Modeling Deformation-Induced Fluid Flow in Cortical Bone’s Canalicular–Lacunar System

To explore the potential role that load-induced fluid flow plays as a mechano–transduction mechanism in bone adaptation, a lacunar–canalicular scale bone poroelasticity model is developed and implemented. The model uses micromechanics to homogenize the pericanalicular bone matrix, a system of straight circular cylinders in the bone matrix through which bone fluids can flow, as a locally anisotropic poroelastic medium. In this work, a simplified two-dimensional model of a periodic array of lacunae and their surrounding systems of canaliculi is used to quantify local fluid flow characteristics in the vicinity of a single lacuna. When the cortical bone model is loaded, microscale stress, and strain concentrations occur in the vicinity of individual lacunae and give rise to microscale spatial variations in the pore fluid pressure field. Furthermore, loading of the bone matrix containing canaliculi generates fluid pressures in the contained fluids. Consequently, loading of cortical bone induces fluid flow in the canaliculi and exchange of fluid between canaliculi and lacunae. For realistic bone morphology parameters, and a range of loading frequencies, fluid pressures and fluid–solid drag forces in the canalicular bone are computed and the associated energy dissipation in the models compared to that measured in physical in vitro experiments on human cortical bone. The proposed model indicates that deformation-induced fluid pressures in the lacunar–canalicular system have relaxation times on the order of milliseconds as opposed to the much shorter times (hundredths of milliseconds) associated with deformation-induced pressures in the Haversian system.     

Design of a Modular Bioreactor to Incorporate Both Perfusion Flow and Hydrostatic Compression for Tissue Engineering Applications

Physiological models have demonstrated that cells undergo a cyclic regimen of hydrostatic compression and fluid shear stress within the lacunar-canalicular porosity of bone. A new modular bioreactor was designed to incorporate both perfusion fluid flow and hydrostatic compression in an effort to more accurately simulate the mechanical loading and stress found in natural bone in vivo. The bioreactor design incorporated custom and off-the-shelf components to produce levels of mechanical stimuli relevant to the physiologic range, including hydrostatic compression exceeding 300 kPa and perfusion shear stress of 0.7 dyne/cm². Preliminary findings indicated that the novel system facilitated the viable growth of cells on discrete tissue engineering scaffolds. The bioreactor has established an experimental platform for ongoing investigation of the interactive effect of perfusion fluid flow and hydrostatic compression on multiple cell types.     

多尺度分析骨质疏松大鼠骨微结构变化

目的 多尺度分析骨质疏松大鼠的骨微结构变化。 方法 20只5月龄雌性SD大鼠随机选取12只实施双侧去卵巢(ovariectomy, OVX)手术,术后 8 周形成骨质疏松大鼠模型,另外 8 只作为假手术( SHAM) 对照组。 利用Micro-CT 和 SR-Nano-CT 定量分析骨质疏松大鼠在组织尺度下皮质骨和松质骨以及细胞尺度下骨细胞、骨陷窝小管和细胞外基质的微结构变化。 结果 组织尺度下,OVX 组皮质骨的截面积较 SHAM 组显著增大(P<0. 05),皮质骨骨密度和厚度较 SHAM 组虽有变化,但不显著;OVX 组骨小梁的骨密度、体积分数、厚度和骨小梁数量较 SHAM组显著降低(P<0. 01),骨小梁分离度显著增加(P<0. 01)。 细胞尺度下,OVX 组骨陷窝半轴长较 SHAM 组没有显 著差异,但 OVX 组骨陷窝厚度和骨小管直径较 SHAM 组显著增大(P<0. 05);同时,细胞尺度下 OVX 组皮质骨孔隙率较 SHAM 组显著增大(P<0. 05)。 结论 OVX 大鼠骨在组织和细胞尺度出现不同程度的微结构变化。 其中,组织尺度主要是松质骨丢失,皮质骨变化不大;细胞尺度骨陷窝小管网络孔隙显著增大,将直接影响皮质骨骨密度和强度。 多尺度分析骨质疏松大鼠骨微结构变化对于骨质疏松症的临床诊断及病理分析有潜在的应用价值。     

