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Developing a Biomechanical Simulation Model and Novel Prototypic Design for the Mitigation of Lumbar Spinal Disc Stress in Student Backpacks

Meryl Liu
Spruce Creek High School
Port Orange, Florida, 32128
meryl.liu@gmail.com

Abstract. Many students are having to carry excessive amounts of weight in their backpacks in primary and secondary schooling. Thousands of children are treated for backpack-related injuries every year, and continuous applied strain has been linked in many studies to chronic and idiopathic lower back pain. The purpose of this project was to develop and simulate a new potential backpack design utilizing a theoretical biomechanical model in order to analyze the efficiency of applying exterior support to alleviate strain on lumbar spinal discs L4/L5 and L5/S1. Using anthropometric data collected from CDC statistics of 16-year-old male and female high school students, a simulation was conducted based on the 10th, 50th, and 90th percentiles, using the 3DSSPP simulation software program, configured with a static biomechanical model created for simulating backpack wear. The compression and shear forces were compared between the novel new design and current backpack models, with results demonstrating a significant reduction of forces (around 44-67% and 25-38% for compression and shear forces, respectively). The prototype was further evaluated by recruiting 12 high school students, and it was found that the new design was able to significantly redistribute and reduce compression and shear forces on the lumbar spine, even at very heavy carriage loads. It can be concluded that the design and engineering elements of the novel prototypic backpack design effectively contributed to a preventative measure of backpack-related chronic injuries and intravertebral disc herniation among high school students. Future research directions were given to improve the applicability of the new design.

Keywords: Biomechanics, Ergonomics, 3DSSPP.

1 Introduction

1.1 Background Information

Increased backpack carriage loads throughout childhood and adolescence have been generally attributed through research to the chronic degeneration of the intervertebral lumbar spinal discs due to the compression of the vertebrae and the stress on the spine, with disc height decreasing over time [1, 2]. As a disc progresses into prolapse and extrusion due to compression, the nucleus pulposus breaks through the anulus fibrosus, causing the final stage of disc herniation. Moreover, there are many parts of the body affected, stemming from long-term wear of high carriage loads, including the appendicular joints, which can sustain 7 pounds of weight for each pound of a load. Additionally, potential nerve damage can occur, with increased reports of numbing appendages resulting from an improper usage of the student’s backpack [3-7]. The cervical area is strained, and the posterior shoulders can become rounded as the four natural curvatures of the body are disrupted, thus affecting the balance and standing weight distribution of the body as well. Therefore, it is imperative that a proper backpack wearing position is established and enforced [8-10].

Chronic lower back injuries are one of the most common health issues present for American people today. Eighty percent of adults in the United States suffer from some degree of lower back pain (LBP) during their lives, according to the United States National Institute of Health [11]. It was reported that back injuries were the cause of 10- 30% of medical claims in the United States and Europe, with the rate of back injuries increasing from previous years. Yet, despite heightened awareness of these statistics and taking action to protect the adult workforce, the Centers for Disease Control and Prevention (CDC) reports that back injuries still account for up to 30% of medical compensations cases every year. Additionally, the American Chiropractic Association estimates that a staggering 3.1 million people are suffering from lower back pain in the United States and that one half of the entire American working community has complained of back pain related to their occupation. [12] The total cost of LBP-related injuries could reach more than $90 billion per year in the U.S [13] . Many of such backpain problems find their root cause in early age and adolescent habits, as studies showed that more than up to 70% of the teens can have a lifetime prevalence of lower back pain, without treatment or preventive intervention/correction [14].

There are many factors that lead to lower back pain, including physical, bodily conditions and health status, sports, and daily, sustained activities such as lifting weights and carrying loads. Among these aforementioned factors, carrying heavy backpacks are one of the most prevalent factors [15], as it exerts a constant load that must be counteracted by the spine, and together with repetitive, dynamic body movement and improper body posture such as excessive slouching and lordosis, it can easily lead to long-term strain, that develops to LBP and disc herniation at an older age. Nowadays, high school students often are found to be carrying more objects and weight in their backpacks, partially due to the increasing level of study and activities involved in the everyday school, as well as disregard for carrying weights exceeding a tolerable threshold. In conjunction, back pain and shoulder/neck discomfort has become more a common problem reported in high school students as well. School backpack have been found to be directly associated with back pain, especially the strain and forces exerted in the L4/L5 and L5/S1 lumbar discs of the spine: the lumbar and sacral intersection. Exposed to such heavy stress for a sustained period, this can lead to long term -- even permanent -- back problems and injuries in later adult life. Children under 18 carrying a heavy backpack have higher risks of musculoskeletal disorders, as they are still in a growing developmental phase; their body is more prone to the injuries of the heavy carriage in the back. The American Chiropractic Association recommends a backpack should not weigh more than 10 percent of a child’s body weight; however [16], most high school students often carry backpacks exceeding recommended load.

