BIOMECHANICAL MODELING OF SPINAL LOADING DUE TO 

JARRING AND JOLTING FOR HEAVY EQUIPMENT OPERATORS 

Waters TR*^, Li F^, Huston RL^, and Kittusamy NK* 

* National Institute for Occupational Safety and Health

^ University of Cincinnati, Department of Mechanical, 

Industrial and Nuclear Engineering 

Corresponding Author e-mail: trw1@cdc.gov 

This paper describes the development of a multi-body biomechanical model that can be used to assess the 

risk of low back disorders due to occupational exposure to jarring and jolting from operation of heavy

mobile equipment (e.g., trucks, haulers, graders, tractors, etc.) The four-element dynamic spinal model is

capable of providing estimates of the force and acceleration responses of the head/neck, upper, lower, and

middle torso resulting from vibration input collected in field studies. The paper also presents a method for 

using the model output to assess an individual's risk of low back disorder due to a specific jarring and 

jolting exposure. 

Introduction Biomechanical Model 

In order to estimate the loading on the spine due to

jarring and jolting, we developed a specialized multi-body

biomechanical model of the human skeletal system. The 

jarring and jolting model is derived from a general multibody dynamics computer simulator, called DYNOCOMBS, 

developed by Huston et al. 1990, 1991. The general model

represents the human body by a series of connected 

elements simulating the limbs, torso, head and neck. 

Computer algorithms have been developed using 3 

dimensional multi-body dynamic computer modeling to

provide a dynamic analysis (kinematics and kinetics) of 

arbitrary collections of elements allowing for both

translation and rotation between adjacent elements. These 

elements are connected by spring and damper elements to 

simulate the response of soft tissues connecting the arms, 

head, neck, trunk and legs. By applying equations of

dynamic equilibrium to the elements of the simulation

model, the model is capable of estimating the kinetic joint

reaction forces and kinematic spinal responses resulting 

from the dynamic exposures. Figure 1 shows the

configuration of a whole human body model of the heavy 

equipment operator at a workstation. It consists of 17 rigid 

bodies as illustrated, representing the lower torso, back, 

upper torso, head, neck, and upper arms, lower arms, hands 

and upper legs, lower legs and feet. The springs and 

dampers are placed between each adjacent body. Each body 

has 6 degrees of freedom. 

In a comprehensive review of the literature relating 

whole body vibration (WBV) to low back pain (LBP), it

was noted that operators of heavy equipment in occupations

such as mining, construction and agriculture are repeatedly

exposed to high levels of transient jarring and jolting, as 

well as steady state WBV (Bovenzi and Hulshof, 1998). It

has been shown experimentally that repeated exposure to 

WBV and jarring and jolting is associated with an increased 

risk of developing low back disorders (LBDs). Researchers 

have suggested that high levels of mechanical loading to the 

spine due to WBV and transient jarring and jolting may

cause micro-fractures of the lumbar vertebral endplates or

transient pressure changes that over time may result in

adverse health effects arising from material fatigue 

processes. Due to limitations in existing biomechanical

models of spinal loading, however, it has been difficult to

accurately predict the health effects to the spine associated 

with exposure to mechanical shock. 

Noteworthy attempts to develop biodynamic models to

study human response to WBV have been reported by 

Matsumoto and Griffin, 1998; Pankoke, Buck, and Woelfel,

1998; Amirouche and Ider, 1988; and Kitazaki and Griffin,

1997. The majority of these efforts used finite element (FE)

models as opposed to finite-segment (multibody) dynamic

models. Recently, however, there have been significant 

advances in whole-body modeling that are directly

applicable to the study of human exposure to WBV and 

jarring and jolting. These advances are based upon

modeling the human body as a multi-body system rather

than a finite-element model. The principal advantage of

multi-body modeling (sometimes called “lumpedparameter” modeling) is that it can simulate large-scale

dynamics, which can then be used with finite element 

models or injury models to evaluate stresses and predict

tissue damage. As with finite element models, a multi-body

model can employ as many bodies as needed to study a 

given phenomena. 

