Multi-scale biomechanical study of transport phenomena in the intervertebral disc

Intervertebral disc (IVD) degeneration is primarily involved in back pain, a morbidity that strongly affects the quality of life of individuals nowadays. Lumbar IVDs undergo stressful mechanical loads while being the largest avascular tissues in our body: Mechanical principles alone cannot unravel the intricate phenomena that occur at the cellular scale which are fundamental for the IVD regeneration. The present work aimed at coupling biomechanical and relevant molecular transport processes for disc cells to provide a mechanobiological finite element framework for a deeper understanding of degenerative processes and the planning of regenerative strategies. Given the importance of fluid flow within the IVD, the influence of poroelastic parameters such as permeabilities and solid-phase stiffness of the IVD subtissues was explored. A continuum porohyperelastic material model was then implemented. The angles of collagen fibers embedded in the annulus fibrosus (AF) were calibrated. The osmotic pressure of the central nucleus pulposus (NP) was also taken into account. In a parallel study of the human vertebral bone, microporomechanics was used together with experimental ultrasonic tests to characterize the stiffness of the solid matrix, and to provide estimates of poroelastic coefficients. Fluid dynamics analyses and microtomographic images were combined to understand the fluid exchanges at the bone-IVD interface. The porohyperelastic model of a lumbar IVD with poroelastic vertebral layers was coupled with a IVD transport model of three solutes - oxygen, lactate and glucose - interrelated to reproduce the glycolytic IVD metabolism. With such coupling it was possible to study the effect of deformations, fluid contents, solid-phase stiffness, permeabilities, pH, cell densities of IVD subtissues and NP osmotic pressure on the solute transport. Moreover, cell death governed by glucose deprivation and lactate accumulation was included to explore the mechanical effect on cell viability. Results showed that the stiffness of the AF had the most remarkable role on the poroelastic behavior of the IVD. The permeability of the thin cartilage endplate and the NP stiffness were also relevant. The porohyperelastic model was shown to reproduce the local AF mechanics, provided the fiber angles were calibrated regionally. Such back-calculation led to absolute values of fibers angles and to a global IVD poromechanical behavior in agreement with experiments in literature. The inclusion of osmotic pressure in the NP also led to stress values under confined compression comparable to those measured in healthy and degenerated NP specimens. For the solid bone matrix, axial and transverse stiffness coefficients found experimentally in the present work agreed with universal mass density-elasticity relationships, and combined with continuum microporomechanics provided poroelastic coefficients for undrained and drained cases. The effective permeability of the vertebral bony endplate calculated with fluid dynamics was highly correlated with the porosity measured in microtomographic images. The coupling of transport and porohyperelastic models revealed a mechanical effect acting under large volume changes and high compliance, favored by healthy rather than degenerated IVD properties. Such effect was attributed to strain-dependent diffusivities and diffusion distances and was shown to be beneficial for IVD cells due to the load-dependent increases of glucose levels. Cell density, NP osmotic pressure and porosity were the most important parameters affecting the coupled mechano-transport of metabolites. This novel study highlights the restoration of both cellular and mechanical factors and has a great potential impact for novel designs of treatments focused on tissue regeneration. It also provides methodological features that could be implemented in clinical image-based tools and improve the multiscale understanding of the human spine mechanobiology

Editorial: Mechanobiology and the microenvironment: Computational and experimental approaches

Peer ReviewedPostprint (published version

Multiservice UAVs for Emergency Tasks in Post-disaster Scenarios

UAVs are increasingly being employed to carry out surveillance, parcel delivery, communication-support and other specific tasks. Their equipment and mission plan are carefully selected to minimize the carried load an overall resource consumption. Typically, several single task UAVs are dispatched to perform different missions. In certain cases, (part of) the geographical area of operation may be common to these single task missions (such as those supporting post-disaster recovery) and it may be more efficient to have multiple tasks carried out as part of a single UAV mission using common or even additional specialized equipment. In this paper, we propose and investigate a joint planning of multitask missions leveraging a fleet of UAVs equipped with a standard set of accessories enabling heterogeneous tasks. To this end, an optimization problem is formulated yielding the optimal joint planning and deriving the resulting quality of the delivered tasks. In addition, a heuristic solution is developed for large-scale environments to cope with the increased complexity of the optimization framework. The developed joint planning of multitask missions is applied to a specific post-disaster recovery scenario of a flooding in the San Francisco area. The results show the effectiveness of the proposed solutions and the potential savings in the number of UAVs needed to carry out all the tasks with the required level of quality

