Random-walk models of cell dispersal included in mechanobiological simulations of tissue differentiation

Maximum likelihood phylogeographic inference of cell motility and cell division from spatial lineage tracing data

MOTIVATION

Recently developed spatial lineage tracing technologies induce somatic mutations at specific genomic loci in a population of growing cells and then measure these mutations in the sampled cells along with the physical locations of the cells. These technologies enable high-throughput studies of developmental processes over space and time. However, these applications rely on accurate reconstruction of a spatial cell lineage tree describing both past cell divisions and cell locations. Spatial lineage trees are related to phylogeographic models that have been well-studied in the phylogenetics literature. We demonstrate that standard phylogeographic models based on Brownian motion are inadequate to describe the spatial symmetric displacement (SD) of cells during cell division.

RESULTS

We introduce a new model-the SD model for cell motility that includes symmetric displacements of daughter cells from the parental cell followed by independent diffusion of daughter cells. We show that this model more accurately describes the locations of cells in a real spatial lineage tracing of mouse embryonic stem cells. Combining the spatial SD model with an evolutionary model of DNA mutations, we obtain a phylogeographic model for spatial lineage tracing. Using this model, we devise a maximum likelihood framework-MOLLUSC (Maximum Likelihood Estimation Of Lineage and Location Using Single-Cell Spatial Lineage tracing Data)-to co-estimate time-resolved branch lengths, spatial diffusion rate, and mutation rate. On both simulated and real data, we show that MOLLUSC accurately estimates all parameters. In contrast, the Brownian motion model overestimates spatial diffusion rate in all test cases. In addition, the inclusion of spatial information improves accuracy of branch length estimation compared to sequence data alone. On real data, we show that spatial information has more signal than sequence data for branch length estimation, suggesting augmenting lineage tracing technologies with spatial information is useful to overcome the limitations of genome-editing in developmental systems.

AVAILABILITY AND IMPLEMENTATION

The python implementation of MOLLUSC is available at https://github.com/raphael-group/MOLLUSC.

A review on design of scaffold for osteoinduction: Toward the unification of independent design variables

Biophysical stimulus quantifies the osteoinductivity of the scaffold concerning the mechanoregulatory mathematical models of scaffold-assisted cellular differentiation. Consider a set of independent structural variables ($) that comprises bulk porosity levels ([Formula: see text]) and a set of morphological features of the micro-structure ([Formula: see text]) associated with scaffolds, i.e., [Formula: see text]. The literature suggests that biophysical stimulus ([Formula: see text]) is a function of independent structural variables ($). Limited understanding of the functional correlation between biophysical stimulus and structural features results in the lack of the desired osteoinductivity in a scaffold. Consequently, it limits their broad applicability to assist bone tissue regeneration for treating critical-sized bone fractures. The literature indicates the existence of multi-dimensional independent design variable space as a probable reason for the general lack of osteoinductivity in scaffolds. For instance, known morphological features are the size, shape, orientation, continuity, and connectivity of the porous regions in the scaffold. It implies that the number of independent variables ([Formula: see text]) is more than two, i.e., [Formula: see text], which interact and influence the magnitude of [Formula: see text] in a unified manner. The efficiency of standard engineering design procedures to analyze the correlation between dependent variable ([Formula: see text]) and independent variables ($) in 3D mutually orthogonal Cartesian coordinate system diminishes proportionally with the increase in the number of independent variables ([Formula: see text]) (Deb in Optimization for engineering design-algorithms and examples, PHI Learning Private Limited, New Delhi, 2012). Therefore, there is an immediate need to devise a framework that has the potential to quantify the micro-structural's morphological features in a unified manner to increase the prospects of scaffold-assisted bone tissue regeneration.

Prediction of Bone Healing around Dental Implants in Various Boundary Conditions by Deep Learning Network

Tissue differentiation varies based on patients' conditions, such as occlusal force and bone properties. Thus, the design of the implants needs to take these conditions into account to improve osseointegration. However, the efficiency of the design procedure is typically not satisfactory and needs to be significantly improved. Thus, a deep learning network (DLN) is proposed in this study. A data-driven DLN consisting of U-net, ANN, and random forest models was implemented. It serves as a surrogate for finite element analysis and the mechano-regulation algorithm. The datasets include the history of tissue differentiation throughout 35 days with various levels of occlusal force and bone properties. The accuracy of day-by-day tissue differentiation prediction in the testing dataset was 82%, and the AUC value of the five tissue phenotypes (fibrous tissue, cartilage, immature bone, mature bone, and resorption) was above 0.86, showing a high prediction accuracy. The proposed DLN model showed the robustness for surrogating the complex, time-dependent calculations. The results can serve as a design guideline for dental implants.

