Mechanisms of corneal epithelial wound healing

Discrete and continuous mathematical models of sharp-fronted collective cell migration and invasion

Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion are routinely employed and known to capture key experimental observations, linear diffusion fails to predict well-defined sharp fronts that are often observed experimentally. This observation has motivated the use of nonlinear degenerate diffusion; however, these nonlinear models and the associated parameters lack a clear biological motivation and interpretation. Here, we take a different approach by developing a stochastic discrete lattice-based model incorporating biologically inspired mechanisms and then deriving the reaction-diffusion continuum limit. Inspired by experimental observations, agents in the simulation deposit extracellular material, which we call a substrate, locally onto the lattice, and the motility of agents is taken to be proportional to the substrate density. Discrete simulations that mimic a two-dimensional circular barrier assay illustrate how the discrete model supports both smooth and sharp-fronted density profiles depending on the rate of substrate deposition. Coarse-graining the discrete model leads to a novel partial differential equation (PDE) model whose solution accurately approximates averaged data from the discrete model. The new discrete model and PDE approximation provide a simple, biologically motivated framework for modelling the spreading, growth and invasion of cell populations with well-defined sharp fronts. Open-source Julia code to replicate all results in this work is available on GitHub.

Modelling the Effect of Matrix Metalloproteinases in Dermal Wound Healing

With over 2 million people in the UK suffering from chronic wounds, understanding the biochemistry and pharmacology that underpins these wounds and wound healing is of high importance. Chronic wounds are characterised by high levels of matrix metalloproteinases (MMPs), which are necessary for the modification of healthy tissue in the healing process. Overexposure of MMPs, however, adversely affects healing of the wound by causing further destruction of the surrounding extracellular matrix. In this work, we propose a mathematical model that focuses on the interaction of MMPs with dermal cells using a system of partial differential equations. Using biologically realistic parameter values, this model gives rise to travelling waves corresponding to a front of healthy cells invading a wound. From the arising travelling wave analysis, we observe that deregulated apoptosis results in the emergence of chronic wounds, characterised by elevated MMP concentrations. We also observe hysteresis effects when both the apoptotic rate and MMP production rate are varied, providing further insight into the management (and potential reversal) of chronic wounds.

Mathematical Modeling Can Advance Wound Healing Research

Significance: For over 30 years, there has been sustained interest in the development of mathematical models for investigating the complex mechanisms underlying each stage of the wound healing process. Despite the immense associated challenges, such models have helped usher in a paradigm shift in wound healing research. Recent Advances: In this article, we review contributions in the field that span epidermal, dermal, and corneal wound healing, and treatments of nonhealing wounds. The recent influence of mathematical models on biological experiments is detailed, with a focus on wound healing assays and fibroblast-populated collagen lattices. Critical Issues: We provide an overview of the field of mathematical modeling of wound healing, highlighting key advances made in recent decades, and discuss how such models have contributed to the development of improved treatment strategies and/or an enhanced understanding of the tightly regulated steps that comprise the healing process. Future Directions: We detail some of the open problems in the field that could be addressed through a combination of theoretical and/or experimental approaches. To move the field forward, we need to have a common language between scientists to facilitate cross-collaboration, which we hope this review can support by highlighting progress to date.

Continuum descriptions of spatial spreading for heterogeneous cell populations: Theory and experiment

Variability in cell populations is frequently observed in both in vitro and in vivo settings. Intrinsic differences within populations of cells, such as differences in cell sizes or differences in rates of cell motility, can be present even within a population of cells from the same cell line. We refer to this variability as cell heterogeneity. Mathematical models of cell migration, for example, in the context of tumour growth and metastatic invasion, often account for both undirected (random) migration and directed migration that is mediated by cell-to-cell contacts and cell-to-cell adhesion. A key feature of standard models is that they often assume that the population is composed of identical cells with constant properties. This leads to relatively simple single-species homogeneous models that neglect the role of heterogeneity. In this work, we use a continuum modelling approach to explore the role of heterogeneity in spatial spreading of cell populations. We employ a three-species heterogeneous model of cell motility that explicitly incorporates different types of experimentally-motivated heterogeneity in cell sizes: (i) monotonically decreasing; (ii) uniform; (iii) non-monotonic; and (iv) monotonically increasing distributions of cell size. Comparing the density profiles generated by the three-species heterogeneous model with density profiles predicted by a more standard single-species homogeneous model reveals that when we are dealing with monotonically decreasing and uniform distributions a simple and computationally efficient single-species homogeneous model can be remarkably accurate in describing the evolution of a heterogeneous cell population. In contrast, we find that the simpler single-species homogeneous model performs relatively poorly when applied to non-monotonic and monotonically increasing distributions of cell sizes. Additional results for heterogeneity in parameters describing both undirected and directed cell migration are also considered, and we find that similar results apply.

