On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.

Understanding the ideal wound healing mechanistic behavior using in silico modelling perspectives: A review

Complexity of the entire body precludes an accurate assessment of the specific contributions of tissues or cells during the healing process, which might be expensive and time consuming. Because of this, controlling the wound's size, depth, and dimensions may be challenging, and there is not yet an efficient and reliable chronic wound model representation. Furthermore, given the inherent challenges associated with conducting non-invasive in vivo investigations, it becomes peremptory to explore alternative methodologies for studying wound healing. In this context, biologically-realistic mathematical and computational models emerge as a valuable framework that can effectively address this need. Therefore, it might improve our approach to understanding the process at its core. This article will examines all facets of wound healing, including the kinds, pathways, and most current developments in wound treatment worldwide, particularly in silico modelling utilizing both mathematical and structure-based modelling techniques. It may be helpful to identify the crucial traits through the feedback loop of computer models and experimental investigations in order to build innovative therapies to cure wounds. Hence the effectiveness of personalised medicine and more targeted therapy in the healing of wounds may be enhanced by this interdisciplinary expertise.

Models for Implant-Induced Capsular Contracture Post Breast Cancer Surgery

Capsular contracture is a painful deformation of scar-tissue that may form around an implant in post-breast cancer reconstruction or cosmetic surgery. Inflammation due to surgical trauma or contamination in the tissue around the implant could account for recruitment of immune cells, and transdifferentiation of resident fibroblasts into cells that deposit abnormally thick collagen. Here we examine this hypothesis using a mathematical model for interacting macrophages, fibroblasts, myofibroblasts, and collagen. Our model demonstrates that cellular response can, together with inflammatory cell recruitment, account for prognoses.

Analysis of Factors Affecting Good Neovascularization After Indirect Bypass Surgery: A Two-center Retrospective Study

OBJECTIVE

The purpose of this study was to analyze factors affecting good neovascularization after indirect bypass surgery.

METHODS

From August 2000 to July 2020, postoperative image results and medical records of 132 patients (159 hemispheres) who underwent EDAS of indirect bypass surgery at two institutions were reviewed retrospectively. Based on DSA results, angiogenesis after indirect bypass was divided into "good" or "poor" according to the Matsushima criteria. STA flap length affecting GPN were analyzed in the entire group (n = 159) and a MMD group (n = 134).

RESULTS

In the entire group, GPN after EDAS was observed in 94 (59.1%) hemispheres. Age, MMD, hypertension, and bone flap size were identified as significant factors in univariate analysis. Also, in the MMD group, 86 (64.2%) hemispheres showed GPN. Hypertension and bone flap size were significant factors in both univariate and multivariate analyses. Cutoff values of bone flap size and GPN were 47.91 cm2 in the entire group and the MMD group.

CONCLUSIONS

In all patients who received EDAS, good postoperative neovascularization was significant in those with a young age, MMD, without hypertension, and large bone flap size. No hypertension and large bone flap size were meaningful factors in the MMD group. AUROC showed that an appropriate bone flap size was 47.91 cm2. However, a further controlled prospective study is needed.

Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives

Keloids are fibroproliferative disorders described by excessive growth of fibrotic tissue, which also invades adjacent areas (beyond the original wound borders). Since these disorders are specific to humans (no other animal species naturally develop keloid-like tissue), experimental in vivo/in vitro research has not led to significant advances in this field. One possible approach could be to combine in vitro human models with calibrated in silico mathematical approaches (i.e., models and simulations) to generate new testable biological hypotheses related to biological mechanisms and improved treatments. Because these combined approaches do not really exist for keloid disorders, in this brief review we start by summarising the biology of these disorders, then present various types of mathematical and computational approaches used for related disorders (i.e., wound healing and solid tumours), followed by a discussion of the very few mathematical and computational models published so far to study various inflammatory and mechanical aspects of keloids. We conclude this review by discussing some open problems and mathematical opportunities offered in the context of keloid disorders by such combined in vitro/in silico approaches, and the need for multi-disciplinary research to enable clinical progress.

Computational mechanobiology model evaluating healing of postoperative cavities following breast-conserving surgery

Breast cancer is the most commonly diagnosed cancer type worldwide. Given high survivorship, increased focus has been placed on long-term treatment outcomes and patient quality of life. While breast-conserving surgery (BCS) is the preferred treatment strategy for early-stage breast cancer, anticipated healing and breast deformation (cosmetic) outcomes weigh heavily on surgeon and patient selection between BCS and more aggressive mastectomy procedures. Unfortunately, surgical outcomes following BCS are difficult to predict, owing to the complexity of the tissue repair process and significant patient-to-patient variability. To overcome this challenge, we developed a predictive computational mechanobiological model that simulates breast healing and deformation following BCS. The coupled biochemical-biomechanical model incorporates multi-scale cell and tissue mechanics, including collagen deposition and remodeling, collagen-dependent cell migration and contractility, and tissue plastic deformation. Available human clinical data evaluating cavity contraction and histopathological data from an experimental porcine lumpectomy study were used for model calibration. The computational model was successfully fit to data by optimizing biochemical and mechanobiological parameters through Gaussian process surrogates. The calibrated model was then applied to define key mechanobiological parameters and relationships influencing healing and breast deformation outcomes. Variability in patient characteristics including cavity-to-breast volume percentage and breast composition were further evaluated to determine effects on cavity contraction and breast cosmetic outcomes, with simulation outcomes aligning well with previously reported human studies. The proposed model has the potential to assist surgeons and their patients in developing and discussing individualized treatment plans that lead to more satisfying post-surgical outcomes and improved quality of life.

