Modelling actin polymerization: the effect on confined cell migration.

The aim of this work is to model cell motility under conditions of mechanical confinement. This cell migration mode may occur in extravasation of tumour and neutrophil-like cells. Cell migration is the result of the complex action of different forces exerted by the interplay between myosin contractility forces and actin processes. Here, we propose and implement a finite element model of the confined migration of a single cell. In this model, we consider the effects of actin and myosin in cell motility. Both filament and globular actin are modelled. We model the cell considering cytoplasm and nucleus with different mechanical properties. The migration speed in the simulation is around 0.1 µm/min, which is in agreement with existing literature. From our simulation, we observe that the nucleus size has an important role in cell migration inside the channel. In the simulation the cell moves further when the nucleus is smaller. However, this speed is less sensitive to nucleus stiffness. The results show that the cell displacement is lower when the nucleus is stiffer. The degree of adhesion between the channel walls and the cell is also very important in confined migration. We observe an increment of cell velocity when the friction coefficient is higher.

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.

Challenges in the Modeling of Wound Healing Mechanisms in Soft Biological Tissues.

Numerical models have become one of the most powerful tools in biomechanics and mechanobiology allowing highly detailed simulations. One of the fields in which they have broadly evolved during the last years is in soft tissue modeling. Particularly, wound healing in the skin is one of the processes that has been approached by computational models due to the difficulty of performing experimental investigations. During the last decades wound healing simulations have evolved from numerical models which considered only a few number of variables and simple geometries to more complex approximations that take into account a higher number of factors and reproduce more realistic geometries. Moreover, thanks to improved experimental observations, a larger number of processes, such as cellular stress generation or vascular growth, that take place during wound healing have been identified and modeled. This work presents a review of the most relevant wound healing approximations, together with an identification of the most relevant criteria that can be used to classify them. In addition, and looking towards the actual state of the art in the field, some future directions, challenges and improvements are analyzed for future developments.

Multi-scale finite element model of growth plate damage during the development of slipped capital femoral epiphysis.

Slipped capital femoral epiphysis (SCFE) is one of the most common disorders of adolescent hips. A number of works have related the development of SCFE to mechanical factors. Due to the difficulty of diagnosing SCFE in its early stages, the disorder often progresses over time, resulting in serious side effects. Therefore, the development of a tool to predict the initiation of damage in the growth plate is needed. Because the growth plate is a heterogeneous structure, to develop a precise and reliable model, it is necessary to consider this structure from both macro- and microscale perspectives. Thus, the main objective of this work is to develop a numerical multi-scale model that links damage occurring at the microscale to damage occurring at the macroscale. The use of this model enables us to predict which regions of the growth plate are at high risk of damage. First, we have independently analyzed the microscale to simulate the microstructure under shear and tensile tests to calibrate the damage model. Second, we have employed the model to simulate damage occurring in standardized healthy and affected femurs during the heel-strike stage of stair climbing. Our results indicate that on the macroscale, damage is concentrated in the medial region of the growth plate in both healthy and affected femurs. Furthermore, damage to the affected femur is greater than damage to the healthy femur from both the micro- and macrostandpoints. Maximal damage is observed in territorial matrices. Furthermore, simulations illustrate that little damage occurs in the reserve zone. These findings are consistent with previous findings reported in well-known experimental works.

Nonlinear finite element simulations of injuries with free boundaries: application to surgical wounds.

Wound healing is a process driven by biochemical and mechanical variables in which a new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work, we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Because of the regularity of this morphology, we approximate the evolution of the wound through its cross section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem; while allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction, we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the nonlinear problem, we use the finite element method (FEM) and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds.

Numerical modelling of the angiogenesis process in wound contraction.

Angiogenesis consists of the growth of new blood vessels from the pre-existing vasculature. This phenomenon takes place in several biological processes, including wound healing. In this work, we present a mathematical model of angiogenesis applied to skin wound healing. The developed model includes biological (capillaries and fibroblasts), chemical (oxygen and angiogenic growth factor concentrations) and mechanical factors (cell traction forces and extracellular matrix deformation) that influence the evolution of the healing process. A novelty from previous works, apart from the coupling of angiogenesis and wound contraction, is the more realistic modelling of skin as a hyperelastic material. Large deformations are addressed using an updated Lagrangian approach. The coupled non-linear model is solved with the finite element method, and the process is studied over two wound geometries (circular and elliptical) of the same area. The results indicate that the elliptical wound vascularizes two days earlier than the circular wound but that they experience a similar contraction level, reducing its size by 25 %.

A lattice-based approach to model distraction osteogenesis.

