Three Dimensional Modeling of the Cerebrospinal Fluid Dynamics and Brain Interactions in the Aqueduct of Sylvius

A computational fluid dynamics (CFD) method is presented to investigate the flow of cerebro-spinal fluid (CSF) in the cerebral aqueduct. In addition to former approaches exhibiting a rigid geometry, we propose a model which includes a deformable membrane as the wall of this flow channel. An anatomical shape of the aqueduct was computed from magnetic resonance images (MRI) and the resulting meshing was immersed in a marker-and-cell (MAC) staggered grid for to take into account fluid–structure interactions. The time derivatives were digitized using the Crank–Nicolson scheme. The equation of continuity was modified by introducing an artificial compressibility and digitized by a finite difference scheme.

Calculations were validated with the simulation of laminar flow in a rigid tube. Then, comparisons were made between simulations of a rigid aqueduct and a deformable one. We found that the deformability of the walls has a strong influence on the pressure drop for a given flow.     

Computational investigation of subject-specific cerebrospinal fluid flow in the third ventricle and aqueduct of Sylvius

The cerebrospinal fluid flow in the third ventricle of the brain and the aqueduct of Sylvius was studied using computational fluid dynamics (CFD) based on subject-specific boundary conditions derived from magnetic resonance imaging (MRI) scans. The flow domain geometry was reconstructed from anatomical MRI scans by manual image segmentation. The movement of the domain boundary was derived from MRI brain motion scans. Velocimetric MRI scans were used to reconstruct the velocity field at the inferior end of the aqueduct of Sylvius based on the theory of pulsatile flow in pipes. A constant pressure boundary condition was assigned at the foramina of Monro. Three main flow features were observed: a fluid jet emerging from the aqueduct of Sylvius, a moderately mobile recirculation zone above the jet and a mobile recirculation below the jet. The flow in the entire domain was laminar with a maximum Reynolds number of 340 in the aqueduct. The findings demonstrate that by combining MRI scans and CFD simulations, subject-specific detailed quantitative information of the flow field in the third ventricle and the aqueduct of Sylvius can be obtained.     

Computational modeling of the mechanical behavior of the cerebrospinal fluid system

A computational fluid dynamics (CFD) model of the cerebrospinal fluid system was constructed based on a simplified geometry of the brain ventricles and their connecting pathways. The flow is driven by a prescribed sinusoidal motion of the third ventricle lateral walls, with all other boundaries being rigid. The pressure propagation between the third and lateral ventricles was examined and compared to data obtained from a similar geometry with a stenosed aqueduct. It could be shown that the pressure amplitude in the lateral ventricles increases in the presence of aqueduct stenosis. No difference in phase shift between the motion of the third ventricle walls and the pressure in the lateral ventricles because of the aqueduct stenosis could be observed. It is deduced that CFD can be used to analyze the pressure propagation and its phase shift relative to the ventricle wall motion. It is further deduced that only models that take into account the coupling between ventricles, which feature a representation of the original geometry that is as accurate as possible and which represent the ventricle boundary motion realistically, should be used to make quantitative statements on flow and pressure in the ventricular space.     

Multiphysics simulation of blood flow and LDL transport in a porohyperelastic arterial wall model