Mathematical investigation of normal and abnormal wound healing dynamics: local and non-local models

The movement of cells during (normal and abnormal) wound healing is the result of biomechanical interactions that combine cell responses with growth factors as well as cell-cell and cell-matrix interactions (adhesion and remodelling). It is known that cells can communicate and interact locally and non-locally with other cells inside the tissues through mechanical forces that act locally and at a distance, as well as through long non-conventional cell protrusions. In this study, we consider a non-local partial differential equation model for the interactions between fibroblasts, macrophages and the extracellular matrix (ECM) via a growth factor (TGF-$ \beta $) in the context of wound healing. For the non-local interactions, we consider two types of kernels (i.e., a Gaussian kernel and a cone-shaped kernel), two types of cell-ECM adhesion functions (i.e., adhesion only to higher-density ECM vs. adhesion to higher-/lower-density ECM) and two types of cell proliferation terms (i.e., with and without decay due to overcrowding). We investigate numerically the dynamics of this non-local model, as well as the dynamics of the localised versions of this model (i.e., those obtained when the cell perception radius decreases to 0). The results suggest the following: (ⅰ) local models explain normal wound healing and non-local models could also explain abnormal wound healing (although the results are parameter-dependent); (ⅱ) the models can explain two types of wound healing, i.e., by primary intention, when the wound margins come together from the side, and by secondary intention when the wound heals from the bottom up.

Simulation of Angiogenesis in Three Dimensions: Development of the Retinal Circulation

A theoretical model is used to describe the three-dimensional development of the retinal circulation in the human eye, which occurs after the initial spread of vasculature across the inner surface of the retina. In the model, random sprouting angiogenesis is driven by a growth factor that is produced in tissue at a rate dependent on oxygen level and diffuses to existing vessels. Vessel sprouts connect to form pathways for blood flow and undergo remodeling and pruning. These processes are controlled by known or hypothesized vascular responses to hemodynamic and biochemical stimuli, including conducted responses along vessel walls. The model shows regression of arterio-venous connections on the surface of the retina, allowing perfusion of the underlying tissue. A striking feature of the retinal circulation is the formation of two vascular plexuses located at the inner and outer surfaces of the inner nuclear layer within the retina. The model is used to test hypotheses regarding the formation of these structures. A mechanism based on local production and diffusion of growth factor is shown to be ineffective. However, sprout guidance by localized structures on the boundaries of the inner nuclear layer can account for plexus formation. The resulting networks have vascular density, perfusion and oxygen transport characteristics consistent with observed properties. The model shows how stochastic generation of vascular sprouts combined with a set of biologically based response mechanisms can lead to the generation of a specialized three-dimensional vascular structure with a high degree of organization.

Computational models for generating microvascular structures: Investigations beyond medical imaging resolution

Angiogenesis, arteriogenesis, and pruning are revascularization processes essential to our natural vascular development and adaptation, as well as central players in the onset and development of pathologies such as tumoral growth and stroke recovery. Computational modeling allows for repeatable experimentation and exploration of these complex biological processes. In this review, we provide an introduction to the biological understanding of the vascular adaptation processes of sprouting angiogenesis, intussusceptive angiogenesis, anastomosis, pruning, and arteriogenesis, discussing some of the more significant contributions made to the computational modeling of these processes. Each computational model represents a theoretical framework for how biology functions, and with rises in computing power and study of the problem these frameworks become more accurate and complete. We highlight physiological, pathological, and technological applications that can be benefit from the advances performed by these models, and we also identify which elements of the biology are underexplored in the current state-of-the-art computational models. This article is categorized under: Cancer > Computational Models Cardiovascular Diseases > Computational Models.

How quickly does a wound heal? Bayesian calibration of a mathematical model of venous leg ulcer healing

Chronic wounds, such as venous leg ulcers, are difficult to treat and can reduce the quality of life for patients. Clinical trials have been conducted to identify the most effective venous leg ulcer treatments and the clinical factors that may indicate whether a wound will successfully heal. More recently, mathematical modelling has been used to gain insight into biological factors that may affect treatment success but are difficult to measure clinically, such as the rate of oxygen flow into wounded tissue. In this work, we calibrate an existing mathematical model using a Bayesian approach with clinical data for individual patients to explore which clinical factors may impact the rate of wound healing for individuals. Although the model describes group-level behaviour well, it is not able to capture individual-level responses in all cases. From the individual-level analysis, we propose distributions for coefficients of clinical factors in a linear regression model, but ultimately find that it is difficult to draw conclusions about which factors lead to faster wound healing based on the existing model and data. This work highlights the challenges of using Bayesian methods to calibrate partial differential equation models to individual patient clinical data. However, the methods used in this work may be modified and extended to calibrate spatiotemporal mathematical models to multiple data sets, such as clinical trials with several patients, to extract additional information from the model and answer outstanding biological questions.

