Annals of Biomedical Engineering

, Volume 43, Issue 4, pp 1036–1050 | Cite as

Mechanical Stimulation of Bone Marrow In Situ Induces Bone Formation in Trabecular Explants

  • E. Birmingham
  • T. C. Kreipke
  • E. B. Dolan
  • T. R. Coughlin
  • P. Owens
  • L. M. McNamara
  • G. L. Niebur
  • P. E. McHugh


Low magnitude high frequency (LMHF) loading has been shown to have an anabolic effect on trabecular bone in vivo. However, the precise mechanical signal imposed on the bone marrow cells by LMHF loading, which induces a cellular response, remains unclear. This study investigates the influence of LMHF loading, applied using a custom designed bioreactor, on bone adaptation in an explanted trabecular bone model, which isolated the bone and marrow. Bone adaptation was investigated by performing micro CT scans pre and post experimental LMHF loading, using image registration techniques. Computational fluids dynamic models were generated using the pre-experiment scans to characterise the mechanical stimuli imposed by the loading regime prior to adaptation. Results here demonstrate a significant increase in bone formation in the LMHF loaded group compared to static controls and media flow groups. The calculated shear stress in the marrow was between 0.575 and 0.7 Pa, which is within the range of stimuli known to induce osteogenesis by bone marrow mesenchymal stem cells in vitro. Interestingly, a correlation was found between the bone formation balance (bone formation/resorption), trabecular number, trabecular spacing, mineral resorption rate, bone resorption rate and mean shear stresses. The results of this study suggest that the magnitude of the shear stresses generated due to LMHF loading in the explanted bone cores has a contributory role in the formation of trabecular bone and improvement in bone architecture parameters.


Trabecular bone Bone marrow Shear stress Low magnitude high frequency loading Vibration Mechanobiology 


Bone is a dynamic material that is capable of adapting its structure, composition and mass in response to functional demands from mechanical loads. Studies have elucidated the relationship between strain in the bone and bone adaptation, by demonstrating removal of mineralised tissue from regions where mechanical loads are low, and, conversely, new tissue deposition and micro-architecture adaptation in regions subjected to repeated high mechanical strain.9,15,16,40,45 More recently, small mechanical loads [<10 micro-strain (µε)] applied at high frequencies (10–100 Hz),30 viz. low magnitude high frequency (LMHF) loading, have been shown to have an anabolic effect on bone tissue.46 Sheep subjected to LMHF vibration with an acceleration of 0.3 g peak–peak demonstrated increased bone volume, bone mineral content and trabecular number.48,49 Similarly, bone loss was halted in the spine and femur in post-menopausal women exposed to LMHF loading of 0.2 g at 30 Hz for less than 20 min a day compared to controls who used placebo loading devices.50 LMHF loading has also been found to inhibit bone resorption in a growing mouse skeleton.60 While the benefit of such loading regimes has been demonstrated in various human 32,50,57 and animal models,23,29,4648,60 the mechanical signals that are transmitted to bone cells to stimulate the biological response remain unclear and are not fully understood.

The measured bone strains associated with LMHF vibration can be less than 10 µε.29,46,48 In contrast, peak strains of 2000–3000 µε have been reported to be induced during typical physiological activities such as running or jumping, which are known to lead to bone growth and remodelling.10,38 Therefore, it is unclear whether the small strains occurring in LMHF vibration are sufficient to explain its anabolic effects. Interestingly, increasing the frequency of the LMHF signal from 45 to 90 Hz results in greater increases in both bone volume and trabecular thickness, but the higher frequency does not generate higher bone strain.30 Furthermore, the anabolic effects of LMHF loading (0.3 or 0.6 g at 45 Hz) have been observed in trabecular bone in non-load bearing applications.23 Taken together these studies suggest that the response of bone tissue to LMHF vibration is not driven by the bone strain. This study proposes that shear stress generated within the bone marrow due to LMHF loading is the driving factor behind the anabolic response.

LMHF loading has the greatest effect on bone formation in regions rich in trabecular bone. Trabecular bone is a porous structure filled with bone marrow, which is home to a host of cells including hematopoietic progenitors that can differentiate to blood cells, immune cells, and osteoclasts, and MSCs, which are precursors of fibroblasts, endothelial cells, adipocytes and osteoblasts.35 However, the mechanical environment of trabecular bone marrow remains poorly characterised.26 It alters with aging and conditions such as osteoporosis44 due to an increase in the adipose fraction of marrow.31,59 The low levels of bone strain during LMHF loading, in addition to the sensitivity of marrow cells to such loading, suggest that bone marrow is instrumental in the transmission of the mechanical signals to MSCs. However, other studies have questioned the effectiveness of LMHF loading and whether it is an isolated effect within bone. For example LMHF loading (0.6 g at 45 Hz) did not attenuate bone loss in mouse muscle disuse models.39 Similarly, no bone growth was found in ovariectomized rats exposed to LMHF loading (0.3 g at 90 Hz).7