In silico and in vivo studies of the effect of surface curvature on the osteoconduction of porous scaffolds

Recent evidence shows that the curvature of porous scaffold plays a significant role in guiding tissue regeneration. However, the underlying mechanism remains controversial to date. In this study, we developed an in silico model to simulate the effect of surface curvature on the osteoconduction of scaffold implants, which comprises the primary aspects of bone regeneration. Selective laser melting was used to manufacture a titanium scaffold with channels representative of different strut curvatures for in vivo assessment. The titanium scaffold was implanted in the femur condyles of rabbits to validate the mathematical model. Simulation results suggest that the curvature affected the distribution of growth factors and subsequently induced the migration of osteoblast lineage cells and bone deposition to the locations with higher curvature. The predictions of the mathematical model are in good agreement with the in vivo assessment results, in which newly formed bone first appeared adjacent to the vertices of the major axes in elliptical channels. The mechanism of curvature-guided osteoconduction may provide a guide for the design optimization of scaffold implants to achieve enhanced bone ingrowth.

A Hybrid Model for Predicting Bone Healing around Dental Implants

BACKGROUND

The effect of the short-term bone healing process is typically neglected in numerical models of bone remodeling for dental implants. In this study, a hybrid two-step algorithm was proposed to enable a more accurate prediction for the performance of dental implants.

METHODS

A mechano-regulation algorithm was firstly used to simulate the tissue differentiation around a dental implant during the short-term bone healing. Then, the result was used as the initial state of the bone remodeling model to simulate the long-term healing of the bones. The algorithm was implemented by a 3D finite element model.

RESULTS

The current hybrid model reproduced several features which were discovered in the experiments, such as stress shielding effect, high strength bone connective tissue bands, and marginal bone loss. A reasonable location of bone resorptions and the stability of the dental implant is predicted, compared with those predicted by the conventional bone remodeling model.

CONCLUSIONS

The hybrid model developed here predicted bone healing processes around dental implants more accurately. It can be used to study bone healing before implantation surgery and assist in the customization of dental implants.

The recent advances in the mathematical modelling of human pluripotent stem cells

Human pluripotent stem cells hold great promise for developments in regenerative medicine and drug design. The mathematical modelling of stem cells and their properties is necessary to understand and quantify key behaviours and develop non-invasive prognostic modelling tools to assist in the optimisation of laboratory experiments. Here, the recent advances in the mathematical modelling of hPSCs are discussed, including cell kinematics, cell proliferation and colony formation, and pluripotency and differentiation.

Are the Effects of Independent Biophysical Factors Linearly Additive? A 3D Tumor Migration Model

Interstitial fluid flow plays a critical role in tumor cell invasion, yet this role has not been explored extensively in combination with other microenvironmental factors. Here, we establish a novel computational model of three-dimensional breast cancer cell migration to unveil the effect of interstitial fluid flow in the dependence of various extracellular matrix (ECM) physical properties. Our model integrates several principal factors: fluid dynamics, autologous chemotaxis, collagen fiber network structure, ECM stiffness, and cell-fiber and cell-flow interaction. First, independently with an aligned collagen fiber network and interstitial fluid flow, this model is validated by successfully reproducing the cell migration patterns. In the model, the interstitial fluid flow leads to directional symmetry breaking of chemotactic migration and synergizes with the ECM orientation to regulate cell migration. This synergy is universal in both the mesenchymal and the amoeboid migration modes, despite the fact that the cell-ECM interaction are different. Consequently, we construct a cell displacement function depending on these factors. Our cell migration model enables three-dimensional cancer migration prediction, mechanism exploration, and inhibition treatment design in a complex tumor microenvironment.

