Fahse et al

*J. Fehr, Institute of Engineering and Computational Mechanics (ITM), University of Stuttgart, Stuttgart, Germany.

# Dynamic Human Body Models in Vehicle Safety: An Overview

N. Fahse  F. Kempter  S. Maier  M. Roller  M. Millard  J. Fehr  Institute of
Engineering and Computational Mechanics (ITM), University of Stuttgart,
Stuttgart, Germany  Fraunhofer Institute for Industrial Mathematics (ITWM),
Fraunhofer-Gesellschaft, Kaiserslautern, Germany  Institute of Sport and
Movement Science (Inspo), University of Stuttgart, Stuttgart, Germany
<EMAIL_ADDRESS>N. Fahse  F. Kempter  S. Maier  M. Roller  M.
Millard  J. Fehr

(20 September 2022)

###### Abstract

[Summary] Significant trends in the vehicle industry are autonomous driving,
micromobility, electrification and the increased use of shared mobility
solutions. These new vehicle automation and mobility classes lead to a larger
number of occupant positions, interiors and load directions. As safety systems
interact with and protect occupants, it is essential to place the human, with
its variability and vulnerability, at the center of the design and operation
of these systems. Digital human body models (HBMs) can help meet these
requirements and are therefore increasingly being integrated into the
development of new vehicle models. This contribution provides an overview of
current HBMs and their applications in vehicle safety in different driving
modes. The authors briefly introduce the underlying mathematical methods and
present a selection of HBMs to the reader. An overview table with guideline
values for simulation times, common applications and available variants of the
models is provided. To provide insight into the broad application of HBMs, the
authors present three case studies in the field of vehicle safety: (i) in-
crash finite element simulations and injuries of riders on a motorcycle; (ii)
scenario-based assessment of the active pre-crash behavior of occupants with
the Madymo multibody HBM; (iii) prediction of human behavior in a take-over
scenario using the EMMA model.

, , , , , and (2022), Dynamic Human Body Models in Vehicle Safety: An
Overview, TODO, TODO.

###### keywords:

Human Body Model, Multibody Model, Finite Element Analysis, Vehicle Safety

††articletype: Review

##  1 Introduction

Mary Ward was the first victim of a traffic accident when she was killed in
1869 by a steam-powered automobile 19. Today vehicles are much safer 81 due to
improvements in traffic regulations, the structural design of cars, and the
addition of specific safety systems. The structural design of a modern vehicle
is heavily influenced by safety concerns. For example, the chassis is designed
to crumple and absorb energy during an accident, the doors have been stiffened
to prevent passengers from being crushed during an impact from the side, and
the hood is designed to flex and cushion the impact of a pedestrian. In
addition, modern vehicles include several safety systems that did not exist in
Mary Ward’s time: pre-tensioned seat belts, front air-bags, and side air-bags.

The development of many vehicle safety systems has been supported by
experimental and computerized crash simulations that include representations
of the human form. During an experimental crash test, an anthropomorphic test
device (ATD) is used to predict the response of a human passenger. ATDs are
instrumented passive mechanical devices that can mimic the geometry, mass
distribution, joints and passive joint stiffness of the human body. These test
devices have been used to develop many safety systems, and remain part of the
certification process of modern vehicles 16, 84. Unfortunately, physical crash
tests with ATDs are expensive, cannot be done without a physical prototype of
the car, and can only provide an indication of an injury. In contrast,
computer models of the human body can be simulated without a physical
prototype of a car and capture enough anatomical detail to make specific
tissue-level injury predictions. In this work, we review the state of the art
of human body models used in vehicle safety, the most commonly used
mathematical methods that are used with these models, and conclude the paper
with three application examples using digital HBMs that cover a range of
different driving scenarios.

There are a wide variety of different types of human body models (HBMs) that
are needed to address the complexities of car design: there are ergonomic
models used to assess comfort, rigid-body models that are used to predict
movement while driving, and detailed musculoskeletal and finite-element models
used to predict injury during car accidents. While ATDs must be physically
robust to produce reproducible results and are uniaxial by design, digital
HBMs can use anatomically accurate joints and tissue models. These digital
twins serve to act as a virtual microscope to study reachability, kinematics,
comfort, and injury mechanisms. The number and variety of models is likely to
increase in response to the greater variety of vehicles that are being
developed, and the increasing number of passenger types that must be
considered.

Several HBMs were developed in the last decade with an increasing level of
detail and biofidelity. For a first approximation, the human body can be
modeled as a rigid multibody system (MBS) that gets its mobility from
idealized joints that connect each segment (an example featuring the knee
joint appears in the left panel Fig. 1) as is done in the model SAMMIE (System
for Aiding Man Machine Interaction Evaluation) 7, 8. Additional detail can be
added to a rigid body model by replacing idealized joints with anatomically
accurate representations that include ligaments, cartilage, and the network of
muscles that surround a joint (right panel Fig.1). Rigid body models, however,
have limitations: bones are assumed to be rigid and tissues are spatially
lumped. In contrast, finite element (FE) models can be used to accurately
capture both the geometry and material properties of a variety of tissues
making it possible to predict injury 106.

Figure 1:  On the left a simple multibody system serves as an approximation of
the knee joint. On the right in a detailed FE knee model approach, the femur
and tibia bones may be connected by the ligaments of the knee, separated by
the meniscus, driven by the muscles of the leg, and surrounded by wobbling
masses elements. Note that only a few of the ligaments of the knee are
depicted.

Typically MBS models have fewer degrees-of-freedom (DOFs) than FE models.
Within the context of an individual MBS model, different coordinate systems
can be used to make equivalent versions of the same model. In a redundant
coordinate system each body segment has three linear and three rotational
coordinates and joints are represented mathematically as constraints and have
equations of motion that are differential algebraic equations (DAEs) in
structure. While DAEs can be simulated forward in time, applying inverse
kinematics and inverse dynamics methods to a system of DAEs is challenging. As
a benefit, however, redundant coordinate systems make it possible to use
anatomically detailed joint models that include ligaments and compliant
cartilage. In contrast, a minimal coordinate system treats the joint
coordinates as the DOFs and results in a smaller set of equations. In the
special case that the model has a tree-like structure and contains no closed-
loops, the equations of motion take the form of a system of ordinary
differential equations (ODEs) that can be easily used with both forward and
inverse methods.

In either case, the coordinate system ultimately does not affect the $f$
degrees-of-freedom (DOFs) of the model: specifying $f$ generalized (minimal)
coordinates $\bm{y}$ of a model will uniquely specify the position of the
model in space. The equations-of-motion for a holonomic MBS with a tree-like
structure are

$\bm{M}(\bm{y},t)\cdot\ddot{\bm{y}}={\bm{k}}_{\mathrm{c}}(\bm{y},\dot{\bm{y}},t)+{\bm{k}}_{\mathrm{e}}(\bm{y},\dot{\bm{y}},t),$
(1)

where $\bm{M}\in\mathbb{R}^{f\times f}$ represents the global mass matrix,
${\bm{k}}_{\mathrm{c}}\in\mathbb{R}^{f\times 1}$ the vector of the generalized
Coriolis and centrifugal forces and
${\bm{k}}_{\mathrm{e}}\in\mathbb{R}^{f\times 1}$ the vector of the generalized
applied forces 125.

While MBS models are accurate enough for simulating voluntary motion, FE
models are needed to accurately simulate the movements and injuries that take
place during a car crash. The human body can be described as an elasto-plastic
dynamic continuum system and modeled using the FE method 3. The FE approach
allows the representation of nonlinear material behavior, large deformations,
and multiphysics coupling. The FE equation

$\bm{M}\cdot\ddot{\bm{q}}+\bm{f}_{\mathrm{int}}(\bm{q},\dot{\bm{q}})=\bm{f}_{\mathrm{ext}},$
(2)

consists of the symmetric and usually diagonal mass matrix
$\bm{M}\in\mathbb{R}^{N\times N}$; the nodal coordinates $\bm{q}$, nodal
velocities $\dot{\bm{q}}$, and nodal accelerations $\ddot{\bm{q}}$. The vector
of nodal forces from the internal forces (element stresses) comes from the
material laws (the relation between stress, strain, strain rate and loading
history) $\bm{f}_{\mathrm{int}}(\bm{q},\dot{\bm{q}})$ and the vector of the
external surface and volume forces $\bm{f}_{\mathrm{ext}}\in\mathbb{R}^{N}$. A
crude approximation for the number of DOFs $N$ is three times the number of
nodes of the FE model. States associated with active tissues, such as muscle,
further increase the DOF count of the model.

Active muscle models are being increasingly included in HBMs due to the
potential influence of muscle activity on the risk of injury 90. Muscle is an
incompressible tissue 116 that is driven by a vast array of microscopic
contractile fibers. Models of muscle often ignore the volume of muscle, and
instead is treated as an array of massless contractile cables. The tension
that muscle can generate is challenging to model because the stress, stiffness
115, and damping 55 all vary with chemical activation, strain 31, strain-rate
39, and state history 38.

Figure 2:  The most commonly used muscle model is a phenomenological Hill-type
muscle model (A). A Hill-type muscle has two main parts: an elastic tendon,
and a contractile element that acts at a pennation angle $\alpha$ to the
tendon. When normalized force $\tilde{f}^{\mathrm{M}}$ is plotted against the
normalized length of the muscle $\tilde{\ell}^{\mathrm{M}}$ the nonlinear and
scale-invariant force-length relationship arises 123, 30. Similarly, when
normalized muscle force is plotted against normalized contraction velocity
$\tilde{v}^{\mathrm{M}}$ (C) Hill’s hyperbolic force-velocity relationship
appears 39. During lengthening, the pattern of force development is not as
consistent, but usually involves enhanced forces 48, 79. Splines are often
used to represent the nonlinear force-length
$\mathbf{\mathrm{f}^{\mathrm{L}}}(\tilde{\ell}^{\mathrm{M}})$ and force-
velocity $\mathbf{\mathrm{f}^{\mathrm{V}}}(\tilde{v}^{\mathrm{M}})$
relationships 80.

The most commonly used muscle model is the phenomenological Hill-type model
39, 121, 103 because it strikes a balance between accuracy and computational
cost. Modern Hill-type models 128, 80 are formulated in a normalized
space111Note that normalization is indicated with a tilde, forces are
normalized by $f^{\mathrm{M}}_{\circ}$, CE lengths by
$\ell^{\mathrm{M}}_{\circ}$, CE velocities by $v^{\mathrm{M}}_{\circ}$, and
tendon lengths by $\ell^{\mathrm{T}}_{s}$. which allows a Hill model to be fit
to any musculotendon actuator by knowing only a few architectural parameters
of the biological muscle: the maximum isometric force
$f^{\mathrm{M}}_{\circ}$, the length $\ell^{\mathrm{M}}_{\circ}$ at which the
CE develops $f^{\mathrm{M}}_{\circ}$, the pennation angle $\alpha$ between the
CE and the tendon at $\ell^{\mathrm{M}}_{\circ}$, the maximum shortening
velocity $v^{\mathrm{M}}_{\circ}$ of the CE, and the slack length
$\ell^{\mathrm{T}}_{s}$ of the tendon. Embedded in the formulation of the Hill
model are three experimental characteristics: Hill’s 39 force-velocity
relation $\mathbf{\mathrm{f}^{\mathrm{V}}}(\tilde{v}^{\mathrm{M}})$, Gordon et
al.’s active-force-length
$\mathbf{\mathrm{f}^{\mathrm{L}}}(\tilde{\ell}^{\mathrm{M}})$ relation 31, the
passive force-length relation
$\mathbf{\mathrm{f}^{\mathrm{PE}}}(\tilde{\ell}^{\mathrm{M}})$ of the CE 30,
123, and the nonlinear force-length relation
$\mathbf{\mathrm{f}^{\mathrm{T}}}(\tilde{\ell}^{\mathrm{T}})$ of the tendon
72, 71. The normalized tension developed by a Hill-type CE is the sum of the
active and passive forces

$\tilde{f}^{\mathrm{M}}=a\,\mathbf{\mathrm{f}^{\mathrm{L}}}(\tilde{\ell}^{\mathrm{M}})\,\mathbf{\mathrm{f}^{\mathrm{V}}}(\tilde{v}^{\mathrm{M}})+\mathbf{\mathrm{f}^{\mathrm{PE}}}(\tilde{\ell}^{\mathrm{M}})$
(3)

developed by the CE, where $a$ is the chemical activation of the muscle. The
activation of the muscle is driven by the input signal $u$ of the nervous
system

$\dot{a}=\left\\{\begin{array}[]{lr}(u-a)/(\tau_{\mathrm{A}}\,(0.5+1.5a))&\text{
if }u>a,\\\
(u-a)/(\tau_{\mathrm{D}}/(0.5+1.5a))&\text{otherwise}\end{array}\right.$ (4)

where the time constants $\tau_{\mathrm{A}}$ and $\tau_{\mathrm{D}}$ that are
largely determined by rates at which calcium ions can be pumped into and out
of sarcomeres, respectively. The tendon is often modeled as a nonlinear
massless elastic 128, 80 that is assumed to be in a perfect force equilibrium

$\tilde{f}^{\mathrm{M}}\cos\alpha-\mathbf{\mathrm{f}^{\mathrm{T}}}(\tilde{\ell}^{\mathrm{T}})=0$
(5)

with the CE. This force equilibrium equation can be solved for
$\tilde{v}^{\mathrm{M}}$ by inverting
$\mathbf{\mathrm{f}^{\mathrm{V}}}(\tilde{v}^{\mathrm{M}})$, or by regularizing
this equation with a numerical damping term and applying a root solving method
to solve for a $\tilde{v}^{\mathrm{M}}$ that satisfies Eqn. 5 80. The final
result is a first order ODE that has two states
$(a,\tilde{\ell}^{\mathrm{M}})$ and can replicate Hill’s 39 and Gordon et
al.’s 31 experiments by construction. Often large muscles are represented in
MBS and FE models by an array of Hill-type contractile elements that attach
to, and wrap around, bony geometry 109.

