Size does matter: an integrative in vivo-in silico approach for the treatment of critical size bone defects

Although bone has a unique restorative capacity, i.e., it has the potential to heal scarlessly, the conditions for spontaneous bone healing are not always present, leading to a delayed union or a non-union. In this work, we use an integrative in vivo - in silico approach to investigate the occurrence of non-unions, as well as to design possible treatment strategies thereof. The gap size of the domain geometry of a previously published mathematical model was enlarged in order to study the complex interplay of blood vessel formation, oxygen supply, growth factors and cell proliferation on the final healing outcome in large bone defects. The multiscale oxygen model was not only able to capture the essential aspects of in vivo non-unions, it also assisted in understanding the underlying mechanisms of action, i.e., the delayed vascularization of the central callus region resulted in harsh hypoxic conditions, cell death and finally disrupted bone healing. Inspired by the importance of a timely vascularization, as well as by the limited biological potential of the fracture hematoma, the influence of the host environment on the bone healing process in critical size defects was explored further. Moreover, dependent on the host environment, several treatment strategies were designed and tested for effectiveness. A qualitative correspondence between the predicted outcomes of certain treatment strategies and experimental observations was obtained, clearly illustrating the model's potential. In conclusion, the results of this study demonstrate that due to the complex non-linear dynamics of blood vessel formation, oxygen supply, growth factor production and cell proliferation and the interactions thereof with the host environment, an integrative in silico-in vivo approach is a crucial tool to further unravel the occurrence and treatments of challenging critical sized bone defects.

In 5–10% of fracture patients, the bone fractures do not heal in the normal healing period (delayed healing) or do not heal at all (non-union). In order to investigate the causes of impaired healing and design potential treatment strategies, we have used a combined experimental and computational approach. More specifically, large bone defects were analyzed in mouse models and simulated by a previously published computational model. After showing that the predictions of the computational model match the observations of the experimental model, we have used the computational model to investigate the underlying mechanisms of action. In particular, the results indicated that the new blood vessels do not reach the central fracture zone in time due to the large defect size, which leads to insufficient oxygen delivery, increased cell death and disrupted bone healing. The healing, however, could be rescued by adequate blood vessel ingrowth from the overlying soft tissues. Moreover, potential treatment strategies were designed based on the influence of these soft tissues. In conclusion, this study demonstrates the potential of a combined experimental and computational approach to contribute to the understanding of pathological processes like the impaired bone regeneration in large bone defects and design future treatments thereof.

Reporter cell activity within hydrogel constructs quantified from oxygen-independent bioluminescence

By providing a three-dimensional (3D) support to cells, hydrogels offer a more relevant in vivo tissue-like environment as compared to two-dimensional cell cultures. Hydrogels can be applied as screening platforms to investigate in 3D the role of biochemical and biophysical cues on cell behaviour using bioluminescent reporter cells. Gradients in oxygen concentration that result from the interplay between molecular transport and cell metabolism can however cause substantial variability in the observed bioluminescent reporter cell activity. To assess the influence of these oxygen gradients on the emitted bioluminescence for various hydrogel geometries, a combined experimental and modelling approach was implemented. We show that the applied model is able to predict oxygen gradient independent bioluminescent intensities which correlate better to the experimentally determined viable cell numbers, as compared to the experimentally measured bioluminescent intensities. By analysis of the bioluminescence reaction dynamics we obtained a quantitative description of cellular oxygen metabolism within the hydrogel, which was validated by direct measurements of oxygen concentration within the hydrogel. Bioluminescence peak intensities can therefore be used as a quantitative measurement of reporter cell activity within a hydrogel, but an unambiguous interpretation of these intensities requires a compensation for the influence of cell-induced oxygen gradients on the luciferase activity.

A causal relation between bioluminescence and oxygen to quantify the cell niche

Bioluminescence imaging assays have become a widely integrated technique to quantify effectiveness of cell-based therapies by monitoring fate and survival of transplanted cells. To date these assays are still largely qualitative and often erroneous due to the complexity and dynamics of local micro-environments (niches) in which the cells reside. Here, we report, using a combined experimental and computational approach, on oxygen that besides being a critical niche component responsible for cellular energy metabolism and cell-fate commitment, also serves a primary role in regulating bioluminescent light kinetics. We demonstrate the potential of an oxygen dependent Michaelis-Menten relation in quantifying intrinsic bioluminescence intensities by resolving cell-associated oxygen gradients from bioluminescent light that is emitted from three-dimensional (3D) cell-seeded hydrogels. Furthermore, the experimental and computational data indicate a strong causal relation of oxygen concentration with emitted bioluminescence intensities. Altogether our approach demonstrates the importance of oxygen to evolve towards quantitative bioluminescence and holds great potential for future microscale measurement of oxygen tension in an easily accessible manner.

