1 Introduction

Despite the available technology and engineering enhancements in fields of preventive, passive and acitve safety, the problem of human lives being lost in pedestrian accidents remains present. 4763 pedestrians died on the roads of the European Union in the year 2018 and pedestrian fatalities in Europe in general had consistently accounted for approximately 20% of all road fatalities in the 2010–2018 period [114]. While UK data from the COVID-19 lockdown period of 2020 showed a temporary decrease in the number of pedestrian fatalities [27], the numbers after the lockdown period remain high. In 2021, 343 pedestrians lost their lives in Germany [159], 414 in France [116], and 527 in Poland [70]. In the USA, there were 7485 pedestrian fatalities in 2021 [135]; this was a 54% increase in the span of a decade from 2010 to 2020; meanwhile, in the same period, total count of all other traffic deaths increased only by 13%. Despite new legislative efforts and technical improvements, government, industry and research still face the problem of pedestrian accidents taking a heavy toll on even the most developed countries.

An approach to tackling this problem is by thorough understanding the physical process of the vehicle-pedestrian impact itself. There are multiple parties who have a need of an in-depth analysis of the mechanics of vehicle–pedestrian accidents:

  • Individual forensic experts help courts and insurance companies reconstruct pedestrian accidents to determine the culpability in individual cases;

  • multidisciplinary teams reconstruct accidents for purposes of state initiatives such as GIDAS [118] or CIDAS [17]; this knowledge is then shared with policymakers or the industrial sector;

  • authorities and consumer organizations design test procedures for assessment of a vehicle’s passive safety, specifically in terms of pedestrian collisions;

  • automotive industry needs tools to determine whether its products conform to requirements of normative acts and consumer testing protocols;

  • researchers and engineers study factors influencing vehicle-pedestrian impact (crashworthiness studies), propose changes to vehicles, or design additional safety equipment.

These applications require reliable, biofidelic (i.e. comparable in their mechanical response to the natural properties of biological organisms) mechanical surrogates of a pedestrian body capable of being analysed in various configurations.

1.1 Mechanics of Pedestrian Impact

A study by [133] showed that, in accidents, 80% of pedestrians are impacted with the front-end or front corners of a vehicle. For the frontal pedestrian impact configurations, five patterns of post-impact pedestrian kinematics were recognized by [133]: wrap projection, forward projection, somersault, roof vault, fender vault (see: Table 1). An example of a wrap projection impact, simulated using a CTS PRIMUS dummy (175 cm, 78 kg) [144], is demonstrated in Fig. 1. Other distinct configurations are: dragging of the pedestrian under the vehicle’s chassis [34]; sideswipe collisions, when an impact to the side of the vehicle causes a rotation of the pedestrian’s body [156].

The mechanical process of vehicle-to-pedestrian impact can be separated into three general phases:

  • contact phase—between the first impact of the pedestrian (usually of their lower extremities), and the separation of the pedestrian from a vehicle

  • flight phase—between the moment of separation from the vehicle and the moment of the first ground contact

  • sliding phase—between the first ground contact, through bouncing, sliding or tumbling of the pedestrian, until coming to full rest

Some researchers distinguish another phase, the transport phase, between the contact and flight phases [1]. The transport phase takes into account the time when the pedestrian has already impacted the vehicle, but remains carried on the vehicle, and the duration of the phase depends on the intensity of vehicle’s braking.

The throw distance, a.k.a. projection distance, is defined as the distance between the initial vehicle-pedestrian impact and the final rest position of the pedestrian [11]. The most common subject of analysis is the longitudinal throw distance, i.e. measured along the longitudinal direction of the vehicle motion. Multiple factors influence the throw distance, including vehicle shape, braking intensity or the position of the pedestrian relative to the front end of the vehicle.

During the contact phase, two major impacts of the pedestrian with the vehicle are usually distinguished [198]: primary impact, between the pedestrian’s lower extremities and the front of the vehicle, and secondary impact, when the head strikes the bonnet or the windshield. Between the primary and secondary impact, other impacts such as shoulder or chest impact may occur as well. Time offset between primary and secondary impact (see: Fig. 1) is dependent on the impact configuration, and it is shorter for forward projection cases than for wrap projection cases [34].

Fig. 1
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Time sequence in [ms] of a 50 km/h collision of a small family car with a pedestrian surrogate, a CTS Primus dummy—a wrap projection configuration [25]

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Table 1 Frequency of occurrence and description of pedestrian post-impact kinematics patterns
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1.2 Pedestrian Accident Reconstruction

The aim of pedestrian-vehicle accident reconstruction is usually to assess the velocity of the vehicle impact, determine the location of the impact and to determine the pedestrian’s position in relation to the vehicle [33]. The analysis of evidence (e.g., pedestrian injuries, bloodstains, vehicle damage, paint flakes in clothes) yields general qualitative information on the course of an accident [113, 169]. However, in practise of accident reconstruction, there is often a need for more quantitative conclusions, e.g. regarding the vehicle’s collision velocity. Generally, it is not recommended to assess collision velocity directly from vehicle damage or severity of pedestrian injuries [42]. Event data recorders (EDR) pose to be a promising source of objective information on vehicle collision velocity. However, the accuracy of reconstruction of vehicle’s trajectory and velocity using various EDR models has been shown to sometimes be unsatisfactory [40]. Moreover, while the recently approved Regulation 160 of UN ECE, with the 01 series of amendments, imposes certification of EDR present on board of new vehicles, events with vulnerable road users (pedestrians in particular) are not mandatory to be recorded by every vehicle’s EDR. From a physical point of view, the disproportion of mass between a pedestrian and a vehicle results in a low change in vehicle velocity in the case of an impact [35], and thus pedestrian impacts may sometimes not be registered at all. Also, as stated in [88], only 15–20% of vehicles on European roads are equipped with EDR.

In view of the above, recreating pedestrian accidents by using mechanical simulations presents to be a valid approach to reconstruction. Mechanical surrogates for a pedestrian body are required, but it is naturally impossible to recreate accidents using the actual bodies of the participants. Thus, for instance, pedestrian accidents can be simulated by crash tests with dummies. Pedestrian test dummies, particularly the recent designs [144], have a kinematic response comparable to that of a human pedestrian in terms of pedestrian final rest position and location of damage on the vehicle. The caveat is, crash tests are costly and a typical forensic investigation rarely economically warrants more than a couple of crash tests, if any at all. This limits the number of crash test scenarios that can be analyzed for each investigated case. Thus, pedestrian accident reconstruction is currently largely based on mathematical modelling techniques, which can both provide quantitative results and cover multiple scenarios cost-effectively.

There are different approaches to the mathematical estimation of pedestrian kinematics:

  • projectile models, where a pedestrian is assumed to be a point mass [146];

  • empirical models, described by single-argument regression equations, which are based on statistical approximation of results of dummy experiments or real accident analyses [42, 132, 160];

  • two- and three-segment 2D analytical models, which assume the pedestrian body to be made of stiff segments connected with a hinge joint [156, 197];

  • numerical models of an entire human body.

