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Effect of vehicular vibrations on L-4 lumbar vertebrae – A finite element study
, R.M. Raveeshc, B. Rakesha, S. Bhaskard, Geetha Kuntojie, B.A. Chethanf
⁎Corresponding author: A. Manoj. amanojprabhu@nitc.ac.in
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Received: ,
Accepted: ,
This article was originally published by Reed Elsevier India Pvt. Ltd. and was migrated to Scientific Scholar after the change of Publisher.
Abstract
Abstract
Lower Back Pain (LBP) is a global health issue, with increasing prevalence, partly attributed to vehicular vibrations experienced by motorcyclists. The L4 lumbar vertebra is responsible for greater mobility and flexibility of the body, but also is the most crucial body element affected by vehicular vibrations. Anthropometric properties, types of speed humps, and vehicle types are the critical variables that impact bone health during riding, need to be studied. To understand the potential zones of injury, computational simulation can be performed under the influence of vehicle vibrations while crossing different types of speed humps at varying speeds. In the present study, finite element method (FEM) is used to evaluate stress and deformation in the bone. The L4 cortical bone is modelled by considering the CT-Scan data and assumed to be homogeneous and isotropic material. Vibration data is collected using two vehicle types (Type I and Type II) on four different humps (Trapezoidal, Bitumen Semi-circular, Rubber Semi-circular, and Rumble strip). The bone's dynamic behavior is studied using FEM simulation, which involved static structural, modal and transient dynamic analyses. The findings from static analysis indicate that the most concentrated stress is located in the lower pedicle region and is an expected commonplace for injuries because of vibrations. In transient dynamic analysis, Type I vehicle showed a 25 % higher stress than Type II.
Abstract
Graphical abstract
Image 1
Abstract
Highlights
•Finite element analysis was used to study the effect of vehicular vibrations on the L4 lumbar vertebra.•Vibration data was collected using two vehicle types on four different speed humps at varying speeds.•Static analysis showed maximum stress in the lower pedicle region, a common area for vibration-induced injuries.•In transient dynamic analysis, Type I vehicle exhibited 25 % higher stress compared to Type II vehicle.•Type I vehicle showed 33 % higher total deformation than Type II vehicle when crossing a rumble strip.
Keywords
L-4 lumbar spine
Vibration analysis
Static structural analysis
Modal analysis
Transient dynamic analysis
1 Introduction
The human spine, also called the vertebral column, supports, stabilizes, and enables mobility in the body. It comprises of 33 vertebrae divided into five regions: cervical, thoracic, lumbar, sacral, and coccygeal. Globally, Lower Back Pain (LBP) is the leading cause of Years Lived with Disabilities (YLDs). Greater attention is needed to mitigate the increasing burden and the impact LBP is having on health and social systems. LBP was 377.5 million in 1990, and this increased to 577.0 million in 2017,1 which is almost 50 % more prevalent. The lumbar spine, or lower back, is a critical area of the body that is multifunctional by providing support for the upper body and helping with movement and flexibility.2,3 The study of mechanics on the lumbar bone is essential to understand the spine functions and it responds to various forces and loads.
Motorbikes and cars are highly applicable for day today activities to move freely without much effort and used in regular basis for commuting.4 The lumbar spine is impacted when motorcycles traverse over speed humps and severity depends on rider anthropometric characteristics, road conditions (such as even roads, uneven roads, and pot-holes), and the specific type of speed hump with specific speeds encountered.5 There are several ways for analysis of the impact of lumbar bone such as experimental method and FEM, usually FEM is preferred because of highly promising tool in orthopaedics and other clinical fields.6 When compared to all lumbar bones (L1 to L5), L3 and L4 are the most critical because they bear the most load compared to L1 and L2. Whereas L5 is almost fixed to the sacrum bone and doesn't play a critical role in flexibility and movement.7
Over the years, extensive research was conducted on the human spine using finite element simulation to enhance comprehension of spinal disorder and the effectiveness of treatments.8–15 The cortical bone was investigated for stress levels that were more than the usual compression strength of human cortical bone during flexion, which presents a significant risk of failure in the posterior region and neighbouring levels.16 Lumbar rotation manipulation (LRM) application in both sitting and side-lying positions showed comparable stress distribution across different disk conditions, but higher intradiscal pressure and stress in the sitting position, particularly in moderately degenerated disks, while healthy disks exhibited more noticeable displacement.17 Zafer et al. estimated intervertebral disc stress values in the lumbar spine under various forces, revealing differences in segmental movements and stability levels among different vertebral levels.18 For the purpose of examining the probability of bone fracture, Kim et al. created finite element models of the lumbar spine at the L2 vertebra.19 Schmidt et al. investigated the lumbar spine's response to routine dynamic activities while taking biomechanics under various pressures, which was especially important for people with scoliosis.20 Significant research on lumbar intersegmental disc was carried out,21–24 compressive forces were estimated using intradiscal pressure measurements, proposing a method to estimate spinal forces in different body positions.14 Tony et al. investigated the biomechanical response of the L-4 lumbar spine during motorcycle riding over a speed hump at 20 km/h, utilizing a 3D model based on CT scan data, revealing stress concentrations in specific regions (pedicle and lamina areas) and resonance patterns within the lumbar spine.25 Significant research was conducted on lumbar fusion surgery,26–28 the choice of fixation method significantly impacted the biomechanical performance of the lumbar spine, with bilateral pedicle screws providing greater stability and reduced cage subsidence but potentially increasing facet joint forces at adjacent levels.29 Amiri et al.30 developed a custom dummy model with a viscoelastic lumbar spine for frontal crash and vibration simulations, addressing limitations in current dummies.