 For modeling jarring and jolting exposure, the general

DYNACOMBS model was adjusted by combining elements 

into a simpler 4-body spinal model shown in Figure 2. In

this configuration, the four elements consist of the lower 

torso (pelvis), the middle torso (back), upper torso (chest) 

and the head/neck (head and neck are combined in this 

model configuration). 

A 4-body spinal model is more efficient than a 17 

segment model for obtaining gross-motion simulation, 

without sacrificing accuracy. The mass and geometric 
properties of the 4-body spinal system are based on the

general whole body model’s published anatomical data. 

Other mechanical parameters are determined by 

comparing model responses to published experimental data. 

Results from the new 4-body model can be used to estimate 

risk of low back disorder due to jarring and jolting exposure. 

17

8

3 

1 

2

15 

1

6

9

10

 Y 

 X 

Figure 1. DYNACOMBS Multi-body lumped parameter 

model.

m4

m3

m2

m1

Joint C7/T1

Joint T12/L1

Joint L5/S1

Z 

X Body/Seat Interface

Input Seat Signal

d3 k3 

d2

d1

k2 

k1 

Figure 2. New 4-body model of spine/neck, and head. 

The USAF has published some values for the spring

and damping parameters for specific lumped parameter

models (USAF, 1970), but special algorithms were 

developed for calculating these variables for the proposed

model. Due to space limitations, it is not possible to provide 

details of the algorithm development, however, they were

based a series of linearization, scaling, and modal parameter

analyses. 

Given suitable initial conditions and input seat 

accelerations profiles, the DYNOCOMBS model solves the 

governing dynamic equations by using a fourth-order

Runge-Kutta integrator. The output then presents the

kinematics and kinetics results of the system. For each body 

of the spinal system DYNOCOMBS computes the

displacement, rotation angle, velocity and angular velocity, 

acceleration and angular acceleration as well as mass center 

positions, and internal force and moment. 

 

Estimating Risk of LBDs 

Based on the output of the jarring and jolting model,

spinal health effects can be estimated in two ways. First,

potential tissue damage can be estimated by comparing the 

predicted spinal forces directly to assumed spinal tissue 

tolerance limits. Second, the model output can be used to

calculate the ISO 2631-5 exposure limit values (i.e, Part 5:

Method for evaluation of vibration containing multiple

shocks). These exposure limit values include the Daily

Equivalent Static Compression Stress (Sed) and the 

Cumulative Adverse Health Effects Factor (R). These 

measures provide an estimate of the daily and cumulative

exposure limit for exposure to jarring and jolting.

In order to evaluate the effects of internal pressure

changes, the Palmgren-Miner fatigue approach is applied.

Essential exposure-related factors are the number and

magnitudes of the peak compression in the spine. The peak

compression in the spine is affected by anthropometrics data 

(body mass, size of endplates) and posture. The assessment

is based on the person subjected to the vibration in a seated

upright posture. 

The procedures for determining the spinal response 

to an acceleration dose and subsequent risk assessment 

requires the following steps: 

(1) Obtain experimental seat accelerations in the field 

(2) Use DYNOCOMBS to calculate the spine accelerations

(3) Use custom software to identify and count peak values 

(4) Calculate the acceleration dose (Dk) from Equation 1 

below. 

 (Equation 1)

1/ 6

6





 



 = ∑

i

Dk Aik

Aik

th where is the i peak of the response acceleration, and 

k is the direction. 

(5) Calculate average daily dose by normalizing the 

acceleration dose as shown in Equation 2 below. 

( / ), (Equation 2) 2

1/ 6

m s

t

t D D

m

d

kd k 



 



 =

dt mt

Dk

where is the duration of the daily exposure, and is

the period over which has been measured. 

(6) Calculate the daily equivalent static compression dose

using Equation 3 below. 

( ) ( )

1/ 6

, ,

6 S m D Mpa

k x y z

ed k kd 



 



 = ∑=

0.015 /( / )

2

m Mpa m s x =

0.035 /( / )

2

m Mpa m s y =

0.032 /( / )

2

m Mpa m s z =

, Equation (3)

where 
If is below 0 , then the probability of an adverse 

health effect at lifetime exposure is low. If is above

, then probability of an adverse health effect at

lifetime exposure is high. 

