Poroelastic Finite Element Model Research Articles

Analysis of the impact responses in a degenerated spinal motion segment FE model

A three-dimensional non-linear poroelastic finite element model of an L3/L4 motion segment was used to analyze the biomechanical effects of degeneration under impact loading on the spinal segment. A previously developed degeneration algorithm was applied to generate a degenerated disc model. Regional variation in intact vertebral body bone morphology was simulated by assigning different void ratios of 4.0–5.02, which were assessed for 27 regions of vertebral cancellous bone. For the osteoporotic structure of the vertebral body, the body was divided into 5 regions with 10–24 void ratios. Different material properties were assigned to the annulus fibers; hereupon our annulus model reflected variation in tensile behavior of multiple layer annulus samples. The impact load applied to the top of the L3 vertebral body was assumed to be a triangular impulsive force with a maximum compressive impact load of 3 kN and 20ms impact duration time. Calculated results indicated that the effect of the degeneration was predominant at the center of the vertebral body. The maximum von Mises stress was found at the region of near the endplate. The degeneration increased the averaged stress at the center of the vertebral body of L3 from 1.54 MPa to 1.69 MPa, the stress remaining relatively small at L4. Decreased fluid volume ratio of the degenerated nucleus tended to increase pressure slightly at the nucleus, and the averaged stress at the nucleus was almost doubled compared to the intact case. The innermost layers of the anterior annulus showed the highest stress concentration, followed by outermost anterior and posterior regions, for both the degenerated and the intact models. Despite an irregular stress distribution in the degenerated model, pore pressure showed relatively uniform distribution.

Biomechanical Response of a Lumbar Intervertebral Disc to Manual Lifting Activities

Determination of damage to a lumbar disc caused by lifting using a poroelastic finite element model study. Compare the biomechanical response of a lumbar disc under 8 different lifting conditions and identify the loading conditions that produce the greatest deformations and highest stresses in various tissue components of the disc. Lifting has been associated epidemiologically with back injuries and back pain complaints. Forces high enough to cause mechanical damage to the disc have been predicted using analytical methods. Using kinematic data from series of lifts obtained in our laboratories and an electromyography (EMG)-driven muscle optimization model, representative force patterns for each of 8 lifts were obtained and used as input into a poroelastic finite element model. Disc tissue displacements and stresses were determined for all the 8 lift conditions. RESULTS.: Lifting the box from a maximally lateral flexed posture up to waist level (Task 5) produced the largest translational and rotational motions of all studied. This lift activity also produced maximum von Mises stresses in all disc components: annulus, nucleus, and endplates. The largest facet joint forces were also observed during lift Task 5. Asymmetric lifting involving lateral bending of the trunk produced large motions that might cause localized disc tissue injury. Stresses larger than the failure strength of the corresponding disc tissues were experienced during asymmetric lifting. Lifting that involves lateral bending of the trunk was the most hazardous type of loading with regard to damage to the disc.

Relationship between disc injury and manual lifting: A poroelastic finite element model study

Understanding how failure originates in a lumbar motion segment subjected to loading conditions that are representative of manual lifting is important because it will pave the way for a better formulation of the exposure-injury relationship. The aim of the current investigation was to use a poroelastic finite element model of a human lumbar disc to determine its biomechanical characteristics under loading conditions that corresponded to three different, commonly occurring lifting activities and to identify the most hazardous type of loading with regard to damage to the disc. The current study showed that asymmetric lifting may increase the risk of back injury and pain. Lifting that involved lateral bending (asymmetric lifting) of the trunk was found to produce stresses at a localized area in the annulus, annuluar fibres, end plates, and facet joints that were higher than their respective tissue failure strength. Thus asymmetric lifting, if performed over a large number of cycles, might help to propagate this localized failure of the disc tissue to a larger area, owing to fatigue. The analyses also showed that largest fluid exchange between the nucleus and the end plates occurred during asymmetric lifting. If the fluid exchange is restricted owing to end plate calcification or sclerosis of the subchondral bone, high intradiscal pressure might develop, leading to higher disc bulge causing back pain.

