Journal of Biomedical Engineering and Technology
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Journal of Biomedical Engineering and Technology. 2017, 5(1), 6-11
DOI: 10.12691/jbet-5-1-2
Open AccessArticle

Does Temperature Effects the Growth of Microcracks in Tibia due to Volleyball?

M. Tsili1, and D. Zacharopoulos1

1School of Engineering, Democritus University of Thrace, Xanthi, Greece

Pub. Date: April 10, 2017

Cite this paper:
M. Tsili and D. Zacharopoulos. Does Temperature Effects the Growth of Microcracks in Tibia due to Volleyball?. Journal of Biomedical Engineering and Technology. 2017; 5(1):6-11. doi: 10.12691/jbet-5-1-2


In present paper we considered if temperature plays role to the growth of microcracks in a tibia due to volleyball. We dealed with three particular points of bone and we based upon theories: of adaptive elasticity and upon energy density. We showed that both: neglecting or accounting temperature after a long time tibia at points of our interest will be strengthened (the mean length of their microcracks will be decreased). The result coincides with that of corresponding problem at macroscopic area. We concluded that temperature does not effects the growth of microcracks.

theory of adaptive elasticity accounting and neglecting temperature SED theory tibia locally at some points volleyball microcracks strengthened

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[1]  Burstein, A., Reilly, D. and Martens, M. (1976). “Aging of bone tissue mechanical properties. J. Bone Joint Surg.” A58, 82-86.
[2]  Thompson, D. (1980): “Age changes in bone mineralization, cortical thickness, and haversian canal area.” Calcif Tissue Int. 31, 5-11.
[3]  Grynpas, M. D.and Holmyard, D. (1988): “Changes inquality of bone mineral on aging and in disease.” Scan Microsc. 2, 1045-1054.
[4]  Hui, S. L., Slemenda, C. W. and Johnston, C.C. (1988): Age and bone mass as predictors of fracture in a prospective study. J. Clin. Invest. 81, 1804-1809.
[5]  Kiebzak G. M. (1991). “Age-related bone changes.” Exp. Gerontol. 26, 171-187.
[6]  Simmons, E. D., Pritzker, K. P. and Grynpas, M. D. (1991). “Age - related changes in the human femoral cortex.” J. Orthop. Res.9, 155-167.
[7]  Melvin JW. “Fracture mechanics of bone.” J. Biomech. Eng. 1993. Nov; 115(4B):549-554.
[8]  Currey, J. D., Brear, K. and Zioupos, P. (1996). “The effects of aging and changes in mineral content in degrading the toughness of human femora.” J. Biomech. 29, 257-260.
[9]  Francis, R.M. (1996). “Low bone mineral content is common but osteoporotic fractures are rare in elderly rural Gambian women.” J. Bone Miner. Res.11, 1019-1025.
[10]  Aspray, T. J., Prentice, A., Cole, T. J., Sawo, Y., Reeve, J. and Francis RM. (1996). “Low bone mineral content is comon but osteoporotic fractures are rare in elderly rural Gambian women.” J. Bone Miner. Res.11, 1019-1025
[11]  Yeni, Y. N. and Norman, T. L. (2000). “Fracture toughness of human femoral neck: Effect of microstructure, composition and age.” Bone 26, 499-504.
[12]  Wang, X., Shen, X., Li, X. and Agrawal C. M. (2002). “Age- related changes in the collagen network and toughness of bone.” Bone 31, 1-7.
[13]  Akkus, O., Adar, F. and Schaffler, M. B. (2004). “Age-related changes in physicochemical properties of mineral crystals are related to impaired mechanical function of cortical bone.” Bone 34, 443-453.
[14]  Ritchie. R, Kinney H., Kruzic R., and Nalla R. (2005). “A fracture mechanics and mechanistic approach to the failure of cortical bone.” Fatigue Fract. Engng Mater Struct. Fatigue Fract. Engng Mater Struct 28, 345-37
[15]  Behiri, JC. and Bonfield W. (1989): “Orientation depen-dence of the fracture mechanics of cortical bone.” J. Biomech,. 22, 863-872.
