Influence of vascular porosity on fluid flow and nutrient transport in loaded cortical bone

Load-induced fluid flow is a key factor in triggering bone modeling and remodeling processes that maintain bone mass and architecture. To provide an enhanced understanding of fluid flow in bone, unique computational models of a tibial section were developed. The purpose of the study was to examine the effects of incorporating vascular porosity on pore fluid pressure and resulting lacunocanalicular flow and to determine the role of load-induced fluid flow in tracer transport. Simulations revealed large local pressure gradients surrounding the vascular canals that were dependent on the magnitude and state (i.e., compressive or tensile) of the stress. Fluid velocity magnitudes were increased by over an order of magnitude in the dual-porosity model, relative to the single-porosity model. Fluid flow had a marked effect on tracer perfusion within the cortex. After 10 loading cycles, a 9-fold increase in tracer concentration, relative to diffusion alone, was observed in the compressive region where fluid exchange was greatest between the lacunocanalicular porosity and the vascular canals. Agreement was achieved between computational results and experimental investigations of electrokinetic phenomenon, tracer transport, cellular stimulation, and functional adaptation. The models produced substantial improvements in bone fluid flow simulation and underscored the significance of incorporating vascular porosity in models designed to quantify fluid pressure and flow characteristics within mechanically loaded cortical bone.     

Fluid pressure relaxation depends upon osteonal microstructure: modeling an oscillatory bending experiment.

When bone is mechanically loaded, bone fluid flow induces shear stresses on bone cells that have been proposed to be involved in bone's mechanosensory system. To investigate bone fluid flow and strain-generated potentials, several theoretical models have been proposed to mimic oscillatory four-point bending experiments performed on thin bone specimens. While these previous models assume that the bone fluid relaxes across the specimen thickness, we hypothesize that the bone fluid relaxes primarily through the vascular porosity (osteonal canals) instead and develop a new poroelastic model that integrates the microstructural details of the lacunar-canalicular porosity, osteonal canals, and the osteonal cement lines. Local fluid pressure profiles are obtained from the model, and we find two different fluid relaxation behaviors in the bone specimen, depending on its microstructure: one associated with the connected osteonal canal system, through which bone fluid relaxes to the nearby osteonal canals; and one associated with the thickness of a homogeneous porous bone specimen (approximately 1 mm in our model), through which bone fluid relaxes between the external surfaces of the bone specimen at relatively lower loading frequencies. Our results suggest that in osteonal bone specimens the fluid pressure response to cyclic loading is not sensitive to the permeability of the osteonal cement lines, while it is sensitive to the applied loading frequency. Our results also reveal that the fluid pressure gradients near the osteonal canals (and thus the fluid shear stresses acting on the nearby osteocytes) are significantly amplified at higher loading frequencies.     

Computer modelling of bone’s adaptation: the role of normal strain,shear strain and fluid flow

Bone loss is a serious health problem. In vivo studies have found that mechanical stimulation may inhibit bone loss as elevated strain in bone induces osteogenesis, i.e. new bone formation. However, the exact relationship between mechanical environment and osteogenesis is less clear. Normal strain is considered as a prime stimulus of osteogenic activity; however, there are some instances in the literature where osteogenesis is observed in the vicinity of minimal normal strain, specifically near the neutral axis of bending in long bones. It suggests that osteogenesis may also be induced by other or secondary components of mechanical environment such as shear strain or canalicular fluid flow. As it is evident from the literature, shear strain and fluid flow can be potent stimuli of osteogenesis. This study presents a computational model to investigate the roles of these stimuli in bone adaptation. The model assumes that bone formation rate is roughly proportional to the normal, shear and fluid shear strain energy density above their osteogenic thresholds. In vivo osteogenesis due to cyclic cantilever bending of a murine tibia has been simulated. The model predicts results close to experimental findings when normal strain, and shear strain or fluid shear were combined. This study also gives a new perspective on the relation between osteogenic potential of micro-level fluid shear and that of macro-level bending shear. Attempts to establish such relations among the components of mechanical environment and corresponding osteogenesis may ultimately aid in the development of effective approaches to mitigating bone loss.     