Impact of Wound Dressing on Mechanotransduction within Tissues of Chronic Wounds

Chronic wounds are significant public health problems impacting the health-related quality of individuals' lives (due to disability, decreased productivity, and loss of independence) and an immense economic burden to healthcare systems around the world. In this study, our main objective is to investigate how mechanotransduction can impact the healing process in chronic wounds. We have developed new three-dimensional models of wound tissue to study the distribution of forces within these tissues exerted by wound dressings with different characteristics. The roles of mechanical forces on wound healing have gained significant clinical attention; the application of mechanical forces is expected to influence the physiology of tissue surrounding a wound. We aim to investigate whether the force transmission within wound tissue is impacted by the dressing characteristics and whether this impact may differ with wound tissue's properties. Our results show that wound dressings with lower stiffnesses promote force transmission within a wound tissue. This impact is even more significant on stiffer wound tissues. Furthermore, we show that size of wound dressing alters forces that transmit within the wound tissue where dressings with 9 cm length show higher stresses. The wound tissue stiffening has been associated with healing of a wound. Our results demonstrate that wounds with stiffer tissue experience higher stresses. Taken all together, our findings suggest that low stiffness of wound dressing and its size may be introduced as a criterion to explain parameters predisposing a chronic wound to heal. This study's findings on the role of dressings and tissue characteristics demonstrate that precision dressings are required for wound management and understanding how a dressing impacts mechanotransduction in wound tissue will lead to design of novel dressings promoting healing in chronic wounds.

Quantitative predictive approaches for Dupuytren disease: a brief review and future perspectives

In this study we review the current state of the art for Dupuytren's disease (DD), while emphasising the need for a better integration of clinical, experimental and quantitative predictive approaches to understand the evolution of the disease and improve current treatments. We start with a brief review of the biology of this disease and current treatment approaches. Then, since certain aspects in the pathogenesis of this disorder have been compared to various biological aspects of wound healing and malignant processes, next we review some in silico (mathematical modelling and simulations) predictive approaches for complex multi-scale biological interactions occurring in wound healing and cancer. We also review the very few in silico approaches for DD, and emphasise the applicability of these approaches to address more biological questions related to this disease. We conclude by proposing new mathematical modelling and computational approaches for DD, which could be used in the absence of animal models to make qualitative and quantitative predictions about the evolution of this disease that could be further tested in vitro.

Systems biology of angiogenesis signaling: Computational models and omics

Angiogenesis is a highly regulated multiscale process that involves a plethora of cells, their cellular signal transduction, activation, proliferation, differentiation, as well as their intercellular communication. The coordinated execution and integration of such complex signaling programs is critical for physiological angiogenesis to take place in normal growth, development, exercise, and wound healing, while its dysregulation is critically linked to many major human diseases such as cancer, cardiovascular diseases, and ocular disorders; it is also crucial in regenerative medicine. Although huge efforts have been devoted to drug development for these diseases by investigation of angiogenesis‐targeted therapies, only a few therapeutics and targets have proved effective in humans due to the innate multiscale complexity and nonlinearity in the process of angiogenic signaling. As a promising approach that can help better address this challenge, systems biology modeling allows the integration of knowledge across studies and scales and provides a powerful means to mechanistically elucidate and connect the individual molecular and cellular signaling components that function in concert to regulate angiogenesis. In this review, we summarize and discuss how systems biology modeling studies, at the pathway‐, cell‐, tissue‐, and whole body‐levels, have advanced our understanding of signaling in angiogenesis and thereby delivered new translational insights for human diseases.

This article is categorized under:

Cardiovascular Diseases > Computational Models

Cancer > Computational Models

Mechanobiological wound model for improved design and evaluation of collagen dermal replacement scaffolds

Skin wounds are among the most common and costly medical problems experienced. Despite the myriad of treatment options, such wounds continue to lead to displeasing cosmetic outcomes and also carry a high burden of loss-of-function, scarring, contraction, or nonhealing. As a result, the need exists for new therapeutic options that rapidly and reliably restore skin cosmesis and function. Here we present a new mechanobiological computational model to further the design and evaluation of next-generation regenerative dermal scaffolds fabricated from polymerizable collagen. A Bayesian framework, along with microstructure and mechanical property data from engineered dermal scaffolds and autograft skin, were used to calibrate constitutive models for collagen density, fiber alignment and dispersion, and stiffness. A chemo-bio-mechanical finite element model including collagen, cells, and representative cytokine signaling was adapted to simulate no-fill, dermal scaffold, and autograft skin outcomes observed in a preclinical animal model of full-thickness skin wounds, with a focus on permanent contraction, collagen realignment, and cellularization. Finite element model simulations demonstrated wound cellularization and contraction behavior that was similar to that observed experimentally. A sensitivity analysis suggested collagen fiber stiffness and density are important scaffold design features for predictably controlling wound contraction. Finally, prospective simulations indicated that scaffolds with increased fiber dispersion (isotropy) exhibited reduced and more uniform wound contraction while supporting cell infiltration. By capturing the link between multi-scale scaffold biomechanics and cell-scaffold mechanochemical interactions, simulated healing outcomes aligned well with preclinical animal model data. STATEMENT OF SIGNIFICANCE: Skin wounds continue to be a significant burden to patients, physicians, and the healthcare system. Advancing the mechanistic understanding of the wound healing process, including multi-scale mechanobiological interactions amongst cells, the collagen scaffolding, and signaling molecules, will aide in the design of new skin restoration therapies. This work represents the first step towards integrating mechanobiology-based computational tools with in vitro and in vivo preclinical testing data for improving the design and evaluation of custom-fabricated collagen scaffolds for dermal replacement. Such an approach has potential to expedite development of new and more effective skin restoration therapies as well as improve patient-centered wound treatment.