Atherosclerosis localizes at a bend andor bifurcation of an artery, and low density lipoproteins (LDL) accumulate in the intima. Hemodynamic factors are known to affect this localization and LDL accumulation, but the details of the process remain unknown. It is thought that the LDL concentration will be affected by the filtration flow, and that the velocity of this flow will be affected by deformation of the arterial wall. Thus, a coupled model of a blood flow and a deformable arterial wall with filtration flow would be invaluable for simulation of the flow field and concentration field in sequence. However, this type of highly coupled interaction analysis has not yet been attempted. Therefore, we performed a coupled analysis of an artery with multiple bends in sequence. First, based on the theory of porous media, we modeled a deformable arterial wall using a porohyperelastic model (PHEM) that was able to express both the filtration flow and the viscoelastic behavior of the living tissue, and simulated a blood flow field in the arterial lumen, a filtration flow field and a displacement field in the arterial wall using a fluid-structure interaction (FSI) program code by the finite element method (FEM). Next, based on the obtained results, we further simulated LDL transport using a mass transfer analysis code by the FEM. We analyzed the PHEM in comparison with a rigid model. For the blood flow, stagnation was observed downward of the bends. The direction of the filtration flow was only from the lumen to the wall for the rigid model, while filtration flows from both the wall to the lumen and the lumen to the wall were observed for the PHEM. The LDL concentration was high at the lumenwall interface for both the PHEM and rigid model, and reached its maximum value at the stagnation area. For the PHEM, the maximum LDL concentration in the wall in the radial direction was observed at the position of 3% wall thickness from the lumenwall interface, while for the rigid model, it was observed just at the lumenwall interface. In addition, the peak LDL accumulation area of the PHEM moved about according to the pulsatile flow. These results demonstrate that the blood flow, arterial wall deformation, and filtration flow all affect the LDL concentration, and that LDL accumulation is due to stagnation and the presence of filtration flow. Thus, FSI analysis is indispensable.     

Three-dimensional cerebrospinal fluid flow within the human ventricular system

Cerebrospinal fluid (CSF) is a Newtonian fluid and can, therefore, be modelled using computational fluid dynamics (CFD). Previous modelling of the CSF has been limited to simplified geometric models. This work describes a geometrically accurate three dimensional (3D) computational model of the human ventricular system (HVS) constructed from magnetic resonance images (MRI) of the human brain. It is an accurate and full representation of the HVS and includes appropriately positioned CSF production and drainage locations. It was used to investigate the pulsatile motion of CSF within the human brain. During this investigation CSF flow rate was set at a constant 500 ml/day, to mimic real life secretion of CSF into the system, and a pulsing velocity profile was added to the inlets to incorporate the effect of cardiac pulsations on the choroid plexus and their subsequent influence on CSF motion in the HVS. Boundary conditions for the CSF exits from the ventricles (foramina of Magendie and Lushka) were found using a "nesting" approach, in which a simplified model of the entire central nervous system (CNS) was used to examine the effects of the CSF surrounding the ventricular system (VS). This model provided time varying pressure data for the exits from the VS nested within it. The fastest flow was found in the cerebral aqueduct, where a maximum velocity of 11.38 mm/s was observed over five cycles. The maximum Reynolds number recorded during the simulation was 15 with an average Reynolds number of the order of 0.39, indicating that CSF motion is creeping flow in most of the computational domain and consequently will follow the geometry of the model. CSF pressure also varies with geometry with a maximum pressure drop of 1.14 Pa occurring through the cerebral aqueduct. CSF flow velocity is substantially slower in the areas that are furthest away from the inlets; in some areas flow is nearly stagnant.     

Three-dimensional cerebrospinal fluid flow within the human ventricular system

Cerebrospinal fluid (CSF) is a Newtonian fluid and can, therefore, be modelled using computational fluid dynamics (CFD). Previous modelling of the CSF has been limited to simplified geometric models. This work describes a geometrically accurate three dimensional (3D) computational model of the human ventricular system (HVS) constructed from magnetic resonance images (MRI) of the human brain. It is an accurate and full representation of the HVS and includes appropriately positioned CSF production and drainage locations. It was used to investigate the pulsatile motion of CSF within the human brain. During this investigation CSF flow rate was set at a constant 500 ml/day, to mimic real life secretion of CSF into the system, and a pulsing velocity profile was added to the inlets to incorporate the effect of cardiac pulsations on the choroid plexus and their subsequent influence on CSF motion in the HVS. Boundary conditions for the CSF exits from the ventricles (foramina of Magendie and Lushka) were found using a “nesting” approach, in which a simplified model of the entire central nervous system (CNS) was used to examine the effects of the CSF surrounding the ventricular system (VS). This model provided time varying pressure data for the exits from the VS nested within it. The fastest flow was found in the cerebral aqueduct, where a maximum velocity of 11.38 mm/s was observed over five cycles. The maximum Reynolds number recorded during the simulation was 15 with an average Reynolds number of the order of 0.39, indicating that CSF motion is creeping flow in most of the computational domain and consequently will follow the geometry of the model. CSF pressure also varies with geometry with a maximum pressure drop of 1.14 Pa occurring through the cerebral aqueduct. CSF flow velocity is substantially slower in the areas that are furthest away from the inlets; in some areas flow is nearly stagnant.     