Stochastic cellular automata model of neurosphere growth: Roles of proliferative potential, contact inhibition, cell death, and phagocytosis

Neural stem and progenitor cells isolated from the central nervous system form, under specific culture conditions, clonal cell clusters known as neurospheres. The neurosphere assay has proven to be a powerful in vitro system to study the behavior of such cells and the development of their progeny. However, the theory of neurosphere growth has remained poorly understood. To overcome this limitation, we have, in the present paper, developed a cellular automata model, with which we examined the effects of proliferative potential, contact inhibition, cell death, and clearance of dead cells on growth rate, final size, and composition of neurospheres. Simulations based on this model indicated that the proliferative potential of the founder cell and its progenitors has a major influence on neurosphere size. On the other hand, contact inhibition of proliferation limits the final size, and reduces the growth rate, of neurospheres. The effect of this inhibition is particularly dramatic when a stem cell becomes encapsulated by differentiated or other non-proliferating cells, thereby suppressing any further mitotic division - despite the existing proliferative potential of the stem cell. Conversely, clearance of dead cells through phagocytosis is predicted to accelerate growth by reducing contact inhibition. A surprising prediction derived from our model is that cell death, while resulting in a decrease in growth rate and final size of neurospheres, increases the degree of differentiation of neurosphere cells. It is likely that the cellular automata model developed as part of the present investigation is applicable to the study of tissue growth in a wide range of systems.

Cellular automata model for human articular chondrocytes migration, proliferation and cell death: An in vitro validation

Articular cartilage is characterized by low cell density of only one cell type, chondrocytes, and has limited self-healing properties. When articular cartilage is affected by traumatic injuries, a therapeutic strategy such as autologous chondrocyte implantation is usually proposed for its treatment. This approach requires in vitro chondrocyte expansion to yield high cell number for cell transplantation. To improve the efficiency of this procedure, it is necessary to assess cell dynamics such as migration, proliferation and cell death during culture. Computational models such as cellular automata can be used to simulate cell dynamics in order to enhance the result of cell culture procedures. This methodology has been implemented for several cell types; however, an experimental validation is required for each one. For this reason, in this research a cellular automata model, based on random-walk theory, was devised in order to predict articular chondrocyte behavior in monolayer culture during cell expansion. Results demonstrated that the cellular automata model corresponded to cell dynamics and computed-accurate quantitative results. Moreover, it was possible to observe that cell dynamics depend on weighted probabilities derived from experimental data and cell behavior varies according to the cell culture period. Thus, depending on whether cells were just seeded or proliferated exponentially, culture time probabilities differed in percentages in the CA model. Furthermore, in the experimental assessment a decreased chondrocyte proliferation was observed along with increased passage number. This approach is expected to having other uses as in enhancing articular cartilage therapies based on tissue engineering and regenerative medicine.

Brownian-like deviation of neighboring cells in the early embryogenesis of the zebrafish

We investigate cell trajectories during zebrafish early embryogenesis based on 3D+time photonic microscopy imaging data. To remove the collective flow motion and focus on fluctuations, we analyze the deviations of pairs of neighboring cells. These deviations resemble Brownian motion and reveal different behaviors between pairs containing daughter cells generated by cell division and other pairs of neighboring cells. This observation justifies a common practice of using white noise fluctuations in modeling cell movement.

Effect of ultrasound on bone fracture healing: A computational mechanobioregulatory model

Bone healing process is a complicated phenomenon regulated by biochemical and mechanical signals. Experimental studies have shown that ultrasound (US) accelerates bone ossification and has a multiple influence on cell differentiation and angiogenesis. In a recent work of the authors, a bioregulatory model for providing bone-healing predictions was addressed, taking into account for the first time the salutary effect of US on the involved angiogenesis. In the present work, a mechanobioregulatory model of bone solidification under the US presence incorporating also the mechanical environment on the regeneration process, which is known to affect cellular processes, is presented. An iterative procedure is adopted, where the finite element method is employed to compute the mechanical stimuli at the linear elastic phases of the poroelastic callus region and a coupled system of partial differential equations to simulate the enhancement by the US cell angiogenesis process and thus the oxygen concentration in the fractured area. Numerical simulations with and without the presence of US that illustrate the influence of progenitor cells' origin in the healing pattern and the healing rate and simultaneously demonstrate the salutary effect of US on bone repair are presented and discussed.