Using a continuum model to decipher the mechanics of embryonic tissue spreading from time-lapse image sequences: An approximate Bayesian computation approach

Advanced imaging techniques generate large datasets capable of describing the structure and kinematics of tissue spreading in embryonic development, wound healing, and the progression of many diseases. These datasets can be integrated with mathematical models to infer biomechanical properties of the system, typically identifying an optimal set of parameters for an individual experiment. However, these methods offer little information on the robustness of the fit and are generally ill-suited for statistical tests of multiple experiments. To overcome this limitation and enable efficient use of large datasets in a rigorous experimental design, we use the approximate Bayesian computation rejection algorithm to construct probability density distributions that estimate model parameters for a defined theoretical model and set of experimental data. Here, we demonstrate this method with a 2D Eulerian continuum mechanical model of spreading embryonic tissue. The model is tightly integrated with quantitative image analysis of different sized embryonic tissue explants spreading on extracellular matrix (ECM) and is regulated by a small set of parameters including forces on the free edge, tissue stiffness, strength of cell-ECM adhesions, and active cell shape changes. We find statistically significant trends in key parameters that vary with initial size of the explant, e.g., for larger explants cell-ECM adhesion forces are weaker and free edge forces are stronger. Furthermore, we demonstrate that estimated parameters for one explant can be used to predict the behavior of other similarly sized explants. These predictive methods can be used to guide further experiments to better understand how collective cell migration is regulated during development.

A stochastic model of corneal epithelium maintenance and recovery following perturbation

Various biological studies suggest that the corneal epithelium is maintained by active stem cells located in the limbus, the so-called limbal epithelial stem cell hypothesis. While numerous mathematical models have been developed to describe corneal epithelium wound healing, only a few have explored the process of corneal epithelium homeostasis. In this paper we present a purposefully simple stochastic mathematical model based on a chemical master equation approach, with the aim of clarifying the main factors involved in the maintenance process. Model analysis provides a set of constraints on the numbers of stem cells, division rates, and the number of division cycles required to maintain a healthy corneal epithelium. In addition, our stochastic analysis reveals noise reduction as the epithelium approaches its homeostatic state, indicating robustness to noise. Finally, recovery is analysed in the context of perturbation scenarios.

Extended logistic growth model for heterogeneous populations

Cell proliferation is the most important cellular-level mechanism responsible for regulating cell population dynamics in living tissues. Modern experimental procedures show that the proliferation rates of individual cells can vary significantly within the same cell line. However, in the mathematical biology literature, cell proliferation is typically modelled using a classical logistic equation which neglects variations in the proliferation rate. In this work, we consider a discrete mathematical model of cell migration and cell proliferation, modulated by volume exclusion (crowding) effects, with variable rates of proliferation across the total population. We refer to this variability as heterogeneity. Constructing the continuum limit of the discrete model leads to a generalisation of the classical logistic growth model. Comparing numerical solutions of the model to averaged data from discrete simulations shows that the new model captures the key features of the discrete process. Applying the extended logistic model to simulate a proliferation assay using rates from recent experimental literature shows that neglecting the role of heterogeneity can, at times, lead to misleading results.

Logistic Proliferation of Cells in Scratch Assays is Delayed

Scratch assays are used to study how a population of cells re-colonises a vacant region on a two-dimensional substrate after a cell monolayer is scratched. These experiments are used in many applications including drug design for the treatment of cancer and chronic wounds. To provide insights into the mechanisms that drive scratch assays, solutions of continuum reaction-diffusion models have been calibrated to data from scratch assays. These models typically include a logistic source term to describe carrying capacity-limited proliferation; however, the choice of using a logistic source term is often made without examining whether it is valid. Here we study the proliferation of PC-3 prostate cancer cells in a scratch assay. All experimental results for the scratch assay are compared with equivalent results from a proliferation assay where the cell monolayer is not scratched. Visual inspection of the time evolution of the cell density away from the location of the scratch reveals a series of sigmoid curves that could be naively calibrated to the solution of the logistic growth model. However, careful analysis of the per capita growth rate as a function of density reveals several key differences between the proliferation of cells in scratch and proliferation assays. Our findings suggest that the logistic growth model is valid for the entire duration of the proliferation assay. On the other hand, guided by data, we suggest that there are two phases of proliferation in a scratch assay; at short time, we have a disturbance phase where proliferation is not logistic, and this is followed by a growth phase where proliferation appears to be logistic. These two phases are observed across a large number of experiments performed at different initial cell densities. Overall our study shows that simply calibrating the solution of a continuum model to a scratch assay might produce misleading parameter estimates, and this issue can be resolved by making a distinction between the disturbance and growth phases. Repeating our procedure for other scratch assays will provide insight into the roles of the disturbance and growth phases for different cell lines and scratch assays performed on different substrates.

Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM™ assay data using the Fisher-Kolmogorov model

Background

Standard methods for quantifying IncuCyte ZOOM™ assays involve measurements that quantify how rapidly the initially-vacant area becomes re-colonised with cells as a function of time. Unfortunately, these measurements give no insight into the details of the cellular-level mechanisms acting to close the initially-vacant area. We provide an alternative method enabling us to quantify the role of cell motility and cell proliferation separately. To achieve this we calibrate standard data available from IncuCyte ZOOM™ images to the solution of the Fisher-Kolmogorov model.

Results

The Fisher-Kolmogorov model is a reaction-diffusion equation that has been used to describe collective cell spreading driven by cell migration, characterised by a cell diffusivity, D, and carrying capacity limited proliferation with proliferation rate, λ, and carrying capacity density, K. By analysing temporal changes in cell density in several subregions located well-behind the initial position of the leading edge we estimate λ and K. Given these estimates, we then apply automatic leading edge detection algorithms to the images produced by the IncuCyte ZOOM™ assay and match this data with a numerical solution of the Fisher-Kolmogorov equation to provide an estimate of D. We demonstrate this method by applying it to interpret a suite of IncuCyte ZOOM™ assays using PC-3 prostate cancer cells and obtain estimates of D, λ and K. Comparing estimates of D, λ and K for a control assay with estimates of D, λ and K for assays where epidermal growth factor (EGF) is applied in varying concentrations confirms that EGF enhances the rate of scratch closure and that this stimulation is driven by an increase in D and λ, whereas K is relatively unaffected by EGF.

Conclusions

Our approach for estimating D, λ and K from an IncuCyte ZOOM™ assay provides more detail about cellular-level behaviour than standard methods for analysing these assays. In particular, our approach can be used to quantify the balance of cell migration and cell proliferation and, as we demonstrate, allow us to quantify how the addition of growth factors affects these processes individually.

Tissue-engineered membrane based on chitosan for repair of mechanically damaged corneal epithelium

In this study, hydroxyethyl chitosan (HECTS), a water-soluble derivative of chitosan, was used to create a blend membrane and its function and application as a scaffold in repair of mechanically damaged corneal epethelia were examined. The results showed that HECTS significantly promoted growth of corneal epithelial cells (CEpCs) in vitro and that CEpCs grew well on the HECTS-based blend membrane. Fluorescent imaging showed that CEpCs were interconnected and formed layers on the membrane. After transplanting the CEpCs-seeded membranes onto the damaged corneal epithelium, we found that the epithelium was repaired faster compared with control. The repaired corneal epithelium with the membrane had a more compact structure and a smoother surface than control when observed by histology and scanning electron microscope. These results demonstrate an ability of the tissue-engineered scaffold to speed up the repair of mechanically damaged corneal epithelium.

Corneal epithelial wound healing promoted by verbascoside-based liposomal eyedrops

Different liposomal formulations were prepared to identify those capable of forming eyedrops for corneal diseases. Liposomes with neutral or slightly positive surface charge interact very well with the cornea. Then these formulations were loaded with verbascoside to heal a burn of corneal epithelium induced by alkali. The cornea surface affected involved in wound was monitored as a function of time. Experimental results were modeled by balance equation between the rate of healing, due to the flow of phenylpropanoid, and growth of the wound. The results indicate a latency time of only three hours and furthermore the corneal epithelium heals in 48 hours. Thus, the topical administration of verbascoside appears to reduce the action time of cells, as verified by histochemical and immunofluorescence assays.

