Qianhong Wu

In situ permeability measurement of the mammalian lacunar–canalicular system

Bone is capable of adapting its mass and structure under mechanical cues. Bone cells respond to various mechanical stimuli including substrate strain, fluid pressure, and fluid flow (shear stress) in vitro. Although tissue-level strains are well documented experimentally, microfluidic parameters around bone cells are quantified mainly through theoretical modeling. A key model parameter, the Darcy permeability of the bone lacunar-canalicular system (LCS), is difficult to measure using traditional methods due to the co-existence of the larger vascular and smaller LCS porosities. In this paper, we developed a novel method to measure the LCS permeability by rapid compaction of intact mammalian bones and recording the intramedullary pressure (IMP). Six canine metacarpals were subjected to three step compression tests with peak loads of 50, 100, or 200lbs, while the IMP was simultaneously recorded using a catheter pressure transducer. The loading ramp time was chosen to be ~2ms, which was long enough to allow pressure equilibrium to be established between the marrow cavity and the vascular pores, but short enough to observe the LCS fluid flowing into and out of the vascular pores. This loading scheme permitted us to differentiate the contribution of the two intermingled porosities to the IMP responses. The time constant of the IMP pressurization and relaxation due to the LCS was found to be 8.1+/-3.6s (n=18). The mid-shaft cortex of the metacarpals mainly consisted of osteons with an average radial thickness of 65+/-27microm, which served as the characteristic distance for the LCS fluid to relax. The LCS permeability was obtained via poroelastic analysis to be 2.8+/-1.8x10(-)(23)m(2), which was smaller than previous theoretical predictions (order of 10(-)(19) to 10(-)(22)m(2)), but within the range of previous experimentally based estimations (order of 10(-)(22) to 10(-)(25)m(2)). Our results also show that osteoblasts and osteocytes experience hydraulic pressures that differ by three orders of magnitude under physiological compressive strains. These estimates of the in vivo mechanical environments may be used to design in vitro models for elucidating the cellular and molecular mechanisms of bone adaptation and pathological bone loss.

Effect of low-magnitude, high-frequency vibration on osteogenic differentiation of rat mesenchymal stromal cells.

Whole body vibration (WBV), consisting of a low‐magnitude, high‐frequency (LMHF) signal, is anabolic to bone in vivo and may act through alteration of the lineage commitment of mesenchymal stromal cells (MSC). We investigated the effect of LMHF vibration on rat bone marrow‐derived MSCs (rMSCs) in an in vitro system. We subjected rMSCs to repeated (six) bouts of 1‐h vibration at 0.3g and 60 Hz in the presence of osteogenic (OS) induction medium. The OS differentiation of rMSCs under the loaded and non‐loaded conditions was assessed by examining cell proliferation, alkaline phosphatase (ALP) activity, mRNA expression of various osteoblast‐associated markers [ALP, Runx2, osterix (Osx), collagen type I alpha 1 (COL1A1), bone sialoprotein (BSP), osteopontin (OPN), and osteocalcin (OCN)], and matrix mineralization. LMHF vibration did not enhance the OS differentiation of rMSCs. Surprisingly, the mRNA level of Osx, a transcription factor necessary for osteoblast formation, was decreased, and matrix mineralization was inhibited. Our findings suggest that LMHF vibration may exert its anabolic effects in vivo via mechanosensing of a cell type different from MSCs.

Dynamic compression of highly compressible porous media with application to snow compaction

A new experimental and theoretical approach is presented to examine the dynamic lift forces that are generated in the compression of both fresh powder snow and wind-packed snow. At typical skiing velocities of 10 to 30ms

A comprehensive skiing mechanics theory with implications to snowboard optimization.

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Riding on Air: A New Theory for Lift Mechanics of Downhill Skiing and Snowboarding

the duration of contact of a ski or snowboard with the snow will vary from 0.05 to 0.2s depending on the length of the planing surface and its speed. No one, to our knowledge, has previously measured the dynamic behaviour of snow on such a short time scale and, thus, there are no existing measurements of the excess pore pressure that can build-up in snow on this time scale. Using a novel porous cylinder–piston apparatus, we have measured the excess pore pressure that would build-up beneath the piston surface and have also measured its subsequent decay due to the venting of the air from the snow at the porous wall of the cylinder. In further experiments, in which the air is slowly and deliberately drained to avoid a build-up in pore pressure, we have been able to separate out the force exerted by the ice crystal phase as a function of its instantaneous deformation. A theoretical model for the pore pressure relaxation in the porous cylinder is then developed using consolidation theory. Dramatically different dynamic behaviour is observed for two different snow types, one (wind-packed) giving a steady continuous relaxation of the excess pore pressure and the other (fresh powder) leading to a piston rebound with negative pore pressure. A feature of the rebound is the apparent debonding of sintered ice crystals after maximum compression. This behaviour is described well by introducing a debonding coefficient where the debonding force is proportional to the expansion velocity of the medium. The experimental and theoretical approach presented herein and the previous generalized lubrication theory for compressible porous media, have laid the foundation for understanding the detailed dynamic response of soft porous layers to rapid deformation.