Discrete particle model for cement infiltration within open-cell structures: Prevention of osteoporotic fracture

This paper proposes a discrete particle model based on the random-walk theory for simulating cement infiltration within open-cell structures to prevent osteoporotic proximal femur fractures. Model parameters consider the cement viscosity (high and low) and the desired direction of injection (vertical and diagonal). In vitro and in silico characterizations of augmented open-cell structures validated the computational model and quantified the improved mechanical properties (Young's modulus) of the augmented specimens. The cement injection pattern was successfully predicted in all the simulated cases. All the augmented specimens exhibited enhanced mechanical properties computationally and experimentally (maximum improvements of 237.95 ± 12.91% and 246.85 ± 35.57%, respectively). The open-cell structures with high porosity fraction showed a considerable increase in mechanical properties. Cement augmentation in low porosity fraction specimens resulted in a lesser increase in mechanical properties. The results suggest that the proposed discrete particle model is adequate for use as a femoroplasty planning framework.

The Use of Finite Element Analyses to Design and Fabricate Three-Dimensional Scaffolds for Skeletal Tissue Engineering

Computational modeling has been increasingly applied to the field of tissue engineering and regenerative medicine. Where in early days computational models were used to better understand the biomechanical requirements of targeted tissues to be regenerated, recently, more and more models are formulated to combine such biomechanical requirements with cell fate predictions to aid in the design of functional three-dimensional scaffolds. In this review, we highlight how computational modeling has been used to understand the mechanisms behind tissue formation and can be used for more rational and biomimetic scaffold-based tissue regeneration strategies. With a particular focus on musculoskeletal tissues, we discuss recent models attempting to predict cell activity in relation to specific mechanical and physical stimuli that can be applied to them through porous three-dimensional scaffolds. In doing so, we review the most common scaffold fabrication methods, with a critical view on those technologies that offer better properties to be more easily combined with computational modeling. Finally, we discuss how modeling, and in particular finite element analysis, can be used to optimize the design of scaffolds for skeletal tissue regeneration.

In silico bone mechanobiology: modeling a multifaceted biological system

Mechanobiology, the study of the influence of mechanical loads on biological processes through signaling to cells, is fundamental to the inherent ability of bone tissue to adapt its structure in response to mechanical stimulation. The immense contribution of computational modeling to the nascent field of bone mechanobiology is indisputable, having aided in the interpretation of experimental findings and identified new avenues of inquiry. Indeed, advances in computational modeling have spurred the development of this field, shedding new light on problems ranging from the mechanical response to loading by individual cells to tissue differentiation during events such as fracture healing. To date, in silico bone mechanobiology has generally taken a reductive approach in attempting to answer discrete biological research questions, with research in the field broadly separated into two streams: (1) mechanoregulation algorithms for predicting mechanobiological changes to bone tissue and (2) models investigating cell mechanobiology. Future models will likely take advantage of advances in computational power and techniques, allowing multiscale and multiphysics modeling to tie the many separate but related biological responses to loading together as part of a larger systems biology approach to shed further light on bone mechanobiology. Finally, although the ever‐increasing complexity of computational mechanobiology models will inevitably move the field toward patient‐specific models in the clinic, the determination of the context in which they can be used safely for clinical purpose will still require an extensive combination of computational and experimental techniques applied to in vitro and in vivo applications. WIREs Syst Biol Med 2016, 8:485–505. doi: 10.1002/wsbm.1356

For further resources related to this article, please visit the WIREs website.

Role of oxygen as a regulator of stem cell fate during the spontaneous repair of osteochondral defects

The complexity of the in vivo environment makes it is difficult to isolate the effects of specific cues on regulating cell fate during regenerative events such as osteochondral defect repair. The objective of this study was to develop a computational model to explore how joint specific environmental factors regulate mesenchymal stem cell (MSC) fate during osteochondral defect repair. To this end, the spontaneous repair process within an osteochondral defect was simulated using a tissue differentiation algorithm which assumed that MSC fate was regulated by local oxygen levels and substrate stiffness. The developed model was able to predict the main stages of tissue formation observed by a number of in vivo studies. Following this, a parametric study was conducted to better understand why interventions that modulate angiogenesis dramatically impact the outcome of osteochondral defect healing. In the simulations where angiogenesis was reduced, by week 12, the subchondral plate was predicted to remain below the native tidemark, although the chondral region was composed entirely of cartilage and fibrous tissue. In the simulations where angiogenesis was increased, more robust cell proliferation and cartilage formation were observed during the first 4 weeks, however, by week 12 the subchondral plate had advanced above the native tidemark although any remaining tissue was either hypertrophic cartilage or fibrous tissue. These results suggest that osteochondral defect repair could be enhanced by interventions where angiogenesis is promoted but confined to within the subchondral region of the defect. © 2015 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1026-1036, 2016.

