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Journal of Orthopaedic Surgery and Research logoLink to Journal of Orthopaedic Surgery and Research
. 2025 Nov 4;20:951. doi: 10.1186/s13018-025-06408-5

The effect of walking speed on spinal loads and trunk muscle forces using subject-specific musculoskeletal modeling: A database for clinical and modeling applications

Ali Jamshidian 1, Alireza Rouyin 1,#, Hamed Nazemi 1,#, Navid Arjmand 1,✉, Marwan El-Rich 2
PMCID: PMC12584331  PMID: 41188961

Abstract

Background

Gait analysis of patients with spinal disorders at different walking speeds helps clinicians diagnose conditions and investigate treatment/rehabilitation effectiveness. A subject-specific database for trunk muscle forces and lumbar spine loads of healthy individuals during different walking speeds is therefore useful.

Methods

Ten healthy participants walked at three speeds (slow, normal, and fast) while motion and force-plate data were collected. Force in trunk muscles and loads on the lumbar spine discs were estimated using subject-specific musculoskeletal simulations in OpenSim. Model predictions at different walking speeds were statistically compared.

Results

The time-dependent subject-specific force in all major trunk muscles and compression/shear loads at all lumbar spine discs (T12-S1) were reported for all walking speeds. Significant differences were observed in the average of peak compression between the fast and both slow/normal walking speed conditions across all lumbar discs (p <  0.001). With the exception of the L4-S1 discs, significant differences in the average of peak anterior–posterior and medio-lateral shear loads were also found between the fast and both slow/normal walking speed conditions. Significant differences (p <  0.007) in the average of peak muscle forces were generally found between the fast and both slow/normal walking speed conditions.

Conclusions

This study presents a normative, subject-specific database of lumbar loading and muscle forces during walking at multiple speeds. These data provide a useful reference for future research in spinal biomechanics and musculoskeletal modeling. Furthermore, the database may serve as a baseline for assessing altered gait patterns and spinal loads in individuals with spinal disorders, supporting future clinical applications.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13018-025-06408-5.

Keywords: Gait, Walking speed, Spinal loads, Trunk muscle forces, Musculoskeletal modeling, Subject-specific database

Introduction

Walking, an important daily activity, is recommended for the rehabilitation of lower back pain (LBP) patients and those undergoing spinal surgeries [1, 2]. Moreover, gait (walking) analysis helps clinicians diagnose conditions, investigate treatment efficacy, and evaluate the effects of physiotherapy and surgical interventions [3–5]. Both in vivo and modeling investigations have indicated increases in spinal loads during walking activity compared to upright standing posture. For instance, in vivo measurements using telemeterized vertebral body replacements indicate that the resultant load on these implants for walking is 171% of that for standing [6]. This is further corroborated by intradiscal pressure measurement [7] and musculoskeletal modeling [8] investigations. In addition, previous measurement and modeling studies have revealed that both lumbar spine loads and trunk muscle electromyography (EMG) activities increase with walking speed [8–12]. A previous study employed a spine finite element model to investigate biomechanical effects of lower limb amputation. This study also investigated spinal loads in healthy individuals and reported that increased walking speed correlates with elevated L5-S1 disc loads [13]. While these studies have contributed valuable insights, none have provided a time-dependent, subject-specific database of spinal loads and trunk muscle forces across all lumbar spine discs during walking at different speeds. Moreover, to our knowledge, no open-access resource currently exists that offers this level of anatomical and temporal detail in healthy individuals. Therefore, investigating trunk muscle forces and spinal loads in healthy individuals at varying gait speeds can aid in the design and evaluation of rehabilitation and diagnosis programs.

Furthermore, proper design of patient-specific surgical plans and instruments (e.g., intervertebral cages) using finite element modeling simulations requires accurate estimations of spinal loads during walking [6]. However, prior studies have used general non-individualized and simplistic loadings (usually a compressive follower load and a moment) in finite element models of the spine to explore the effectiveness of fixation systems and surgical techniques [14–24]. Such general simplistic loadings are known to differ from the complex in vivo loadings that the spine experiences during physical activities and thus may result in erroneous findings [25]. A subject-specific database for force in trunk muscles and loads on the lumbar spine at varying walking speeds can, hence, help finite element modeling simulations consider more realistic loading conditions for the design of patient-specific surgical plans and instruments. For example, incorporating subject-specific loading data from musculoskeletal simulations into finite element (FE) spine models can aid surgeons in selecting optimal pedicle screw diameters to reduce the risk of post-operative failure, or choosing appropriate rod stiffness or shape to achieve better fixation outcomes [14–16].