Projectile and empirical models are the easiest to use, as they are described by easily solvable, one-variable equations. The equations usually describe the relationship between impact velocity and pedestrian throw distance. Projectile and empirical models provide no detailed information on the course of the impact (e.g. location of head-to-windscreen impact) or the pedestrian’s injuries. Application of projectile and empirical models is limited to central collisions. These models cannot be applied to the analysis of cases where a pedestrian is impacted by a vehicle’s corner, i.e. when pedestrian exhibits fender vault type of movement [42]. Furthermore, most empirical models were developed in the last century, and further study of their applicability in collisions with newer vehicle models may be required [21]. Two- and three-segment models, while they correspond well with experimental data [156], are limited to 2D cases and have found limited application in the practice of accident reconstruction.

Given the limitations of other mathematical techniques, numerical human body modelling has found widespread use in pedestrian accident reconstruction. Numerical models can be used to study impacts in various conditions and, from a practical point of view, they are a visually attractive way of presenting the results of a forensic investigation. General description, validation and application of human body models, created using multibody techniques and dedicated specifically for pedestrian accident reconstruction, are described further in Chapters 2, 4, 5.

1.3 Vehicle Certification

Years of research in the area of vehicle passive safety have led to the introduction of normative acts and regulations defining requirements for the protection of vulnerable road users (VRUs), including pedestrians as the most susceptible group.

Many advances in this field have been made by the International Harmonized Research Activities (IHRA) Pedestrian Safety Working Group. Through worldwide research—including accident data analysis and the development of numerical pedestrian models—unified test procedures for pedestrian safety have been created.

Nowadays, there is Regulation (EU) 2019/2144 of the European Parliament and of the Council in force which sets type-approval requirements for motor vehicles and their trailers, and systems, components, and separate technical units intended for such vehicles, as regards their general safety and the protection of vehicle occupants and vulnerable road users, amending Regulation (EC) 78/2009. Currently, UN Regulation No 127, also applies in the European Union in respect to type-approval of motor vehicles concerning the approval of motor vehicles with regard to their pedestrian safety performance.

Fig. 2
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Visualisation of a vehicle-to-pedestrian accident and the use of numerical impactors that represent critical parts of the human body: A a headform, B upper legform C lower legform

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Remarkably, unlike occupant safety tests, vulnerable road user safety certification procedures of the above-mentioned Regulations do not involve usage of full-scale test dummies. The vehicle front-end is tested by means of impactor tests ( Fig. 2) at a fixed velocity and a fixed impact angle. This allows the tests to be normalised and reduces the costs of the certification procedure, but at the expense of not being able to recreate the complexity of full-scale pedestrian body kinematics (see: Fig. 1). The vehicle manufacturers, however, tend to aim above the basic requirements of Regulations and use (or even develop themselves) numerical mechanical surrogates of full-scale pedestrians. This allows them to test their vehicles in a vast array of configurations, without a need for costly physical crash testing.

1.4 Motivation

While the current state of the art in relation to human body models (HBMs) in the field of biomechanics of impact is often studied [191, 208], there have been few review attempts focusing strictly on validation and application of pedestrian models [60, 79, 99, 156]. Interestingly, to the knowledge of the authors of this paper, there has been no review of HBMs implemented in dedicated commercial road accident reconstruction programmes yet.

The aim of this review study is to present historical and current numerical models used for simulating pedestrian impact. Additional focus of the study is similarities and differences in areas of validation and application between models designed primarily for accident reconstruction and advanced models which are used in detailed studies and industrial applications.

2 Multibody Models

The most common approach to creating computational pedestrian models is multibody (MB) modelling. The principle behind this approach is to model mechanical systems as kinematic chains consisting of rigid, undeformable bodies connected by kinematic pairs (also known as kinematic constraints or joints). The motion of such bodies is computed using the Newton-Euler equations.

2.1 Historical Models

The history of MB solvers utilized for vehicle impact simulation dates as far back as the 1960s [94], when the first numerical vehicle occupant simulations were created. One of the first reviews of these packages and models was done by [64]. Multiple iterations of programming packages, often referred to as Crash Victim Simulation (CVS) packages, were developed in the 1960s and 1970s, including CAL-2D [94, 95], MVMA-2D by HRSI/UMTRI [137], or their 3D iterations [7]. Nowadays, access to many reports and user manuals from those times is limited, yet it is clear that those early programmes laid the foundation for modern MB solvers used for impact modelling, e.g. MADYMO [89]. The primary programming language used for most of these solvers was FORTRAN.

An overview of the earliest MB pedestrian models was provided by [196]. The models had been developed by many parties using different programmes. The examples are: PRAKIMOD model by Renault/Peugeot [74, 75] and a pedestrian model by Citroen [24]; both models were based on the MVMA program. Some of the early pedestrian models were 2D models. The earliest representations of vehicles used for pedestrian impact included either 2D-straight line segments, 3D planes or 3D hyperellipsoids.

2.2 Commercial Multibody Models

Table 2 Examples of multibody pedestrian models available in commercial software
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Table 3 Description of a selection of multibody pedestrian models available in commercial software
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There are multiple commercial packages equipped with predefined MB pedestrian models. Visualisation and a short description of a selection of those models are provided, respectively, in Tables 2 and 3.

MADYMO (currently branded as Simcenter MADYMO) is a popular multibody solver and software package used mainly in the automotive industry. Since its introduction by the Research Institute for Road Vehicles TNO, Netherlands [89, 178], it has been continuously developed, in chronological order, by TNO, Tass International B.V. and from 2017 by Siemens Industry Software and Services B.V.

Two main types of MB pedestrian models are available in the commercial MADYMO distribution. One is the ellipsoidal model [167, 177]. The first version of this model was developed by TNO in partial cooperation with Chalmers University of Technology [73]. The family of models by [177] represents adult specimens of the Western European population as of 1984 between 8 and 70 years of age: 5th female, 50th male, 95th male. A family of 3- and 6-year-old ellipsoid child pedestrian models is also available, with their dimensions based on the Q-Series child dummy. In addition to the models of a predefined size, a native MADYMO Scaler [41] can scale the default 50th percentile adult male model to a given sex, stature or weight, including that of a child.

MADYMO model library also has a second type of pedestrian model, a 50th percentile male facet model [167]. Similarly to the ellipsoidal model, the facet model has MB rigid bodies, but its geometry is represented by a rigid mesh of facet surfaces covering rigid bodies, with contact forces calculated using the standard MB solver. The facet models share an identical geometry to MADYMO active human model [96, 167] but are not equipped with any controllers. The facet model is not scalable.

MADYMO active human multibody model [167] can also technically be used for pedestrian simulations. It is equipped with controllers that allow modelling of active behaviour of human muscles. However, while one study reported the use of the active model in the pedestrian context [3], the controllers were deactivated, and therefore its response could be deemed equivalent to a standard facet pedestrian model.