Planning UAV Activities for Efficient User Coverage in Disaster Areas

Climate changes brought about by global warming as well as man-made environmental changes are often the cause of sever natural disasters. ICT, which is itself responsible for global warming due to its high carbon footprint, can play a role in alleviating the consequences of such hazards by providing reliable, resilient means of communication during a disaster crisis. In this paper, we explore the provision of wireless coverage through UAVs (Unmanned Aerial Vehicles) to complement, or replace, the traditional communication infrastructure. The use of UAVs is indeed crucial in emergency scenarios, as they allow for the quick and easy deployment of micro and pico cellular base stations where needed. We characterize the movements of UAVs and define an optimization problem to determine the best UAV coverage that maximizes the user throughput, while maintaining fairness across the different parts of the geographical area that has been affected by the disaster. To evaluate our strategy, we simulate a flooding in San Francisco and the car traffic resulting from people seeking safety on higher ground

Poroelastic osmoregulation of living cell volume

Cells maintain their volume through fine intracellular osmolarity regulation. Osmotic challenges drive fluid into or out of cells causing swelling or shrinkage, respectively. The dynamics of cell volume changes depending on the rheology of the cellular constituents and on how fast the fluid permeates through the membrane and cytoplasm. We investigated whether and how poroelasticity can describe volume dynamics in response to osmotic shocks. We exposed cells to osmotic perturbations and used defocusing epifluorescence microscopy on membrane-attached fluorescent nanospheres to track volume dynamics with high spatiotemporal resolution. We found that a poroelastic model that considers both geometrical and pressurization rates captures fluid-cytoskeleton interactions, which are rate-limiting factors in controlling volume changes at short timescales. Linking cellular responses to osmotic shocks and cell mechanics through poroelasticity can predict the cell state in health, disease, or in response to novel therapeutics.Peer ReviewedPostprint (published version

Regional annulus fibre orientations used as a tool for the calibration of lumbar intervertebral disc finite element models

The highly organized collagen network of human lumbar a nnulus fibrosus (AF) is fundamental to preserve the mechanical inte grity of the interverte bral discs. In the healthy AF, fibres are embedded in a hydrated matrix and arranged in a criss-cross fashion, giving an anisotropic structure capab le to undergo large st rains. Quantitative anatomical examinations revealed particular fibre orientation patterns, possibly coming from regional adaptations of the AF mechan ics. Based on such hypothesis, this study aimed to show that the regional differen ces in AF mechanical behaviour can be reproduced by considering only fibre orientatio n changes. Using the finite element (FE) method, AF matrix was modelled as a poro-hy perelastic material, where the porous solid was treated as a comp ressible continuum following a Neo-Hookean constitutive law. Strain-dependent permeability was assumed and all material parameters were taken from the literature. Fibre reinforcement wa s accounted for by adding an extra-term to the porous matrix strain energy density func tion, only active along th e fibre directions. Through such term, fibre orientations were then adjusted, to reproduce AF tensile behaviours measured for four different regi ons: posterior outer (PO), anterior outer (AO), posterior inner (PI) and anterior inne r (AI). Curve calibrations resulted in the following optimal angles, calculated with respect to the circumferential axis: 28º for PO, 23º for AO, 43º for PI and 31º for AI. In average, we obtained fibres 30% more transversal in the inner than in the outer AF against 38% as measured by Cassidy et al. (1989). Fibres more axial in the posterior than in the anterior AF were also measured by Holzapfel et al. (2005), with angle values comparable to our computed average values. Since all the hyperelastic and fluid-phase material parameters remained unchanged throughout the AF, calibration based only on fibre patterns variations may be an effective tool to calibrate the regional AF mechanics in a realistic way.Postprint (published version

Derivation and characterisation of endothelial cells from patients with chronic thromboembolic pulmonary hypertension

