Abstract
A mathematical model is developed to explain the fundamental conundrum as to how during cyclic mechanical loading there can be net solute (e.g., nutrient, tracer) transport in bone via the lacunar-canalicular porosity when there is no net fluid movement in the canaliculi over a loading cycle. Our hypothesis is that the fluid space in an osteocytic lacuna facilitates a nearly instantaneous mixing process of bone fluid that creates a difference in tracer concentration between the inward and outward canalicular flow and thus ensures net tracer transport to the osteocytes during cyclic loading, as has been shown experimentally. The sequential spread of the tracer from the osteonal canal to the lacunae is investigated for an osteon experiencing sinusoidal loading. The fluid pressure in the canaliculi is calculated using poroelasticity theory and the mixing process in the lacunae is then simulated computationally. The tracer concentration in lacunae extending radially from the osteonal canal to the cement line is calculated as a function of the loading frequency, loading magnitude, and number of loading cycles as well as the permeability of the lacunar-canalicular porosity. Our results show that net tracer transport to the lacunae does occur for cyclic loading. Tracer transport is found to increase with higher loading magnitude and higher permeability and to decrease with increasing loading frequency. This work will be helpful in designing experimental studies of tracer movement and bone fluid flow, which will enhance our understanding of bone metabolism as well as bone adaptation. © 2000 Biomedical Engineering Society.
PAC00: 8716Uv, 8719Rr, 8716Ac
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REFERENCES
Cane, V., G. Marotti, G. Volpi, D. Zaffe, S. Palazzini, F. Remaggi, and M. A. Muglia. Size and density of osteocyte lacunae in different regions of long bones. Calcif. Tissue Int.34:558–563, 1982.
Cooper, R. R., J. W. Milgram, and R. A. Robinson. Morphology of the osteon. J. Bone Jt. Surg. 48A:1239–1271, 1966.
Cowin, S. C., S. Weinbaum, and Y. Zeng. A case for bone canaliculi as the anatomical site of strain generated potentials. J. Biomech. 28:1281–1296, 1995.
Cowin, S. C. Bone poroelasticity. J. Biomech. 32:218–238, 1999.
Curtis, T. A., S. H. Ashrafi, and D. F. Weber. Canalicular communication in the cortices of human long bones. Anat. Rec. 212:336–344, 1985.
Dilliman, R. M. Movement of ferritin in the 2-day-old chick femur. Anat. Rec. 209:445–453, 1984.
Fritton, S. P., K. J. McLeod, and C. T. Rubin. Quantifying the strain history of bone: spatial uniformity and selfsimilarity of low magnitude strains. J. Biomech. 33:317–325, 2000.
Fyhrie, D. P. and J. H. Kimura. Cancellous bone biomechanics. J. Biomech. 32:1139–1148, 1999.
Haines, R. W., L. Mehta, and A. Mohiuddin. Nutrition of interstitial lamellae of bone. Anat. Anz. Jena. 154:233–236, 1983.
Ham, W. Some histophysiological problems peculiar to calcified tissues. J. Bone Jt. Surg. 34A:706–728, 1952.
Hillsley, M. V. and J. A. Frangos. Osteoblast hydraulic conductivity is regulated by calcitonin and parathyroid hormone. J. Bone Miner. Res. 11:114–124, 1996.
Hughes, S. P. F. and P. J. Kelly. The mechanism of ion transfer in bone. In: Bone Circulation, edited by J. Arlet, R. P. Ficat, and D. S. Hungerford. Baltimore: Williams and Wilkins, 1984, pp. 207–212.
Jande, S. S. and L. F. Belanger. Electron microscopy of osteocytes and the pericellular matrix in rat trabecular bone. Calcif. Tissue Int. 6:280–289, 1971.
Ker, R. F., M. B. Bennett, R. M. Alexander, and R. C. Kester. Foot strike and the properties of the human heel pad. Proc. Inst. Mech. Eng., Part H 203:191–196, 1989.
Knothe Tate, M. L. and U. Knothe. An ex vivo model to study transport processes and fluid flow in loaded bone. J. Biomech. 33:247–254, 2000.
Knothe Tate, M. L. and P. Niederer. A theoretical FE-based model developed to predict the relative contribution of convective and diffusive transport mechanisms for the maintenance of local equilibria within cortical bone. Advances in Heat and Mass Transfer in Biotechnology (ASME) HTD-Vol. 362/BED-Vol. 40:133–142, 1998.