Identifying vulnerable regions of the lumbar spine (such as the intervertebral disc, pedicle and lamina areas of the vertebra) to fractures caused by whole-body vibrations and determining safe vibration thresholds31,32 is important to enable quality riding experience. Bovenzi et al.33 developed the relationship between whole-body vibration exposure and low back pain, emphasizing the connection between occupational exposure and spinal disorders. Pope et al.34 examined the impact of whole-body vibration (WBV) on the lumbar spine's health, considering natural frequency, posture, and muscle response. Low back pain in bus drivers, considering different road types and bus models, the potential for improved driver comfort and health by considering bus design, seat attenuation, and route assignments is researched to address the impact of WBV on LBP in bus drivers.35,36
There is a necessity to analyse the lumbar spine under the influence of vehicular vibrations at specific speeds and on particular road humps. Additionally, there is a scarcity of research on finite element analysis of the lumbar spine subjected to static structural and transient dynamic analysis. Therefore, it is essential to explore the evaluation of Von-Misses Stresses and Total deformation developed in the lumbar segment, as this area requires further attention and investigation.
This study focusses the impact of transmitted force when riding over speed humps, using CT scan data to reconstruct the lumbar spine and it is considered as homogeneous and isotropic material.37–39 Additionally, the acceleration-time data of the lumbar spine under the influence of vehicle vibrations while driving over a various speed humps at different speeds is captured and the most stress induced part inside the L4 lumbar spine segment, is identified.
2 Methodology
2.1 Material property of bone
The material characteristics of the L4 lumbar vertebra, which is a cortical bone type, are Young's Modulus = 9 GPa, Density = 1910 kg/m3, and Poisson's Ratio = 0.3. It is considered as homogeneous and isotropic.
2.2 Factors impacting L4 lumbar bone during vehicle vibrations
The lumbar spine is impacted when motorcycles traverse over speed humps and severity depends on rider anthropometric characteristics, road conditions (such as even roads, uneven roads, and pot-holes), and the specific type of speed hump with specific speeds encountered.
2.2.1 Anthropometric properties
Anthropometric detail of the healthy male subject is taken for vibration analysis of lumbar bone is shown in Table 1.
| Anthropometric parameters | Present study data | Standard Range of parameters25 |
| Age (years) | 24 | 18–28 |
| Height (cm) | 167 | 152–170 |
| Weight (kg) | 58 | 58–74 |
| BMI (kg/m2) | 18.7 | 22–28 |
| Driving experience (years) | 6 | 2.5–7.5 |
2.2.2 Types of speed humps
Speed humps are commonly used to reduce vehicle speeds in areas with pedestrian traffic or near schools, promoting safer road conditions. As per Indian Road Congress code 9940 various types and shapes of speed humps include Trapezoidal, Bitumen Semi-circular, Rubber Semi-circular hump, and Rumble strip. In practical scenarios, the dimensions of speed humps may undergo slight alterations compared to IRC-99 standards, primarily due to the increased wear and tear caused by vehicles. Hence actual measurements of speed humps (Trapezoidal, Bitumen Semi-circular, Rubber Semi-circular hump, and Rumble strip) are considered for study as shown in Table 2.
| Type of hump | Hump Dimensions (mm) | Illustrations |
| Trapezoidal hump | Image 1 | Image 2 |
| Bitumen semi-circular hump | Image 3 | Image 4 |
| Rubber semi-circular hump | Image 5 | Image 6 |
| Rumble strip | Image 7 | Image 8 |
2.2.3 Speed and type of vehicle
Vibration data is collected using a moped without a gear (Type I vehicle) and a bike with a gear (Type II vehicle). All necessary vibration data is collected using these two vehicles with speed trails 10 kmph, 20 kmph and 30 kmph for the simulation of L4 lumbar spine model of motorist exposed to vibration from speed hump.