A Coupled Mechanobiological Model of Muscle Regeneration In Cerebral Palsy

Cerebral palsy is a neuromusculoskeletal disorder associated with muscle weakness, altered muscle architecture, and progressive musculoskeletal symptoms that worsen with age. Pathological changes at the level of the whole muscle have been shown; however, it is unclear why this progression of muscle impairment occurs at the cellular level. The process of muscle regeneration is complex, and the interactions between cells in the muscle milieu should be considered in the context of cerebral palsy. In this work, we built a coupled mechanobiological model of muscle damage and regeneration to explore the process of muscle regeneration in typical and cerebral palsy conditions, and whether a reduced number of satellite cells in the cerebral palsy muscle environment could cause the muscle regeneration cycle to lead to progressive degeneration of muscle. The coupled model consisted of a finite element model of a muscle fiber bundle undergoing eccentric contraction, and an agent-based model of muscle regeneration incorporating satellite cells, inflammatory cells, muscle fibers, extracellular matrix, fibroblasts, and secreted cytokines. Our coupled model simulated damage from eccentric contraction followed by 28 days of regeneration within the muscle. We simulated cyclic damage and regeneration for both cerebral palsy and typically developing muscle milieus. Here we show the nonlinear effects of altered satellite cell numbers on muscle regeneration, where muscle repair is relatively insensitive to satellite cell concentration above a threshold, but relatively sensitive below that threshold. With the coupled model, we show that the fiber bundle geometry undergoes atrophy and fibrosis with too few satellite cells and excess extracellular matrix, representative of the progression of cerebral palsy in muscle. This work uses in silico modeling to demonstrate how muscle degeneration in cerebral palsy may arise from the process of cellular regeneration and a reduced number of satellite cells.

Simulation of angiogenesis in three dimensions: Application to cerebral cortex

The vasculature is a dynamic structure, growing and regressing in response to embryonic development, growth, changing physiological demands, wound healing, tumor growth and other stimuli. At the microvascular level, network geometry is not predetermined, but emerges as a result of biological responses of each vessel to the stimuli that it receives. These responses may be summarized as angiogenesis, remodeling and pruning. Previous theoretical simulations have shown how two-dimensional vascular patterns generated by these processes in the mesentery are consistent with experimental observations. During early development of the brain, a mesh-like network of vessels is formed on the surface of the cerebral cortex. This network then forms branches into the cortex, forming a three-dimensional network throughout its thickness. Here, a theoretical model is presented for this process, based on known or hypothesized vascular response mechanisms together with experimentally obtained information on the structure and hemodynamics of the mouse cerebral cortex. According to this model, essential components of the system include sensing of oxygen levels in the midrange of partial pressures and conducted responses in vessel walls that propagate information about metabolic needs of the tissue to upstream segments of the network. The model provides insights into the effects of deficits in vascular response mechanisms, and can be used to generate physiologically realistic microvascular network structures.

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.

Use of a panel of four microRNAs in CSF as a predicted biomarker for postoperative neoangiogenesis in moyamoya disease

INTRODUCTION AND AIMS

At present, the treatment for moyamoya disease (MMD) primarily consists of combined direct and indirect bypass surgery. Nevertheless, more than half of indirect bypass surgeries fail to develop good collaterals from the dura and temporal muscle. This study aimed to investigate whether microRNAs (miRNAs) in cerebrospinal fluid (CSF) could serve as biomarkers for the prediction of postoperative collateral formation.

METHODS

Moyamoya disease patients with indirect bypass surgery were divided into angiogenesis and non-angiogenesis groups, CSF was obtained, and miRNA sequencing was performed using the CSF. Candidate miRNAs were filtered and subsequently verified through qRT-PCR. The diagnostic utility of these differential miRNAs was investigated by using receiver operating characteristic (ROC) curve analysis. Finally, the potential biological processes and signaling pathways associated with candidate miRNAs were analyzed using R software.

RESULTS

The expression levels of four miRNAs (miR-92a-3p, miR-486-3p, miR-25-3p, and miR-155-5p) were significantly increased in the angiogenesis group. By combining these four miRNAs (area under the curve [AUC] =0.970), we established an accurate predictive model of collateral circulation after indirect bypass surgery in MMD patients. GO and KEGG analyses demonstrated a high correlation with biological processes and signaling pathways related to angiogenesis.

CONCLUSION

The 4-miRNA signature is a good model to predict angiogenesis after indirect bypass surgery and help the surgeon to select a appreciate bypass strategy.