Despite general safety guidelines having been published [17], the studies related to adolescence backpack issues are still very limited, partially due to the complexity and multifactorial nature of the lower back problem and large degree of variability in the human anthropometry and shapes/weights of the different backpack. Heavy backpacks mainly impact the human body by posing external forces and torque on the torso, interacting with internal factors and individual characteristics, thus generating greater internal loads on the individual, altering posture and even gaits to become unnatural. An accurate simulation of LBP should account for both external load and internal loads effects, including the individual human characteristics, spinal structure, spine load model, torso kinematics such as body posture, along with the consideration of human body anthropometric data (stature, body mass distribution, segmental dimensions, age, biological sex etc.)[18].

On the other hand, directly and empirically measuring the pressure exerted on the lower back, especially on the fibrocartilaginous lumbar spinal discs, is nearly impossible. Such physical measures could be surgically invasive, unfeasible, and pose risks and danger to the participants. As an alternative, biomechanical models and simulations provide an accurate, safe and effective way to investigate the impact of various external exertions on the human musculoskeletal system. Biomechanical simulation integrates findings and knowledge from the physical and engineering sciences with the principles of human physiology, biology and behavioral sciences, in order to suggest protection from injuries and disorders from these loads [19]. Biomechanical models have been previously utilized in modeling and predicting lower back pain [18].

As a unique population group, the understanding of impact wearing heavy backpacks on adolescents are still limited, and furthermore, most analyses are focused on the evaluation of current available commercial backpacks. There are few studies that take a further step and utilize biomechanical modeling to simulate the effectivity of a proposed, novel design to actively help mitigate forces exerted on the spinal discs and, thus, chronic LBP. In order to prevent LBP from an early age, a comprehensive analysis based on biomechanical modeling is in demand, and moreover, improvement of current backpack designs should be based on the results derived from these models.

2 Method

2.1 Problem Description

The objective of this study is to utilize a Biomechanical simulation model to investigate the stress/strain on the vertebral column, specifically focusing on lumbar spinal discs L4-L5 and L5-S1, and the musculoskeletal systems caused by the weight of student backpacks and varying standing postures, to compare and analyze how exterior vertebral back support may alleviate possible damage and excessive stress in order to propose and model a conceptual external structure applied to current function student backpacks that provides sufficient support, reinforces a healthy, normal standing posture, and reduces and prevents possible musculoskeletal disorders, injuries to the spine, deformations, etc.

It is hypothesized that if stress on the lumbar spinal discs from heavy backpack wear disproportionate to human body weight is analyzed mathematically, along with external structures that possibly alleviate the amount of strain, then the proposed structure resulting from the elements derived from previous analyses, which provides additional back support, will be able to sustain a healthy standing posture and substantially minimize the amount of strain on the lumbar spinal discs, which would effectively prevent herniation, bulging, compression, and injury inflicted on the spinal area and nearby tissues from heavy backpacks, as the conceptual model would enforce a straight, perpendicular alignment, not leaning forward on the torso and pushes the waist forward to maintain optimal posture. Additionally, a pivot operated by hand from pushing down on handles extending to the front in order to reduce the amount of weight dragging down on the back may also mitigate the amount of stress caused by the heavy backpack compressing down on the spine.

Therefore, the goal of this project would ultimately be to develop and test a theoretical biomechanical model to simulate the forces operating during backpack wear to compare the efficiency of a novel proposed prototypic design designed to alleviate spinal forces to previous existing conventional student backpacks (first phase). Meeting the design criteria of efficiency would require a substantial reduction in the compression and shear forces acting upon the L4-L5 and L5-S1 lumbar spinal discs. Then, a proof-of-concept validation test would be conducted on human subjects with the physically constructed prototype compared against conventional backpack designs to validate the engineering and design principles under dynamic and variable conditions.