A biphasic approach for the study of lift generation in soft porous media

PURPOSE Lift mechanics of downhill skiing or snowboarding is a new theory developed by the corresponding author and colleagues in 2006 and published in Medicine & Science in Sports & Exercise®. This theory, hereafter called the Wu-Weinbaum theory, captures the lift contributions due to both the transiently trapped air inside a snow layer and the solid phase (snow crystals) for the first time and examines the stability and control of skiing/snowboarding. However, it has two major shortcomings. First, it only predicts a single equilibrium position for a given gliding condition because of its limitations on the numerical simulation. Second, it is only applicable to rectangular boards. In the current study, we shall treat these limitations by improving the numerical methods as well as extending the Wu-Weinbaum theory to more complex planar shapes. METHODS A modified mathematical model is developed where a width factor, f(x), which characterizes the variation of width from the leading to the trailing edge of a ski/snowboard, is introduced. RESULTS We have performed a thorough reexamination of the force and moment balance on a rectangular board on the basis of an improved numerical scheme and obtained multiple equilibrium positions for a skier or snowboarder gliding over a compressed snow layer at a certain speed. Furthermore, the performance of a commercial ski/snowboard with a specified shape was studied on the basis of our revised model, which revealed different pore pressure distribution underneath the sliding surface compared with a rectangular board. CONCLUSIONS This study, along with the Wu-Weinbaum theory, has laid the foundation for the optimization of a ski/snowboard from a lift generation point of view.

Exact and approximate solutions for transient squeezing flow

A simplified mathematical model is derived to describe the lift mechanics of downhill skiing and snowboarding, where the lift contributions due to both the transiently trapped air and the compressed solid phase (snow crystals) are determined. To our knowledge, this is the first time that anyone has attempted to realistically estimate the relative contribution of the pore air pressure to the total lift in skiing and snowboarding. The model uses Shimizu’s empirical relation to predict the local variation in Darcy permeability due to the snow compression. The forces and moments on the skier or snowboarder are used to predict the angle of attack of the planing surface, the penetration depth at the leading edge and the shift in the center of pressure for two typical snow types, fresh and wind-packed snow. Our model predicts that, when there are no edging or turning maneuvers and the velocity of the snowboarder or skier, U = 20 m/s, for fine-grained, wind-packed snow approximately 50% of the total lift force is generated by the trapped air for snowboarding and 40% for skiing. For highly permeable fresh powder snow the lift contribution from the pore air pressure drops substantially. The force and moment balance on the planing surface due to the trapped air and the snow crystals are then used to develop a theory for control and stability in response to changes in the center of mass as the individual shifts his/her weight.

Permeability Measurements for Random Soft Porous Medium and its Implications to Lift Generation

Lift generation in highly compressible porous media under rapid compression continues to be an important topic in porous media flow. Although significant progress has been made, how to model different lifting forces during the compression process remains unclear. This is mainly because the input parameters of the existing theoretical studies, including the Darcy permeability of the porous media and the viscous damping coefficient of its solid phase, were manually adjusted so as to match the experimental data. In the current paper, we report a biphasic approach to experimentally and theoretically treat this limitation. Synthetic fibrous porous materials, whose permeability were precisely measured, were subsequently exposed to sudden impacts using a porous-walled cylinder-piston apparatus. The obtained time-dependent compression of the porous media, along with the permeability data, was applied in two different theoretical models to predict the pore pressure generation, a plug flow model and a consolidation...

Lift Generation in Soft Porous Media Under Rapid Compaction

In this paper, we report two novel theoretical approaches to examine a fast-developing flow in a thin fluid gap, which is widely observed in industrial applications and biological systems. The problem is featured by a very small Reynolds number and Strouhal number, making the fluid convective acceleration negligible, while its local acceleration is not. We have developed an exact solution for this problem which shows that the flow starts with an inviscid limit when the viscous effect has no time to appear and is followed by a subsequent developing flow, in which the viscous effect continues to penetrate into the entire fluid gap. An approximate solution is also developed using a boundary layer integral method. This solution precisely captures the general behavior of the transient fluid flow process and agrees very well with the exact solution. We also performed numerical simulation using Ansys-CFX. Excellent agreement between the analytical and the numerical solutions is obtained, indicating the validity ...

From red cells to snowboarding: a new concept for a train track.

In the past decade, foundations have been laid for understanding the lift generation in a soft porous medium under rapid compaction (Feng and Weinbaum [1], Wu, et al. [2,3], Barabadi, et al. [4], Al‐Chidiac, et al. [5]). One of the key parameters that affect lift generation is the variation of the Darcy permeability as a function of its compression. This critical component is experimentally investigated in the current study using a permeameter. Two soft, synthetic, porous materials were chosen for the study. The microstructures of these materials were characterized using a Scanning Electronic Microscope. By carefully controlling the air flows through the materials contained in a long Plexiglas tube, consistent results were obtained for their permeability as a function of porosity. One observed a highly non‐linear relationship between the permeability and the porosity for both materials. A noticeable difference in the permeability in the high porosity range was observed when the microstructure was altered ...