Three primary methods have been used to determine activities in trunk muscles and loads on the spinal discs during walking: in vivo measurements of trunk muscle activity [9, 11, 12, 26, 27], invasive measurements of spinal loads via telemeterized implants [6], pressure transducer insertion into the disc to determine the intradiscal pressure [7], and musculoskeletal modeling investigations [8, 28]. Among modeling investigations of walking, Banks et al. [29] investigated the effects of optimization algorithms on spinal load estimations by comparing EMG-informed models with static optimization. However, their study did not include walking at multiple speeds [29]. Callaghan et al. [11], investigated gait at three cadences in five individuals focusing only on L4-L5 disc forces and moments, and relied on surface EMG for selected muscles. While surface EMG is widely used, it is limited by signal cross-talk and inability to capture deep muscle activities. Needle EMG can access deep muscles but is invasive and not feasible for larger-scale or repeated measurements. Additionally, force estimations based on EMG require assumptions regarding EMG–force relationship, introducing further uncertainties. Despite these limitations, EMG-based studies, such as that of Callaghan et al. [11], have contributed valuable insights into spinal loading during walking [11]. Direct measurements of spinal loads, such as through needle insertion into intervertebral discs or implanted telemetry devices, are invasive, costly, and ethically unsuitable for use in healthy individuals. Moreover, many in vivo studies are constrained by small sample sizes, limiting the generalizability of their findings. While these approaches remain crucial for validating biomechanical models, musculoskeletal modeling offers a scalable, non-invasive alternative suitable for broader population studies. To date, no study, including those employing musculoskeletal models, has evaluated spinal intervertebral loads at various walking speeds across all lumbar spine levels. Thus, there remains a clear gap in the literature for a subject-specific database that provides detailed, speed-dependent estimates of spinal loading and trunk muscle forces.

The present investigation, therefore, aims to:

  1. Develop a database for lumbar spine loads (T12-S1) and trunk muscle forces during three different walking speeds (slow, normal, and fast) using detailed, validated, and subject-specific musculoskeletal models of ten healthy individuals, and

  2. Statistically compare musculoskeletal model predictions for peak force in trunk muscles and loads on the lumbar spine discs at the foregoing three walking speeds.

Such databases and comparisons are useful for designing effective rehabilitation strategies, diagnosing conditions, investigating treatment/physiotherapy efficacy, and properly designing patient-specific surgical plans and instruments. We hypothesize that the predicted forces in trunk muscles and loads on the lumbar spine discs increase with walking speed.

Methods

Subjects

Ten healthy male participants (age: 25.9  ±  1.4 years, body mass: 70.4 ±  7.7 kg, height: 179.8 ±  6.4 cm, and BMI: 21.8 ±  1.9 kg/m2), all of whom had not experienced any lower back disorders in the preceding six months, were recruited for this study (Table 1). Biometric information, including sex, body mass, body height, age, and body segment dimensions were collected. Data collection was carried out under the supervision of an experienced physical therapist. Approval from the institutional ethics committee (ID: IR.IUMS.REC.1401.740) was obtained, along with informed consent from the participants involved in the study. Informed consent was secured for the publication of the information and/or image(s) in an online open-access format.

Table 1.

Demography of the participants

Participant Age
(year)		 Height
(cm)		 Weight
(kg)		 Body mass index
(kg/m2)
1 26 174 63.5 22.0
2 26 178 75.0 23.7
3 27 184 65.0 19.2
4 27 173 64.5 21.6
5 23 176 66.0 21.3
6 24 183 62.0 18.5
7 25 192 80.5 21.8
8 26 185 80.0 23.4
9 27 183 82.6 24.7
10 28 170 65.0 22.5
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Data collection

Forty-two reflective markers were affixed to the participants’ skin in accordance with the Plug-in Gait Model (Fig. 1). Motion data were collected during walking tasks utilizing a ten-camera 120 Hz Vicon movement system (Vicon, Ltd., Oxford, UK). In addition, two adjacent Kistler 1200 Hz force-plates (Kistler Instrument AG, Switzerland) measured ground reaction forces (GRFs) and moments as required for subsequent musculoskeletal modeling simulations. To promote natural gait patterns and minimize targeting behavior from the participants, the force plates were covered.

Fig. 1.

