María José Gómez-Benito

A 3D Computational Simulation of Fracture Callus Formation: Influence of the Stiffness of the External Fixator

The stiffness of the external fixation highly influences the fracture healing pattern. In this work we study this aspect by means of a finite element model of a simple transverse mid-diaphyseal fracture of an ovine metatarsus fixed with a bilateral external fixator. In order to simulate the regenerative process, a previously developed mechanobiological model of bone fracture healing was implemented in three dimensions. This model is able to simulate tissue differentiation, bone regeneration, and callus growth. A physiological load of 500 N was applied and three different stiffnesses of the external fixator were simulated (2300, 1725, and 1150 N/mm). The interfragmentary strain and load sharing mechanism between bone and the external fixator were compared to those recorded in previous experimental works. The effects of the stiffness on the callus shape and tissue distributions in the fracture site were also analyzed. We predicted that a lower stiffness of the fixator delays fracture healing and causes a larger callus, in correspondence to well-documented clinical observations.

A cell-regulatory mechanism involving feedback between contraction and tissue formation guides wound healing progression

Wound healing is a process driven by cells. The ability of cells to sense mechanical stimuli from the extracellular matrix that surrounds them is used to regulate the forces that cells exert on the tissue. Stresses exerted by cells play a central role in wound contraction and have been broadly modelled. Traditionally, these stresses are assumed to be dependent on variables such as the extracellular matrix and cell or collagen densities. However, we postulate that cells are able to regulate the healing process through a mechanosensing mechanism regulated by the contraction that they exert. We propose that cells adjust the contraction level to determine the tissue functions regulating all main activities, such as proliferation, differentiation and matrix production. Hence, a closed-regulatory feedback loop is proposed between contraction and tissue formation. The model consists of a system of partial differential equations that simulates the evolution of fibroblasts, myofibroblasts, collagen and a generic growth factor, as well as the deformation of the extracellular matrix. This model is able to predict the wound healing outcome without requiring the addition of phenomenological laws to describe the time-dependent contraction evolution. We have reproduced two in vivo experiments to evaluate the predictive capacity of the model, and we conclude that there is feedback between the level of cell contraction and the tissue regenerated in the wound.

Apo2L/TRAIL is an indirect mediator of apoptosis induced by interferon-α in human myeloma cells

Interferon‐α (IFN‐α) is currently used for the therapy of multiple myeloma (MM) though it is only effective in some patients. IFN‐α induces apoptosis in some MM cell lines and it has been proposed to occur through an autocrine loop involving Apo2L/TRAIL. We have analysed the sensitivity to IFN‐α and Apo2L/TRAIL of five MM cell lines and found no correlation between the apoptosis inducing ability of both cytokines. IFN‐α‐induced apoptosis in MM cells was not prevented by a caspase‐8 selective inhibitor (Z‐IETD‐fmk) or blocking Apo2L/TRAIL. However, human monocytes treated with IFN‐α release bioactive Apo2L/TRAIL to culture media which was cytotoxic for MM cells resistant to IFN‐α. We propose that Apo2L/TRAIL released from IFN‐α‐stimulated blood monocytes would be a major mediator of the anti‐myeloma effect of IFN‐α in vivo.

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.

In silico Mechano-Chemical Model of Bone Healing for the Regeneration of Critical Defects: The Effect of BMP-2

The healing of bone defects is a challenge for both tissue engineering and modern orthopaedics. This problem has been addressed through the study of scaffold constructs combined with mechanoregulatory theories, disregarding the influence of chemical factors and their respective delivery devices. Of the chemical factors involved in the bone healing process, bone morphogenetic protein-2 (BMP-2) has been identified as one of the most powerful osteoinductive proteins. The aim of this work is to develop and validate a mechano-chemical regulatory model to study the effect of BMP-2 on the healing of large bone defects in silico. We first collected a range of quantitative experimental data from the literature concerning the effects of BMP-2 on cellular activity, specifically proliferation, migration, differentiation, maturation and extracellular matrix production. These data were then used to define a model governed by mechano-chemical stimuli to simulate the healing of large bone defects under the following conditions: natural healing, an empty hydrogel implanted in the defect and a hydrogel soaked with BMP-2 implanted in the defect. For the latter condition, successful defect healing was predicted, in agreement with previous in vivo experiments. Further in vivo comparisons showed the potential of the model, which accurately predicted bone tissue formation during healing, bone tissue distribution across the defect and the quantity of bone inside the defect. The proposed mechano-chemical model also estimated the effect of BMP-2 on cells and the evolution of healing in large bone defects. This novel in silico tool provides valuable insight for bone tissue regeneration strategies.

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.

Influence of high-frequency cyclical stimulation on the bone fracture-healing process: mathematical and experimental models

Mechanical stimulation affects the evolution of healthy and fractured bone. However, the effect of applying cyclical mechanical stimuli on bone healing has not yet been fully clarified. The aim of the present study was to determine the influence of a high-frequency and low-magnitude cyclical displacement of the fractured fragments on the bone-healing process. This subject is studied experimentally and computationally for a sheep long bone. On the one hand, the mathematical computational study indicates that mechanical stimulation at high frequencies can stimulate and accelerate the process of chondrogenesis and endochondral ossification and consequently the bony union of the fracture. This is probably achieved by the interstitial fluid flow, which can move nutrients and waste from one place to another in the callus. This movement of fluid modifies the mechanical stimulus on the cells attached to the extracellular matrix. On the other hand, the experimental study was carried out using two sheep groups. In the first group, static fixators were implanted, while, in the second one, identical devices were used, but with an additional vibrator. This vibrator allowed a cyclic displacement with low magnitude and high frequency (LMHF) to be applied to the fractured zone every day; the frequency of stimulation was chosen from mechano-biological model predictions. Analysing the results obtained for the control and stimulated groups, we observed improvements in the bone-healing process in the stimulated group. Therefore, in this study, we show the potential of computer mechano-biological models to guide and define better mechanical conditions for experiments in order to improve bone fracture healing. In fact, both experimental and computational studies indicated improvements in the healing process in the LMHF mechanically stimulated fractures. In both studies, these improvements could be associated with the promotion of endochondral ossification and an increase in the rate of cell proliferation and tissue synthesis.

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.

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.

Computational model of mesenchymal migration in 3D under chemotaxis

Abstract 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.