Quantifying load-induced solute transport and solute-matrix interaction within the osteocyte lacunar-canalicular system


  • Bin Wang,

    1. Department of Mechanical Engineering, University of Delaware, Newark, DE, USA
    2. Key Laboratory for Biorheological Science and Technology of Ministry of Education, Bioengineering College, Chongqing University, Chongqing, PR China
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    • The first two authors contributed equally to this work.

  • Xiaozhou Zhou,

    1. Department of Mechanical Engineering, University of Delaware, Newark, DE, USA
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    • The first two authors contributed equally to this work.

  • Christopher Price,

    1. Department of Mechanical Engineering, University of Delaware, Newark, DE, USA
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  • Wen Li,

    1. Graduate Program in Biomechanics and Movement Sciences, University of Delaware, Newark, DE, USA
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  • Jun Pan,

    1. Key Laboratory for Biorheological Science and Technology of Ministry of Education, Bioengineering College, Chongqing University, Chongqing, PR China
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  • Liyun Wang

    Corresponding author
    1. Department of Mechanical Engineering, University of Delaware, Newark, DE, USA
    2. Graduate Program in Biomechanics and Movement Sciences, University of Delaware, Newark, DE, USA
    • Center for Biomedical Engineering Research, Department of Mechanical Engineering, 130 Academy Street, Newark, DE 19716, USA
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Osteocytes, the most abundant cells in bone, are essential in maintaining tissue homeostasis and orchestrating bone's mechanical adaptation. Osteocytes depend upon load-induced convection within the lacunar-canalicular system (LCS) to maintain viability and to sense their mechanical environment. Using the fluorescence recovery after photobleaching (FRAP) imaging approach, we previously quantified the convection of a small tracer (sodium fluorescein, 376 Da) in the murine tibial LCS under intermittent cyclic loading. In the present study, we first expanded the investigation of solute transport using a larger tracer (parvalbumin, 12.3 kDa), which is comparable in size to some signaling proteins secreted by osteocytes. Murine tibiae were subjected to sequential FRAP tests under rest-inserted cyclic loading while the loading magnitude (0, 2.8, or 4.8 N) and frequency (0.5, 1, or 2 Hz) were varied. The characteristic transport rate k and the transport enhancement relative to diffusion (k/k0) were measured under each loading condition, from which the peak solute velocity in the LCS was derived using our LCS transport model. Both the transport enhancement and solute velocity increased with loading magnitude and decreased with loading frequency. Furthermore, the solute-matrix interaction, quantified in terms of the reflection coefficient through the osteocytic pericellular matrix (PCM), was measured and theoretically modeled. The reflection coefficient of parvalbumin (σ = 0.084) was derived from the differential fluid and solute velocities within loaded bone. Using a newly developed PCM sieving model, the PCM's fiber configurations accounting for the measured interactions were obtained for the first time. The present study provided not only new data on the micro-fluidic environment experienced by osteocytes in situ but also a powerful quantitative tool for future study of the PCM, the critical interface that controls both outside-in and inside-out signaling in osteocytes during normal bone adaptation and in pathological conditions. © 2013 American Society for Bone and Mineral Research.


Osteocytes, the most numerous cells in bone, play a central role in tissue metabolism1, 2 and the adaptation of bone to its mechanical environment.3 Viable osteocytes are a prerequisite for maintaining bone's proper material properties and structural integrity, as shown by the observations that apoptosis and/or autophagy of osteocytes leads to decreased bone properties in glucocorticoid excess4, 5 and triggers bone turnover in fatigue loading.6, 7 In normal adult bone, osteocytes are thought to serve as the primary sensors of external mechanical signals and the central orchestrators of osteoblastic bone formation and osteoclastic bone resorption.3, 8 During daily physical activities, bone experiences dynamic strains of varying magnitude and frequency.9 These dynamic strains have been hypothesized to induce fluid flows within the lacunar-canalicular system (LCS), the extensive microscopic pore network surrounding the osteocytes.10–13 At the individual osteocyte level, the LCS is constructed from approximately 40 to 100 tubular canalicular channels (∼0.5 µm in diameter and ∼20 to 30 µm in length) containing osteocytic processes that emanate from each ellipsoidal lacunar cavity (∼20 × 10 × 10 µm in the three principle axes) where the osteocyte body is housed.14–16 A pericellular matrix (PCM) containing proteoglycans has been proposed and recently confirmed12, 15, 17, 18 to exist within the annular space between the cell process and canalicular wall and is anchored to the intracellular domain through integrins and focal adhesions.19 It is through these PCM-filled microfluidic channels that mechanical loading drives interstitial fluid to flow and influences osteocyte function through two distinct means. Firstly, because the mineralized bone matrix is largely impermeable, load-induced fluid flow acts to enhance the supply of nutrients (eg, glucose) and disposal of wastes (eg, lactic acid) to and from osteocytes, and thus provides the “life support” to maintain osteocyte viability.10, 20 Secondly, load-induced fluid flow and its secondary effects including shearing stress on the cell membrane,12 drag forces on transmembrane filaments21, 22 and/or focal adhesion complexes involving integrin and the cytoskeleton,23 or streaming potentials acting on ion channels,24, 25 provide potent stimulation to osteocytes, thereby permitting the conversion of external mechanical signals into cellular biochemical responses (ie, mechanotransduction).13, 26 In response to mechanical simulation, osteocytes modulate the secretion of various autocrine/paracrine regulatory molecules such as adenosine-5'-triphosphate, nitric oxide, prostaglandins, osteoprotegerin and its soluble ligand (RANKL), dentin matrix protein-1, sclerostin, and fibroblasts growth factor-23 in vitro or in situ.3, 26 Thus, load-induced convection of both interstitial fluid and solutes (nutrients and signaling molecules) is critical for the control and regulation of osteocyte metabolism, mechanotransduction, and cell signaling.

