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Angiogenesis is the formation of new blood vessels from the pre-existing vasculature. It is essential for normal tissue growth and regeneration, and also plays a key role in many diseases [Carmeliet in Nat Med 9:653-660, 2003]. Cytoskeletal components have been shown to be important for angiogenic sprout initiation and maintenance [Kniazeva and Putnam in Am J Physiol 297:C179-C187, 2009] as well as endothelial cell shape control during invasion [Elliott et al. in Nat Cell Biol 17:137-147, 2015]. The exact nature of cytoskeleton-mediated forces for sprout initiation and progression, however, remains poorly understood. Questions on the importance of tip cell pulling versus stalk cell pushing are to a large extent unanswered, which among others has to do with the difficulty of quantifying and resolving those forces in time and space. We developed methods based on time-lapse confocal microscopy and image processing-further termed 4D displacement microscopy-to acquire detailed, spatially and temporally resolved extracellular matrix (ECM) deformations, indicative of cell-ECM mechanical interactions around invading sprouts. We demonstrate that matrix deformations dependent on actin-mediated force generation are spatio-temporally correlated with sprout morphological dynamics. Furthermore, sprout tips were found to exert radially pulling forces on the extracellular matrix, which were quantified by means of a computational model of collagen ECM mechanics. Protrusions from extending sprouts mostly increase their pulling forces, while retracting protrusions mainly reduce their pulling forces. Displacement microscopy analysis further unveiled a characteristic dipole-like deformation pattern along the sprout direction that was consistent among seemingly very different sprout shapes-with oppositely oriented displacements at sprout tip versus sprout base and a transition zone of negligible displacements in between. These results demonstrate that sprout-ECM interactions are dominated by pulling forces and underline the key role of tip cell pulling for sprouting angiogenesis.

Bone healing is a complex biological procedure in which several cellular actions, directed by biochemical and mechanical signals, take place. Experimental studies have shown that ultrasound accelerates bone ossification and has a multiple influence on angiogenesis. In this study a mathematical model predicting bone healing under the presence of ultrasound is demonstrated. The primary objective is to account for the ultrasound effect on angiogenesis and more specifically on the transport of the Vascular Endothelial Growth Factor (VEGF). Partial differential equations describing the spatiotemporal evolution of cells, growth factors, tissues and ultrasound acoustic pressure and velocity equations determining the development of the blood vessel network constitute the present model. The effect of the ultrasound characteristics on angiogenesis and bone healing is investigated by applying different boundary conditions of acoustic pressure at the periosteal region of the bone model, which correspond to different intensity values. The results made clear that ultrasound enhances angiogenesis mechanisms during bone healing. The proposed model could be regarded as a step towards the monitoring of the effect of ultrasound on bone regeneration., (Copyright © 2018. Published by Elsevier Ltd.)

Since their first introduction, stents have revolutionised the treatment of atherosclerosis; however, the development of in-stent restenosis still remains the Achilles' heel of stent deployment procedures. Computational modelling can be used as a means to model the biological response of arteries to different stent designs using mechanobiological models, whereby the mechanical environment may be used to dictate the growth and remodelling of vascular cells. Changes occurring within the arterial wall due to stent-induced mechanical injury, specifically changes within the extracellular matrix, have been postulated to be a major cause of activation of vascular smooth muscle cells and the subsequent development of in-stent restenosis. In this study, a mechanistic multi-scale mechanobiological model of in-stent restenosis using finite element models and agent-based modelling is presented, which allows quantitative evaluation of the collagen matrix turnover following stent-induced arterial injury and the subsequent development of in-stent restenosis. The model is specifically used to study the influence of stent deployment diameter and stent strut thickness on the level of in-stent restenosis. The model demonstrates that there exists a direct correlation between the stent deployment diameter and the level of in-stent restenosis. In addition, investigating the influence of stent strut thickness using the mechanobiological model reveals that thicker strut stents induce a higher level of in-stent restenosis due to a higher extent of arterial injury. The presented mechanobiological modelling framework provides a robust platform for testing hypotheses on the mechanisms underlying the development of in-stent restenosis and lends itself for use as a tool for optimisation of the mechanical parameters involved in stent design.

