed the muscle activities
and joint forces of the lower limb with knee normal and knee lock postures
under vertical whole-body vibration, based on inverse dynamics and using
the AnyBody Modeling System.
In Ref. [112], a virtual exoskeleton for lower-limb rehabilitation was
constrained to a human musculoskeletal model in OpenSim software to
65A Review of Computational Musculoskeletal Analysis
study its behavior and to evaluate the design parameters. By using OpenSim
built-in tools and a human musculoskeletal model, four different models
were implemented in order to study the behavior of the system in different
operating conditions, and in particular the interactions that are generated
between the human musculoskeletal structure and the exoskeleton.
6. CONCLUSION
In this paper, we surveyed computational musculoskeletal modeling,
analysis, and simulation of human lower extremities. We illustrated that with
increasing the complexity and level of detail of human models, a need for
high-performance numerical time-varying schema has emerged. Hence,
in this chapter, we first reviewed the experimental kinematic approaches
for studying human walking, including vision-based and nonvision-based
techniques. Then, we divided biomechanical dynamic models into three
categories: (i) skeletal models in which all effects of muscles are modeled
as simply as torques applied to joints, (ii) musculoskeletal models where mus-
cle groups are included in the system dynamics, and (iii) NMS models in
which human movements produced by the muscular and skeletal systems
are controlled by the CNS.
The skeletal model has been used extensively in the robotic field to
develop realistic and smooth human walking using rigid multibody systems
via inverted pendulum modeling, passive walking dynamics, ZMP, optimi-
zation, and control-based approaches. On the other hand, the musculoskel-
etal and NMS models have been used quite extensively in biomechanical
fields. We reviewed current methods for numerical simulation of musculo-
skeletal modeling including optimization and control-based approaches. We
realized that inverted pendulum, ZMP, and passive dynamics walking
models are based on the idealized models with few DOFs, in contrast,
optimization- and control-based methods are important approaches for sim-
ulating natural human walking with higher DOFs and physical details. The
control-based methods are suitable for applications in neurological studies of
human movement, while the optimization-based methods are advantageous
for conducting “what-if” scenarios.
Finally, we surveyed efforts on improving the understanding of
the physical interaction of human limbs with their physical environment.
We realized that for optimal design of exoskeletons, an integrated
musculoskeletal-exoskeleton system is necessary to understand how much
force the exoskeleton model generates before manufacturing the real
66 A. Alamdari and V.N. Krovi
exoskeleton. We also realized that, in order to simulate in the real operating
conditions, a virtual exoskeleton could be properly constrained to a human
musculoskeletal model within a biomechanical simulation platform. Then,
analysis of simulation results might suggest potential kinematic and dynamic
modifications of the real system in order to test the new design.
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