Quantitative measurement of in situ fluid and solute flow, as well as the properties of the LCS microfluidic environment, has been a challenge in bone because of the presence of a mineralized matrix and the small dimensions of the flow channels. As a result, mathematical modeling has been the primary research tool in the study of bone fluid dynamics.27 Previous models based on bone's poroelasticity have predicted that 1) flow velocity and solute transport increase with loading magnitude;12, 21, 28, 29 and 2) increasing loading frequency increases fluid shear stress12, 21 but decreases solute transport.28, 29 Although previous in vivo tracer perfusion studies30, 31 qualitatively agree with the trends predicted by the theoretical models, the magnitude- and frequency-dependencies of solute/fluid flows have yet to be quantified experimentally. Because of its destructive manner, tracer perfusion technique (requiring sectioning of the bone) provides only static snapshots of tracer localization and cannot be used to compare the effects of various loading conditions on the same samples.32 Thus, noninvasive approaches are needed to track the temporal dynamics of fluid and solute convection in vivo or in situ. To this end, we recently developed a novel in situ approach combining fluorescence recovery after photobleaching (FRAP) imaging and cellular LCS transport modeling, which we have tested through computer simulations and animal studies.29, 33 By irreversibly photobleaching exogenously injected tracer molecules within individual osteocyte lacunae and recording their subsequent fluorescence recovery owing to solute convection and/or diffusion from neighboring lacunae, convection within the canaliculi can be obtained by fitting the experimental data to an LCS transport model built upon measured LCS anatomical parameters. The challenge of imaging loaded murine tibiae in situ was overcome by inserting 4-second resting periods between adjacent loading cycles.33

The first objective of the present study was to quantify the dependencies of load-induced fluid and solute convection on loading magnitude and frequency using a larger tracer (parvalbumin, molecular weight of 12.3 kDa) that is comparable in size to signaling protein molecules relevant to osteocyte cell-cell communication and bone adaptation.3, 34 By using the FRAP approach, we aimed to quantitatively measure the osteocyte's microfluidic environment such as the fluid and solute convection rates under various physiological loading conditions. The delay of the solute velocity relative to the fluid velocity, termed the reflection coefficient, indicated the hindrance effects of the PCM on parvalbumin and other similarly sized proteins. Our quantification of the reflection coefficient represented the first functional measurement of the sieving properties of the submicron-thick “cell coating” that is thought to be a critical component of the osteocyte mechanosensory apparatus.3, 13 The second objective was to use this experimentally measured reflection coefficient, in combination with a mathematical model describing solute-matrix interaction, to infer the structural parameters of the PCM. Despite its descriptive nature, the present study provided not only new quantitative data on fluid flow experienced by osteocytes in situ but also a powerful tool for in vivo investigations of the structure and properties of the PCM, the important cell-matrix interface that controls both outside-in (ie, force transduction) and inside-out signaling (ie, molecular dispersion) in osteocytes.

Materials and Methods

FRAP specimen preparation

Adult 20- to 22-week-old C57BL/6J (B6) male mice (N = 8, The Jackson Laboratory, Bar Harbor, ME, USA) were injected via the tail vein with 2 mg parvalbumin conjugated with Alexa Fluor 488 (Molecular Probes/Invitrogen Corp., Carlsbad, CA, USA) dissolved in 0.5 mL of phosphate-buffered saline (PBS) under inhaled isoflurane anesthesia. In contrast to our previous study,33 older animals were used because their stiffer bones allowed application of larger loads (see the section of the Optical Strain Measurements). We also chose the larger tracer, parvalbumin, in the present study 1) to study the transport characteristics of larger signaling proteins;34 2) to compare against the transport of smaller molecules;33 and 3) to increase the sensitivity to detect load-induced transport enhancement.29 The tracer was allowed to circulate for 2 hours before sacrifice by CO2 inhalation.34 The left tibia was harvested, cleansed of soft/adherent tissues, and tested within 0.5 to 3 hours postmortem. The right contralateral tibiae were immediately frozen, stored, and then thawed before testing. The animal study was approved by the Institutional Animal Care and Use Committee of the University of Delaware.

FRAP experimental protocols

Testing system

Details of the combined loading/imaging system were described previously (Fig. 1 of Price and colleagues33). Briefly, in situ mechanical loading and FRAP imaging of murine tibiae were performed on a custom apparatus consisting of an electromagnetically actuated loading device (Electroforce LM1 Test Bench, Bose Corporation, Eden Prairie, MN, USA) integrated with an inverted confocal laser-scanning microscope (Zeiss LSM 510, Carl Zeiss Inc., Thornwood, NY, USA). A 40 × 0.8 numerical aperture water dipping lens attached to an objective inverter was used to capture images. A relatively flat region of the anterior-medial surface of the tibia (∼25% to 50% distal from the proximal tibial plateau) was imaged in a PBS bath maintained at 37°C. Loads were applied to the distal end of the tibia through the Bose actuator, whereas the proximal tibial plateau was fixed at the reaction bracket where the load magnitude was measured.