2.2 Biomechanical Model

In order to begin creating a model that to a degree of accuracy, represents a complete understanding of the standing human body and carriage load as a system, the model will be considered in the sagittal plane of the human body (an anatomical boundary that divides the body into symmetric left and right components) as a reference point to study the forces involved.

At the backpack level Fig. 1 illustrates the biomechanical model at the backpack level.

Fig. 1. Biomechanical model developed for simulation at the backpack level. h1: length of the backpack, h2: depth of the backpack; w: weight of the backpack; h3: distance from the top of the backpack to the shoulder; T1, T2: forces on the backpack straps; TB: forces acting on the touching point of the backpack to torso; θ1, θ2, α: angles of the straps and backpack to the reference axis.

According to the Newton’s law, at the backpack level, the condition of equilibrium requires

(1)

So we have

(2)

And

(3)

Given the value of backpack weight and dimensions, we can derive the value of the forces on shoulders.

At the shoulder level Fig. 2 illustrates the biomechanical model at the shoulder level.

Fig. 2. Biomechanical model at the shoulder level. 𝑇S: counter forces of the shoulders on the backpack straps; 𝑇SY, 𝑇SZ: forces components on the y and z axis; 𝜃1, 𝜃2: angles of the straps to the reference axis.

At the shoulder level, according to the Newton’s laws,

(4)

At the lower back level Fig. 3 illustrates the biomechanical model at the backpack level

Fig. 3. Biomechanical model at the lower back L5/S1level. 𝐹m: muscle forces on the lower back; 𝐹c: compression force; 𝐹s: sheer force; 𝑏, ℎ: distance of the center of gravity and external forces to the lower back; beta: angle of the shear forces to the horizontal axis; 𝐸: distance of muscle force to the spine.

(5)

Or

(6)

The forces acting parallel to the disc compression forces can be described as

(7)

Or

(8)

The reactive shear force across the L5/S1 disc can be solved by the similar equilibrium conditions.

(9)

Or

(10)

2.3 Biomechanical Simulation

With data on commercial backpack dimensions and anthropometrics (including weight and dimensions and angles of the torso), we can easily derive the physical forces acting on the shoulders. However, for the L4/L5 and L5/S1 lumbar spinal discs, the measures of compression and shear forces can only be estimated by considering the external forces on the shoulder based on the static model outlined above, and human anthropometric data. This data includes body stature and weight. In this case, a static strength simulation software, 3D SSPP was used to predict the compression force and shear forces operating at the L4/L5 and L5/S1 disc level. Developed by the Center for Ergonomics at the University of Michigan, 3D SSPP is aimed at investigating and analyze human material handling tasks. It utilizes principles and models in Biomechanics to derive the static strength exerted for tasks such as lifting, pushing and carrying loads (Umich.edu). Fig. 4 shows a screenshot of the 3D SSPP software.

Fig. 4. Screenshot of 3D SSPP.

2.4 Data Collection

Human anthropometric data was retrieved from the Center of Disease Control and Prevention, more specifically, the 10th, 50th (mean) and 90th percentile value on body height and body weight for U.S female and male at the age of 16 (Fig. 5). (Fryer, Ogden & Flegal, 2016). The student backpack dimensions were collected from online retail. Using equations (1) – (4), the external forces on the shoulder level and lower back were calculated, by using three levels of backpack weight (7 kg, 10.5 kg and 14 kg, respectively, simulating the backpack weight of 5%, 10% and 15% of the average male body weight).

Fig. 5 Illustration of Normal Distribution percentile value

2.5 New Design Prototype

Based on the analysis of posture and main areas affected from backpack carriage load, a conceptual model of a new backpack design was proposed, with a mechanism providing optimum back support and enforcing proper posture when carrying a heavy backpack (sketches, etc.). Three factors were included in the new design: the strap design, the lumbar support pad and manually operated pivot first-class lever support at the waist to redistribute and mitigate partial carriage weight. A new posture and weight were used to derive forces on shoulders and lower back utilizing the equilibrium conditions, as seen in Fig. 6.

Fig. 6 Illustration of Prototypic Design

Therefore, the proposed design would ultimately lead to a substantial reduction in the compression and shear forces acting upon the L4/L5 and L5-S1 lumbar spinal discs. The proposed backpack design is simulated using the 3DSSPP program to compare the forces between typical conventional backpack use in students without enforcement of proper posture and with the proposed design. The above comparison was repeated for female and male anthropometric data, at 10th, 50th and 90th percentile values and for 7kg, 10.5kg and 14kg backpack weight, respectively.