Comparative analysis of continuum angiogenesis models

Although discrete approaches are increasingly employed to model biological phenomena, it remains unclear how complex, population-level behaviours in such frameworks arise from the rules used to represent interactions between individuals. Discrete-to-continuum approaches, which are used to derive systems of coarse-grained equations describing the mean-field dynamics of a microscopic model, can provide insight into such emergent behaviour. Coarse-grained models often contain nonlinear terms that depend on the microscopic rules of the discrete framework, however, and such nonlinearities can make a model difficult to mathematically analyse. By contrast, models developed using phenomenological approaches are typically easier to investigate but have a more obscure connection to the underlying microscopic system. To our knowledge, there has been little work done to compare solutions of phenomenological and coarse-grained models. Here we address this problem in the context of angiogenesis (the creation of new blood vessels from existing vasculature). We compare asymptotic solutions of a classical, phenomenological “snail-trail” model for angiogenesis to solutions of a nonlinear system of partial differential equations (PDEs) derived via a systematic coarse-graining procedure (Pillay et al. in Phys Rev E 95(1):012410, 2017. https://doi.org/10.1103/PhysRevE.95.012410). For distinguished parameter regimes corresponding to chemotaxis-dominated cell movement and low branching rates, both continuum models reduce at leading order to identical PDEs within the domain interior. Numerical and analytical results confirm that pointwise differences between solutions to the two continuum models are small if these conditions hold, and demonstrate how perturbation methods can be used to determine when a phenomenological model provides a good approximation to a more detailed coarse-grained system for the same biological process.

Mathematical modelling, parameter estimation and computational simulation for skin wound healing under Copaiferalangsdorffi treatments

We present three mathematical models which simulate the wound healing time for 10% oil-resin (10% OR), 10% hydroalcoholic extract (10% EH) (Copaifera langsdorffii drugs), Lanette cream (LC) and Collagenase treatments. Wound healing is a complex process consisting of inflammatory, proliferative and remodelling phases. The experiments were made on rats with wounds on their backs. The mathematical models consider the interplay among neutrophils, macrophages, which play an essential role in skin wound healing, pro-inflammatory (IL-6) and anti-inflammatory (IL-10) cytokines. The ordinary differential equations (ODE) models reproduce the cellular dynamics of wound healing on the skin, suggesting levels of macrophages and neutrophils cellularity, consistent with the values of total cellularity obtained in the laboratory. The partial differential equations (PDE) model replicate the dispersion along the wound radius, suggesting that the balance of the interleukins is better modelled on copaíba-based treatments (CBT). The cell density is directly influenced by neutrophils in the wound bed and by macrophages at the wound edge. It was possible to find the time for wound healing for all treatments by inserting the diffusive terms.

Inverse Poly-High Internal Phase Emulsions Poly(HIPEs) Materials from Natural and Biocompatible Polysaccharides

This paper shows one of the few examples in the literature on the feasibility of novel materials from natural and biocompatible polymers like inulin (INU) or glycol chitosan (GCS) templated by the formation of o/w (inverse) high internal phase emulsion (HIPE). To the best of our knowledge, this is the first example of inverse polyHIPEs obtained from glycol chitosan or inulin. The obtained polyHIPEs were specifically designed for possible wound dressing applications. The HIPE (pre-crosslinking emulsion) was obtained as inverse HIPE, i.e., by forming a cream-like 80:20 v/v o/w emulsion by using the isopropyl myristate in its oil phase, which is obtained from natural sources like palm oil or coconut oil. The surfactant amount was critical in obtaining the inverse HIPE and the pluronic F127 was effective in stabilizing the emulsion comprising up to 80% v/v as internal phase. The obtained inverse HIPEs were crosslinked by UV irradiation for methacrylated INU or by glutaraldehyde-crosslinking for GCS. In both cases, inverse poly-HIPEs were obtained, which were physicochemically characterized. This paper introduces a new concept in using hydrophilic, natural polymers for the formation of inverse poly-HIPEs.

Evaluating snail-trail frameworks for leader-follower behavior with agent-based modeling

Branched networks constitute a ubiquitous structure in biology, arising in plants, lungs, and the circulatory system; however, the mechanisms behind their creation are not well understood. A commonly used model for network morphogenesis proposes that sprouts develop through interactions between leader (tip) cells and follower (stalk) cells. In this description, tip cells emerge from existing structures, travel up chemoattractant gradients, and form new networks by guiding the movement of stalk cells. Such dynamics have been mathematically represented by continuum "snail-trail" models in which the tip cell flux contributes to the stalk cell proliferation rate. Although snail-trail models constitute a classical depiction of leader-follower behavior, their accuracy has yet to be evaluated in a rigorous quantitative setting. Here, we extend the snail-trail modeling framework to two spatial dimensions by introducing a novel multiplicative factor to the stalk cell rate equation, which corrects for neglected network creation in directions other than that of the migrating front. Our derivation of this factor demonstrates that snail-trail models are valid descriptions of cell dynamics when chemotaxis dominates cell movement. We confirm that our snail-trail model accurately predicts the dynamics of tip and stalk cells in an existing agent-based model (ABM) for network formation [Pillay et al., Phys. Rev. E 95, 012410 (2017)10.1103/PhysRevE.95.012410]. We also derive conditions for which it is appropriate to use a reduced, one-dimensional snail-trail model to analyze ABM results. Our analysis identifies key metrics for cell migration that may be used to anticipate when simple snail-trail models will accurately describe experimentally observed cell dynamics in network formation.