Aside from MADYMO, multiple commercial vehicle dynamics/traffic accident reconstruction programmes are equipped with multibody human body models, furthermore referred to as MB forensic models: HVE [38], PC-CRASH [107], Virtual CRASH [97, 98], CYBID V-SIM [193]. The models of PC-CRASH, Virtual CRASH and CYBID V-SIM were originally designed for pedestrian applications. The HVE human body model was originally a vehicle occupant, but can also be used successfully for pedestrian impact simulation. Notably, PC-CRASH, Virtual CRASH and HVE multibody solvers utilise a similar contact algorithm to MADYMO, i.e. an algorithm based on calculation of the depth of penetration (expressed in [\(m\)]). The pedestrian model in CYBID V-SIM utilises an algorithm based on the calculation of the intersection volume, expressed in [\(m^3\)], of two bodies in contact.

Multibody forensic models are notably simpler than MADYMO models as they have fewer body segments and more simplified contact characteristics. Their major advantage is that they can be easily scaled to any given stature or mass. An additional advantage of these models is that they are part of robust software packages. Their user can integrate data collected on-scene during an investigation into the software, create digital environment of an accident site and simulate vehicle motion dynamics using mathematical models of vehicle subsystems. This substantially streamlines the process of pedestrian accident reconstruction.

2.3 Noncommercial Models

In addition to the models available in commercial simulation packages, many researchers created their in-house MB pedestrian models. As evidenced by the history of vehicle impact simulation, the development of a multibody solver poses to be a challenge in itself. Thus, many researchers decided to use the established MADYMO solver for their multibody simulations investigation. The solver was used to create numerous non-commercial pedestrian models [2, 36, 49, 82, 111, 203]. Some of the models based on the MADYMO solver were also known in the literature under different names: Chalmers pedestrian model (Chalmers University of Technology, Sweden) [203, 205], RARU model (Road Accident Research Unit of Adelaide University, Australia) model [36], JARI model (Japan Automobile Research Institute) [111]. Except for the facet child pedestrian model by [206], most multibody models created with the MADYMO solver were made using ellipsoidal surface representation.

There are other commercial MB solvers that show some potential in human body modelling in the area of the automotive industry, i.e. ADAMS [54]. Nevertheless, at the moment, few in-house multibody pedestrian models have been reported to be created with solvers other than MADYMO. The pedestrian model by [69] is one of the exceptions, as it was created using the PC-CRASH multibody solver. Another in-house model created with a solver different than MADYMO is VIRTHUMAN [184]. It is a hybrid MB model (for definition of hybrid models, see: Sect. 5.5) developed for ESI Virtual Performance Solution (VPS) software. The model combines MB functionalities with FE representation of the outer body surface. The formulation of contact surfaces is different than MADYMO facet models. The outer FE surface of each segment is made up of parts connected to the MB structure with one-dimensional springs and dampers, which properties were tuned to assure the model’s biofidelity. The authors also developed their own procedure to scale the model to various sizes and mass properties [47]. The VIRTHUMAN model can be used both as an occupant and as a pedestrian [185].

2.4 Customization of Multibody Models

Due to the popularity of MADYMO pedestrian models, there have been attempts to create modifications to their parts. This was done either by modifying a model’s characteristics, or by using more detailed MB segment models, or by replacing MB segments with FE models. For instance, detailed FE head models (FEHMs) [195] are frequently utilised for simulations with MB pedestrian models [34, 152, 187, 199].

[134] optimised joint and contact characteristics of the upper body of the MADYMO facet model by performing a validation against cadaveric data. The customised facet model was later supplied with a new model of a lower extremity and used as a pedestrian model [84].

Several alternative lower extremity models were proposed [51, 62, 202, 204]. Lower extremity MB models were often designed to be equipped with: (a) a detailed knee joint; (b) frangible joints to simulate leg fractures.

While the frequency of life-threatening upper extremity injuries in pedestrian accidents is low [105], differences in the shoulder complex model may influence the kinematics of the model and, consequently, the response of more sensitive organs, for example the head [111]. In line with this, [112] proposed a more biofidelic structure of the shoulder complex of an IHRA pedestrian model. [16] proposed a modified contact characteristic for the shoulder complex of the MADYMO facet pedestrian model. Outside of the scope of pedestrian impact modelling, [101] developed an MB upper arm model as an augmentation to the MADYMO ellipsoidal pedestrian model and they used it for the analysis of workplace accidents.

Children bodies have notably different material properties from adults. To develop a family of 3, 6, 9 and 15-year-old child pedestrian models, [82] calculated and applied scaling factors to modify the joint and contact characteristics obtained originally from a 50th percentile adult model of [205].

3 Finite Element Models

When there is a need for a more detailed study concerning not only kinematics but also the stress–strain behaviour of a pedestrian body, finite element (FE) models are a suitable solution. By using full-scale FE surrogates of a human body, researchers can not only study the whole-body kinematics of a vehicle-pedestrian interaction, but also gain detailed insight into severity of injuries. This yields data for the structural design and functional development of vehicle front-ends. Over the past decades, many attempts have been made to develop biofidelic, finite element models of a pedestrian. There were attempts to create full families of pedestrian FE models of various sizes and ages. Examples of such models are presented in Fig. 4.

3.1 Families of Finite Element Pedestrian Models

Total Human Model for Safety (THUMS) [52] is a human finite element model jointly developed by Toyota Motor Corporation and Toyota Central R &D Labs. THUMS models can be used as both a pedestrian [87] and as an occupant [52]. The current THUMS system includes the following pedestrian models: child models, 3-, 6-, 10-year-old [50]; the average size male model (AM50) [87]; the small size female model (AF05); the large size male model (AM95). The average-size male model (AM50), which consists of nearly 2 million finite elements, is described in Table 4. Developers of the THUMS family of models in the LS-DYNA solver format made it freely available in January 2021.

Global Human Body Models Consortium (GHBMC) models are full-scale human body models developed jointly by NHTSA and various automotive companies. GHBMC system includes a family of occupant and pedestrian models. GHBMC pedestrian models come in two versions: a detailed pedestrian (P) and a simplified pedestrian (PS). Currently, GHBMC pedestrian models are: a 6-year-old child model (6YO-PS) [100]; an average-sized male model (M50-P/ M50-PS) [174, 175]; a small-sized female model (F05-P/ F05-PS) [121]; a large-size male model (M95-P/ M95-PS) [120]. The geometry of the M50-P model was obtained by upright magnetic resonance imaging (MRI) of a specimen in standing posture.

[57] presented a family of VIVA+ FE human body models. For VRU simulations, two standing-posture models are available: an average male (50M) and, remarkably, an average woman (50F). It is worth noting that this is one of the first efforts to develop a model of an average-sized female, and that the female, not male, model was selected as the base model during the development process. The geometry of the female model was largely based on various statistical shape models of body parts and medical images that had previously been used to develop an occupant model [117]. VIVA+ models are distributed in the open source model, in line with Open Science practise.