Fluid mechanical stimuli are known to upregulate cell differentiation and matrix formation. Since wall shear stress plays an important role various studies tried to estimate the scaffold fluid dynamic environment. However, because of the geometrical complexity, nearly all studies created their CFD model based on a submodel of the entire scaffold assuming that the model covers heterogeneity sufficiently. However to the authors' knowledge no study exist providing guidelines in this matter. In a previous study we demonstrated that submodels are influenced by the boundary conditions, inevitable when flow channels are chopped off. For the current study we therefore developed μCT based models of two complete scaffold geometries (one titanium and one hydroxyapatite). Imposing a 0.04 ml/min flow rate resulted in a surface area averaged wall shear stress of 1.41 mPa for titanium and 1.09 mPa for hydroxyapatite. In order to get insight in required model size we subdivided the domain in regions of different size. From our results we propose a model size between 6 and 10 times the average pore size. The wall shears stress should be calculated on a region at least one pore size away from the boundaries. These guidelines could be of use for computationally more costly simulations where it is not possible to simulate the complete scaffold domain., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Scaffold permeability is a key parameter combining geometrical features such as pore shape, size and interconnectivity, porosity and specific surface area. It can influence the success of bone tissue engineering scaffolds, by affecting oxygen and nutrient transport, cell seeding efficiency, in vitro three-dimensional (3D) cell culture and, ultimately, the amount of bone formation. An accurate and efficient prediction of scaffold permeability would be highly useful as part of a scaffold design process. The aim of this study was (i) to determine the accuracy of computational fluid dynamics (CFD) models for prediction of the permeability coefficient of three different regular Ti6Al4V scaffolds (each having a different porosity) by comparison with experimentally measured values and (ii) to verify the validity of the semi-empirical Kozeny equation to calculate the permeability analytically. To do so, five CFD geometrical models per scaffold porosity were built, based on different geometrical inputs: either based on the scaffold's computer-aided design (CAD) or derived from 3D microfocus X-ray computed tomography (micro-CT) data of the additive manufactured (AM) scaffolds. For the latter the influence of the spatial image resolution and the image analysis algorithm used to determine the scaffold's architectural features on the predicted permeability was analysed. CFD models based on high-resolution micro-CT images could predict the permeability coefficients of the studied scaffolds: depending on scaffold porosity and image analysis algorithm, relative differences between measured and predicted permeability values were between 2% and 27%. Finally, the analytical Kozeny equation was found to be valid. A linear correlation between the ratio Φ(3)/S(s)(2) and the permeability coefficient k was found for the predicted (by means of CFD) as well as measured values (relative difference of 16.4% between respective Kozeny coefficients), thus resulting in accurate and efficient calculation of the permeability of regular AM scaffolds., (Copyright © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.)

Surface microroughness can induce contact osteogenesis (bone formation initiated at the implant surface) around oral implants, which may result from different mechanisms, such as blood platelet-biomaterial interactions and/or interaction with (pre-)osteoblast cells. We have developed a computational model of implant endosseous healing that takes into account these interactions. We hypothesized that the initial attachment and growth factor release from activated platelets is crucial in achieving contact osteogenesis. In order to investigate this, a computational model was applied to an animal experiment [7] that looked at the effect of surface microroughness on endosseous healing. Surface-specific model parameters were implemented based on in vitro data (Lincks et al. Biomaterials 1998;19:2219-32). The predicted spatio-temporal patterns of bone formation correlated with the histological data. It was found that contact osteogenesis could not be predicted if only the osteogenic response of cells was up-regulated by surface microroughness. This could only be achieved if platelet-biomaterial interactions were sufficiently up-regulated as well. These results confirmed our hypothesis and demonstrate the added value of the computational model to study the importance of surface-mediated events for peri-implant endosseous healing., (Copyright © 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.)

As part of a tissue engineering (TE) therapy, cell-seeded scaffolds can be cultured in perfusion bioreactors in which the flow-mediated wall shear stress and the nutrient transport are factors that influence in vitro proliferation and osteogenic differentiation of the seeded progenitor cells. In this study both computational fluid dynamics simulations on idealized boundary conditions and circumstances and microparticle image velocimetry measurements on realistic conditions were carried out to quantify the fluid dynamic microenvironment inside a bone TE construct. The results showed that differences between actual and designed geometry and time-dependent character of the fluid flow caused a 19% difference in average fluid velocity and a 27% difference in wall shear stress between simulations and measurements. The computational fluid dynamics simulation enabled higher resolution and three-dimensional fluid flow quantification that could be quantitatively compared with a microparticle image velocimetry measurement. The coupling of numerical and experimental analysis provides a reliable and high-resolution bi-modular tool for quantifying the fluid dynamics that represent the basis to determine the relation between the hydrodynamic environment and cell growth and differentiation within TE scaffolds.

