Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Deep dermal burn injury results in scarless wound healing in the ovine fetus

Early to mid-term fetuses heal cutaneous incisional wounds without scars; however, fetal response to burn injury has not been ascertained. We present a fetal model of thermal injury and subsequent analysis of fetal and lamb response to burn injury. A reproducible deep dermal burn injury was created in the fetus by application of water at 66 degrees C for 7 seconds, and at 82 degrees C for 10 seconds to the lamb. Macroscopically, the area of fetal scald was undetectable from day 7 post injury, while all lamb scalds were readily identified and eventually healed with scarring. Using a five-point histopathology scoring system for alteration in tissue morphology, differences were detected between control and scalded skin at all stages in lamb postburn, but no difference was detected in the fetal model after day 7. There were also large differences in content of alpha-smooth muscle actin and transforming growth factor-beta1 between control and scalded lamb and these differences were statistically significant at day 14 (P < 0.01). This novel model of fetal and lamb response to deep dermal injury indicates that the fetus heals a deep burn injury in a scarless fashion. Further elucidation of this specific fetal process of burn injury repair may lead to improved outcome for patients with burn injury.

Matrix metalloproteinases during wound healing - a double edged sword

The extracellular matrix (ECM) provides a framework for cells and gives skin its tensile strength and elasticity. Loss of its integrity necessitates the clearing of damaged components and the deposition of firstly a provisional matrix and later remodelling of the ECM to support a functionally intact tissue. Matrix metalloproteinases (MMPs) are an important family of enzymes that function in the breakdown of the ECM and modulate the function of many biologically active molecules housed in the ECM. Through their enzymatic actions MMPs play a role in fundamental processes such as immune cell infiltration and ECM remodelling during wound repair. Their tight control is necessary for timely wound healing and excessive MMP activity participates in the development and persistence of chronic wounds, while reduced activity contributes to fibrosis. A number of inhibitors have been designed to target this activity and improve wound healing with limited success. Novel strategies are currently being investigated to improve wound healing by targeting MMP modulating molecules.

Novel solutions for a model of wound healing angiogenesis

We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al (2000 IMA J. Math. App. Med. 17 395–413) assuming two conjectures hold. In the previous work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime. We construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.

Wound healing from the outback: novel wound healing therapeutics from native Australian plants

Introduction Chronic wounds are an area of major concern. The on-going and in-direct costs are substantial, reaching far beyond the costs of the hospitalization and associated care. As a result, pharmacological therapies have been developed to address treatment insufficiencies, however, the availability of drugs capable of promoting the wound repair process still remain limited. The wound healing properties of various herbal plants is well recognised amongst indigenous Australians. Hence, based on traditional accounts, we evaluated the wound healing potential of two Australian native plants. Methods Bioactive compounds were methanol extracted from dried plant leaves that were commercially sourced. Primary keratinocyte (Kc) and fibroblast (Fib) cells (denoted as Kc269, Kc274, Kc275, Kc276 and Fib274) obtained from surgical discarded tissue were cultured in 48-well plates and incubated (37⁰C, 5% CO2) overnight. The growth media was discarded and replaced with fresh growth media plus various concentrations (15.12 µg/mL, 31.25 µg/mL, 62.5 µg/mL, 125 µg/mL, 250 µg/mL and 500 µg/mL) of the plant extracts. Cellular responses were measured using the alamarBlue® assay and the CyQUANT® assay. Plant extracts in the aqueous phase were prepared by boiling whole leaves in water and taking aqueous phase samples at various (1, 2 , 5 minutes boiling) time points. Plant leaves were either added before the water was boiled (cold boiled) or after the water was boiled (hot boiled). The final concentrations of the aqueous plant extracts were 3.3 ng/mL (± 0.3 ng/mL) per sample. The antimicrobial properties of the plant extracts were tested using the well diffusion assay method against Staphylococcus aureus, Klebsiella pnuemoniae and methicillin resistant S. aureus and Bacillus cereus. Results Assay results from the almarBlue® and CYQUANT® assays indicated that extracts from both native plants at various time points (0, 24 and 48 hours) and concentrations (31.25 mg/mL, 62.5 mg/mL, and 125 mg/mL) were significantly higher (n=3, p=0.03 for Kc269, p=0.04 for Kc274, p=0.02 for Fib274, p=0.04 for Kc275 and p=0.001 for Kc276) compared with the untreated controls. Neither plant extract demonstrated cytotoxic effects. Significant antimicrobial activity against methicillin resistant Staphylococcus aureus (p=0.0009 for hot boiled plant A, n=2, p=0.034 for cold boiled plant A, n=2) K. pnuemoniae (p=0.0009 for hot boiled plant A, n=2, p=0.002 for cold boiled plant A, n=2) and B. cereus (p=0.0009 for hot boiled plant A, n=2, p=0.003 for cold boiled plant A, n=2) was observed at concentrations of 3.2 ng/mL for plant A and 3.4 ng/mL for plant B. Conclusion Both native plants contain bioactive compounds that increase cellular metabolic rates and total nucleic acid content. Neither plant was shown to be cytotoxic. Furthermore, both exhibited significant antimicrobial activity.