Once a model is developed, there are two different families of methods that
can be used to simulate multibody (1) and FE systems (2): inverse methods and
forwards methods. Although both inverse and forwards methods can be applied to
multibody (1) and the FE systems (2), FE systems are almost exclusively
simulated using forward dynamics. There are two inverse methods, inverse
kinematics and inverse dynamics, that are often applied to MBS systems. The
inverse kinematic method is frequently used with HBM models when analyzing
experimental data. Unfortunately it is rarely possible to measure joint angles
in a human participant, instead the positions $\mathbf{x}$ of motion capture
markers placed on the skin are measured using camera systems. The generalized
positions $\bm{y}$ of the model that best fit observed motion are solved for
by minimizing the sum of squared errors between the $\mathrm{P}$ recorded
marker positions $\mathbf{x}$ and the model’s virtual marker positions
$\mathbf{z}(\bm{y})$

$\min\sum_{i}^{\mathrm{P}}\left(\mathbf{x}_{i}-\mathbf{z}_{i}(\bm{y})\right)^{\mathrm{T}}\cdot\left(\mathbf{x}_{i}-\mathbf{z}_{i}(\bm{y})\right)$
(6)

using the Levenberg-Marquardt algorithm 67, 78. By repeating this process at
every point in time, the full trajectory of a model $\bm{y}(t)$ can be
constructed and numerically differentiated to yield generalized velocities
$\dot{\bm{y}}(t)$ and accelerations $\ddot{\bm{y}}(t)$. Inverse dynamics
analysis is an additional method that uses
$(\bm{y},\dot{\bm{y}},\ddot{\bm{y}})$ and Eqn. 1 to solve for the external
forces ${\bm{k}}_{\mathrm{e}}$ that must have been applied to the model during
the experiment. In the context of driving, inverse dynamics is often used to
solve for the net muscle forces developed in the leg during a breaking
maneuver. In addition, inverse dynamics can also be used to evaluate Eqn. 1 as
a constraint using synthetically generated
$(\bm{y},\dot{\bm{y}},\ddot{\bm{y}})$ as is done in the direct collocation
method 119. Since inverse dynamics does not require any computationally
expensive numerical operations, such as matrix inversion or numerical
integration, it is often used in optimization, parameter identification, and
in the analysis of pre-recorded human motion.

In contrast to inverse methods, forward dynamics can be used to predict the
trajectory that a model will take over time given only its initial state and a
function to evaluate the forces applied to the system. Using the FE system as
an example, the forward dynamic method begins with the initial positions
$\bm{q}_{0}$ and velocities $\dot{\bm{q}}_{0}$

$\displaystyle\begin{split}\bm{M}\cdot\ddot{\bm{q}}+\bm{f}_{\mathrm{int}}(\bm{q},\dot{\bm{q}})&=\bm{f}_{\mathrm{ext}}\\\
\text{with}\hskip 28.45274ptt&\in[t_{0},t_{\mathrm{end}}],\\\
\bm{q}(t_{0})&=\bm{q}_{0},\\\ \dot{\bm{q}}(t_{0})&=\dot{\bm{q}}_{0},\\\
\bm{q}&=\hat{\bm{q}}\text{ on }\partial\mathrm{B}_{q},\\\
\bm{\sigma}&=\hat{\bm{t}}\text{ on }\partial\mathrm{B}_{\sigma}\end{split}$
(7)

and a numerical integration scheme that steps forwards in time from
$[t_{0},t_{\mathrm{end}}]$ using the value of $\ddot{\bm{q}}$ from the
equations of motion. The boundary conditions $\bm{q}=\hat{\bm{q}}\text{ on
}\partial\mathrm{B}_{q}$, and the initial stress
$\bm{\sigma}=\hat{\bm{t}}\text{ on }\partial\mathrm{B}_{\sigma}$, as well as
the initial positions are often crucial for valid and realistic simulation
results. The choice of suitable integration method for numerical simulation
depends on the type of FE equation, smoothness of the data, and the response
of interest. For highly-dynamic impact situations, explicit integration
schemes are preferred and state-of the art, since the penalty-based contact
algorithms introduce noise 3.

There are different driving situations (upper part Fig. 3) each with its own
loads and quantities of interest: vehicle entry/exit, low dynamic driving,
high dynamic driving, physical limit, pre-crash, in-crash, and post-crash.
Those different loading conditions and quantities of interest lead to specific
HBMs (examples appear in lower part Fig. 3). However, the models are not
limited to this domain and are also used to investigate other driving
situations. The assignment is based on a personal assessment by the authors.
During vehicle entry and exit, or during low-dynamic driving, the acceleration
of the car is minimal the purpose of simulation is often to assess kinematic
quantities such as the ergonomics and reachability of different parts of the
car. However, this changes during highly dynamic driving when the acceleration
of the vehicle is large enough to influence the movements of the passengers.
In this more aggressive phase of driving, occupant motion and muscle activity
are frequently studied to determine how much the passenger will move during
the task and how much effort is required to maintain a seated position. The
final three phases are all associated with a crash: the pre-crash phase which
consists of the seconds before impact; the in-crash phase which often lasts
only 100-200 ms, and the post-crash phase which begins after the vehicle has
come to rest. The accelerations experienced during the in crash phase can be
quite high. During a frontal crash against a non-deformable barrier the
occupant of the car can be decelerated from $v^{\mathrm{occ}}_{\mathrm{in-
crash}}=43\;\mathrm{km}/\mathrm{h}$ to $v^{\mathrm{occ}}_{\mathrm{post-
crash}}=0\;\mathrm{km}/\mathrm{h}$ within 105 ms, see 99.

Figure 3:  Driving situations with examples of different HBMs suitable for the
specific driving phase. For the sake of brevity, we will explain the
abbreviation of the single HBMs later in Sec. 2.

The severity of injury is classified differently from medical and economic
institutions. The medical _Abbreviated Injury Scale_ (AIS) 1 rates injuries of
the whole body from ’non-injured’ (0) to ’untreatable’ (6). From an economic
perspective, the years of life lost, mortality rate, and the subsequent costs
due to road traffic are important figures monitored by national traffic safety
organizations and insurance companies.

The paper continues with an overview of available HBMs and a series of case
studies. Our most comprehensive example in Sec. 3 presents an analysis of a
novel motorcycle safety system using: (i) in-crash FE simulations and injury
evaluation of riders on a motorcycle equipped with a novel safety system; (ii)
validation experiments using a Driver-in-the Loop system to access the
accuracy of a Madymo multibody HBMs pre-crash behavior; (iii) a prediction of
human behavior during a take-over scenario using the muscle-actuated EMMA
model 105. The paper concludes with current research trends in vehicle safety
simulation.

##  2 Human Body Models in Vehicle Safety

A variety of HBMs have been developed to strike a balance between model detail
and simulation runtime for the wide range of automotive design concerns. Tab.
1 shows how the level of detail varies widely across the HBMs we consider,
from models that are kinematic and driven by tabulated experimental data to
models that include accurate representations of detailed anatomical structures
of the body. The level of detail in the model directly translates into a
greater memory footprint, larger data structures, and longer mathematical
operations during simulation: detail is resource intensive. As such, it is
most common to use kinematic and multibody models to solve optimization
problems that may require hundreds to thousands of simulations of a specific
scenario. In contrast, when high levels of detail are needed an FE model is
typically used and the crash scenario is often only simulated a few times.
Model choice is often guided by the level of detail required for the study,
and limited by the computational costs of running the simulations.

###  2.1 Kinematic Human Body Models

At the lowest end of modeling complexity, kinematic models are mainly used to
evaluate ergonomics. These models only consider the kinematic motion variables
and introduce joint angle limits to evaluate reachability. Examples for this
class of HBMs are RAMSIS 6 and Jack 95 which are both connected to
anthropometric databases to evaluate the ergonomics of a specific age, sex, or
population. It is further possible to visualize reach envelopes and to
evaluate the visibility of instruments, mirrors, and the environment 6, 95. In
addition, RAMSIS can generate realistic postures and movements with a
probability-based model that relies on pre-recorded posture studies and can
evaluate the discomfort of these postures 6. RAMSIS is widely used in the
automotive industry to evaluate the interaction between the human and product
during the early design phase 124.

###  2.2 Multibody Human Body Models

Multibody HBMs offer a balance between the level of detail of the model and
the computational cost of simulation. This balance makes it possible to use
multibody models in many different phases of driving from vehicle entry/exit,
ergonomic simulations, low-dynamic driving, high-dynamic driving simulations
and pre-crash simulations. In addition, the level of detail in a multibody
model can vary dramatically, from HBMs that are driven by joint torques and
treat contacts as rigid constraints 4, to HBMs that are driven by hundreds of
lumped-parameter muscles and approximate contact forces using compliant
contact volumes 113.

#### OpenSim

OpenSim is an open-source software system that allows users to simulate a wide
variety of movements of musculoskeletal models 13 that can vary from simple
joint torque driven models to models that contain hundreds of nonlinear muscle
actuators. It is possible to interface with the OpenSim software via Python,
Matlab and C++, among others. OpenSim includes functionality for
forward/inverse kinematics, forward/inverse dynamics, and optimal control 13,
112 making it a tool that can be used to analyze complex experimental data, or
synthesize physics-informed human movement predictions. Most often OpenSim is
used to compute physics-based estimates of the muscle forces and joint contact
loads from an experimental recording of a human participant. In 44 OpenSim is
used to evaluate the car-pedestrian impact.

#### AnyBody

AnyBody 12 provides similar dynamic and kinematic functionality compared to
OpenSim but focuses exclusively on solving an inverse problem: estimating the
muscle forces and joint loads of a participant from motion capture data of an
experiment. As long as the model and input data are identical, both OpenSim
and AnyBody produce the same results 54. However, because AnyBody has focused
on solving inverse problems, they have been able to make incredibly detailed
musculoskeletal models that include hundreds of muscles and detailed joint
models. This additional level of detail does result in differences when
simulations of AnyBody models and OpenSim models are compared 54, 107, 120.

Figure 4:  Simulation of the assembly of an engine of two workers in IPS IMMA
.

Figure 5:  Simulation of a family of DHM sitting in a car holding the steering
wheel.

Figure 6:  The skeleton of the EMMA4Drive manikin based on the THUMS Skeleton.

#### IPS IMMA

The Intelligently Moving Manikin (IMMA) 32 is an MBS focused on evaluating
human ergonomics 40 that has been applied to study human tasks in a production
environment, and also to study the ergonomics of seated reaching tasks in a
vehicle. IPS IMMA is a biomechanical model that consists of 82 bone segments
connected by joints, giving a total of 162 degrees of freedom. The model
creates a human-like posture due based on these constraints, by solving an
optimization problem. This includes finding a stable equilibrium (balance),
which minimizes a proprietary objective function that contains terms related
to ergonomics, joint torque, and posture. The posture of the manikin is
controlled by the user defines by defining where to grasp an object and/or
where the manikin should look, without the need to touch any joint angles. IPS
IMMA creates a motion using a sequence of optimized static postures (quasi-
static simulation). These movements are specified by defining a series of
boundary poses in a sequence editor. Using the sequence of boundary conditions
as a guide, the IPS IMMA system computes a series of postures interpolating
between the sequence of poses that predicts quasi-static human movements. IPS
IMMA also includes a reachability analysis and mountability feature, which
ensures collision-free assembly movements. Depending on the task, the movement
strategy is adjusted automatically. This feature also allows for the
examination of the mountability of objects by humans. As manikins are
controlled by defining constraints, which remain the same for manikins with
another anthropometry, a defined scenario can be recalculated for a whole
manikin family without any further control effort.

In recent days IPS IMMA was extended to simulate manikins sitting in a car or
a truck, see Fig. 6. Herein, different objective functions are used to create
the static posture tailored to these use cases. Therefore IPS IMMA can also be
used for static reachability analysis or visibility studies like RAMSIS. For
dynamic use cases, the EMMA model has been developed in recent years.

##### EMMA

EMMA (Ergo-dynamic Moving Manikin) is a multibody model that has been used to
synthesize human motions when coupled with an optimal control solver and a
cost function. The movements of EMMA are induced by Hill-type muscles 39, 70
which are represented as cables, or by joint actuators which act directly on
the joints of the model. EMMA’s synthesized movements are driven to minimize
cost functions that consist of several terms including the sum of squared
control signals, the kinetic energy of the system, and the execution time of
the movement. Although optimal control problems applied to musculoskeletal
systems can be difficult to solve, long scenarios have been simulated using a
specialized optimal control problem formulation, discrete mechanics and
optimal control for constrained systems (DMOCC) 68, and an interior point
optimization method 4, 104.