Modeling cell adhesion and proliferation: a cellular-automata based approach

BACKGROUND

Cell adhesion is a process that involves the interaction between the cell membrane and another surface, either a cell or a substrate. Unlike experimental tests, computer models can simulate processes and study the result of experiments in a shorter time and lower costs. One of the tools used to simulate biological processes is the cellular automata, which is a dynamic system that is discrete both in space and time.

METHOD

This work describes a computer model based on cellular automata for the adhesion process and cell proliferation to predict the behavior of a cell population in suspension and adhered to a substrate. The values of the simulated system were obtained through experimental tests on fibroblast monolayer cultures.

RESULTS

The results allow us to estimate the cells settling time in culture as well as the adhesion and proliferation time. The change in the cells morphology as the adhesion over the contact surface progress was also observed. The formation of the initial link between cell and the substrate of the adhesion was observed after 100 min where the cell on the substrate retains its spherical morphology during the simulation. The cellular automata model developed is, however, a simplified representation of the steps in the adhesion process and the subsequent proliferation.

CONCLUSION

A combined framework of experimental and computational simulation based on cellular automata was proposed to represent the fibroblast adhesion on substrates and changes in a macro-scale observed in the cell during the adhesion process. The approach showed to be simple and efficient.

Design, materials, and mechanobiology of biodegradable scaffolds for bone tissue engineering

A review about design, manufacture, and mechanobiology of biodegradable scaffolds for bone tissue engineering is given. First, fundamental aspects about bone tissue engineering and considerations related to scaffold design are established. Second, issues related to scaffold biomaterials and manufacturing processes are discussed. Finally, mechanobiology of bone tissue and computational models developed for simulating how bone healing occurs inside a scaffold are described.

Diffusion model to describe osteogenesis within a porous titanium scaffold

In this study, we develop a two-dimensional finite element model, which is derived from an animal experiment and allows simulating osteogenesis within a porous titanium scaffold implanted in ewe's hemi-mandible during 12 weeks. The cell activity is described through diffusion equations and regulated by the stress state of the structure. We compare our model to (i) histological observations and (ii) experimental data obtained from a mechanical test done on sacrificed animal. We show that our mechano-biological approach provides consistent numerical results and constitutes a useful tool to predict osteogenesis pattern.

An agent-based model approach to multi-phase life-cycle for contact inhibited, anchorage dependent cells

Cellular agent-based models are a technique that can be easily adapted to describe nuances of a particular cell type. Within we have concentrated on the cellular particularities of the human Endothelial Cell, explicitly the effects both of anchorage dependency and of heightened scaffold binding on the total confluence time of a system. By expansion of a discrete, homogeneous, asynchronous cellular model to account for several states per cell (phases within a cell's life); we accommodate and track dependencies of confluence time and population dynamics on these factors. Increasing the total motility time, analogous to weakening the binding between lattice and cell, affects the system in unique ways from increasing the average cellular velocity; each degree of freedom allows for control over the time length the system achieves logistic growth and confluence. These additional factors may allow for greater control over behaviors of the system. Examinations of system's dependence on both seed state velocity and binding are also enclosed.