A finite element analysis for the prediction of load-induced fluid flow and mechanochemical transduction in bone

Interstitial fluid flow through the lacunocanalicular cavities of mechanically loaded bone provides the biophysical basis for a number of postulates regarding mechanotransduction in bone. Recently, the existence of load-induced fluid flow and its influence on molecular transport through bone has been confirmed using tracer methods to visualize fluid flow induced by in vivo four-point-bending of rat tibiae. In this paper, we present a theoretical two-stage approach for the calculation of load-induced flow fields and for the evaluation of their influence on molecular transport in bone loaded in four-point bending, analogous to the aforementioned experimental model. In the first stage, the fluid velocities are calculated using a three-dimensional, poroelastic finite element model. In the second stage, mass transport analysis, this calculated fluid flow serves as a forced convection flow and its contribution to the total transport potential is determined. Based on this combined approach, the overall tracer concentration in the loaded bone is significantly higher than that in the unloaded bone. Furthermore, augmentation of mass transport through convective flow is more pronounced in the tension band of the tissue, as compared to the compression band. In general, augmentation of tracer concentration via convective mechanisms is most pronounced in areas corresponding to lowest fluid velocities, which is indicative of fluid flow direction and areas of increased "dwell time" or accumulation during the loading cycle. This theoretical model, in combination with the corresponding experimental model, provides unique insight into the role of mechanical loads in modulating local flow distributions and concentration gradients within bone tissue.     

Parallel-plate fluid flow systems for bone cell stimulation

Bone responds to changes in its mechanical environment, but the mechanisms by which it does so are poorly understood. One hypothesis of mechanosensing in bone states that osteocytes can sense the flow of fluid through the canalicular system. To study this in vitro a number of fluid flow devices have been designed in which cells are placed between parallel plates in sealed chambers. Fluid flows through the chambers at controlled rates, most commonly driven by a peristaltic pump. In addition to fluid flow, high pressures have been observed in these chambers, but the effect of this on the cellular responses has generally been ignored or considered irrelevant, something challenged by recent cellular experiments using pressure only. We have, therefore, devised a system in which we can considerably reduce the pressure while maintaining the flow rate to enable study of their effects individually and in combination. As reducing pressure also reduces the risk of leaks in flow chambers, our system is suitable for real-time microscopical experiments. We present details of the new systems and of experiments with osteoblasts to illustrate the effects of fluid flow with and without additional pressure on the translocation of β-catenin to the nucleus.     

Estimation of bone permeability using accurate microstructural measurements

While interstitial fluid flow is necessary for the viability of osteocytes, it is also believed to play a role in bone's mechanosensory system by shearing bone cell membranes or causing cytoskeleton deformation and thus activating biochemical responses that lead to the process of bone adaptation. However, the fluid flow properties that regulate bone's adaptive response are poorly understood. In this paper, we present an analytical approach to determine the degree of anisotropy of the permeability of the lacunar-canalicular porosity in bone. First, we estimate the total number of canaliculi emanating from each osteocyte lacuna based on published measurements from parallel-fibered shaft bones of several species (chick, rabbit, bovine, horse, dog, and human). Next, we determine the local three-dimensional permeability of the lacunar-canalicular porosity for these species using recent microstructural measurements and adapting a previously developed model. Results demonstrated that the number of canaliculi per osteocyte lacuna ranged from 41 for human to 115 for horse. Permeability coefficients were found to be different in three local principal directions, indicating local orthotropic symmetry of bone permeability in parallel-fibered cortical bone for all species examined. For the range of parameters investigated, the local lacunar-canalicular permeability varied more than three orders of magnitude, with the osteocyte lacunar shape and size along with the 3-D canalicular distribution determining the degree of anisotropy of the local permeability. This two-step theoretical approach to determine the degree of anisotropy of the permeability of the lacunar-canalicular porosity will be useful for accurate quantification of interstitial fluid movement in bone.     