EMMA uses a special case to solve optimal control problems that include
contact: if the contact sequence is known ahead of time the optimal control
problem can be broken up into a series of discrete phases. Each discrete phase
of the optimal control problem is defined by the set of bodies that are in
contact, since the equations of motion need to be modified to include the
contact. As is commonly done when simulating walking 64 and running 110,
contact is treated as a kinematic constraint with additional phase-specific
constraints added to the optimal control problem to ensure that the contact
does not exceed friction limits. Transitions between phases are made assuming
that contact is plastic, and momentum conserving. As such, every phase
transition is accomplished by applying the principle of impulse momentum to
evaluate the generalized velocity vector of the system after each contact.
Finally, the duration of each contact is left as a free variable that the
solver modifies to improve the cost of the solution. Since the duration of a
phase can even go to zero, effectively eliminating the phase, this approach
can be applied to a wide variety of problems.

Typically a multi-phase optimal control problem is limited by the duration and
complexity of the task being simulated. However, because EMMA makes use of a
discrete mechanics formulation DMOCC 68, the physical properties (impulse,
angular momentum) of the system are conserved even for large discretization
steps, which allows EMMA to simulate tasks that have a long duration. Thus far
EMMA has been used to simulate a person lifting a box 104, pulling an
emergency brake in a car 105, and getting into a truck 5. EMMA is currently
being used to simulate the voluntary motions that occur just prior to the
start of a crash, bridging the gap between MBS and FE models, see Fig. 6.

#### Simcenter Madymo

Simcenter Madymo is a combined MBS and FE simulation system that features
full-scale omnidirectional multibody models 33. There are a number of advanced
elements that distinguish Simcenter Madymo such as elastic ellipsoid contact
models, detailed facet models represented with meshes, flexible components
such as ribs, and FE elements to represent important deformable elements 34.
The focus of Simcenter Madymo is the simulation of active muscle-induced human
motion during the pre-crash phase, and as such, the models are referred to as
Active Human Body Models (AHBMs).

The AHBM is a detailed model of a 50% male from the RAMSIS database (a
$75.3\;\mathrm{kg}$ and $1.76\;\mathrm{m}$) that features a seated (Fig. 8
left) and a standing variant (Fig. 8 right) with the body being supported by a
skeleton that has 182 rigid bodies, 8 flexible bodies (abdomen and thorax) and
compliant joints 113. The AHBM is not fixed, but supports modification of the
joints and surface meshes of the model. The outer surface of the model uses FE
shells to accurately model contact forces with the seat, interior, and safety
systems. Effort has been put into defining the contact stiffness of different
parts of the vehicle and the AHBM to improve the realism of contact
simulation.

Figure 7:  Active Human Body Model in the occupant (left) and in the
pedestrian/standing version (right). The red lines correspond to the muscle
elements. The spine is modeled as flexible elements 113.

Figure 8:  Frontal and side view of the AHBM head and neck model showing 32
(2x16) different muscles modeled with 136 muscle elements. The rotation angles
are also depicted.

Two unique features of Madymo’s AHBM are its posture stabilization control
system, and its anatomically detailed active musculature of the extremities
(Fig. 8) and neck (Fig. 8). The posture stabilization system consists of a set
of reflex controllers that have been carefully designed to mimic the reflex
responses of the human body across a range of bandwidths. These reflex
controllers are used to activate the muscles (Fig. 9) of the head and neck,
arms, and legs, while the spine is driven by torque actuators. While all of
the controllers are important, the controller for the head and neck is
particularly important because the cervical spine is frequently injured 96
during car accidents.

Both the musculoskeletal model (Fig. 8) and control of the head and neck is
complex (Fig. 9). While the pose of the model’s head is described by only
three coordinates (pitch, roll, and yaw), the neck and head are driven by 136
muscle elements belonging to 32 different muscle groups that represent the
most relevant muscles of the head and neck. Reflex and stabilization studies
of the head and neck 23, 35 have shown that the neck’s muscular recruitment is
driven by input to the somatosensory system, and that the response is
frequency-dependent. For static poses and low frequency movements, the
vestibular system is used to achieve an upright position of the head relative
to the inertial system. However, in more dynamic situations with higher
frequency content, the system tries to control the relative pose between the
head and torso (head-in-space stabilization).

Accordingly, the AHBM uses this postural control concept and tries to assume a
specific pose as quickly as possible under the influence of disturbing forces
acting on the body. Reflexes are incorporated into the head and neck
controller (HNC) 25, 85 using a model of the somatosensory system to trigger
reflexes, which are subject to a conduction delay, and are modified by a
frequency-dependent gain prior to activating the muscles (Fig. 9).

The input to the HNC system (Fig. 8) is the desired orientation trajectory of
the head which is defined as the orientation of the head in the inertial
system (using roll-pitch-yaw), and the orientation of the head with respect to
the T1 vertebrae (also using roll-pitch-yaw) which are delayed prior to
reaching the muscles. The extra coordinate system allows the system to
smoothly switch between using an inertial system orientation reference and a
head-in-space orientation reference. The error signal between the desired and
actual head orientation is delayed before reaching the muscles. As the signal
path is shorter to the neck than to the extremities, the transmission delay
for activating the muscles of the neck is shorter than for the arms or legs.

Different muscle groups are stimulated to counteract the deflection of the
head and neck, and to stabilize the movement of the head using co-contraction.
With its 32 muscles, discretized to 136 muscle elements, the AHBM has a highly
over-actuated head and neck. A simplified linear and decoupled control system
is used(Fig. 9) The control system consists of three time-delayed PID
controllers and a co-contraction factor $\textit{CCR}_{\textrm{Neck}}$. A
higher co-contraction level makes the HNC less sensitive to external
disruptive forces. A spatial activation pattern derived from experimental data
92, 65 is used to activate the over-actuated neck model. Madymo’s control
strategy is not hard-coded but can be customized by using the Matlab Madymo
coupling strategy. For example, Kempter et al. 50 implemented a completely
different control strategy in which every individual muscle of the neck was
controlled by its own stretch-reflex controller. By using the Matlab-Madymo
coupling strategy, it is possible to update the HNC as more about this complex
biological system is learned.

Figure 9:  Control approach of the Madymo AHBM.

Many properties of the AHBM model have been experimentally validated, and
calibrated. The passive properties of the AHBM have been validated using PMHS
tests 113. Many active properties of the model have been indirectly validated
by comparing the response of the entire head and neck model to in-vivo sled
tests 9, 14, 56, Driver-in-the-Loop (DiL) tests 20, 51, 53, and tests in real
vehicles 42, 91. An overview of available tests is provided by the OSCCAR
consortium 88.

###  2.3 Passive Finite Element Models

The FE method has been used extensively 126 to create HBMs that accurately
capture the geometry and injury mechanics of the musculoskeletal system, the
nervous system, and internal organs of the body. Passive FE models were
originally developed to mimic the response of a PMHS to occupant restraint
systems. The word passive is used to denote the fact that these models do not
include active muscles, nor any active actuation. Even though muscles remain
inactive in a passive FE model, these models are sophisticated and can predict
injury to bones, connective tissue, and internal organs. A broad selection of
element formulations have been developed to strike a balance between accuracy
and runtime during simulation.

Element formulations range in terms of geometry (hexahedral and tetrahedral
are typical), computational properties (DOF, numerical features), the physical
interactions (large deformations, contact), and injury mechanisms (fracture,
rupture, tearing) that are supported. The geometry of the structures in an HBM
is often based on CT or MRI images and contains many irregular shapes that are
difficult to mesh. Even though irregular shapes can be easily meshed using
tetrahedral elements, the preferred element for HBMs is the hexahedral element
due to its superior numerical robustness during simulation. The formulation of
the element, however, is not the only modeling component that affects
simulation time.

A variety of joint models are used in HBM models to capture the desired level
of detail. Idealized joints, such as spherical and revolute joints, are often
used to reduce computation when injury to the joint is not the focus of the
simulation. In contrast, anatomically accurate joint models are used when
injury to the cartilage, bursa, and ligaments of a joint are of interest. A
wide variety of models have been developed to balance detail against
simulation time for the many crash scenarios that must be considered during
the design phase.

Current state-of-the-art HBMs in vehicle safety (Fig. 10) include Toyota’s
Total HUman Model for Safety (THUMS) 49, the VIVA+ 47 models, and the GHBMC
111, 29, 10 models.

Figure 10:  Selection of female and male HBMs (partially blanked) in their
default positions (77).

Six THUMS model versions have been developed and evaluated 118 since 2000.
VIVA+ is a family of open-source models that have been developed as a part of
the EU-VIRTUAL consortium 69. These models are derived from the VIVA+ OpenHBM
— a 50th percentile female model from Chalmers University, Gothenburg, Sweden
— that was developed to study Whiplash Associated Disorders (WAD) of women
during rear-end collisions 93. The Global Human Body Models Consortium (GHBMC)
is composed of North American car manufacturers and research institutions.
Using MRI and CT data of a 26 year old male, the GHBMC developed its first
$50^{th}$ percentile male HBM in 2011 27, and have continued to develop models
as shown in Tab. 1. The additions to the GHBMC family include both male and
female models, child and adult models, occupant and pedestrian models,
simplified and detailed models, and models of large and small people. In
addition, variants of these models have been developed such as the SAFER HBM
98, and the THUMS TUC-VW AHBM 127. Even though there are many passive FE HBMs,
these types of models continue to be developed and used during product
development.

Current research focuses on making passive FE models that more accurately
match population demographics, and can be used in a wider variety of
simulation scenarios. As the proportion of older adults in society increases,
there is a focus on accurately capturing changes in age-related material
properties 108 of the body. There is also a growing focus on specialized
algorithms to account for human variability by scaling existing models to
represent the anthropometric properties of another person 66, 43. As the
variety of simulation scenarios has grown, tools are being developed to
position HBMs 58, 11 in a specific posture, such as the PIPER framework 97, 58
or the Oasys PRIMER positioning tool 11. For some accident scenarios, however,
the passive assumption of the human body is increasingly perceived as an
unacceptable simplification.

###  2.4 Active Finite Element Models

Active safety systems begin to act in the phase prior to the crash, when
accelerations are lower, and muscle activity influences the response of the
body. As summarized in 90 muscle activation influences the injury pattern in
the pre-crash and in-crash phases: neck muscle activity reduces the load on
the cervical capsular ligament below the injury threshold and increases the
load tolerance of the cervical spine from 1.8 kN to 3.1-3.7 kN; and active
bracing of the leg’s muscles increases the likelihood of injuries such as
femoral shaft fracture. Accordingly, efforts have been made to make active FE
HBMs by including models of muscles and control systems.

Nearly all of the MBS and FE models mentioned in this work represent volumes
of muscle by using arrays of Hill-type muscle cables that act independently.
While this approach reasonably approximates fiber paths in long skinny
muscles, this approach cannot capture the curving paths that are produced when
short bulky muscles bulge. In contrast, the GHBMC model embeds Hill-type
cables within a passive tissue volume making it possible to capture the fiber
geometry even for many types of muscles. Despite the existence of some
advanced active 3D muscle models, none yet exist in production-ready code.

While muscle is mechanically complex, the way the nervous system controls
muscle is perhaps even more challenging. Since many active FE HBMs focus on a
specific crash scenario, early models used open-loop control with pre-defined
muscle activation patterns that were calculated offline from experimental EMG
or by solving an application-specific optimization problem 46. Closed-loop
reflex control was later introduced to improve the response of the arms 89,
127, and the neck 86 during crash simulations.

