|Year : 2019 | Volume
| Issue : 10 | Page : 1356-1364
Percentage difference of hand dimensions and their correlation with hand grip and pinch strength among schoolchildren in Saudi Arabia
KA Alahmari, VN Kakaraparthi, RS Reddy, Paul Samuel Silvian, I Ahmad, K Rengaramanujam
Department of Medical Rehabilitation Sciences, College of Applied Medical Sciences, King Khalid University, Abha, KSA
|Date of Acceptance||16-May-2019|
|Date of Web Publication||14-Oct-2019|
Dr. V N Kakaraparthi
Department of Medical Rehabilitation Sciences, College of Applied Medical Sciences, King Khalid University, P.O Box Number 3665, Guraigar, Abha
Source of Support: None, Conflict of Interest: None
| Abstract|| |
Aims: The study aimed to assess the percentage difference of hand dimensions and their correlation with grip and pinch strength among school children in Saudi Arabia. Materials and Methods: Anthropometric measurements, hand dimensions, grip, and pinch strength measurements were obtained from 200 healthy schoolchildren in both genders aged 6-16 years. A Jamar electronic handgrip dynamometer was used to measure handgrip strength in kg. Pinch dynamometer was used to measure the two-point pinch strength, three-point pinch strength and lateral pinch strength in kg. Hand circumference was measured following hand arch at the maximum palm level. Hand span from the tip of the thumb to the tip of the little finger with the hand opened as broad as possible. Hand length from the tip of the middle finger to the midline of the distal wrist crease. Palm length from the distal wrist crease to the base of the middle finger. Results: The percentage of difference of hand dimensions between both the genders was statistically significant. Both handgrip and pinch strength were significantly correlated with anthropometric measurements and hand dimensions. Body mass index had mild correlation with both handgrip strength and pinch strength (P < 0.05). Age, hand circumference, hand span, hand length and palm length had moderate to strong correlation with both grip and pinch strength (P < 0.01). Conclusion: The current study provides a source of perspective reference values in clinical settings for hand dimensions. The present study showed significant correlations with handgrip and pinch grip strengths among schoolchildren in Saudi Arabia.
Keywords: Grip strength, hand dimensions, pinch strength, schoolchildren
|How to cite this article:|
Alahmari K A, Kakaraparthi V N, Reddy R S, Silvian PS, Ahmad I, Rengaramanujam K. Percentage difference of hand dimensions and their correlation with hand grip and pinch strength among schoolchildren in Saudi Arabia. Niger J Clin Pract 2019;22:1356-64
|How to cite this URL:|
Alahmari K A, Kakaraparthi V N, Reddy R S, Silvian PS, Ahmad I, Rengaramanujam K. Percentage difference of hand dimensions and their correlation with hand grip and pinch strength among schoolchildren in Saudi Arabia. Niger J Clin Pract [serial online] 2019 [cited 2020 May 28];22:1356-64. Available from: http://www.njcponline.com/text.asp?2019/22/10/1356/269006
| Introduction|| |
Handgrip strength (HGS) and pinch strength (PS) play an important role in hand function mainly to identify the level of impairment and to establish treatment requirements. Especially in children, normative data remains essential as a means of understanding the valuation data and establishing accurate treatment outcomes. Grip strength is a consistent clinical parameter used to assess nutritional status and physical capability in children and adults. It mainly reflects the ultimate strength derived from the mutual contraction of the intrinsic and extrinsic muscles of the hand, causing the flexion of hand joints. Grip strength measurement is widely used in many areas as a functional assessment of overall strength and also used in experimental and epidemiologic studies in children. Additionally, evaluating HGS by using a dynamometer is noninvasive, inexpensive, and very simple to implement , whereas pinch is a type of prehension utilizing two or three fingers to manage objects in synchronization with thumb movements - without interaction with the palm. Three primary types of PS measurements have been assessed in clinical settings: tip to tip, three-jaw pinch and lateral pinch. A tip-to-tip pinch grasps small objects and is the most gentle and accurate of the digital pinches. Three-jaw pinch is considered a transitional strength of the fingers, and lateral pinch (also known as a key pinch) is mainly used while turning a key.