3D hybrid wound devices for spatiotemporally controlled release kinetics

This paper presents localized and temporal control of release kinetics over 3-dimensional (3D) hybrid wound devices to improve wound-healing process. Imaging study is performed to extract wound bed geometry in 3D. Non-Uniform Rational B-Splines (NURBS) based surface lofting is applied to generate functionally graded regions. Diffusion-based release kinetics model is developed to predict time-based release of loaded modifiers for functionally graded regions. Multi-chamber single nozzle solid freeform dispensing system is used to fabricate wound devices with controlled dispensing concentration. Spatiotemporal control of biological modifiers thus enables a way to achieve target delivery to improve wound healing.

Aqueous extract of Centella asiatica promotes corneal epithelium wound healing in vitro

ETHNOPHARMACOLOGICAL RELEVANCE

Centella asiatica is a traditional herbal medicine that has been shown to have pharmacological effect on skin wound healing, and could be potential therapeutic agent for corneal epithelial wound healing.

AIM OF THE STUDY

This study was done to evaluate the effects of Centella asiatica on the proliferation and migration of rabbit corneal epithelial (RCE) cells in the in vitro wound healing model.

MATERIALS AND METHODS

RCE cells were cultured with or without supplementation of Centella asiatica aqueous extract. Viability and proliferation of the RCE cells was determined by MTT assay and cell cycle was analyzed by flow cytometry. In vitro re-epithelization was studied by scratch assay and migration rate was evaluated quantitatively by image analyzer. Expression of corneal specific differentiation markers, CK12 and connexin 43, were studied via RT-PCR.

RESULTS

It was found that supplementation of Centella asiatica did not show any significant effect on the RCE cells proliferation at the concentration up to 500ppm, while at the concentration of 1000ppm significantly inhibited RCE cells proliferation (p<0.05). However, at the concentration up to 62.5ppm, RCE cells shows significant enhancement of migration rate compared to the control group (p<0.05). It was also found that the supplementation of Centella asiatica aqueous extract did not alter the expression of differentiation markers and cell cycle.

CONCLUSION

In conclusion, supplementation of Centella asiatica aqueous extract at low concentrations could be useful to promote corneal epithelium wound healing.

Models of collective cell spreading with variable cell aspect ratio: a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multiscale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (PME). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the PME to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

Migration of breast cancer cells: understanding the roles of volume exclusion and cell-to-cell adhesion

We study MCF-7 breast cancer cell movement in a transwell apparatus. Various experimental conditions lead to a variety of monotone and nonmonotone responses which are difficult to interpret. We anticipate that the experimental results could be caused by cell-to-cell adhesion or volume exclusion. Without any modeling, it is impossible to understand the relative roles played by these two mechanisms. A lattice-based exclusion process random-walk model incorporating agent-to-agent adhesion is applied to the experimental system. Our combined experimental and modeling approach shows that a low value of cell-to-cell adhesion strength provides the best explanation of the experimental data suggesting that volume exclusion plays a more important role than cell-to-cell adhesion. This combined experimental and modeling study gives insight into the cell-level details and design of transwell assays.

Simulation of lung alveolar epithelial wound healing in vitro

The mechanisms that enable and regulate alveolar type II (AT II) epithelial cell wound healing in vitro and in vivo remain largely unknown and need further elucidation. We used an in silico AT II cell-mimetic analogue to explore and better understand plausible wound healing mechanisms for two conditions: cyst repair in three-dimensional cultures and monolayer wound healing. Starting with the analogue that validated for key features of AT II cystogenesis in vitro, we devised an additional cell rearrangement action enabling cyst repair. Monolayer repair was enabled by providing 'cells' a control mechanism to switch automatically to a repair mode in the presence of a distress signal. In cyst wound simulations, the revised analogue closed wounds by adhering to essentially the same axioms available for alveolar-like cystogenesis. In silico cell proliferation was not needed. The analogue recovered within a few simulation cycles but required a longer recovery time for larger or multiple wounds. In simulated monolayer wound repair, diffusive factor-mediated 'cell' migration led to repair patterns comparable to those of in vitro cultures exposed to different growth factors. Simulations predicted directional cell locomotion to be critical for successful in vitro wound repair. We anticipate that with further use and refinement, the methods used will develop as a rigorous, extensible means of unravelling mechanisms of lung alveolar repair and regeneration.