3.2 Other FE Models

Various FE models were developed by researchers associated with Honda automotive brand. [209] developed an ellipsoidal pedestrian model and used it for simulations with an FE vehicle body. This model led further to development of four pedestrian models by [115]: a large male, an average male, a small female and a 6-year-old child. The geometry of models of both [115, 209] was originally based on the MB model by [49] and on GEBOD antrhopometry data [19]. The final models consisted of 15 segments and 14 joints, and were translated into a PAM CRASH FE solver format. Another FE model was developed by [63], with a special focus on modelling the pelvis and lower extremities.

As part of the HUMOS2 project [181], an original HUMOS (Human Model for Safety) FE occupant model [138] was scaled to match dimensions of various specimens: 5th percentile female, 50th percentile male and 95th percentile male. Additionally, a tool was developed to position the models to use them as pedestrians.

In the early 2000’s, JAMA (Japan Automobile Manufacturers Association, Inc.) [161] decided to consolidate efforts of Japanese automotive manufacturers and jointly develop a human body model. The results of these efforts led to the development of models of human body models models, including pedestrians [165], which, at various stages of the model’s development process, were used in a variety of pedestrian safety studies [48, 122].

[56] developed a CHARM-70F model of a 70-year-old female pedestrian. The mesh of the body was created through computer tomography of an elderly female cadaver, which weighed 62 kg and was 1.58 m tall.

CHARM-10 FE model of a 10-year-old child occupant and pedestrian was developed by [153]. The geometry was primarily based on the collected CT and MRI imaging data [90].

[126] developed a pedestrian version of a PIPER 6-year-old child occupant model. The original child occupant model was developed as part of PIPER project [10], with its geometry approximated from CT scans of children of different ages, lying in supine position. The occupant models were capable of being scaled using GEBOD database [19]. Parallel to the development of the model, a PIPER software framework, including a dedicated joint positioning tool, was developed. The PIPER model is available under open source licence.

[78] describe the development of a 6-year-old pedestrian model (TUST 6YO). The geometry of the model was obtained from CT images of paediatric standing posture.

4 Validation

4.1 Validation Sources

There are various sources for the validation of human-body pedestrian models, the primary being results of in-depth road accident investigations. If an accident is well documented, particularly with regard to vehicle and pedestrian kinematics at the time of impact, then such data can be used to simulate the event and assess the model’s accuracy. However, even the most in-depth accident data capture usually only the state after the impact, and general information on the initial conditions, and no detailed time-response data on the mechanical properties of individual segments of the human body are available.

Another solution is the usage of pedestrian crash test dummies, as the experiments can be conducted in a known environment and registered accurately. However, the low biofidelity of dummies is often a downside to this approach, and human body models by their nature should not aim to recreate an artificial device such as a dummy.

The validation of advanced pedestrian body models is currently largely reliant on results of Post Mortem Human Subject (PMHS) experiments, which involve using cadavers of voluntary donors as specimens for testing [140]. The PMHS-based validation is usually carried out on two levels: component-level and full-body-level. The numerical model validation procedure uses either individual signals from the experiments or corridors derived from multiple specimens.

4.1.1 Component-Level Validation Using Cadaver Data

On the component level of validation, a.k.a. sub-model validation [77], responses of individual body segments are studied under static, quasi-static and dynamic loads. Reference data is mostly obtained from PMHS tests using impactors of different sizes (rectangular, cylindrical, spherical), masses (e.g. 23.4 kg in [12]; 5.6 kg in [110]) and impact velocities (e.g. average of 10.9 m/s in [166]). Non-impact experiments with cadaver specimens can also provide insight on the behaviour of the body [162].

Different measurements can be obtained from PMHS experiments. For instance, when an impactor strikes a cadaver specimen, contact force can be obtained directly from the impact hammer sensors [12], the displacement of the impactor can be measured by means of high speed video analysis [182], and accelerations acting on the human body can be measured from accelerometers mounted on the surface of or inside of the cadaver specimen [12, 182]. Similar signals can easily be obtained in numerical simulations with pedestrian models, and direct comparisons can be made.

Types of signals which are most often analysed as part of the component-level validation process are: force–deflection, contact force-time, pressure–time, moment-bending angle (for joints), values of peak forces. The presence of direct injuries is also observed, such as the location and number of rib fractures per configuration or rupture of ligaments.

4.1.2 Full-Scale Validation Using Cadaver Data

The full-body kinematics of advanced pedestrian models are also validated using PMHS full-scale tests. During the preparatory phase of PMHS full-scale experiments, cadavers before the crash are suspended and maintain an upright, pedestrian-like position. Then, they are released, usually just before the impact with a vehicle. The signals studied are most often kinematic data obtained from high-speed video analysis of markers/photo targets attached to the specimens before the test. The common registered signals are: displacement–time and relative velocity–time relationships, 2D-trajectories of segments (vertical vs horizontal displacement) [49, 61]. Accelerometers mounted to body segments were used, too [49, 150].

The results of two full-scale pedestrian PMHS experiments were extensively used for the validation of pedestrian models: [49, 61]. Recently, a new PMHS study by [150] has been published, but so far only the response of the MADYMO MB pedestrian model has been compared with these results [151].

4.2 Validation: Multibody Models

The earliest pedestrian models were validated mainly using results from dummy tests [196]. The dummy models were ONSER 50 dummy [24], Part 572 dummy, SIERRA 292/050 dummy. Validation of the models using cadaver test results was also attempted [119].

The validation of the MADYMO pedestrian ellipsoidal model has been documented by [177] and in the model manual [167]. The validation process consisted of two parts. First, dynamic response of individual body segments, i.e. shoulder, thorax, abdomen, pelvis was validated based on results of PMHS impactor tests in different configurations (lateral, oblique), see Fig. 3 [12, 166, 182]. A good agreement with reference corridors was acheived. Then, full-scale pedestrian impact simulations were carried out, with multiple PMHS tests as a reference (e.g. [49, 205]). Linear position and velocity of the head impact, and maximum linear acceleration/bumper force were analysed.

Fig. 3
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Impactor dynamic tests: a PMHS test [166]; b MB simulation, MADYMO [177]; c FE simulation, THUMS model [171]

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Fig. 4
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Examples of FE pedestrian models. a THUMS Version 4 for Euro NCAP TB024 Pedestrian AM50. b GHBMC Pedestrian Model Simplified Version (PS)

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Table 4 Description of example pedestrian FE models
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[23] scaled the MADYMO adult pedestrian model and compared its response during the initial impact phase of the vehicle against data from a PMHS experiment with a female specimen [49]. Body segment trajectories (head, pelvis, knee, ankle), resultant head velocity and head accelerations were comparable to the reference values.

The newest efforts concerning improvement of the MADYMO ellipsoid model were reported by [3]. Contact and joint characteristics were optimised to achieve a better response comparing to reference impactor and full-scale PMHS tests. In addition to this, the modified model’s compliance to the requirements of EuroNCAP TB024 pedestrian model certification protocol [66] was confirmed.