The position of marrow within the trabecular bone structure suggests that LMHF loading is likely to induce inertial motion in the marrow, possibly generating shear stresses and thereby affecting the resident cells.14 MSCs exposed to shear stress in vitro exhibit increased proliferation,43 expression of osteogenic differentiation markers,25,34 and inhibition of adipogenic markers.33 However, the influence of shear stress in vivo remains unknown. Computational and numerical models have been used to predict shear stress generated within trabecular bone marrow due to LMHF vibration and compression.5,14,19 An analytical continuum level mixture theory19 predicted shear stresses (~0.5 Pa) in trabecular bone during cyclic low amplitude strains. Three-dimensional finite element (FE) models of marrow within realistic trabecular structures14 showed that there is sufficient shear stress generated within the marrow during LMHF to stimulate MSC osteogenic differentiation.

In vitro studies of trabecular bone explants21,28 have been used to examine bone formation in response to compression of the bone matrix and have shown the viability of cells within the bone and marrow.17,18,38 Greater bone growth was found in samples exposed to the mechanical loading compared to static samples,17,38 reproducing the in vivo effects of mechanical strain on bone growth. However, such approaches have not yet been applied to investigate the anabolic response of bone to LMHF loading.

The first hypothesis of this study was that the anabolic effect of LMHF loading is characterised by an increase in trabecular bone architecture quality and quantity. This hypothesis was tested using porcine trabecular bone explants, with marrow in situ, which were stimulated by LMHF loading in a custom bioreactor. The bone explants were scanned pre and post stimulation by micro computed tomography (µ-CT), and images were registered to determine how the bone volume and architecture changed over the course of stimulation. Flourochrome dyes were also used to label newly formed bone.

The second hypothesis of this study was that the trabecular bone volume and architecture were related to shear stress generated in the marrow due to LMHF loading. The pre-experiment µ-CT scans of the bone explants were used to create FE meshes of the experimental samples and computational fluid dynamics (CFD) models were solved to determine the shear stress generated within the bone marrow specific to each experimentally LMHF loaded sample. This allowed for the exploration of the relationship between shear stress in the marrow and bone formation and remodelling.

Materials and Methods

LMHF Bioreactor Design

A custom built bioreactor chamber was used to apply LMHF loading to live trabecular bone explants in vitro. The chamber holds three bone explants in individual chambers firmly in place between two flat platens on threaded bars (Fig. 1). Media was perfused through the chamber within a 1.5 mm annular space surrounding the explant. The media was pumped at constant speed of 0.9 mL/min through the chamber using a peristaltic pump (Ismatec, REGLO) with gas permeable PharMed Ismaprene tubing (Ismatec). The entire chamber was subjected to a controlled sinusoidal acceleration with a peak of ±0.3 g at 30 Hz using a linear voice coil actuator (H2W Technologies), which provides a short stroke with closed loop position control. The motor was controlled with a programmable motor controller (Elmo Motion Control) (Fig. 1).
Figure 1

(a) LMHF Bioreactor with bone explants in place in the chamber, showing media being pumped from media reservoirs into the individual explants, and two chambers attached to the actuator. (b) Schematic of a chamber with bone explants in place detailing the media path

Bone Tissue Culture

Porcine vertebrae (C1–C6) were obtained from the slaughterhouse within 2 h of slaughter. Bone explants were harvested in an approach similar to previous studies.18,38 Working in sterile conditions, skin, muscle and flesh were removed, and the vertebrae were dissected apart. The superior endplates were cut off to reveal the trabecular bone beneath. Using a diamond coring drill (Starlite Industries, Rosemount, PA), 8 mm diameter trabecular bone explants 15–20 mm long were prepared from C2 to C6. All cutting was performed under constant irrigation using ice cold Dulbecco’s Phosphate Buffered Saline (PBS, Sigma Aldrich) and 5% Antimycotic-Antibiotic (AB-AM, Sigma Aldrich). Bone explants were stored in cold PBS with AB-AM until parallel ends were cut using a low speed diamond saw (Buehler, Lake Bluff, IL) to approximately 10 mm lengths. Bone explants were placed in media containing Dulbecco’s Modified Enriched Media (high glucose, DMEM, Sigma Aldrich), 10% Fetal Bovine Serum, 2% AB-AM, 20 mM β-glycerol phosphate and 50 µM ascorbic acid-2-phosphate (AA2P) and were imaged by µ-CT (Scanco µ-CT-80, Brüttisellen, Switzerland) at 20 µm isotropic resolution using a 70 kVp x-ray source at 114 mA and 200 ms integration time in a sterile fixture holder containing the same media as mentioned above. The samples were thresholded after applying Gaussian filter with a standard deviation of 0.7 and support of ±2 voxels. A constant threshold was used to segment bone and marrow. This threshold was approximately midway between the background and bone peaks of the intensity histogram. The selected value corresponds to 136 (mg Ha)/cc based on the scanner calibration. The threshold was chosen the same for all scans, and for both the pre- and post-scan, to avoid introducing a bias.