Figure 1.

Study design. (A) To study the dependency of solute transport on loading magnitude, murine tibiae were subjected to axial loads at varying peak magnitudes of 2.8 N and 4.8 N while the loading frequency and resting time remained constant (0.5 Hz and 4 seconds). (B) To study the dependency of solute transport on loading frequency, murine tibiae were subjected to axial loads at varying frequencies of 0.5 Hz, 1 Hz, and 2 Hz while the peak loading magnitude and resting time remained constant (2.8 N and 4 seconds). In both studies, all samples were subjected to a static control condition (0.2 N tare load).

Loading protocol

Intermittent cyclic loading with a peak-peak magnitude of 2.8 N or 4.8 N, loading period of 2, 1, or 0.5 seconds (corresponding to a frequency of 0.5, 1, or 2 Hz), and a 4-second resting period were applied to intact tibiae as described previously.33 As highlighted previously,33 the challenge of imaging loaded bone was overcome by 1) the insertion of a 4-second resting period, which has been found to increase bone's anabolic response,35 and 2) the alternating use of the load and displacement feedback control modes to precisely control both the loading magnitude and the position of the bone for imaging. Each loading cycle began with a haversine loading/unloading waveform, followed by a 4-second resting/imaging period.

Imaging protocol

As described previously,16, 33, 34, 36 a cluster of fluorescently labeled lacunae approximately 25 to 40 µm below the tibial periosteal surface were identified. The imaging setup included 488 nm excitation, 505 to 530 nm emission, 512 × 512-pixel images, scanning speed of ∼1 second/frame, in-plane (x-y) resolution of 0.22 µm/pixel, and a pinhole of ∼4.2 to 6.4 Airy units. The FRAP imaging sequence was synchronized with the rest-inserted loading protocol as described previously (Fig. 1C of Price and colleagues33). The imaging/loading sequence repeated itself approximately 40 to 60 times until the fluorescence of the photobleached lacunae leveled off.

FRAP experimental groups

The overall experimental design consisted of a two-part investigation (Fig. 1). In the first part, the magnitude-dependency of solute convection was tested in 7 murine tibiae (n = 5 mice) that were either statically held at the tare load (nonloaded) or compressed intermittently with a loading magnitude (peak-to-peak) of 2.8 N or 4.8 N at a fixed loading frequency of 0.5 Hz (loading period = 2 second, Fig. 1A). One to three lacunae per tibia were chosen to undergo sequential FRAP tests beginning with the 4.8 N loading, followed by the 2.8 N and nonloaded conditions. Repeated FRAP measurements on the same lacunae were utilized to improve detection power by accounting for intrinsic variability among different anatomical locations and samples.33 Trials that exhibited unusually high autofading (>10%) or those showing vertical drifting of the images were excluded from analysis. If drifting was observed during trials under either of the loading conditions, the test sequence was aborted for the particular lacuna, and a different lacuna was chosen for a new sequence. For the second part of the investigation, the frequency-dependence of solute convection was tested in 5 murine tibiae (n = 3 mice) in which the tibiae were subjected to sequential FRAP tests with a fixed peak load (2.8 N) and a loading frequency that was varied from 0.5, 1, 2 Hz, corresponding to a loading period of 2, 1, or 0.5 seconds (Fig. 1B).

FRAP data analysis

The FRAP test sequences were exported from the confocal microscope and analyzed for two outcomes.

Transport enhancement quantification

As described previously,33 time series of 8-bit tiff images from each FRAP sequence were imported into the custom FRAP image analysis program, written in MATLAB (The Mathworks Inc., Natick, MA, USA).16 The time course of fluorescence intensity [I(t)] within the photobleached lacuna, including that before photobleaching [I0], immediately after photobleaching [Ib], and the post-bleach steady-state intensity [I], were calculated. For each FRAP test, the time-dependent intensity recovery data were normalized as equation image and the logarithmic transformation of ln[1-In(t)] was fitted with a linear regression to obtain the transport rate k from the slope of the fitting line equation image. The transport enhancement for each loaded case was calculated relative to the nonloaded case in the same lacuna (k/k0). The averaged anatomical parameters for all studied lacunae were also summarized and imported into the three-compartment model detailed below.

Solute velocity calculation

A three-compartment LCS transport model29 was customized to simulate transport enhancement for each input solute velocity as described previously.33 Briefly, the model consisted of three compartments representing the photobleached lacuna and two neighboring reservoirs (Fig. 2 of Price and colleagues33). In this LCS transport model, the model parameters were obtained from the pre-bleach FRAP images or data from the literature.15, 16 Given a range of peak solute velocities and the known diffusivity of parvalbumin in the LCS (D = 157.4 µm2/s),34 the temporal parvalbumin concentration profiles within the photobleached lacuna were simulated computationally29 and the transport enhancements (k/k0) calculated. The solute velocities corresponding to the observed transport enhancements within the FRAP experiments, vs, were obtained.

Figure 2.