Differences in osteonal micromorphology between tensile and compressive cortices of a bending skeletal system: Indications of potential strain-specific differences in bone microstructure

Background: It has been hypothesized that bone has the capacity to accommodate regional differences in tension and compression strain mode and/or magnitude by altering its osteonal microstructure. We examined a simple cantilevered bone to determine whether regional differences in particular strain-related features are reflected in the microstructural organization of compact bone. Methods & Results: The artiodactyl (e.g., sheep and deer) calcaneus has a predominant loading condition which is typified by prevailing compressive and tensile strains on opposite cortices, and variations in strain magnitudes across each of these cortices. Microscopic examination showed osteon density and cortical porosity differences between tension (caudal) and compression (cranial) cortices, averaging 11.4% more osteons in the compression cortex (P < 0.01) and 80.2% greater porosity in the tension cortex (P < 0.01). There is 43.5% more interstitial bone in the compression cortex (P < 0.01). Osteons in the compression cortex also have smaller areas in contrast to the larger area per osteon in the tension cortex. Although no definite transcortical gradient in osteonal density or cortical porosity is found, fractional area of interstitial bone is largest and osteon population density is lowest in the endocortical regions of both tension and compression cortices. The endocortical regions also have greater porosity than their corresponding middle and pericortical regions (P < 0.01). Conclusions: These osteonal microstructure and cortical porosity differences may be adaptations related to regional differences in strain mode and/or strain magnitude. This may be related to the disparity in mechanical properties of compact bone in tension vs. compression. These differences may reflect a capacity of bone to process local and regional strain-related information. © 1994 Wiley-Liss, Inc.

1 This article is a US Government work and, as such, is in the public dotmain in the United states of America

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Electrical signal transmission and gap junction regulation in a bone cell network: A cable model for an osteon

A cabel model is formulated to estimate the spatial distribution of intracellular electric potential and current, from the cement line to the lumen of an osteon, as the frequency of the loading and the conductance of the gap junction are altered. The model predicts that the characteristic diffusion time for the, spread of current along the membrane of the osteocytic processes, 0.03 sec, is nearly the same as the predicted pore pressure relaxation time in Zenget al. (Annals of Biomedical Engineering. 1994) for the draining of the bone fluid into the osteonal canal. This approximate equality of characteristic times causes the cable to behave as a high-pass, low-pass filter cascade with a maximum in the spectral response for the intracellular potential at approximately 30 Hz. This behavior could be related to the experimetns of Rubin and McLeod (Osteoporosis, Academic Press, 1996) which show that live bone appears to be selectively responsive to mechanical loading in a specific frequency range (15–30 Hz) for several species.     

Modeling Fluorescence Recovery After Photobleaching in Loaded Bone: Potential Applications in Measuring Fluid and Solute Transport in the Osteocytic Lacunar-Canalicular System

Solute transport through the bone lacunar-canalicular system is essential for osteocyte viability and function, and it can be measured using fluorescence recovery after photobleaching (FRAP). The mathematical model developed here aims to analyze solute transport during FRAP in mechanically loaded bone. Combining both whole bone-level poroelasticity and cellular-level solute transport, we found that load-induced solute transport during FRAP is characterized by an exponential recovery rate, which is determined by the dimensionless Strouhal (St) number that characterizes the oscillation effects over the mean flows, and that significant transport occurs only for St values below a threshold, when the solute stroke displacement exceeds the distance between the source and sink (the canalicular length). This threshold mechanism explains the general flow behaviors such as increasing transport with increasing magnitude and decreasing frequency. Mechanical loading is predicted to enhance transport of all tracers relative to diffusion, with the greatest enhancement for medium-sized tracers and less enhancement for small and large tracers. This study provides guidelines for future FRAP experiments, based on which the model can be used to quantify bone permeability, solute–matrix interaction, and flow velocities. These studies should provide insights into bone adaptation and metabolism, and help to treat various bone diseases and conditions.     