Simulation of fracture healing incorporating mechanoregulation of tissue differentiation and dispersal/proliferation of cells

Modelling the course of healing of a long bone subjected to loading has been the subject of several investigations. These have succeeded in predicting the differentiation of tissues in the callus in response to a static mechanical load and the diffusion of biological factors. In this paper an approach is presented which includes both mechanoregulation of tissue differentiation and the diffusion and proliferation of cell populations (mesenchymal stem cells, fibroblasts, chondrocytes, and osteoblasts). This is achieved in a three-dimensional poroelastic finite element model which, being poroelastic, can model the effect of the frequency of dynamic loading. Given the number of parameters involved in the simulation, a parameter variation study is reported, and final parameters are selected based on comparison with an in vivo experiment. The model predicts that asymmetric loading creates an asymmetric distribution of tissues in the callus, but only for high bending moments. Furthermore the frequency of loading is predicted to have an effect. In conclusion, a numerical algorithm is presented incorporating both mechanoregulation and evolution of cell populations, and it proves capable of predicting realistic difference in bone healing in a 3D fracture callus.

Simulation of the disc degeneration with a poroelastic finite element model

To predict the degeneration process in the intervertebral disc, a finite element model of the spinal motion segment model was developed. The relationship between the biomechanical characteristics of fluid and solid matrix of the disc and cancellous core of the vertebral body, modeled as 20 node poroelastic elements, during the degeneration process was investigated. Excess von Mises stress in the disc element was assumed to be a possible source of degeneration under compressive loading condition. Recursive calculation was continued until the desired convergence was attained by changing the permeability and void ratio of those elements. The degenerated disc model showed that relatively small compressive stresses were generated in the nucleus elements compared to normal disc. Its distribution along the sagittal plane was consistent with a previously reported experimental result. Contrasts to this result, pore pressures in the nucleus were higher than those in the normal disc. Total stress, sum of compressive stress and pore pressure, indicated similar values for two different models. This study presented a new approach to study the likely mechanism responsible for the initiation and progression of the degenerative process within the intervertebral disc.

Poro-elastic finite element model to predict the failure progression in a lumbar disc due to cyclic loading

There is a steady and concentrated effort to improve finite element models of the spinal motion segment that can simulate various clinical situations accurately. Recent developments in the area of poro-elastic finite element models including fluid structure interaction with in the disc have made it possible to understand the relationship between disc failure mechanisms and time dependent loading. The development of such a finite element model is presented here and used to predict the failure progression in a lumbar disc due to a physiologically relevant cyclic loading. This will help to understand how repetitive lifting is of importance in the development of back injuries.

Inclusion of regional poroelastic material properties better predicts biomechanical behavior of lumbar discs subjected to dynamic loading

Understanding the relationship between repetitive lifting and the breakdown of disc tissue over several years of exposure is difficult to study in vivo and in vitro. The aim of this investigation was to develop a three-dimensional poroelastic finite element model of a lumbar motion segment that reflects the biological properties and behaviors of in vivo disc tissues including swelling pressure due to the proteoglycans and strain-dependent permeability and porosity. It was hypothesized that when modeling the annulus, prescribing tissue specific material properties will not be adequate for studying the in vivo loading and unloading behavior of the disc. Rather, regional variations of these properties, which are known to exist within the annulus, must also be included. Finite element predictions were compared to in vivo measurements published by Tyrrell et al. (1985) of percent change in total stature for two loading protocols, short-term creep loading and standing recovery and short-term cyclic loading with standing recovery. The model in which the regional variations of material properties in the annulus had been included provided an overall better prediction of the in vivo behavior as compared to the model in which the annulus properties were assumed to be homogenous. This model will now be used to study the relationship between repetitive lifting and disc degeneration.