Meanwhile, a decrease in HGS and PS can lead to considerable functional limitations, which can lead to a reduction in essential daily life activities and affects the quality of life. This is mainly because the hand functionality is important for most activities involving the upper limbs, such as eating, writing, carrying loads, lifting things, opening or closing doors and so on. Adequate grip and pinch strength require in most sporting activities to improve performance and avoid overuse injuries. Several factors influence grip and pinch strength which include age, gender, nutritional status, muscle strength, fatigue, restricted movement, pain and anthropometric parameters. These strength measurements are quick evaluations that provide relevant clinical data designed to utilize in rehabilitation process.
Furthermore, normative data for a specific healthy population in a country may alter over time due to changes in lifestyle. Data from 2001 to 2002 and from 2006 to 2007 showed an average decrease in the hand strength of approximately 4.5 kg in adolescents of both sexes between the ages of 12.5 and 17.5 years in Spain. In England, the grip strength data collected from 10-year-old children who are attending different schools fell by 6.3% over a 10-year period from 1998 to 2008. Grip strength data collected from 2087 participants aged 6-19 years, selected from 15 locations across Canada, showed that HGS decreased by 5 kg in a typical 12-year-old boy from 1981 to 2009 and 3 kg in a typical girl.
Body height and weight are the main indicators of human growth and correlated with grip and pinch strength. Nevill and Holder (2002) concluded that the greater the size of the hand, the greater the strength of the hand. Nicolay and Walker (2005) indicated that the size of the hand and forearm generally serve as superior predictors of grip strength than the body height and body mass. In addition, Fallahi et al. showed hand length, palm length, forearm length, forearm circumference and wrist circumference were significantly associated with grip strength in different populations.
The percentage difference (% difference) will find the percent difference between two positive numbers greater than zero. In general, it mainly indicates a relative change in the variables between the groups. These relative changes play a crucial role in calculation and in measurement of productivity. These studies in the past have investigated the percentage difference of hand dimensions in different populations., Differences in the stature of Australian men and women can be observed in comparison to those of the British population. On the other hand, Australian and Dutch males are almost the same in size, but the data for females differ considerably when compared to males.
However, to our knowledge, there is no study conducted regarding the percentage differences of hand dimensions and its correlation with grip and pinch strength in Saudi children. Therefore, the purpose of this study was to determine the correlation of anthropometric variables and hand dimensions with grip and pinch strength among school children in Saudi Arabia which will be useful to provide substantial data for practice.
| Materials and Methods|| |
Two hundred healthy school children (boys and girls) aged 6-16 years had been recruited for the study. All the participants were randomly selected from different schools from Abha, Saudi Arabia. However, the study excluded participants with joint problems of the hand, wrist and elbow, history of recent fracture, congenital/neurological disorders, and deformities of the upper limb. All the children and their parents signed an informed consent form after receiving a brief description of the study and university ethics committee approved this study.
Instrumentation and procedures
The Clinical Assessment Committee of the American Society of Hand Therapists guidelines recommended the procedure for grip strength and pinch strength measurements conducted in this study. The study measured grip strength using a Jamar hydraulic dynamometer (Hydraulic Hand Dynamometer Fabrication Enterprises Inc, Irvington, NY, USA) set at second handle position. To measure HGS and PS, the subject remained comfortably seated in a chair with their back straight by maintaining shoulder in adduction, elbow in 90° flexion, forearm in neutral position, wrist in neutral position between 0°-30° of extension and 0°-15° of ulnar deviation, and feet flat on the floor [Figure 1]. For the measurement of pinch grip strength, the study used a pinch dynamometer (Pinch Gauge Jamar Dynamometer, model no. PG-30; B and L Engineering, Tustin, CA). The tip-to-tip pinch was performed between the soft tissues of the thumb and the index finger as shown in [Figure 2]. The three-jaw pinch was performed between the soft tissues of the thumb, index and middle fingers. Lateral pinch was performed between the soft tissues of the thumb pad to the lateral side of the index finger. Pinch dynamometer had an accuracy of 0.1 lb. for both the right and left hands. To avoid dropping, the researchers supported the pinch dynamometer lightly at the bottom and the pinch gauges at the distal end. In children, the hand dominance was acknowledged when the subject reported preference for function in activities of daily living. The study permitted all the children to practice using both handheld dynamometer and pinch dynamometer to allow them to become acquainted with the procedures. To provide proper grip and pinch strength measurements the dynamometers were calibrated regularly.