Distraction osteogenesis is a well-known technique in which new bone tissue is created when a distraction displacement is applied through an external frame. This orthopedic process is nowadays focus of intense research, both experimentally and numerically, as there are still many aspects not well understood. The aim of this study is to simulate bone distraction by means of a combined discrete-continuum approach based on a lattice formulation. Existing computational models simulate the main processes of distraction osteogenesis from a continuum perspective, considering as state variables the population of cells and tissue distributions. Results of the continuum and lattice-based approaches are similar with respect to the global evolution of the different cells but rather different in terms of the type of ossification process. Differences in the size of the soft interzone in the gap have also been found. In addition, the discrete-continuum formulation allows including a more realistic approach of the migration/proliferation process with a discrete random walk model instead of the Fick's law used in continuum approaches. Also, blood vessel growth can be simulated explicitly in this model with the inclusion of the endothelial cells. Further study is needed to provide additional insights to understand coupled phenomena at different scales in the cell-tissue interactions. However this work provides a first preliminary step for improving multiscale models.

Evaluation of residual stresses due to bone callus growth: a computational study.

Mechanical environment in callus is determinant for the evolution of bone healing. However, recent mechanobiological computational works have underestimated the effect that growth exerts on the mechanical environment of callus. In the present work, we computationally evaluate the significance of growth-induced stresses, commonly called residual stresses, in callus. We construct a mechanobiological model of a callus in the metatarsus of a sheep in two different stages: one week and four weeks after fracture. The magnitude of stresses generated during callus growth is compared with the magnitude of stresses when only external loads are applied to the callus. We predict that residual stresses are relevant in some areas, mainly located at the periosteal side far from the fracture gap. Therefore, the inclusion of these residual stresses could represent a significant impact on the callus growth and predict a different evolution of biological processes occurring during bone healing.

Three-dimensional simulation of mandibular distraction osteogenesis: mechanobiological analysis.

Distraction osteogenesis is a surgical process for reconstruction of skeletal deformities, which has been widely investigated from the clinical perspective. However, little has been analyzed about the capability of numerical models to predict the clinical outcome generated by distraction. Therefore, this article presents a finite element analysis of the mechanobiological behavior of a pediatric patient's mandible with hemifacial microsomia during the distraction process. It focuses on the three-dimensional simulation of a long bone defect in the ramus of the mandible and introduces additional aspects to be considered in the computational simulation as compared to the bidimensional simulation. The evolution of the different tissues within the gap is evaluated and in order to check the effectiveness of the model, the predicted numerical outcome will be compared from a qualitative point of view with radiographies provided by the surgeons. It is shown that the morphology of the mandible changed in a similar manner than that observed clinically. These results reveal that three-dimensional models are useful tools in the predictive assessment of mandibular distraction osteogenesis.

Effect of the fixator stiffness on the young regenerate bone after bone transport: computational approach.

Bone transport is a well accepted technique for the treatment of large bony defects. This process is mechanically driven, where mechanical forces play a central role in the development of tissues within the distracted gap. One of the most important mechanical factors that conditions the success of bone regeneration during distraction osteogenesis is the fixator stiffness not only during the distraction phase but also during the consolidation phase. Therefore, the aim of the present work is to evaluate the effect of the stiffness of the fixator device on the interfragmentary movements and the tissue outcome during the consolidation phase. A previous differentiation model (Claes and Heigele, 1999) is extended in order to take into account the different behaviors of the tissues in tension and compression. The numerical results that were computed concur with experimental findings; a stiff fixator promotes bone formation while the excessive motion induced by extremely flexible fixators is adverse for bony bridging. Experimental interfragmentary movement is similar to that computed numerically.

Flow injection photoinduced chemiluminescence determination of imazalil in water samples.

In this work, a fast, simple and economic method is proposed for the determination of imazalil in water samples by flow injection photoinduced chemiluminescence. In this method, imazalil degrades in basic media through the use of a photoreactor, and the resulting photofragments react with ferricyanide and generate the direct chemiluminescence signal. To the authors' knowledge, this is the first time that a chemiluminescence method has been proposed for the determination of this fungicide. All physical and chemical parameters in the flow injection chemiluminescence system were optimized in the experimental setting. In the absence of preconcentration, the linear dynamic range for imazalil was 0.75-5 mg L(-1) and the detection limit was 0.171 mg L(-1). The application of solid-phase extraction with C18 cartridges allowed the elimination of interference ions, the reduction of the linear dynamic range to 15-100 µg L(-1), and a detection limit of 3.4 µg L(-1). This detection limit is below the maximum concentration level established by the Regulations of the Hydraulic Public Domain for pesticide dumping. The sample throughput after solid-phase extraction of the analyte was 12 samples h(-1). The intraday and interday coefficients of variation were below 9.9% in all cases. This method was applied to the analysis of environmental water samples, and recoveries of between 95.7 and 110% were obtained.