Modeling Changes in Intervertebral Disc Mechanics with Degeneration

Mechanical response of the spine to various dynamic loading conditions can be analyzed by way of in vitro and in vivo studies. Ethical concerns, interpretation of conclusions reached in animal studies, and lack of detailed stress distributions in the disc components are the major disadvantages of relying solely on in vivo studies. Intraspecimen variability, difficulty in including muscle activity, and inability to mimic fluid exchange into the disc during unloading are some of the disadvantages of in vitro models. The poroelastic finite element models can provide a method of understanding the relationship between biomechanical performance of the disc due to cyclic loading and disc degeneration. A poroelastic finite element model, including regional variation of strain-dependent permeability and osmotic pressure, was used to study the effect of disc degeneration on biomechanical properties as well as propagation of failure in the disc components when cyclic loading was applied to the lumbar disc. The results predicted that healthy discs were much more flexible than degenerated discs, and the disc stiffness decreased with increasing the number of load cycles independent of degenerative condition. Failure was found to progress as the drained elastic properties of the disc components decreased due to the presence of failure. Poroelastic finite element modeling, including strain-dependent permeability and osmotic pressure, is the most advanced analytical tool currently available that can be used to understand how cyclic loading affects the biomechanical characteristics of a degenerated lumbar disc. However, a complete understanding of behavior of the intervertebral disc will ultimately be achieved only with use of a combination of computational models together with in vitro and in vivo experimental methods. Finite element models of discs with varying degrees of disc degeneration will help clinicians understand the initiation and progression of disc failure and degeneration and will assist in the development of approaches to stimulate the regeneration of disc tissues.

Stochastic poromechanical modeling of anthropogenic land subsidence

A key issue in poromechanical modeling, e.g. for predicting anthropogenic land subsidence due to fluid withdrawal, is the evaluation and use of representative mechanical properties for the deforming porous medium at a regional scale. One such property is the vertical uniaxial rock compressibility c M which can be obtained through either laboratory oedometer tests or in situ measurements, and typically exhibits quite a marked scattering. This paper addresses the influence of the c M uncertainty on the predicted land settlement using a stochastic simulation approach where c M is regarded as a random variable and a large number of equally likely c M realizations are generated and implemented into a poroelastic finite element model. A compressibility law, characterized by a log-normal distribution with depth-dependent mean, constant variance and exponential covariance, is assumed. The Monte Carlo simulation provides a set of responses which can be analyzed statistically. The results from a number of numerical experiments show how the c M variance and covariance affect the reliability of the simulated land subsidence and provide a quantitative evaluation of the intrinsic uncertainty of the model prediction.

Computer assisted planning and orbital surgery: Patient-related prediction of osteotomy size in proptosis reduction

Proptosis is characterized by a protrusion of the eyeball due to an increase of the orbital tissue volume. To recover a normal eyeball positioning, the most frequent surgical technique consists in the osteotomy of orbital walls combined with the manual loading on the eyeball. Only a rough clinical rule is currently available for the surgeons but it is useless for this technique. The first biomechanical model dealing with proptosis reduction, validated in one patient, has been previously proposed by the authors. This paper proposes a rule improving the pre-operative planning of the osteotomy size in proptosis reduction. Patient-related poroelastic finite element models combined with sensitivity studies were used to propose two clinical rules to improve the pre-operative planning of proptosis reduction. This poroelastic model was run on 12 patients. Sensitivity studies permitted to establish relationships between the osteotomy size, the patient-related orbital volume, the decompressed tissue volume and the eyeball backward displacement. The eyeball displacement and the osteotomy size were non-linearly related: an exponential rule has been proposed. The patient-related orbital volume showed a significant influence: a bi-quadratic analytical equation liking the osteotomy size, the orbital volume and the targeted eyeball protrusion has been established. Two process rules derived from patient-related biomechanical FE models have been proposed for the proptosis reduction planning. The implementation of the process rules into a clinical setting is easy since only a sagittal radiography is required. The osteotomy size can be monitored using optical guided instruments.

An experimental and finite element poroelastic creep response analysis of an intervertebral hydrogel disc model in axial compression

A hydrogel intervertebral disc (IVD) model consisting of an inner nucleus core and an outer anulus ring was manufactured from 30 and 35% by weight Poly(vinyl alcohol) hydrogel (PVA-H) concentrations and subjected to axial compression in between saturated porous endplates at 200 N for 11 h, 30 min. Repeat experiments (n=4) on different samples (N=2) show good reproducibility of fluid loss and axial deformation. An axisymmetric nonlinear poroelastic finite element model with variable permeability was developed using commercial finite element software to compare axial deformation and predicted fluid loss with experimental data. The FE predictions indicate differential fluid loss similar to that of biological IVDs, with the nucleus losing more water than the anulus, and there is overall good agreement between experimental and finite element predicted fluid loss. The stress distribution pattern indicates important similarities with the biological IVD that includes stress transference from the nucleus to the anulus upon sustained loading and renders it suitable as a model that can be used in future studies to better understand the role of fluid and stress in biological IVDs.