Many additional control systems have been introduced to address the growing
list of applications for active FE models. The latest versions of the THUMS 5
and 6 45, 49 contain simple 1D Hill-type muscles with angle-based controllers
for posture maintenance. The VIVA+ model provides a posture controller for the
neck that includes both vestibular and stretch reflexes 59, 101. Similarly,
the GHBMC models now include a number of stretch reflex controllers 21, 60 and
a head and neck controller that features both vestibular and stretch reflexes
10. The SAFER HBM 90, based on THUMS v3.0, has been tested with four different
PID spinal posture controllers 90 in which a variety of pre-crash maneuvers
and crash scenarios were evaluated. In addition, the SAFER HBM now includes
two error angular position feedback postural control schemes - one for the
neck and one for the trunk. Future research will likely continue to develop
control systems to emulate in-vivo responses since muscle activity influences
the pattern of injury 90.

model |  simulation times11footnotemark: 1 |  common analyses |  domains |  DOFs |  variants22footnotemark: 2
---|---|---|---|---|---
RAMSIS |  $30\;\mathrm{s}$ to evaluate 50 positioning iterations |  forward and inverse kinematics |  ergonomics |  $65$ |  can be scaled to arbitrary anthropometries
_applications_ : evaluate anthropometrics-, posture-, visibility-, roominess-,
discomfort-, reachability-, safety-, and operability-ergonomics criteria in
the digital vehicle development 124
OpenSim |  - |  inverse dynamics; optimal control |  biomechanics; sports medicine |  $21$ (Gait-Model) |  can be scaled to arbitrary anthropometries
_applications_ : investigation of stiff-knee gait of a 12-year-old subject 13
inverse and forward dynamics and neuromuscular control of mammal motion 112
_comments_ : open-source
EMMA |  $45$ s to solve a simple optimal control problem |  optimal control |  early stage of safety system development |  $40$ |  Can be scaled to arbitrary anthropometries
_applications_ : simulation of dynamic driving maneuvers 105
AHBM |  $21$ min for $2$ s 50 |  forward simulation |  passive safety in impacts |  $108$33footnotemark: 3 |  M50-O/P
_applications_ : occupant loading in rotated seats configurations 2 Scenario
bases safety performance assessment integrated vehicle safety systems 122
GHBMC |  $96$ h for $304$ ms on $20$ CPUs44footnotemark: 4 |  forward simulation |  injury prediction on tissue level |  $2.3\;10^{6}$ elem. |  F05-O/P; M50-O/P; M95-O/P;
_applications_ : lumbar spine loads in reclined seating positions 102 human
response to underbody blasts 41 injuries of obese persons in sled tests an
belt loading 28 _comments_ : commercial; free academic test-licenses
simpl. GHBMC |  $\sim 5$ times faster than full GHBMC 111 |  forward simulation |  injury values on kinematic values |  $0.8\;10^{6}$ elem. |  6YO-P; F05-O/P; M50-O/P; M95-O/P;
_applications_ : feedback postural muscle control 10 _comments_ : commercial;
free academic test-licenses
THUMS |  $58$ h for $304$ ms on $20$ CPUs44footnotemark: 4 |  forward simulation |  injury prediction on tissue level |  $1.9\;10^{6}$ elem. |  3YO-O/P; 6YO-O/P; 10YO-O/P; F05-O/P; M50-O/P; M95-O/P;
_applications_ : rib fracture mechanism of elderly occupant 117 sport
accidents involving children and adults 114 influence of (autonomous) seating
position, direction and angle on injuries 57 _comments_ : open access since
2021; _special models_ : elderly, obese, pregnant, whiplash
VIVA+ |  $35$ h for $304$ ms on $20$ CPUs44footnotemark: 4 |  forward simulation |  injury prediction on tissue level |  $0.5\;10^{6}$ elem. |  50F-O/P; 50M-O/P
_applications_ : addressing gender diversity, initially focusing on head and
neck injuries 93 virtual testing in vehicle safety assessment, i.e. (standing)
vulnerable road users 47 _comments_ : open access, head and neck submodel for
speedup available100
11footnotemark: 1unless otherwise specified, the values are given for
calculations on a standard PC.
22footnotemark: 2abbreviations: F: female; M: male; number corresponds to
percentile; O: occupant model; P: pedestrian model;
33footnotemark: 3$108$ rigid general coordinates, from 182 rigid bodies, 190
kinematic joints, 2174 FE elements from the skin
44footnotemark: 4further explanations on the calculation times of GHBMC, THUMS
and VIVA+ are given in Sec. 3.1
Table 1:  Overview of popular HBMs with which the authors have gained
experience. The information in the table reflects the authors’ view.

##  3 Applications

Digital HBMs are used in many technical and artistic fields. To provide
insight into the application of HBMs in the context of vehicle safety, the
capabilities of some of the different HBMs, introduced in Sec. 2, are
presented in three case studies. In the first study, the application of a
detailed FE model in the development phase of a new motorcycle safety system
shows how complex models can contribute to a deep understanding of the events
during a motorcycle accident and help in the evaluation of integrated safety
systems. The latter examples feature multibody systems used in the early
development phase of new safety systems. In a scenario-based assessment of the
pre-crash phase, the MADYMO AHBM is applied to gain a further understanding of
the initial position of the head at the start of the in-crash phase. Hereby,
data from a Driver-in-the-Loop setup, showing the range and variance of motion
in the pre-crash phase, is utilized to account for the occupants’ behavior. In
a third example, the EMMA model generates realistic movements with the help of
optimal control to improve active and integral vehicle safety.

###  3.1 Case Study – Safe Motorcycle

As omnidirectional tools, HBMs can be used in a wide range of applications. In
the following, this is demonstrated with a comprehensive summary of the
application of state-of-the-art FE HBMs as motorcyclists in crash impacts from
77. Examples of current open and commercially available models are shown, a
positioning workflow in the specific application for riders of a motorized
two-wheeler is demonstrated and an impact response study on variations of
HBMs, including a comparison versus computational models of ATDs, is
discussed.

#### Positioning HBMs for Motorcycle Rider Postures

Positioning HBM FE models and initializing the actual simulation is an
intricate and often laborious task. The default positions of most models are
either standing postures of pedestrians or seated postures of car occupants.
Three state-of-the-art models in the LS-Dyna software environment are used:
the VIVA+ 50F and 50M 47, 87, the THUMS 49, and the GHBMC 29 models (Fig. 10).
The posture of a motorcyclist is determined by their anthropometric
measurements and the geometry of the motorcycle. The pelvis sits on the seat,
the hands grip the handlebar, the feet rest on the footrests, and the head
angle complies with the rider’s line of vision. This posture is maintained by
static muscle power. The developed workflow, which can be similarly applied to
car occupants, consists of two preparation steps, pre-positioning (I) and seat
and contact initialization (II), before the actual crash simulation (III)
(Fig. 11).

  * •

(I) Posture pre-positioning: Each of the individual HBMs are prepositioned
using the positioning and personalization tool PIPER 97. It is an academically
developed open-source tool comparable to commercial solutions of other FE
preprocessors based on HBM-specific metadata. For positioning, it provides
functions for interactive manipulation of FE structures within the software
through lightweight and, therefore, fast physics models and the definition of
simulations for transient manipulation. Here, PIPER is used to define a
transient simulation by prescribing the motion of the skeletal structure via
elastic elements. The target position is determined by the joint angles of the
lower and upper extremity joints with fixed landmarks for the spine and head.
Assigning global damping in the explicit numerical simulation allows a faster
positioning for a short simulation time.

  * •

(II) Seating and contact initialization: For interaction with the motorcycle,
a subsequent simulation is run. The rider-to-motorcycle contact surfaces, the
seat, the handles, the footrests, and the other cockpit surfaces are initially
scaled and distorted. Then, these geometries are morphed into the motorcycle’s
actual geometry. This rotates the wrists and pushes the motorcycle against the
human body. Prescribed spring elements are also used to push the head back,
press the pelvis into the seat, and hold the feet to the footrests. Gravity is
not applied yet.

  * •

(III) Crash: The final step is the actual impact simulation. It starts shortly
before impact deceleration, with an initial velocity and a prescribed impact
trajectory for the motorcycle cockpit, similar to a crash pulse used for sled
tests. The imposed motion is a multi-axial linear and angular motion. It is
derived from a multibody simulation of the vehicle interaction of a
motorcycle, a rider, and a passenger car as the accident opponent, explained
in 74, as part of a simulation strategy that involves multiple models 73. The
prescribed model is a motorcycle with additional passive safety equipment,
airbags, thigh belts, and leg impact protection, as explained in 76, 75. It
restrains the rider to the two-wheeler, decelerates its movements, and
prevents hard accident contacts by airbags.

Between the three separate simulation steps, the nodal coordinates of the mesh
are transferred via Matlab procedures. This means mesh deformations are
carried over into the subsequent simulation; other information, such as the
element stresses due to deformations, is lost. The final postures at the end
of step (II) agree reasonably well (Fig. 12). For the female variant, adjusted
footrests and handlebars are considered. The comparison demonstrates
anthropometric differences of current HBMs, although the resulting postures
are similar overall. The comparison of the final hand positioning shows that
the HBMs differ in many modeling aspects. Here, the VIVA+ and GHBMC hands are
non-deformable rigid bodies, which results in the fingers either piercing the
handles, as shown for VIVA+, or thinner handles must be formed, as applied for
the GHBMC. Only THUMS allows for realistic gripping of the handles.

Figure 11:  Multi-step pre-positioning, seating, and contact initialization
procedure for crash impact simulation of HBMs.

Figure 12:  Positioned and seated HBMs in the resulting motorcyclist’s riding
postures (77).

#### Variations of ATD and HBM Impact Response

Evaluating the primary impact kinematic response demonstrates significant
differences between HBMs and ATDs in a lateral impact of a passenger car with
35 km/h against the stationary motorcycle (Fig. 13). The models are partially
displayed transparently to illustrate the mechanical and human skeletal
structure. The side airbag deploys within 35 ms and is pushed down by the
riders, with the car acting as a reaction surface. The spine of the HBM is
laterally more flexible than the mechanical replication of the ATD, observable
at $75\;\mathrm{ms}$ by a delayed head motion and at 150 ms by a more
continuously deflected cervical and thoracic spine. The head is accelerated
from the upper body like a whip. Virtual sensor histories (Fig. 15 (A)),
reveal higher linear accelerations at a later time. The result shown is
expected, as ATD are designed to be biofidelic in very specific load cases,
mostly to depict car occupants. Here, human models are a meaningful
omnidirectional supplement.

Figure 13:  Rider trajectories of Hybrid III 50th percentile ATD (top) and
VIVA+ 50M HBM (bottom) for lateral car impact (77).

Comparing multiple HBM variants shows minor variations in impact kinematics
(Fig. 14). At each snapshot, the main skeletal structure is overlayed. The
trajectories of head COG, C7, T12, and L5 are continuously traced. Overall the
skeletal structures show similar initial position and impact responses for the
HBMs upon impacting the airbags. Differences arise from variations in
anthropometry and mass distribution from underlying body scans and/or the
modeling of materials, joints, and contact definition. For linear
acceleration, this leads to some greater variations (Fig. 15 (B)). Like
different real-world humans with similar - but of course not identical -
physiques, this results in a corridor that, in turn, challenges the robustness
of a safety solution. Working with several models to represent expected
variance may be advised.

The available models vary significantly in the calculation times, see Tab. 2.
The VIVA+ model with only 490K elements is the computational least costly
model of the three. The VIVA+ model is not as densely meshed as the THUMS and
the GHBMC model. The GHBMC model with 1.9M nodes is the most complex. The
calculation factor increases to over 1 000 000 for the crash simulation, which
means that for $1$ second simulation time over $1\,000\,000$ seconds elapse
until we receive the results. For all models, the calculation factor is
smaller in the prepositioning and the seating and contact initialization
problems.

Table 2:  Calculation times for the safe motorcycle study with HBMs. All simulations where performed with LS-Dyna R 9.3.1 mpp single precision version using 20 CPUs. (I) prepositioning (problem time = $250\;\mathrm{ms}$) | calc. factor
---|---
VIVA+ 50M | $7.8\;\mathrm{h}$ |  $\sim$ 113 000
THUMS AM50 | $19.6\;\mathrm{h}$ |  $\sim$ 282 000
GHBMC M50-O | $57.0\;\mathrm{h}$ |  $\sim$ 821 000
(II) seating and contact initialization (problem time = $250\;\mathrm{ms}$)
VIVA+ 50M | $13.2\;\mathrm{h}$ |  $\sim$ 190 000
THUMS AM50 | $20.6\;\mathrm{h}$ |  $\sim$ 296 000
GHBMC M50-O | $60.5\;\mathrm{h}$ |  $\sim$ 872 000
(III) crash simulation (problem time = $304\;\mathrm{ms}$, scenario 7)
VIVA+ 50M | $35.2\;\mathrm{h}$ |  $\sim$ 420 000
THUMS AM50 | $58.2\;\mathrm{h}$ |  $\sim$ 690 000
GHBMC M50-O | $95.5\;\mathrm{h}$ |  $\sim$ 1 130 000

Figure 14:  Rider trajectories (top) and comparison (bottom) of male HBMs for
lateral car impact (77).

Figure 15:  Resulting head COG linear accelerations for ATDs and HBMs. Note:
THUMS AM50 does not provide a head COG acceleration sensor (77).

HBMs enable a close examination of injury mechanisms. Typically, injury
criteria like the head injury criterion (HIC) 61 are derived from sensor
loads. These criteria are associated with injury probabilities such as from
82. These, in turn, are based on injury classifications like AIS 1. Based on
these injury probabilities, limits are set for recommendations of consumer
ratings or regulations to certify passive safety systems. Here, HBMs provide
much more profound insight. They offer the possibility of a virtual magnifying
glass that allows observing human injury mechanisms that are strain or stress-
based (Fig. 16).

Figure 16:  THUMS accident response (partially blanked) with illustrations of
exemplary strain- and stress-based assessments of various body parts of
different HBMs.

###  3.2 Case Study – MADYMO AHBM in a Driver-in-the-Loop Simulator and
Scenario-based Assesment

The Simcenter Madymo AHBM shows a lower numerical complexity than the FE
models from the previous example. The calculation factor on Linux with Madymo
R7.7 on a 12 core Intel i7-8700 processor with $3.20\;\mathrm{GHz}$ and
$64\;\mathrm{GB}$ RAM is $21\;\mathrm{min}\;4\;\mathrm{s}$ of calculation time
for $2\;\mathrm{s}$ problem time, see 50.

The lower computational cost of such a model facilitates the consideration of
human behavior in the phase prior to a crash. As shown in 22 human occupants
show different postures during naturalistic driving due to driving or non-
driving related tasks. This leads to differences in the occupants’ initial
postures before a potential crash. As the loading in the pre-crash phase is
considerably lower than during a crash, see Fig. 3, the occupant behavior is
highly affected by the muscular intervention. This active behavior can be
investigated in volunteer tests, showing often high variability in the
behavior of different test persons. It’s still a big challenge to account for
this intrinsic variability in the occupant posture and behavior in the
simulation with HBMs.

