Lumbar intervertebral disc segmentation for computer modeling and simulation.

BACKGROUND AND OBJECTIVE: The present work had as its main objective the development of a method for localizing and automatically segmenting lumbar intervertebral discs (IVD) in 3D from magnetic resonance imaging (MRI), with the goal of supporting the generation of finite element (FE) models from actual lumbar spine anatomy, by providing accurate and personalized information on the shape of the patient's IVD. The extension of the method to allow performing separate segmentations of the IVD's two main structures - annulus fibrosus (AF) and nucleus pulposus (NP) - as well as automatically detecting degenerated IVD where this distinction is no longer possible was also an objective of the work. METHODS: The method presented here evolves from 2D segmentations in the sagittal profile using Gabor filters towards 3D segmentations. It works by detecting the spine curves and intensity regions corresponding to IVD. As so, the 2D method from Zhu et al. (2013) was partially implemented, modified and adapted to 3D use, and then tested with eight spines from two separated online datasets. The 3D adaptation was achieved by using vertebral body segmentation masks to approximate the shape of the vertebrae and to adjust the spine curves accordingly. RESULTS: The method showed average values of 85%, 83% and 96% for the Dice coefficient, sensitivity and specificity, respectively. The method correctly identified 65 of 68 (96%) IVD as either healthy or degenerated. The method's Dice coefficient is within the range of existing 3D IVD segmentation methods in the literature (81-92%). The method took on average 6-7 s to perform a full 3D segmentation, which is well within the range of the existing methods (2 s - 19 min). CONCLUSIONS: The developed method can be used to generate accurate 3D models of the IVD based on MRI, with AF/NP distinction and detection of marked degeneration by comparing each IVD with the remaining spine levels. Further work shall improve the method towards distinguishing between specific levels of degeneration for clinically oriented FE modeling.

Computational modeling of lumbar disc degeneration before and after spinal fusion.

BACKGROUND: Advancing age and degeneration frequently lead to low back pain, which is the most prevalent musculoskeletal disorder worldwide. Degenerative changes in intervertebral discs and musculo-ligamentous incapacity to compensate sagittal imbalance are typically amongst the sources of instability, with spinal fusion techniques being the main treatment options to relieve pain. The aims of this work were to: (i) assess the link between ligament degeneration and spinal instability by determining the role of each ligament per movement, (ii) evaluate the impact of disc height reduction in degenerative changes, and (iii) unveil the most advantageous type of posterior fixation in Oblique Lumbar Interbody Fusion to prevent adjacent disc degeneration. METHODS: Two L3-L5 finite element models were developed, being the first in healthy condition and the second having reduced L4-L5 height. Different degrees of degeneration were tested, combined with different fixation configurations for Oblique Lumbar Interbody Fusion. FINDINGS: Facet capsular ligament and anterior longitudinal ligament were the most influential ligaments for spinal stability, particularly with increasing degeneration and disc height reduction. Pre-existent degeneration had lower influence than the fusion procedure for the risk of adjacent disc degeneration, being the highest stability and minimal degeneration achieved with bilateral fixation. Right unilateral fixation was more suited to reduce disc stress than left unilateral fixation. INTERPRETATION: Bilateral fixation is the best option to stabilize the spinal segment, but unilateral right fixation may suffice. This has direct implications for clinical practice, and the extension to a population-based study will allow for more efficient fusion surgeries.

Gravity stress tibiotalar laxity evaluation with a biomedical gyroscopes device - cadaver study with progressive sectioning of lateral ankle ligaments.

PURPOSE: Despite the evidence on the role of gravity stress test to access the instability of other ankle injuries, there is limited literature regarding gravity stress on the lateral ankle ligament's insufficiency. The objective of our study was to objectively measure the tibiotalar angular movement under gravity stress after progressive sectioning of the lateral ankle ligaments. METHODS: We performed sequential sectioning of the anterior talofibular (ATFL), calcaneofibular (CFL), and posterior talofibular ligaments (PTFL) in twelve ankle specimens. Under gravity stress, we measured the angular movement of the talus in relation to the tibia. The measuring device is based on a three-axis gyroscope and accelerometer. RESULTS: Comparing to the intact condition, the plantar flexion increased on average 1.78° (95% confidence interval [CI] 1.15;2.42), 5.13° (95%CI 3.10;7.16) and 8.63° (95%CI 6.05;11.22), the rotation increased by 1.00° (95 CI -0.51;2.51), 3.68° (95%CI 1.97;5.40) and 15.62° (95%CI 10.09;21.14), and the varus increased 2.89° (95% CI 1.39, 4.39), 8.12° (95% CI 5.16, 11.07) and 11.68° (95% CI 7.91, 15.46), after sectioning the ATFL, CFL, and PTFL, respectively. The overall changes were statistically significant. CONCLUSIONS: There was a significant tibiotalar laxity after sectioning of lateral ankle ligaments when the foot position is influenced only by gravity. The tibiotalar angular displacement was significant when the CFL and PTFL were cut which suggests that the gravity test could be used to assess combined lateral ankle ligament injury. This evidence might be a step forward in the development of lateral ankle ligaments gravity stress tests. LEVEL OF EVIDENCE: 5 (cadaver study).

