Inverse method based on 3D nonlinear physically constrained minimisation in the framework of traction force microscopy.

Traction force microscopy is a methodology that enables to estimate cellular forces from the measurement of the displacement field of an extracellular matrix (ECM)-mimicking hydrogel that a cell is mechanically interacting with. In this paper, a new inverse and physically-consistent methodology is developed and implemented in the context of 3D nonlinear elasticity. The proposed method searches for a displacement field that approximates the measured one, through the imposition of fulfillment of equilibrium with real and known forces acting in the hydrogel. The overall mathematical formulation leads to a constrained optimisation problem that is treated through a Lagrange operator and that is solved numerically by means of a nonlinear finite element framework. In order to illustrate the potential and enhanced accuracy of the proposed inverse method, it is applied to a total of 5 different real cases of cells cultured in a 3D hydrogel that is considered to behave as a nonlinear elastic material. Different error indicators are defined in order to compare ground truth simulated displacements and tractions to the ones recovered by the new inverse as well as by the forward method. Results indicate that the evaluation of displacement gradients leads to errors, in terms of recovered tractions, that are more than three times lower (on average) for the inverse method compared to the forward method. They highlight the enhanced accuracy of the developed methodology and the importance of appropriate inverse methods that impose physical constraints to traction and stress recovery in the context of traction force microscopy.

An iterative finite element-based method for solving inverse problems in traction force microscopy.

BACKGROUND AND OBJECTIVE: During the last years different model solutions were proposed for solving cell forces under different conditions. The solution relies on a deformation field that is obtained under cell relaxation with a chemical cocktail. Once the deformation field of the matrix is determined, cell forces can be computed by an inverse algorithm, given the mechanical properties of the matrix. Most of the Traction Force Microscopy (TFM) methods presented so far relied on a linear stress-strain response of the matrix. However, the mechanical response of some biopolymer networks, such as collagen gels is more complex. In this work, we present a numerical method for solving cell forces on non-linear materials. METHODS: The proposed method relies on solving the inverse problem based on an iterative optimization. The objective function is defined by least-square minimization of the difference between the target and the current computed deformed configuration of the cell, and the iterative formulation is based on the solution of several direct mechanical problems. The model presents a well-posed discretized inverse elasticity problem in the absence of regularization. The algorithm can be easily implemented in any kind of Finite Element (FE) code as a sequence of different standard FE analysis. RESULTS: To illustrate the proposed iterative formulation we apply the theoretical model to some illustrative examples by using real experimental data of Normal Human Dermal Fibroblast cells (NHDF) migrating inside a 2 mg/ml collagen-based gel. Different examples of application have been simulated to test the inverse numerical model proposed and to investigate the effect of introducing the correct cell properties onto the obtained cell forces. The algorithm converges after a small number of iterations, generating errors of around 5% for the tractions field in the cell contour domain. The resulting maximum traction values increased by 11% as a consequence of doubling the mechanical properties of the cell domain. CONCLUSIONS: With the results generated from computations we demonstrate the application of the algorithm and explain how the mechanical properties of both, the cell and the gel, domains are important for arriving to the correct results when using inverse traction force reconstruction algorithms, however, have only a minor effect on the resulting traction values.

A web-based application for automated quantification of chemical gradients induced in microfluidic devices.