Researchers verbally encouraged all the children and gave them instructions to exert maximum strength during each trial. Three trials were performed alternately for every arm. To decrease fatigue in the children, the attempts included alternating the hands with about 2 minutes of rest each for every attempt. The evaluator recorded the mean of the three trials for further evaluation. The study furthermore requested that all children attempt a maximal effort for each trial by squeezing the dynamometer as hard as possible for 10 seconds. During testing, if any participant was unable to maintain the correct position, the researchers discontinued the evaluation and re-attempted. They evaluated grip strength first, followed by tip-to-tip, lateral and three-jaw PS measurements.
This study collected basic demographic data, including age, gender, height, and weight. All the participants were informed about the procedure the study. The researchers measured height with a stadiometer (Pelstar, Alsip, IL, USA) to the nearest 0.1 cm. Body weight was measured using a portable digital weighing scale (Camry, model EB-932, China, Ltd.) to the nearest 0.1 kg. Later, body mass index (BMI) was calculated using the method (BMI = body mass index (kg)/standing height (m)2). For measurement of hand dimensions, all the subjects were instructed to sit in a comfortable position during the entire data collection procedure.
Measurement techniques of different hand dimensions in this study followed NASA-1024's guidelines. Researchers measured hand circumference following hand arch at the highest palm level. To measure the hand span, the subjects were instructed to stretch and spread out their hand, placing it on a piece of paper on a table. The distance from the tip of the thumb to the tip of the little finger was measured. Hand length was measured from the tip of the middle finger to the midline of the distal wrist crease when the forearm and hand were in supination and placed on the table. Palm length is the distance measured from origin of the palm to the origin of the middle finger. All these measurements were completed with an inch tape.
This study calculated all statistical analyses using Statistical Package for Social Sciences (SPSS version 20.0, IBM Corporation, New York, NY, USA). It calculated descriptive statistics to determine the demographic characteristics of the subjects. Pearson r correlation was used to analyze the relationship between HGS and PS through anthropometric measurements. The study employed an independent sample t-test to analyze the differences in anthropometric measurements in both genders. In addition, the percentage difference between different hand dimensions, PS, and HGS was calculated for boys and girls separately within the sample. Percentage difference was calculated using the formula percentage difference = (new value + initial value)/Difference × 100. Difference = (new value - initial value). Statistical significance in this study was set at the P value of < 0.005.
| Results|| |
Study population and normative data
[Table 1] illustrates age, gender, standing height, weight, and BMI of both genders in the sample.
Percentage difference of hand dimensions, HGS and PS
With respect to BMI, significant differences revealed themselves among boys and girls. [Table 2] presents the percentage difference for hand dimensions, PS, and HGS as measured and recorded. The statistical analysis (t-test) of the data indicated a significant difference in hand circumference, hand span, hand length and palm length between both sexes (P < 0.01). The percentage difference between the hand dimensions of boys and girls varied from 1.07% to 1.46% and 0.11% to 0.41%. Percentage difference between hand dimensions of right-hand individuals of males and females ranged from 4.29% to 8.37% for the right hand and from 3.25% to 7.31% for the left hand.
|Table 2: Mean, standard deviation and percentage difference of hand dimensions in centimeters and PS and HGS in kilograms for boys and girls participated in the study|
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[Table 2] reveals a significant difference in HGS between males and females in which the right hand was stronger than the left hand. Moreover, the percentage difference for HGS between both genders varied from 5.84% to 10.79%, while between the right hand and left hand in both boys and girls the difference varied from 23.30% to 28.19%. However, boys demonstrated greater HGS than their girls' counterparts (P < 0.001). [Table 2] shows functional differences between the mean scores of PSs; the percentage of difference varied from 2.30% to 3.02% in boys and 9.52% to 11.88% in girls. However, in both the genders the percentage of difference in PSs varied from 43.82% to 58.66% in the right hand and ranged from 50.64% to 66.66% in the left hand, demonstrating that the boys had more PS than the girls (P < 0.001).
