Final Report Summary - SEVBIOM (Mechanistic and evolutive development of spine biomechanical modelling)
In this project, different aspects of intervertebral disc modelling have been addressed in order to obtain reliable local predictions of the disc tissue mechanical response and further allow the coupling of finite element (FE) simulations to mechanobiological studies of the disc tissues. The points covered were the following:
1. Annulus fibre configuration effects on the local disc mechanics
In this part of the project, different annulus fibrosus fibre configurations that included radial and/or tangential fibre orientation gradients were simulated as reported in anatomical studies of healthy intervertebral discs. Ability of the annulus fibre to stabilise intervertebral joints mechanically was assessed by hypothesising that most efficient fibre configurations should be able to simultaneously maximise the fibre stress, minimise the matrix shear strains and limit the local concentrations of fibre stress. Based on such hypotheses, the effects of different annulus configurations simulated were evaluated in a L3-L5 lumbar spine FE model (FEM). Results indicated that radial fibre orientation gradients were not suitable to resist axial compressive loads, while their performance was pointed out under axial compression. Tangential gradients were appropriate to mechanically stabilise the intervertebral disc under sagittal flexion and transversal fibres best resisted to disc bulging due to local annulus compressions. Thus, the annulus fibrous organisation appeared both load- and geometry-specific, which suggested that the annulus fibre-reinforced models should be level-specific in particular. The level specificity seemed strongly supported by reported anatomical evidences.
Annulus fibre calibration and global validation of a L4-L5 poroelastic disc model.
By considering the previous results about fibre orientation effects, this part of the project aimed to reproduce the regional differences in annulus mechanical behaviour by parametrising only the fibre orientations in different tangential and radial areas of the annulus fibrosus. A fibre-reinforced poro-hyperealstic annulus tissue model was calibrated as such so that virtual tissue samples could reproduce the tensile behaviour of in vitro tested specimens. Both radial and tangential angle variations were found. The back-calculated fibre angles and the resulting regional patterns of angle variations were comparable with anatomical descriptions reported in the literature. Moreover, once integrated into a L4-L5 intervertebral disc FEM, the calibrated fibre-induced annulus anisotropy allowed the disc model reproducing the overall creep response of a L4-L5 disc specimen tested in vitro.
Numerical instabilities in intervertebral poroelastic modelling
The first simulations based on poroelasticity performed at the beginning of the project showed that the predicted fluid flow velocities oscillated abnormally along the annulus fibrosus structure under physiological load rates, i.e. 1Hz. The detailed study of the effects of both the disc structure and constitutive equation terms revealed that oscillations were due to the numerical integration of Darcy's Law integrated into the FE solver. Because of the large spatial variations of the consolidation at material discontinuities, the first spatial derivative of the pore pressure oscillated strongly form one integration point to another. Refining the overall mesh of the model according to a pre-existing rule about pore pressure oscillation depending on mesh size (Vermeer-Verruijt criterion) induced extremely high computation times and did not solve the problem. Indeed, successful limitation of the oscillations was achieved by a combination of local mesh refinement and material property interpolations at discontinuities. Simulating swelling processes created an added intradiscal pressure that seemed to act as a penalty factor, helping to further limit the oscillations under fast loads. These improvements of the disc model implicitly led to a more realistic description of the organ ultrastructure, showing that tissue transition areas and mechanistic descriptions should not be neglected in intervertebral disc models used for mechanobiology studies.
Influence of the cartilage endplate composition on the intervertebral disc hydration
Intervertebral disc swelling, hydration and transport properties strongly depend on the fluid that exits and enters the disc through the disc-vertebra interface called the vertebral endplate. Interestingly this interface seems to allow faster fluid inflow from the vertebral to the disc than fluid outflow from the disc to the vertebra. Indeed such mechanism allows for disc height recovery in about eight hours despite almost 16 hours of daily physical activity during which the disc is cyclically compressed and progressively dehydrates. Until now, only the disc valve theory was able to explain such phenomenon, based on cartilage endplate porosity changes when fluid exits or enters the disc. Unfortunately, the disc valve theory cannot explain that in vitro measurements can contradict the in vivo phenomenon. Simulating accurately such mechanisms is highly relevant to prepare the disc models for mechanobiological studies. Thus, the problem was addressed and based on the known cartilage endplate composition, we hypothesised that permeability gradients related to proteoglycan concentrations may induce the in vivo direction-dependent fluid flows. By using a micro-FEM of the central cartilage endplate and including such gradients, we calculated the accumulation of fluid with the nucleus pulposus tissue along a load cycle of activity and rest periods. Permeability gradients in the cartilage endplates mostly affected the boundary consolidation of the tissue which was enough to both limit nucleus fluid loss during activity and favour rehydration during rest. The simulation of nucleus osmosis did not affect this inflow/outflow relationship that was therefore proven to be dues to endplate composition gradient. It is interesting to note that the cartilage endplate maybe the first disc structure to be altered along degenerative progressions and mechanical factors are thought to significantly affect such alteration.