The objective of this study was to see whether a mathematical model of fracture healing was able to mimic bone formation around an unloaded screw-shaped titanium implant as it is well-believed that both processes exhibit many biological similarities. This model describes the spatio-temporal evolution of cellular activities, ranging from mesenchymal stem cell migration, proliferation, differentiation to bone formation, which are initiated and regulated by the growth factors present at the peri-implant site. For the simulations, a finite volume code was used and adequate initial and boundary conditions were applied. Two sets of analyses have been performed, in which either initial and boundary condition or model parameter values were changed with respect to the fracture healing model parameter values. For a number of combinations, the spatio-temporal evolution of bone density was well-predicted. However reducing cell proliferation rate and increasing osteoblast differentiation and osteogenic growth factor synthesis rates, the simulation results were in agreement with the experimental data.

While mathematical models are able to capture essential aspects of biological processes like fracture healing and distraction osteogenesis, their predictive capacity in peri-implant osteogenesis remains uninvestigated. We tested the hypothesis that a mechano-regulatory model has the potential to predict bone regeneration around implants. In an in vivo bone chamber set-up allowing for controlled implant loading (up to 90 microm axial displacement), bone tissue formation was simulated and compared qualitatively and quantitatively with histology. Furthermore, the model was applied to simulate excessive loading conditions. Corresponding to literature data, implant displacement magnitudes larger than 90 microm predicted the formation of fibrous tissue encapsulation of the implant. In contradiction to findings in orthopedic implant osseointegration, implant displacement frequencies higher than 1 Hz did not favor the formation of peri-implant bone in the chamber. Additional bone chamber experiments are needed to test these numerical predictions.

Several mechanoregulatory tissue differentiation models have been proposed over the last decade. Corroboration of these models by comparison with experimental data is necessary to determine their predictive power. So far, models have been applied with various success rates to different experimental set-ups investigating mainly secondary fracture healing. In this study, the mechanoregulatory models are applied to simulate the implant osseointegration process in a repeated sampling in vivo bone chamber, placed in a rabbit tibia. This bone chamber provides a mechanically isolated environment to study tissue differentiation around titanium implants loaded in a controlled manner. For the purpose of this study, bone formation around loaded cylindrical and screw-shaped implants was investigated. Histologically, no differences were found between the two implant geometries for the global amount of bone formation in the entire chamber. However, a significantly larger amount of bone-to-implant contact was observed for the screw-shaped implant compared to the cylindrical implant. In the simulations, a larger amount of bone was also predicted to be in contact with the screw-shaped implant. However, other experimental observations could not be predicted. The simulation results showed a distribution of cartilage, fibrous tissue and (im)mature bone, depending on the mechanoregulatory model that was applied. In reality, no cartilage was observed. Adaptations to the differentiation models did not lead to a better correlation between experimentally observed and numerically predicted tissue distribution patterns. The hypothesis that the existing mechanoregulatory models were able to predict the patterns of tissue formation in the in vivo bone chamber could not be fully sustained.

The combined use of experimental and mathematical models can lead to a better understanding of fracture healing. In this study, a mathematical model, which was originally established by Bailón-Plaza and van der Meulen (J Theor Biol 212:191-209, 2001), was applied to an experimental model of a semi-stabilized murine tibial fracture. The mathematical model was implemented in a custom finite volumes code, specialized in dealing with the model's requirements of mass conservation and non-negativity of the variables. A qualitative agreement between the experimentally measured and numerically simulated evolution in the cartilage and bone content was observed. Additionally, an extensive parametric study was conducted to assess the influence of the model parameters on the simulation outcome. Finally, a case of pathological fracture healing and its treatment by administration of growth factors was modeled to demonstrate the potential therapeutic value of this mathematical model.

A finite element (FE) numerical model of an oral implant was implemented with the theory of bone adaptation to predict the response over time of the bone tissue to the implant and to explain a phenomenon regarding the clinical situation: the bone loss due to an overload stress. An adaptation routine, based on Beaupré theory, was developed to interface with the FE packages. The value of the mechanical stimulus, corresponding to the overload stress, was evaluated by applying the Taylor crack propagation theory. The predictions obtained by the numerical analyses demonstrated that the overload resorption is blocked only with spongy bone of 'good quality'. [ABSTRACT FROM AUTHOR]