Correlation of age, BMI, hand circumference, hand span, hand length, and palm length with HGS
The study analyzed the correlation of age, BMI, hand circumference, hand span, hand length and palm length with HGS in boys and girls. (Summararized in [Table 3]) This study showed BMI (r = 0.33 (M), 0.41 (F)) was significantly correlated (P < 0.05) with HGS in both boys and girls. All the hand dimensions were significantly correlated (P < 0.001) with HGS in both the genders. It was also observed from this study that a significant difference (P < 0.001) exists between the right and left hand HGS in both the genders. The data indicates the right hand can generate more HGS than the left hand among the school children in Saudi Arabia.
|Table 3: Correlation of age, BMI, hand circumference, hand span, hand length, palm length with HGS in boys and girls|
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Correlation of age, BMI, hand circumference, hand span, hand length, and palm length with PS
This study analyzed all PS measurements in both genders correlated with age, BMI, hand circumference, hand span, hand length and palm length (summarized in [Table 4] and [Table 5]) The study found correlation of BMI (P < 0.05) (r = 0.37 (M), 0.31 (F)) with PS measurements in both boys and girls in its sample. All the hand dimesions were strongly correlated (P < 0.001) with PS measurements in both genders.
|Table 4: Correlation of age, BMI, hand circumference, hand span, hand length, palm length with PS in boys|
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|Table 5: Correlation of age, BMI, hand circumference, hand span, hand length, palm length with PS in girls|
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| Discussion|| |
To our knowledge, this is the first study conducted to examine the percentage of hand dimensions and its effect on HGS and PS in both genders among the school children in Saudi Arabia. The mean HGS in this study for the boys was 34.54 ± 11.73 and girls was 27.33 ± 10.03 (P < 0.001). Such values were less when compared with the Western population, which signifies that HGS varies in different populations. Genetic factors, environmental factors, and nutritional deficiencies may contribute to such inter-population differences. This study also contributes to the idea that boys have a higher mean value for HGS than girls, probably due to the difference in the kind of activity of each gender. In fact, boys usually have more muscular strength in general than females, mainly due to the difference in the size of the muscle in view of the male testosterone hormone responsible for enhancing that size; specifically, the hormone increases the compose II filaments with more rapid movement of glycolytic proteins.
The mean tip-to-tip PS varied as 3.86-3.95 (M), 2.30-2.53 (F), three-jaw PS varied as 4.65-4.77 (M), 2.56 -2.86 (F), lateral PS varied as 5.54-5.71 (M), 2.77-3.12 (F). These PS measurements in this study were lower than those scores of previous studies conducted among Western children population. Using different pinch gauges might affect these PS measurements: a concept supported by several studies., Some studies have detected many important variations of PS in boys and girls, with boys having higher PS measurements than the girls, which supports our present research., Gender-specific muscle fibers have a relevant role in these discrepancies.
This study showed that hand dimensions like hand circumference, hand span, hand length, palm length were significantly correlated with the HGS and PS in children. Hand circumference and palm length significantly correlated with the grip and pinch strengths, these findings were supported by a previous study that showed individuals with larger hand circumference or longer palm length have a stronger grip power in all age groups. Hand span plays a vital role and influences strength measurements, studies have recommended that both finger length and finger variables influence strength of the hand. The present research also helps in understanding that hand span has a significant positive correlation (P < 0.001) with HGS and PS measurements. Regarding the influence of hand length on strength measurements, the researchers established that hand length is one of the vital variables in grip and pinch strength. This finding is similar to that reported in previous study. In the present study, there was a significant difference in hand dimensions between boys and girls, which is a conclusion supported by many researchers across the globe. All the hand dimensions which has been taken for the study were significantly correlating (P < 0.001) with grip and pinch strength. Such variables are part of objective assessment in everyday clinical setup, mainly to determine the need for assessment and to measure the progress of the interventions.
In this study, it was concluded that the percentage of difference in hand dimensions between the right and left hands of boys and girls was substantial. These differences must be considered in the design of hand tools or equipment controlled by hands. Correct tool design is important for preventing upper extremity musculoskeletal disorders. In addition to this finding, this percentage difference of hand dimensions may also be due to the practice of sports activities that require hands, especially the dominant hand, to serve as tools for throwing and catching the ball. This bilateral percentage of difference of hand dimensions can be explained by more intense physical activity of one side over the other. Frequent use of the dominant side leads to muscle strengthening, muscle and bone development of the respective side. These differences in hand dimensions are important in predicting the grip and pinch strength in children and are likely to have better results in grip and pinch strength.