(A) The osteocyte PCM model contained 1/3 of the fibers (solid lines) oriented in the direction of the fluid flow (right arrows), termed the longitudinal array, and 2/3 of the fibers (dashed lines) perpendicular to the fluid flow, termed the transverse array. (B) A periodic fluid unit (dashed circle) was created to derive the fluid flow field around the fiber. The area of the periodic unit was equal to the average area each fiber occupies in the flow's cross-section plane.

Optical strain measurements

The mice used in this study were 2 to 4 weeks older than those in our previous study,33 and thus the compliance of the tibiae was quantified in a separate set of 5 tibiae using the optical strain measurements described previously.20 Briefly, the tibiae were speckled with Yellow-Green FluoSpheres (10-micron, Invitrogen) and subjected to incrementally increasing uni-axial compressive loads (up to 6 N in 1-N steps). At each specified load level, 10 images (2584 × 500 pixels, 1.26 µm/pixel) were captured using a CCD camera (∼0.5 s/frames) through a 2.5× objective (EC-Epiplan-NEOFLUR, Carl Zeiss, Inc.). Axial strain was quantified between two manually chosen speckle patterns using a digital image correlation algorithm (IMAQ Vision Builder, National Instruments, Austin, TX, USA). The mean compliance of the tibiae was obtained by linear regression on the strain versus load curves.

Reflection coefficient determination

The reflection coefficient (σ = 1–vs/vf) characterizes the hindrance of the solute velocity (vs) relative to that of fluid velocity (vf) owing to the steric and hydrodynamic interactions between solutes and the PCM fibers in the LCS. The fluid flow velocity vf, previously measured using a very small tracer (sodium fluorescein, Stokes radius ≈0.45 nm) was 58.9 µm/s for a surface strain of 477 µε at a loading frequency of 0.5 Hz and 4-second resting period.33 In the present study, we measured the velocity of parvalbumin (Stokes radius = 1.31 nm),34 vs as a function of various loading magnitudes at 0.5 Hz with a 4-second resting period (detailed in the Results section). The solute velocity vs for the same surface bone strain (477 µε) was obtained by interpolating the current experimental data.

Osteocyte PCM's sieving model

Although the fibers in the osteocyte PCM are likely distributed in three dimensions with some degrees of randomness, the PCM was approximated herein as an orthogonal fiber network composed of 1/3 longitudinal fibers and 2/3 transverse fibers relative to the fluid flow direction (Fig. 2A). The fibers were modeled as a single species of cylinders with uniform radius (rf).

The longitudinal fiber array

In this case, the fibers were oriented along the flow direction, forming a periodic array with uniform fiber spacing. The reflection coefficient of a hexagonally ordered fiber array has been solved by Zhang and colleagues37 using a periodic flow unit approach (Fig. 2A), where solutes were absent from the space immediately surrounding the fibers because of steric exclusion. The reflection coefficient was calculated as one minus the ratio of the solute flux and the fluid flux over the unit flow cross-sectional area. The result was adapted in our study for a square array:

equation image(1)

where α = rs/R, β = rf/R, rs was the solute radius, and R was the radius of the periodic unit surrounding a fiber (Fig. 2B) and estimated from the total volume fraction of the PCM (kvf) as R = rf(kvf/3)−0.5.

The transverse fiber array

In this case, the fibers were arranged perpendicular to the flow direction periodically. As in the longitudinal fiber array, a periodic unit flow surrounding each individual fiber was constructed (Fig. 2B). Using the general solution of the flow field obtained by Happel,38 we obtained the close-form radial and circumferential velocities, which satisfied the following boundary conditions: at the fiber surface, both the radial and circumferential velocities were zero (no-slip boundary conditions); at the periodic unit surface, the radial velocity was equal to the radial velocity at infinity and the fluid shear stress was zero. The reflection coefficient owing to the solute-fiber steric exclusion effect was obtained as:

equation image(2)

The reflection coefficient of the osteocyte PCM

The sieving effect of the PCM was the weighted average of the longitudinal and transverse fibers:

equation image(3)

It is noted that the reflection coefficient is fully determined from the solute size, fiber size, and fiber volume fraction (or the fiber spacing). Details of the derivations can be found in the Supplemental Material (Appendix) published online.

Osteocyte PCM's plausible configurations

The ranges of fiber volume fractions in the osteocyte PCM that matched the measured reflection coefficient of parvalbumin were derived using the above PCM sieving model. The solute radius (1.31 nm) of parvalbumin was determined using the Einstein-Stokes equation.34 Because the species and identities of the fibers in the osteocyte PCM have not been fully identified the fiber size was estimated for several possible candidates, including the glycosaminoglycan side chain (0.5 nm radius),12 globular core proteins of aggrecan and hyaluronic acid (1 to 2 nm radius),39 as well as the repeated endothelial glycocalyx structure seen in the cryo electron microscopy (4 to 6 nm radius).40, 41 For each candidate fiber, the corresponding osteocyte PCM fiber volume fraction that gave rise to the measured reflection coefficient was obtained by numerically solving equations 1 through 3.

Statistical analysis

All statistical analyses and regressions were performed using the Prism software package (GraphPad Software, La Jolla, CA, USA). A paired Student's t test was used to detect differences in transport enhancement between the two loading magnitudes, followed by a one-sample t test and a Wilcoxon signed rank test against a hypothetical transport enhancement of one (the pure diffusion, nonloaded condition). One-way ANOVA analyses followed by Bonferroni's multiple comparison tests were performed to detect significant differences among groups with varying loading frequencies. The significance level was set at p < 0.05.