Advances in microfabrication have allowed the development and popularization of microfluidic devices, which are powerful tools to recreate three-dimensional (3-D) biologically relevant in vitro models. These microenvironments are usually generated by using hydrogels and induced chemical gradients. Going further, computational models enable, after validation, the simulation of such conditions without the necessity of real experiments, thus saving costs and time. In this work we present a web-based application that allows, based on a previous numerical model, the assessment of different chemical gradients induced within a 3-D extracellular matrix. This application enables the estimation of the spatio-temporal chemical distribution inside microfluidic devices, by defining a first set of parameters characterizing the chip geometry, and a second set characterizing the diffusion properties of the hydrogel-based matrix. The simulated chemical concentration profiles generated within a synthetic hydrogel are calculated remotely on a server and returned to the website in less than 3 min, thus offering a quick automatic quantification to any user. To ensure the day-to-day applicability, user requirements were investigated prior to tool development, pre-selecting some of the most common geometries. The tool is freely available online, after user registration, on http://m2be.unizar.es/insilico_cell under the software tab. Four different microfluidic device geometries were defined to study the dependence of the geometrical parameters onto the gradient formation processes. The numerical predictions demonstrate that growth factor diffusion within 3-D matrices strongly depends not only on the physics of diffusion, but also on the geometrical parameters that characterizes these complex devices. Additionally, the effect of the combination of different hydrogels inside a microfluidic device was studied. The automatization of microfluidic device geometries generation provide a powerful tool which facilitates to any user the possibility to automatically create its own microfluidic device, greatly reducing the experimental validation processes and advancing in the understanding of in vitro 3-D cell responses without the necessity of using commercial software or performing real testing experiments.

Traction Force Microscopy in 3-Dimensional Extracellular Matrix Networks.

Cell migration through a three-dimensional (3-D) matrix depends strongly on the ability of cells to generate traction forces. To overcome the steric hindrance of the matrix, cells need to generate sufficiently high traction forces but also need to distribute these forces spatially in a migration-promoting way. This unit describes a protocol to measure spatial maps of cell traction forces in 3-D biopolymer networks such as collagen, fibrin, or Matrigel. Traction forces are computed from the relationship between measured force-induced matrix deformations surrounding the cell and the known mechanical properties of the matrix. The method does not rely on knowledge of the cell surface coordinates and takes nonlinear mechanical properties of the matrix into account. © 2017 by John Wiley & Sons, Inc.

A phenomenological cohesive model for the macroscopic simulation of cell-matrix adhesions.

Cell adhesion is crucial for cells to not only physically interact with each other but also sense their microenvironment and respond accordingly. In fact, adherent cells can generate physical forces that are transmitted to the surrounding matrix, regulating the formation of cell-matrix adhesions. The main purpose of this work is to develop a computational model to simulate the dynamics of cell-matrix adhesions through a cohesive formulation within the framework of the finite element method and based on the principles of continuum damage mechanics. This model enables the simulation of the mechanical adhesion between cell and extracellular matrix (ECM) as regulated by local multidirectional forces and thus predicts the onset and growth of the adhesion. In addition, this numerical approach allows the simulation of the cell as a whole, as it models the complete mechanical interaction between cell and ECM. As a result, we can investigate and quantify how different mechanical conditions in the cell (e.g., contractile forces, actin cytoskeletal properties) or in the ECM (e.g., stiffness, external forces) can regulate the dynamics of cell-matrix adhesions.

Inducing chemotactic and haptotactic cues in microfluidic devices for three-dimensional in vitro assays.

Microfluidic devices allow for the production of physiologically relevant cellular microenvironments by including biomimetic hydrogels and generating controlled chemical gradients. During transport, the biomolecules interact in distinct ways with the fibrillar networks: as purely diffusive factors in the soluble fluid or bound to the matrix proteins. These two main mechanisms may regulate distinct cell responses in order to guide their directional migration: caused by the substrate-bound chemoattractant gradient (haptotaxis) or by the gradient established within the soluble fluid (chemotaxis). In this work 3D diffusion experiments, in combination with ELISA assays, are performed using microfluidic platforms in order to quantify the distribution of PDGF-BB and TGF-ß1 across collagen and fibrin gels. Furthermore, to gain a deeper understanding of the fundamental processes, the experiments are reproduced by computer simulations based on a reaction-diffusion transport model. This model yields an accurate prediction of the experimental results, confirming that diffusion and binding phenomena are established within the microdevice.