Knothe Tate, M. L., P. Niederer, and U. Knothe. In vivo tracer transport through the lacunocanalicular system of rat bone in an environment devoid of mechanical loading. Bone 22:107–117, 1998.
Kufahl, R. H. and S. Saha. A theoretical model for stressgenerated fluid flow in the canaliculi-lacunae network in bone tissue. J. Biomech. 23:171–180, 1990.
Li, G., J. T. Bronk, K. An, and P. J. Kelly. Permeability of cortical bone of canine tibiae. Microvasc. Res. 34:302–310, 1987.
Marotti, G., M. A. Muglia, and D. Zaffe. A SEM study of osteocyte orientation in alternately structured osteons. Bone 6:331–334, 1985.
Marotti, G., M. Ferretti, F. Remaggi, and C. Palumbo. Quantitative evaluation on osteocyte canalicular density in human secondary osteons. Bone 16:125–128, 1995.
Marotti, G., D. Farneti, F. Remaggi, and F. Tartari. Morphometric investigation on osteocytes in human auditory ossicles. Anat. Anz. 180:449–453, 1998.
Maroudas, A., R. A. Stockwell, A. Nachemson, and J. Urban. Factors involved in the nutrition of human lumbar intervertebral disc: cellularity and diffusion of glucose in vitro. J. Anat. 120:113–130, 1975.
McCarthy, I. D. and S. P. F. Hughes. Is there a blood-bone barrier? In: Bone Circulation and Bone Necrosis, edited by J. Arlet and B. Mazieres. New York: Springer, 1987, pp. 30–34.
McCarthy, I. D. and S. P. F. Hughes. Transport of small molecules across capillaries in bone. In: Blood Flow: Theory and Practice, edited by D. E. M. Taylor and A. L. Stevens. New York: Academic, 1983, pp. 313–329.
Montgomery, R. J., B. D. Sutker, J. T. Bronk, S. R. Smith, and P. J. Kelly. Interstitial fluid flow in cortical bone. Microvasc. Res. 35:295–307, 1988.
Neuman, W. F. and M. W. Newman. The Chemical Dynamics of Bone Mineral. Chicago: Chicago University Press, 1958.
Neuman, W. F. and W. K. Ramp. The concept of a bone membrane: some implications. In: Cellular Mechanisms for Calcium Transfer and Homeostasis, edited by G. Nichols, Jr. and R. H. Wasserman. New York: Academic, 1971, pp. 197–209.
Piekarski, K. and M. Munro. Transport mechanism operating between blood supply and osteocytes in long bones. Nature (London) 269:80–82, 1977.
Rouhana, S. W., M. W. Johnson, D. R. Chakkalakal, R. A. Harper, and J. L. Katz. Permeability of compact bone. Joint ASME-ASCE Conference Biomechanics Symposium AMD43:169–172, 1981.
Rubin, C. T., K. J. McLeod, and S. D. Bain. Functional strains and cortical bone adaptation: epigenetic assurance of skeletal integrity. J. Biomech. 23:43–54, 1990.
Sauren, Y. M. H. F., R. H. P. Mieremet, and C. G. Groot. An electron microscopic study on the presence of proteoglycans in the mineralized matrix of rat and human compact lamellar bone. Anat. Rec. 232:36–44, 1992.
Skerry, T. M., R. Suswillo, A. J. el. Hai, N. N. Ali, R. A. Dodds, and L. E. Lanyon. Load-induced proteoglycan orientation in bone tissue in vivo and in vitro. Calcif. Tissue Int. 46:318–326, 1990.
Weinbaum, S., S. C. Cowin, and Y. Zeng. A model of the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses. J. Biomech. 27:339–360, 1994.
Wilkes, C. H., and M. B. Visscher. Some physiological aspects of bone marrow pressure. J. Bone Jt. Surg. 57A:49–57, 1975.
Zeng, Y., S. C. Cowin, and S. Weinbaum. A fiber matrix for fluid flow and streaming potentials in the canaliculi of an osteon. Ann. Biomed. Eng. 22:280–292, 1994.
Zhang, D., S. Weinbaum, and S. C. Cowin. Estimates of the peak pressure in the bone pore water. J. Biomech. Eng. 120:697–703, 1998.
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Wang, L., Cowin, S.C., Weinbaum, S. et al. Modeling Tracer Transport in an Osteon under Cyclic Loading. Annals of Biomedical Engineering 28, 1200–1209 (2000). https://doi.org/10.1114/1.1317531
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DOI: https://doi.org/10.1114/1.1317531