Estimation of bone permeability considering the morphology of lacuno-canalicular porosity

Load-induced interstitial fluid flow in lacuno-canalicular porosity is believed to play an important role in cellular activities regulating adaptive bone remodeling. To investigate interstitial fluid behavior based on poroelasticity, it is important to determine the anisotropic permeability tensor reflecting the morphological features of the lacuno-canalicular porosity as fluid channels. In this study, we presented an estimation method of trabecular permeability by describing the analytical relationship between the volume orientation (VO) fabric tensor, which represents the canalicular orientation, and the permeability tensor. The relationship showed that the trabecular permeability tensor is proportional to the product of the volume fraction of the interstitial fluid and the VO fabric tensor of the canaliculi. We applied the proposed method to a two-dimensional fluorescent image of a trabecular cross section to quantify the canalicular anisotropy and the trabecular permeability tensor. The results indicated that the canaliculi are predominantly oriented in the radial direction of the trabecula, and the permeability depends strongly on the canalicular morphology.     

Effect of lacunocanalicular architecture on hydraulic conductance in bone tissue: implications for bone health and evolution

Bone tissue health depends largely on efficient fluid and solute transport between the blood supply and cells that are the living component of the tissue. We hypothesized that the lacunocanalicular hydraulic network, which is defined by the pericellular fluid space that is common to all bone tissue, is optimized to transport fluid and solutes between the blood supply and bone cells. An analytical study was carried out to evaluate the effect of osteonal architecture, including the osteon diameter, number of annular lamellar regions, and number and length of canalicular channels, on fluid transport between the blood supply and bone cells. On the basis of this analysis, we conclude that osteon size is limited to the distance over which fluid and solutes can be transported efficiently between the blood supply and cells. This analytic model suggests that hydraulic conductivity is highest in lamellar regions closest to the Haversian canal (HC) and decreases with increasing distance from the blood supply, reaching a plateau after the fifth lamella (169 micro m radius). Furthermore, an increase in the diameter of the HC, or a decrease in the length of canaliculi, reduces the hydraulic conductivity within the lacunocanalicular network. Applying the principle of minimal expenditure of energy to this analysis, the path distance comprising five or six lamellar regions represents an effective limit for fluid and solute transport between the blood supply and cells; beyond this threshold, hydraulic resistance in the network increases and additional energy expenditure is necessary for further transportation. This suggests that transport is optimized to meet metabolic demands concomitant with a minimal expenditure of energy. This fundamental new insight into bone structure and physiology may provide a new basis of understanding for tissue engineering, bone physiology in health and disease, and evolutionary biology.     

Effect of fluid shear stress on the permeability of the arterial endothelium

The localization of atherosclerotic lesions is due, in part, to regional variations in the permeability of arterial endothelium to macromolecules. In turn, endothelial permeability may be influenced by fluid shear stresses. The spatial variation in endothelial permeability is reviewed and evidence for shear stress dependence upon permeability is presented. These results are examined in light of various signaling mechanisms that increase permeability by increasing the transport of water and macromolecules through the junctions separating endothelial cells. Signaling pathways cause a change in the dense peripheral band of actin and actin stress fibers or alter the phosphorylation of junction proteins which affects their ability to localize in junctions. Future directions to clarify the effect of shear stress on permeability are considered. © 2002 Biomedical Engineering Society. PAC2002: 8716Dg, 8714Ee, 8719Tt, 8716Uv     

Knee-Loading Modality Drives Molecular Transport in Mouse Femur

Mechanical loading is well known to stimulate bone remodeling. Load-driven interstitial fluid flow and molecular transport have been postulated to play a role in the enhancement of bone formation. In order to evaluate load-driven molecular transport in a lacunocanalicular network, we conducted fluorescence recovery after photobleaching (FRAP) experiments using lacunae stained with uranine (376 Da). Loads were applied to a mouse femur ex vivo with a novel knee-loading modality, where the distal epiphysis was loaded with a sinusoidal force at 2 Hz. The lacunae in the diaphysis located 25% (∼4 mm) proximal to the loading site were photobleached and sequentially imaged, and a time constant for fluorescence recovery was determined both with and without knee loading. The time constant was estimated as the period to recover 63% of fluorescent intensity using a best-fit exponential curve. The results reveal that the applied loads shortened the time constant from 33 ± 9 s with non-loading control to 25 ± 11 s with knee loading (p = 0.0014). The strain in the measurement site was <100 μstain along the femoral midshaft, which was an order of magnitude smaller than the minimum effective strain threshold for bone remodeling. Taken together, the current study supports the notion that molecular transport in cortical bone is enhanced by the loads applied to the epiphysis without inducing significant in situ strain in the diaphysis.     