Model-Based Analysis Reveals a Sustained and Dose-Dependent Acceleration of Wound Healing by VEGF-A mRNA (AZD8601)

Intradermal delivery of AZD8601, an mRNA designed to produce vascular endothelial growth factor A (VEGF‐A), has previously been shown to accelerate cutaneous wound healing in a murine diabetic model. Here, we develop population pharmacokinetic and pharmacodynamic models aiming to quantify the effect of AZD8601 injections on the dynamics of wound healing. A dataset of 584 open wound area measurements from 131 mice was integrated from 3 independent studies encompassing different doses, dosing timepoints, and number of doses. Evaluation of several candidate models showed that wound healing acceleration is not likely driven directly by time‐dependent VEGF‐A concentration. Instead, we found that administration of AZD8601 induced a sustained acceleration of wound healing depending on the accumulated dose, with a dose producing 50% of the maximal effect of 92 µg. Simulations with this model showed that a single dose of 200 µg AZD8601 can reduce the time to reach 50% wound healing by up to 5 days.

Lattice and continuum modelling of a bioactive porous tissue scaffold

A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. We derive a model on a square grid lattice to demonstrate the importance of explicitly modelling the network structure of the porous scaffold and compare results from this model with those from a modified continuum model from the literature. We capture two-way coupling between cell growth and fluid flow by allowing cells to block pores, and by allowing the shear stress of the fluid to affect cell growth and death. We explore a range of parameters for both models and demonstrate quantitative and qualitative differences between predictions from each of these approaches, including spatial pattern formation and local oscillations in cell density present only in the lattice model. These differences suggest that for some parameter regimes, corresponding to specific cell types and scaffold geometries, the lattice model gives qualitatively different model predictions than typical continuum models. Our results inform model selection for bioactive porous tissue scaffolds, aiding in the development of successful tissue engineering experiments and eventually clinically successful technologies.

Predictive Approach Identifies Molecular Targets and Interventions to Restore Angiogenesis in Wounds With Delayed Healing

Impaired angiogenesis is a hallmark of wounds with delayed healing, and currently used therapies to restore angiogenesis have limited efficacy. Here, we employ a computational simulation-based approach to identify influential molecular and cellular processes, as well as protein targets, whose modulation may stimulate angiogenesis in wounds. We developed a mathematical model that captures the time courses for platelets, 9 cell types, 29 proteins, and oxygen, which are involved in inflammation, proliferation, and angiogenesis during wound healing. We validated our model using previously published experimental data. By performing global sensitivity analysis on thousands of simulated wound-healing scenarios, we identified six processes (among the 133 modeled in total) whose modulation may improve angiogenesis in wounds. By simulating knockouts of 25 modeled proteins and by simulating different wound-oxygenation levels, we identified four proteins [namely, transforming growth factor (TGF)-β, vascular endothelial growth factor (VEGF), fibroblast growth factor-2 (FGF-2), and angiopoietin-2 (ANG-2)], as well as oxygen, as therapeutic targets for stimulating angiogenesis in wounds. Our modeling results indicated that simultaneous inhibition of TGF-β and supplementation of either FGF-2 or ANG-2 could be more effective in stimulating wound angiogenesis than the modulation of either protein alone. Our findings suggest experimentally testable intervention strategies to restore angiogenesis in wounds with delayed healing.

Computational Modeling to Quantify the Contributions of VEGFR1, VEGFR2, and Lateral Inhibition in Sprouting Angiogenesis

Sprouting angiogenesis is a necessary process in regeneration and development as well as in tumorigenesis. VEGF-A is the main pro-angiogenic chemoattractant and it can bind to the decoy receptor VEGFR1 or to VEGFR2 to induce sprouting. Active sprout cells express Dll4, which binds to Notch1 on neighboring cells, in turn inhibiting VEGFR2 expression. It is known that the balance between VEGFR2 and VEGFR1 determines tip selection and network architecture, however the quantitative interrelationship of the receptors and their interrelated balances, also with relation to Dll4-Notch1 signaling, remains yet largely unknown. Here, we present an agent-based computer model of sprouting angiogenesis, integrating VEGFR1 and VEGFR2 in a detailed model of cellular signaling. Our model reproduces experimental data on VEGFR1 knockout. We show that soluble VEGFR1 improves the efficiency of angiogenesis by directing sprouts away from existing cells over a wide range of parameters. Our analysis unravels the relevance of the stability of the active notch intracellular domain as a dominating hub in this regulatory network. Our analysis quantitatively dissects the regulatory interactions in sprouting angiogenesis. Because we use a detailed model of intracellular signaling, the results of our analysis are directly linked to biological entities. We provide our computational model and simulation engine for integration in complementary modeling approaches.

Eden Model Simulation of Re-Epithelialization and Angiogenesis of an Epidermal Wound

Among the vital processes of cutaneous wound healing are epithelialization and angiogenesis. The former leads to the successful closure of the wound while the latter ensures that nutrients are delivered to the wound region during and after healing is completed. These processes are regulated by various cytokines and growth factors that subtend their proliferation and migration into the wound region until full healing is attained. Wound epithelialization can be enhanced by the administration of epidermal stem cells (ESC) or impaired by the presence of an infection. This paper uses the Eden model of a growing cluster to independently simulate the processes of epithelialization and angiogenesis in a cutaneous wound for different geometries. Further, simulations illustrating bacterial infection are provided. Our simulation results demonstrate contraction and closure for any wound geometry due to a collective migration of epidermal cells from the wound edge in fractal form and the diffusion of capillary sprouts with the laying down of capillary blocks behind moving tips into the wound area.