Experiments with Driver-in-the-Loop (DiL) simulator tests can contribute to
these additional aspects by providing experimental data which cannot be
investigated in standard laboratory sled tests. DiL test allows to put the
occupant into new (virtually) interior concepts while exposed to a mixed-
reality scenario and to study the interaction under (limited) external
loading. Different test series, see 50, 53, 20 were performed to gain a better
understanding of human behavior in such situations. To analyze the driver’s
behavior in experiments, the kinematics and muscle activation are monitored,
see Fig. 17. Furthermore, the platform motion emulating the virtual vehicle
state is tracked.

A. Driver-in-the-Loop (DiL) simulator setup

B. Internal and external signal flow for simulation and experimental data
acquisition

Figure 17:  Setup of the Driver-in-the-Loop (A) simulator with a Porsche
racing simulator, a Stewart motion platform and an Optitrack motion capture
system consisting of four cameras attached to the ceiling and EMG measurement
where the electrodes are placed on the neck muscle ©University of
Stuttgart/Uli Regenscheid. Internal and external signal flow for simulation
and experimental data acquisition (B) to collect synchronized measurements
(blue) of the human driver (green) sitting inside the simulator.

As shown in 52 a rotated head posture influences the muscle behavior prior and
during the virtual braking scenario. In a volunteer study, approved by the
local ethical committee, 17 healthy subjects were tested. As shown in Fig. 18
there is a huge variability in initial posture and dynamic behavior of the
participants of the study. The subjects were asked to hold a specific head
posture during the whole scenario of whether a nominal view (nom), or a
shoulder view to the right (sho), depending on the experimental plan in a
randomized order.

Figure 18:  Initial head postures (A) shown as initial yaw angle and
longitudinal position for nominal view (red) and shoulder view (blue) as mean
$\pm$ standard deviation. Head longitudinal displacement over time during
braking (B).

Based on the experimental data, suitable controller parameters can be
identified to replicate the experimental results of each subject. To do so,
the experimental setup is modelled in the multibody simulation framework
Madymo, where the platform motion is applied as a prescribed motion
constraint. Parameters characterizing the AHBM’s musculature or its control
strategy can be used to span a parameter space. Within this space, suitable
parameter sets can be identified which minimizes the deviations between
simulation and experiments. Often this optimization is performed on the
kinematic signals, while the muscle activity is used to plausibilize the
resulting parameter range, e.g. muscle onset times can be compared to check
the resulting delay values. The individual subject-specific parameters can
furthermore be used to define parameter ranges that allow to replicate the
variability of the human behavior observed in the experiments. Instead of one
nominal head position during a pre-crash maneuver, the simulation predicts a
range of possible head postures accounting for the identified variability in
the occupants’ behavior. This could enable the development of more advanced
safety systems with improved robustness.

For the usage of more advanced or more flexible control strategies with the
AHBM, the provided Matlab-Madymo coupling feature can be used. For example, in
50, an approach is presented to control the AHBM based on muscle-level
controller, i.e., to model the monosynaptic stretch reflex 21, or muscle-
length controller.

Another interesting use case for the AHBM is scenario-based assessments.
Scenario-based testing means moving away from single test cases toward a
virtual, cost-effective and holistic evaluation of a broader range of
scenarios a vehicle safety system would encounter in real-world applications.
Active and passive safety systems are combined with each other. The safety
system should act appropriately in every possible situation to gain more
insight into the system’s performance by covering a broader area of the
assumed field of application. To define all the possible crash scenarios, in
37, 122, a simulation framework for the scenario-based safety performance
assessment of integrated vehicle safety systems is presented.

The framework includes a scenario, a vehicle crash, and an occupant pre- and
in-crash simulation, thus allowing a traceable simulation of realistic driving
scenarios. The AHBM is used to simulate the occupant’s pre- and in-crash
behavior. Input for the pre-crash occupant simulation is the vehicle under
test’s translational and rotational acceleration at the center of gravity from
the pre-crash scenario simulation of the active safety simulation.

The pre-crash scenario simulation is a co-simulation framework 36, 122. With
the commercial software tool ANDATA, vehicle scenarios, as shown in Fig. 19 on
the left can be created and simulated.

Figure 19:  (A) Exemplary pre-crash trajectory of the vehicle under test
(blue) and the target vehicle (red); (B) Corresponding $x$-, $y$-, and
$\omega_{z}$\- acceleration of the vehicle under test.

Based on a specific scene, i.e. a particular crossing scenario, the user can
extract the vehicle’s trajectories under test and the target vehicle.
Afterward, with a more advanced vehicle dynamic model in Carmaker, the virtual
driver model tries to follow the trajectory from ANDATA. Furthermore, Carmaker
can simulate the sensors and actuators of the active safety devices, i.e. an
autonomous emergency braking (AEB) system. The model has a relatively low
computational effort 122. Therefore, the co-simulation framework can simulate
various scenarios to distinguish if the critical situation is resolved by the
intervention of the active safety system or if a crash is unavoidable. The
corresponding $x$-, $y$-, and $\omega_{z}$\- acceleration of the vehicle under
test, shown for one trajectory in Fig. 19 right are the input for the Madymo
pre-crash occupant simulation model.

The interior/occupant model answers the important sub-question of how the pre-
crash movement affects the occupant position in the pre-crash phase.
Especially the head position at the time of the crash severely influences the
injury outcome of the crash.

For the simulation, the generic vehicle interior model 2 (Fig. 20) with
control panel, steering panel and the AHBM positioned on the driver seat is
used. Fig. 20 additionally shows the transition of the occupant within the
$740\;\mathrm{ms}$ long pre-crash phase, for the example trajectory depicted
in Fig. 19. The final position of the pre-crash phase is then the input to the
in-crash simulation, which is then made either with FE models or the AHBM. As
the injury values of the AHBM are validated against PMHS the AHBM can also be
used in the in-crash phase to predict injury values.

Figure 20:  (A) Two timeframes of the simulation of the driver in the generic
vehicle interior with fastened seat belt; (B) Head movement during simulation

Figure 21:  Considered pre-crash trajectories of the vehicle under test in
blue, resulting from the scenario simulation in the event of a frontal
collision with the target vehicle in red. The vehicle under test trajectories
(in blue) are illustrated relative to the position of the target vehicle
(red). Only those pre-crash trajectories resulting in a frontal collision are
shown.

Now, the difficulty is to simulate all those scenarios from Fig. 21 with the
AHBM and evaluate the occupant’s positions. The typical calculation time for
one pre-crash scenario is around 2 hours for 2 seconds of simulation time. In
37, 36 the usage of surrogate models is suggested to speed up those many
simulations; the discussion of those methods is out of this paper’s scope.
Nevertheless, such a simulation framework can examine the active occupant’s
possible range of motion. Therefore, generic pulses emulating the maximum
accelerations of an AEB braking and driving limits in a curve, i.e.. (i) the
$C0$ steady lateral x-acceleration in the tuple with
$a_{x}^{max}=\\{0,\,4.25,\,8.5\\}\frac{m}{s^{2}}$ ramped up with
$\dot{a}=23\,\frac{m}{s^{3}})$, (ii) the $C0$ steady transversal
y-acceleration in the tuple with
$a_{y}^{max}=\\{-4.5,\,0,\,4.5\\}\frac{m}{s^{2}}$ with a maximum acceleration
in the y-direction of $4.5\,\frac{m}{s^{2}}$ ramped up with
$\dot{a}=23\,\frac{m}{s^{3}})$ (iii) combination of both; and (iv) scenarios
form the scenario pool, see Fig. 21 to represent a maximum positive lateral
acceleration plus mirrored transversal accelerations. For each combination of
the generic acceleration signals in x- and y-direction with maximum
$a_{i,j}^{max}=(a_{x,i}^{max},a_{j}^{max})$ a Madymo simulation is performed
with $t\in[0,3]\;\mathrm{s}$. The simulations of those nine results are
depicted in Fig. 22 It can be seen that negative transversal acceleration
leads to a negative y-position (head moves to the left). The AHBM tends to
move his head slightly to the right (positive head position). Furthermore, the
head moves to the front with breaking. A clear correlation is observable which
is a clear indication that passive and active safety devices should be
considered holistically, as one influences another.

Overall the controller of the AHBM can minimize the head and occupant motion
to a realistic small movement. Without the stabilization provided by the
muscles, the head would move a lot.

Figure 22:  Head displacements describing the occupants’ range of movement
resulting from simulations with generic vehicle acceleration signals in blue
with corresponding indices i, j and driving scenarios with positive
longitudinal acceleration in red. The end position at the time of collision is
indicated by the dots.

###  3.3 Case Study – EMMA: Investigation of the Reachability of the Steering
Wheel from a Reclined Posture

The following exemplary utilization of the EMMA model investigates the
reachability of the steering wheel from a reclined posture with and without
actively moving the backrest to support the passenger. The reclined starting
pose imitates a passenger in a zero-gravity posture with the arms laying on
armrests. This position is assumed to become common in highly automated
vehicles when the occupant is not actively controlling the vehicle 94.
Nevertheless, for level three and four automated driving, the occupant must be
able to take over control of the vehicle in case of an emergency 83. To
evaluate the integration of an actively moving backrest, the time to
straighten up and reach the steering wheel is examined with and without
support from the backrest.

Figure 23:  Visualization of the EMMA model in the initial reclined posture
that is used for the investigation of the reachability of the steering wheel.

The EMMA model is used to simulate the movement of the upper body of the
occupant from the reclined posture to the steering wheel. Therefore a model of
the upper body is used and – as shown in the initial reclined posture in Fig.
23 – the lower limbs are not modeled in detail but represented by a single
body that is fixed to the seat. The joints in the upper extremities are
controlled by muscles whereas the other joints are actuated using joint
actuators. In addition to this, the final hand positions on the steering wheel
and the position of the upper and lower torso are constrained. In the scenario
with active backrest support, the raising of the backrest is, in addition to
the movements of EMMA, part of the solution of the optimal control problem.
The weighting factors of the objective function of the optimal control problem
are set to achieve a smooth, targeted and natural movement.

The simulation results show that an active backrest can help to support the
passenger in reaching the steering wheel in a shorter time. The results of the
simulations are obtained by solving the described optimal control problem,
which takes about $45$ seconds on a standard PC and are shown in Fig. 24. The
rows of the figure show the process of reaching the steering wheel from a
reclined posture. In the first row of the figure, the frames of the simulation
with active backrest support are shown. Hereby, the first frame shows the
initial position and the last frame the final position. It can be seen that
the backrest is raised to support the passenger and the driving posture is
reached within $1.3$ s. The second row shows the frames at the same simulation
times, but with passive backrest support. Here the passenger is not able to
reach the final position within the same period of time. The steering wheel is
now reached at approximately $1.6$ s. These two simulations show that an
active backrest can help reach the steering wheel faster and thus the driver
can take over the driving task in a shorter time.

Figure 24:  Reaching the steering wheel from a reclined posture. The upper
frame series shows a simulation with an active backrest whereas the lower
series shows a simulation with a passive backrest. In the last frame shown the
passenger reaches the steering wheel only in the scenario with the support
from the active backrest.

Although this early study is limited in its ability to realistically represent
a takeover scenario in all details, it does show that active backrest support
can help the driver grip the steering wheel more quickly. While this is an
important finding for the development of highly automated vehicles, it is
still important to point out the special capabilities of the simulation setup.
In this study, it was possible to optimize a technical product together with
the active movement of the human as a whole. This is a unique feature of the
EMMA model that cannot be achieved with motion capture methods and enables
further improvement of human-machine interaction in various technical
applications.

##  4 Discussion

This contribution provides an overview of current HBMs and their applications
in vehicle safety. Therefore, the underlying mathematical methods are
introduced and a selection of HBMs is presented in detail. The application of
HBMs in vehicle safety is exemplified by three case studies. The following is
a summary of key aspects of the application of HBMs that emerge from the case
studies presented:

  * •

The safe motorcycle case study is a comprehensive example of the application
of HBMs for the development of safe new mobility solutions featuring a multi-
method approach for the calculation of boundary conditions for the in-crash
phase. This case study shows that for new mobility solutions, the pre-
positioning of HBMs needs special attention because available HBMs are
provided for use with conventional vehicles. Additionally, the study shows
that there are only minor variations between different HBMs but significant
differences between HBMs and ATDs due to the omnidirectionality of HBMs. This
and the ability to closely examine injury mechanics further motivate the use
of HBMs in the development of new mobility solutions.

  * •

In the second case study, the MADYMO AHBM is utilized for a scenario-based
assessment of the pre-crash phase to gain a further understanding of the
initial position of the head at the start of the in-crash phase. This study
demonstrates the use of HBMs to identify controller parameters that replicate
experimental results of human behavior. In addition, it is another example of
combining models of varying complexity into an overall framework to gain
insight into complex issues. Here, the study shows the need to consider
passive and active safety systems holistically.

  * •

The reachability of the steering wheel from a reclined posture is investigated
with the use of an optimal control approach in the last case study. It
demonstrates the ability to optimize a technical product while taking into
account active human behavior, as one influences the other. This is a unique
feature of the EMMA model that cannot be achieved with motion capture methods.

The presented case studies show that HBMs are a valuable tool for the
development of safe new mobility solutions. They can be used to evaluate the
safety of a totally new mobility solution, to evaluate passive and active
safety systems holistically and to optimize the human-machine interaction by
taking into account active human behavior.