Effects of the loading magnitude

Twelve lacunae successfully underwent a series of FRAP tests in the presence of intermittent cyclic compression of varying loading magnitudes, 4.8 N, 2.8 N, and 0 (nonloaded condition). The loading frequency and resting period were kept constant (0.5 Hz and 4 seconds, respectively). In a representative FRAP experiment (Fig. 3), the normalized fluorescence recovery ratio demonstrated faster exponential increase with increasing loading magnitude (Fig. 3A), which was more pronounced after the logarithmic transformation of the fluorescence data (Fig. 3B). The rates of transport (k), defined as the slopes of lines fitting the transformed data (Fig. 3B), were normalized with that of nonloaded condition (k0) to demonstrate the enhancement in solute transport (Fig. 3C). For the 12 lacunae tested, the transport enhancement increased significantly from 1.31 ± 0.16 to 1.50 ± 0.23 when the loading increased from 2.8 N to 4.8 N peak load, respectively (p < 0.05). The transport enhancements under either loading magnitude were significant when compared with the nonloaded condition (transport enhancement of 1.0; p < 0.05). A linear relationship (R2 = 0.998) was found between the mean transport enhancement and the loading magnitude:

equation image(4)
Figure 3.

Effects of loading magnitude on the transport of parvalbumin in the bone LCS. (A) Representative plots of normalized fluorescence recovery ratio [In(t) = [I(t) − Ib]/(I∞ − Ib)] of the same target lacuna sequentially subjected to FRAP under varying peak loading conditions (0, 2.8 N, 4.8 N). The experimental data fit very well with nonlinear regression curves (y = 1–e-kt) where k was the transport rate. (B) Increasing load magnitude increased solute transport rate (k) during the FRAP experiment, which is readily seen in the greater slopes of the linear fits of the logarithmic transformation of the [1 − In (t)] for these representative tests. (C) Mean transport enhancement (k/k0) (n = 12 lacunae) increased linearly with increasing loading magnitude (y = 0.107x + 1.0, R2 = 0.998).

Effects of the loading frequency

Ten lacunae successfully underwent a series of FRAP tests under loading conditions where the loading frequency was varied from 0.5, 1, to 2 Hz as well as a nonloaded condition. The loading magnitude and resting period were kept constant (2.8 N peak-load and 4 seconds, respectively). Transport enhancement decreased from 1.32 ± 0.09, 1.19 ± 0.09, to 1.14 ± 0.11 when the loading frequency increased from 0.5 Hz, 1 Hz, to 2 Hz, respectively (Fig. 4). Significance differences in transport enhancement were detected between the cases of 0.5 Hz versus 1 Hz and 0.5 Hz versus 2 Hz. All three loaded conditions showed significant enhancement in transport compared with the nonloaded static condition using both a one-sample t test and a Wilcoxon matched pairs signed rank test (p < 0.05).

Figure 4.

Effects of loading frequency on solute transport enhancement in the bone LCS. Enhancement tended to decrease with increasing loading frequency (n = 10 lacunae). Significant differences (p < 0.05) were detected among all pairs except 1 Hz versus 2 Hz.

Surface strains on the loaded tibiae

Using a separate set of 5 tibiae from similarly aged B6 mice (20- to 22-week-old, n = 5), the corresponding surface strains during tibial end compression were optically measured on the anteriomedial surface, the same location utilized in the FRAP measurements described earlier. Measured strains were found to be linearly related to the applied load (R2 = 0.98, Fig. 5):

equation image(5)
Figure 5.

Average tibial surface strain increased linearly with increasing axial load (y = 106.33x, R2 = 0.98) as measured on a separate set of male B6 murine tibiae (n = 5, 20 to 22 weeks old).

The surface strains induced by 2.8 N and 4.8 N loading of the tibia were 298 µε and 510 µε, respectively.

Solute velocities in the bone LCS

Using the LCS parameters found in this and previous studies (listed in Table 1), the simulated transport enhancements (k/k0) at various solute velocities vs (0 to 80.6 µm/s) were obtained (Fig. 6), showing an overall power relationship (k/k0 = 1 + 0.000373 ûvmath image, R2 = 0.99 and vs in the unit of µm/s). Interpolating the data shown in Fig. 6, the mean velocity of parvalbumin convection through the LCS canaliculi under different loading magnitudes and frequencies was found (Table 2). For the 4.8 N loading at 0.5 Hz, the mean solute velocity was 55.8 µm/s. As the loading magnitude decreased to 2.8 N, the solute velocity was reduced to 43.1 µm/s. Further reduction in the solute velocity was seen when the loading frequency was increased from 0.5 Hz to 1 and 2 Hz (Table 2).

Table 1. Parameters Used in the LCS Transport Model
Canalicular length d (µm)Lacunar major radius a (µm)Lacunar minor radius b (µm)Contributing canalicular number nExtracellular canalicular cross-sectional area AC (µm2)Extracellular lacunar cross-sectional area AL (µm2)Diffusivity in LCS (µm2/s)Solute velocity (µm/s)
  • a

    Calculated as 22% of the total number of canaliculi that resided outside of the photobleaching laser cone.16

  • b

    Calculated using the contributing canalicular number and the measured annual fluid cross-sectional area between cell process and the canalicular wall in a single canaliculus.15

  • c

    Calculated using the gap between the lacunar wall and cell body (0.23 µm) based on our electron microscopy data (unpublished data).