Comparison of Efficency of Translation Between a Deformable Swimmer Versus a Rigid Body in a Bounded Fluid Domain: Consequences for Subcellular Transport

In this paper, we compare the translation efficiencies of a deformable circle that swims by means of low amplitude periodic tangential surface waves versus a rigid circle, moving in a bounded fluid domain. The swimmer is found to be much more efficient than the rigid body. We believe that this result gives some support to the active hypothesis of subcellular transport, where it is supposed that the organelle can generate by itself a propulsive flux, (by changes of form or metabolic activities) instead of just being carried by the motion of an external agent, like a molecular motor.     

Measurement of the distribution of red blood cell deformability using an automated rheoscope

BACKGROUND: Red blood cells (RBCs) have to deform markedly to pass through the smallest capillaries of the microcirculation. Techniques for measuring RBC deformability often result in an indication of the mean value. A deformability distribution would be more useful for studying diseases that are marked by subpopulations of less deformable cells because even small fractions of rigid cells can cause circulatory problems. METHODS: We present an automated rheoscope that uses advanced image analysis techniques to determine a RBC deformability distribution (RBC-DD) by analyzing a large number of individual cells in shear flow. The sensitivity was measured from density-separated fractions of one blood sample and from cells rendered less deformable by heat treatment. A preliminary experiment included the RBC-DDs of a patient with sickle cell anemia, one on dialysis and being treated with erythropoietin, and one with elliptocytosis. RESULTS: Measurement of the RBC-DD was highly reproducible. The sensitivity test showed markedly different deformability distributions of density-separated cells and yielded distinct RBC-DDs after each additional minute of heat treatment. CONCLUSION: The automated rheoscope enabled the determination of RBC-DDs from which less deformable subpopulations can be established. The shape of an RBC-DD may be valuable in assessing cell fractions with normal and anomalous deformability within pathologic blood samples.     

Computationally efficient finite element evaluation of natural patellofemoral mechanics

Finite element methods have been applied to evaluate in vivo joint behavior, new devices, and surgical techniques but have typically been applied to a small or single subject cohort. Anatomic variability necessitates the use of many subject-specific models or probabilistic methods in order to adequately evaluate a device or procedure for a population. However, a fully deformable finite element model can be computationally expensive, prohibiting large multisubject or probabilistic analyses. The aim of this study was to develop a group of subject-specific models of the patellofemoral joint and evaluate trade-offs in analysis time and accuracy with fully deformable and rigid body articular cartilage representations. Finite element models of eight subjects were used to tune a pressure-overclosure relationship during a simulated deep flexion cycle. Patellofemoral kinematics and contact mechanics were evaluated and compared between a fully deformable and a rigid body analysis. Additional eight subjects were used to determine the validity of the rigid body pressure-overclosure relationship as a subject-independent parameter. There was good agreement in predicted kinematics and contact mechanics between deformable and rigid analyses for both the tuned and test groups. Root mean square differences in kinematics were less than 0.5 deg and 0.2 mm for both groups throughout flexion. Differences in contact area and peak and average contact pressures averaged 5.4%, 9.6%, and 3.8%, respectively, for the tuned group and 6.9%, 13.1%, and 6.4%, respectively, for the test group, with no significant differences between the two groups. There was a 95% reduction in computational time with the rigid body analysis as compared with the deformable analysis. The tuned pressure-overclosure relationship derived from the patellofemoral analysis was also applied to tibiofemoral (TF) articular cartilage in a group of eight subjects. Differences in contact area and peak and average contact pressures averaged 8.3%, 11.2%, and 5.7% between rigid and deformable analyses in the tibiofemoral joint. As statistical, probabilistic, and optimization techniques can require hundreds to thousands of analyses, a viable platform is crucial to component evaluation or clinical applications. The computationally efficient rigid body platform described in this study may be integrated with statistical and probabilistic methods and has potential clinical application in understanding in vivo joint mechanics on a subject-specific or population basis.     