EVI1 controls proliferation in acute myeloid leukaemia through modulation of miR-1-2.

BACKGROUND: The EVI1(ecotropic virus integration site 1) gene codes for a zinc-finger transcription factor, whose transcriptional activation leads to a particularly aggressive form of acute myeloid leukaemia (AML). Although, EVI1 interactions with key proteins in hematopoiesis have been previously described, the precise role of this transcription factor in promoting leukaemic transformation is not completely understood. Recent works have identified specific microRNA (miRNA) signatures in different AML subgroups. However, there is no analysis of miRNAs profiles associated with EVI1 overexpression in humans. METHODS: We performed QT-RT-PCR to assess the expression of 250 miRNAs in cell lines with or without EVI1 overexpression and in patient samples. We used ChIP assays to evaluated the possible binding of EVI1 binding to the putative miRNA promoter. Proliferation of the different cell lines transfected with the anti- or pre-miRs was quantified by MTT. RESULTS: Our data showed that EVI1 expression was significantly correlated with the expression of miR-1-2 and miR-133-a-1 in established cell lines and in patient samples. ChIP assays confirmed that EVI1 binds directly to the promoter of these two miRNAs. However, only miR-1-2 was involved in abnormal proliferation in EVI1 expressing cell lines. CONCLUSIONS: Our data showed that EVI1 controls proliferation in AML through modulation of miR-1-2. This study contributes to further understand the transcriptional networks involving transcription factors and miRNAs in AML.

Biomechanical response of a mandible in a patient affected with hemifacial microsomia before and after distraction osteogenesis.

Distraction osteogenesis (DO) has gained wide acceptance in the craniofacial surgery due to the huge possibilities it offers. However this orthopaedic field is under continuous development as it still presents uncertainties. In this context, numerical modelling/analysis may help us to design patient specific treatments once they have been experimentally verified. This paper presents a finite element analysis of the biomechanical behavior of a patient's mandible with hemifacial microsomia (HFM) before and after distraction. In order to check the effectiveness of the clinical protocol, the predicted biomechanical response will also be compared with that of a symmetrical healthy mandible. Strain and displacement fields, masticatory forces as well as reaction forces at the condyles are evaluated in each mandible analyzed. The results show that the present model is a useful tool to understand the normal function of the mandible and to predict changes due to alterations in the mandible geometry, such as those occurring in hemifacial microsomia.

Influence of the frequency of the external mechanical stimulus on bone healing: a computational study.

The mechanical environment considerably affects the evolution of the bone healing process. However, the effect of an external cyclic stimulation on the process has not yet been fully clarified. The aim of the present work is to evaluate the distribution of different mechanical variables in the fracture callus when an external cyclic stimulation is applied at different frequencies, in order to investigate those stimuli most likely to regulate bone healing. To perform this analysis an axisymmetric poroelastic finite element model of a sheep metatarsus fracture has been developed and several mechanical variables quantified within the callus: deviatoric strain, octahedral strain, pore pressure and fluid flow velocity. The applied mechanical stimulus corresponds to a compression displacement of 0.02 mm at frequencies of 1, 50 and 100Hz. The fluid flow velocity experiences considerable variations in amplitude and peak value when the frequency of the external stimulus changes, while the rest of the mechanical variables are not significatively modified. We conclude that the change in the frequency of the external mechanical stimulus directly affects the interstitial fluid flow velocity in the fracture callus. This change in the fluid flow velocity may induce movement of wastes, feeds or growth factors, as well as stimulating cellular differentiation and proliferation by means of changes in the mechanical environment of the callus. In addition, the results of this work suggest that, to obtain a more significant effect of cyclic stimulation, higher frequencies with lower amplitude than those normally used in previous experimental works are needed.

Monitoring in vivo load transmission through an external fixator.

This work presents a portable non-invasive external fixator to assess and monitor fracture healing in real time. To evaluate the potential of this fixator, a transverse osteotomy was performed in the tibia of six adult sheep (mean age 3+/-0.5 years and weight 63+/-5 kg). The fractures were stabilized by a specially designed unilateral external fixator, which was instrumented by means of a set of strain gauges. Strains in the external surface of the fixator were monitored during all the healing process. A wireless, remote monitoring of the implant was developed through a specially designed external telemetric device. The strain gauges were arranged in two different half-bridge Wheatstone configurations, allowing easy post-processing of the signal. Thus, bending loads were measured in two planes of the external fixator acting as a load cell. The load through the fixator was evaluated for the gait cycle during all the healing process. Full weight bearing of the injured leg was observed from the beginning. The load transmission mechanism in the fixator was quite similar in all operated tibias and radiographic images showed a successful healing in all animals. Although the fixator has only been tested in an animal model, after further testing this system may have clinical potential.