2.3 Collection of vibration data
The subject was instructed to operate the motorcycle at predetermined speeds while traversing four distinct speed humps. An accelerometer was employed to record the vibrations transmitted from the speed humps to L4 bone location of the individual. This data was collected through a data acquisition system (DAQ) equipped with a dynamic analyser and connected to a Core 2 Duo processor via an NI USB-9234 card.41,42 Vibration measurements in all directions were conducted using the DEWESOFT software, with the instrument positioned at the individual's L4 vertebra location.
Light-weight strip was used to attach the accelerometer (2.4g) to the L4 back bone location of the subject. The National Institute for Occupational Safety and Health (NIOSH) advised that the weight of the accelerometer and adopter combined should not exceed 20g in order to maintain the experiment's accuracy. Multiple trails were conducted for subject to maintain the result precision. Results of acceleration v/s time were recorded for all cases and the sample data collected is shown in Fig. 1.
From Fig. 1, it can be observed that the maximum acceleration is 5116.95 mm/s2 at a speed of 20 kmph for type I vehicle when moved over Trapezoidal hump. Similarly, acceleration v/s time data is collected for bitumen semi-circular hump, rubber semi-circular hump and rumble strip using both types of vehicles. The maximum acceleration values are tabulated and shown in Table 3 and these datas are used for time-history analysis (transient dynamic analysis).
| Type of Hump | Type of vehicle | Range of Acceleration(mm/sec2) |
| Trapezoidal Hump | I | −6250.65 to + 5150.80 |
| II | −1527.94 to +6971.75 | |
| Bitumen Semi Circular Hump | I | −6901.59 to +16011.16 |
| II | −2936.90 to +11043.63 | |
| Rubber Semi-circular Hump | I | −914.218 to +1405.08 |
| II | −1022.04 to +991.76 | |
| Rumble strip | I | −13060.90 to +13084.52 |
| II | −15377.200 to +17306.4 |
From the values listed in Tables 3 and it can be seen that the maximum acceleration is 17306.4 mm/s2, obtained while riding across rumble strip in type II vehicle with a speed of 30 kmph.
2.4 Modelling of L4 lumbar bone
Raw CT DICOM data of lumbar is collected from Diagnostic centre, then the data is imported into 3D Slicer software. Volume thresholding (500–1500) and scissors tools are used to extract L4 lumbar bone from the whole CT lumbar data. Then the lumbar bone extracted is imported into ANSYS software. Using Geometry Space-claim, the L4 lumbar bone is furthermore refined by reducing triangular facets by 50 %, shrink-wrapping the body, and providing 2 mm elemental size & thresholding at 20°. From mesh convergence study it was evident that Quadratic type element of 4 mm size is enough to give precise answers.
2.5 Finite element analysis
2.5.1 Static structural analysis
An axial compression load of 54 % of the body weight [58 kg × (54/100) = 31.32 × 9.81 N = 307.25 N] is applied at the upper end plates while lower endplates are fixed16 and in order to make the calculations simpler, the stresses exerted by muscles on the lumbar bone are neglected. The model results obtained are verified and compared with Jaffar et al..43
2.5.2 Modal analysis
Modal analysis was performed on the same model using same boundary conditions as in static structural analysis to investigate its dynamic behaviour. In the context of biomedical applications, the first six mode shapes and their corresponding frequencies are of particular significance.44,45 These critical modes and their associated frequencies are utilized for subsequent analysis and evaluation in the biomedical field. This step is crucial in understanding the structural response of the L4 lumbar bone under various loading conditions.
2.5.3 Transient structural analysis
Time history analysis has been conducted to examine the collected vibration data from the vehicle. This vibration data has been utilized to simulate its effects on the L4 lumbar bone. Subsequently, important parameters such as Von-Misses stress, equivalent strain, and deformation have been calculated and presented. This comprehensive analysis sheds light on how the vibrations affect the L4 lumbar bone, providing valuable insights for further investigation.