Although, as the presented case studies suggest, HBMs are already a valuable
tool for developing safe new mobility solutions, there are still some
challenges to overcome. Fig. 25 shows the multidimensional challenge for
vehicle safety. The dashed line traces the path to a future target where
vehicle safety systems are desired to have increased robustness.

Figure 25:  Three-dimensional challenge. The axes represent the occupant
surrogate (red), the accident scenarios (green), and the safety systems (blue)
considered. The dashed line traces the path to a future target where the
safety systems are evaluated considering human variability, real-life crashes
and all available safety systems.

To ensure a safe and comfortable experience for all traffic participants
robust safety systems which account for the variability of the occupants in
terms of for example anthropometry and active behavior are essential. They
should work in autonomous vehicles where new interior and seating positions
should increase the comfort, activity and productivity of driving, see blue
axis in Fig. 25. In addition, new vehicle classes such as e-bikes, light-
weight vehicles (compare Sec. 3.1) and the consideration of real-world crashes
lead to new crash scenarios regarding for example impact angle or velocity,
see green axis in Fig. 25. Furthermore, current crash safety systems are
mainly optimized for average-sized, male occupants seated in a standard
position. Consequently, most car users are insufficiently protected by virtue
of their height, weight, age and sex 24. In the future, the variability in
size, age and sex of the occupants needs to be considered, see E.V.A. (Equal
Vehicles for All) initative 18, see red axis in Fig. 25. Currently, the use of
complementary virtual tests using HBMs is already being sought 15, 17. It
started with consumer rating assessment of active pedestrian protection
systems 63, 62. Although issues such as ensuring integrity and authenticity
and concerns about intellectual property protection when sharing sensitive
simulations need to be addressed first 26, it is expected that this approach
will also extend to certification and regulatory approval of future vehicles.
To achieve this robustness, many simulations have to be carried out.
Therefore, it is necessary to incorporate HBMs with the proper modeling depth
into the development process depending on the questions to be answered by the
simulation.

The depth of detail of the model directly influences the calculation time and
thus also defines which further analyses are possible with the models. Simple
models allow the simulation of long scenarios or alternatively many scenarios
with varying parameters. In addition, such models can be used to integrate
simulations into iterative development cycles that optimize the solution to an
engineering problem, or they can be enabled to move actively by integrating an
optimal control approach. It is becoming increasingly crucial to couple
different simulation models or derive knowledge/features from simulation
results in surrogate models to exploit the advantages of the involved models.
Therefore, surrogate modeling is an important research topic. In addition,
transferring simulation results between models is a promising approach to
achieving highly detailed results on injury risks using finite-element
simulations and robustness by considering the variability with less complex
(surrogate) models.

Regardless of the level of detail, finding a good and efficient description of
the interaction between the models and the environment is a key factor for
realistic and efficient simulation models and can greatly influence the
calculation time.

Within the last years, more and more HBMs were equipped with active
musculature and optimization-based forward dynamic simulations were developed
to predict human behavior in unknown situations. Nevertheless, the human
response to certain situations is still not fully understood. Therefore, in
the coming years, manifold efforts will be needed to better understand the
neuro-muscular system with the help of complex simulations and experiments.

No two people are alike and thus HBMs have to accommodate for this by
incorporating the subject-specific variability in not only the anthropometric
measures but also the active behavior of individuals. The latter additionally
introduces variability between experiments with the same subject. As shown in
the safe motorcycle case study (Sec. 3.1) one tries to take into account the
variability of people by simulating the small female as a 5% ATD in addition
to the 50% ATD as the average male and the behavior of the 50% female as well
as the 50% male HBM. Inter-subject variability in active behavior has been
observed in Driver-in-the-Loop experiments and simulations, as well as in
other volunteer experiments. Therefore, incorporating only one nominal reflex
behavior in the simulation might be insufficient to enable robust protection
for real humans.

Whether in the future every human will be individualized as a digital twin is
an open question. With the possibility to scale HBMs and digitize the
anthropometry of humans via e.g. laser scanners or MRIs, part of the necessary
technologies are already available today.

## Acknowledgments

We gratefully thank Dr. Julian Hay for granting access to his results of the
scenario-based pre-crash occupant simulation as well as for numerous
discussions during the preparation of this paper.

## Funding Information

The study was funded by Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) under Fraunhofer and DFG-Trilateral Transfer Projects "EMMA4Drive"
grant number FE 1583/4-1, under Germany’s Excellence Strategy - EXC 2075 -
390740016 and EXC 310; and the state of Baden-Wuerttemberg via the
Juniorprofessor program and the Innovative Mobility Solutions program.