1. Annulus fibre configuration effects on the local disc mechanics
In this part of the project, different annulus fibrosus fibre configurations that included radial and/or tangential fibre orientation gradients were simulated as reported in anatomical studies of healthy intervertebral discs. Ability of the annulus fibre to stabilise intervertebral joints mechanically was assessed by hypothesising that most efficient fibre configurations should be able to simultaneously maximise the fibre stress, minimise the matrix shear strains and limit the local concentrations of fibre stress. Based on such hypotheses, the effects of different annulus configurations simulated were evaluated in a L3-L5 lumbar spine FE model (FEM). Results indicated that radial fibre orientation gradients were not suitable to resist axial compressive loads, while their performance was pointed out under axial compression. Tangential gradients were appropriate to mechanically stabilise the intervertebral disc under sagittal flexion and transversal fibres best resisted to disc bulging due to local annulus compressions. Thus, the annulus fibrous organisation appeared both load- and geometry-specific, which suggested that the annulus fibre-reinforced models should be level-specific in particular. The level specificity seemed strongly supported by reported anatomical evidences.
Annulus fibre calibration and global validation of a L4-L5 poroelastic disc model.
By considering the previous results about fibre orientation effects, this part of the project aimed to reproduce the regional differences in annulus mechanical behaviour by parametrising only the fibre orientations in different tangential and radial areas of the annulus fibrosus. A fibre-reinforced poro-hyperealstic annulus tissue model was calibrated as such so that virtual tissue samples could reproduce the tensile behaviour of in vitro tested specimens. Both radial and tangential angle variations were found. The back-calculated fibre angles and the resulting regional patterns of angle variations were comparable with anatomical descriptions reported in the literature. Moreover, once integrated into a L4-L5 intervertebral disc FEM, the calibrated fibre-induced annulus anisotropy allowed the disc model reproducing the overall creep response of a L4-L5 disc specimen tested in vitro.
Numerical instabilities in intervertebral poroelastic modelling
The first simulations based on poroelasticity performed at the beginning of the project showed that the predicted fluid flow velocities oscillated abnormally along the annulus fibrosus structure under physiological load rates, i.e. 1Hz. The detailed study of the effects of both the disc structure and constitutive equation terms revealed that oscillations were due to the numerical integration of Darcy's Law integrated into the FE solver. Because of the large spatial variations of the consolidation at material discontinuities, the first spatial derivative of the pore pressure oscillated strongly form one integration point to another. Refining the overall mesh of the model according to a pre-existing rule about pore pressure oscillation depending on mesh size (Vermeer-Verruijt criterion) induced extremely high computation times and did not solve the problem. Indeed, successful limitation of the oscillations was achieved by a combination of local mesh refinement and material property interpolations at discontinuities. Simulating swelling processes created an added intradiscal pressure that seemed to act as a penalty factor, helping to further limit the oscillations under fast loads. These improvements of the disc model implicitly led to a more realistic description of the organ ultrastructure, showing that tissue transition areas and mechanistic descriptions should not be neglected in intervertebral disc models used for mechanobiology studies.
Influence of the cartilage endplate composition on the intervertebral disc hydration
Intervertebral disc swelling, hydration and transport properties strongly depend on the fluid that exits and enters the disc through the disc-vertebra interface called the vertebral endplate. Interestingly this interface seems to allow faster fluid inflow from the vertebral to the disc than fluid outflow from the disc to the vertebra. Indeed such mechanism allows for disc height recovery in about eight hours despite almost 16 hours of daily physical activity during which the disc is cyclically compressed and progressively dehydrates. Until now, only the disc valve theory was able to explain such phenomenon, based on cartilage endplate porosity changes when fluid exits or enters the disc. Unfortunately, the disc valve theory cannot explain that in vitro measurements can contradict the in vivo phenomenon. Simulating accurately such mechanisms is highly relevant to prepare the disc models for mechanobiological studies. Thus, the problem was addressed and based on the known cartilage endplate composition, we hypothesised that permeability gradients related to proteoglycan concentrations may induce the in vivo direction-dependent fluid flows. By using a micro-FEM of the central cartilage endplate and including such gradients, we calculated the accumulation of fluid with the nucleus pulposus tissue along a load cycle of activity and rest periods. Permeability gradients in the cartilage endplates mostly affected the boundary consolidation of the tissue which was enough to both limit nucleus fluid loss during activity and favour rehydration during rest. The simulation of nucleus osmosis did not affect this inflow/outflow relationship that was therefore proven to be dues to endplate composition gradient. It is interesting to note that the cartilage endplate maybe the first disc structure to be altered along degenerative progressions and mechanical factors are thought to significantly affect such alteration.