Extracellular vesicle-mimetic nanovesicles transport LncRNA-H19 as competing endogenous RNA for the treatment of diabetic wounds

Diabetic wounds, one of the most enervating complications of diabetes mellitus, affect millions of people worldwide annually. Vascular insufficiency, caused by hyperglycemia, is one of the primary causes and categories of diabetic impaired wound healing. Recently, long noncoding RNA (LncRNA)-H19, which is significantly decreased in diabetes and may be crucial in triggering angiogenesis, has attracted increasing interest. The possible relationship between the decrease of LncRNA-H19 and the impairment of angiogenesis in diabetes could involve impairment of the insulin-phosphatidylinositol 3-kinase (PI3K)-Akt pathway via the interdiction of LncRNA-H19. Thus, a therapeutic strategy utilizing LncRNA-H19 delivery is feasible. In this study, we investigated the possibility of using high-yield extracellular vesicle-mimetic nanovesicles (EMNVs) as an effective nano-drug delivery system for LncRNA, and studied the function of EMNVs with a high content of LncRNA-H19 (^H19EMNVs). The results, which were exciting, showed that ^H19EMNVs had a strong ability to neutralize the regeneration-inhibiting effect of hyperglycemia, and could remarkably accelerate the healing processes of chronic wounds. Our results suggest that bioengineered EMNVs can serve as a powerful instrument to effectively deliver LncRNA and will be an extremely promising multifunctional drug delivery system in the immediate future.

High-Fat Diet and Alcohol Intake Promotes Inflammation and Impairs Skin Wound Healing in Wistar Rats

The wound-healing process is complex and remains a challenging process under the influence of several factors, including eating habits. As improper diets may lead to disorders such as dyslipidemia, insulin resistance, and chronic inflammation, potentially affecting the tissue ability to heal, we decided to investigate the effect of a high-fat diet and alcohol intake on the inflammatory process and skin wound healing in Wistar rats. Male rats (n = 30) were individually housed in cages with food and water ad libitum (registration number 213/2014). After anesthesia, at day 40, three circular wounds (12 mm diameter) were made on the back of each animal, which were then randomly assorted into five treatment groups: C1 (control 1)-water via gavage and standard chow diet; C2 (control 2)-water (no gavage) and standard chow diet; AL (alcohol)-water (no gavage) and alcohol (40%) via gavage and standard chow diet; HF (high fat)-water (no gavage) and high-fat diet (50%); and HF + AL (alcohol/high fat)-water (no gavage), alcohol (40%) via gavage, and high-fat diet. Animals were treated for 61 days. Every seven days, the area and the rate of wound contraction were evaluated. Tissue samples were removed for histopathological analysis and biochemical analyses. Our results showed that wound contraction was not complete in the HF + AL rats. Two specific indices of wound-healing impairment (total cell number and levels of the inflammatory cytokine TGF-β) were increased in the HF + AL rats. We also observed decreased type I and III collagen fibers in the HF, AL, and HF + AL groups and increased oxidative stress markers in the same groups. We suggest that a high-fat diet combined with alcohol intake contributed to delayed skin wound healing through increase of the inflammatory phase and promoting oxidative stress, which may have led to morphological alterations and impaired matrix remodeling.

Use of animal models for the imaging and quantification of angiogenesis

Angiogenesis is the process of developing new blood vessels from the original vascular network; it is necessary for normal physiological processes, such as embryonic development and wound healing. Angiogenesis is also involved in pathological events, including myocardial ischemia and tumor growth. To investigate the molecular mechanisms of this important process, a variety of methods and models are employed. These strategies can also be used to provide insight into the etiology of angiogenesis-related diseases, thereby contributing to the development of new diagnostics and treatments. Commonly used animal models include the chorioallantoic membrane and yolk sac membrane of chick embryos, the mouse retina and aortic ring, and angiogenesis reactors implanted into mice. These animal models have been instrumental in the study of the angiogenic process. For example, the chorioallantoic membrane undergoes robust angiogenesis during the development of chick embryos, and, because its surface is easily accessible, this membrane provides a convenient model for experimentation. Here, we discuss the methods that employ animal models for the imaging and quantification of angiogenesis. In addition, we propose potential novel directions for future investigations in this area.

Effect of a high-fat diet and alcohol on cutaneous repair: A systematic review of murine experimental models

BACKGROUND AND PURPOSE

Chronic alcohol intake associated with an inappropriate diet can cause lesions in multiple organs and tissues and complicate the tissue repair process. In a systematic review, we analyzed the relevance of alcohol and high fat consumption to cutaneous and repair, compared the main methodologies used and the most important parameters tested. Preclinical investigations with murine models were assessed to analyze whether the current evidence support clinical trials.

METHODS

The studies were selected from MEDLINE/PubMed and Scopus databases, according to Fig 1. All 15 identified articles had their data extracted. The reporting bias was investigated according to the ARRIVE (Animal Research: Reporting of in Vivo Experiments) strategy.

RESULTS

In general, animals offered a high-fat diet and alcohol showed decreased cutaneous wound closure, delayed skin contraction, chronic inflammation and incomplete re-epithelialization.

CONCLUSION

In further studies, standardized experimental design is needed to establish comparable study groups and advance the overall knowledge background, facilitating data translatability from animal models to human clinical conditions.