3 Results and discussions
3.1 Static structural analysis
The Static structural analysis is applied to the L-4 lumbar spine finite element model to find its steady-state static response. The model is simulated with loads of 75 kg, 100 kg, and 125 kg with considering 54 % of the body weight. The results obtained are compared with Jaffer et al. (2010) and the percentage errors are shown in Table 4. It shows that the stress values at the specified bone locations are nearly the same, with an average error of less than 10 %, which is considered acceptable. Additionally, the model was simulated with a subject weighing 58 kgs, and the static analysis yielded estimates of stress, strain, and total deformation. The simulation results indicate that the maximum stress was observed on the lower surface of the pedicle region of the L4 lumbar vertebra, with a value of 0.626 MPa. The maximum total deformation was found at the superior articular process and mammillary process, measuring 2.33 × 10−3 mm, while the maximum equivalent strain was identified at the superior articular facet, measuring 8.37 × 10−5 as shown in Fig. 2.
| Sl No | Regions | Von Mises Stress (MPa) | |||||||||
| 75 kg (397.3N) | 100 kg (529.74N) | 125 kg (662.17N) | SubjectConsidered 58 kg (307.24N) | ||||||||
| Jaffar et al. | Present study | % Error | Jaffar et al. | Present study | % Error | Jaffar et al. | Present study | % Error | |||
| 1 | The facet surface | 0.179 | 0.177 | 1.296 | 0.265 | 0.280 | −5.660 | 0.515 | 0.510 | 0.971 | 0.149 |
| 2 | Edges of the facet area | 0.233 | 0.239 | −2.575 | 0.435 | 0.432 | 0.690 | 0.870 | 0.842 | 3.218 | 0.242 |
| 3 | Superior surface of the body | 0.292 | 0.282 | 3.322 | 0.398 | 0.393 | 1.256 | 0.678 | 0.673 | 0.737 | 0.312 |
| 4 | Posterior surface of the body | 0.451 | 0.454 | −0.687 | 0.615 | 0.605 | 1.626 | 0.754 | 0.756 | −0.265 | 0.430 |
| 5 | Upper surface of the Pedicle | 0.687 | 0.677 | 1.456 | 0.924 | 0.903 | 2.241 | 1.082 | 1.120 | −3.512 | 0.524 |
| 6 | Lower surface of the pedicle | 0.695 | 0.808 | −16.259 | 0.959 | 1.079 | −12.461 | 1.237 | 1.348 | −8.973 | 0.626 |
3.2 Modal analysis
The frequency dependent vibration magnitude distribution was estimated using the modal analysis. The first six modal frequencies of the L-4 lumbar spine model are 3443.5Hz, 4175.5Hz, 4605.7Hz, 5551.1Hz, 5904.3Hz and 6363.6Hz. The vibration displacement magnitude was found to be 834.63 mm at 3443.5 Hz and a minimum of 580.55 mm at 4175.5 Hz. After the second mode, further increases in frequency result in an increase in deformation length.
3.3 Transient dynamic analysis
A time history study (transient dynamic analysis) has been conducted using the L-4 lumbar vertebrae finite element model to decide its transient state response at a given elapsed time. The model was simulated with the lower end plate and lower end facets fixed, and then acceleration was applied axially along the z-direction. The dynamic analysis yielded estimates of stress and total deformation.
Using two vehicles Type I and Type II, time history analysis is carried out for each of the four types of speed humps, namely trapezoidal humps, bitumen semi-circular humps, rubber semi-circular humps, and rumble strip. Three different speeds are considered in the analysis: 10, 20, and 30 kmph. Equivalent Von-mises stress and total deformation are generated, and the results are compared with each other.
3.3.1 Equivalent Von-mises stress
3.3.1.1 Type I vehicle
From stress analysis it was seen that, regardless of the speed, the highest stress occurs at the lamina of the pedicle region for a Type I vehicle. In Fig. 3, at speeds of 10 kmph and 20 kmph, the maximum stress recorded is 2.32 × 10−3 MPa and 1.198 × 10−3 MPa respectively, this stress is due to increased undulations and longer travel time on the rumble strip compared to other hump types. At a speed of 30 kmph, the bitumen semi-circular hump causes the highest stress reaching 1.122 × 10−3 MPa, primarily due to the vehicle's high-speed causing a sudden impact and prolonging the air travel time.