Reply to Comment "Assessing Porous Media Permeability in Non-Darcy Flow: A Re-Evaluation Based on the Forchheimer Equation".

In the name of the authors of the paper "Permeability versus Design in TPMS Scaffolds", published in Materials in 2019 and already counting six citations in Google Scholar to date, I would like to formally respond to the comment manuscript now entitled "Assessing Porous Media Permeability in Non-Darcy Flow: A Re-Evaluation Based on the Forchheimer Equation" [...].

Influence of femoral stem geometry, material and extent of porous coating on bone ingrowth and atrophy in cementless total hip arthroplasty: an iterative finite element model.

This work presents a computational model for the concurrent study of bone remodelling and ingrowth around cementless femoral stems in total hip arthroplasty. It is assumed that biological fixation depends upon the magnitude of relative displacement at the bone-stem interface as well as an ongoing updating of interface conditions during the remodelling process. The remodelling model determines the distribution of bone density by producing the stiffest structure for a given set of biological conditions at the point of equilibrium in bone turnover. Changes in bone density and patterns of ingrowth are compared for different stem geometries, materials and lengths of surface coating. Patterns of bone ingrowth on the tapered stem were independent of extent of porous coating, while ingrowth varied with the length of coating on the cylindrical stem. This model integrates knowledge of under what mechanical conditions bone ingrowth occurs on prosthetic stem surfaces with remodelling behaviour over time.

Numerical and experimental evaluation of TPMS Gyroid scaffolds for bone tissue engineering.

The combination of computational methods with 3D printing allows for the control of scaffolds microstructure. Lately, triply periodic minimal surfaces (TPMS) have been used to design porosity-controlled scaffolds for bone tissue engineering (TE). The goal of this work was to assess the mechanical properties of TPMS Gyroid structures with two porosity levels (50 and 70%). The scaffold stiffness function of porosity was determined by the asymptotic homogenisation method and confirmed by mechanical testing. Additionally, microCT analysis confirmed the quality of the printed parts. Thus, the potential of both design and manufacturing processes for bone TE applications is here demonstrated.

Permeability versus Design in TPMS Scaffolds.

Scaffolds for bone tissue engineering are porous structures that serve as support for cellular growth and, therefore, new tissue formation. The present work assessed the influence of the porous architecture of triply periodic minimal surface (TPMS) scaffolds on their macroscopic permeability behavior, combining numerical and experimental methods. The TPMS scaffolds considered were Schwartz D, Schwartz P, and Gyroid, which have been previously studied for bone tissue engineering, with 70% porosity. On the experimental side, these scaffolds were produced by MultiJet 3D printing and tested for fluid passage to calculate their permeability through Darcy's Law. On the numerical side, finite element (FE) models of the scaffolds were simulated on ABAQUS® for fluid passage under compression to assess potential fluid concentration spots. The outcomes revealed that the design of the unit cell had a noticeable effect on both calculated permeability and FE computed fluid flow velocity, regardless of the identical porosity, with the Gyroid scaffold having higher permeability and the Schwartz P a lower probability of fluid trapping. Schwartz D had the worst outcomes in both testing modalities, so these scaffolds would most likely be the last choice for promoting cell differentiation onto bone cells. Gyroid and Schwartz P would be up for selection depending on the application and targeted bone tissue.

Stress-induced birefringence in the isotropic phases of lyotropic mixtures.