Recent Advances in Analytical Modeling of Lumbar Disc Degeneration

Review of the most recent advances in the development of poro-elastic analytical models that include physiologic parameters used for understanding lumbar disc degeneration due to repetitive loading. To discuss how poro-elastic finite element models that include physiologic parameters such as strain-dependent permeability and porosity and regional variation of poro-elastic material properties of a motion segment can be used to understand the effect of disc degeneration due to cyclic loading on the disc biomechanical properties. Mechanical response of the spine to various dynamic loading conditions can be analyzed using in vitro and in vivo studies. Ethical concerns, interpretation of conclusions reached using animal studies, and lack of detailed stress distributions in the disc components are the major disadvantages in using in vivo studies for understanding disc degeneration process. Intraspecimen variability, noninclusion of muscle activity, and difficulty of influx of fluid into the disc during unloading are some of the disadvantages while using in vitro models to understand disc degeneration. The poro-elastic finite element models can provide a method that can circumvent the disadvantages mentioned above and allow a way to understand the relationship between biomechanical performance of the disc due to cyclic loading and disc degeneration. Several types of finite element model were developed in understanding relationship between disc degeneration and associated changes in biomechanical properties. Simplest among them include material and geometric nonlinearity of the disc and was used to predict failure in the disc anulus and endplates under static loading conditions. Response of the lumbar disc under creep loading was studied using poro-elastic models. These models were further refined by including swelling pressure and variable permeability due to change in porosity under load to understand time-dependent deformation of a lumbar disc in a multiple creep compression expansion loading. Regional variation of strain dependent permeability and osmotic pressure was included to further refine the poro-elastic finite element model. This refined model was used to study the effect of disc degeneration on biomechanical properties when cyclic loading was applied to the lumbar disc. The refined model that included regional variation of strain-dependent permeability and osmotic pressure was validated by comparing diurnal change in total stature measured in vivo. The study showed that disc height loss was larger after considerable number of cyclic loadings both in normal and degenerated discs. Cyclic loading also showed that Grade I discs were much more flexible than Grade IV discs. The disc stiffness also decreased as the load cycle increased. A number of different approaches have been used to address the issue of disc degeneration. Poro-elastic finite element model including strain-dependent permeability and osmotic pressure is the most popular analytical tool currently available that can be used to understand how cyclic loading affects the biomechanical characteristics of a degenerated lumbar disc. However, it is important to note that a complete understanding of the behavior of the intervertebral disc will ultimately be arrived using a combination of analytical models, such as the models presented here, in addition to in vitro and in vivo experimental methods.

Biomechanical assessment of stability in the metastatic spine following percutaneous vertebroplasty: effects of cement distribution patterns and volume

Percutaneous vertebroplasty is a minimally invasive, radiologically guided procedure whereby bone cement is injected into structurally weakened vertebrae to provide added biomechanical stability. In addition to treating osteoporotic vertebral fractures, this technique is also used to relieve pain by stabilizing metastatically compromised vertebrae that are at risk of pathologic burst fracture. Optimal cement distribution patterns to improve biomechanical stability to metastatically involved vertebral bodies remain unknown. This study aimed to determine the effect of cement location and volume of cement injected during percutaneous vertebroplasty on improving vertebral stability in a metastatically-compromised spinal motion segment using a parametric poroelastic finite element model. A three-dimensional parametric finite element model of a thoracic spinal motion segment was developed and analyzed using commercially available software. A total of 16 metastatic pre and post vertebroplasty scenarios were investigated using a serrated spherical representation of tumor tissue and various geometric representations of polymethylmethacrylate (PMMA). The effect of vertebroplasty on vertebral bulge, a measure of posterior vertebral body wall motion as an indicator of burst fracture initiation, was assessed. In all cases, vertebroplasty reduced vertebral bulge, but the risk of the initiation of burst fracture was minimized with cement located posterior to the tumor, near the posterior vertebral body wall. Vertebral bulge decreased by up to 62% with 20% cement injection. These findings demonstrate that location and distribution of cement within the vertebral body has a noticeable effect on the restoration of biomechanical stability following percutaneous vertebroplasty.