Comparison of deformable and elastic foundation finite element simulations for predicting knee replacement mechanics

Rigid body total knee replacement (TKR) models with tibiofemoral contact based on elastic foundation (EF) theory utilize simple contact pressure-surface overclosure relationships to estimate joint mechanics, and require significantly less computational time than corresponding deformable finite element (FE) methods. However, potential differences in predicted kinematics between these representations are currently not well understood, and it is unclear if the estimates of contact area and pressure are acceptable. Therefore, the objectives of the current study were to develop rigid EF and deformable FE models of tibiofemoral contact, and to compare predicted kinematics and contact mechanics from both representations during gait loading conditions with three different implant designs. Linear and nonlinear contact pressure-surface overclosure relationships based on polyethylene material properties were developed using EF theory. All other variables being equal, rigid body FE models accurately estimated kinematics predicted by fully deformable FE models and required only 2% of the analysis time. As expected, the linear EF contact model sufficiently approximated trends for peak contact pressures, but overestimated the deformable results by up to 30%. The nonlinear EF contact model more accurately reproduced trends and magnitudes of the deformable analysis, with maximum differences of approximately 15% at the peak pressures during the gait cycle. All contact area predictions agreed in trend and magnitude. Using rigid models, edge-loading conditions resulted in substantial overestimation of peak pressure. Optimal nonlinear EF contact relationships were developed for specific TKR designs for use in parametric or repetitive analyses where computational time is paramount. The explicit FE analysis method utilized here provides a unique approach in that both rigid and deformable analyses can be run from the same input file, thus enabling simple selection of the most appropriate representation for the analysis of interest.     

Role of the subcommissural organ in the pathogenesis of congenital hydrocephalus in the HTx rat

The present investigation was designed to clarify the role of the subcommissural organ (SCO) in the pathogenesis of hydrocephalus occurring in the HTx rat. The brains of non-affected and hydrocephalic HTx rats from embryonic day 15 (E15) to postnatal day 10 (PN10) were processed for electron microscopy, lectin binding and immunocytochemistry by using a series of antibodies. Cerebrospinal fluid (CSF) samples of non-affected and hydrocephalic HTx rats were collected at PN1, PN7 and PN30 and analysed by one- and two-dimensional electrophoresis, immunoblotting and nanoLC-ESI-MS/MS. A distinct malformation of the SCO is present as early as E15. Since stenosis of the Sylvius aqueduct (SA) occurs at E18 and dilation of the lateral ventricles starts at E19, the malformation of the SCO clearly precedes the onset of hydrocephalus. In the affected rats, the cephalic and caudal thirds of the SCO showed high secretory activity with all methods used, whereas the middle third showed no signs of secretion. At E18, the middle non-secretory third of the SCO progressively fused with the ventral wall of SA, resulting in marked aqueduct stenosis and severe hydrocephalus. The abnormal development of the SCO resulted in the permanent absence of Reissner’s fibre (RF) and led to changes in the protein composition of the CSF. Since the SCO is the source of a large mass of sialilated glycoproteins that form the RF and of those that remain CSF-soluble, we hypothesize that the absence of this large mass of negatively charged molecules from the SA domain results in SA stenosis and impairs the bulk flow of CSF through the aqueduct.     