## References

  * 1 AAAM, Abbreviated Injury Scale 2005 - Update 2008, Association for the Advancement of Automotive Medicine (AAAM), Barrington, IL, 2008.
  * 2 J. Becker et al., Occupant Safety in Highly Automated Vehicles Challenges of Rotating Seats in Future Crash Scenarios, Proceedings of the IRCOBI Conference, IRC-20-51, Munich, Germany, 2020. 529–542. URL http://www.ircobi.org/wordpress/downloads/irc20/pdf-files/51.pdf.
  * 3 T. Belytschko, W. K. Liu, and B. Moran, Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons, Chichester, 2000.
  * 4 S. Björkenstam et al., Inverse Dynamics for Discrete Geometric Mechanics of Multibody Systems With Application To Direct Optimal Control, Journal of Computational and Nonlinear Dynamics 13 (2018), no. 10.
  * 5 S. Björkenstam et al., Digital Human Motion Planning of Operation Sequences Using Optimal Control of Hybrid Systems, DHM2020: Proceedings of the 6th International Digital Human Modeling Symposium, vol. 11, (L. Hanson et al., eds.), IOS Press, 2020. 115.
  * 6 H. Bubb et al., The Development of RAMSIS in Past and Future as an Example for the Cooperation Between Industry and University, International Journal of Human Factors Modelling and Simulation 1 (2006), no. 1, 140–157.
  * 7 K. Case, R. Marshall, and S. Summerskill, Digital Human Modelling Over Four Decades, International Journal of the Digital Human 1 (2016), no. 2, 112–131. URL https://www.inderscienceonline.com/doi/abs/10.1504/IJDH.2016.077408.
  * 8 K. Case, J. M. Porter, and M. C. Bonney, SAMMIE: A Computer Aided Design Tool for Ergonomists, Proceedings of the Human Factors Society Annual Meeting, vol. 30, SAGE Publications Sage CA: Los Angeles, CA, 1986. 694–698.
  * 9 H. Y. Choi et al., Experimental and Numerical Studies of Muscular Activations of Bracing Occupant, Proceedings of the 19th International Technical Conference on the Enhanced Safety of Vehicle (ESV), Washington, DC, 2005\. 1–10. URL www-nrd.nhtsa.dot.gov/pdf/nrd-01/esv/esv19/05-0139-O.pdf.
  * 10 M. A. Correia, S. D. McLachlin, and D. S. Cronin, Vestibulocollic and Cervicocollic Muscle Reflexes in a Finite Element Neck Model During Multidirectional Impacts, Annals of Biomedical Engineering 49 (2021), no. 7, 1645–1656. URL https://doi.org/10.1007/s10439-021-02783-2.
  * 11 C. Costa et al., Effect of Postural Adjustment Methods on Mesh Quality and Simulation Time of Human Body Models, Proceedings of the IRCOBI Conference, IRC-21-54, Munich, Germany, 2021. 490–510. URL http://www.ircobi.org/wordpress/downloads/irc21/pdf-files/2154.pdf.
  * 12 M. Damsgaard et al., Analysis of Musculoskeletal Systems in the AnyBody Modeling System, Simulation Modelling Practice and Theory 14 (2006), no. 8, 1100–1111.
  * 13 S. L. Delp et al., OpenSim: Open-Source Software To Create and Analyze Dynamic Simulations of Movement, IEEE Transactions on Biomedical Engineering 54 (2007), no. 11, 1940–1950.
  * 14 S. Ejima et al., A Study on Occupant Kinematics Behaviour and Muscle Activities During Pre-Impact Braking Based on Volunteer Tests, Proceedings of the IRCOBI Conference, Maastricht, The Netherlands, 2007. 31–45. URL http://www.ircobi.org/wordpress/downloads/irc0111/2007/Session1/1_2.pdf.
  * 15 Euro NCAP, 2025 Road Map – European New Car Assessment Programme, , Euro NCAP, 2 Place du Luxembourg, 1050 Brussels, Belgium, 2017.
  * 16 Euro NCAP, European New Car Assessment Programme (Euro NCAP): Assessment Protocol – Adult Occupant Protection, Version 9.1.3, , Euro NCAP, 2 Place du Luxembourg, 1050 Brussels, Belgium, 2021. URL https://cdn.euroncap.com/media/67264/euro-ncap-assessment-protocol-aop-v913.pdf.
  * 17 Euro NCAP, Euro NCAP Vision 2030 – A Safer Future for Mobility, European New Car Assessment Programme (Euro NCAP), Leuven, Belgium, 2022. URL https://cdn.euroncap.com/media/74468/euro-ncap-roadmap-vision-2030.pdf.
  * 18 E.V.A, THE E.V.A. INITIATIVE - Cars should protect everyone., 2019. URL https://www.volvocars.com/intl/v/car-safety/eva-initiative-cars-equally-safe, accessed: August 23, 2022.
  * 19 I. Fallon and D. O’Neill, The World’s First Automobile Fatality, Accident Analysis & Prevention 37 (2005), no. 4, 601–603.
  * 20 J. Fehr et al., Biomechanis and Mechatronics for the Design of Integral Vehicle Safety Systems, 25th International Congress of Theoretical and Applied Mechanics – Book of Abstracts, (A. Corigliano, ed.), 2021. 2076–2077. URL https://iutam.org/publications/ictam-proceedings/ictam_2020/.
  * 21 L. Feller et al., Incorporating Muscle Activation Dynamics into the Global Human Body Model, Proceedings of the IRCOBI Conference, IRC-16-71, Malaga, Spain, 2016. URL http://www.ircobi.org/wordpress/downloads/irc16/pdf-files/71.pdf.
  * 22 J. B. Fice, J.-S. Blouin, and G. P. Siegmund, Head Postures During Naturalistic Driving, Traffic Injury Prevention 19 (2018), no. 6, 637–643. URL https://doi.org/10.1080/15389588.2018.1493582, pMID: 29944432\.
  * 23 P. A. Forbes et al., Dependency of Human Neck Reflex Responses on the Bandwidth of Pseudorandom Anterior-Posterior Torso Perturbations, Experimental Brain Research 226 (2013), no. 1, 1–14.
  * 24 J. Forman et al., Automobile Injury Trends in the Contemporary Fleet: Belted Occupants in Frontal Collisions, Traffic Injury Prevention 20 (2019), no. 6, 607–612. URL https://doi.org/10.1080/15389588.2019.1630825, pMID: 31283362\.
  * 25 F. Fraga et al., Development of a Motorcycle Rider Model with Focus on Head and Neck Biofidelity, Recurring to Line Element Muscle Models and Feedback Control, Proceedings of the 21st International Technical Conference on the Enhanced Safety of Vehicles (ESV), vol. 15, 2009. 18.
  * 26 E. Galijatovic et al., Integrity of Virtual Testing for Crash Protection, Frontiers in Future Transportation 3 (2022), 1–12. URL https://www.frontiersin.org/articles/10.3389/ffutr.2022.914489.
  * 27 F. S. Gayzik et al., Development of a Full Body CAD Dataset for Computational Modeling: A Multi-Modality Approach, Annals of Biomedical Engineering 39 (2011), no. 10, 2568. URL https://doi.org/10.1007/s10439-011-0359-5.
  * 28 B. D. Gepner et al., Performance of the Obese GHBMC Models in the Sled and Belt Pull Test Conditions, Proceedings of the IRCOBI Conference, IRC-18-60, Athens, Greece, 2018. URL http://www.ircobi.org/wordpress/downloads/irc18/pdf-files/60.pdf.
  * 29 GHBMC, Global Human Body Model Consortium-owned GHBMC Model. Distributed by Elemance., 2022. URL https://www.elemance.com/models/, accessed: September 16, 2022\.
  * 30 S. Gollapudi and D. Lin, Experimental determination of sarcomere force–length relationship in type-I human skeletal muscle fibers, Journal of biomechanics 42 (2009), no. 13, 2011–2016.
  * 31 A. Gordon, A. Huxley, and F. Julian, The variation in isometric tension with sarcomere length in vertebrate muscle fibres, The Journal of physiology 184 (1966), no. 1, 170–192.
  * 32 L. Hanson et al., Industrial Path Solutions – Intelligently Moving Manikins, S. Scataglini and G. Paul, (eds.), DHM and Posturography, Academic Press, 2019. 115–124.
  * 33 R. Happee et al., A Mathematical Human Body Model for Frontal and Rearward Seated Automotive Impact Loading, 983150, SAE International, 1998, 10.4271/983150. URL https://doi.org/10.4271/983150.
  * 34 R. Happee et al., Application of MADYMO Occupant Models in LS-DYNA/MADYMO Coupling, 4th European LS-DYNA Users Conference, 2003. 3–10. URL https://www.dynalook.com/conferences/international-conf-2000/session4-3.pdf.
  * 35 R. Happee et al., Dynamic Head-Neck Stabilization and Modulation with Perturbation Bandwidth Investigated Using a Multisegment Neuromuscular Model, Journal of Biomechanics 58 (2017), 203–211. URL http://www.sciencedirect.com/science/article/pii/S0021929017302579.
  * 36 J. Hay, A Surrogate Model-enhanced Simulation Framework for Safety Performance Assessment of Integrated Vehicle Safety Systems, Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, Vol. 75, Shaker Verlag, Aachen, 2022.
  * 37 J. Hay et al., Ersatzmodell- gestützte Effektivitätsbewertung integraler Fahrzeugsicherheitssysteme, 13. VDI-Tagung Fahrzeugsicherheit, 13, VDI Wissensforum GmbH, Berlin, Germany, 2022.
  * 38 W. Herzog and T. Leonard, The history dependence of force production in mammalian skeletal muscle following stretch-shortening and shortening-stretch cycles, Journal of biomechanics 33 (2000), no. 5, 531–542.
  * 39 A. V. Hill, The Heat of Shortening and the Dynamic Constants of Muscle, Proceedings of the Royal Society of London. Series B - Biological Sciences 126 (1938), no. 843, 136–195. URL http://rspb.royalsocietypublishing.org/content/126/843/136.short.
  * 40 D. Högberg et al., DHM Based Test Procedure Concept for Proactive Ergonomics Assessments in the Vehicle Interior Design Process, Congress of the International Ergonomics Association, Springer, 2018. 314–323.
  * 41 Z. S. Hostetler et al., Analyzing the Force Variation and Response of a Human Body Finite Element Model in the Underbody Blast Environment, Proceedings of the IRCOBI Conference, IRC-21-63, Munich, Germany, 2021. 616–625. URL http://www.ircobi.org/wordpress/downloads/irc21/pdf-files/2155.pdf.
  * 42 P. Huber et al., Passenger Kinematics in Braking, Lane Change and Oblique Driving Maneuvers, Proceedings of the IRCOBI Conference, Lyon, France, 2015. 783–802.
  * 43 E. Hwang et al., Rapid Development of Diverse Human Body Models for Crash Simulations through Mesh Morphing, SAE 2016 World Congress and Exhibition, SAE International, 2016. https://doi.org/10.4271/2016-01-1491. URL https://doi.org/10.4271/2016-01-1491.
  * 44 K. S. Indrani, N. A. Hakansson, and H. M. Lankarani, A Method to Identify the Difference in Kinematic Behavior of Human Model Lower Extremities with Respect to Muscle Activation During Crash Impact, Interdisciplinary Applications of Kinematics, (A. Kecskeméthy et al., eds.), Springer International Publishing, Cham, 2019. 115–127.
  * 45 M. Iwamoto and Y. Nakahira, Development and Validation of the Total HUman Model for Safety (THUMS) Version 5 Containing Multiple 1D Muscles for Estimating Occupant Motions with Muscle Activation During Side Impacts, Proceedings of the 59th Stapp Car Crash Conference, vol. 59, New Orleans, LA, USA, 2015. 53–90.
  * 46 M. Iwamoto et al., Development of a Human Body Finite Element Model with Multiple Muscles and Their Controller for Estimating Occupant Motions and Impact Responses in Frontal Crash Situations., Stapp Car Crash Journal 56 (2012), 231–68.
  * 47 J. D. John et al., Hello, world! VIVA+: A Human Body Model Lineup to Evaluate Sex-Differences in Crash Protection, Frontiers in Bioengineering and Biotechnology 10 (2022).
  * 48 G. Joyce, P. Rack, and D. Westbury, The mechanical properties of cat soleus muscle during controlled lengthening and shortening movements, The Journal of physiology 204 (1969), no. 2, 461–474.
  * 49 D. Kato et al., Development of Human-Body Model THUMS Version 6 Containing Muscle Controllers and Application to Injury Analysis in Frontal Collision after Brake Deceleration, Proceedings of the IRCOBI Conference, IRC-18-32, Athens, Greece, 2018. 207–223.
  * 50 F. Kempter, F. Bechler, and J. Fehr, Calibration Approach for Muscle Activated Human Models in Pre-Crash Maneuvers with a Driver-in-the-Loop Simulator, E. B. Lars Hanson, Dan Högberg, (ed.), DHM2020, Proceedings in 6th Digital Human Modeling Symposium, Advances in Transdisciplinary Engineering, vol. 11, Skövde, Sweden, 2020\. 227 – 236, 10.3233/ATDE200029. URL http://dx.doi.org/10.3233/ATDE200029.
  * 51 F. Kempter et al., On the Validation of Human Body Models with a Driver-in-the-Loop Simulator, The 5th Joint Int. Conference on Multibody System Dynamics (IMSD 2018), Lisboa, Portugal, 2018. 10.18419/opus-12094. URL http://dx.doi.org/10.18419/opus-12094.
  * 52 F. Kempter et al., Potential to Volunteer Testing Using a Driving Simulator with Motion Capture and EMG Data Acquisition, Proceedings of the IRCOBI Conference, IRC-21-75, Munich, Germany, 2021. URL http://www.ircobi.org/wordpress/downloads/irc21/pdf-files/2175.pdf.
  * 53 F. Kempter et al., Role of Rotated Head Postures on Volunteer Kinematics and Muscle Activity in Braking Scenarios Performed on a Driving Simulator, Annals of Biomedical Engineering (2022). Submitted for publication.
  * 54 Y. Kim et al., Similarities and Differences Between Musculoskeletal Simulations of OpenSim and AnyBody Modeling System, Journal of Mechanical Science and Technology 32 (2018), no. 12, 6037–6044.
  * 55 R. Kirsch, D. Boskov, and W. Rymer, Muscle stiffness during transient and continuous movements of cat muscle: perturbation characteristics and physiological relevance, IEEE Transactions on Biomedical Engineering 41 (1994), no. 8, 758–770.
  * 56 S. Kirschbichler et al., Detailed Analysis of 3D Occupant Kinematics and Muscle Activity During the Pre-Crash Phase as Basis for Human Modeling Based on Sled Tests, Proceedings of the 22nd International Technical Conference on the Enhanced Safety of Vehicles (ESV), Washington, D.C., 2011. 1–8.
  * 57 Y. Kitagawa et al., Occupant Kinematics in Simulated Autonomous Driving Vehicle Collisions: Influence of Seating Position, Direction and Angle, 61st Stapp Car Crash Conference, The Stapp Association, 2017. https://doi.org/10.4271/2017-22-0005. URL https://doi.org/10.4271/2017-22-0005.
  * 58 C. Klein et al., A Method for Reproducible Landmark-based Positioning of Multibody and Finite Element Human Models, Proceedings of the IRCOBI Conference, IRC-21-53, Munich, Germany, 2021. 477–489. URL http://www.ircobi.org/wordpress/downloads/irc21/pdf-files/2153.pdf.
  * 59 C. Kleinbach, Simulation of Occupant Kinematics using Active Human Body Models, Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, Vol. 60, Shaker Verlag, Aachen, 2019.
  * 60 C. Kleinbach et al., Implementation and Validation of the Extended Hill-Type Muscle Model with Robust Routing Capabilities in LS-DYNA for Active Human Body Models, BioMedical Engineering OnLine 16 (2017), no. 109, 1–28. URL https://doi.org/10.1186/s12938-017-0399-7.
  * 61 M. Kleinberger et al., Development of Improved Injury Criteria for the Assessment of Advanced Automotive Restraint Systems, NHTSA Docket No. 98-4405-9, National Highway Transport Safety Association (NHTSA), Washington, DC, 1998. URL https://www.nhtsa.gov/sites/nhtsa.gov/files/criteria.pdf.
  * 62 C. Klug and J. Ellway, Technical Bulletin 024 – Pedestrian Human Model Certification, Version 3.0.1, European New Car Assessment Programme (Euro NCAP), Leuven, Belgium, 2021. URL https://cdn.euroncap.com/media/66108/tb-024-pedestrian-human-model-certification-v301.pdf.
  * 63 C. Klug et al., Development Of a Certification Procedure For Numerical Pedestrian Models, Proceedings of the 26th ESV Conference, 19-0310, Eindhoven, Netherlands, 2019. 1–24. URL https://www-esv.nhtsa.dot.gov/Proceedings/26/26ESV-000310.pdf.
  * 64 K. H. Koch, K. Mombaur, and P. Soueres, Optimization-based walking generation for humanoid robot, IFAC Proceedings Volumes 45 (2012), no. 22, 498–504.
  * 65 E. Larsson et al., Active Human Body Model Predictions Compared to Volunteer Response in Experiments with Braking, Lane Change, and Combined Manoeuvres, Proceedings of the IRCOBI Conference, IRC-19-50, Florence, Italy, 2019. URL http://www.ircobi.org/wordpress/downloads/irc19/pdf-files/50.pdf.
  * 66 K.-J. Larsson et al., Evaluation of the Benefits of Parametric Human Body Model Morphing for Prediction of Injury to Elderly Occupants in Side Impact, Proceedings of the IRCOBI Conference, IRC-19-33, Florence, Italy, 2019\. 150–174. URL http://www.ircobi.org/wordpress/downloads/irc19/pdf-files/33.pdf.
  * 67 K. Levenberg, A method for the solution of certain non-linear problems in least squares, Quarterly of applied mathematics 2 (1944), no. 2, 164–168.
  * 68 S. Leyendecker et al., Discrete Mechanics and Optimal Control for Constrained Systems, Optimal Control Applications and Methods 31 (2010), no. 6, 505–528.
  * 69 A. Linder et al., VIRTUAL-a European approach to foster the uptake of virtual testing in vehicle safety assessment, 8th Transport Research Arena TRA 2020, April 27-30, 2020, Helsinki, Finland.(Conference canceled), 2020.
  * 70 R. Maas and S. Leyendecker, Muscle Paths in Biomechanical Multibody Simulations, Proceedings of the ECCOMAS Multibody Dynamics Conference, Zagreb, Croatia, 2013.
  * 71 C. Maganaris and J. Paul, Tensile properties of the in vivo human gastrocnemius tendon, Journal of biomechanics 35 (2002), no. 12, 1639–1646.
  * 72 S. Magnusson et al., Load-displacement properties of the human triceps surae aponeurosis in vivo, The Journal of physiology 531 (2001), no. 1, 277–288.
  * 73 S. Maier and J. Fehr, Efficient Simulation Strategy to Design a Safer Motorcycle, Multibody System Dynamics (2023).
  * 74 S. Maier et al., Evaluation of a Novel Passive Safety Concept for Motorcycles with Combined Multi-Body and Finite Element Simulations, Proceedings of the IRCOBI Conference, IRC-20-38, Munich, Germany, 2020. 250–265, 10.18419/opus-11899.
  * 75 S. Maier et al., Characterisation of an Energy Absorbing Foam for Motorcycle Rider Protection in LS-DYNA, Proceedings of the 13th European LS-DYNA Users Conference, Ulm, Germany, 2021. 10.18419/opus-12000.
  * 76 S. Maier et al., Finite Element Simulations of Motorcyclist Interaction with a Novel Passive Safety Concept for Motorcycles, Proceedings of the IRCOBI Conference, IRC-21-17, Munich, Germany, 2021. 60–78, 10.18419/opus-11900.
  * 77 S. Maier et al., Positioning and Simulation of Human Body Models on a Motorcycle with a Novel Restraint System, Proceedings of the IRCOBI Conference, IRC-22-22, Porto, Portugal, 2022. 82–96, 10.18419/opus-12377.
  * 78 D. W. Marquardt, An algorithm for least-squares estimation of nonlinear parameters, Journal of the society for Industrial and Applied Mathematics 11 (1963), no. 2, 431–441.
  * 79 H. Mashima, Force-velocity relation and contractility in striated muscles, The Japanese journal of physiology 34 (1984), no. 1, 1–17.
  * 80 M. Millard et al., Flexing computational muscle: modeling and simulation of musculotendon dynamics, Journal of biomechanical engineering 135 (2013), no. 2.
  * 81 National Safety Council, Injury Facts, Car Crash Deaths and Rates, 2022. URL https://injuryfacts.nsc.org/motor-vehicle/historical-fatality-trends/deaths-and-rates/, accesed August 23, 2022.
  * 82 NHTSA, Injury Risk Curves and Protection Reference Values, National Highway Transport Safety Association (NHTSA), Washington, DC, 1995\. URL https://one.nhtsa.gov/cars/rules/rulings/80g/80GII.html, accessed July 10, 2021.
  * 83 NHTSA, Preliminary Statement of Policy Concerning Automated Vehicles, NHTSA 14-13, 2013. URL http://www.nhtsa.gov/staticfiles/rulemaking/pdf/Automated_Vehicles_Policy.pdf, accessed September 12, 2022.
  * 84 NHTSA, Crash Simulation Vehicle Models, National Highway Transport Safety Association (NHTSA), Washington, DC, 2021. URL https://www.nhtsa.gov/crash-simulation-vehicle-models, accessed June 27, 2022.
  * 85 L. v. R. Nicolás Nemirovsky, A New Methodology For Biofidelic Head-Neck Postural Control, Proceedings of the IRCOBI Conference, Hanover, Germany, 2010.
  * 86 J. M. Ólafsdóttir, J. Östh, and K. Brolin, Muscle Responses in Dynamic Events - Volunteer Experiments and Numerical Modelling for the Advancement of Human Body Models for Vehicle Safety Assessment, chap. Modelling Reflex Recruitment of Neck Muscles in a Finite Element Human Body Model for Predicting Omnidirectional Head Kinematics, Chalmers University of Technology, Sweden, 2017.
  * 87 OpenVT, VIRTUAL OpenVT Gitlab Platform Repository, 2021. URL https://openvt.eu/fem/viva/vivaplus_v0_2/, accessed September 9, 2021.
  * 88 OSCCAR, Future Occupant Safety for Crashes in Cars, 2022. URL https://www.osccarproject.eu/, accessed September 16, 2022.
  * 89 J. Östh, K. Brolin, and D. Bråse, A Human Body Model with Active Muscles for Simulation of Pretensioned Restraints in Autonomous Braking Interventions, Traffic injury prevention 16 (2015), 304–313.
  * 90 J. Östh, E. Larsson, and L. Jakobsson, Human Body Model Muscle Activation Influence on Crash Response, Proceedings of the IRCOBI Conference, IRC-22-101, Porto, Portugal, 2022. URL http://www.ircobi.org/wordpress/downloads/irc22/pdf-files/22101.pdf.
  * 91 J. Östh et al., The Occupant Response to Autonomous Braking: A Modeling Approach That Accounts for Active Musculature, Traffic Injury Prevention 13 (2012), no. 3, 265–277. PMID: 22607249.
  * 92 J. Östh et al., A Female Head-neck Model for Rear Impact Simulations, Journal of Biomechanics 51 (2017), 49–56. URL https://doi.org/10.1016/j.jbiomech.2016.11.066.
  * 93 J. Östh et al., The VIVA OpenHBM Finite Element $50^{th}$ Percentile Female Occupant Model: Whole Body Model Development and Kinematic Validation, Proceedings of the IRCOBI Conference, Antwerp, Belgium, 2017. 443–466. URL http://www.ircobi.org/wordpress/downloads/irc17/pdf-files/60.pdf.
  * 94 M. Östling and A. Larsson, Occupant Activities and Sitting Positions in Automated Vehicles in China and Sweden, Proceedings of the 26th ESV Conference, 19-0083, Eindhoven, Netherlands, 2019. 1–9. URL https://www-esv.nhtsa.dot.gov/Proceedings/26/26ESV-000083.pdf.
  * 95 C. B. Phillips and N. I. Badler, Jack: A Toolkit For Manipulating Articulated Figures, Proceedings of the 1st Annual ACM SIGGRAPH Symposium on User Interface Software, 1988. 221–229.
  * 96 J. Pink et al., Economic and health-related quality of life outcomes of whiplash associated disorders, Spine 41 (2016), no. 17, 1378–1386.
  * 97 PIPER, Position and Personalize Advanced Human Body Models for Injury Prediction, PIPER Project, 2016. URL http://www.piper-project.eu/, accessed September 15, 2011.
  * 98 B. Pipkorn et al., Validation of the SAFER Human Body Model Kinematics in Far-Side Impacts, Proceedings of the IRCOBI Conference, IRC-21-52, Munich, Germany, 2021. URL http://www.ircobi.org/wordpress/downloads/irc21/pdf-files/2152.pdf.
  * 99 L. Prochowski, K. Zielonka, and A. Żuchowski, The Analysis of Occupant Motion in Frontal Barrier Impact of a Chassis Frame Vehicle, Journal of KONES Powertrain and Transport 18 (2011), no. 1, 491–502.
  * 100 I. P. A. Putra et al., Optimization of Female Head-Neck Model with Active Reflexive Cervical Muscles in Low Severity Rear Impact Collisions, Annals of Biomedical Engineering (2020). URL https://doi.org/10.1007/s10439-020-02512-1.
  * 101 v. P. A. Putra et al., Comparison of Control Strategies for the Cervical Muscles of an Average Female Head-Neck Finite Element Model, Traffic Injury Prevention (2019), 1–7. URL https://doi.org/10.1080/15389588.2019.1670818, pMID: 31617760\.
  * 102 K. Rawska et al., Submarining Sensitivity Across Varied Anthropometry in an Autonomous Driving System Environment, Traffic Injury Prevention 20 (2019), S123–S127. URL https://doi.org/10.1080/15389588.2019.1655734, pMID: 31539280\.
  * 103 J. Ritchie and D. Wilkie, The dynamics of muscular contraction, The Journal of physiology 143 (1958), no. 1, 104.
  * 104 M. Roller et al., Optimal Control of a Biomechanical Multibody Model for the Dynamic Simulation of Working Tasks, ECCOMAS Thematic Conference on Multibody Dynamics, Prague, Czech Republic, June, 2017. 19–22.
  * 105 M. Roller et al., A Digital Human Model for the Simulation of Dynamic Driving Maneuvers, E. B. Lars Hanson, Dan Högberg, (ed.), DHM2020, Proceedings in 6th Digital Human Modeling Symposium, Advances in Transdisciplinary Engineering, vol. 11, Skövde, Sweden, 2020. 269 – 276, 10.3233/ATDE200033. URL http://dx.doi.org/10.3233/ATDE200033.
  * 106 O. Sander et al., Towards an Efficient Numerical Simulation of Complex 3D Knee Joint Motion, Computing and Visualization in Science 16 (2013), no. 3, 119–138. URL http://dx.doi.org/10.1007/s00791-014-0227-6.
  * 107 A. Sandholm et al., Evaluation of a Geometry-Based Knee Joint Compared to a Planar Knee Joint, The Visual Computer 27 (2011), no. 2, 161–171.
  * 108 S. L. Schoell et al., Development and Validation of an Older Occupant Finite Element Model of a Mid-Sized Male for Investigation of Age-related Injury Risk, Stapp Car Crash Journal 59 (2015), 359–383.
  * 109 A. Scholz et al., A Fast Multi-obstacle Muscle Wrapping Method Using Natural Geodesic Variations, Multibody System Dynamics 36 (2016), no. 2, 195–219.
  * 110 G. Schultz and K. Mombaur, Modeling and optimal control of human-like running, IEEE/ASME Transactions on mechatronics 15 (2009), no. 5, 783–792.
  * 111 D. Schwartz et al., Development of a Computationally Efficient Full Human Body Finite Element Model, Traffic Injury Prevention 16 (2015), 49–56.
  * 112 A. Seth et al., OpenSim: Simulating Musculoskeletal Dynamics and Neuromuscular Control To Study Human and Animal Movement, PLoS Computational Biology 14 (2018), no. 7, e1006223.
  * 113 Simcenter Madymo, Models Manual, Siemens Industry Software and Services BV SISS, Rijswijk, Netherlands, 2020th edn., 2020.
  * 114 S. Smit et al., Investigation of Injury Mechanisms in Sledging Accidents Involving Children and Adults, Proceedings of the IRCOBI Conference, IRC-21-64, Munich, Germany, 2021. 616–625. URL http://www.ircobi.org/wordpress/downloads/irc21/pdf-files/2155.pdf.
  * 115 H. Sugi and T. Tsuchiya, Stiffness changes during enhancement and deficit of isometric force by slow length changes in frog skeletal muscle fibres., The Journal of physiology 407 (1988), no. 1, 215–229.
  * 116 J. Swammerdam, The Book of Nature II, London (UK): Seyffert (1758), 122–132.
  * 117 Y. Takahira et al., Cross-Sectional Analysis of Rib Fracture Mechanism of Elderly Occupant in Frontal Collision using THUMS, Proceedings of the IRCOBI Conference, IRC-21-55, Munich, Germany, 2021. 511–520. URL http://www.ircobi.org/wordpress/downloads/irc21/pdf-files/2155.pdf.
  * 118 Toyota Motor Corporation, Total Human Model For Safety (Thums): Revolutionizing Crash Simulation to Support Safe Mobility for All, 2021\. URL https://www.toyota.co.jp/thums/contents/pdf/Toyota_THUMS_History_English.pdf, accessed: September 14, 2022.
  * 119 O. Von Stryk, Numerical solution of optimal control problems by direct collocation, Optimal control, Springer, 1993. 129–143.
  * 120 D. W. Wagner et al., Consistency Among Musculoskeletal Models: Caveat Utilitor, Annals of Biomedical Engineering 41 (2013), no. 8, 1787–1799.
  * 121 D.-R. Wilkie, The mechanical properties of muscle, British medical bulletin 12 (1956), no. 3, 177–182.
  * 122 P. Wimmer et al., Surrogate Model Based Safety Performance Assessment of Integrated Vehicle Safety Systems, NAFEMS World Congress (2021). URL https://www.nafems.org/publications/resource_center/bm_jul_21_5/.
  * 123 T. Winters et al., Whole muscle length-tension relationships are accurately modeled as scaled sarcomeres in rabbit hindlimb muscles, Journal of biomechanics 44 (2011), no. 1, 109–115.
  * 124 H.-J. Wirsching, Chapter 4 - Human Solutions RAMSIS, S. Scataglini and G. Paul, (eds.), DHM and Posturography, Academic Press, 2019. 49–55, https://doi.org/10.1016/B978-0-12-816713-7.00004-0. URL https://www.sciencedirect.com/science/article/pii/B9780128167137000040.
  * 125 C. Woernle, Mehrkörpersysteme (in German), Springer, Heidelberg, 2011, 10.1007/978-3-642-15982-4. URL http://dx.doi.org/10.1007/978-3-642-15982-4.
  * 126 K. Yang et al., Development of Numerical Models for Injury Biomechanics Research: A Review of 50 Years of Publications in the Stapp Car Crash Conference, Stapp Car Crash Journal 50 (2006), 429–490.
  * 127 E. Yigit, Reaktives FE-Menschmodell im Insassenschutz: Simulation der Insassenkinematik in der Pre-Crash-Phase, 114th edn., AutoUni - Schriftenreihe, Springer, 2018, https://doi.org/10.1007/978-3-658-21226-1.
  * 128 F. E. Zajac, Muscle and Tendon: Properties, Models, Scaling, and Application to Biomechanics and Motor Control, Critical reviews in Biomedical Engineering 17 (1989), no. 4, 359–411. URL http://e.guigon.free.fr/rsc/article/Zajac89.pdf.