Fig. 1

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Skin marker placements for a representative participant

Walking procedures

Participants were asked to walk barefoot at their preferred speed along a 4-m straight path with natural arm swing. The force plates were placed at the midpoint of the path to ensure accurate data acquisition during steady-state walking. For each participant, six trials were recorded at three different speeds in the following order: walking at a normal and comfortable speed, simulating their usual daily walking pattern (normal walking), walking slower than the normal speed (slow walking), and walking safely as fast as possible without running (fast walking) (Table 2). Gait trials were considered acceptable only when both feet fully contacted the covered force plates during the gait cycle, ensuring valid GRF data for subsequent modeling simulations.

Table 2.

Subject-specific and average ±  standard deviation of the three different walking speeds (slow, normal, and fast)

Participant Average walking speed (m/s)
Slow walking Normal walking Fast walking
1 0.73 0.96 1.45
2 0.63 0.92 1.31
3 0.49 0.82 1.14
4 0.72 1.01 1.45
5 0.82 1.01 1.37
6 0.62 0.83 1.28
7 0.60 0.78 1.02
8 0.71 0.88 1.47
9 0.66 0.93 1.31
10 0.68 0.80 1.24
Average ± Standard Deviation 0.67 ± 0.09 0.89 ± 0.09 1.30 ± 0.14
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Data processing

All the captured data were synchronized and preprocessed through Vicon Nexus software (Vicon United Kingdom, Oxford, UK). This process included reconstructing and labeling of the markers, followed by filtering the trajectory data. A 4th order, low-pass Butterworth filter with a cut-off frequency of 10 Hz was applied to force-plate data. The trajectories of optical markers were smoothed via a 12th order Woltring filter operating in Mean Square Error mode, while the reconstruction of occluded or missing markers was achieved through spline filling.

Musculoskeletal modeling

All acceptable trials for each participant and speed were considered for these musculoskeletal modeling simulations. To estimate trunk muscle forces and spinal loads during walking at the three different walking speeds, we employed the Full-Body Lumbar Spine Model [30] in OpenSim [31] (Fig. 2). The OpenSim Scaling Tool was used for subject-specific modeling, i.e., to adjust segmental lengths based on the marker data and scale segmental masses according to total body mass. Such a geometric scaling for each participant, included adjustments to muscle cross-sectional areas, muscle lengths, and their attachments that in turn scaled their moment arms and lines of action [32, 33]. Simulations were conducted using kinematic data derived from the OpenSim Inverse Kinematics Tool, applied to motion capture marker trajectories. Muscle forces were then estimated using the Static Optimization Tool, which minimizes the sum of squared muscle activations. Muscle tension strength was assumed to be 0.6 MPa for all muscles in all subjects, consistent with prior literature [34]. Finally, spinal loads, including intervertebral joint forces and moments, were estimated using the Joint Reaction Analysis Tool in OpenSim (Fig. 3).

Fig. 2.

Fig. 2

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Full-body lumbar spine (FBLS) model used in OpenSim for subject-specific modeling

Fig. 3.

Fig. 3

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Workflow for creating subject-specific musculoskeletal models

Model validation

In this study, a pre-validated and widely-used lumbar spine model [30, 35, 36] was employed to compute loads on the lumbar spine discs and force in trunk muscles. The changes in average peak lumbar spine loads on the T12-L1 through L5-S1 discs, were nevertheless validated against values reported elsewhere [8] in which spinal loads were analyzed at level walking using a combination of experimental and modeling approaches. The average peak compression forces at the L4-L5 disc were validated [8] against the intradiscal pressure values measured in vivo [7]. Moreover, the predicted patterns of force in global and local trunk muscles have been previously validated against EMG data [11, 12, 27].