A computational study of leukocyte adhesion and its effect on flow pattern in microvessels

Three-dimensional computational modeling and simulation are presented on the adhesive rolling of deformable leukocytes over a P-selectin coated surface in parabolic shear flow in microchannels. The computational model is based on the immersed boundary method for cell deformation and Monte Carlo simulation for receptor/ligand interaction. The simulations are continued for at least 1 s of leukocyte rolling during which the instantaneous quantities such as cell deformation index, cell/substrate contact area, and fluid drag remain statistically stationary. The characteristic ‘stop-and-go’ motion of rolling leukocytes, and the ‘tear-drop’ shape of adherent leukocytes as observed in experiments are reproduced by the simulations. We first consider the role of cell deformation and cell concentration on rolling characteristics. We observe that compliant cells roll slower and more stably than rigid cells. Our simulations agree with previous in vivo observation that the hydrodynamic interactions between nearby leukocytes affect cell rolling, and that the rolling velocity decreases inversely with the separation distance, irrespective of cell deformability. We also find that cell deformation decreases, and the cells roll more stably with reduced velocity fluctuation, as the cell concentration is increased. However, the effect of nearby cells on the rolling characteristics is found to be more significant for rigid cells than compliant cells. We then address the effect of cell deformability and rolling velocity on the flow resistance due to, and the fluid drag on, adherent leukocytes. While several earlier computational works have addressed this problem, two key features of leukocyte adhesion, such as cell deformation and rolling, were often neglected. Our results suggest that neglecting cell deformability and rolling velocity may significantly overpredict the flow resistance and drag force. Increasing the cell concentration is shown to increase the flow resistance and reduce the fluid drag. The reduced drag then results in slower and more stable rolling of the leukocytes with longer pause time and shorter step distance. But the increase/decrease in the flow resistance/fluid drag due to the increase in the cell concentration is observed to be more significant in case of rigid cells than compliant cells.     

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.     

Hydrodynamic deformation and removal of Staphylococcus epidermidis biofilms treated with urea, chlorhexidine, iron chloride, or DispersinB

The force-deflection and removal characteristics of bacterial biofilm were measured by two different techniques before and after chemical, or enzymatic, treatment. The first technique involved time lapse imaging of a biofilm grown in a capillary flow cell and subjected to a brief shear stress challenge imparted through increased fluid flow. Biofilm removal was determined by calculating the reduction in biofilm area from quantitative analysis of transmission images. The second technique was based on micro-indentation using an atomic force microscope. In both cases, biofilms formed by Staphylococcus epidermidis were exposed to buffer (untreated control), urea, chlorhexidine, iron chloride, or DispersinB. In control experiments, the biofilm exhibited force-deflection responses that were similar before and after the same treatment. The biofilm structure was stable during the post-treatment shear challenge (1% loss). Biofilms treated with chlorhexidine became less deformable after treatment and no increase in biomass removal was seen during the post-treatment shear challenge (2% loss). In contrast, biofilms treated with urea or DispersinB became more deformable and exhibited significant biofilm loss during the post-treatment flow challenge (71% and 40%, respectively). During the treatment soak phase, biofilms exposed to urea swelled. Biofilms exposed to iron chloride showed little difference from the control other than slight contraction during the treatment soak. These observations suggest the following interpretations: (1) chemical or enzymatic treatments, including those that are not frankly antimicrobial, can alter the cohesion of bacterial biofilm; (2) biocidal treatments (e.g., chlorhexidine) do not necessarily weaken the biofilm; and (3) biofilm removal following treatment with agents that make the biofilm more deformable (e.g., urea, DispersinB) depend on interaction between the moving fluid and the biofilm structure. Measurements such as those reported here open the door to development of new technologies for controlling detrimental biofilms by targeting biofilm cohesion rather than killing microorganisms.     

