José Jaime García

The Micromechanical Role of the Annulus Fibrosus Components Under Physiological Loading of the Lumbar Spine

To date, studies that have investigated the kinematics of spinal motion segments have largely focused on the contributions that the spinal ligaments play in the resultant motion patterns. However, the specific roles played by intervertebral disk components, in particular the annulus fibrosus, with respect to global motion is not well understood in spite of the relatively large literature base with respect to the local ex vivo mechanical properties of the tissue. The primary objective of this study was to implement the nonlinear and orthotropic mechanical behavior of the annulus fibrosus in a finite element model of an L4/L5 functional spinal unit in the form of a strain energy potential where the individual mechanical contributions of the ground substance and fibers were explicitly defined. The model was validated biomechanically under pure moment loading to ensure that the individual role of each soft tissue structure during load bearing was consistent throughout the physiologically relevant loading range. The fibrous network of the annulus was found to play critical roles in limiting the magnitude of the neutral zone and determining the stiffness of the elastic zone. Under flexion, lateral bending, and axial rotation, the collagen fibers were observed to bear the majority of the load applied to the annulus fibrosus, especially in radially peripheral regions where disk bulging occurred. For the first time, our data explicitly demonstrate that the exact fiber recruitment sequence is critically important for establishing the range of motion and neutral zone magnitudes of lumbar spinal motion segments.

A biphasic hyperelastic model for the analysis of fluid and mass transport in brain tissue.

A biphasic hyperelastic finite element model is proposed for the description of the mechanical behavior of brain tissue. The model takes into account finite deformations through an Ogden-type hyperelastic compressible function and a hydraulic conductivity dependent on deformation. The biphasic equations, implemented here for spherical symmetry using an updated Lagrangian algorithm, yielded radial coordinates and fluid velocities that were used with the convective–diffusive equation in order to predict mass transport in the brain. Results of the model were equal to those of a closed-form solution under infinitesimal deformations, however, for a wide range of material parameters, the model predicted important increments in the infusion sphere, reductions of the fluid velocities, and changes in the species content distribution. In addition, high localized deformation and stresses were obtained at the infusion sphere. Differences with the infinitesimal solution may be mainly attributed to geometrical nonlinearities related to the increment of the infusion sphere and not to material nonlinearities.

A nonlinear biphasic model of flow-controlled infusion in brain: Fluid transport and tissue deformation analyses

A biphasic nonlinear mathematical model is proposed for the concomitant fluid transport and tissue deformation that occurs during constant flow rate infusions into brain tissue. The model takes into account material and geometrical nonlinearities, a hydraulic conductivity dependent on strain, and nonlinear boundary conditions at the infusion cavity. The biphasic equations were implemented in a custom written code assuming spherical symmetry and using an updated Lagrangian finite element algorithm. Results of the model showed that both, geometric and material nonlinearities play an important role in the physics of infusions, yielding important differences from infinitesimal analyses. Geometrical nonlinearities were mainly due to the significant enlargement of the infusion cavity, while variations of the parameters that describe the degree of nonlinearity of the stress-strain curve yielded significant differences in all distributions. For example, a parameter set showing stiffening under tension yielded maximum values of radial displacement and porosity not localized at the infusion cavity. On the other hand, a parameter set showing softening under tension yielded a slight decrease in the fluid velocity for a three-fold increase in the flow rate, which can be explained by the substantial increase of the infusion cavity, not considered in linear analyses. This study strongly suggests that significant enlargement of the infusion cavity is a real phenomenon during infusions that may produce collateral damage to brain tissue. Our results indicate that more experimental tests have to be undertaken in order to determine material nonlinearities of brain tissue over a range of strains. With better understanding of these nonlinear effects, clinicians may be able to develop protocols that can minimize the damage to surrounding tissue.

A nonlinear biphasic model of flow-controlled infusions in brain: mass transport analyses.