Deciphering mechanical regulation of chondrogenesis in fibrin-polyurethane composite scaffolds enriched with human mesenchymal stem cells: a dual computational and experimental approach

Fibrin-polyurethane composite scaffolds support chondrogenesis of human mesenchymal stem cells (hMSCs) derived from bone marrow and due to their robust mechanical properties allow mechanical loading in dynamic bioreactors, which has been shown to increase the chondrogenic differentiation of MSCs through the transforming growth factor beta pathway. The aim of this study was to use the finite element method, mechanical testing, and dynamic in vitro cell culture experiments on hMSC-enriched fibrin-polyurethane composite scaffolds to quantitatively decipher the mechanoregulation of chondrogenesis within these constructs. The study identified compressive principal strains as the key regulator of chondrogenesis in the constructs. Although dynamic uniaxial compression did not induce chondrogenesis, multiaxial loading by combined application of dynamic compression and interfacial shear induced significant chondrogenesis at locations where all the three principal strains were compressive and had a minimum magnitude of 10%. In contrast, no direct correlation was identified between the level of pore fluid velocity and chondrogenesis. Due to the high permeability of the constructs, the pore fluid pressures could not be increased sufficiently by mechanical loading, and instead, chondrogenesis was induced by triaxial compressive deformations of the matrix with a minimum magnitude of 10%. Thus, it can be concluded that dynamic triaxial compressive deformations of the matrix is sufficient to induce chondrogenesis in a threshold-dependent manner, even where the pore fluid pressure is negligible.

Analysis of initial cell spreading using mechanistic contact formulations for a deformable cell model

Adhesion governs to a large extent the mechanical interaction between a cell and its microenvironment. As initial cell spreading is purely adhesion driven, understanding this phenomenon leads to profound insight in both cell adhesion and cell-substrate interaction. It has been found that across a wide variety of cell types, initial spreading behavior universally follows the same power laws. The simplest cell type providing this scaling of the radius of the spreading area with time are modified red blood cells (RBCs), whose elastic responses are well characterized. Using a mechanistic description of the contact interaction between a cell and its substrate in combination with a deformable RBC model, we are now able to investigate in detail the mechanisms behind this universal power law. The presented model suggests that the initial slope of the spreading curve with time results from a purely geometrical effect facilitated mainly by dissipation upon contact. Later on, the spreading rate decreases due to increasing tension and dissipation in the cell's cortex as the cell spreads more and more. To reproduce this observed initial spreading, no irreversible deformations are required. Since the model created in this effort is extensible to more complex cell types and can cope with arbitrarily shaped, smooth mechanical microenvironments of the cells, it can be useful for a wide range of investigations where forces at the cell boundary play a decisive role.

How cells spread on a newly encountered surface is an important issue, since it hints at how cells interact physically with the specific material in general. It has been shown before that many cell types have very similar early spreading behavior. This observation has been linked to the mechanical nature of the phenomenon, during which a cell cannot yet react by changing its structure and behavior. Understanding in detail how this passive spreading occurs, and what clues a cell may later respond to is the goal of this work. At the same time, the model we develop here should be very valuable for more complex situations of interacting cells, since it is able to reproduce the purely mechanical response in detail. We find that spreading is limited mainly by energy dissipation upon contact and later dissipation in the cell's cortex and that no irreversible deformation occurs during the spreading of red blood cells on an adhesive surface.

Fluorescent oxygen sensitive microbead incorporation for measuring oxygen tension in cell aggregates

Molecular oxygen is a main regulator of various cell functions. Imaging methods designed as screening tools for fast, in situ, 3D and non-interfering measurement of oxygen tension in the cellular microenvironment would serve great purpose in identifying and monitoring this vital and pivotal signalling molecule. We describe the use of dual luminophore oxygen sensitive microbeads to measure absolute oxygen concentrations in cellular aggregates. Stable microbead integration, a prerequisite for their practical application, was ensured by a site-specific delivery method that is based on the interactions between streptavidin and biotin. The spatial stability introduced by this method allowed for long term measurements of oxygen tension without interfering with the cell aggregation process. By making multiple calibration experiments we further demonstrated the potential of these sensors to measure local oxygen tension in optically dense cellular environments.