  • d

    Measured previously.34–80.6
Figure 6.

Simulated transport enhancements at various solute velocities (0 to 80.6 µm/s) using the three-compartment transport model with experimentally derived anatomical parameters (Table 1) in loaded murine tibiae. The transport enhancement followed a power relationship with the solute velocity (y = 1 + 0.000373x1.787, R2 = 0.99).

Table 2. Peak Solute Velocity in the Bone LCS Obtained at Different Load Conditions
Load magnitude (N)Frequency (Hz)Peak surface strain (µε)Sample size (n)Transport enhancement (TE: mean ± SD)Solute velocity for mean TE (µm/s)Velocity range for TE-SD to TE + SD (µm/s)
4.80.5510121.50 ± 0.2355.840.0–69.3
2.80.5298221.31 ± 0.1643.129.5–53.9
2.81298101.19 ± 0.0933.324.0–40.8
2.82298101.14 ± 0.1128.513.1–38.5

Reflection coefficient in the PCM

The fluid velocity was found to be 58.9 µm/s under an intermittent loading of 477 µε, based on the FRAP measurements of sodium fluorescein reported earlier.33 From our measurements of the TEM images of lacunae, we found the gap between the lacunar wall and the cell membrane to be 0.23 µm instead of the 1 µm assumed in our earlier study.33 The transport model was modified accordingly with an improved accuracy in the present study (Table 1) for calculating the velocity data reported herein. The solute velocity (vs = 53.9 µm/s) for the strain level of 477 µε was derived by using equations 5 and 4 and interpolating the data in Fig. 6, yielding a reflection coefficient of parvalbumin through the osteocyte PCM of σf = 1–vs/vf = 0.084.

Theoretical predictions of the PCM's sieving behaviors

The effects of the solute size, fiber size, and fiber volume fraction on the reflection coefficient were assessed (Fig. 7) using the sieving model. For a given solute radius (rs = 1 nm in this example), the reflection coefficient was found to increase nearly linearly with the fiber volume fraction (from 0.5% to 10%) and decrease with the fiber radius (Fig. 7A). The reflection coefficient for a solute passing through the osteocyte PCM increased dramatically with the solute size rs and decreased with the fiber radius rf (the fiber volume fraction = 5%, Fig. 7B). It is noted that for a given fiber volume fraction, larger fiber radius was associated with larger fiber-fiber spacing and thus decreased reflection coefficient (Fig. 7A, B).

Figure 7.

The reflection coefficient of the PCM as a function of fiber radius rf, solute radius rs, and fiber volume fraction kvf. Three different values of fiber radius (0.5, 1, and 2 nm) were chosen for parametric study using equations 1 to 3. (A) The fiber volume fraction was varied from 0% to 10% with the solute radius set at 1 nm; (B) the solute radius was varied with the fiber volume fraction set at 5%.

Plausible osteocyte PCM configurations

The plausible fiber volume fraction kvf of the osteocyte PCM was estimated based on the reflection coefficient of parvalbumin (0.084) measured in the experiments. The radius of parvalbumin was known (rs = 1.31 nm).34 For fiber candidates of various radii (0.5, 1, 1.5, 2, 4, to 6 nm), the fiber volume fraction that matched the experimental reflection coefficient was 0.4%, 1.9%, 4.3%, 7.5%, 25.5%, and 44.5%, respectively (Fig. 8). In a square array configuration, these data would correspond to a fiber edge-to-edge spacing (= 2R2rf) of 26.4, 23.1, 22.1, 21.3, 19.4, and 19.2 nm, respectively.

Figure 8.

The fiber volume fraction kvf of the PCM was estimated using the PCM sieving model (equations 1 to 3) to match the measured reflection coefficient for parvalbumin (0.084). Because of the unknown identity and size of the PCM fibers, different fiber radii were selected and varied from 0.5 to 6 nm.


The present study illustrated the power of FRAP imaging approaches for quantifying the microfluidic environment experienced by osteocytes under mechanical loading. The demonstrated capability of probing the interactions between the signaling molecules and the submicron-thick osteocyte PCM may help advance the study of osteocyte mechanotransduction, which is currently performed mostly in vitro, to in situ and in vivo conditions. Load-induced fluid flow within the bone LCS serves as not only an important transport enhancement mechanism in bone but also a potent stimulation for bone cells.13 Despite its physiological importance, in situ quantification of bone fluid flow under physiologically relevant loading conditions had until recently been unresolved.33 By synchronizing confocal imaging with intermittent cyclic mechanical loading, we have used FRAP, a laser perturbation method, to quantify the convection of parvalbumin, a protein tracer (12.3 kDa) that represented similarly sized signaling molecules (such as sclerostin, osteoprotegerin, and its soluble ligand [RANKL]),3, 34 through the bone LCS. This investigation elucidated how loading magnitude and frequency controlled the transport of parvalbumin, as well as how the applied loading conditions (300 to 500 µε at 0.5 to 2 Hz) influenced solute convective speed within the osteocyte canaliculi. By comparing the current solute velocity data to fluid velocity data previously obtained using a much smaller tracer,33 we estimated the reflection coefficient of parvalbumin in the bone LCS to be 0.084. To our knowledge, this is the first in situ measurement of the molecular interactions between large proteins like parvalbumin and the osteocyte PCM, a key component in bone mechanotransduction.13 Furthermore, this measurement allowed us to explore possible configurations and properties of the PCM.