Computational techniques for the assessment of fracture repair

The combination of high-resolution three-dimensional medical imaging, increased computing power, and modern computational methods provide unprecedented capabilities for assessing the repair and healing of fractured bone. Fracture healing is a natural process that restores the mechanical integrity of bone and is greatly influenced by the prevailing mechanical environment. Mechanobiological theories have been proposed to provide greater insight into the relationships between mechanics (stress and strain) and biology. Computational approaches for modelling these relationships have evolved from simple tools to analyze fracture healing at a single point in time to current models that capture complex biological events such as angiogenesis, stochasticity in cellular activities, and cell-phenotype specific activities. The predictive capacity of these models has been established using corroborating physical experiments. For clinical application, mechanobiological models accounting for patient-to-patient variability hold the potential to predict fracture healing and thereby help clinicians to customize treatment. Advanced imaging tools permit patient-specific geometries to be used in such models. Refining the models to study the strain fields within a fracture gap and adapting the models for case-specific simulation may provide more accurate examination of the relationship between strain and fracture healing in actual patients. Medical imaging systems have significantly advanced the capability for less invasive visualization of injured musculoskeletal tissues, but all too often the consideration of these rich datasets has stopped at the level of subjective observation. Computational image analysis methods have not yet been applied to study fracture healing, but two comparable challenges which have been addressed in this general area are the evaluation of fracture severity and of fracture-associated soft tissue injury. CT-based methodologies developed to assess and quantify these factors are described and results presented to show the potential of these analysis methods.

Mechanical regulation of bone regeneration: theories, models, and experiments

How mechanical forces influence the regeneration of bone remains an open question. Their effect has been demonstrated experimentally, which has allowed mathematical theories of mechanically driven tissue differentiation to be developed. Many simulations driven by these theories have been presented, however, validation of these models has remained difficult due to the number of independent parameters considered. An overview of these theories and models is presented along with a review of experimental studies and the factors they consider. Finally limitations of current experimental data and how this influences modeling are discussed and potential solutions are proposed.

Computational simulation of the early stage of bone healing under different configurations of locking compression plates

Flexible fixation or the so-called 'biological fixation' has been shown to encourage the formation of fracture callus, leading to better healing outcomes. However, the nature of the relationship between the degree of mechanical stability provided by a flexible fixation and the optimal healing outcomes has not been fully understood. In this study, we have developed a validated quantitative model to predict how cells in fracture callus might respond to change in their mechanical microenvironment due to different configurations of locking compression plate (LCP) in clinical practice, particularly in the early stage of healing. The model predicts that increasing flexibility of the LCP by changing the bone-plate distance (BPD) or the plate working length (WL) could enhance interfragmentary strain in the presence of a relatively large gap size (> 3 mm). Furthermore, conventional LCP normally results in asymmetric tissue development during early stage of callus formation, and the increase of BPD or WL is insufficient to alleviate this problem.

Role of mathematical modeling in bone fracture healing

Bone fracture healing is a complex physiological process commonly described by a four-phase model consisting of an inflammatory phase, two repair phases with soft callus formation followed by hard callus formation, and a remodeling phase, or more recently by an anabolic/catabolic model. Data from humans and animal models have demonstrated crucial environmental conditions for optimal fracture healing, including the mechanical environment, blood supply and availability of mesenchymal stem cells. Fracture healing spans multiple length and time scales, making it difficult to know precisely which factors and/or phases to manipulate in order to obtain optimal fracture-repair outcomes. Deformations resulting from physiological loading or fracture fixation at the organ scale are sensed at the cellular scale by cells inside the fracture callus. These deformations together with autocrine and paracrine signals determine cellular differentiation, proliferation and migration. The local repair activities lead to new bone formation and stabilization of the fracture. Although experimental data are available at different spatial and temporal scales, it is not clear how these data can be linked to provide a holistic view of fracture healing. Mathematical modeling is a powerful tool to quantify conceptual models and to establish the missing links between experimental data obtained at different scales. The objective of this review is to introduce mathematical modeling to readers who are not familiar with this methodology and to demonstrate that once validated, such models can be used for hypothesis testing and to assist in clinical treatment as will be shown for the example of atrophic nonunions.

A mathematical model for cell differentiation, as an evolutionary and regulated process

We introduce an approach which allows one to introduce the concept of cell plasticity into models for tissue regeneration. In contrast to most of the recent models for tissue regeneration, cell differentiation is considered a gradual process, which evolves in time and which is regulated by an arbitrary number of parameters. In the current approach, cell differentiation is modelled by means of a differentiation state variable. Cells are assumed to differentiate into an arbitrary number of cell types. The differentiation path is considered as reversible, unless differentiation has fully completed. Cell differentiation is incorporated into the partial differential equations (PDEs), which model the tissue regeneration process, by means of an advection term in the differentiation state space. This allows one to consider the differentiation path of cells, which is not possible if a reaction-like term is used for differentiation. The boundary conditions, which should be specified for the general PDEs, are derived from the flux of the fully non-differentiated cells and from the irreversibility of the fully completed differentiation process. An application of the proposed model for peri-implant osseointegration is considered. Numerical results are compared with experimental data. Potential lines of further development of the present approach are proposed.