Decrease in the osteocyte lacunar density accompanied by hypermineralized lacunar occlusion reveals failure and delay of remodeling in aged human bone

Aging decreases the human femur’s fatigue resistance, impact energy absorption, and the ability to withstand load. Changes in the osteocyte distribution and in their elemental composition might be involved in age‐related bone impairment. To address this question, we carried out a histomorphometric assessment of the osteocyte lacunar distribution in the periosteal and endosteal human femoral cortexes of 16 female and 16 male donors with regard to age‐ and sex‐related bone remodeling. Measurements of the bone mineral density distribution by quantitative backscattered electron imaging and energy dispersive X‐ray analysis were taken to evaluate the osteocyte lacunar mineral composition and characteristics. Age‐dependent decreases in the total osteocyte lacunar number were measured in all of the cases. This change signifies a risk for the bone’s safety. Cortical subdivision into periosteal and endosteal regions of interest emphasized that, in both sexes, primarily the endosteal cortex is affected by age‐dependent reduction in number of osteocyte lacunae, whereas the periosteal compartment showed a less pronounced osteocyte lacunar deficiency. In aged bone, osteocyte lacunae showed an increased amount of hypermineralized calcium phosphate occlusions in comparison with younger cases. With respect to Frost’s early delineation of micropetrosis, our microanalyses revealed that the osteocyte lacunae are subject to hypermineralization. Intralacunar hypermineralization accompanied by a decrease in total osteocyte lacunar density may contribute to failure or delayed bone repair in aging bone. A decreased osteocyte lacunar density may cause deteriorations in the canalicular fluid flow and reduce the detection of microdamage, which counteracts the bone’s structural integrity, while hypermineralized osteocyte lacunae may increase bone brittleness and render the bone fragile.     

The Interactions between the Chronic Exposure to Aluminum and Liver Regeneration on Bile Flow and Organic Anion Transport in Rats

The chronic exposure to Aluminum (Al) may compromise different liver functions, mainly during the hepatic regeneration. The aim of this study is to investigate the interactions between the chronic i.p. exposure to Al and hepatic regeneration (HR) on bile flow and organic anion transport in experimental animals. For this purpose, we studied bile flow and fractional transfer rates for the transport of hepatic organic anions (hepatic uptake, sinusoidal efflux, and canalicular excretion), as well as parameters related with the oxidative stress (OS), on rats chronically treated with Al at 0 and 2 days of HR. The Al treatment and time of HR caused a decrease in the biliary flow and in the hepatic uptake and canalicular excretion constants. In addition, Al and HR increased the lipoperoxidation associated with a reduction of the glutathione content and glutathione peroxidase and catalase enzyme’s activities. Since the effects of Al and HR on biliary flow and transport systems were additive, but not on the oxidative status, different mechanisms might be involved on these alterations. Even though the OS may play a key role on the hepatic deleterious effects, there is no unique cause–effect relationship between OS and liver dysfunction in this experimental animal model.     

Bone poroelasticity

Poroelasticity is a well-developed theory for the interaction of fluid and solid phases of a fluid-saturated porous medium. It is widely used in geomechanics and has been applied to bone by many authors in the last 30 years. The purpose of this work is, first, to review the literature related to the application of poroelasticity to the interstitial bone fluid and, second, to describe the specific physical and modeling considerations that establish poroelasticity as an effective and useful model for deformation-driven bone fluid movement in bone tissue. The application of poroelasticity to bone differs from its application to soft tissues in two important ways. First, the deformations of bone are small while those of soft tissues are generally large. Second, the bulk modulus of the mineralized bone matrix is about six times stiffer than that of the fluid in the pores while the bulk moduli of the soft tissue matrix and the pore water are almost the same. Poroelasticity and electrokinetics can be used to explain strain-generated potentials in wet bone. It is noted that strain-generated potentials can be used as an effective tool in the experimental study of local bone fluid flow, and that the knowledge of this technique will contribute to the answers of a number of questions concerning bone mineralization, osteocyte nutrition and the bone mechanosensory system.     

Fluid-induced osteolysis: modelling and experiments

A model to calculate bone resorption driven by fluid flow at the bone–soft tissue interface is developed and used as a basis for computer calculations, which are compared to experiments where bone is subjected to fluid flow in a rat model. Previous models for bone remodelling calculations have been based on the state of stress, strain or energy density of the bone tissue as the stimulus for remodelling. We believe that there is experimental support for an additional pathway where an increase in the amount of the cells directly involved in bone removal, the osteoclasts, is caused by fluid pressure, flow velocity or other parameters related to fluid flow at the bone–soft tissue interface, resulting in bone resorption.     