Sed .5Mpa

Sed

0.8Mpa

(7) Calculate the cumulative adverse health effects factor 

(R) using Equation 4 below. 

1/ 6 6

















25Mpa

Sui

1

1/ 6

















−

⋅ = ∑=

n

i ui

ed

S c

S days R Equation (4) 

where: days is the number of exposure days per year

(typically, days=240 days/year), n is the number of years of 

exposure, c is a constant representing the static stress due to

gravitational force (a value of c is normally

used for driving posture)

and , is the ultimate

strength of the lumbar spine for a person of age 

 with being the age at which the exposure

starts. Since the value varies with the bone density of

the vertebrae, it is normally reduced with age. When

, then probability of an adverse health effect is

considered to be low. When , then the probability

of an adverse health effect is considered to be high. 

= 0.

066(b + i)Mpa

Sui

R > 1.2

Sui = 6.75 − 0.

(b + i) years b

R < 0.8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0

100

200

300

400

500

600

Time(sec)

Z L5-S1 Force(N)

Figure 3b. Compression force between L5 and S1, both

static and dynamic components, 75% male, sitting upright, 

no backrest. 

0 10 20 30 40 50 60 70 0

0.2

0.4

0.6

0.8

1

1.2

1.4

Lifetim e (age)

Cumulate Adverse Health Effects Factor R

R< 0.8: low probability of an advers e health effec t

R> 1.2: high probability of an advers e health effec t

Example Output 

Figure 3a depicts the graph of the force estimated at the

seat for a typical 2 second sample of data for a fork-truck

driver over smooth pavement and Figure 3b depicts the 

graph of the L5/S1 spinal force for the same exposure event. 

Figure 4a. Cumulative adverse health effects factor (R) for 

a low risk jarring and jolting exposure.

0 10 20 30 40 50 60 70 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Lifetim e (age)

Cumulate Adverse Health Effects Factor R

R< 0.8: low probability of an advers e health effec t

R> 1.2: high probability of an advers e health effec t Figure 4a depicts a plot of the cumulative adverse 

health effects factor (R) for a low risk jarring and jolting

exposure obtained in a field study and Figure 4b depicts and

a plot of the cumulative adverse health effects factor (R) for 

a high risk jarring and jolting exposure obtained in a field 

study. 

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1. 200

300

400

500

600

700

800

900

Time(sec)

Z contact force(N)

8 2

Figure 4b. Cumulative adverse health effects factor (R) for 

a high risk jarring and jolting exposure.

Model Validation 

Validation and tuning of the model will be

accomplished by comparing actual acceleration values 

collected from the head of an operator driving a vehicle over

a rough road to the predicted head accelerations obtained 

from the model using the seat acceleration data from the

vehicle as input. Correlation coefficients for peak 

accelerations will be compared, as well as temporal shifts in

spinal response acceleration peaks to insure that the model is

behaving properly. 

Figure 3a. Contact force between buttocks and seat surface, 

both static and dynamic components, 75% male, sitting

upright, no backrest. 
Conclusions 

Based upon our preliminary analysis, the model appears 

to adequately respond to acceleration inputs from the seat, 

however, further validation testing is needed to determine its 

ultimate accuracy. Used of the model in conjunction with 

the ISO method appears to provide a meaningful way of 

evaluating the potential health impacts of jarring and jolting 

exposure on the health of the low back, but it remains to be 

tested in an epidemiological study. Finally, it is likely that 

the proposed model and evaluation methods will provide a 

satisfactory way of evaluating the effectiveness of various 

interventions, such as new seat designs and new material 

properties that can be used to reduce exposure to levels that 

will be considered safe for nearly all heavy equipment 

operators. 

References 

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a Biodynamic Human Model Subjected to Low 

Accelerations – A Correlation Study”, Journal of Sound and 

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Epidemiologic Studies on the Relationship Between 

Exposure to Whole-Body Vibration and Low Back Pain,” 

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Huston RL, "Multibody Dynamics - Modeling and Analysis 

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