A physical prototype was then developed. PVC Pipes was used to cut/glued into the shape of a lever with pivot (fulcrum) attached to the sides of the waist belt and extend at a 45-degree angle to support the bottom of the backpack, which will be padded with a wooden board. Functionally this creates a 1st class lever with an ideal mechanical advantage greater than one that when manually pushed will lift the load upwards (bulk of the backpack). The curvature of the spine was then measured in order to construct an appropriately shaped cushion on the back of the backpack that when attached aligns with the student body and encourages posture correction/maintenance. The new backpack prototype is illustrated in Fig 7.

Fig 7. Physical Backpack prototype

2.6 Phase 2: Proof-of-Concept Prototype Analysis

A comparative analysis was conducted on the new backpack prototype against a conventional similar backpack. Twelve high school students (with 50% female and 50% male based on biological sex) were recruited to participate in this study. A 32 by 32 grid pressure pad by Tactilus™ was placed on the participant’s shoulder in order to measure the posterior shoulder pressure induced by the backpack. Participants’ anthropometric data (including body height and weight) were also collected. 3DSSPP was used to estimate the direct compression and shear forces being exerted on the L4/L5 and L5/S1 lumbar spinal discs, by using the anthropometric data and should pressure data. A within subject 2x2 design was applied with two independent variables, backpack type (conventional vs. prototype) and carrying load (15 pounds vs. 30 pounds). In order to eliminate any possible order effect, a Latin Square experimentation method was utilized to counterbalance the orders. This study was reviewed and approved by IRB committee and every participant signed an informed consent form before beginning the experiment. Fig 8. shows the Tactilus™ Pressure Map. The dependent variables are the exterior forces on the shoulder and the compression and shear forces at the L5/S1 disc. ANOVA was used to test the effects of the independent variables, with a significance level set at 5%.

Fig 8. Tactilus™ Pressure Map.

3 Results

3.1 Data

Anthropometry data and backpack data. The following Table 1 shows the Anthropometric from CDC.

The backpack data are determined as follows
Length = 18 inches (ℎ1)
Width = 11 inches
Depth = 8 inches (ℎ2)
Shoulder distance to backpack = 3 inches (ℎ3)

3.2 Simulation results

Based on the backpack weight of 7kg, 10.5kg and 14kg, the lower back simulation results are summarized in Table 2 and 3, for female and male, respectively.

To further summarize the results, the main differences between female and male, between the current design and proposed design are illustrated in Table 4 and Table 5.

Results demonstrated that with the new design (reduced load by the waist/hand lever support) and improved body posture (curved lumbar support and new strap design), the forces of both L4/L5 and L5/S1 discs will be significantly reduced, as shown in Table 3. This implies that the new design will help to relieve the pressure forces at the lower back for adolescent populations of varying anthropometric profiles, thus preventing the lower back from injury as a result of carrying a heavy backpack load.

3.3 Prototype Analysis Results

To further confirm the results from the conceptual Biomechanical model described above, a physical prototype was constructed, and twelve participants were recruited to test the new prototype compared to existing conventional backpacks. Fig 9 illustrates the screenshot for one of the participants.

Fig 9. Screenshot of Tactilus posterior shoulder pressure map data

Table 5 shows the descriptive statistics for both factors.

A three-way ANOVA found the forces exterted on the posterier shoulders from the new prototype were significantly lower than the conventional backback, with p-value < .01; the weight of the carrying load also was found significant with p-value <.01, as well as the interaction between the variables backpack type and weight (p-value < .01).

For example to demonstrate the differences between prototype and conventional backapcks on the L5/S1 spinal disc, the effects of the individual factors (backpack type and carrying loads) are both found significant for both L5/S1 compression force and L5/S1 shear forces. The interaction effect, however, were not found significant for both cases. The detail results are shown in Table 6 (compression force) and Table 7 (shear force). Shear and compression forces at the spinal level were calculated by using models 1-4 configured with posterior shoulder data collected from human participants, as parameters for the 3DSSPP biomechanical simulation model once more.

Overall, the results demonstrate that the prototype, when assessed on 12 human participants, significantly reduced forces (lbs) acting upon the L5/S1 vertebral discs, with an 11.66% decrease in compression and 10.84% decrease in shear forces on the L5/S1 vertebral disc.