As documented in [167], the MADYMO facet model was validated using results of cadaver tests. Additionally, [73] compared the kinematic response of the MADYMO facet model with the cadaver tests by [49].

VIRTHUMAN model was validated in a series of component-level validation simulations for multiple body segments including the head, neck, torso, lower and upper extremities [184]. Also, a full body validation was carried out, too [184], and it was based on the PMHS pedestrian impact test by [61], while using the deformation characteristics of the vehicle parts from [157]. The analysed criteria for the full-body simulation were: trajectory of head, thorax and pelvis; location of the head impact (wrap around distance) and the corresponding time of the head strike. The results of the simulation were comparable to the results of the PMHS experiment.

MB forensic models available in reconstruction software were often validated by means of comparison of body motion with video data either from dummy crash tests [9, 29, 107,108,109] or CCTV (closed-circuit television) recordings [4, 13]. The main focus in those studies was on the model’s ability to recreate locations where pedestrians or dummies impacted the vehicle. Another often-studied criterion was pedestrian throw distance. Forensic experts often estimate collision velocities through established relationships between throw distance and collision velocity (see: Sect. 1.2). TTEhe Validation of some pedestrian models reflects this approach to collision reconstruction. Simulated pedestrian throw results are often compared against available throw distance data from dummy tests [9, 98, 108, 109] or from real accidents [4, 9, 13]. Analytical projectile methods are also used as a reference [108, 136].

As part of the verification of pedestrian models, a realistic sensitivity of the kinematics of pedestrian models to the geometry of impact vehicles has been shown for most MB forensic models [97, 136]. Notably, throw distances of many pedestrian models are higher than reference data, especially in impact with higher velocity or with box-shaped vehicles [98, 108]. In addition, the results show that throw distance of pedestrian models tends to be highly sensitive to initial impact location across the vehicle front [136].

MB forensic models were generally not validated against PMHS data. [69] compared the motion response of their custom MB model based on the PC-CRASH solver with video frames from cadaveric and dummy tests. The research involved tuning the physical parameters (coefficients of restitution and friction) of the initially proposed model individually for each collision configuration to obtain a response comparable to the reference tests. [193] visually compared the response of their lower leg model in one simulation with cadaver tests by [91], but no quantitative measure of the simulation accuracy was given.

4.3 Validation: Finite Element Models

Historically, there were FE pedestrian models for which body segments were assumed to be rigid and for which there were no validation data [115]. Currently, as researchers aim to model the properties of a human body in the most minute details, robust validation remains a prerequisite for any pedestrian impact simulations.

4.3.1 Component-Level Validation of Finite Element Models

Multiple teams of researchers reported component-level validation simulations of their FE pedestrian models [56, 57, 87, 100, 120, 175, 192]. Below is a selection of component-level validation configurations, based on [87, 192], is given:

  • lower extremity model: quasi-static three-point femur bending, dynamic toe impact experiments, shearing and bending of the knee joint, four-point bending of the knee joint;

  • head model: frontal skull impact, lateral head impact, head rotation/brain kinematics test, head rotation/brain injury test;

  • chest, abdomen, pelvis models: lateral chest impact with impactors, location and number of rib fractures, pelvic lateral impact, pelvic fracture location;

The validation of individual body segments tends to be a subject of separate studies by itself [86, 145]; individual validated body segments are assembled into a complete pedestrian body. Some developers first report component-level validation of models in occupant postures, and then reposition and remesh the models to a pedestrian posture [87, 126]. However, it is also common to report the component-level validation procedure for a model already in the pedestrian posture [121]. When the authors report validation of their full-body pedestrian models, individual component tests are either described in detail as part of the main article [87, 192], or an abridged tabular matrix of all validation cases is provided [50, 57, 153].

Validation for a special subset, such as elderly or child specimens, often requires narrowing the subset of available results of cadaver component-level experiments to only the most relevant cases [10, 50, 56].

4.3.2 Full-Body Validation Of Finite Element Pedestrian Models

Several developers compared the responses of their FE pedestrian models with full-body PMHS [87, 120, 121, 165, 175, 192, 209]. The validation criteria were mostly based on the trajectory corridors of the body segments. Comparison of injuries sustained by cadaver specimens and pedestrian models is also used as a criterion for validation [120, 121, 175].

While it cannot be considered a validation per se, [153] verified the full-body response of their FE model impacted by a vehicle against results from a similar simulation with a MADYMO MB pedestrian model scaled to the dimensions of a 10-year-old child. The scaled MADYMO model was not validated either, but a generally good comparison of kinematic responses between the two models was noted.

5 Application of Pedestrian Models

Pedestrian models are primarily used in two areas of application: road accident reconstruction and pedestrian safety analyses.

5.1 Road Accident Reconstruction

It is no surprise that there are numerous examples of reconstruction of pedestrian accident cases using MB forensic models, as it is their primary area of application [29, 44,45,46, 55, 71, 127]. MADYMO pedestrian model has been used for reconstruction purposes as well [23, 152, 173, 190, 199]. In line with current best-practise recommendations [33], analysis of the uncertainty of accident reconstruction [85] has also been applied to simulations of pedestrian impact with MB models [213]. FE models are used much more rarely for accident reconstruction. [72, 190]

An optimisation approach to accident reconstruction using pedestrian models is discussed in Sect. 5.6.

5.2 Industrial Applications

The RARU model, the JARI model and the original TNO MADYMO pedestrian model [177] played a role in developing subsystem testing procedure by IHRA [105, 111]. Simulations with model by [2] were used to derive a proposal for joint torques properties for a Polar I dummy.

Pedestrian models are used to evaluate the performance of new means of protecting vulnerable road users, including adaptive bumpers [154].

5.3 EuroNCAP TB024

Simulations with pedestrian human body models have been suggested as means of replacing some physical tests. An example of bringing this idea into practise is the assessment of deployable systems for pedestrian protection (DS) in line with the EuroNCAP VRU Testing Protocol [32]. There are three areas of the Protocol where pedestrian models are used:

  • detection of pedestrians, i.e. determination of hardest to detect pedestrian size

  • timing of system deployment

  • bonnet deflection due to body loading

Details on each of these areas have been described, e.g. in [32, 67]. In summary, the Testing Protocol determines that certain procedures either can be or must be (depending on the procedure) carried out using CAE simulations, as long as the pedestrian models used for the simulations have been certified according to Technical Bulletin 024 [66]. Otherwise, if no satisfactory test data is provided, the vehicle is assessed with its active systems disabled, and this can naturally be detrimental to the vehicle’s final safety rating.

The development of the TB024 certification procedure as part of the CoHerent project was described by [67]. Generic vehicle FE models were developed as part of the project and are used for TB024 certification. In practise, this means that only FE pedestrian models or MB pedestrian models that support MB-FE coupling can be validated in line with this certification.

