Jérôme Noailly

The role of endplate poromechanical properties on the nutrient availability in the intervertebral disc

OBJECTIVE To investigate the relevance of the human vertebral endplate poromechanics on the fluid and metabolic transport from and to the intervertebral disc (IVD) based on educated estimations of the poromechanical parameter values of the bony endplate (BEP). METHODS 50 micro-models of different BEP samples were generated from μCTs of lumbar vertebrae and allowed direct determination of porosity values. Permeability values were calculated by using the micro-models, through the simulation of permeation via computational fluid dynamics. These educated ranges of porosity and permeability values were used as inputs for mechano-transport simulations to assess their effect on both the distributions of metabolites within an IVD model and the poromechanical calculations within the cartilaginous part of the endplate i.e., the cartilage endplate (CEP). RESULTS BEP effective permeability was highly correlated to local variations of porosity (R(2) ≈ 0.88). Universal patterns between bone volume fraction and permeability arose from these results and from other experimental data in the literature. These variations in BEP permeability and porosity had negligible effects on the distributions of metabolites within the disc. In the CEP, the variability of the poromechanical properties of the BEP did not affect the predicted consolidation but induced higher fluid velocities. CONCLUSIONS The present paper provides the first sets of thoroughly identified BEP parameter values that can be further used in patient-specific poromechanical studies. Representing BEP structural changes through variations in poromechanical properties did not affect the diffusion of metabolites. However, attention might be paid to alterations in fluid velocities and cell mechano-sensing within the CEP.

Automatic Model Generation Framework for Computational Simulation of Cochlear Implantation

Recent developments in computational modeling of cochlear implantation are promising to study in silico the performance of the implant before surgery. However, creating a complete computational model of the patient’s anatomy while including an external device geometry remains challenging. To address such a challenge, we propose an automatic framework for the generation of patient-specific meshes for finite element modeling of the implanted cochlea. First, a statistical shape model is constructed from high-resolution anatomical μCT images. Then, by fitting the statistical model to a patient’s CT image, an accurate model of the patient-specific cochlea anatomy is obtained. An algorithm based on the parallel transport frame is employed to perform the virtual insertion of the cochlear implant. Our automatic framework also incorporates the surrounding bone and nerve fibers and assigns constitutive parameters to all components of the finite element model. This model can then be used to study in silico the effects of the electrical stimulation of the cochlear implant. Results are shown on a total of 25 models of patients. In all cases, a final mesh suitable for finite element simulations was obtained, in an average time of 94 s. The framework has proven to be fast and robust, and is promising for a detailed prognosis of the cochlear implantation surgery.

Material property discontinuities in intervertebral disc porohyperelastic finite element models generate numerical instabilities due to volumetric strain variations

Numerical studies of the intervertebral disc (IVD) are important to better understand the load transfer and the mechanobiological processes within the disc. Among the relevant calculations, fluid-related outputs are critical to describe and explore accurately the tissue properties. Porohyperelastic finite element models of IVD can describe accurately the disc behaviour at the organ level and allow the inclusion of fluid effects. However, results may be affected by numerical instabilities when fast load rates are applied. We hypothesized that such instabilities would appear preferentially at material discontinuities such as the annulus-nucleus boundary and should be considered when testing mesh convergence. A L4-L5 IVD model including the nucleus, annulus and cartilage endplates were tested under pure rotational loads, with different levels of mesh refinement. The effect of load relaxation and swelling were also studied. Simulations indicated that fluid velocity oscillations appeared due to numerical instability of the pore pressure spatial derivative at material discontinuities. Applying local refinement only was not enough to eliminate these oscillations. In fact, mesh refinements had to be local, material-dependent, and supplemented by the creation of a material transition zone, including interpolated material properties. Results also indicated that oscillations vanished along load relaxation, and faster attenuation occurred with the incorporation of the osmotic pressure. We concluded that material discontinuities are a major cause of instability for poromechanical calculations in multi-tissue models when load velocities are simulated. A strategy was presented to address these instabilities and recommendations on the use of IVD porohyperelastic models were given.