Factores clínicos y demográficos predictores de éxito del misoprostol en el tratamiento médico del aborto espontáneo / Predictors of success of misoprostol in the treatment of first trimester spontaneous abortion

Objetivos: Determinar posibles predictores de éxito del misoprostol en el tratamiento del aborto espontáneo del primer trimestre. Método: Estudio observacional descriptivo y prospectivo, realizado entre febrero de 2009 y febrero de 2010. Inclusión consecutiva de 248 mujeres con diagnostico ecográfico de aborto espontáneo del primer trimestre con tratamiento médico o quirúrgico, siendo las pacientes las que eligieron la opción terapéutica de acuerdo a los criterios de inclusión para el manejo con misoprostol. En el grupo tratamiento médico se aplicó 800 mcg de misoprostol vaginal/24horas/2 dosis, considerándose como criterio de éxito un endometrio homogéneo con grosor <15 mm en la ecografía realizada al 8° día del tratamiento. Resultados: Influyen en la tasa de éxito del misoprostol la edad de las pacientes (mejor resultado cuanto más joven, p=0,025), número de embarazos (responden mejor las primigestas, p=0,024), existencia o no de abortos (p=0,05) o legrados previos (p=0,028) (la tasa de éxito del misoprostol es mayor en las mujeres que no tienen ningún aborto o legrado previo), y tipo de sangrado vaginal que aparece como efecto secundario del misoprostol (mejorando el pronóstico cuando dicho sangrado es igual o mayor que menstruación, p=0,041). Conclusiones: Hubo predictores de éxito del misoprostol que pueden orientar el manejo, sabiendo que hubo mejor resultado en pacientes jóvenes, primigestas, sin abortos ni legrados previos y con un sangrado vaginal igual o mayor que menstruación.

Objectives: To determine possible predictors of success of misoprostol in the treatment of first trimester spontaneous abortion. Methods: Descriptive observational study and prospectively from February 2009 to February 2010. It were included 248 women which were diagnosed by ultrasound of spontaneous abortion in the first trimester and received medical or surgical treatment, depending on the patient's own choice, provided that the established clinical conditions were present. The protocol applied in the medical treatment group was 800 mcg of vaginal misoprostol/24h/2 dose. It was considered as criteria of success, the presence of a homogeneous endometrium with a thickness <15 mm in the ultrasound examination performed on the 8 th day of treatment. Results: The following variables influence the success rate of misoprostol: patient age (the younger the better outcome, p = 0.025), number of pregnancies (primiparous respond better, p = 0.024), presence or absence of abortions ( p = 0.05) or previous curettage (p = 0.028) (the success rate of misoprostol is higher in women who have no previous abortion or curettage), and type of vaginal bleeding that occurs as a side effect of misoprostol (improving prognosis when bleeding is equal to or greater than the rule, p = 0.041). Conclusions: We found predictors of success of misoprostol, which can guide the management knowing that better results can get obtained in younger patients, primigravida, no previous abortions or curettage and with a vaginal bleeding equal to or greater than the rule.

Early re-feeding in the management of acute diarrhoea in infants of 0-1 year of age.

We compared early versus late re-feeding in the management of acute diarrhoea in the first year of life. In the study group (73 groups) breast feeding was resumed or early re-feeding was performed in non-breast-fed infants, so that the feeding regimen used prior to the onset of the disease was reached within 2-3 days. In the control group (49 patients) late re-feeding was performed so that the infants returned to their original feeding pattern after 4-6 days. there were no significant differences between the two groups in the number of stools and stool output per day, or in the duration of the disease. No weight gain or loss during the diet was noted more frequently in the late re-feeding group (67.2% versus 2.3.4%). This study confirms the favourable effect on body weight of early re-feeding in the management of acute diarrhoea.

Obstructive intramural haematoma--a rare cause of mechanical ileus in children.

The authors report on an infant of three weeks of age, suffering from mycotic septicaemia (Candida), in the course of which the syndrome of disseminated intravascular coagulation (DIC) occurred. The digestive expression of DIC was represented by numerous intestinal intramural haematomas, one of which was large enough to produce the clinical signs of mechanical ileus. The aetiology of the intestinal intramural haematoma is discussed and its relatively frequent occurrence in infants with DIC is stressed.