The magnitude- and frequency-dependent behaviors of fluid flow found in this study bridge a gap in our understanding of bone adaptation at the tissue level and mechanotransduction at the cellular level. Although the anabolic effect of mechanical loading on bone has long been accepted as a general rule (Wolf's law), the specific loading parameter(s) responsible for these effects remain less well defined. Two specific loading parameters, load magnitude and frequency, have been the foci of in vivo bone adaptation experiments.42 Since the pioneering work of Lanyon and Rubin using strain gages,43–47 quantitative studies of in vivo bone formation under controlled mechanical loading revealed a complicated phenomenon with the following key observations: 1) dynamic loading was more anabolic than static forces,44 and a small number of loading cycles can counter disuse-induced bone loss45 with higher frequencies/strain rates inducing increased protection;48–50 2) thresholds for anabolic responses in bone appear to depend on strain magnitude and strain rate,51 which may vary with genetic background,52 site, and age;53, 54 and 3) insertion of resting periods between cycles increased anabolic responses to loading.35, 55 These in vivo experiments demonstrated a complex nonlinear relationship between loading magnitude/frequency and anabolic activities.51 In parallel, at the tissue and cellular level, tissue histology/immunohistochemistry and in vitro cell culture studies have established that 1) osteocytes are the putative mechanosensors within bone; 2) load-induced fluid flow and its secondary effects trigger osteocyte responses that coordinate bone resorption and formation;56 and 3) both the frequency and magnitude of applied mechanical stimulation (in term of fluid flow shear stress) regulate the release of secondary messengers (eg, intracellular calcium and extracellular ATP) and the expression of regulatory genes and proteins in the SOST/sclerostin/Wnt and RANKL/OPG pathways.26 However, the lack of knowledge regarding the links between tissue strains and their resultant cellular level signals (eg, fluid flows for mechanosensing and solute flows for cell-cell signaling) poses a great barrier to the prescription of patient-specific exercise regimens and the exploitation of their full anabolic potentials in treating bone diseases such as osteoporosis and bone loss.

This study aimed to overcome this barrier by quantifying the magnitude- and frequency-dependencies of load-induced convection through the bone LCS, and comparing these data with previous theoretical and experimental findings. We found that for the range of strains tested in this study (≤510 µε under ≤4.8 N compressive end load)) transport enhancement increased linearly with peak strain (k/k0 = 1 + 0.001 × Strain [µε], based on equations 4 and 5) and declined with increasing load frequency (Fig. 4). These findings agree with the predictions from our two-level poroelastic model.29 Although the intermittent loading regime used in our investigations was different from the sinusoidal loading utilized in previously tracer perfusion studies,30, 31 comparable trends for solute flows as a function of loading magnitude and frequency were observed. These results suggest that the transport needs required for optimal cell metabolism and cell mechanosensing are not fully aligned. For a given load magnitude, higher frequencies decrease the efficiency of solute transport through convection (Fig. 4) but increase fluid-flow stimulation to bone cells, which has been thought to account for the prevention of bone loss using high-frequency loads and vibrations (f∼10 to 50 Hz).48, 49 However, it is clear from this study that high-frequency loads do not enhance the exchange of signaling molecules among osteocytes (Table 2). It is tempting to ask whether there exists an optimal frequency domain where both needs are satisfied and maximal bone formation achieved. Indeed, maximal in vivo bone formation was found in animal bones subjected to a frequency of 5Hz compared with 1 and 10 Hz.51 Alternatively, the diverse needs of the osteocyte may be met by the broad spectrum of mechanical strains consisting of a limited number of large-magnitude, low-frequency events and numerous low-magnitude, high-frequency events during daily activities.13, 42

Another important contribution of this study is the development of a combined in situ and analytical toolset to study the osteocyte PCM, a critical component in mechanosensing and cell-cell signaling. The presence of a pericellular matrix around osteocytes, similar to endothelial glycocalyx, was first proposed nearly two decades ago by Weinbaum and colleagues12 to explain the surprisingly long relaxation times measured in strain-induced streaming potentials.57 Subsequent electron microscopic studies revealed the existence and certain features of such a matrix including the presence of both periodic transverse tethering fibers15 and perlecan, a large heparin sulfate proteoglycan.17 Filling the annular fluid space between the canalicular wall and cell process, the gel-like PCM has the ability to control mass32, 58 and fluid transport12 in the LCS. The osteocyte PCM has also gained much appreciation in its involvement in force transfer and mechanosensing.22, 23 The chemical composition and ultrastructure of the osteocyte PCM, however, remain poorly understood, primarily because of its enclosure within the mineralized bone matrix, its small dimension (∼100 nm in thickness), and the difficulty in its preservation.15, 17 Although the PCM can be visualized under an electron microscope after tedious chemical preparations, the images are two-dimensional projections with a finite thickness, making it difficult to truly assess the structural details and functions of the PCM. The present study provided a promising in situ, and potentially, in vivo approach for probing the structure and function of the PCM.