[16]  Yeni, Y. N., Brown, C. U., Wang, Z. and Norman, T. L. (1997). “The influence of bone morphology on fracture toughness of the human femur and tibia.” Bone 21, 453-459.
[17]  Yeni, Y. N., Brown, C.U. and Norman, T.L. (1998). “Influence of bone composition and apparent density on fracture toughness of the human femur and tibia.” Bone 22, 79-84.
[18]  Feng, Z., Rho, J., Han, S. and Ziv, I. (2000). “Orientation and loading condition dependence of fracture toughness in cortical bone.” Mater. Sci. Engng CC11, 41-46.
[19]  Brown, C. U., Yeni, Y. N. and Norman, TL.(2000). “Fracture toughness is dependent on bone location-A study of the femoral neck, femoral shaft and the tibial shaft.” J. Biomed. Mater. Res.49, 380-389.
[20]  Phelps, J. B., Hubbard, G. B., Wang, X. and Agrawal C. M. (2000): “Microstructural heterogeneity and the fracture toughness of bone.” J. Biomed. Mater. Res.51, 735-471.
[21]  Yeni, Y. N. and Norman, T. L. (2000). “Fracture toughness of human femoral neck: Effect of microstructure, composition and age.” Bone 26, 499-504.
[22]  Seeman, E. (1999). “The structural basis of bone fragility in men.” Bone 25, 143-147.
[23]  Rimnac, C. M., Petko, A. A., Santners, T. J. and Wright, T. M (1993). “The effect of temperature, stress and microstructure on the creep of compact bovine bone.” J. Biomech.26, 219-228.
[24]  Ford C.M. and Keaveny, T.M. (1996). “The dependence of shear failure properties of trabecular bone on apparent density and trabecular orientation.” J. Biomech. 29, 1309-1317.
[25]  Carter, D. R. and Hayes, W. C. (1976): “Fatigue life of compact bone-I. Effects of stress amplitude, temperature and density.” J. Biomech.9, 27-34, Biomech. 26, 219-228.
[26]  Norman, T.L., Nivargikar, S. V. and Burr, D. B. (1996). “Resistance to crack growth in human cortical bone is greater in shear than in tension.” J. Biomech.29, 1023-1031.
[27]  Feng, Z., Rho, J., Han, S. and Ziv, I. (2000). “Orientation and loading condition dependence of fracture toughness in cortical bone.” Mater. Sci. Engng CC11, 41-46.
[28]  Feng X. and McDonald J. (2011). “Disorders of Bone Remodeling,” Annu Rev Pathol.; 6: 121-145.
[29]  Cowin S. and Hegedus D. (1976). “Bone remodeling I: Theory of adaptive elasticity” J. Elastic. 6, pp. 313-326.
[30]  Hegedus D. και Cowin S. (1976). “Bone remodeling II: Theory of adaptive elasticity” J. Elastic. 6, pp. 337-352.
[31]  Sih G.C. (1985). “Mechanics and Physics of energy density theory”, Theoret., Appl., Fract. , Mech., 44, pp. 157-173.
[32]  Sih G.C (1972-1982). “Mechanics of fracture, Introductory chapters”, Vol. I- VII, edited by G.C. Sih, Martinus Nijhoff, The Hague.
[33]  Sih GC(1988). “Thermomechanics of solids: nonequilibrium and irreversibility”, Theoretical and Applied Fracture Mechanics, 99, pp. 175-198.
[34]  Τsili M. (2008). “The hyperthrophy of tibia induced by the volleyball” in: journal of bioengineering , Volume .4. number 1.
[35]  Harless E. (1860). “The static moments of human limbs (in German). Treatsises of the Math-Phys. Class of the Royal Acad. of Sci. of Bavaria, 8, pp.69 και 257.
[36]  Andriachi T., Ogle J. and Galante J. (1977). “Walking speed as a base for normal and abnormal gait measurement.” J. Biomech., 10, pp. 261-268.
[37]  Rohrle H., Scholten R., Sigolloto C. et., al., (1984). “Joint forces in the human pelvis - leg skeleton during walking.” J. Biomech., 17, pp. 409-424.
[38]  Whalen R., Carter D. and Steele C. (1988). “Influence of the physical activity on the regulation of bone activity.” J. Biomech., 21., pp., 825-837.
[39]  Αlexander N. and Jayes A. (1980). “Fourier analysis on forces exerted in walking and running.” J. Biomech. 13. pp. 383-390.