Minocycline enhances the mesenchymal stromal/stem cell pro-healing phenotype in triple antimicrobial-loaded hydrogels

Mesenchymal stromal/stem cells (MSCs) have demonstrated pro-healing properties including an anti-inflammatory cytokine profile and the promotion of angiogenesis via expression of growth factors in pre-clinical models. MSCs encapsulated in poly(ethylene glycol) diacrylate (PEGdA) and thiolated gelatin poly(ethylene glycol) (Gel-PEG-Cys) crosslinked hydrogels have led to controlled cellular presentation at wound sites with favorable wound healing outcomes. However, the therapeutic potential of MSC-loaded hydrogels may be limited by non-specific protein adsorption on the delivery matrix that could facilitate the initial adhesion of microorganisms and subsequent virulent biofilm formation. Antimicrobials loaded concurrently in the hydrogels with MSCs could reduce microbial bioburden and promote healing, but the antimicrobial effect on the MSC wound healing capacity and the antibacterial efficacy of the hydrogels is unknown. We demonstrate that minocycline specifically induces a favorable change in MSC migration capacity, proliferation, gene expression, extracellular matrix (ECM) attachment, and adhesion molecule and growth factor release with subsequent increased angiogenesis. We then demonstrate that hydrogels loaded with MSCs, minocycline, vancomycin, and linezolid can significantly decrease bacterial bioburden. Our study suggests that minocycline can serve as a dual mechanism for the regenerative capacity of MSCs and the reduction of bioburden in triple antimicrobial-loaded hydrogels.

STATEMENT OF SIGNIFICANCE

Wound healing is a complex biological process that can be hindered by bacterial infection, excessive inflammation, and inadequate microvasculature. In this study, we develop a new formulation of poly(ethylene glycol) diacrylate and thiolated gelatin poly(ethylene glycol) crosslinked hydrogels loaded with minocycline, vancomycin, linezolid, and mesenchymal stromal/stem cells that induces a favorable wound healing phenotype in mesenchymal stromal/stem cells and prevents bacterial bioburden on the hydrogel. This combinatorial approach to biomaterial development has the potential to impact wound healing for contaminated full thickness cutaneous wounds.

Using approximate Bayesian computation to quantify cell-cell adhesion parameters in a cell migratory process

In this work, we implement approximate Bayesian computational methods to improve the design of a wound-healing assay used to quantify cell–cell interactions. This is important as cell–cell interactions, such as adhesion and repulsion, have been shown to play a role in cell migration. Initially, we demonstrate with a model of an unrealistic experiment that we are able to identify model parameters that describe agent motility and adhesion, given we choose appropriate summary statistics for our model data. Following this, we replace our model of an unrealistic experiment with a model representative of a practically realisable experiment. We demonstrate that, given the current (and commonly used) experimental set-up, our model parameters cannot be accurately identified using approximate Bayesian computation methods. We compare new experimental designs through simulation, and show more accurate identification of model parameters is possible by expanding the size of the domain upon which the experiment is performed, as opposed to increasing the number of experimental replicates. The results presented in this work, therefore, describe time and cost-saving alterations for a commonly performed experiment for identifying cell motility parameters. Moreover, this work will be of interest to those concerned with performing experiments that allow for the accurate identification of parameters governing cell migratory processes, especially cell migratory processes in which cell–cell adhesion or repulsion are known to play a significant role.

Cell motility is a central process in wound healing and relies on complex cell-cell interactions. A team of mathematicians led by Ruth Baker and Kit Yates at the University of Oxford utilised computer simulations to re-design wound-healing assays that efficiently identify cell motility parameters. New experimental designs through computer simulation can more accurately identify cell motility parameters by expanding the size of the domain upon which the experiment is performed, as opposed to increasing the number of experimental replicates. The results describe time and cost-saving alterations for an experimental method for evaluate complex cell-cell interactions.

Review on experiment-based two- and three-dimensional models for wound healing

Traumatic and chronic wounds are a considerable medical challenge that affects many populations and their treatment is a monetary and time-consuming burden in an ageing society to the medical systems. Because wounds are very common and their treatment is so costly, approaches to reveal the responses of a specific wound type to different medical procedures and treatments could accelerate healing and reduce patient suffering. The effects of treatments can be forecast using mathematical modelling that has the predictive power to quantify the effects of induced changes to the wound-healing process. Wound healing involves a diverse and complex combination of biophysical and biomechanical processes. We review a wide variety of contemporary approaches of mathematical modelling of gap closure and wound-healing-related processes, such as angiogenesis. We provide examples of the understanding and insights that may be garnered using those models, and how those relate to experimental evidence. Mathematical modelling-based simulations can provide an important visualization tool that can be used for illustrational purposes for physicians, patients and researchers.

Mathematical Models for Immunology: Current State of the Art and Future Research Directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

Spatio-temporal Models of Lymphangiogenesis in Wound Healing

Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis), very few have been proposed for the regeneration of the lymphatic network. Lymphangiogenesis is a markedly different process from angiogenesis, occurring at different times and in response to different chemical stimuli. Two main hypotheses have been proposed: (1) lymphatic capillaries sprout from existing interrupted ones at the edge of the wound in analogy to the blood angiogenesis case and (2) lymphatic endothelial cells first pool in the wound region following the lymph flow and then, once sufficiently populated, start to form a network. Here, we present two PDE models describing lymphangiogenesis according to these two different hypotheses. Further, we include the effect of advection due to interstitial flow and lymph flow coming from open capillaries. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from biological data. The models are then solved numerically and the results are compared with the available biological literature.