Assessment of compliance to the requirements of the EuroNCAP TB024 pedestrian model certification protocol has recently become the subject of numerous studies. The study by [68] presented anonymised results for different human body models, and it was shown that certain models at their then-state did not satisfy the acceptable tolerance corridors for head impact time or body segment’s centre of gravity trajectories. Since then, publications reporting improvements and compliance of various models have been published: MADYMO [3], GHBMC Simplified Pedestrian AM50 [26], TUST 6yo [78]. TB024 in its initial version provided kinematic corridors for the 50th percentile male model only. However, the current version (v. 3.0.1.) requires validation of 6YO and 5th percentile female models as well.

5.4 Crashworthiness Studies

Due to fast computation times, MB pedestrian models can be used to simulate a whole Design of Experiment (DoE) matrix in a relatively short period of time. Therefore, the DoE approach was used to study influence of vehicle shape [141] or vehicle kinematics [214] on pedestrian injury and kinematics. The simulation results obtained with a MADYMO-based custom pedestrian model were used by [84] to create and train a predictive model capable of assessing injuries only from the front design of the vehicle. The influence of the position of the pedestrian in relation to vehicle was also studied. [155] studied the influence of rotation angles of pedestrian on injury risk, while [215] analysed the influence of gait type on injury. [43] investigated the influence of non-struck leg on pedestrian pelvis kinematics using a modified FE pedestrian model by [63].

MB forensic models were also used in crashworthiness studies, for example, to assess the values of biomechanical injury criteria under different conditions [4, 20, 127, 210, 215]. However, since forensic models have not been reported to be validated for crashworthiness analyses, their ability for accurate injury prediction is doubtful.

When applying MB pedestrian models, either FE [34, 130] or MB [83] vehicle models have been used.

5.5 Coupling

It is a common practise to first use MB models to determine impact conditions and then carry out a further detailed analysis. By the same token, results from reconstructions with MB forensic models provided boundary conditions for simulations with MADYMO [80, 125] or FE [201] models. MADYMO MB models were also used as a tool to determine the boundary conditions for subsequent FE simulations [34, 123, 129, 207]. The coupling of MB and FE simulations is also a valid approach in both accident reconstruction [34, 152] and crashworthiness analyses [81, 130]. In most coupling cases, the coupling configuration is FE vehicle—MB pedestrian, but FE parts (skull/brain models in particular) for an MB model are also utilized [34, 152, 187, 199]. Human body models which combine MB and FE functionalities are known in the literature as hybrid models [139]. The main advantage of the hybrid approach is that it allows for the simulation of complex systems that have both rigid and deformable components, which cannot be efficiently modeled using either MB methods or FE methods alone. By combining these two techniques, the hybrid approach can provide a more accurate and comprehensive representation of the system dynamics.

5.6 Optimization

Optimisation methods are often used in pedestrian impact analysis. The principle behind those methods is to carry out numerous simulations to find one set of input parameters which would minimise the value of target function.

For safety analysis, optimisation is usually employed to create car front shapes with the best pedestrian crashworthiness response [76]. However, there are examples where optimisation was used to assist the development of pedestrian models themselves, i.e. to develop a body segment model with a desired contact response [62, 134].

Moreover, optimisation methods are an often-used technique for reconstruction of road accidents [33], used to recreate various vehicular impact configurations [83]. In the case of pedestrian accident reconstruction, the target function would often be a difference in vehicle and/or pedestrian rest position between simulation and accident, and the sought-after parameters are usually collision velocity and the initial impact configuration (linear and angular position of vehicles and pedestrians).

Examples of the application of optimisation techniques in relation to accident reconstruction with MADYMO pedestrian models have been carried out [152, 173, 190, 199]. It is also a standard approach to reconstructions with PC-CRASH, Virtual CRASH or V-SIM programmes, too.

For optimisation, many safety analysis or forensic software packages are equipped with their own optimisation modules [22, 33, 168]. External commercial packages are also used for optimisation in pedestrian simulations [62, 143, 200], with MATLAB being a notable example [76, 77, 142, 211].

Attempts have also been made to run MATLAB optimisation with FE solvers for purposes of pedestrian modelling [77].

5.7 Other Applications

MB forensic models are used in a variety of applications outside of the typical reconstruction. Examples are: supporting statistical analyses of accident configurations [6, 17, 18], preparation of pedestrian detection staged experiments [180], supporting study of influence of driver behaviour on pedestrian injuries [210], being a reference point to determine the feasibility of formulas describing pedestrian after-impact motion [212].

Obviously, pedestrian models have originally been validated for pedestrian impact applications, and so initial attempts required creating modifications to apply the models for other VRU impact purposes, e.g. a bespoke knee model for a cyclist model [14] However, now it remains common practise to use them for a multitude of impact scenarios: cyclist [124, 158, 176, 194], solowheel or doublewheel electric self-balancing scooters [149, 188] or powered standing scooters [92, 128, 131].

Other applications include sports biomechanics [170], fall from heights [30, 102, 186] and workplace accidents [101, 103].

6 Discussion

6.1 Quality of Reference Data Used for Validation

Many studies used results of accident investigations as initial conditions for simulations with advanced pedestrian models [23, 65, 80]. One of the most important factors in pedestrian accidents is vehicle-pedestrian collision velocity, which in most cases is unknown and can only be estimated. The estimations of impact velocity are usually based on throw distance formulas or skid marks [113], and due to variability of many parameters (vehicle model, road surface properties, unknown braking intensity) should always be estimated after an uncertainty study. It is not always the case, and thus quality of velocity estimations is sometimes debatable. In addition to that, accidents are often initially reconstructed using pedestrian models (e.g. as in [80]), so it could be argued that in such studies results from one model influence results of simulations that use other, more advanced models. Currently, CCTV video recordings of accidents can be considered to be one of the most reliable objective means for collision velocity estimation; thus, accident-based validation of models should primarily use these new sources of information [4].

While being a valuable source of information, PMHS tests are not without flaws. Experiments with cadaver specimens are (usually) one-time, hardly repeatable tests with inherent uncertainties such as material properties of a particular human specimen. There is also a risk of overtuning the model when validation is based only on results from a narrow group of specimens.

6.2 Validation vs Phases of Pedestrian Impact

Many kinematic analyses, including frame-by-frame analyses, focus only on the model behaviour up to the moment of head-windscreen impact [49, 69, 107] or, at most, up to the moment of separation of the body from the vehicle [108, 109]. Motion of the model during the flight phase, i.e. in-air rotation or flight height, has received some attention [11, 104, 109, 127, 151], but more research is still required. In the practise of accident reconstruction, the in-air trajectory of the pedestrian registered on a CCTV or dash camera is often one of the few reliable pieces of evidence available to the forensic expert. Juxtaposition of simulation against video recordings is a standard approach to assessing impact velocity, and so the pedestrian’s flight phase should receive more attention in terms of the models’ validation.

Ground contact after the flight phase is relatively rarely studied using advanced pedestrian body models. On that note, simulations with the MADYMO pedestrian model by [151], which recreated the PMHS full body experiments by [150], showed that the accurate prediction of ground contact injuries is generally limited by the accuracy of pedestrian-vehicle contact response.

