Evaluation of nucleus pulposus fluid velocity and pressure alteration induced by cartilage endplate sclerosis using a poro-elastic finite element analysis

The nucleus pulposus (NP) in the intervertebral disk (IVD) depends on diffusive fluid transport for nutrients through the cartilage endplate (CEP). Disruption in fluid exchange of the NP is considered a cause of IVD degeneration. Furthermore, CEP calcification and sclerosis are hypothesized to restrict fluid flow between the NP and CEP by decreasing permeability and porosity of the CEP matrix. We performed a finite element analysis of an L3-L4 lumbar functional spine unit with poro-elastic constitutive equations. The aim of the study was to predict changes in the solid and fluid parameters of the IVD and CEP under structural changes in CEP. A compressive load of 500 N was applied followed by a 10 Nm moment in extension, flexion, lateral bending, and axial rotation to the L3-L4 model with fully saturated IVD, CEP, and cancellous bone. A healthy case of L3-L4 physiology was then compared to two cases of CEP sclerosis: a calcified cartilage endplate and a fluid constricted sclerotic cartilage endplate. Predicted NP fluid velocity increased for the calcified CEP and decreased for the calcified + less permeable CEP. Decreased NP fluid velocity was prominent in the axial direction through the CEP due to a less permeable path available for fluid flux. Fluid pressure and maximum principal stress in the NP were predicted to increase in both cases of CEP sclerosis compared to the healthy case. The porous medium predictions of this analysis agree with the hypothesis that CEP sclerosis decreases fluid flow out of the NP, builds up fluid pressure in the NP, and increases the stress concentrations in the NP solid matrix.

A Chemo-poroelastic Analysis of Mechanically Induced Fluid and Solute Transport in an Osteonal Cortical Bone

It is well known that transport of nutrients and wastes as solute in bone fluid plays an important role in bone remodeling and damage healing. This work presents a chemo-poroelastic model for fluid and solute transport in the lacunar-canalicular network of an osteonal cortical bone under cyclic axial mechanical loading or vascular pressure. Analytical solutions are obtained for the pore fluid pressure, and fluid and solute velocities. Numerical results for fluid and calcium transport indicate that under a cyclic stress of 20 MPa, the magnitudes of the fluid and calcium velocities increase with an increase in the loading frequency for the frequency range considered (≤ 3 Hz) and peak at the inner boundary. The peak magnitude of calcium velocity reaches 18.9 μm/s for an osteon with a permeability of 1.5 × 10^-19 m² under a 3 Hz loading frequency. The magnitude of calcium velocity under a vascular pressure of 50 mmHg is found to be two orders of magnitude smaller than that under the mechanical load. These results have the potential to be important in understanding fundamental aspects of cortical bone remodeling as transport characteristics of calcium and other nutrients at the osteon scale influence bone metabolism.

Microplastics elutriation system. Part A: Numerical modeling

The elutriation process has shown its efficiency to extract microplastics from sand and began to spread in the scientific community. This extraction technic requires knowing with accuracy the extraction velocities of particles. This study aims to test whether numerical modeling could help to calculate these velocities. From hydrodynamic equations, a numerical model has been developed and the outputs are compared to experimental extraction data. The results show, for the calculated velocities, the experimental plastic extraction yields will be higher than 90% for <10% of sand contamination. The model also allows determining that, with the actual protocol, the maximum plastic density which can be extracted is about 1450kg·m^-3 whereas the detrimental resuspension, which may occur during the column filling step, is highlighted. From model calculations, it arises that changes in the column dimensioning and the protocol operations need to be considered.

Comparative assessment of intrinsic mechanical stimuli on knee cartilage and compressed agarose constructs

A well-established cue for improving the properties of tissue-engineered cartilage is mechanical stimulation. However, the explicit ranges of mechanical stimuli that correspond to favorable metabolic outcomes are elusive. Usually, these outcomes have only been associated with the applied strain and frequency, an oversimplification that can hide the fundamental relationship between the intrinsic mechanical stimuli and the metabolic outcomes. This highlights two important key issues: the firstly is related to the evaluation of the intrinsic mechanical stimuli of native cartilage; the second, assuming that the intrinsic mechanical stimuli will be important, deals with the ability to replicate them on the tissue-engineered constructs. This study quantifies and compares the volume of cartilage and agarose subjected to a given magnitude range of each intrinsic mechanical stimulus, through a numerical simulation of a patient-specific knee model coupled with experimental data of contact during the stance phase of gait, and agarose constructs under direct-dynamic compression. The results suggest that direct compression loading needs to be parameterized with time-dependence during the initial culture period in order to better reproduce each one of the intrinsic mechanical stimuli developed in the patient-specific cartilage. A loading regime which combines time periods of low compressive strain (5%) and frequency (0.5Hz), in order to approach the maximal principal strain and fluid velocity stimulus of the patient-specific cartilage, with time periods of high compressive strain (20%) and frequency (3Hz), in order to approach the pore pressure values, may be advantageous relatively to a single loading regime throughout the full culture period.