Morphometric analysis of osteonal architecture in bones from healthy young human male subjects using scanning electron microscopy

The shape and structure of bones is a topic that has been studied for a long time by morphologists and biologists with the goal of explaining the laws governing their development, aging and pathology. The osteonal architecture of tibial and femoral mid‐diaphyses was examined morphometrically with scanning electron microscopy in four healthy young male subjects. In transverse sections of the mid‐diaphysis, the total area of the anterior, posterior, lateral and medial cortex sectors was measured and analysed for osteonal parameters including osteon number and density, osteon total and bone area and vascular space area. Osteons were grouped into four classes including cutting heads (A), transversely cut osteons (B), longitudinally cut osteons (C) and sealed osteons (D). The morphometric parameters were compared between the inner (endosteal) and outer (periosteal) half of the cortex. Of 5927 examined osteons, 24.4% cutting heads, 71.1% transversely cut osteons, 2.3% longitudinally cut osteons and 2.2% sealed osteons were found. The interosteonic bone (measured as the area in a lamellar system that has lost contact with its own central canal) corresponded to 51.2% of the endosteal and 52.4% of the periosteal half‐cortex. The mean number of class A cutting heads and class B osteons was significantly higher in the periosteal than in the endosteal half‐cortex (P < 0.001 and P < 0.05, respectively), whereas there was no significant difference in density. The mean osteon total area, osteon bone area and vascular space area of both classes A and B were significantly higher (P < 0.001 for all three parameters) in the endosteal than in the periosteal half‐cortex. The significant differences between the two layers of the cortex suggest that the osteoclast activity is distributed throughout the whole cortical thickness, with more numerous excavations in the external layer, but larger resorption lacunae closer to the marrow canal. A randomly selected population of 109 intact class B osteons was examined at higher magnification (350×) to count osteocyte lacuna and to analyse their relationship with osteon size parameters. The distribution frequency of the mean number of osteocyte lacunae increased with the increment in the sub‐classes of osteon bone area, whereas the density did not show significant differences. The number of osteocyte lacunae had a direct correlation with the osteon bone area and the mean osteon wall thickness, as well as the mean number of lamellae. The osteocyte lacunae density showed an inverse relationship. These data suggest a biological regulation of osteoblast activity with a limit to the volume of matrix produced by each cell and proportionality with the number of available cells in the space of the cutting cone (total osteon area). The collected data can be useful as a set of control parameters in healthy human bone for studies on bone aging and metabolic bone diseases.     

Some osteocytes released from their lacunae are embedded again in the bone and not engulfed by osteoclasts during bone remodeling

It is generally accepted that osteocytes derive from osteoblasts that have secreted the bone around themselves. Osteocytes are cells embedded in the lacunae in the bone, and they are characteristically in contact with other cells by many slender cytoplasmic processes in canaliculi. During bone remodeling, many osteocytes in the bone are released from their lacunae by osteoclasts; however it remains unclear what happens to these released osteocytes. The cortical bone of the rat mandibular body was used in this study. Mandibles were fixed, decalcified, and then embedded in Epon 812. Specimens were sectioned in the frontal direction into serial 0.5 microm-thick semithin or 0.1 microm-thick ultrathin sections, and then examined by light or transmission electron microscopy. Cells that fitted in the osteocytic lacunae with canaliculi extending to the bone were identified as osteocytes in this study. Among many osteocytes released by osteoclasts in cutting cones, there were osteocytes half-released from their lacunae. These cells fitted in their lacunae with canaliculi extending to the bone and showed developed cell organelles in the cytoplasm. In closing cones, many osteocytes were situated in the bone away from cement lines; however, there were half-embedded osteocytes in the bone formed on cement lines. These cells fitted in their lacunae with canaliculi extending to the bone formed below cement lines and showed developed cell organelles in the cytoplasm. These results show that half-embedded osteocytes in closing cones derive from half-released osteocytes in cutting cones. Osteocytes encircled by osteoclasts were sometimes observed on one section, but serial sections showed that these osteocytes fitted in their remaining lacunae in the bone on other sections. This shows that not all osteocytes released from their lacunae are engulfed by osteoclasts. Consequently, the present results suggests that some osteocytes released from their lacunae are embedded again in the bone and not engulfed by osteoclasts during bone remodeling.     