A biphasic nonlinear mathematical model is proposed for the mass transport that occurs during constant flow-rate infusions into brain tissue. The model takes into account geometric and material nonlinearities and a hydraulic conductivity dependent upon strain. The biphasic and convective-diffusive transport equations were implemented in a custom-written code assuming spherical symmetry and using an updated Lagrangian finite element algorithm. Results of the model indicate that the inclusion of these nonlinearities produced modest changes in the interstitial concentration but important variations in drug penetration and bulk concentration. Increased penetration of the drug but smaller bulk concentrations were obtained at smaller strains caused by combination of parameters such as increased Youngs modulus and initial hydraulic conductivity. This indicates that simulations of constant flow-rate infusions under the assumption of infinitesimal deformations or rigidity of the tissue may yield lower bulk concentrations near the infusion cavity and over-predictions of the penetration of the infused agent. The analyses also showed that decrease in the infusion flow rate of a fixed amount of drug results in increased penetration of the infused agent. From the clinical point-of-view, this may promote a safer infusion that delivers the therapeutic range over the desired volume while avoiding damage to the tissue by minimizing deformation and strain.

A patient-specific, finite element model for noncommunicating hydrocephalus capable of large deformation.

A biphasic model for noncommunicating hydrocephalus in patient-specific geometry is proposed. The model can take into account the nonlinear behavior of brain tissue under large deformation, the nonlinear variation of hydraulic conductivity with deformation, and contact with a rigid, impermeable skull using a recently developed algorithm. The model was capable of achieving over a 700 percent ventricular enlargement, which is much greater than in previous studies, primarily due to the use of an anatomically realistic skull recreated from magnetic resonance imaging rather than an artificial skull created by offsetting the outer surface of the cerebrum. The choice of softening or stiffening behavior of brain tissue, both having been demonstrated in previous experimental studies, was found to have a significant effect on the volume and shape of the deformed ventricle, and the consideration of the variation of the hydraulic conductivity with deformation had a modest effect on the deformed ventricle. The model predicts that noncommunicating hydrocephalus occurs for ventricular fluid pressure on the order of 1300 Pa.

Implications of Transvascular Fluid Exchange in Nonlinear, Biphasic Analyses of Flow-Controlled Infusion in Brain

A nonlinear, coupled biphasic-mass transport model that includes transvascular fluid exchange is proposed for flow-controlled infusions in brain tissue. The model accounts for geometric and material nonlinearities, a hydraulic conductivity dependent on deformation, and transvascular fluid exchange according to Starling’s law. The governing equations were implemented in a custom-written code assuming spherical symmetry and using an updated Lagrangian finite-element algorithm. Results of the model indicate that, using normal physiological values of vascular permeability, transvascular fluid exchange has negligible effects on tissue deformation, fluid pressure, and transport of the infused agent. As vascular permeability may be increased artificially through methods such as administering nitric oxide, a parametric study was conducted to determine how increased vascular permeability affects flow-controlled infusion. Increased vascular permeability reduced both tissue deformation and fluid pressure, possibly reducing damage to tissue adjacent to the infusion catheter. Furthermore, the loss of fluid to the vasculature resulted in a significantly increased interstitial fluid concentration but a modestly increased tissue concentration. From a clinical point of view, this increase in concentration could be beneficial if limited to levels below which toxicity would not occur. However, the modestly increased tissue concentration may make the increase in interstitial fluid concentration difficult to assess in vivo using co-infused radiolabeled agents.

Evaluation of the friction coefficient, the radial stress, and the damage work during needle insertions into agarose gels

Agarose hydrogels have been extensively used as a phantom material to mimic the mechanical behavior of soft biological tissues, e.g. in studies aimed to analyze needle insertions into the organs producing tissue damage. To better predict the radial stress and damage during needle insertions, this study was aimed to determine the friction coefficient between the material of commercial catheters and hydrogels. The friction coefficient, the tissue damage and the radial stress were evaluated at 0.2, 1.8, and 10mm/s velocities for 28, 30, and 32 gauge needles of outer diameters equal to 0.36, 0.31, and 0.23mm, respectively. Force measurements during needle insertions and retractions on agarose gel samples were used to analyze damage and radial stress. The static friction coefficient (0.295±0.056) was significantly higher than the dynamic (0.255±0.086). The static and dynamic friction coefficients were significantly smaller for the 0.2mm/s velocity compared to those for the other two velocities, and there was no significant difference between the friction coefficients for 1.8 and 10mm/s. Radial stress averages were 131.2±54.1, 248.3±64.2, and 804.9±164.3Pa for the insertion velocity of 0.2, 1.8, and 10mm/s, respectively. The radial stress presented a tendency to increase at higher insertion velocities and needle size, which is consistent with other studies. However, the damage work did not show to be a good predictor of tissue damage, which appears to be due to simplifications in the analytical model. Differently to other approaches, the method proposed here based on radial stress may be extended in future studies to quantity tissue damage in vivo along the entire needle track.