## Author Biography

Niklas Fahse. In 2019 Niklas Fahse completed his first master’s studies in
Engineering Science and Mechanics at the Georgia Institute of Technology in
Atlanta, Georgia, USA. He then proceeded with a second master’s degree in
Autonomous Systems at the University of Stuttgart, Germany. After graduating
in 2021, he began doctoral studies in Mechanical Engineering at the Institute
of Engineering and Computational Mechanics at the University of Stuttgart,
Germany. His thesis will focus on surrogate models for the interaction between
active human models and the vehicle interior in the context of driving
simulations.  Fabian Kempter. In 2017 Fabian Kempter completed his master’s
degree in Mechanical Engineering at the University of Stuttgart, Germany.
Subsequently, he started to pursue a PhD degree in mechanics at the Institute
of Engineering and Computational Mechanics at the University of Stuttgart,
Germany. The focus of his research is the study of human variability in
passenger behavior and its consideration in virtual surrogate models with
active musculature.  Steffen Maier. Steffen Maier is working as a research
associate and doctoral student in the field of driving safety at the Institute
of Engineering and Computational Mechanics (ITM) of the University of
Stuttgart since 2018. He strives to improve computational modeling of powered
two-wheelers and their riders as well as scientific methods to assess a
rider’s protection. Before, he completed his master’s studies at the
University of Stuttgart in Mechanical Engineering and at the Georgia Institute
of Technology in Atlanta in Engineering Science and Mechanics.  Michael
Roller. Dr.-Ing Michael Roller obtained his diploma in Technomathematics at TU
Kaiserslautern in 2011. He finished his doctoral degree in 2016 at Karlsruhe
of Technologies in the field of structural mechanics with focus on tire
simulation. From 2011 until now he is working as a researcher at the
Fraunhofer Institute for Industrial Mathematics in Kaiserslautern with focus
on structural mechanics and biomechanics. The focus of research in the field
of digital human models is to generate physically reliable and realistic human
motion without any motion capture data.  Matthew Millard. Matthew Millard
completed his PhD in Systems Design Engineering in 2011 from the University of
Waterloo in Canada. Following his PhD, he has taken up Postdoctoral
fellowships at Stanford University, the University of Duisburg-Essen,
Heidelberg University, and now works at the University of Stuttgart. During
this time, he has worked on various topics, from modeling human balance to
foot-ground contact modeling and predicting exoskeleton-supported lifting
motions. Currently, his research focuses on the computerized prediction of
neck injury during car accidents.  Jörg Fehr. Apl. Prof. Dr.-Ing. Jörg Fehr,
studied Mechatronics in Stuttgart and Mechanical Engineering in Madison,
Wisconsin, USA. He completed his PhD on Model Order Reduction in 2011 from the
University of Stuttgart. After a period as a simulation engineer at TRW
Automotive GmbH. In 2014 Jörg Fehr joined as Junior Professor at the Institute
for Engineering and Computational Mechanics and Cluster of Excellence
Simulation Technology (SRC SimTech) of the University of Stuttgart. He is on
the board of Industrial Consortium SimTech. Since 2020 he is deputy director
and professor after successful completion of the final evaluation. One goal of
his current research is the development of optimal HBMs for the simulation of
vehicle safety systems and the speedup of the simulations using linear and
nonlinear model reduction methods.