Intrinsic viscoelasticity of blood cell suspensions: effects of erythrocyte deformability

The intrinsic viscoelasticity of erythrocyte suspensions holds great potential for specifying the deformability of the individual, noninteracting cells in an oscillatory shear flow field. In order to extrapolate to zero cell concentration, the complex viscoelastic modulus was measured as a function of hematocrit using 2 Hertz oscillatory flow and a shear rate of 10/sec. This was done for both normal cells and cells with severely reduced deformability when hardened with glutaraldehyde. Suspension media were blood plasma, isotonic saline, and Dextran solutions. The real parts of the complex intrinsic visco-elasticities were obtained by an extrapolation using a regression fit to Huggins' equation. For normal cells in native plasma the values ranged from 1.7 to 2, increasing to the range 2.4 to 3.1 when the plasma was diluted with isotonic saline solution. For hardened cells the value obtained was near 3.5. These results are compared with theories for suspensions of both rigid and deformable particles. Several theories for deformable particles predict an increase in intrinsic viscoelasticity with increases in the ratio of the viscosity of the interior of the particle to that of the suspending medium. This ratio controls the balance between rotational and deformational response of the cell in the flow field. The trends of these theories were observed in the measurements.     

Effect of image registration on 3D absorbed dose calculations in 177Lu-DOTATOC peptide receptor radionuclide therapy

Peptide receptor radionuclide therapy (PRRT) is an effective MRT (molecular radiotherapy) treatment, which consists of multiple administrations of a radiopharmaceutical labelled with ¹⁷⁷Lu or ⁹⁰Y. Through sequential functional imaging a patient specific 3D dosimetry can be derived. Multiple scans should be previously co-registered to allow accurate absorbed dose calculations. The purpose of this study is to evaluate the impact of image registration algorithms on 3D absorbed dose calculation.A cohort of patients was extracted from the database of a clinical trial in PRRT. They were administered with a single administration of ¹⁷⁷Lu-DOTATOC. All patients underwent 5 SPECT/CT sequential scans at 1 h, 4 h, 24 h, 40 h, 70 h post-injection that were subsequently registered using rigid and deformable algorithms. A similarity index was calculated to compare rigid and deformable registration algorithms. 3D absorbed dose calculation was carried out with the Raydose Monte Carlo code.The similarity analysis demonstrated the superiority of the deformable registrations (p < .001).Average absorbed dose to the kidneys calculated using rigid image registration was consistently lower than the average absorbed dose calculated using the deformable algorithm (90% of cases), with percentage differences in the range [−19; +4]%. Absorbed dose to lesions were also consistently lower (90% of cases) when calculated with rigid image registration with absorbed dose differences in the range [−67.2; 100.7]%. Deformable image registration had a significant role in calculating 3D absorbed dose to organs or lesions with volumes smaller than 100 mL.Image based 3D dosimetry for ¹⁷⁷Lu-DOTATOC PRRT is significantly affected by the type of algorithm used to register sequential SPECT/CT scans.     

Impact responses of the flexed human knee using a deformable impact interface

Blunt impact trauma to the patellofemoral joint during car accidents, sporting activities, and falls can produce a range of injuries to the knee joint, including gross bone fracture, soft tissue injury, and/or microinjuries to bone and soft tissue. Currently, the only well-established knee injury criterion applies to knee impacts suffered during car accidents. This criterion is based solely on the peak impact load delivered to seated cadavers having a single knee flexion angle. More recent studies, however, suggest that the injury potential, its location, and the characteristics of the damage are also a function of knee flexion angle and the stiffness of the impacting structure. For example, at low flexion angles, fractures of the distal patella are common with a rigid impact interface, while at high flexion angles splitting of the femoral condyles is more evident. Low stiffness impact surfaces have been previously shown to distribute impact loads over the anterior surface of the patella to help mitigate gross and microscopic injuries in the 90 deg flexed knee. The objective of the current study was to determine if a deformable impact interface would just as effectively mitigate gross and microscopic injuries to the knee at various flexion angles. Paired experiments were conducted on contralateral knees of 18 human cadavers at three flexion angles (60, 90, 120 deg). One knee was subjected to a fracture level impact experiment with a rigid impactor, and the opposite knee was impacted with a deformable interface (3.3 MPa crush strength honeycomb material) to the same load. This (deformable) impact interface was effective at mitigating gross bone fractures at approximately 5 kN at all flexion angles, but the frequency of split fracture of the femoral condyles may not have been significantly reduced at 120 deg flexion. On the other hand, this deformable interface was not effective in mitigating microscopic injuries observed for all knee flexion angles. These new data, in concert with the existing literature, suggest the chosen impact interface was not optimal for knee injury protection in that fracture and other minor injuries were still produced. For example, in 18 cadavers a total of 20 gross fractures and 20 subfracture injuries were produced with a rigid interface and 5 gross fractures and 21 subfracture injuries with the deformable interface selected for the current study. Additional studies will be needed to optimize the knee impact interface for protection against gross and microscopic injuries to the knee.     