In this work, the frequency dependence of the known mechano-optical effect which occurs in the micellar isotropic phases (I) of mixtures of potassium laurate (KL), decanol (DeOH), and water is investigated in the range from 200mHz to 200Hz. In order to fit the experimental data, a model of superimposed damped harmonic oscillators is proposed. In this phenomenological approach, the micelles (microscopic oscillators) interact very weakly with their neighbors. Due to shape anisotropy of the basic structures, each oscillator i (i=1,2,3,...,N) remains in its natural oscillatory rotational movement around its axes of symmetry with a frequency ω_{0i}. The system will be in the resonance state when the frequency of the driving force ω reaches a value near ω_{0i}. This phenomenological approach shows excellent agreement with the experimental data. One can find f∼2.5, 9.0, and 4.0Hz as fundamental frequencies of the micellar isotropic phases I, I_{1}, and I_{2}, respectively. The different micellar isotropic phases I, I_{1}, and I_{2} that we find in the phase diagram of the KL-DeOH-water mixture are a consequence of possible differences in the intermicellar correlation lengths. This work reinforces the possibilities of technological applications of these phases in devices such as mechanical vibration sensors.

Defect-antidefect correlations in a lyotropic liquid crystal from a cosmological point of view.

In this work, we analyze the defect and antidefect distribution in the nematic calamitic phase of a lyotropic liquid crystal [the ternary mixture formed by potassium laurate (KL), decanol (DeOH), and water]. We obtain defects with wedge disclinations of strength +/-1/2, and the scaling exponent determined by the defect-antidefect correlation was 0.29+/-0.07. This value is in good agreement with the theoretical value of 14 obtained by the Kibble mechanism. The constant of the scaling relation of the defect and antidefect distribution is also discussed. We compare our results with the values obtained by Digal [Phys. Rev. Lett. 83, 5030 (1999)] who used a thermotropic liquid crystal.

Computational model of mesenchymal migration in 3D under chemotaxis.

Cell chemotaxis is an important characteristic of cellular migration, which takes part in crucial aspects of life and development. In this work, we propose a novel in silico model of mesenchymal 3D migration with competing protrusions under a chemotactic gradient. Based on recent experimental observations, we identify three main stages that can regulate mesenchymal chemotaxis: chemosensing, dendritic protrusion dynamics and cell-matrix interactions. Therefore, each of these features is considered as a different module of the main regulatory computational algorithm. The numerical model was particularized for the case of fibroblast chemotaxis under a PDGF-bb gradient. Fibroblasts migration was simulated embedded in two different 3D matrices - collagen and fibrin - and under several PDGF-bb concentrations. Validation of the model results was provided through qualitative and quantitative comparison with in vitro studies. Our numerical predictions of cell trajectories and speeds were within the measured in vitro ranges in both collagen and fibrin matrices. Although in fibrin, the migration speed of fibroblasts is very low, because fibrin is a stiffer and more entangling matrix. Testing PDGF-bb concentrations, we noticed that an increment of this factor produces a speed increment. At 1 ng mL-1 a speed peak is reached after which the migration speed diminishes again. Moreover, we observed that fibrin exerts a dampening behavior on migration, significantly affecting the migration efficiency.

Nonlinear refractive index measurements of discotic and calamitic nematic lyotropic phases.

In this work, through the Z-scan technique, we report on measurements of the nonlinear refractive index (n{2}) in discotic and calamitic nematic phases at room temperature in lyotropic mixtures of potassium laurate, decanol and D(2)O . This technique presents high sensitivity when compared to conventional interferometry. The nonlinear optical birefringence (Deltan{2}) of these nematic phases was also determined. The sign and absolute value of this relevant nonlinear parameter are discussed in terms of structural changes in the micellar configuration which takes place in each nematic lyotropic phase.

Computational analysis of polyethylene wear in anatomical and reverse shoulder prostheses.

The wear of ultra-high molecular weight polyethylene, UHMWPE, components has been associated with the failure of joint prostheses in the hip, knee, and shoulder. Considering that in vitro experiments are generally too expensive and time-consuming, computational models are an attractive alternative to study the wear behavior of UHMWPE components. The objective of the present study was to develop a computational wear model to evaluate the wear resistance of anatomical and reverse shoulder prostheses. The effects of the wear law and the updating of the UHMWPE surface on the prediction of wear were also considered. Apart from Archard's law, a new wear law, so-called second generation law, which includes the concept of cross-shear and a pressure-independent wear factor, was considered. The wear analyses were performed considering three shoulder joint motions. The muscle and joint reaction forces applied were estimated by an inverse biomechanical model of the upper limb. The results show that abrasive wear is as important for the reverse components as it is for the anatomical. Nevertheless, the volumetric wears estimated over 1 year are within the range considered clinically desirable to reduce the risk of osteolysis. For the anatomical components, the predictions from Archard's law compare better, than those of the second generation law, to the experimental and clinical data available in the literature. Yet, the opposite result is obtained for the reverse components. From the numerical point of view, an updating procedure for the UHMWPE surface is mandatory to improve the numerical predictions.