Surface flow boundary conditions in modeling land subsidence due to fluid withdrawal.

Land subsidence due to subsurface fluid (water, gas, oil) withdrawal is often predicted by either finite element or finite difference numerical models based on coupled poroelastic theory, where the soil is represented as a semi-infinite medium bounded by the traction-free (ground) surface. One of the variables playing a most important role on the final outcome is the flow condition used on the traction-free boundary, which may be assumed as either permeable or impermeable. Although occasionally justified, the assumption of no-flow surface seems to be in general rather unrealistic. A permeable boundary where the fluid pressure is fixed to the external atmospheric pressure appears to be more appropriate. This paper addresses the response, in terms of land subsidence, obtained with a coupled poroelastic finite element model that simulates a distributed pumping from a horizontal aquifer confined between two relatively impervious layers, and takes either a permeable boundary surface, i.e., constant hydraulic potential, or an impermeable boundary, i.e., a zero Neumann flow condition. The analysis reveals that land subsidence is rather sensitive to the flow condition implemented on the traction-free boundary. In general, the no-flow condition leads to an overestimate of the predicted ground surface settlement, which could even be 1 order of magnitude larger than that obtained with the permeable boundary.

Effect of a degraded core on the mechanical behaviour of tissueengineered cartilage constructs: A poro-elastic finite element analysis

The structure and functionality of tissue-engineered cartilage is determined by the tissue culture conditions and mechanical conditioning during growth. The quality of tissue-engineered cartilage can be evaluated using tests such as the confined compression test. Tissue-engineered cartilage constructs usually consist of an outer layer of cartilage and an inner core of either undeveloped cartilage or degrading scaffold material. A biphasic poro-elastic finite element model was used to demonstrate how such a core influences the reaction force-time curve obtained from a confined compression test. The finite element model predicted that higher volumes of degraded scaffold in the inner core would reduce the aggregate modulus calculated from the confined compression test and raised the estimate of tissue permeability. The predicted aggregate modulus reduced from 0.135 MPa, for a homogenous construct, to 0.068 MPa, for a construct that was only 70% cartilaginous. It was found that biphasic poro-elastic finite modelling should be used in preference to a one-dimensional model that assumed homogeneity in estimating the properties of tissue-engineered cartilage.

Prediction of tissue decompression in orbital surgery

Objective. A method to predict the relationships between decompressed volume of orbital soft tissues, backward displacement of globe after osteotomy, and force exerted by the surgeon, was proposed to improve surgery planning in exophthalmia reduction. Design. A geometric model and a poroelastic finite element model were developed, based on computed tomography scan data. Background. The exophthalmia is characterized by a protrusion of the eyeball. Surgery consists in an osteotomy of the orbit walls to decompress the orbital content. A few clinical observations ruling on an almost linear relationship between globe backward displacement and tissue-decompressed volume are described in the literature. Methods. Fast prediction of decompressed volume is derived from the geometric model: a sphere in interaction with a cone. Besides, a poroelastic finite element model involving morphology, material properties of orbital components and surgical gesture was implemented. Results. The geometric model provided a better decompression volume estimation than the finite element model. Besides, the finite element model permitted to quantify the backward displacement, the surgical gesture and the stiffness of the orbital content. Conclusions. The preliminary results obtained for one patient, in accordance with the clinical literature, were relatively satisfying. An efficient aid for location and size of osteotomies was derived and seemed to be able to help in the surgery planning. Relevance To our knowledge, this paper concerns the first biomechanical study of exophthalmia reduction. The approach permitted to improve the treatment of orbitopathy and can be used in a clinical setting.

Biomechanical responses of the intervertebral joints to static and vibrational loading: a finite element study

Objective. This study was performed to investigate the time-dependent responses of the intervertebral joint to static and vibrational loads. Design. A poroelastic finite element model was established to analyse the fluid flow, stress distribution and deformation of the intervertebral disc. Background. Long-term exposure to whole body vibration is highly associated with disc degeneration and low back pain. It is hypothesized that moderate vibrational loading may increase the efficiency of fluid and nutritional transport of the intervertebral disc while prolonged static and excessive vibrational loading may have deleterious effect. Methods. A three-dimensional finite element model was established using the actual geometry of the L4–L5 lumber motion segment. Nonlinear poroelastic properties were assigned to the intervertebral disc and cancellous bone. Static and vibrational loads were applied and the responses of fluid flow and stress distributions were analysed. Results. The finite element model showed that the loads carried by the annulus and the facets increased with time under static loading. The fluid flow and deformation of the intervertebral disc were dependent on the loading frequency. Conclusion. Vibration loading may be able to enhance disc fluid exchange via the fluid pumping mechanism. Relevance The predicted responses implied that vibrational motion may be important in facilitating fluid and metabolic transport of the intervertebral disc.

Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal, proteoglycan depleted and collagen degraded articular cartilage

Degradation of collagen network and proteoglycan (PG) macromolecules are signs of articular cartilage degeneration. These changes impair cartilage mechanical function. Effects of collagen degradation and PG depletion on the time-dependent mechanical behavior of cartilage are different. In this study, numerical analyses, which take the compression-tension nonlinearity of the tissue into account, were carried out using a fibril reinforced poroelastic finite element model. The study aimed at improving our understanding of the stress-relaxation behavior of normal and degenerated cartilage in unconfined compression. PG and collagen degradations were simulated by decreasing the Young's modulus of the drained porous (nonfibrillar) matrix and the fibril network, respectively. Numerical analyses were compared to results from experimental tests with chondroitinase ABC (PG depletion) or collagenase (collagen degradation) digested samples. Fibril reinforced poroelastic model predicted the experimental behavior of cartilage after chondroitinase ABC digestion by a major decrease of the drained porous matrix modulus (−64±28%) and a minor decrease of the fibril network modulus (−11±9%). After collagenase digestion, in contrast, the numerical analyses predicted the experimental behavior of cartilage by a major decrease of the fibril network modulus (−69±5%) and a decrease of the drained porous matrix modulus (−44±18%). The reduction of the drained porous matrix modulus after collagenase digestion was consistent with the microscopically observed secondary PG loss from the tissue. The present results indicate that the fibril reinforced poroelastic model is able to predict specifically characteristic alterations in the stress-relaxation behavior of cartilage after enzymatic modifications of the tissue. We conclude that the compression-tension nonlinearity of the tissue is needed to capture realistically the mechanical behavior of normal and degenerated articular cartilage.

Investigation of the vibrational modes of edge-constrained fibrous samples placed in a standing wave tube.

In earlier work it was suggested that the frictional constraint of a porous sample around its circumference in a standing wave tube resulted in shearing resonances of the sample. In the present work that effect has been confirmed by direct measurement of the spatial distribution of the velocity of the solid phase of a fibrous sample placed in a rigidly terminated standing wave tube and driven into motion by a plane, incident sound field. The measurements were performed using a standing wave tube to which a transparent downstream section was attached. A laser Doppler velocimeter was then used to measure the velocity of the solid phase of acoustically driven samples. The materials considered here were two types of aviation-grade glass fiber. A poroelastic finite element model was used to simulate the response of the constrained fibrous samples. Good agreement between measured and predicted mode shapes was found both when the samples were constrained only around their edges, and when an additional constraint plane was inserted axially through the samples. The present results confirm that glass fiber samples placed in a standing wave tube exhibit shearing modes and that those modes are associated with previously observed transmission loss minima.

Ground settlements above tunnels in fractured crystalline rock: numerical analysis of coupled hydromechanical mechanisms

Vertical settlements with magnitudes reaching 12 cm were measured in fractured crystalline rock several hundred metres above the Gotthard highway tunnel in central Switzerland. Such magnitudes of surface subsidence were unexpected, especially in granitic gneisses and appear to be related to large-scale consolidation of fractures resulting from fluid drainage and pore pressure changes following tunnel construction. This paper focuses on the mechanisms involved in the development of such surface displacements and presents the preliminary results of 2-D discontinuum (i.e. distinct-element) and 2-D continuum modelling (i.e. finite-element). Results show that settlements are most sensitive to horizontal joints, as would be expected, but that vertical fractures also contribute to the settlement profile through a 'Poisson ratio' effect. However, these models also suggest that fracture deformation alone cannot explain the total subsidence measured. As such, 2-D poro-elastic finite-element models are presented to demonstrate the contributing effect of consolidation of the intact rock matrix.