Remarkably, no simulation has been reported in which the pedestrian throw distance for the FE pedestrian models was measured. FE simulation of pedestrian impacts usually end at 0.1s after the impact with the vehicle [72, 175], while in reality a pedestrian comes to a full stop only at about 1.5–2.0 s after the initial impact.

6.3 Criticism of Validation Procedures

Validation of many forensic models has been done by means of full-scale dummy experimental tests. It could be argued that this approach is inherently flawed, as the purpose of most software developers was to provide its users with computational human models, and not digital equivalents of a particular dummy model. Also, many validation papers do not provide any detailed description of the dummies used [9, 108], and thus biofidelity of those devices cannot be ascertained.

The above comments notwithstanding, most pedestrian models that were actually validated using dummy test results are those dedicated to forensic accident reconstruction. Inaccuracy of vehicle models used, uncertainty of initial conditions, and sometimes even inaccuracy of measured evidence (such as final rest position of the pedestrian) is inherent in the practise of reconstruction. No numerical reconstruction with a pedestrian model, or any other type of road accident reconstruction for that matter, should be treated as a definitive recreation of a particular event. Thus, an assumption that it is enough for the digital model response to be equivalent to a dummy’s (at least in terms of global kinematic parameters such as throw distance or impact area location) could be considered valid. However, remarkably, most of the MB forensic models implemented in commercial reconstruction packages have not yet been validated by means of component-level or full-body simulations of PMHS tests.

Efforts were made to validate the response of the model using video recordings of dummy impact tests. However, some of the older studies lacked objective assessment (e.g. comparison of surface marker trajectory). [107,108,109]. Future investigators should address this if dummy experiments are to be used for validation of pedestrian models. On that note, PMHS studies, where the trajectory of body segments is often registered in detail [49, 61], could be considered more useful for validation.

Contemporary FE pedestrian models of THUMS, GHBMC and JAMA are reported to be validated using both component-level and full-body-level reference data. This is however not always the case, and often full-body-level validation of pedestrian models is not reported, for instance in studies by [56, 57]. In a study by [153], the developers conducted only a full-body verification, not validation, by comparing their simulation results with results from a not validated, 10-year-old pedestrian model scaled from MADYMO MB pedestrian model as a reference. This omission of validation for full-body pedestrian applications could be coming from the fact that many pedestrian models are morphed from occupant models, and it is occupant-wise validation that has the most priority when the models are initially developed.

The quality of the human body model model is often quantified using objective rating methods, for instance ISO/TS 18571 standard used in the work of [56]. The model rating scores are based on comparison of similarity of two curves, which are results of a numerical simulation and a reference experiment; a higher rating score is meant to show better biofidelity. [175] argued that such approach is not entirely correct; HBMs are originally meshed from different body specimens than cadaver specimens used in most validation experiments, and so the experimental and simulation configurations are hardly comparable. In addition, the researchers indicated that the simple linear scaling of the reference results has significant limitations. Due to these considerations, [175] in their study decided to keep only the qualitative level of model validation.

6.4 Reconstruction

In practise of accident reconstruction, advanced pedestrian body models are rarely used by individual witness experts. As noted previously, FE simulations are generally too time consuming for a standard accident reconstruction.

MADYMO MB model was suggested as a means of vehicle accident reconstruction, especially in conjunction with optimisation techniques [152, 173, 190, 199]. However, [152] noted that optimisation techniques for MADYMO pedestrian model are best used for rest-position based accident reconstruction (due to lower non-linearity of displacement parameters compared to pedestrian injuries). Recent studies [5, 151] suggest that inability to reliably model ground impact limits the applicability of the MADYMO pedestrian model in the area of individual vehicle reconstruction. By extension, care should be exercised when using MB forensic models, too, especially for more detailed injury analyses.

6.5 Practical Problems of Running Simulations with Pedestrian Models

The history of development of pedestrian models often showed the ingenuity of researchers when faced with limitations of numerical solvers. For instance, a decision to create a facet child pedestrian model by [206] was actually rooted in initial problems with the magnitude of ellipsoid penetration. Severity of penetration precluded the use of the standard contact algorithm, and thus the authors decided to discretise ellipsoidal surfaces with a facet surface mesh. Another example is a model of [69] and their decision to split each spherical joint into three revolute joints. This allowed the author to bypass limitation of the solver and to declare separate motion restraints on each of rotation directions.

MADYMO model of [177], in order to achieve a good correlation of the contact response in different impact directions, was supplied with additional ellipsoidal surfaces on the lateral and rear part of the pelvis to model the volume of flesh in these areas. Such an approach is rarely used in MB forensic models, as their solvers usually allow only one contact surface per rigid body.

Numerous publications exist which attempted to recreate the geometry and contact properties of a car body [23, 49, 177, 205], usually modelled using ellipsoidal surfaces. Facet models of pedestrian-impacting vehicle parts have been modelled, too. [106]. These vehicle models were used in the analyses of the influence of vehicle properties on pedestrian injury criteria. In the case of dedicated reconstruction software such as PC-CRASH, Virtual CRASH, CYBID V-SIM or HVE, the programs are usually supplied with databases of thousands of vehicle models (dimensions, body shapes) as well as default values of contact stiffness. The latter, however, are usually assumed to be the same for all vehicle models, so recreating the exact properties of a particular model needs to involve manual tuning. Also, reconstruction software often uses generalised stiffness for the entirety of the vehicle body, thus not taking into account differences in stiffness between, e.g., windscreen and A-pillars.

A major issue of some FE pedestrian models is their lack of robustness in longer simulations due to the explicit time-integration error accumulation. Moreover, the complexity of the material model, the element formulation and thus the number of integration points in finite elements directly influence the computation time. [57] noted that, for instance, VIVA model has a runtime of 90 min on 32 cores for a simulation time of 50 ms (timestep of 0.33 μs); in the same paper, it is said that the occupant version of GHBMC detailed model runs a simulation of 60 ms on 48 cores in 16 min (timestep of 28 μs), and the detailed occupant GHBMC model runs a simulation of 60 ms on 48 cores in 538 min (timestep of 0.1 μs). In contrast, the authors of the current paper ran a basic pedestrian impact simulation with a V-SIM 5.0.62 forensic pedestrian MB model. The runtime was approximately 4.5 s using an 8-core processor for a simulation time of 4 s (timestep of 200 μs). This can be attributed to the model’s simplified geometry and low number of degrees of freedom of the whole system (see: Table 3).

The above could be the reasons for a relative paucity of practical application of FE models in accident reconstruction, in which applications all phases of pedestrian kinematics often need to be simulated (see: Sect. 6.2). Due to robustness and numerical stability, MB models are also good for large-scale studies. This is showcased by a research by [214] who conducted a Design of Experiment matrix of 10,000 simulations with MADYMO pedestrian MB model in various impact configurations.