A Finite Element Dual Porosity Approach to Model Deformation-Induced Fluid Flow in Cortical Bone

Fluid flow through the osteocyte canaliculi network is widely believed to be a main factor that controls bone adaptation. The difficulty of in vivo measurement of this flow within cortical bone makes computational models an appealing alternative to estimate it. We present in this paper a finite element dual porosity macroscopic model that can contribute to evaluate the interstitial fluid flow induced by mechanical loads in large pieces of bone. This computational model allows us to predict the macroscopic fluid flow at both vascular and canalicular porosities in a whole loaded bone. Our results confirm that the general trend in the fluid flow field predicted is similar to the one obtained with previous microscopic models, and that in a whole bone model it is able to estimate the zones with higher bone remodeling.     

Confocal microscopy of cementocytes and their lacunae and canaliculi in rat molars

 The present study was designed to analyze the morphological characteristics of cementocytes and osteocytes. The maxillae of 10-week-old Wistar rats were used for observations. Non-decalcified ground sections stained vitally with fluorescence dyes and decalcified frozen sections stained with FITC-phalloidin were examined by confocal microscopy. Calcein and alizarin red stained the calcification front of bone, cementum, and dentin intensely. In addition, lacunae and canaliculi of cementocytes and osteocytes as well as dentinal canals were stained with the fluorescent dyes. The staining of lacunae and canaliculi was less intense than that of the calcification front of bone, cementum and dentin. The canaliculi of cementocytes and osteocytes were connected with the canaliculi extending from the calcification front of cementum and bone, respectively. The canalicular density was less in the cellular cementum than in the bone. Areas devoid of canaliculi were numerous in the cellular cementum, whereas areas devoid of canaliculi were scarce in the alveolar bone. Further, the lacunae of cementocytes showed various shapes, from oval to tubular, while the lacunae of osteocytes were invariably oval. The cell body and the cytoplasmic processes of cementocytes were positive for FITC-phalloidin within the extracellular matrix of cellular cementum, which was negative. The distribution of actin filaments in the osteocytes and the cementocytes was predominantly cortical and appeared to be closely associated with the cell membrane of the cell bodies and the cytoplasmic processes. Intense staining was seen at the proximal part of the cytoplasmic processes in both osteocytes and cementocytes, showing a punctuated structure of the cells that was more frequent in osteocytes than in cementocytes. The stress fiber known to be present in most of the cultured cells was not evident in the these cells in situ. The cells incorporated in the cementodentinal junction were strongly stained with FITC-phalloidin. The distribution pattern of the cytoplasmic processes stained with FITC-phalloidin was similar to that of the canaliculli stained vitally. The cytoplasmic processes of osteocytes and cementocytes were connected with those of cells lining the surface of bone and cementum. The present result – that lacunae and canaliculi of cementocytes were stained vitally with the fluorescence dyes – suggests that cementocytes may have a role in secondary calcification of cellular cementum. Further, the lower density of cytoplasmic processes in cementocytes than in osteocytes suggests a lack of complexity in the intercellular network within the cellular cementum. Accepted: 13 January 1997     