This study has some limitations. The sample taken from the southern region of Saudi Arabia (Abha), which may not represent the measurements throughout Saudi Arabia. Therefore, a wide range of socio-cultural and economic aspects was not representative in this study. More research is nevertheless needed, ideally while using the same consistent procedures in another area of the country.
| Conclusion|| |
The conclusion of this study was that the percentage of difference in hand dimensions was significant and correlated with HGS, tip-to-tip PS, three-jaw PS and lateral PS in school-aged children in Saudi Arabia. It would be of great benefit to repeat this study by taking into consideration other dimensions such as handbreadth, maximum handbreadth, hand thickness, and grip diameter. Understanding the effects of such factors on HGS and PS measurements might provide additional insight for implementing this study's model. It is estimated that this study may be useful as a diagnostic tool for objective evaluation of hand functions.
Financial support and sponsorship
Conflicts of interest
There are no conflicts of interest.
| References|| |
Clerke A, Clerke J. A literature review of the effect of handedness on isometric grip strength differences of the left and right hands. Am J Occup Ther 2001;55:206-11.
Casanova JS, Grunert BK. Adult prehension: Patterns and nomenclature for pinches. J Hand Ther 1989;2:231-44.
Mathiowetz V, Weber K, Volland G, Kashman N. Reliability and validity of grip and pinch strength evaluations. J Hand Surg 1984;9:222-6.
Ruiz JR, Ortega FB, Gutierrez A, Meusel D, Sjöström M, Castillo MJ. Health-related fitness assessment in childhood and adolescence: A European approach based on the AVENA, EYHS and HELENA studies. J Public Health 2006;14:269-77.
Ploegmakers JJ, Hepping AM, Geertzen JH, Bulstra SK, Stevens M. Grip strength is strongly associated with height, weight and gender in childhood: A cross sectional study of 2241 children and adolescents providing reference values. J Physiother 2013;59:255-61.
Hogrel JY, Decostre V, Alberti C, Canal A, Ollivier G, Josserand E, et al
. Stature is an essential predictor of muscle strength in children. BMC Musculoskeletal Disord 2012;13:176.
Milenkovic S, Dragovic M. Modification of the Edinburgh handedness inventory: A replication study. Laterality 2013;18:340-8.
Jürimäe T, Hurbo T, Jürimäe J. Relationship of handgrip strength with anthropometric and body composition variables in prepubertal children. HOMO 2009;60:225-38.
Schreuders TA, Roebroeck ME, Goumans J, van Nieuwenhuijzen JF, Stijnen TH, Stam HJ. Measurement error in grip and pinch force measurements in patients with hand injuries. Phys Ther 2003;83:806-15.
Crosby CA, Wehbé MA. Hand strength: Normative values. J Hand Surg 1994;19:665-70.
Moliner-Urdiales D, Ruiz JR, Ortega FB, Jiménez-Pavón D, Vicente-Rodriguez G, Rey-López JP, et al
. Secular trends in health-related physical fitness in Spanish adolescents: The AVENA and HELENA studies. J Sci Med Sport 2010;13:584-8.
Cohen D, Voss C, Taylor M, Delextrat A, Ogunleye A, Sandercock G. Ten-year secular changes in muscular fitness in English children. Acta Paediatr 2011;100:e175-7.
Tremblay MS, Shields M, Laviolette M, Craig CL, Janssen I, Gorber SC. Fitness of Canadian children and youth: Results from the 2007-2009 Canadian health measures survey. Health Rep 2010;21:7-20.
Wind AE, Takken T, Helders PJ, Engelbert RH. Is grip strength a predictor for total muscle strength in healthy children, adolescents, and young adults? Eur J Pediatr 2010;169:281-7.
Nevill AM, Holder RL. Modelling handgrip strength in the presence of confounding variables: Results from the Allied Dunbar national fitness survey. Ergonomics 2000;43:1547-58.
Nicolay CW, Walker AL. Grip strength and endurance: Influences of anthropometric variation, hand dominance, and gender. Int J Ind Ergon 2005;35:605-18.
Fallahi A, Jadidian A. The effect of hand dimensions, hand shape and some anthropometric characteristics on handgrip strength in male grip athletes and non-athletes. J Human Kinet 2011;29:151-9.