Outputs and statistical analysis

The time-dependent subject-specific force in trunk muscles (LTPT: longissimus thoracis pars thoracic, LTPL: longissimus thoracis pars lumborum, ILPT: iliocostalis lumborum pars thoracic, ILPL: iliocostalis lumborum pars lumborum, EO: external oblique, IO: internal oblique, MF: multifidus and PS: psoas) and the spinal loads (anterior–posterior shear, mediolateral shear and compression) at all lumbar discs (T12-L1 through L5-S1) for slow, normal, and fast walking speeds were reported in the Supplementary Materials as an Excel file (database). All reported muscle forces and spinal loads were normalized to the participant’s total body weight (%BW). Model predictions of peak compression and shear loads along with the combined left and right muscle forces for the slow, normal, and fast walking conditions were normalized to the participant’s total body weight (%BW). For different walking speeds, the left and right muscle forces were first summed, and then the average, median, and standard deviation of peak total muscle forces, as well as spinal loads (for all participants and trials) as a percentage of body weight (%BW) were reported here. The normality of the data (spinal loads and muscle forces) was assessed using the Kolmogorov‒Smirnov test. To determine whether average peak values differed significantly across conditions, one-way ANOVAs were conducted. When significant, we tested the three planned pairwise speed comparisons (slow–normal, slow–fast, normal–fast) and applied a Bonferroni adjustment to control the family-wise error rate. The significance level was set at p <  0.05 after Bonferroni correction.

Results

Prior to conducting musculoskeletal simulations, all trials were visually inspected. A total of 53 out of 180 trials were excluded due to incomplete GRF data or missing motion capture markers. As a result, 127 valid modeling simulations were conducted in OpenSim for 10 participants walking at three different speeds. Our model predicted peak compressive loads of approximately 638 N (92.9% BW) at the L4–L5 disc during normaspeed walking for participants with an average body mass of 70.4 kg. This corresponded to an intradiscal pressure of ~ 0.54 MPa [37], assuming a disc cross-sectional area of 1800 mm2 [38]. This estimate fell within the measured intradiscal pressure range (0.53–0.65 MPa) reported by Wilke et al. 1999 for a 70 kg individual during walking [7]. The normality of the data was confirmed (p > 0.05). The averages of the three investigated walking speeds (0.67 ±  0.09 m/s for slow, 0.89 ± 0.09 m/s for normal, and 1.3 ±  0.14 m/s for fast) were significantly different (p <  0.001) (Table 2). For all walking speeds, the coefficient of variation, calculated as the standard deviation divided by the average, remained below 15%.

Database

In agreement with previous studies [6, 8], we found that peak force in trunk muscles and loads on the lumbar spine discs occurred in the stance phase of each foot. For this reason, the normalized spinal loads and trunk muscle forces relative to participant’s body weight (%BW) throughout only the stance phase of each foot during the gait cycle (in percentage of the stance phase) were reported in the Supplementary Materials (Excel file) for all participants and trials. Moreover, subject-specific normalized peak trunk muscle forces and spinal loads (%BW) across all lumbar spine discs and walking speeds were reported in the Supplementary Materials (Excel file). The normalized force in trunk muscle and loads on the lumbar spine discs (%BW) were depicted for a representative participant during the gait cycle (Figs. 4, 5). The positive directions for spinal loads are defined as follows: compression: upward, anterior–posterior shear force: anterior, and mediolateral shear force: toward right lateral.

Fig. 4.

Fig. 4

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Time series of spinal loads as a percentage of body weight (%BW) for T12-S1 discs during one gait cycle at different walking speeds for a representative participant (participant 5, weight: 66 kg, height: 176 cm)

Fig. 5.

Fig. 5

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Time series of muscle forces as percentage of body weight (%BW) for longissimus thoracis pars thoracic (LTPT), longissimus thoracis pars lumborum (LTPL), iliocostalis lumborum pars thoracic (ILPT), iliocostalis lumborum pars lumborum (ILPL), external oblique (EO), internal oblique (IO), multifidus (MF) and psoas (PS) during one gait cycle at different walking speeds for a representative participant (participant 5, weight: 66 kg, height: 176 cm)

Peak spinal loads

Across all lumbar discs, the average peak compression loads were significantly higher (p <  0.001) in the fast-walking condition compared to both slow and normal speed conditions (Fig. 6). With the exception of the L5-S1 and L4-L5 discs, statistically significant differences in the average of peak anterior–posterior and mediolateral shear loads were also found between the fast and both slow and normal walking speed conditions. No significant differences were found in the average of peak spinal loads between the normal and slow walking speed conditions (p > 0.05 for all discs) (Figs. 6, 7).

Fig. 6.

Fig. 6

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Average (indicated by the cross symbol), median (indicated by the horizontal line inside each box), and standard deviation (indicated by the additional error bars) of peak spinal loads as a percentage of body weight (%BW) for different walking speeds. Significant differences between different walking speed conditions are shown by *

Fig. 7.