4 Discussion and Conclusions

Students are carrying heavy backpacks that exceed the recommended carriage limit; long term exposure to heavy loads leading to discomfort at the lower back level, especially back pain and injury in the L4/L5 and L5/S1 disc in the vertebrae. This lower back pain largely is due to the unnatural posture caused by the load and unbalanced weight distribution of the backpack on the torso. A new design of student school backpacks was proposed based on the principles of human biomechanics, more specifically to use proper design of straps and lumbar support to reinforce a more natural standing posture and alleviation, including distributing external forces on the shoulder and lower back by using a pivot lever at the waist level. A theoretical biomechanics model was developed and a simulation study was conducted based on the 10th, 50th and 90th percentile high school 16-year old student anthropometric data in the 3DSSPP program. The compression force and shear force were compared between the new designed back pack and current backpack model with varying weights, with results showing that with the reinforced natural posture, the reduction of the forces on the L4/L5 and L5/S1 are significant (with around 44%-67% for the compression force and about 25%-38% for the shear force, respectively), thus helping to prevent discomfort and back pain, even at the very heavy carriage level. The design was able to meet the goals and criteria originally established in that it was able to decrease significantly the strain on the lumbar vertebrae and discs, ultimately aiding in the prevention of backpack-related injuries.

The study utilized a theoretical biomechanics model to assess the effectiveness of the new design. In order to simplify the model, it was assumed that the center of gravity of the backpack was at the center of the backpack, although this could change with different sizes of the backpack and different load distribution; additionally, the friction and materials of the backpack were not considered, which could have possibly correlated with an effect on the comfort of carrying the backpack.

This innovative design consisted of external structures intended to provide back support to reduce spinal and muscular stress. 12 voluntary participants were tested during wear while wearing a Tactilus™ pressure mapping system on the shoulders to measure PSI on the shoulders. The results show a significant difference between the prototype and control, with mean percent decreases by 11.66% and 10.84% in the compression and shear forces, respectively. An important trend observed in the data between the control and prototype is that testing at the 30lb weight displays a greater difference in the capability of the prototype to displace more weight; this is consistent with design principles at heavier loads. Significant statistical differences in the forces on the shoulder and spinal discs, as demonstrated by p-values <.05 in the dependent variables, reaffirm the design’s intention. Thus, it can be concluded that the prototypic backpack design and the proposed mechanisms and structures effectively play a role in contributing to a preventative measure of backpack-related chronic injuries among high school students, even at very high carriage loads. The results imply,

  • The manual redistribution of weight by the user as a self-serving model is capable of effectively translating into sustained vertebral back support at certain thresholds of potentially health-endangering carriage load without loss of efficiency nor damage to the model, thus supporting key engineering goals.
  • Additionally, the prototype assisted in maintaining the natural curvature of the lumbar lordosis, a component of stress resistance.
  • A prolonged application of the prototype may greatly alleviate the effects of longterm lumbar spinal compression enacted on a day-to-day basis, though a longterm study is needed to analyze potentially unexpected trends.

Future directions of study would also include the application of tested design elements to other fields of interest, such as the military or exercise/recreational activities. A more streamlined, uniform prototype that advances from its rudimentary basis in terms of material consideration, cost-effectivity and ergonomic applications of proposed prototypic structures that were tested on the backpack design, should be developed. Additionally, limited usage of both arms is a possible limitation and implementing motion and external structures is an important consideration for further development of the model. Varying anthropometric profiles in students, for example, lead to variability in the placement of the pressure mapping system and the fit of the prototype. Moreover, this study could utilize a greater sample size to minimize bias

According to the U.S. Consumer Product Safety Commission, at least 14,000 children are treated for backpack-related injuries every year. Quite often, students’ backpacks are too heavy in relationship to their own body weight, as the American Academy of Orthopedic Surgeons recommends that a backpack should be no more than 10-15 percent of a student’s bodyweight, while many children are carrying backpacks as heavy as forty, fifty, and sixty pounds due to the amount of textbooks and classwork required in school every day. Furthermore, many students develop consistent, poor habits, wearing backpacks incorrectly on one shoulder or hanging far too low, or having a poor, hunched posture, therefore increasing the compression on the spine and increasing the risk for injury. This research and investigation is important scientifically in that it analyzes and tests a possible conceptual way to provide back support on a conventional backpack that efficiently reduces strain and reinforces a healthy posture, which is crucial to students, especially in middle and high school as coursework becomes more demanding, tiring, and rigorous. Many will suffer from chronic back problems and pain in the future and irreversible damage to the spine, surrounding muscles, ligaments, and tissues stemming from a constant compression from a heavy backpack are a key factor of many of the back problems resulting later on in elderly life as well. If the design of the model can be put to use and commercialized in the market, it can considerably resolve the preventable health issues of the youth today.