Experimental characterization and computational modelling of two-dimensional cell spreading for skeletal regeneration

Limited cell ingrowth is a major problem for tissue engineering and the clinical application of porous biomaterials as bone substitutes. As a first step, migration and proliferation of an interacting cell population can be studied in two-dimensional culture. Mathematical modelling is essential to generalize the results of these experiments and to derive the intrinsic parameters that can be used for predictions. However, a more thorough evaluation of theoretical models is hampered by limited experimental observations. In this study, experiments and image analysis methods were developed to provide a detailed spatial and temporal picture of how cell distributions evolve. These methods were used to quantify the migration and proliferation of skeletal cell types including MG63 and human bone marrow stromal cells (HBMSCs). The high level of detail with which the cell distributions were mapped enabled a precise assessment of the correspondence between experimental results and theoretical model predictions. This analysis revealed that the standard Fisher equation is appropriate for describing the migration behaviour of the HBMSC population, while for the MG63 cells a sharp front model is more appropriate. In combination with experiments, this type of mathematical model will prove useful in predicting cell ingrowth and improving strategies and control of skeletal tissue regeneration.

Collective migration of an epithelial monolayer in response to a model wound

Using an original microfabrication-based technique, we experimentally study situations in which a virgin surface is presented to a confluent epithelium with no damage made to the cells. Although inspired by wound-healing experiments, the situation is markedly different from classical scratch wounding because it focuses on the influence of the free surface and uncouples it from the other possible contributions such as cell damage and/or permeabilization. Dealing with Madin-Darby canine kidney cells on various surfaces, we found that a sudden release of the available surface is sufficient to trigger collective motility. This migration is independent of the proliferation of the cells that mainly takes place on the fraction of the surface initially covered. We find that this motility is characterized by a duality between collective and individual behaviors. On the one hand, the velocity fields within the monolayer are very long range and involve many cells in a coordinated way. On the other hand, we have identified very active "leader cells" that precede a small cohort and destabilize the border by a fingering instability. The sides of the fingers reveal a pluricellular actin "belt" that may be at the origin of a mechanical signaling between the leader and the followers. Experiments performed with autocrine cells constitutively expressing hepatocyte growth factor (HGF) or in the presence of exogenous HGF show a higher average velocity of the border and no leader.

Mathematical modelling of aerosolised skin grafts incorporating keratinocyte clonal subtypes

Severe burns can be very traumatic for the patient, and while burns caused by industrial or domestic accidents are common, there are also increasing numbers of burns associated with terrorism. A novel technique to assist in the healing process is to spray skin cells, keratinocytes, that are cultured from the patient's own tissue, directly onto the burn site. This process involves taking some undamaged skin from the patient, allowing the skin cells to proliferate rapidly in the laboratory over a period of 5-10 days, harvesting and separating the cells and then spraying them onto the burn. This paper deals with keratinocytes that have been cultured in vitro for a short period of time (early passage cultured cells). The spraying process has yet to be optimised with respect to the seeding density required for fastest re-epithelisation and thus there is a need for this process to be modelled. In this paper, we review some of the skin biology and develop a mathematical model of the growth patterns of cell colonies after they have been applied using a aerosolised technique. The model allows us to predict coverage over time and can be used as a decision support tool for clinicians.

Looking inside an invasion wave of cells using continuum models: proliferation is the key

Recently, a suite of cell migration assays were conducted to investigate the migration of neural crest (NC) cells along the gut during the development of the enteric nervous system (ENS). The NC cells colonise the gastro-intestinal tract as a rostro-caudal wave. Local behaviour was shown to be controlled by position relative to the leading edge of the wavefront. The assays involved chick-quail grafting techniques allowing the total invading population to be considered as a two-species system. A two-species continuum model with logistic proliferation and a migration mechanism is developed here to simulate the chick-quail graft experiments and provide a means of looking at the processes occurring within the invasion wave. Five migration mechanisms are considered--linear diffusion, two cases of nonlinear diffusion, chemokinesis and chemotaxis. The model results agree with the experimental observations, regardless of the specific type of migration mechanism. The results show that NC cell invasion is driven by proliferation and cell motility at the leading edge of the wave. Furthermore, logistic proliferation exerts the dominant control on the system. This observation is confirmed by analysing some simplified invasion models. Once the basic experiments were mathematically replicated, the mathematical models were used in turn to make some predictions that were yet to be experimentally tested. This involved conducting a sensitivity analysis of the system by interrupting the proliferation and/or migration ability of the leading edge. Numerical results show that the system is stable against these changes. Of the three experiments suggested, one was carried out and the experimental results were concordant with the theoretical predictions. The outcome of two other suggested experiments are predicted and left for future experimental validation.