A contact model with ingrowth control for bone remodelling around cementless stems.

This work presents a computational model for bone remodelling around cementless stems. The problem is formulated as a material optimisation problem considering the bone and stem surfaces to be in contact. To emphasise the behaviour of the bone/stem interface, the computer model detects the existence of bone ingrowth during the remodelling; consequently, the contact conditions are changed for a better interface simulation. The trabecular bone is modelled as a strictly orthotropic material with equivalent properties computed by homogenisation. The distribution of bone relative density is obtained by the minimisation of a function that considers both the bone structural stiffness and the biological cost associated with metabolic maintenance of bone tissue. The situation of multiple load conditions is considered. The remodelling law, obtained from the necessary conditions for an optimum, is derived analytically from the optimisation problem and solved numerically using a suitable finite element mesh. The formulation is applied to an implanted femur. Results of bone density and ingrowth distribution are obtained for different coating conditions. Bone ingrowth does not occur over the entire coated surfaces. Indeed, we observed regions where separation or high relative displacement occurs that preclude bone ingrowth attachment. This prediction of the model is consistent with clinical observations of bone ingrowth. Thus, this model, which detect bone ingrowth and allow modification of the interface conditions, are useful for analysis of existing stems as well as design optimisation of coating extent and location on such stems.

Induction of orientational order in the isotropic phase of a nematic liquid crystal.

The orientational properties of an isotropic dense liquid composed by anisotropic molecules, such as a liquid crystal in an isotropic phase, is studied. Using a Langevin-like equation it will be shown that the rotational motion of each molecule can be divided in two elements describing two kinds of physical motion. The first describes the Brownian rotational motion and another the coherent rotation induced by the external fields. It will be shown that, even at the isotropic phase, an order parameter describing the mean degree of alignment of the molecules around a given point can be defined. This order parameter also separates the order coming from the coherent motion from the order generated by the anisotropy in the thermal fluctuations. At the end the proposed model is compared with an experiment and it is shown that the coherent motion is enough to explain the experimental results.

Temperature dependence of the coefficient of electronic polarizability in calamitic nematic liquid crystals.

In this report the temperature dependence of the coefficient of electronic polarizability (straight phi(i)) is determined by means of the thermal expansion coefficient (beta) and ordinary/extraordinary refractive indexes measurements near the calamitic nematic-isotropic phase transition in a lyotropic mixture of sodium decylsulphonate, decanol, and water. These parameters (straight phi(i) and beta) were related to the extraordinary and ordinary refractive indexes via the temperature derivative of the Vuks's equation. The results showed that near the nematic-isotropic phase transition, the measured value of straight phi(i) was found to be about two orders of magnitude smaller than that obtained for thermotropic, showing a remarkable difference in the molecular electronic polarizability strength between lyotropic and thermotropic liquid crystals.

Shape optimization of a cementless hip stem for a minimum of interface stress and displacement.

The primary stem stability is an essential factor for success of cementless hip stems. A correct choice of the stem geometry can improve the stem stability and, consequently, increase the life time of a hip implant. In this work, it is proposed a computational model for shape optimization of cementless hip stems. The optimization problem is formulated by the minimization of relative displacement and stress on bone/stem interface using a multi-criteria objective function. Also multiple loads are considered to incorporate several daily life activities. Design variables are parameters that characterize the geometry of selected cross sections, which are subject to geometric constraints to ensure a clinically admissible shape. The stem/bone set is considered a structure in equilibrium with contact conditions on interface. The contact formulation allows us to analyze different lengths of porous coating. The optimization problem is solved numerically by a steepest descent method. The interface stress and relative displacement are obtained solving the contact problem by the finite element method. Numerical examples are presented for a two-dimensional model of a hip stem, however, the formulation is general and can be applied to the three-dimensional case. The model gives indications about the relation between shape, porous coating and prosthesis stability.

Human proximal femur bone adaptation to variations in hip geometry.