Fig. 7

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Radar plots of the average peak T12–S1 spinal loads as a percentage of body weight (%BW) at different walking speeds

Peak trunk muscle forces

With the exception of the MF and IO muscles, significant differences (p <  0.007) in the average of peak muscle forces were found between the fast and both slow and normal walking speed conditions (Figs. 8, 9).

Fig. 8.

Fig. 8

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Average, median, and standard deviation of peak muscle forces as a percentage of body weight (%BW) for longissimus thoracis pars thoracic (LTPT), longissimus thoracis pars lumborum (LTPL), iliocostalis lumborum pars thoracic (ILPT), iliocostalis lumborum pars lumborum (ILPL), external oblique (EO), internal oblique (IO), multifidus (MF) and psoas (PS) at different walking speeds

Fig. 9.

Fig. 9

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Average ±  standard deviation of peak muscle forces as a percentage of body weight (%BW) for longissimus thoracis pars thoracic (LTPT), longissimus thoracis pars lumborum (LTPL), iliocostalis lumborum pars thoracic (ILPT), iliocostalis lumborum pars lumborum (ILPL), external oblique (EO), internal oblique (IO), multifidus (MF) and psoas (PS) at different walking speeds

Discussion

A comprehensive subject-specific database for force in major trunk muscles and loads on the lumbar spine discs was developed at three different walking speeds and the effect of walking speeds on these parameters was investigated via musculoskeletal modeling simulations. For this, a total of 127 subject-specific musculoskeletal modeling simulations on ten healthy male participants were conducted in OpenSim software. Our findings are consistent with prior research indicating that spinal loads increase with walking speed. In particular, Alexander et al. [39] reported elevated L5-S1 loads in healthy individuals at faster walking speeds. That study also noted a nonlinear relationship between walking speed and musculoskeletal forces, where small increases in speed at lower levels had minimal effects, but faster speeds led to disproportionately higher loads. Furthermore, our results aligned with a previous study that investigated the effect of walking speed on spinal loads in healthy and lower-limb amputee populations, showing that fast walking elevates spinal loads [13]. In our study, transitioning from slow or normal to fast walking resulted in significant increases in average peak spinal compression and shear forces, as well as trunk muscle forces, with the exception of the MF and IO, partially supporting our initial hypothesis. The subject-specific data on trunk muscle forces and spinal loads (%BW) across the stance phase at each walking speed were provided in the Supplementary Materials. Therefore, the novelty of this study lies in developing a database that includes time-dependent subject-specific forces in all major trunk muscles and spinal loads at all lumbar spine discs (T12-L1 through L5-S1) during three different walking speeds; an aspect currently missing in the literature.

Analysis of results

Changes in spinal loads (compression, anterior–posterior and medio-lateral) during walking at different gait speeds showed a cyclic trend at all T12–S1 segments (Fig. 4). As walking speed increased from 0.67 m/s (slow) to 1.3 m/s (fast), the average of peak compression loads increased significantly (p  < 0.001) across all lumbar levels (Fig. 6) by ~ 25–30% (in %BW). Similarly, as walking speed increased from 0.89 m/s (normal) to 1.3 m/s (fast) the average of peak compression loads increased significantly (p < 0.001) across all lumbar levels by 22–30% (in %BW). Furthermore, the peak compression load always occurred immediately after contralateral toe off which was in agreement with previous experimental findings [6]. Changes in the average peak anterior–posterior and medio-lateral loads at T12 through S1 levels were, however, smaller; i.e., 8–19%BW and 7–10%BW, respectively. The average peak compression loads (in %BW) increased gradually from the T12-L1 disc to the L5-S1 disc (by 72–125%), while anterior–posterior and mediolateral peak load changes between different lumbar levels were relatively smaller, i.e., in the range of 8–20% (for anterior–posterior shear) and 6–10% (for mediolateral shear) (Figs. 6, 7).

Changes in the forces of all trunk muscles were cyclic and the maximal values generally occurred at toe-off (Fig. 5); a finding in agreement with previous in vivo EMG data [11, 12, 26]. The oblique abdominal muscle had two peak forces during the double support phases: the initial peak was observed right after the heel strike followed by a second peak at toe off, both consistent with previously reported EMG activity patterns for these muscles [12]. Our findings indicated that as walking speeds increased from slow to fast, the average of peak forces for global muscles significantly increased (p <  0.007) by 7%BW (LTPT), 6%BW (ILPT), and 6%BW (EO) while that of local muscles increased by 2%BW (LTPL) and 4%BW (ILPL) (Figs. 8, 9). Similarly, as walking speeds increased from normal to fast, the average of peak forces for global muscles significantly increased (p <  0.007) by 7%BW (LTPT), 6%BW (ILPT), and 4%BW (EO) while that of local muscles increased by 2%BW (LTPL) and 3%BW (ILPL).