Growth factors in the anterior segment: role in tissue maintenance, wound healing and ocular pathology

A number of growth factors and their associated receptors, including epidermal growth factor, transforming growth factor-beta, keratinocyte growth factor, hepatocyte growth factor, fibroblast growth factor and platelet-derived growth factor have been detected in the anterior segment of the eye. On binding to cellular receptors, these factors activate signalling cascades, which regulate functions including mitosis, differentiation, motility and apoptosis. Production of growth factors by corneal cells and their presence in the tear fluid and aqueous humour is essential for maintenance and renewal of normal tissue in the anterior eye and the prevention of undesirable immune or angiogenic reactions. Growth factors also play a vital role in corneal wound healing, mediating the proliferation of epithelial and stromal tissue and affecting the remodelling of the extracellular matrix (ECM). These functions depend on a complex interplay between growth factors of different types, the ECM, and regulatory mechanisms of the affected cells. Imbalances may lead to deficient wound healing and various ocular pathologies, including edema, neovascularization and glaucoma. Growth factors may be targeted in therapeutic ophthalmic applications, through exogenous application or selective inhibition, and may be used to elicit specific cellular responses to ophthalmic materials. A thorough understanding of the mechanism and function of growth factors and their actions in the complex environment of the anterior eye is required for these purposes. Growth factors, their function and mechanisms of action as well as the interplay between different growth factors based on recent in vitro and in vivo studies are presented.

Traveling Wave Model to Interpret a Wound-Healing Cell Migration Assay for Human Peritoneal Mesothelial Cells

The critical determinants of the speed of an invading cell front are not well known. We performed a "wound-healing" experiment that quantifies the migration of human peritoneal mesothelial cells over components of the extracellular matrix. Results were interpreted in terms of Fisher's equation, which includes terms for the modeling of random cell motility (diffusion) and proliferation. The model predicts that, after a short transient, the invading cell front will move as a traveling wave at constant speed. This is consistent with the experimental findings. Using the model, a relationship between the rate of cell proliferation and the diffusion coefficient was obtained. We used the model to deduce the cell diffusion coefficients under control conditions and in the presence of collagen IV and compared these with other published data. The model may be useful in analyzing the invasive capacity of cancer cells as well in predicting the efficacy of growth factors in tissue reconstruction, including the development of monolayer sheets of cells in skin engineering or the repair of injured corneas using grafts of cultured cells.

Theoretical models of wound healing: past successes and future challenges

The complex biology of wound healing is an area in which theoretical modelling has already made a significant impact. In this review article, the authors describe the key features of wound healing biology, divided into four components: epidermal wound healing, remodelling of the dermal extracellular matrix, wound contraction, and angiogenesis. Within each of these categories, previous modelling work is described, and the authors identify what they regard as the main challenges for future theoretical work.

Comparison of corneal epithelial cellular growth on synthetic cornea materials

The application of artificial corneas for severely wounded ocular surfaces has always encountered the problem of biocompatibility with corneal epithelial cells (CECs). For the eye to stay healthy, it must continually have a complete sheet of CECs across the artificial corneal surface. Various surface modifications of different polymeric materials have been examined to determine which have the best cellular growth rates. A mathematical model of corneal cell growth profiles on synthetic materials was formulated based upon a linear mitotic growth rate. Experimental data reported for the CEC growth on modified poly(vinyl alcohol), silicone rubber, polystyrene, and polycarbonate was analyzed using the model to estimate the linear mitotic rate constant (k). The model proved to be useful in comparing data from different investigators. Plasma-induced graft copolymerized poly(hydroxyethyl methacrylate) (pHEMA) on silicone rubber provided the best growth rate from this particular set of data.

Autonomous gel/enzyme oscillator fueled by glucose: Preliminary evidence for oscillations

A novel prototype gel oscillator that functions by dissipating the chemical energy of glucose by an enzyme-mediated reaction is proposed. The product of the reaction modulates the degree of swelling and hence the permeability of a poly(N-isopropylacrylamide-co-methacrylic acid) gel membrane which in turn regulates the flow of substrate to the enzyme. No external energy is required aside from the chemical energy of glucose present externally at constant concentration. A negative chemomechanical feedback loop is established which, coupled with hysteresis in the membrane permeability characteristics, produces pulsing oscillations. In this study, we introduce a simple model which provides guidelines for experimental design, and report preliminary experimental evidence for oscillation. Application of this prototype system to the episodic delivery of drugs and hormones is envisaged. (c) 1999 American Institute of Physics.