Value of the bone biopsy in the diagnosis of industrial fluorosis

Summary Iliac crest biopsies taken from 43 men with industrial fluorosis were compared with control bone samples. The bone fluoride content was determined, histological examinations were made on stained sections and microradiographs, and morphometric analysis performed on the microradiographs alone.In the subjects with fluorosis, the bone fluoride content (5617±2143 ppm) was found to be significantly higher (P<0.00005) than in control subjects (1036±627 ppm). It decreased slowly, however, after exposure had ceased (to about 50% in 20 years). The histological changes consisted of a nonspecific remodeling activity (resulting in increased trabecular bone volume and cortical porosity, as well as hypervascularization and linear formation defects) and modifications of the perilacunar walls (i.e., presence of mottled lacunae and enlarged lacunae). These histological changes were found more likely to occur when the bone fluoride content was high but no correlation between the two parameters was observed.Although certain clinical and radiological data associated with a high urine fluoride content can sometimes establish a diagnosis of skeletal fluorosis, many cases require the use of bone biopsy, which also provides a direct evaluation of the bone fluoride content and can establish the absence of any other bone disease.     

Solute transport to the endothelial intercellular cleft: the effect of wall shear stress

The interendothelial cleft is the major transport pathway across the endothelium for hydrophilic solutes including albumin and low density lipoprotein. Previous models of arterial wall transport have assumed that the entire endothelial cell surface is available for transport from the fluid (blood) phase. One of the consequences of a cleft-mediated solute uptake mechanism is the limited area available for mass transport. This effect, together with the influence of a predominantly longitudinal cleft orientation in relation to flow, dramatically alters the fluid–phase mass transport characteristics relative to what has been assumed previously in analyzing vascular solute uptake problems. We have used a finite element computational model to simulate fluid phase transport to a longitudinal endothelial cleft under realistic wall shear rate conditions. Our numerical results show reduced dependence of the mass transfer rate on the wall shear rate compared to the classical Leveque solution for mass transport in a cross-flow configuration and confirm the significance of the wall and not the fluid as the limiting resistance to transport of macromolecules. © 2002 Biomedical Engineering Society. PAC2002: 8719Rr, 8716Uv, 8716Dg, 8710+e, 8715Vv     

The pathway of bone fluid flow as defined by in vivo intramedullary pressure and streaming potential measurements

The pathway for intracortical fluid flow response to a step-load was identified in vivo using intramedullary pressure (ImP) and streaming potential (SP) measurements, and allowed the development of a load-induced flow mechanism which considers mechanotransduction and mechanoelectrotransduction phenomena. An avian model was used for monitoring, simultaneously, ImP and SP under axial loading which generated peak strains of approximately 600 microstrain (). ImP response to step-load decayed more quickly than SP relaxation, in which multiple time constants were observed during the relaxations. While the initial relaxation of SP showed a decay on the order of 200 ms, ImP decayed on the order of approximately 100 ms. After the initial decay (200 ms after loading), ImP quickly relaxed to base line, while SP continued to dominate relaxation. It appears that the decay of ImP is indicative of resistive fluid flow occurring primarily in the vasculature and other intraosseous channels such as lacunar-canalicular pores, and that SP represents the fluid flow in the smaller porosities, i.e., lacunar-canalicular system or even microspores. These results suggest that SP and ImP decays are determined by a hierarchical interdependent system of multiple porosities, and that the temporal dynamics of load-bearing define the manner in which the fluid patterns and pressures are distributed. © 2002 Biomedical Engineering Society. PAC2002: 8719Tt, 8719Rr, 8719Nn     

Mechanotransduction of bone cells<Emphasis Type="Italic">in vitro</Emphasis>: Mechanobiology of bone tissue

Mechanical force plays an important role in the regulation of bone remodelling in intact bone and bone repair. In vitro, bone cells demonstrate a high responsiveness to mechanical stimuli. Much debate exists regarding the critical components in the load profile and whether different components, such as fluid shear, tension or compression, can influence cells in differing ways. During dynamic loading of intact bone, fluid is pressed through the osteocyte canaliculi, and it has been demonstrated that fluid shear stress stimulates osteocytes to produce signalling molecules. It is less clear how mechanical loads act on mature osteoblasts present on the surface of cancellous or trabecular bone. Although tissue strain and fluid shear stress both cause cell deformation, these stimuli could excite different signalling pathways. This is confirmed by our experimental findings, in human bone cells, that strain applied through the substrate and fluid flow stimulate the release of signalling molecules to varying extents. Nitric oxide and prostaglandin E₂ values increased by between two- and nine-fold after treatment with pulsating fluid flow (0.6±0.3 Pa). Cyclic strain (1000 μstrain) stimulated the release of nitric oxide two-fold, but had no effect on prostaglandin E₂. Furthermore, substrate strains enhanced the bone matrix protein collagen I two-fold, whereas fluid shear caused a 50% reduction in collagen I. The relevance of these variations is discussed in relation to bone growth and remodelling. In applications such as tissue engineering, both stimuli offer possibilities for enhancing bone cell growth in vitro.     