Limitations

This study focused on young, normal-weight, male participants thus limiting the application of the provided database for female and overweight/obese individuals. The present findings cannot be directly generalized to older adults, females, or individuals with clinical conditions, as prior studies have reported substantial differences in gait parameters, trunk muscle activations, and spinal loading patterns across sex, age, and health status [40, 41]. For instance, a previous study found that individuals with chronic low back pain exhibited lumbar joint compression loads up to 30–40% higher than healthy controls during walking [28]. Further studies should aim to incorporate more diverse populations to improve the applicability of the present results and contribute to the development of a comprehensive database for clinical assessments and rehabilitation. Moreover, no EMG measurements were collected from trunk muscles to validate the muscle force predictions in this study. While the musculoskeletal model used is pre-validated and widely adopted, the exclusive reliance on static optimization introduces certain limitations, particularly in estimating individual muscle forces, which do not reflect subject-specific recruitment patterns [34]. Future studies should consider incorporating EMG-informed modeling approaches in conjunction with optimization techniques to improve the physiological fidelity of spinal load and muscle force predictions [42–44]. Furthermore, this study examined walking over a short distance and on a flat surface. In future studies, increasing the walkway length and incorporating additional tasks, such as walking on sloped surfaces or stairs, may provide more comprehensive insights. Although our database does not provide subject-specific muscle force trajectories, such data can be obtained from the existing literature [45]. Finally, while the forces exerted by the left and right muscles might be different, the present study focused on the average of forces generated by the left and right trunk muscles.

Conclusions

The developed database provides potentially useful information for designing effective rehabilitation strategies, diagnosing conditions, investigating treatment/physiotherapy efficacy, and properly designing patient-specific surgical plans and instruments. Patients recovering from lumbar fusion surgeries, primarily those experiencing LBP, are often advised to engage in walking as part of their rehabilitation programs; a recommendation that needs to be accomplished by assessing biomechanical factors to ensure the postoperative stability of the surgical fixation devices during walking at different speeds. While prior investigations have typically assumed constant lumbar spine loads during their modeling simulations, the present database provides patient-specific muscle forces and lumbar spine loads during different walking speeds thus facilitating the patient-specific computational modeling investigations. The findings indicated significant changes in lumbar spine loads as a function of the walking speed. Specifically, fast walking resulted in greater lumbar spine loads and trunk muscle forces compared to slow or normal walking. This underscores the importance of providing additional guidance to patients with LBP regarding safe and effective walking practices during rehabilitation. Such advices are crucial to prevent postoperative complications and to ensure the stability of surgical fixation systems.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary Material 1 (4.1MB, xlsx)

Acknowledgements

This work was supported by grants from Sharif University of Technology, Tehran, Iran. Assistance of Mr. M. Mohseni in data collections is greatly appreciated.

Abbreviations

FE

Finite element

LBP

Low back pain

EMG

Electromyography

GRF

Ground reaction force

SD

Standard deviation

BW

Body weight

FBLS

Full-body lumbar spine

LTPT

Longissimus thoracis pars lumborum

ILPT

Iliocostalis lumborum pars thoracic

ILPL

Iliocostalis lumborum pars lumborum

EO

External oblique

IO

Internal oblique

MF

Multifidus

PS

Psoas

Author contributions

NA, AR, and HN designed the study. AJ, AR, and HN performed the musculoskeletal modeling. AJ, AR, HN, and ME performed the data analysis. AJ, AR, HN and NA wrote the first draft of the manuscript. All the authors were involved in the interpretation of the results, manuscript editing, and approval of the final manuscript before submission. All the authors read and approved the final manuscript.

Funding

Sharif University of Technology.

Data availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

The study adhered to the tenets of the Declaration of Helsinki and participants completed a written consent form, approved by Iran University of Medical Sciences Research Ethics Board (ID: IR.IUMS.REC.1401.740).

Consent for publication

Informed consent was obtained to publish the information/image(s) in an online open-access publication.

Competing interests

The authors declare no conflict of interest.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Alireza Rouyin and Hamed Nazemi contributed equally to this work.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary Material 1 (4.1MB, xlsx)

Data Availability Statement

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

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