Musculoskeletal Modeling of the Lumbar Spine to Explore Functional Interactions between Back Muscle Loads and Intervertebral Disk Multiphysics

During daily activities, complex biomechanical interactions influence the biophysical regulation of intervertebral disks (IVDs), and transfers of mechanical loads are largely controlled by the stabilizing action of spine muscles. Muscle and other internal forces cannot be easily measured directly in the lumbar spine. Hence, biomechanical models are important tools for the evaluation of the loads in those tissues involved in low-back disorders. Muscle force estimations in most musculoskeletal models mainly rely, however, on inverse calculations and static optimizations that limit the predictive power of the numerical calculations. In order to contribute to the development of predictive systems, we coupled a predictive muscle model with the passive resistance of the spine tissues, in a L3–S1 musculoskeletal finite element model with osmo-poromechanical IVD descriptions. The model included 46 fascicles of the major back muscles that act on the lower spine. The muscle model interacted with activity-related loads imposed to the osteoligamentous structure, as standing position and night rest were simulated through distributed upper body mass and free IVD swelling, respectively. Calculations led to intradiscal pressure values within ranges of values measured in vivo. Disk swelling led to muscle activation and muscle force distributions that seemed particularly appropriate to counterbalance the anterior body mass effect in standing. Our simulations pointed out a likely existence of a functional balance between stretch-induced muscle activation and IVD multiphysics toward improved mechanical stability of the lumbar spine understanding. This balance suggests that proper night rest contributes to mechanically strengthen the spine during day activity.

Multi-scale immunological and biomechanical model of emphysema progression

This work presents a multi-scale agent-based model of emphysema progression that includes both the slow action of the immune system and the fast action of force redistribution and fracture propagation of the biological tissue. The two scales are coupled because the immune response causes inflammation and adaptation, which affects the biomechanical parameters of the tissue such as his elasticity. During repeated inflammation and breathing cycles, the tissue weakens and breaks down. We found that macrophages lifespan and cytokynes diffusion ratio are the parameters that influence the outcome of the model the most.

Analysis of Uncertainty and Variability in Finite Element Computational Models for Biomedical Engineering: Characterization and Propagation

Computational modeling has become a powerful tool in biomedical engineering thanks to its potential to simulate coupled systems. However, real parameters are usually not accurately known, and variability is inherent in living organisms. To cope with this, probabilistic tools, statistical analysis and stochastic approaches have been used. This article aims to review the analysis of uncertainty and variability in the context of finite element modeling in biomedical engineering. Characterization techniques and propagation methods are presented, as well as examples of their applications in biomedical finite element simulations. Uncertainty propagation methods, both non-intrusive and intrusive, are described. Finally, pros and cons of the different approaches and their use in the scientific community are presented. This leads us to identify future directions for research and methodological development of uncertainty modeling in biomedical engineering.

The effect of bone graft geometry on spinal fusion vertebral stresses

Spinal fusion is a frequent surgical technique in which the success is uncertain due to post-operative changes in the biomechanics of the spine. Bone grafts are good candidates for disc and vertebra substitutes due to their similar bone properties and their good osteogenic properties. However, the effect of the anatomic harvest location of the bone graft on the load transfer is unknown. A physiologic three-dimensional (3D) finite element model of a lumbar spine was modified to model spinal fusion with a fixator and a bone graft. Bone grafts were taken either from the femur, the tibia, or from the fibula in a configuration of three or six fragments. The configurations were submitted to physiological loadings, and strain and stress distributions were calculated within the vertebrae, the fixator and the bone grafts. Quantitative differences were found from one type of bone graft to another. It was found that fibula bone grafts provided better stability by carrying a large part of the load. However, femoral and tibial bone grafts provided a more similar strain distribution within the vertebrae compared to the physiologic model. For tibial bone grafts, load transfer was found to be sensitive to the orientation used during the surgery. The use of a femoral bone graft to replace one vertebra and two intervertebral discs was found to give a better biomechanical function than using a tibial or fibula bone graft. This surgical technique is proposed to be beneficial in the case of severe spinal trauma providing good interface is obtained between the bone graft and the vertebrae.