References

  1. Negrini, S and Carabalona, R.: Backpacks on! Schoolchildren's perceptions of load, associations with back pain and factors determining the load. Spine 27 (2): 197-195 (2002)
  2. Sheir-Neiss, GI, Kruse, R.W., Rahman, T., Jacobson, L. P., Peili, J. A: The association of backpack use and back pain in adolescents. Spine 28(9): 922-30 (2003).
  3. Rai, A: Back Problems Due To Heavy Backpacks in School Children." IOSR Journal of Humanities and Social Science 10.6, 22-26. (2013).
  4. Sayler, M. H., Shamie. A., N.:The Encyclopedia of the Back and Spine Systems and Disorders, 1st edition, Facts On File, (2007).
  5. Skoffer, B.: Lower back pain in 15- to 16-year old children in relation to school furniture and carrying of the school bag. Spine 32(24): 713-717, (2007).
  6. Udesky, L.: Back pain in Children and Teens, https://consumer.healthday.com/encyclopedia/ back-care-6/backache-news-53/back-pain-in-children-and-teens-645950.html, last accessed 2020/03/30.
  7. Walicka-Currys, K., Skalska-Izdebska, R., Rachwa, M., Truszczynska, A.: Influence of the Weight of a School Backpack on Spinal Curvature in the Sagittal Plane of Seven-Year-Old Children. BioMed Research International 2015, 1-6. (2015).
  8. Viry, P, Creveuil C, Marcelli,C.: Nonspecific back pain in children. A search for associated factors in 14-year-old schoolchildren, Rev Rhum Engl Ed, 66(79):381-8, (1999).
  9. American Friends of Tel Aviv University: Heavy Backpacks May Damage Nerves, Muscles and Skeleton, Study Suggests. ScienceDaily. ScienceDaily, 21 Feb. 2013. https://www.sciencedaily. com/releases/2013/02/130221141604.htm, last accessed 2020/03/30.
  10. Pauza, K.: How Backpacks Affect the Adolescent Spine. Dr. Kevin Pauza Biologic Disc Treatment. N.p., 22 July 2016. https://drkevinpauza.com/how-backpacks-affect-the-adolescent- spine/, last accessed 03/0/2020.
  11. Freburger, J. K., Holmes, G. M., Agans, R. P., Jackman, A. M., Darter, J. D., Wallace, A. S., Castel, L. D., Kalsbeek, W. D., Carey, T. S. (2009). The rising prevalence of chronic low back pain. Archives of internal medicine, 169(3), 251–258. https://doi.org/10.1001/archinternmed.2008.543, (2009).
  12. American Chiropratic Association: Back pain facts and statistics, https://www.acatoday. org/Patients/What-is-Chiropractic/Back-Pain-Facts-and-Statistics, last accessed 04/05/2020.
  13. Luo X, Pietrobon R, Sun SX, Liu GG, Hey L.: Estimates and patterns of direct health care expenditures among individuals with back pain in the United States. Spine. 2004;29:79–86. (2004)
  14. Balagué F, Troussier B, Salminen J.: Non-specific low back pain in children and adolescents: risk factors. European Spine Journal. 8(6):429-438. (1999)
  15. Skaggs DL, Early SD, D'Ambra P, Tolo VT, Kay RM.: Back pain and backpacks in school children. J Pediatr Orthop. 2006;26:358–63.(2006).
  16. American Chiropratic Association: Backpack safety, https://www.acatoday.org/Patients/ Health-Wellness-Information/Backpack-Safety, last accessed 04/01/2020.
  17. Academy of Pediatrics: Backpack safety. http://www.aap.org/advocacy/backpack_ safety.pdf, last accessed 04/01/2020.
  18. Davis, K. G., Jorgensen M.: Biomenchanical Modeling for understanding of lower back injuries: A systematic review, Occupational Ergonomics, (5)1, 57-76, (2005).
  19. Chaffin D. B., Andersson, G. B, J., Martin, B. J., Occupational Biomechanics, 4th edition, John Wiley & Sons, New Jersey , (2006).