LMHF Experimental Approach

Trabecular explants were divided into three experimental groups. (1) Static (n = 5): explants were cultured in 6 well plates with 10 mL of media. (2) Flow (n = 3): explants were placed in the bioreactor chamber, where media was circulated through the chamber at a slow flow rate of 0.9 mL/min to provide circulating media but not perfusion through the sample. (3) Vibrated (n = 7): Explants were placed in the bioreactor chamber, where media was again circulated through the chamber at the same flow rate. This group also received vibrational loading each weekday of ±0.3 g at 30 Hz for 1 h.

Following 19 days of culture, all trabecular explants were again imaged by µ-CT, as described previously. Following this, explants were fixed in formalin for 5 days and then dehydrated in increasing concentrations of ethanol. Explants were then infiltrated overnight and embedded in polymethylmethacrylate (DHM, Villa Park, IL). Cell viability was assessed using an alamar blue assay in the Flow group (n = 3). Samples were given regular media and the assay was performed for 24 h on day 4 by adding Alamar Blue (Promega, Madison, WI) to the media and again on day 21. Fluorescence was normalized to media left in the incubator for 24 h without samples. Additionally histological images, using hematoxylin and eosin (H&E, Sigma) staining, were obtained from vibrated samples to determine the condition of the marrow after culture over the course of the experiment.

Bone Formation Labelling

Fluorochrome labels were applied to label bone formation during culture. On day 7 the media was replaced in all groups with media containing 50 µg/mL of Tetracycline (Sigma Aldrich). On day 8 of culture this media was replaced with fresh media, which was allowed to circulate for approximately 8 h followed by a second change of media. On day 14 the media was replaced with fresh media containing 50 µg/mL of Calcein Blue (Sigma Aldrich). On day 15 this media was replaced with fresh media and again this was allowed to circulate for 12 h before being replaced with fresh media.

µ-CT Analysis for Trabecular Microarchitecture

The pre-experiment and post-experiment scans were registered to allow direct comparison of the same region of the explant. The paired images were registered using a normalized mutual information algorithm (NMI) in Analyze (Mayo Clinic, Overland Park, KS). This algorithm applies volume subsampling and greyscale binning to achieve accurate registration. However, it has a limited capture range that can fail to properly align highly misregistered images. To avoid this, an approximate registration was performed by manually transforming the image before applying the NMI algorithm to finalise the registration. Following image registration, bone formation and resorption was quantified using ImageJ (NIH). A volume of at least 125 mm3 was analysed for each bone explant. The volume was restricted in some samples due to motion artefacts during scanning and registration errors, so the maximum possible volume was analysed for each sample. The pre- and post-experiment bone volume/tissue volume (BV/TV), bone surface/bone volume (BS/BV), trabecular thickness (Tb.Th), trabecular spacing (Tb.Sp), trabecular number (Tb.N) and slenderness (Tp.Sp/Tb.Th) were determined. Slenderness is analogous to the slenderness ratio in the Euler buckling formulae; it can be used to indicate increased susceptibility to buckling and, as a consequence, a decreasing slenderness ratio indicates greater energy absorption.24 The structural model index (SMI) was also calculated; this gives an indication of the plate-like (SMI = 0) or rod-like (SMI = 3) geometry of trabecular bone. All trabecular architecture parameters were determined for the registered region using the BoneJ plugin to ImageJ.20 The same filtering and segmentation parameters were used for both scans. Regions of bone resorption and formation were detected using image comparison. Regions present in the first µ-CT scan but not the second were considered resorbed bone areas, while areas only present in the latter scan corresponded to newly formed bone.

Additionally, 3D quantification of bone morphometry parameters was performed using the approach of Schulte et al.51 Briefly, the mineral apposition rate (MAR) was calculated using the mean thickness of the new bone formed divided by the number of days between the µ-CT scans. Similarly the mineral resorption rate (MRR), which is not possible to calculate using traditional bone morphometry techniques, was calculated using the mean thickness of the resorbed bone. The mineralising surface (MS) was calculated using the surface of the formed bone, subtracting the BS of the pre-experiment scan, adding the BS of the post experiment scan and dividing by two, leaving just the surface of the formed bone which was then divided by the original BS. The eroding surface (ES, again this parameter is not possible to calculate using traditional bone morphometry techniques) was calculated using the surface of the resorbed bone, subtracting the BS of the post experiment scan, adding the BS of the pre-experiment scan and dividing by two, leaving the surface of the resorbed bone and dividing it by the total BS at day 0. Finally the bone formation rate (BFR) and bone resorption rate (BRR, once more this parameter is not possible to calculate using traditional techniques) were calculated using the total amount of bone formed (or resorbed for BRR) per the total bone volume at day 0 per day.