Pal A, De S, Sengupta P, Maity P, Dhara PC. Estimation of stature from hand dimensions in Bengalee population, West Bengal, India. Egypt J Forensic Sci 2016;6:90-8.
Ibrahim MA, Khalifa AM, Hassan HA, Tamam HG, Hagras AM. Estimation of stature from hand dimensions in North Saudi population, medicolegal view. Saudi J Forensic Med Sci 2018;1:19-27. [Full text]
Kothiyal K, Tettey S. Anthropometric data of elderly people in Australia. Appl Ergon 2000;31:329-32.
Molenbroek J. Anthropometry of elderly people in the Netherlands; research and applications. Appl Ergon 1987;18:187-99.
Balogun JA, Akomolafe CT, Amusa LO. Grip strength: Effects of testing posture and elbow position. Arch Phys Med Rehabil 1991;72:280-3.
Fess E. Chapter 12: Documentation: Essential elements of an upper extremity assessment battery. Rehabilitation of the Hand: Surgery and Therapy, 4th Edition.. Mosby, St. Louis. 1995:345.
Fess EE. A method for checking Jamar dynamometer calibration. J Hand Ther 1987;1:28-32.
Associates W, Scientific SA, Office TI. Anthropometric source book: A handbook of anthropometric data. Vol. 2. National Aeronautics and Space Administration, Scientific and Technical…; 1978.
Massy-Westropp NM, Gill TK, Taylor AW, Bohannon RW, Hill CL. Hand grip strength: Age and gender stratified normative data in a population-based study. BMC Res Notes 2011;4:127.
Carmelli D, Reed T. Stability and change in genetic and environmental influences on hand-grip strength in older male twins. J Appl Physiol 2000;89:1879-83.
Oseloka IA, Bello BM, Oliver HW, Emmanuel UU, Abraham MS. Association of handgrip strength with body mass index among Nigerian students. IOSR-JPBS 2014;9:1-7.
Griggs RC, Kingston W, Jozefowicz RF, Herr BE, Forbes G, Halliday D. Effect of testosterone on muscle mass and muscle protein synthesis. J Appl Physiol 1989;66:498-503.
Yu JG, Bonnerud P, Eriksson A, Stål PS, Tegner Y, Malm C. Effects of long term supplementation of anabolic androgen steroids on human skeletal muscle. PLoS One 2014;9:e105330.
Fullwood D. Australian norms for hand and finger strength of boys and girls aged 5-12 years. Aust Occup Ther J 1986;33:26-37.
Leong DP, Teo KK, Rangarajan S, Kutty VR, Lanas F, Hui C, et al
. Reference ranges of handgrip strength from 125,462 healthy adults in 21 countries: A prospective urban rural epidemiologic (PURE) study. J Cachexia Sarcopenia Muscle 2016;7:535-46.
Ruiz JR, España-Romero V, Ortega FB, Sjöström M, Castillo MJ, Gutierrez A. Hand span influences optimal grip span in male and female teenagers. J Hand Surg 2006;31:1367-72.
Häger-Ross C, Schieber MH. Quantifying the independence of human finger movements: Comparisons of digits, hands, and movement frequencies. J Neurosci 2000;20:8542-50.
Ager CL, Olivett BL, Johnson CL. Grasp and pinch strength in children 5 to 12 years old. Am J Occup Ther 1984;38:107-13.
King TI. Interinstrument reliability of the Jamar electronic dynamometer and pinch gauge compared with the Jamar hydraulic dynamometer and B&L Engineering mechanical pinch gauge. Am J Occup Ther 2013;67:480-3.
Mohammad YA. Anthropometric characteristics of the hand based on laterality and sex among Jordanian. Int J Ind Ergon 2005;35:747-54.
Marsot J, Claudon L. Design and ergonomics. Methods for integrating ergonomics at hand tool design stage. Int J Occup Saf Ergon 2004;10:13-23.
Visnapuu M, Jürimäe T. Handgrip strength and hand dimensions in young handball and basketball players. J Strength Cond Res 2007;21:923-9.
Krishan K, Kanchan T, DiMaggio JA. A study of limb asymmetry and its effect on estimation of stature in forensic case work. Forensic Sci Int 2010;200:181.e1-5.
[Figure 1], [Figure 2]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5]