As demonstrated in the present study, we were capable of measuring the hindrance of the PCM on the transport of a large protein using FRAP imaging and explored the PCM structure using the PCM sieving model. Whereas a PCM sieving effect has been identified in tracer perfusion experiments32, 58 and our previous FRAP diffusion studies,16 no quantitative relationship has been established between the structure and function of the PCM until now. Despite the fact that the PCM (on the order of 100 nm thick)15 exists beyond the resolution of the light microscopy, we were able to detect its sieving effect on the movement of large proteins. The key to this success is due to beautiful design of the LCS, in which numerous discrete channels (up to 100 in mice) filled with PCM connect to individual lacunae.16 Although the PCM and canalicular channels are “invisible” under the confocal microscopy, individual lacunae (on the order of 10 microns), and their changes in solute concentration (fluorescence intensity) are readily imaged, permitting the observation of the canaliculi's collective draining effect. Because the overall anatomical features of the LCS (ie, the lacunar volume, the number, length, and size of canaliculi) could be established experimentally,16 the velocities of the fluid and solute in the discrete channels, and subsequently, the reflection coefficient could be obtained from the experimental confocal data.33 Furthermore, the current sieving model of the osteocyte PCM provided a powerful tool for analyzing osteocyte PCM structure. As a first-order approximation, we decomposed the osteocyte PCM into three orthogonal square arrays with the fibers oriented either parallel with or perpendicular to the flow direction. Using the sieving model, the PCM fiber configurations accounting for the measured reflection coefficient were explored for several PCM fiber candidates of varying radii (0.5 to 6 nm). It was found that the fiber volume fraction varied greatly (0.5% to 50%), whereas the fiber edge-to-edge distance varied in a narrower range (26 to 19 nm). The ability to measure reflection coefficient and infer the fiber arrangement will greatly help future quantitative examination of fluid flow stimulation on osteocytes in situ and in vivo.

The present study is limited in several respects. Regarding the FRAP experiments, although the loading magnitude and frequency were varied, the studied ranges (maximal 510 µε and 2Hz) comprised only a small segment within the much broader spectrum of the in vivo loading conditions.9 The largest load used in this study was 4.8 N, which was lower than the typical tibial axial loads (∼7 to 13 N) used to induce anabolic bone formation in animals.59, 60 The small load magnitude was adopted in the study mainly because of the imaging limitations in our current setup, where the load was applied at one end of the bone using an actuator. Applying larger loads sometimes caused the region of interest to move out of the image window (about 300 microns). Using two actuators at both ends of the bone may help to overcome this shortcoming. We also limited the loading frequency to 2 Hz because it was difficult to control the loaded bone returning to the equilibrium position under higher frequencies. With the advances of high-speed imaging techniques, we anticipate that a larger dynamic range of loading conditions would be feasible in the future. Another limitation was that the current quantification of solute reflection coefficient required two separate FRAP studies: one with a small tracer (for fluid velocity measurements) and another with a larger solute (for solute velocity measurements), respectively. As a result, variability among the different animals and lacunae under investigation might have introduced some uncertainty to the reflection coefficient estimation. We are currently testing techniques to measure both fluid and solute velocities simultaneously using two different-colored tracers and FRAP imaging. For the reflection coefficient modeling, to obtain an analytical first-order approximation of the PCM's sieving properties, simplifications were made such as the use of a highly idealized fiber orientation (neglecting more complex pore structures), the adoption of single-fiber species in any given PCM, the assumption of rigid and stationary fibers, and the sole consideration of steric exclusion between solutes and fibers. Other biochemical and electrical interactions were not considered because of the observations in both bone and cartilage that solute size was the principle factor in determining transport rate.34, 61 Previous modeling of strain magnification in bone has shown that the PCM fibers were expected to experience <10% strain under a typical 2000 microstrain of loading at the whole bone level.15 The effects of fiber deformations on the steric exclusion between the fibers and solutes are anticipated to be small if the deformations are relatively uniform along the canaliculi (with no apparent change in pore size and geometry). This assumption will be tested experimentally by performing the reflection coefficient measurements at different loading magnitudes with varying PCM deformations. The effects of random fibers and hybrid fiber species are not known and are currently being evaluated using Monte-Carlo simulations.62

In conclusion, the present study provided new quantitative data on the transport of large protein molecules in the bone LCS. Using FRAP imaging, we found that the transport enhancement and solute velocity increased with loading magnitude and decreased with loading frequency. The quantitative relationships established herein help to bridge a knowledge gap between tissue adaptation and cellular response. Furthermore, solute-matrix interaction, in terms of reflection coefficient through the osteocytic PCM, was measured (σ = 0.084) and theoretically modeled. Plausible PCM configurations accounting for the measured interactions were obtained for the first time. This powerful quantitative tool will assist future studies of the PCM, the critical cell-matrix interface that controls both outside-in and inside-out signaling in osteocytes during normal bone adaptation and in pathological conditions.


All authors state that they have no conflicts of interest.


The study was supported by the following funds: NIH AR054385 and P20RR016458 (LW); China CSC Fellowship (BW); and NSF of China 10972243 (JP).

Authors' roles: Study design: BW, XZ, CP, and LW; Data collection: XZ for mathematical modeling; BW, CP, and WL for experimental data; Data and statistical analysis: BW, XZ, CP, and LW; Data interpretation and manuscript drafting: BW, XZ, CP, JP, and LW; Manuscript revising: BW, XZ, CP, WL, JP, and LW. LW takes responsibility for the integrity of the data analysis.