Computational Modelling

The pre-experiment µ-CT scans of the Vibrated group (n = 7) were used to create 3D CFD models of the marrow only to predict the mechanical environment under the applied vibrational loading following the previously developed approach of Coughlin and Niebur.14 Briefly, in each of the 7 cases, a 3 × 3 × 3.5 mm3 trabecular bone region was selected, Gaussian filtered, and resampled by cubic interpolation to 35 µm resolution using Visualization Toolkit (VTK, Kitware). A marching cubes algorithm from VTK was used to discretise the marrow regions into tetrahedral elements. A 30 µm layer of fluid was added around the entire marrow sample to allow continuity of flow from pores on the edges, resulting in a model geometry such as that shown in Fig. 2. Symmetry fluid flow constraints were placed on the faces parallel to the vibration direction, preventing flow across the boundaries. Constant pressure outlets were applied to the surfaces perpendicular to the vibration, allowing free flow (Fig. 2).
Figure 2

3D CFD marrow model with boundary conditions, based on the modelling approach of Coughlin and Niebur.14 Fluid flow was modelled as symmetric on the X and Z surfaces. Constant pressure outlets were applied on the Y surfaces. Sinusoidal velocity was applied on the bone marrow interface in the Y direction. An extra 30 μm layer of fluid was added to the edges of the marrow region to allow continuity of flow. In this image the marrow region is transparent to reveal the trabecular bone geometry within

CFD simulations were performed in Abaqus CFD (version 6.12) using FC3D4 elements. The fluid elements were assigned incompressible Newtonian fluid properties with a density of 0.9 g/cm3 and viscosity of 400 mPa s.8 The bone-marrow interface was assumed to be rigid, with a no slip interface. Nodes on the interface were assigned a sinusoidal velocity equivalent to a ±0.3 g acceleration at 30 Hz along the vertical axis of the explant (the Y-direction in the example of Fig. 2), matching the experimental conditions. The simulations were run for five cycles, however, changes from cycle to cycle were negligible, showing that transient effects can be ignored. To avoid artefacts at the external artificial fluid layer in the model, the shear stress in the marrow was analysed in a sub region (2.85 × 2.85 × 3.3 mm3) at the peak point of shear stress in a cycle. Shear stress was calculated using the reported shear rate based on the second invariant of the rate of strain tensor and multiplying this by the viscosity.5,53 Media flow was assumed to have a negligible effect on the generation of shear stress in the bone explants due to the high viscosity of marrow compared to media and so was not included in the models. Additionally, the modelled region was within the core away from the edges.

Statistical Analysis

Paired t-tests were applied to compare the formed bone with the resorbed bone and to compare pre and post-experiment µ-CT parameters. One-way analysis of variance (ANOVA) followed by pair-wise comparison (Tukey’s HSD test) was used to test for significance between Static, Flow, and Vibrated groups. Regression analyses were performed to assess the relationship between shear stress as calculated in the CFD models and the change in parameters over the course of the experiment as measured by µ-CT. All analyses were performed with Minitab. For all comparisons, the level of significance was p ≤ 0.05.


Fluorochrome Labelling and Bone Explant Viability

Active bone modelling was found in all samples regardless of experimental conditions as indicated by the presence of tetracycline and calcein blue labels. Representative images with regions of bone indicating clear linear labels are included in (Fig. 3) as examples of possible staining of calcium and dye uptake over the course of the experiment. Cell viability was examined at day 4/5 and a worst case example of day 21/22. This was a worst case example as the experimental duration was only 19 days. There was no significant difference between the two time points (Fig. 4a). Additionally, the structure of the marrow was seen to be of good quality in histological sections stained with H&E. A representative image is included in Fig. 4b.
Figure 3

Tetracycline and calcein blue incorporation into trabecular bone explants. All scale bars are 70 μm. Asterisks indicate incorporation of tetracycline (white) and calcein blue (red) into the bone and onto the bone surface. Arrow heads indicate regions of double label

Figure 4

(a) Cell viability as calculated using Alamar Blue over days 4–5 and days 21–22 for the Flow group (n = 3) and (b) representative histological section from the Flow group stained with H&E (×100 magnification)

µ-CT Parameters

On average, bone formation was greater than resorption in the Vibrated group (p < 0.001, Table 1), while there was no statistical difference for the same comparison in the Static or Flow groups (p > 0.05, Table 1).
Table 1