Cell-biomaterial mechanical interaction in the framework of tissue engineering: insights, computational modeling and perspectives

Tissue engineering is an emerging field of research which combines the use of cell-seeded biomaterials both in vitro and/or in vivo with the aim of promoting new tissue formation or regeneration. In this context, how cells colonize and interact with the biomaterial is critical in order to get a functional tissue engineering product. Cell-biomaterial interaction is referred to here as the phenomenon involved in adherent cells attachment to the biomaterial surface, and their related cell functions such as growth, differentiation, migration or apoptosis. This process is inherently complex in nature involving many physico-chemical events which take place at different scales ranging from molecular to cell body (organelle) levels. Moreover, it has been demonstrated that the mechanical environment at the cell-biomaterial location may play an important role in the subsequent cell function, which remains to be elucidated. In this paper, the state-of-the-art research in the physics and mechanics of cell-biomaterial interaction is reviewed with an emphasis on focal adhesions. The paper is focused on the different models developed at different scales available to simulate certain features of cell-biomaterial interaction. A proper understanding of cell-biomaterial interaction, as well as the development of predictive models in this sense, may add some light in tissue engineering and regenerative medicine fields.

Simulation of fracture healing in the tibia: mechanoregulation of cell activity using a lattice modeling approach

In this study, a three-dimensional (3D) computational simulation of bone regeneration was performed in a human tibia under realistic muscle loading. The simulation was achieved using a discrete lattice modeling approach combined with a mechanoregulation algorithm to describe the cellular processes involved in the healing process-namely proliferation, migration, apoptosis, and differentiation of cells. The main phases of fracture healing were predicted by the simulation, including the bone resorption phase, and there was a qualitative agreement between the temporal changes in interfragmentary strain and bending stiffness by comparison to experimental data and clinical results. Bone healing was simulated beyond the reparative phase by modeling the transition of woven bone into lamellar bone. Because the simulation has been shown to work with realistic anatomical 3D geometry and muscle loading, it demonstrates the potential of simulation tools for patient-specific pre-operative treatment planning.

In Silico Prediction of the Mechanobiological Response of Arterial Tissue: Application to Angioplasty and Stenting

One way to restore physiological blood flow to occluded arteries involves the deformation of plaque using an intravascular balloon and preventing elastic recoil using a stent. Angioplasty and stent implantation cause unphysiological loading of the arterial tissue, which may lead to tissue in-growth and reblockage; termed “restenosis.” In this paper, a computational methodology for predicting the time-course of restenosis is presented. Stress-induced damage, computed using a remaining life approach, stimulates inflammation (production of matrix degrading factors and growth stimuli). This, in turn, induces a change in smooth muscle cell phenotype from contractile (as exists in the quiescent tissue) to synthetic (as exists in the growing tissue). In this paper, smooth muscle cell activity (migration, proliferation, and differentiation) is simulated in a lattice using a stochastic approach to model individual cell activity. The inflammation equations are examined under simplified loading cases. The mechanobiological parameters of the model were estimated by calibrating the model response to the results of a balloon angioplasty study in humans. The simulation method was then used to simulate restenosis in a two dimensional model of a stented artery. Cell activity predictions were similar to those observed during neointimal hyperplasia, culminating in the growth of restenosis. Similar to experiment, the amount of neointima produced increased with the degree of expansion of the stent, and this relationship was found to be highly dependant on the prescribed inflammatory response. It was found that the duration of inflammation affected the amount of restenosis produced, and that this effect was most pronounced with large stent expansions. In conclusion, the paper shows that the arterial tissue response to mechanical stimulation can be predicted using a stochastic cell modeling approach, and that the simulation captures features of restenosis development observed with real stents. The modeling approach is proposed for application in three dimensional models of cardiovascular stenting procedures.

Self-organization of developing embryo using scale-invariant approach

BACKGROUND

Self-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos.

METHODS

In this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing C. elegans during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method.