[40]  Bates B., Osterning L. and Sawhill J. (1983). “An assessment of subject variability, subject -shoe interaction and the evaluation of running shoes using ground reaction force data.” J. Biomech., 16., pp.181-191.
[41]  Cavagna P. (1964). “Mechanical work in running” J. Appl. Physiol. 19., pp. 249-256
[42]  Cavagna P. and LaFortune M. (1980). “Ground reaction forces in distance -running.” J. Biomech., 13. pp. 397-406.
[43]  Fukanaga T., Matsuo A., Yuasa K., et., al., (1980). “Effect of running velocity on external mechanical output.” Ergonomics, 23, pp.,123-136
[44]  Winter D. (1983). “Moments of forces and mechanical power in jogging.” J.Biomech., 16, pp., 91-97.
[45]  Frost H.M (1964). “Dynamics of bone remodeling in bone biodynamics.” (edited by Frost H.M) Little and Brown 316, Boston.
[46]  Reilly D.T. and Burstein A. (1975). J. Biomech., 8., p.393.
[47]  Cowin S. and Van -Burskirk W. (1978). “Internal bone remodeling induced by a medullary pin.” J. Biomech. 11, pp. 269-275.
[48]  Wolff. J. (1884). “Das gesetz der transformation der inneren architecture knocken bei pathologism veranderungen der aussen knochenform.” Sitz Ber. Preuss Acad. d. Wiss 22, Sitz Physik- Math. K1.
[49]  Wolff J. (1892). Das gesetz der transformation knocken hirschald, Berlin.
[50]  Τsili M. (2000). “Theoretical solutions for internal bone remodeling of diaphyseal shafts using adaptive elasticity theory.” J. Biomech., 33 pp. 235-239.
[51]  Τsili M. (2008): “Internal bone remodeling induced by the distance - running and the unkown remodeling coefficients” in: of- internet journal of bioengineering vol. 4. number 2.
[52]  Grifith A. (1921). “The phenomena of rupture and flow in solids” Philosophical Transactions of the Royal Society of London A 221, pp., 163-198
[53]  Griffith A. (1924). “The theory of rupture.” In: Proc., Ist., Int., Congr., Appl., Mech. Biereno, C.B. Burgers, J.M(eds). Delft: Tech. Boekhandel en Drukkerij. J. Waltman Jr., pp. 54-63.
[54]  Calbet A., Diaz Herrera P and Rodrignex L. (1999). “High bone mineral density in male elite professional volleyball players.” Osteopor., Inter, 10, pp. 468-474.
[55]  Fehling P., Alekel L. and Classey J., et., al., (1995). “A comparison of bone mineral densities among female athletes in impact loading and active loading sports.” Bone 17., pp. 205-210.
[56]  Ito M., Nakamura T., Ikesa S., et., al., (2001). “Effects of life time volleyball exersize on bone mineral densities in lum barspine, calcaneus and tibia for pro, peri- and postmenopausal women.” Ostepor. Intern., 12, pp.104-111.
[57]  Rittweger J., Beller G., Ehrig G., et., al., (2000). “Bone- muscle strenght indices for the human lower leg.” Bone , 27. pp. 319-326.
[58]  Alfredson N., Nordsatorm P. and Lorentzon R., (1997). “Bone mass in female volleyball players. A comparison of total and regional bone mass in female volleyball players and nonactive females.” Calcif., Tissue, Int., 60, pp. 338-342.
[59]  Hara S., Yanagi H., Amagai H., et., al., (2001). “Effect of physical activity during teenage years, based on type of sport and duration of exersize on bone mineral density of young, premenopausal Japanese women.” Calcif., Tissue Int., 68., pp. 23-30.
[60]  Nikander R., Sievanen H., Heinonen A. et., al., (2005). “Femoral neck structure in adult female athlete, subjected to different loading modalities.” J. Bone Miner., Res. 20., pp. 520-528.
[61]  Nikander R., Sievanen H., Heinonen A. et., al., (2006). “Loading modalities and bone structures at nonweight-bearing upper extremity and weight - bearing lower extremity” A poct- study of adult female athletes.” Bone, 39, pp. 886-894.
[62]  Nichols L., Raugh M., Barrack M. (2007). “Bone mineral density in female high school athletes: Interactions of mentrual function and type of mechanical loading.” Bone 41., pp. 371-377.