An interspecies computational study on limb lengthening.

Distraction osteogenesis is a surgical technique that produces large volumes of new bone by gradually separating two osteotomized bone segments. A previously proposed mechanical-based model that includes the effect of pre-traction stresses (stress level in the gap tissue before each distraction step) during limb lengthening is used here. In the present work, the spatial and temporal patterns of tissue distribution during distraction osteogenesis in different species (sheep, rabbit) and in the human are compared numerically to predict experimental results. Interspecies differential characteristics such as size, distraction protocol, and rate of distraction, among others, are chosen according to experiments. Tissue distributions and reaction forces are then analysed as indicators of the healing pattern. The results obtained are in agreement with experimental findings regarding both tissue distribution and reaction forces. The ability of the model to qualitatively predict the two animal models and the human healing pattern in distraction osteogenesis indicates its potential in understanding the influence of mechanics in this complex process.

Growth mixture model of distraction osteogenesis: effect of pre-traction stresses.

In tensional studies of bone fragments during limb lengthening, it is usually assumed that the stress level in the gap tissue before each distraction step (pre-traction stress) is rather modest. However, during the process of distraction osteogenesis, a large interfragmentary gap is generated and these pre-traction stresses may be important. To date, to the authors' knowledge, no computational study has been developed to assess the effect of stress accumulation during limb lengthening. In this work, we present a macroscopic growth mixture formulation to investigate the influence of pre-traction stresses on the outcome of this clinical procedure. In particular, the model is applied to the simulation of the regeneration of tibial defects by means of distraction osteogenesis. The evolution of pre-traction forces, post-traction forces and peak forces is evaluated and compared with experimental data. The results show that the inclusion of pre-traction stresses in the model affects the evolution of the regeneration process and the corresponding reaction forces.

Modeling distraction osteogenesis: analysis of the distraction rate.

Distraction osteogenesis is a useful technique aimed at inducing bone formation in widespread clinical applications. One of the most important factors that conditions the success of bone regeneration is the distraction rate. Since the mechanical environment around the osteotomy site is one of the main factors that affects both quantity and quality of the regenerated bone, we have focused on analyzing how the distraction rate influences on the mechanical conditions and tissue regeneration. Therefore, the aim of the present work is to explore the potential of a mathematical algorithm to simulate clinically observed distraction rate related phenomena that occur during distraction osteogenesis. Improvements have been performed on a previous model (Gómez-Benito et al. in J Theor Biol 235:105-119, 2005) in order to take into account the load history. The results obtained concur with experimental findings: a slow distraction rate results in premature bony union, whereas a fast rate results in a fibrous union. Tension forces in the interfragmentary gap tissue have also been estimated and successfully compared with experimental measurements.

A damage model for the growth plate: application to the prediction of slipped capital epiphysis.

Despite slipped capital femoral epiphysis (SCFE) being one of the most common disorders of the adolescent hip, its early diagnosis is quite difficult. The main objective of this work is to apply an interface damage model to predict the failure of the bone-growth plate-bone interface. This model allows to evaluate the risk of development of SCFE and to investigate the range of mechanical properties of the physis that may cause slippage of the plate. This paper also studies the influence of different geometrical parameters and body weight of the patient on the development of SCFE. We have demonstrated, thanks to the proposed model, that higher physeal sloping and posterior sloping angles are associated to a higher probability of development of SCFE. In a similar way, increasing body weight results in a more probable slippage.

Computational simulation of fracture healing: influence of interfragmentary movement on the callus growth.

Bone fractures heal through a complex process involving several cellular events. This healing process can serve to study factors that control tissue growth and differentiation from mesenchymal stem cells. The mechanical environment at the fracture site is one of the factors influencing the healing process and controls size and differentiation patterns in the newly formed tissue. Mathematical models can be useful to unravel the complex relation between mechanical environment and tissue formation. In this study, we present a mathematical model that predicts tissue growth and differentiation patterns from local mechanical signals. Our aim was to investigate whether mechanical stimuli, through their influence on stem cell proliferation and chondrocyte hypertrophy, predict characteristic features of callus size and geometry. We found that the model predicted several geometric features of fracture calluses. For instance, callus size was predicted to increase with increasing movement. Also, increases in size were predicted to occur through increase in callus diameter but not callus length. These features agree with experimental observations. In addition, spatial and temporal tissue differentiation patterns were in qualitative agreement with well-known experimental results. We therefore conclude that local mechanical signals can probably explain the shape and size of fracture calluses.