Mean ± SD for the BV/TV seen in the post experiment scans (formation) but not the pre-experiment scans and the volume of bone seen in the pre-experiment scans but not the post experiment scans (resorption)







0.031 ± 0.013

0.032 ± 0.015




0.035 ± 0.009

0.030 ± 0.007




0.050 ± 0.015

0.036 ± 0.016



Significant differences are represented in bold (p < 0.05, paired t test)

The positive bone balance resulted in higher BV/TV (p < 0.001) and Tb.Th (p < 0.001) following culture in the Vibrated group (Table 2), while both the Static and Flow samples had no significant increase in BV/TV over the course of the experiment (Table 2). Consequently, the relative increase in BV/TV and Tb.Th was higher in the Vibrated group than in the other groups (p = 0.0001 vs. Static and p = 0.0033 vs. Flow for BV/TV, p = 0.0016 vs. Static and p = 0.0489 versus Flow for Tb.Th, ANOVA and Tukey’s HSD test, Figs. 5a and 5b).
Table 2

Mean ± SD of trabecular bone architectural parameters for the Static (n = 5), Flow (n = 3) and Vibrated (n = 7) groups



Tb.Th (mm)

Tb.Sp (mm)


Tb.N (1/mm)


BS/BV (1/mm)

Mean ± SD


Mean ± SD


Mean ± SD


Mean ± SD


Mean ± SD


Mean ± SD


Mean ± SD




0.276 ± 0.044


0.150 ± 0.004


0.485 ± 0.069


2.598 ± 0.139


1.706 ± 0.104


0.398 ± 0.056


5.171 ± 0.247



0.275 ± 0.045

0.153 ± 0.007

0.490 ± 0.072

2.536 ± 0.139

1.683 ± 0.092

0.320 ± 0.057

5.029 ± 0.196



0.327 ± 0.021


0.163 ± 0.007


0.424 ± 0.030


3.232 ± 0.509


1.589 ± 0.179


0.629 ± 0.246


8.961 ± 7.426



0.331 ± 0.020

0.168 ± 0.004

0.427 ± 0.029

3.206 ± 0.531

1.571 ± 0.181

0.615 ± 0.261

8.887 ± 7.387



0.233 ± 0.016


0.151 ± 0.010


0.541 ± 0.005


3.596 ± 0.225


1.447 ± 0.025


1.033 ± 0.183


5.893 ± 0.350



0.247 ± 0.016

0.160 ± 0.012

0.540 ± 0.005

3.396 ± 0.225

1.429 ± 0.028

0.873 ± 0.169

5.614 ± 0.318

BV/TV (bone volume/tissue volume), Tb.Th (trabecular thickness), Tb.N (trabecular number), SMI (structural model index), BS/BV (bone surface/bone volume) and slenderness (trabecular spacing/trabecular thickness). p values less than 0.05 were deemed to be significant using a paired t test between the re-experiment scan and the post experiment scan. Significant p values were represented in bold

Figure 5

The mean percentage changes over the course of the experiment in; (a) BV/TV, bone volume/tissue volume, (b) Tb.Th, trabecular thickness, (c) slenderness, trabecular thickness/trabecular spacing, (d) BS/BV, bone surface/bone volume, and the histomorphometric parameters (e) MS, mineralising surface, (f) BFR, bone formation rate. Trabecular bone explants were cultured in a static plate (Static, n = 5), exposed to fluid flow in the bioreactor chamber (Flow, n = 3) or exposed to fluid flow and LMHF loading in the bioreactor chamber (Vibrated, n = 7). A one-way analysis of variance (ANOVA) followed by pair-wise comparison (Tukey’s HSD test) was used to test for significance. (a) p < 0.05 versus Static group, (b) p < 0.05 versus Flow group

Considering the trabecular architecture, the SMI decreased significantly (p < 0.001, Table 2) in the Vibrated group, while no difference in SMI was seen in the Static and Flow groups between the two time points (p = 0.061 and 0.658, respectively). While there was a significant decrease in Tb.N for the Flow (p = 0.002) and Vibrated (p = 0.008) groups (Table 2) between pre and post experiment values, no significant difference in the relative percentage changes between groups was found (Vibrated vs. Static p = 0.9843, Vibrated vs. Flow p = 0.9699). Tb.Sp was found to increase significantly only in the Static group (p = 0.011). A significant decrease in the slenderness of the Vibrated group was also found over the course of the experiment (p < 0.001), but not in the Static group (p = 0.082) or Flow group (p = 0.173, Table 2). Accordingly the relative decreases in slenderness were greater in the Vibrated group than in the static groups (p = 0.0004 vs. Static and p = 0.0209 for Flow, Fig. 5c). A significant decrease in BS/BV was found in the Static (p = 0.042) and Vibrated groups (p < 0.001) between the two time points (Table 2). The relative decrease in the Vibrated group was found to be significantly greater than the Static group (p = 0.0015) but not the Flow group (p = 0.1315) (Fig. 5d). MS was found to be significantly higher in the Vibrated group compared to the Flow group (p = 0.0275, Fig. 5e; Table 3). Moreover, BFR was found to be significantly higher in the Vibrated group compared to both the Static (p = 0.0188) and Flow (p = 0.0318) groups (Fig. 5f; Table 3). No significant differences were found between the Static, Flow and Vibrated groups for MAR, MRR, ES and BRR.
Table 3