MOSAIC: a multiscale model of osteogenesis and sprouting angiogenesis with lateral inhibition of endothelial cells

The healing of a fracture depends largely on the development of a new blood vessel network (angiogenesis) in the callus. During angiogenesis tip cells lead the developing sprout in response to extracellular signals, amongst which vascular endothelial growth factor (VEGF) is critical. In order to ensure a correct development of the vasculature, the balance between stalk and tip cell phenotypes must be tightly controlled, which is primarily achieved by the Dll4-Notch1 signaling pathway. This study presents a novel multiscale model of osteogenesis and sprouting angiogenesis, incorporating lateral inhibition of endothelial cells (further denoted MOSAIC model) through Dll4-Notch1 signaling, and applies it to fracture healing. The MOSAIC model correctly predicted the bone regeneration process and recapitulated many experimentally observed aspects of tip cell selection: the salt and pepper pattern seen for cell fates, an increased tip cell density due to the loss of Dll4 and an excessive number of tip cells in high VEGF environments. When VEGF concentration was even further increased, the MOSAIC model predicted the absence of a vascular network and fracture healing, thereby leading to a non-union, which is a direct consequence of the mutual inhibition of neighboring cells through Dll4-Notch1 signaling. This result was not retrieved for a more phenomenological model that only considers extracellular signals for tip cell migration, which illustrates the importance of implementing the actual signaling pathway rather than phenomenological rules. Finally, the MOSAIC model demonstrated the importance of a proper criterion for tip cell selection and the need for experimental data to further explore this. In conclusion, this study demonstrates that the MOSAIC model creates enhanced capabilities for investigating the influence of molecular mechanisms on angiogenesis and its relation to bone formation in a more mechanistic way and across different time and spatial scales.

Modelling the effect of repositioning on the evolution of skeletal muscle damage in deep tissue injury

Deep tissue injury (DTI) is a localized area of tissue necrosis that originates in the subcutaneous layers under an intact skin and tends to develop when soft tissue is compressed for a prolonged period of time. In clinical practice, DTI is particularly common in bedridden patients and remains a serious issue in todays health care. Repositioning is generally considered to be an effective preventive measure of pressure ulcers. However, limited experimental research and no computational studies have been undertaken on this method. In this study, a methodology was developed to evaluate the influence of different repositioning intervals on the location, size and severity of DTI in bedridden patients. The spatiotemporal evolution of compressive stresses and skeletal muscle viability during the first 48 h of DTI onset was simulated for repositioning schemes in which a patient is turned every 2, 3, 4 or 6 h. The model was able to reproduce important experimental findings, including the morphology and location of DTI in human patients as well as the discrepancy between the internal tissue loads and the contact pressure at the interface with the environment. In addition, the model indicated that the severity and size of DTI were reduced by shortening the repositioning intervals. In conclusion, the computational framework presented in this study provides a promising modelling approach that can help to objectively select the appropriate repositioning scheme that is effective and efficient in the prevention of DTI.

Relating the chondrocyte gene network to growth plate morphology: from genes to phenotype

During endochondral ossification, chondrocyte growth and differentiation is controlled by many local signalling pathways. Due to crosstalks and feedback mechanisms, these interwoven pathways display a network like structure. In this study, a large-scale literature based logical model of the growth plate network was developed. The network is able to capture the different states (resting, proliferating and hypertrophic) that chondrocytes go through as they progress within the growth plate. In a first corroboration step, the effect of mutations in various signalling pathways of the growth plate network was investigated.

Occurrence and treatment of bone atrophic non-unions investigated by an integrative approach

Recently developed atrophic non-union models are a good representation of the clinical situation in which many non-unions develop. Based on previous experimental studies with these atrophic non-union models, it was hypothesized that in order to obtain successful fracture healing, blood vessels, growth factors, and (proliferative) precursor cells all need to be present in the callus at the same time. This study uses a combined in vivo-in silico approach to investigate these different aspects (vasculature, growth factors, cell proliferation). The mathematical model, initially developed for the study of normal fracture healing, is able to capture essential aspects of the in vivo atrophic non-union model despite a number of deviations that are mainly due to simplifications in the in silico model. The mathematical model is subsequently used to test possible treatment strategies for atrophic non-unions (i.e. cell transplant at post-osteotomy, week 3). Preliminary in vivo experiments corroborate the numerical predictions. Finally, the mathematical model is applied to explain experimental observations and identify potentially crucial steps in the treatments and can thereby be used to optimize experimental and clinical studies in this area. This study demonstrates the potential of the combined in silico-in vivo approach and its clinical implications for the early treatment of patients with problematic fractures.