In vitro model of a semicircular canal: Design and validation of the model and its use for the study of canalithiasis

We present an experimental model for a semicircular canal with canalithiasis. Canalithiasis is a pathological condition where free-floating particles disturb the flow field in the semicircular canals. It may lead to a specific form of vertigo known as BPPV or top-shelf vertigo. A careful scaling of the physical and geometrical parameters allows us to study the mechanics of this disease on an enlarged model of a single semicircular canal with laser vibrometry and video particle tracking. Early results confirm the proper operation of the model canal and support the current theories on the mechanisms of BPPV.     

Fluid-induced osteolysis: modelling and experiments

A model to calculate bone resorption driven by fluid flow at the bone-soft tissue interface is developed and used as a basis for computer calculations, which are compared to experiments where bone is subjected to fluid flow in a rat model. Previous models for bone remodelling calculations have been based on the state of stress, strain or energy density of the bone tissue as the stimulus for remodelling. We believe that there is experimental support for an additional pathway where an increase in the amount of the cells directly involved in bone removal, the osteoclasts, is caused by fluid pressure, flow velocity or other parameters related to fluid flow at the bone-soft tissue interface, resulting in bone resorption.     

Blood flow through a stenosis in microcirculation

A theoretical and experimental study concerning two-component fluid pulsating flow through cylindrical ducts having a slight constriction is presented. The model corresponds to blood flows through small diameter vessels (smaller than 400 micron) affected by a singular stenosis. The theoretical approach is based on a asymptotical expansion of the stream function. The physical hypotheses used were based on findings from simultaneous visualization methods. The influence of geometrical, hydrodynamical and structural parameters is systematically examined and related to velocity profiles, hydrostatic pressure, surface stresses.     

A mixture theory model of fluid and solute transport in the microvasculature of normal and malignant tissues. II: Factor sensitivity analysis, calibration, and validation

The treatment of cancerous tumors is dependent upon the delivery of therapeutics through the blood by means of the microcirculation. Differences in the vasculature of normal and malignant tissues have been recognized, but it is not fully understood how these differences affect transport and the applicability of existing mathematical models has been questioned at the microscale due to the complex rheology of blood and fluid exchange with the tissue. In addition to determining an appropriate set of governing equations it is necessary to specify appropriate model parameters based on physiological data. To this end, a two stage sensitivity analysis is described which makes it possible to determine the set of parameters most important to the model’s calibration. In the first stage, the fluid flow equations are examined and a sensitivity analysis is used to evaluate the importance of 11 different model parameters. Of these, only four substantially influence the intravascular axial flow providing a tractable set that could be calibrated using red blood cell velocity data from the literature. The second stage also utilizes a sensitivity analysis to evaluate the importance of 14 model parameters on extravascular flux. Of these, six exhibit high sensitivity and are integrated into the model calibration using a response surface methodology and experimental intra- and extravascular accumulation data from the literature (Dreher et al. in J Natl Cancer Inst 98(5):335–344, 2006). The model exhibits good agreement with the experimental results for both the mean extravascular concentration and the penetration depth as a function of time for inert dextran over a wide range of molecular weights.     

Penetrating annulus fibrosus injuries affect dynamic compressive behaviors of the intervertebral disc via altered fluid flow: an analytical interpretation

Extensive experimental work on the effects of penetrating annular injuries indicated that large injuries impact axial compressive properties of small animal intervertebral discs, yet there is some disagreement regarding the sensitivity of mechanical tests to small injury sizes. In order to understand the mechanism of injury size sensitivity, this study proposed a simple one dimensional model coupling elastic deformations in the annulus with fluid flow into and out of the nucleus through both porous boundaries and through a penetrating annular injury. The model was evaluated numerically in dynamic compression with parameters obtained by fitting the solution to experimental stress-relaxation data. The model predicted low sensitivity of mechanical changes to injury diameter at both small and large sizes (as measured by low and high ratios of injury diameter to annulus thickness), with a narrow range of high sensitivity in between. The size at which axial mechanics were most sensitive to injury size (i.e., critical injury size) increased with loading frequency. This study provides a quantitative hypothetical model of how penetrating annulus fibrosus injuries in discs with a gelatinous nucleus pulposus may alter disc mechanics by changing nucleus pulposus fluid pressurization through introduction of a new fluid transport pathway though the annulus. This model also explains how puncture-induced biomechanical changes depend on both injury size and test protocol.     

Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study

Bone remodelling is the process that maintains bone structure and strength through adaptation of bone tissue mechanical properties to applied loads. Bone can be modelled as a porous deformable material whose pores are filled with cells, organic material and interstitial fluid. Fluid flow is believed to play a role in the mechanotransduction of signals for bone remodelling. In this work, an osteon, the elementary unit of cortical bone, is idealized as a hollow cylinder made of a deformable porous matrix saturated with an interstitial fluid. We use Biot’s poroelasticity theory to model the mechanical behaviour of bone tissue taking into account transverse isotropic mechanical properties. A finite element poroelastic model is developed in the COMSOL Multiphysics software. Elasticity equations and Darcy’s law are implemented in this software; they are coupled through the introduction of an interaction term to obtain poroelasticity equations. Using numerical simulations, the investigation of the effect of spatial gradients of permeability or Poisson’s ratio is performed. Results are discussed for their implication on fluid flow in osteons: (i) a permeability gradient affects more the fluid pressure than the velocity profile; (ii) focusing on the fluid flow, the key element of loading is the strain rate; (iii) a Poisson’s ratio gradient affects both fluid pressure and fluid velocity. The influence of textural and mechanical properties of bone on mechanotransduction signals for bone remodelling is also discussed.     

Modeling of biological doses and mechanical effects on bone transduction

Shear stress, hormones like parathyroid and mineral elements like calcium mediate the amplitude of stimulus signal, which affects the rate of bone remodeling. The current study investigates the theoretical effects of different metabolic doses in stimulus signal level on bone. The model was built considering the osteocyte as the sensing center mediated by coupled mechanical shear stress and some biological factors. The proposed enhanced model was developed based on previously published works dealing with different aspects of bone transduction. It describes the effects of physiological doses variations of calcium, parathyroid hormone, nitric oxide and prostaglandin E2 on the stimulus level sensed by osteocytes in response to applied shear stress generated by interstitial fluid flow. We retained the metabolic factors (parathyroid hormone, nitric oxide and prostaglandin E2) as parameters of bone cell mechanosensitivity because stimulation/inhibition of induced pathways stimulates osteogenic response in vivo. We then tested the model response in terms of stimulus signal variation versus the biological factors doses to external mechanical stimuli. Despite the limitations of the model, it is consistent and has physiological bases. Biological inputs are histologically measurable. This makes the model amenable to experimental verification.     

Micromotion-induced peri-prosthetic fluid flow around a cementless femoral stem

Micromotion-induced interstitial fluid flow at the bone-implant interface has been proposed to play an important role in aseptic loosening of cementless implants. High fluid velocities are thought to promote aseptic loosening through activation of osteoclasts, shear stress induced control of mesenchymal stem cells differentiation, or transport of molecules. In this study, our objectives were to characterize and quantify micromotion-induced fluid flow around a cementless femoral stem using finite element modeling. With a 2D model of the bone-implant interface and full-factorial design, we first evaluated the relative influence of material properties, and bone-implant micromotion and gap on fluid velocity. Transverse sections around a femoral stem were built from computed tomography images, while boundary conditions were obtained from experimental measurements on the same femur. In a second step, a 3D model was built from the same data-set to estimate the shear stress experienced by cells hosted in the peri-implant tissues. The full-factorial design analysis showed that local micromotion had the most influence on peak fluid velocity at the interface. Remarkable variations in fluid velocity were observed in the macrostructures at the surface of the implant in the 2D transverse sections of the stem. The 3D model predicted peak fluid velocities extending up to 2.2 mm/s in the granulation tissue and to 3.9 mm/s in the trabecular bone. Peak shear stresses on the cells hosted in these tissues ranged from 0.1 to 12.5 Pa. These results offer insight into mechanical stimuli encountered at the bone-implant interface.