All MB and FE pedestrian models currently used for impact simulations recreate only passive properties of a human body, i.e. the behaviour during impact is equivalent to an unconscious person’s. However, the motion of the pedestrian lateral to the vehicle’s front plays and important role on the outcomes of an impact. As a compromise, for most simulations, the motion of the pedestrian at the moment of impact is usually simulated by rigid whole-body transformation (usually linear translation with a fixed linear velocity), with joints in a fixed position to recreate the pedestrian’s posture at the time of impact [152, 173]. Additionally, while much research has recently been conducted in the area of modelling active muscle behaviour of an occupant [164], the subject of modelling active muscles for pedestrian models has yet to be explored. An analysis of 305 accident recordings uploaded to YouTube [179] has shown that only 43% of pedestrians exhibit no reaction before the impact, while the rest exhibit behaviours ranging from stopping, slowing down, accelerating, or even jumping away. Future studies with numerical mechanical models of pedestrians should aim to define pedestrians’ pre-crash movement and behaviour more accurately.

6.6 Geometry Sources, Scalability, Morphing

Pedestrian models use different sources for geometry and inertial data. A common approach, especially when creating multibody models, is to use statistical data. GEBOD (Generator of Body Data) [8, 19] is a software/database of anthropometric dimensions of U.S. and German Air Force specimens [39] and it was a source of geometry and mass properties of multiple pedestrian models [36, 38, 49, 203, 206]. RAMSIS software data [147, 148] of a Western European specimen were used to create the default model of [177], but scaling of that model is still by default done using GEBOD database. While the dimensions of the default model by [108] were based on dimensions of a Hybrid III dummy, its scaling is based on [59] and an undefined Slovakian research [31]. [193] based their pedestrian model generator on two sets of data: a U.S. Air Force population [39] and a Polish average population [37].

Another approach is to directly use a geometry of an individual specimen obtained from CT or MRI data. This approach was used by developers of multiple FE models [56, 175, 192].

Geometry of a model can also be generated via morphing. Morphing can generally be described as the process of modyfing the shape of a model’s geometry based on a target set of mesaurements. Regarding the development of pedestrian models, it is common to morph previously developed FE models to a different size or sex. In most cases, the target geometry is obtained from taking anthropometric measurements by means of 3D scanning techniques [120, 121]. Different morphing approaches are used: for instance, radial basis interpolation approach was used for pedestrian models [120, 121], but in the area of human body modelling kriging and moving least squares methods are also used [58].

The influence of pedestrian stature on impact results has long been known [161]. However, while there were attempts to investigate the influence of different anthropometries on results of numerical simulations [189], it is still unclear if minor differences between specimens of different populations, but of identical standing height, have any major impact on results of crashworthinness research or forensic investigation. Also, influence of the manner of scaling of dimensions (which is sometimes done simplistically by linear functions) remains unknown.

Scaling for FE models often involves morphing previously developed FE models to a different size or sex. In most cases, the target geometry is obtained from taking anthropometric measurements by means of 3D scanning techniques [120, 121]. Different morphing approaches are used: for instance, radial basis interpolation approach was used for pedestrian models [120, 121]. Scaling in general tends to be a problem for FE pedestrian models, and developers need to employ additional tools of verifying stability (“runability”) of their models.

Those issues are much more rarely encountered when using MB models, naturally at the cost of the accuracy of the generated model’s geometry.

Scalability of pedestrian models, while being a vital feature used in many studies, poses a problem of the resultant model being not biofidielic. Indeed, many validation simulations have been carried out for the 50th percentile adult model only [108, 177], and no direct data for validation of the other model sizes is available.

Currently, much research in the field of vehicle crashworthiness addresses the problem of equal representation in terms of the passive safety of various size and age groups. These groups include: an average female [117], so far largely underrepresented in the crash test protocols, as well as children [93] or disabled road users [163]. Modelling bodies of children [50, 78, 100, 126, 153] or the elderly pedestrians [56] remain in line with the efforts for introducing equity to the field of road safety.

6.7 Repositioning Tools

Pedestrian postures vary to a large degree depending on the walking or running speed, or the gait cycle phase [173]. Thus, pedestrian models need to be capable of modelling a variety of postures. Additionally, as pointed out previously in this review, pedestrian HBMs were often based on occupant models. As a result, there was a need for repositioning the model’s joints from an occupant to any pedestrian posture. Positioning is rarely an issue for the ellipsoidal MB models, but it is a fundamental problem for models which geometry is based on mesh grids, FE models in particular. Stretching and compression of elements may pose numerical problems. Thus, various approaches to positioning of finite element models to pedestrian postures were proposed [28, 53, 57, 181].

6.8 New Approaches to Model Distribution

It is becoming popular to employ knowledge from different fields, including software engineering, and introduce it to the practice of mechanical engineering. Version control systems (e.g. Git [15]), usually employed for maintenance of programming code, are used to store the model source files, and dedicated pre- and post-processing tools are developed with programming languages such as Python [57]. In the case of models by [57], users can participate in the development of the models by committing their changes to a common repository, which changes are later approved by the core development team before finally introducing them to the model. Additionally, families of THUMS, VIVA+, GHBMC models are distributed free-of-charge, or under terms of academic licences, which can lead to their widespread use amongst the academic community.

On this note, it is worth noting that usage of some human body models for purposes of litigation or investigation is generally limited and regulated by their User Policy, eg. THUMS [172]. Meanwhile, specialized reconstruction software with their human body models is usually distributed under the “as it is” principle, and as is often said explicitly in their User Policy, the responsibility for the accuracy and application of the models lies with the end user.

7 Conlusions

The state-of-the-art review provides the following conclusions:

  1. 1.

    Approaches to validation of pedestrian models can be divided into following subcategories:

    • accident-based (case studies, empirical formulas based on statistics)

    • experimental-based (dummy tests, PMHS studies).

  2. 2.

    The level of detail of validation varies between pedestrian models and is dependent on the models’ intended area of application:

    • pedestrian models for forensic applications rarely use PMHS data as a reference; dummy testing and accident-based approach are the most common validation method

    • advanced multibody and finite element models for crashworthiness analyses, and industrial applications predominantly use PMHS as a validation reference.

  3. 3.

    Due to their numerical efficiency, multibody models of pedestrian bodies are used for large Design of Experiment test matrices. Finite element models are thoroughly validated and are capable of replicating pedestrian’s injuries with great detail. A common approach to pedestrian impact modelling is multibody-finite element coupling (hybrid modelling), where selected parts of a multibody system are replaced with a detailed finite element model.

  4. 4.

    The usefulness of multibody forensic models in the area of crashworthiness analyses can be deemed limited, as, for most of them, no validation has been reported so far in terms of their ability to predict injury.

  5. 5.

    Pedestrian models are used not only for pedestrian applications, but also as other vulnerable road users: cyclists or e-scooter riders. In many commercial reconstruction programs, multibody forensic models of pedestrians are used as occupants as well.

  6. 6.

    Development of pedestrian models dovetailed with the introduction of dedicated joint positioning tools. The open-source distribution of human body models and the introduction of digital testing as a replacement for physical tests could mark the future for automotive engineering.