The study of bone mass distribution at proximal femur may contribute to understand the role of hip geometry on hip fracture risk. We examined how bone mineral density (BMD) of proximal femur adapts to inter individual variations in the femoral neck length (FNL), femoral neck width (FNW) and neck shaft angle (NSA). A parameterized and dimensionally scalable 3-D finite element model of a reference proximal femur geometry was incrementally adjusted to adopt physiological ranges at FNL (3.90-6.90cm), FNW (2.90-3.46cm), and NSA (109-141º), yielding a set of femora with different geometries. The bone mass distribution for each femur was obtained with a suitable bone remodelling model. The BMDs at the integral femoral neck (FN) and at the intertrochanteric (ITR) region, as well as the BMD ratio of inferomedial to superolateral (IM:SL) regions of FN and BMD ratio of FN:ITR were used to represent bone mass distribution. Results revealed that longer FNLs present greater BMD (g/cm(3)) at the FN, mainly at the SL region, and at the ITR region. Wider FNs were associated with reduced BMD at the FN, particularly at the SL region, and at the ITR region. Larger NSAs up to 129° were associated with BMD diminutions at the FN and ITR regions and with increases of the IM:SL BMD ratio while NSAs larger than 129° resulted in decrease of the IM:SL BMD ratio. These findings suggest hip geometry as moderator of the mechanical loading influence on bone mass distribution at proximal femur with higher FNL favoring the BMD of FN and ITR regions and greater FNW and NSA having the opposite effect. Augmented values of FNL and FNW seem also to favor more the BMD at the superolateral than at the inferomedial FN region.

Bone remodelling of the scapula after a total shoulder arthroplasty.

According to Wolff's law, the changes in stress after a prosthesis implantation may modify the shape and internal structure of bone, thus compromising the long-term prosthesis fixation and, consequently, be a significant factor for glenoid loosening. The aim of the present study is to evaluate the changes in the bone adaptation process of the scapula after an anatomical and reverse total shoulder arthroplasty. Five finite element models of the implanted scapula are developed considering the implantation of three anatomical, cemented, all-polyethylene components; an anatomical, cementless, metal-backed component; and a reverse, all-metal component. The methodology followed to simulate the bone adaptation of the scapula was previously validated for the intact model, prior to the prosthesis implantation. Additionally, the influence of the bone quality on the adaptation process is also investigated by considering an osteoporotic condition. The results show that the stress shielding phenomenon is more concerning in cementless, metal-based components than in cemented, all-polyethylene components, regardless of the bone quality. Consequently, as far as the bone adaptation process of the bone is concerned, cemented, all-polyethylene components are better suited for the treatment of the shoulder joint.

Femoral neck bone adaptation to weight-bearing physical activity by computational analysis.

Individual differences in bone mass distribution at the proximal femur may be determined by daily weight-bearing physical activity (PA) since bone self-adapts according to the mechanical loads that is submitted. The aim of this study was to analyse computationally the effect of different weight-bearing PA types in the adaptation of the femoral neck (FN) by analysing regional differences in bone mineral density (BMD) at the integral FN and its superior, inferior, anterior and posterior subregions. To achieve this, it was adopted a 3-D femoral finite element (FE) model coupled with a suitable bone remodeling model. Different PA types were determined based both on ordinary lifestyle and mechanically more demanding PA as low magnitude impacts (L-I), moderate-magnitude impacts from odd directions (O-I) and high-magnitude vertical impacts (H-I). It was observed that as time spent in weight-bearing PA increases, BMD augment around the integral FN, but with different bone mass gain rates between subregions depending on the magnitude and directions of the hip contact forces; H-I was the type of weight-bearing PA which structurally most favor the gain of bone mass superiorly at the FN while both the H-I and the O-I types of PA promoted the largest bone mass gain rates at the anterior and posterior subregions of the FN. Because these types of weight-bearing PA were associated with a more uniform bone mass spatial distribution at the FN, they should provide a potential basis for targeted PA-based intervention programs for improving hip strength.

Annihilation dynamics of stringlike topological defects in a nematic lyotropic liquid crystal.

Topological defects can appear whenever there is some type of ordering. Its ubiquity in nature has been the subject of several studies, from early Universe to condensed matter. In this work, we investigated the annihilation dynamics of defects and antidefects in a lyotropic nematic liquid crystal (ternary mixture of potassium laurate, decanol and deionized-destillated water) using the polarized optical light microscopy technique. We analyzed Schlieren textures with topological defects produced due to a symmetry breaking in the transition of the isotropic to nematic calamitic phase after a temperature quench. As result, we obtained for the distance D between two annihilating defects (defect-antidefect pair), as a function of time t remaining for the annihilation, the scaling law D âˆ t(α), with α = 0.390 and standard deviation σ = 0.085. Our findings go in the direction to extend experimental results related to dynamics of defects in liquid crystals since only thermotropic and polymerics ones had been investigated. In addition, our results are in good quantitative agreement with previous investigations on the subject.