Mean ± SD for 3D trabecular bone morphometry parameters for the Static (n = 5), Flow (n = 3) and Vibrated (n = 7) groups





Pairwise comparison (vibrated and static)

Pairwise comparison (vibrated and flow)

MAR (µm/day)

2.179 ± 0.109

2.175 ± 0.061

2.511 ± 0.364



MRR (µm/day)

2.189 ± 0.132

2.175 ± 0.061

2.421 ± 0.305



MS (%)

9.459 ± 7.810

8.917 ± 4.188

24.480 ± 9.962



ES (%)

8.889 ± 9.001

6.254 ± 4.065

14.044 ± 10.594



BFR (%/day)

0.605 ± 0.252

0.569 ± 0.154

1.120 ± 0.315



BRR (%/day)

0.616 ± 0.296

0.496 ± 0.112

0.807 ± 0.344



Mineral apposition rate (MAR), mineral resorption rate (MRR), mineralising surface (MS), eroding surface (ES), bone formation rate (BFR) and bone resorption rate (BRR) were calculated according to the methods of Schulte et al.51p values less than 0.05 were deemed to be significant using a one-way analysis of variance (ANOVA) followed by pair-wise comparison (Tukey’s HSD test)

CFD Models

Shear stresses were calculated at the peak point of the shear stress cycle. Because the shear stress varies throughout the marrow space (Fig. 6), the mean shear stress and acceleration within the marrow volume for each vibrated bone explant are reported in Table 4. Representative images of the shear stresses generated in the marrow are shown in Fig. 6. The mean value of shear stress ranges from 0.575 to 0.702 Pa. Acceleration did not vary substantially between the seven samples, and the mean values approached the applied acceleration of 0.3 g (2.94 m/s2), suggesting the majority of the marrow was experiencing close to the applied acceleration applied at the bone-marrow interface. Moreover, the minimum acceleration was found to be 1.47 m/s2, which was approximately half the applied value. These accelerations were picked at the peak point of the acceleration cycle, which occurs just after the peak shear stress. For a frequency of 30 Hz the difference between peak shear stress and acceleration was 0.002 s.
Figure 6

Representative contour plot of shear stresses (Pa) in the entire marrow, at the peak point of the loading cycle. Image (a) shows surface of model and section through model, with trabecular bone structure indicated. In these simulations the bone was assumed rigid and was therefore unstressed. Images (b–g) show a section through the 3D model for the six other bone explant simulations

Table 4

Mean shear stress and acceleration for the seven vibrated explants

Sample number

Mean shear stress (Pa)

Mean acceleration (m/s2)






















Correlation Between µ-CT Parameters and Shear Stress

Regression analysis between the mean shear stress within the models and the percentage change in bone morphology parameters established from the µ-CT scans reveals a definite relationship between the bone formation balance (formation/resorption ratio) and shear stress (Fig. 7a). The bone formation balance is the volume of formed bone relative to resorbed bone for a given sample. A value greater than 1 indicates greater formation than resorption and this was seen in all vibrated samples (1.171–2.118). Conversely, in the Static group, the values for bone formation balance range from 0.826 to 1.188 and values for the Flow group ranged from 1.094 to 1.222. Additionally, Tb.N was found to increase with increasing mean shear stress (Fig. 7b). While no significant decrease in Tb.Sp was found in the Vibrated group, the Tb.Sp values in the post experimental scans were found to be correlated to shear stress (Fig. 7c). Examining the shear stress on just the surface elements, representative of the bone/marrow interface, reveals a similar correlation with the mean shear stress of just the surface elements and the percentage change in bone morphology parameters (Fig. 8a–c).
Figure 7

Linear regression analysis measured with the average shear stress throughout the marrow geometry. (a) Bone formation balance (formation/resorption ratio) increased with increasing mean shear stress, (b) trabecular number (Tb.N) increased with increasing mean shear stress and (c) increasing mean shear stress was found to decrease trabecular spacing (Tb.Sp) in the vibrated bone explants. Linear regression measured using the average shear stresses in the modelled geometries

Figure 8

Linear regression analysis with the shear stress in just the elements at the surface of the bone/marrow interface. (a) Bone formation balance (formation/resorption ratio) increased with increasing mean shear stress, (b) trabecular number (Tb.N) increased with increasing mean shear stress and (c) increasing mean shear stress was found to decrease trabecular spacing (Tb.Sp) in the vibrated bone explants