3.3.1.2 Type II vehicle
From analysing stress values, it is observed that, regardless of the speed, the highest stress occurs at the lamina of the pedicle region for a Type II vehicle. In Fig. 4, at a speed of 10 kmph, there's a maximum stress of 0.703 × 10−3 MPa because of the longer length and time spent on the trapezoidal hump. When the speed goes up to 20 kmph, there's a higher stress of 1.74 × 10−3 MPa, this stress is due to increased undulations and longer travel time on the rumble strip compared to other hump types. At 30 kmph speed, the stress is again high at 1.61 × 10−3 MPa on trapezoidal hump, primarily because of the extended length and time spent to travel on the trapezoidal hump.
3.3.2 Total deformation
3.3.2.1 Type I vehicle
Regardless of the speed, the highest deformation occurred at the spinous process region for a Type I vehicle. In Fig. 5, at speeds of 10 kmph and 20 kmph, the maximum total deformation recorded is 5.72 × 10−6 mm and 2.95 × 10−6 mm respectively. The main reason for these peak deformation levels is the maximum stress experienced in the pedicle area, along with the increased undulations and extended duration spent on the rumble strip compared to other types of humps. At a speed of 30 kmph, the bitumen semi-circular hump causes the highest deformation reaching 2.76 × 10−6 mm, primarily due to the vehicle's high-speed causing a sudden impact and prolonging the air travel time; in addition the suspension failure to absorb sudden vibrations.
3.3.2.2 Type II vehicle
Regardless of the speed, the highest total deformation occurs at the spinous process region for a Type II vehicle. In Fig. 6, at a speed of 10 kmph, there is a maximum deformation of 1.73 × 10−6 mm because of the longer length and time spent on the trapezoidal hump. When the speed goes up to 20 kmph, a higher deformation of 4.28 × 10−6 mm is observed. This deformation is due to increased undulations and longer travel time on the rumble strip compared to other hump types. At 30 kmph speed, the deformation is again high at 3.84 × 10−6 mm on trapezoidal hump, primarily because of the extended length and time spent to travel on the trapezoidal hump.
4 Conclusions
This study investigates the effect of vehicular vibrations on the L4 lumbar vertebra using finite element analysis. Vibration data was collected using two vehicle types (Type I and Type II) on four different speed humps (Trapezoidal, Bitumen Semi-circular, Rubber Semi-circular, and Rumble strip) at varying speeds. The L4 cortical bone was modelled using CT-Scan data and assumed to be homogeneous and isotropic. Static structural, modal, and transient dynamic analyses were performed. The conclusions drawn from these studies are as follows.•The Von-Mises stress values obtained from static structural analysis are verified with Jaffar et al. (2010). It is shown that, the model is performing well with less than 10 % error.•Static Structural Analysis is done under the self-weight of the body, maximum stress of 0.626 MPa was observed on the lower surface of the pedicle region, while the maximum total deformation of 2.33 × 10−3 mm occurred at the superior articular process and mammillary process. The highest levels of stress in the bottom section of the pedicle, indicates it's susceptibility to injuries caused by vibration.•A transient dynamic analysis revealed that the maximum stress experienced by the lamina was higher when a Type I vehicle crossed a rumble strip at 10 kmph compared to a Type II vehicle at 20 kmph. The analysis showed that the Type II vehicle resulted in approximately 25 % less stress than the Type I vehicle under these conditions.•The total deformation for the Type I vehicle was 33 % higher (5.72 × 10−6 mm) when crossing a rumble strip at 10 kmph compared to the Type II vehicle, which exhibited a maximum total deformation of 4.28 × 10−6 mm when traversing the same strip at 20 kmph.•The FEA result suggests that compared to Type II vehicle, Type I vehicle exhibits more stress and deformation when crossing over rumble strip at 20kmph.•Type II vehicles have better damping and can absorb more vibrations, suggesting that using a Type II vehicle and avoiding rumble strips can help to reduce lower back pain.
CRediT authorship contribution statement
Y.S. Kishore: Methodology, Software, Data curation, Writing – original draft. B.M. Sreedhara: Conceptualization, Methodology, Supervision, Validation, Writing – review & editing. A. Manoj: Conceptualization, Methodology, Supervision, Validation, Writing – review & editing. R.M. Raveesh: Software. B. Rakesh: Software, Data curation. S. Bhaskar: Conceptualization, Methodology. Geetha Kuntoji: Writing – review & editing. B.A. Chethan: Conceptualization, Methodology.
Declaration of patient consent form
Not applicable.
Ethical statement
Not applicable.
Funding statement
There has been no significant financial support for this work that could have influenced its outcome.
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