Pulmonary endarterectomy (PEA) resected material offers a unique opportunity to develop an in vitro endothelial cell model of chronic thromboembolic pulmonary hypertension (CTEPH). We aimed to comprehensively analyze the endothelial function, molecular signature, and mitochondrial profile of CTEPH-derived endothelial cells to better understand the pathophysiological mechanisms of endothelial dysfunction behind CTEPH, and to identify potential novel targets for the prevention and treatment of the disease. Isolated cells from specimens obtained at PEA (CTEPH-EC), were characterized based on morphology, phenotype, and functional analyses (in vitro and in vivo tubule formation, proliferation, apoptosis, and migration). Mitochondrial content, morphology, and dynamics, as well as high-resolution respirometry and oxidative stress, were also studied. CTEPH-EC displayed a hyperproliferative phenotype with an increase expression of adhesion molecules and a decreased apoptosis, eNOS activity, migration capacity and reduced angiogenic capacity in vitro and in vivo compared to healthy endothelial cells. CTEPH-EC presented altered mitochondrial dynamics, increased mitochondrial respiration and an unbalanced production of reactive oxygen species and antioxidants. Our study is the foremost comprehensive investigation of CTEPH-EC. Modulation of redox, mitochondrial homeostasis and adhesion molecule overexpression arise as novel targets and biomarkers in CTEPH.Peer ReviewedPostprint (published version

Cell contraction induces long-ranged stress stiffening in the extracellular matrix

Animal cells in tissues are supported by biopolymer matrices, which typically exhibit highly nonlinear mechanical properties. While the linear elasticity of the matrix can significantly impact cell mechanics and functionality, it remains largely unknown how cells, in turn, affect the nonlinear mechanics of their surrounding matrix. Here we show that living contractile cells are able to generate a massive stiffness gradient in three distinct 3D extracellular matrix model systems: collagen, fibrin, and Matrigel. We decipher this remarkable behavior by introducing Nonlinear Stress Inference Microscopy (NSIM), a novel technique to infer stress fields in a 3D matrix from nonlinear microrheology measurement with optical tweezers. Using NSIM and simulations, we reveal a long-ranged propagation of cell-generated stresses resulting from local filament buckling. This slow decay of stress gives rise to the large spatial extent of the observed cell-induced matrix stiffness gradient, which could form a mechanism for mechanical communication between cells

A micro-macro evaluation of the vertebral bony endplate permeability based on computational fluid dynamics

The intrinsic permeability is an important parameter that describes the resistance of a porous structure to fluid flo w. It has a key role in poroelastic finite element models of spinal segments, especially at the vertebral endplate, i.e. the interface between intervertebral disc and vertebra. In the understanding of the properties of the complex endplate system, an expli cit evaluation for permeability of subchondral bone is missing. Thus, a new method wa s proposed to evaluate the intrinsic permeability of the bony endplate. CT - based reconstruction s of the bony endplate from a lumbar vertebra were analyzed using computational fluid dynamics , and the i ntrinsic permeability and porosity of the structure were calculated. Results showed that the permeability did not depend on the fluid flow direction, and was statistically similar for both the superior and inferior endplates . Permeability values varied within the range of trabecular bone, while porosity values w ere lower than trabecular bone characteristic values. Finally, i ntrins ic permeability correlated well with porosity through the Kozeny - Karman model, which offer s perspectives for parametric studies involving degenerative or age - related changes at the disc - bone interface.Postprint (published version

Endothelium and subendothelial matrix mechanics modulate cancer cell transendothelial migration

Cancer cell extravasation, a key step in the metastatic cascade, involves cancer cell arrest on the endothelium, transendothelial migration (TEM), followed by the invasion into the subendothelial extracellular matrix (ECM) of distant tissues. While cancer research has mostly focused on the biomechanical interactions between tumor cells (TCs) and ECM, particularly at the primary tumor site, very little is known about the mechanical properties of endothelial cells and the subendothelial ECM and how they contribute to the extravasation process. Here, an integrated experimental and theoretical framework is developed to investigate the mechanical crosstalk between TCs, endothelium and subendothelial ECM during in vitro cancer cell extravasation. It is found that cancer cell actin-rich protrusions generate complex push–pull forces to initiate and drive TEM, while transmigration success also relies on the forces generated by the endothelium. Consequently, mechanical properties of the subendothelial ECM and endothelial actomyosin contractility that mediate the endothelial forces also impact the endothelium's resistance to cancer cell transmigration. These results indicate that mechanical features of distant tissues, including force interactions between the endothelium and the subendothelial ECM, are key determinants of metastatic organotropism.Peer ReviewedPostprint (published version