As an alternate indicator of the role of shear stress, the fraction of the marrow space exceeding a critical shear stress threshold of 0.5 Pa12,25,33,43 was investigated. The fraction of marrow exceeding this threshold was a significant indicator of decreasing MRR (Fig. 9a) and BRR (Fig. 9b). However no significant relationship between other 3D bone morphometry and shear stress thresholds was found. Additionally, when the surface elements were analysed in isolation no significant relationship was found between any 3D bone morphometry parameters and the shear stress in the surface elements. Similar anabolic effects can be seen at the local level by comparing regions of high shear stresses with new bone formed (Fig. 10).
Figure 9

Regression analysis between (a) mineral resorption rate (MRR) and (b) bone resorption rate (BRR) and the percentage of marrow experiencing shear stress greater than 0.5 Pa

Figure 10

Registered 3D μ-CT scans pre- and post-experiment. Section taken through 3D reveals areas of formed and resorbed bone in μ-CT slice. Distribution of shear stress (Pa) within the same section of bone in the CFD model


In this study the effects of LMHF loading on trabecular bone explants were assessed through the use of a custom built bioreactor. Significantly greater bone formation was found in trabecular bone explants exposed to the LMHF loading compared to Static and Flow samples. Overall there was an increase in bone architecture in the loaded samples as indicated by an increase in Tb.Th and decreases in BS/TV and slenderness, while the static and media flow only samples showed no net change in architecture or BV/TV. CFD models generated from the µ-CT scans allowed for the determination of shear stresses and acceleration within the experimental samples. The bone formation balance, trabecular spacing and number were found to be positively correlated with the shear stress generated in the marrow during loading. Furthermore, 3D bone morphometric parameters BRR and MRR were also found to be related to shear stress. In contrast, acceleration showed little variation between samples, and was not correlated with alterations in the bone. As such, these results indicate that shear stress in the bone marrow may be a mechanical regulator of bone remodeling in these explants.

Shear stress is known to regulate cell differentiation and is capable of stimulating an osteogenic response in vitro.1,3,11,52 The magnitude of the calculated shear stress (mean shear stress ranged from 0.575 to 0.702 Pa across the Vibrated group) in the explants was at a level consistent with osteogenic response by MSCs in 2D parallel plate flow chambers34,52 and 3D scaffold fluid flow experiments.11 It is possible that the shear stress generated within the marrow during LMHF loading is directly stimulating the MSCs to differentiate along the osteogenic pathway. Bone marrow has been proposed to have a functional role acting as a stem cell niche within the body, maintaining quiescence, promoting proliferation and directing differentiation of MSCs.22,26,35,58 However, the role of shear stress within the stem cell niche could depend on marrow composition and stem cell location.

Previous in vitro studies of trabecular bone explants have proved successful for examining bone remodelling in response to compressive strain of the bone matrix.17,18,21,28,38 Significant bone growth was found in samples exposed to the compressive mechanical loading compared to static samples,17,38 reproducing the in vivo effects of mechanical strain on bone growth. In contrast, the strain induced on the bone in the present study was minimal, and, complementing previous studies, bone formation was not dependent on matrix strain during LMHF loading.30 Increases in BV/TV, Tb.Th and MAR in the mechanically loaded samples, compared to baseline controls, in these previous studies17,38 were greater than what was seen in the current study. Strong bone formation, in response to osteocyte mediated compressive strain compared to LMHF loading, which seems to bypass the osteocyte network, highlights the crucial role that osteocytes play in acting as the main sensor of strain in bone.4,6,9

As ex vivo bone samples were used in the current study, the bone and marrow were isolated from other factors such as muscle stimulation,42 which were thought to play a role in bone adaption in response to LMHF loading, as well as any physiological or systemic effects on the organism. However, it is not known if the loading history used here represents what a region of trabecular bone would experience in a whole body vibration study in vivo.

The first hypothesis proposed in this study was that LMHF loading is anabolic to trabecular bone architecture and quantity. This was confirmed by greater increases in BV/TV, Tb.Th and decreases in BS/TV and slenderness in the explanted trabecular bone cores when exposed to LMHF loading compared to static and media flow only conditions. Image registration techniques were used to accurately determine changes in trabecular bone over the course of the experiment.36,51 This finding agrees with the numerous other studies which display the positive effect of LMHF on trabecular bone.23,30,47,60 While not all bone architecture parameters were shown to improve, the results of this study show, for the first time, bone adaptation in response to LHMF in ex vivo bone, and thereby provides an ex vivo model that might be applied to understand the relationship between bone adaptation and the local mechanical environment. The second hypothesis stated that trabecular bone volume and architecture were related to the generated shear stress in the marrow due to LMHF loading. The results presented here demonstrate that shear stress generated within the marrow was strongly related to changes in bone architecture under LHMF, and it was proposed here that, shear stress is thus the source of the transmission of LMHF loading into a bone tissue response.