Characterization of the L4–L5–S1 motion segment using the stepwise reduction method

The two aims of this study were to generate data for a more accurate calibration of finite element models including the L5-S1 segment, and to find mechanical differences between the L4-L5 and L5-S1 segments. Then, the range of motion (ROM) and facet forces for the L4-S1 segment were measured using the stepwise reduction method. This consists of sequentially testing and reducing each segment in nine stages by cutting the ligaments, facet capsules, and removing the nucleus. Five L4-S1 human segments (median: 65 years, range: 53-84 years, SD=11.0 years) were loaded under a maximum pure moment of 8Nm. The ROM was measured using stereo-photogrammetry via tracking of three markers and the facet contact forces (CF) were measured using a Tekscan system. The ROM for the L4-L5 segment and all stages showed good agreement with published data. The major differences in ROM between the L4-L5 and L5-S1 segments were found for lateral bending and all stages, for which the L4-L5 ROM was about 1.5-3 times higher than that of the L5-S1 segment, consistent with L5-S1 facet CF about 1.3 to 4 times higher than those measured for the L4-L5 segment. For the other movements and few stages, the L4-L5 ROM was significantly lower that of the L5-S1 segment. ROM and CF provide important baseline data for more accurate calibration of FE models and to understand the role that their structures play in lower lumbar spine mechanics.

Mechanical Behavior of Bamboo Species Guadua angustifolia under Compression along the Thickness of the Culm

The bamboo species Guadua angustifolia is a natural functionally graded material with a high potential to help solving the housing deficit in Latin American countries. Bamboo plantations also play an important role to help reducing the devastation of tropical forests. Many studies have demonstrated the excellent mechanical properties of bamboo along the length of the culm. However, other properties like the strength under circumferential tension and shear are low and the associated types of failure are fragile. Therefore, longitudinal fissures are often initiated in the structural joints which avoid taking advantage of the high resistance along the longitudinal direction. To the best of our knowledge, no study has been devoted to study the mechanical behavior of bamboo along the thickness of the culm or radial direction. This characterization may be crucial to improve the performance of the joints in bamboo structures. The aim of this study was to determine the strength and the Young ́s modulus of Guadua angustifolia along the radial direction. Thus, 27 small hexahedral elements of approximately 11 mm × 6 mm × 7 mm were tested under compression along the thickness of the culm. The stress-strain curves depicted a typical ductile behavior with an average failure strain of 37.8 ± 5.4 %. The failure was characterized by fissures on planes parallel to the fibers and forming angles in the range 35° - 55° with respect to the axis of loading. The secant Young ́s modulus and the radial strength were equal to 44.50 ±9.60 MPa, and 18.50 ±4.20 MPa respectively and there was no significant difference with position along the culm. The initial Young ́s modulus was equal to 96.73 ±52.30 MPa, 37.00 ±24.35 MPa and 48.90 ±7.31 MPa for the bottom, middle and upper portions of the culm and there was a significant difference (p=0.025) between the bottom and middle locations. The high variations of the initial Young ́s modulus may be explained by the irregular form of the surfaces of contact with the testing machine, that were not cut perfectly flat in order to preserve the intact material. These experiments show that Guadua behaves as a ductile material under compression along the thickness of the culm. This property may be used to improve the efficiency of structural joints by applying radial compression.

Influence of Vertebra Stiffness in the Finite Element Analysis of the Intervertebral Disc

Spine finite element models are an essential tool to study the degeneration of the intervertebral disc (IVD). Due to the complex geometry of the vertebras, the anisotropy and heterogeneity of the tissues, and the contact and material nonlinearities [1], spine models demand high computational resources. Considering the relatively low stiffness of the IVD compared to that of the vertebrae, we hypothesized that finite element stress and stress distributions of the IVD do not change substantially if the vertebras are modeled as rigid bodies. This simplification in spine models may considerably reduce the solution time when the interest is the analysis of the IVD.Copyright