Chloride transport by self-exchange and by KCI salt diffusion in gramicidin-treated human red blood cells

The permeability of gramicidin-treated human red blood cell membranes to K⁺ and CI^- has been measured at normal ionic strength (1) by tracer exchange at steady-state distribution of salt, and (2) by net transport of salt in the presence of a salt concentration gradient. Under both conditions KCI was the only inorganic salt in cells and medium. In the studies of self-exchanges the electrical driving force on the ions was zero. Calculation of permeability coefficients from net salt transport was simplified because the experiment was designed as a special case of the Nernst-Planck diffusion regime, i.e. the single salt case. Gramicidin altered the cell membranes from being anion to become cation selective. Gramicidin increased the potassium exchange without affecting, the chloride exchange measurably. The chloride exchange showed saturation kinetics as does chloride exchange in normal cells. The net transport of KCI in the presence of a constant concentration gradient increased to a constant value with increasing gramicidin concentration. At high gramicidin concentrations (0°C, pH 7.2) the “chloride permeability coefficient” calculated from tracer exchange (1.9×10^-6 cm/s) was 290 times the chloride permeability coefficient calculated from net salt transport (0.65×10^-8 cm/s). The latter value corresponds to a chloride conductance of 4.2×10^-6 ohm^-1 cm^-2. The chloride permeability coefficient was 2.1×10^-8 cm/s at 25°C (pH 6.8) indicating a value of 3 for the Q₂₅. It appears that normal red cells are anion selective in the sense that anion permeability exceeds cation permeability with a factor of more than a hundred between 0°C and body temperature. The anion exchange, i.e. the Hamburger shift, is a tightly coupled transport process which is several orders of magnitude faster than anion transport by salt diffusion.     

A model of osteoblast-osteocyte kinetics in the development of secondary osteons in rabbits

The kinetics of osteogenic cells within secondary osteons have been examined within a 2-D model. The linear osteoblast density of the osteons and the osteocyte lacunae density were compared with other endosteal lamellar systems of different geometries. The cell density was significantly greater in the endosteal appositional zone and was always flatter than the central osteonal canals. Fully structured osteons compared with early structuring (cutting cones) did not show any significant differences in density. The osteoblast density may remain constant because some of them leave the row and become embedded within matrix. The overall shape of the Haversian system represented a geometrical restraint and it was thought to be related to osteoblast-osteocyte transformation. To test this hypothesis of an early differentiation and recruitment of the osteoblast pool which completes the lamellar structure of the osteon, the number and density of osteoblasts and osteocyte lacunae were evaluated. In the central canal area, the mean osteoblast linear density and the osteocyte lacunae planar density were not significantly different among sub-classes (with the exclusion of the osteocyte lacunae of the 300-1000 μm(2) sub-class). The mean number of osteoblasts compared with osteocyte lacunae resulted in significantly higher numbers in the two sub-classes, no significant difference was seen in the two middle sub-classes with the larger canals, and there were significantly lower levels in the smallest central canal sub-class. The TUNEL technique was used to identify the morphological features of apoptosis within osteoblasts. It was found that apoptosis occurred during the late phase of osteon formation but not in osteocytes. This suggests a regulatory role of apoptosis in balancing the osteoblast-osteocyte equilibrium within secondary osteon development. The position of the osteocytic lacunae did not correlate with the lamellar pattern and the lacunae density in osteonal radial sectors was not significantly different. These findings support the hypothesis of an early differentiation of the osteoblast pool and the independence of the fibrillar lamellation from osteoblast-osteocyte transformation.