RESULTS AND CONCLUSION

The fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2.

Variability observed in mechano-regulated in vivo tissue differentiation can be explained by variation in cell mechano-sensitivity

Computational simulations of tissue differentiation have been able to capture the main aspects of tissue formation/regeneration observed in animal experiments-except for the considerable degree of variability reported. Understanding and modelling the source of this variability is crucial if computational tools are to be developed for clinical applications. The objective of this study was to test the hypothesis that differences in cell mechano-sensitivity between individuals can explain the variability of tissue differentiation patterns observed experimentally. Simulations of an experiment of tissue differentiation in a mechanically loaded bone chamber were performed. Finite element analysis was used to determine the biophysical environment, and a lattice-modelling approach was used to simulate cell activity. Differences in cell mechano-sensitivity among individuals were modelled as differences in cell activity rates, with the activation of cell activities regulated by the mechanical environment. Predictions of the tissue distribution in the chambers produced the two different classes of results found experimentally: (i) chambers with a layer of bone across the chamber covered by a layer of cartilage on top and (ii) chambers with almost no bone, mainly fibrous tissue and small islands of cartilage. This indicates that the differing cellular response to the mechanical environment (i.e., subject-specific mechano-sensitivity) could be a reason for the different outcomes found when implants (or tissue engineered constructs) are used in a population.

A mechano-regulation model of fracture repair in vertebral bodies

In this study a multi-scale mechano-regulation model was developed in order to investigate the mechanobiology of trabecular fracture healing in vertebral bodies. A macro-scale finite element model of the spinal segment L3-L4-L5, including a mild wedge fracture in the body of the L4 vertebra, was used to determine the boundary conditions acting on a micro-scale finite element model simulating a portion of fractured trabecular bone. The micro-scale model, in turn, was utilized to predict the local patterns of tissue differentiation within the fracture gap and then how the equivalent mechanical properties of the macro-scale model change with time. The patterns of tissue differentiation predicted by the model appeared consistent with those observed in vivo. Bone formation occurred primarily through endochondral ossification. New woven bone was predicted to occupy the majority of the space within the fracture site approximately 7-8 weeks after the fracture event. Remodeling of cancellous bone architecture was then predicted, with complete new trabeculae forming due to bridging of the microcallus between the remnant trabeculae.

Finite element method (FEM), mechanobiology and biomimetic scaffolds in bone tissue engineering

Techniques of bone reconstructive surgery are largely based on conventional, non-cell-based therapies that rely on the use of durable materials from outside the patient's body. In contrast to conventional materials, bone tissue engineering is an interdisciplinary field that applies the principles of engineering and life sciences towards the development of biological substitutes that restore, maintain, or improve bone tissue function. Bone tissue engineering has led to great expectations for clinical surgery or various diseases that cannot be solved with traditional devices. For example, critical-sized defects in bone, whether induced by primary tumor resection, trauma, or selective surgery have in many cases presented insurmountable challenges to the current gold standard treatment for bone repair. The primary purpose of bone tissue engineering is to apply engineering principles to incite and promote the natural healing process of bone which does not occur in critical-sized defects. The total market for bone tissue regeneration and repair was valued at $1.1 billion in 2007 and is projected to increase to nearly $1.6 billion by 2014.Usually, temporary biomimetic scaffolds are utilized for accommodating cell growth and bone tissue genesis. The scaffold has to promote biological processes such as the production of extra-cellular matrix and vascularisation, furthermore the scaffold has to withstand the mechanical loads acting on it and to transfer them to the natural tissues located in the vicinity. The design of a scaffold for the guided regeneration of a bony tissue requires a multidisciplinary approach. Finite element method and mechanobiology can be used in an integrated approach to find the optimal parameters governing bone scaffold performance.In this paper, a review of the studies that through a combined use of finite element method and mechano-regulation algorithms described the possible patterns of tissue differentiation in biomimetic scaffolds for bone tissue engineering is given. Firstly, the generalities of the finite element method of structural analysis are outlined; second, the issues related to the generation of a finite element model of a given anatomical site or of a bone scaffold are discussed; thirdly, the principles on which mechanobiology is based, the principal theories as well as the main applications of mechano-regulation models in bone tissue engineering are described; finally, the limitations of the mechanobiological models and the future perspectives are indicated.