On transport of suspended particulates in tube flow.

Blood cells suspended in shear flows exhibit much larger dispersive motions than those predicted by the Stokes-Einstein formula for Brownian diffusion. The lateral migration and the erratic motions of the 8 microns red blood cells (RBC) is thought to be analogous to a diffusive process. It is shown that the often cited convective-diffusion theory may not be an adequate model for describing the transverse migration of suspended cells in blood flow. A comprehensive review of both the classical theory and of contemporary work in particle transport is presented, with particular emphasis on low Reynolds number tube flows. The mechanisms of Taylor dispersion, the effects of Brownian perturbations on translational and rotational motions of the suspended particles in shear fields, and the influence of integratable and chaotic advections, are individually examined. The classical experiment by Segre and Silberberg (1962) lead us to believe that particle hydrodynamics may play an important role in transverse migrations. In this light, we have further examined the hydrodynamic aspects of the so-called "tubular pinch" effect, the lateral migration of rigid spheres. We have also discussed the transverse motions of liquid drops, and the reversibility of the organization of suspensions in transport. The convective accelerations in the entrance region of a tube can produce relative velocities between fluid medium and various type of particulates if there is a difference in density. The deformable RBC, an "active-type" particle, can provide feedback to the flow from both mass and momentum considerations; the more rigid platelet, a "passive-type" particle, will experience a much smaller relative velocity as compared to the RBC. We may expect that particles of different densities are transported to different equilibrium annular positions before entering the fully developed flow region. The erratic, lateral movement of suspended particulates in steady laminar tube flow can be described by the usual Lagrangian coordinates.     

Finite element analysis of biological soft tissue surrounded by a deformable membrane that controls transmembrane flow

Background

Many biological soft tissues are hydrated porous hyperelastic materials, which consist of a complex solid skeleton with fine voids and fluid filling these voids. Mechanical interactions between the solid and the fluid in hydrated porous tissues have been analyzed by finite element methods (FEMs) in which the mixture theory was introduced in various ways. Although most of the tissues are surrounded by deformable membranes that control transmembrane flows, the boundaries of the tissues have been treated as rigid and/or freely permeable in these studies. The purpose of this study was to develop a method for the analysis of hydrated porous hyperelastic tissues surrounded by deformable membranes that control transmembrane flows.

Results

For this, we developed a new nonlinear finite element formulation of the mixture theory, where the nodal unknowns were the pore water pressure and solid displacement. This method allows the control of the fluid flow rate across the membrane using Neumann boundary condition. Using the method, we conducted a compression test of the hydrated porous hyperelastic tissue, which was surrounded by a flaccid impermeable membrane, and a part of the top surface of this tissue was pushed by a platen. The simulation results showed a stress relaxation phenomenon, resulting from the interaction between the elastic deformation of the tissue, pore water pressure gradient, and the movement of fluid. The results also showed that the fluid trapped by the impermeable membrane led to the swelling of the tissue around the platen.

Conclusions

These facts suggest that our new method can be effectively used for the analysis of a large deformation of hydrated porous hyperelastic material surrounded by a deformable membrane that controls transmembrane flow, and further investigations may allow more realistic analyses of the biological soft tissues, such as brain edema, brain trauma, the flow of blood and lymph in capillaries and pitting edema.