Coupled Immunological and Biomechanical Model of Emphysema Progression

Chronic Obstructive Pulmonary Disease (COPD) is a disabling respiratory pathology, with a high prevalence and a significant economic and social cost. It is characterized by different clinical phenotypes with different risk profiles. Detecting the correct phenotype, especially for the emphysema subtype, and predicting the risk of major exacerbations are key elements in order to deliver more effective treatments. However, emphysema onset and progression are influenced by a complex interaction between the immune system and the mechanical properties of biological tissue. The former causes chronic inflammation and tissue remodeling. The latter influences the effective resistance or appropriate mechanical response of the lung tissue to repeated breathing cycles. In this work we present a multi-scale model of both aspects, coupling Finite Element (FE) and Agent Based (AB) techniques that we would like to use to predict the onset and progression of emphysema in patients. The AB part is based on existing biological models of inflammation and immunological response as a set of coupled non-linear differential equations. The FE part simulates the biomechanical effects of repeated strain on the biological tissue. We devise a strategy to couple the discrete biological model at the molecular /cellular level and the biomechanical finite element simulations at the tissue level. We tested our implementation on a public emphysema image database and found that it can indeed simulate the evolution of clinical image biomarkers during disease progression.

Sensitivity analysis of geometrical parameters to study haemodynamics and thrombus formation in the left atrial appendage: Virtual Haemodynamics and thrombus formation study in LAA

The left atrial appendage (LAA) is a complex and heterogeneous protruding structure of the left atrium (LA). In atrial fibrillation patients, it is the location where 90% of the thrombi are formed. However, the role of the LAA in thrombus formation is not fully known yet. The main goal of this work is to perform a sensitivity analysis to identify the most relevant LA and LAA morphological parameters in atrial blood flow dynamics. Simulations were run on synthetic ellipsoidal left atria models where different parameters were individually studied: pulmonary veins and mitral valve dimensions; LAA shape; and LA volume. Our computational analysis confirmed the relation between large LAA ostia, low blood flow velocities and thrombus formation. Additionally, we found that pulmonary vein configuration exerted a critical influence on LAA blood flow patterns. These findings contribute to a better understanding of the LAA and to support clinical decisions for atrial fibrillation patients.

Theoretical Explorations Generate New Hypotheses About the Role of the Cartilage Endplate in Early Intervertebral Disk Degeneration

Altered cell nutrition in the intervertebral disk (IVD) is considered a main cause for disk degeneration (DD). The cartilage endplate (CEP) provides a major path for the diffusion of nutrients from the peripheral vasculature to the IVD nucleus pulposus (NP). In DD, sclerosis of the adjacent bony endplate is suggested to be responsible for decreased diffusion and disk cell nutrition. Yet, experimental evidence does not support this hypothesis. Hence, we evaluated how moderate CEP composition changes related to tissue degeneration can affect disk nutrition and cell viability. A novel composition-based permeability formulation was developed for the CEP, calibrated, validated, and used in a mechano-transport finite element IVD model. Fixed solute concentrations were applied at the outer surface of the annulus and the CEP, and three cycles of daily mechanical load were simulated. The CEP model indicated that CEP permeability increases with the degeneration/aging of the tissue, in accordance with recent measurements reported in the literature. Additionally, our results showed that CEP degeneration might be responsible for mechanical load-induced NP dehydration, which locally affects oxygen and lactate levels, and reduced glucose concentration by 16% in the NP-annulus transition zone. Remarkably, CEP degeneration was a condition sine-qua-non to provoke cell starvation and death, while simulating the effect of extracellular matrix depletion in DD. This theoretical study cast doubts about the paradigm that CEP calcification is needed to provoke cell starvation, and suggests an alternative path for DD whereby the early degradation of the CEP plays a key role.