In light of the ageing population, the occurrence of bone fractures is expected to rise substantially in the near future. In 5 to 10% of these cases, the healing process does not succeed in repairing the bone, leading to the formation of delayed unions or even non-unions. In this study we used a combination of an animal model mimicking a clinical non-union situation and a mathematical model developed for normal fracture healing to investigate both the causes of non-union formation and potential therapeutic strategies that can be applied to restart the healing process. After showing that the mathematical model is able to simulate key aspects of the non-union formation, we have used it to investigate several treatment strategies. One of these strategies, the treatment of a non-union involving a transplantation of cells from the bone marrow to the fracture site, was also tested in a pilot animal experiment. Both the simulations and the experiments showed the formation of a bony union between the fractured bone ends. In addition, we used the mathematical model to explain some unexpected experimental observations. This study demonstrates the added value of using a combination of mathematical modelling and experimental research as well the potential of using cell transplantation for the treatment of non-unions.

The influence of Young's modulus of loaded implants on bone remodeling: an experimental and numerical study in the goat knee

The aim of this study was to examine the influence of the Young's modulus of the implant material on the bone remodeling in a loaded condition. A combined animal experimental and computational study was set up. The animal experimental group comprised of 16 Saanen goats, each receiving one titanium implant (Young's modulus 110 GPa) and one high-density polyethylene (HDPE) implant (Young's modulus 1 GPa) in the left femoral condyle. Both types of implants received a titanium coating of 100 nm thickness. The implants protruded in the knee joint space and were directly weight bearing. The first group of eight goats was sacrificed after 6 weeks of loading and the second group of eight goats after 6 months of loading. The 16 femoral condyles with the 32 implants were prepared for microfocus computed tomography (micro-CT) scanning and histological sectioning. Three-dimensional trabecular bone parameters were calculated on the micro-CT images for the zones neck, middle, and apex of the implant. The percent of bone contact with the implant was measured on longitudinal histological sections. An axisymmetric finite element (FE) model was created to compare peri-implant bone strains and relative motion between a titanium and a HDPE implant for the experimental loading condition, and to assess the influence of different bone-implant interface (contact) conditions. From the statistical analysis of the 3D bone parameters, the difference between the titanium and HDPE implants was not significantly different (p > 0.05) between the zones (neck, middle, and apex) for both groups of goats. The implants could be considered in their entirety. After 6 weeks of loading, the PE implant presented lower connectivity and smaller marrow spaces in the circular region of 0-500 microm. In the region 500-1500 microm more bone volume was present for the PE implant. After 6 months, the PE implants showed more bone volume and thicker trabeculae than the titanium implants for the entire length of the implant. This effect was already present in the smallest region of interest, 0-500 microm. After 6 months more fibrous encapsulation was found around titanium implants. FE results demonstrated a substantial influence of the interface conditions on peri-implant strains and relative motion. For interface conditions that were representative for the early postoperative situation (involving press-fit and friction), differences in peri-implant bone strain distributions between titanium and HDPE could be related to the experimentally observed differences in amounts of bone and fibrous encapsulation. In contrast, differences in relative motion did not seem to play a role. Both the experimental and computational results suggest that implant stiffness can affect the peri-implant tissue response, which may be related to differences in peri-implant strains.

The remodeling of cardiovascular bioprostheses under influence of stem cell homing signal pathways

Optimizing current heart valve replacement strategies by creating living prostheses is a necessity to alleviate complications with current bioprosthetic devices such as calcification and degeneration. Regenerative medicine, mostly in vitro tissue engineering, is the forerunner of this optimization search, yet here we show the functionality of an in vivo alternative making use of 2 homing axes for stem cells. In rats we studied the signaling pathways of stem cells on implanted bioprosthetic tissue (photooxidized bovine pericardium (POP)), by gene and protein expression analysis. We found that SDF-1alpha/CXCR4 and FN/VLA4 homing axes play a role. When we implanted vascular grafts impregnated with SDF-1alpha and/or FN as carotid artery interpositions, primitive cells were attracted from the circulation. Next, bioprosthetic heart valves, constructed from POP impregnated with SDF-1alpha and/or FN, were implanted in pulmonary position. As shown by CD90, CD34 and CD117 immunofluorescent staining they became completely recellularized after 5 months, had a normal function and biomechanical properties and specifically the combination of SDF-1alpha and FN had an optimal valve-cell phenotype.