A number of limitations to this study should be considered, including the use of osteogenic factors β-glycerol phosphate and ascorbic acid-2-phosphate in the media, which aid in the osteogenic differentiation of MSCs. However, the addition of osteogenic factors has been used in ex vivo trabecular bone studies17,38 previously. β-glycerol phosphate provides a source of inorganic phosphate, while AA2P is believed to enhance proliferation of cells.27 However, dexamethasone, which is typically included in osteogenic media to enhance differentiation, was not used in this study and the same media was used across all experimental groups, and as such the relative differences between LMHF and control groups were not due to the media constituents. Secondly, for the CFD models, marrow was modelled as a homogenous fluid, however it is, in reality, heterogeneous, with varying cellular composition.37,56,61,62 However, how the mechanical properties vary with age and disease states, which are linked to changes in cellular composition, have not been quantified. As such, the calculated shear stress values are an homogenization, and do not necessarily represent the shear stress on individual cells in the marrow. As shear stress increases with increasing loading amplitude of vibration,14 further work is required with additional samples at increasing amplitudes and varying frequencies of vibrations to fully determine the shear stress and bone growth/remodelling correlation. Finally, it was not possible to quantify bone formation from the tetracycline labels, due to the fact that a large amount of diffuse tetracycline staining was visible within the bone. Investigations revealed that pigs are often given tetracycline medicated feeds during their life-time. Due to this large amount of diffuse staining quantification of the labels was deemed impractical. Nonetheless, the image registration of the CT data provided a suitable measure of bone histomorphometry parameters.51

Acceleration has been proposed as an alternate mechanical signal sensed by cells during LMHF vibration.13,55 However, results here show that acceleration varied little with the loaded samples; a minimum value within the marrow was found to be 0.15 g, with the majority of the marrow experiencing the applied 0.3 g. Therefore, trying to determine whether a relationship between bone formation, or other parameters, and acceleration exists was not possible with the current results. Indeed, changing the applied acceleration in the current experimental set-up would also change the applied shear stress as shear stress increases with increasing amplitude for a constant viscosity.14 Using ex vivo bone samples it would be very difficult to determine the roles of shear stress and acceleration separately. An in vitro cell study using osteoblast-like cells (MC3T3-E1) increased shear stress in the system by adding dextran to the media while keeping the acceleration constant. Cyclooxygenase-2 (COX-2, a gene essential for mechanically induced bone formation) expression was found to not be increased by the increasing shear stress during LMHF loading.55 Similarly, COX-2 and nitric oxide, essential for the new bone formation in response to mechanical loading,41,54 in MC3T3-E1s were found to increase with increasing acceleration.2

In summary, in vivo responses to LMHF loading were replicated for the first time in explanted bone samples using a novel bioreactor system. LMHF loading was found to enhance bone formation and improve bone architecture quality, compared to static and media flow-only samples. CFD models of the LMHF loaded bone explants were generated of the experimental samples using the pre-experiment µCT scans. Shear stress generated in the marrow due to LMHF loading was determined from these models. Values of shear stress were found to be in the range (mean values across samples ranged from 0.575 to 0.702 Pa) previously found to be stimulatory to MSCs in vitro. Finally, a positive correlation was demonstrated between the generated shear stress and changes in trabecular bone parameters (bone formation balance, Tb.N and Tb.Sp during loading). These results could have significant implications for the treatment of diseases such as osteoporosis, as they offer an insight into how the LMHF signals function to strengthen bone in vivo.



The authors would like to acknowledge funding from the Irish Research Council, under the EMBARK program, U.S. National Science Foundation grant CMMI 1100207, Science Foundation Ireland under the Short Term Travel Fellowship and the ORS under the Collaborative Exchange Award. The authors would also like to acknowledge M.A. Varsanik for her assistance with the histology images.


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Copyright information

© Biomedical Engineering Society 2014

Authors and Affiliations

  • E. Birmingham
    • 1
  • T. C. Kreipke
    • 2
  • E. B. Dolan
    • 1
  • T. R. Coughlin
    • 2
  • P. Owens
    • 3
  • L. M. McNamara
    • 1
  • G. L. Niebur
    • 2
  • P. E. McHugh
    • 1
  1. 1.Biomechanics Research Centre (BMEC), Mechanical and Biomedical Engineering, College of Engineering and InformaticsNational University of Ireland GalwayGalwayIreland
  2. 2.Bioengineering Graduate ProgramUniversity of Notre DameNotre DameUSA
  3. 3.Centre for Microscopy and Imaging NUIGNational University of Ireland GalwayGalwayIreland

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