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

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

Pattern of cutaneous wound healing in a live fish Clarias batrachus (L.)(Clariidae, Pisces.)

Incisional wounds of the same length and depth were made on skin between dorsal fin and the lateral line canal of Clarias batrachus and the pattern of wound closure has been studied histologically. Following infliction, a marked change in the colour of the skin surrounding the wound was observed which lasted for about 30 h and restored thereafter. Mucus and blood cells plugged the wound gap shortly after infliction. The epidermis surrounding the wound was found to be detached from the basement membrane. Mass movement of epidermal cells was observed from both side of the wound gap. The epidermal cells at the margin of the wound became hypertrophied. The epidermis became normal by 32 days. The dealing of sub-epidermal tissue indicated degenerative and regenerative changes of muscle fibres. The mucus and blood cells were accumulated in the wound gap and later fine blood vessels were formed. Gradually granulation tissue was formed and fibroblasts and myoblasts appeared. Myoblast differentiated into muscle bundles. The epidermal repair was completed within 35 days.

Elevated Circulation Levels of an Antiangiogenic SERPIN in Patients with Diabetic Microvascular Complications Impair Wound Healing through Suppression of Wnt Signaling

Wound healing, angiogenesis and hair follicle maintenance are often impaired in the skin of diabetic patients, but the pathogenesis has not been well understood. Here, we report that circulation levels of kallistatin, a member of the serine proteinase inhibitor (SERPIN) superfamily with anti-angiogenic activities, were elevated in Type 2 diabetic patients with diabetic vascular complications. To test the hypothesis that elevated kallistatin levels could contribute to a wound healing deficiency via inhibition of Wnt/β-catenin signaling, we generated kallistatin-transgenic (KS-TG) mice. KS-TG mice had reduced cutaneous hair follicle density, microvascular density, and panniculus adiposus layer thickness as well as altered skin microvascular hemodynamics and delayed cutaneous wound healing. Using Wnt reporter mice, our results showed that Wnt/β-catenin signaling is suppressed in dermal endothelium and hair follicles in KS-TG mice. Lithium, a known activator of β-catenin via inhibition of glycogen synthase kinase-3β, reversed the inhibition of Wnt/β-catenin signaling by kallistatin and rescued the wound healing deficiency in KS-TG mice. These observations suggest that elevated circulating anti-angiogenic serpins in diabetic patients may contribute to impaired wound healing through inhibition of Wnt/β-catenin signaling. Activation of Wnt/β-catenin signaling, at a level downstream of Wnt receptors, may ameliorate the wound healing deficiency in diabetic patients.Journal of Investigative Dermatology accepted article preview online, 24 January 2014. doi:10.1038/jid.2014.40.

The role of LL-37 in periodontal wound healing

Introduction: As a result of chronic inflammation during periodontal disease the junctional epithelium becomes micro-ulcerated. The inflammatory process is mediated by both bacterial and host cell products. Host defence peptides such as defensins, secretory leucocyte protease inhibitor (SLPI) and the sole human cathelicidin, LL-37, are secreted by both periodontal cells and neutrophils into gingival crevicular fluid (GCF). They have the ability to modulate the immune response in periodontitis and are thought to have a potential role in periodontal wound healing. Objectives: The aims of this study were to determine the role of LL-37 in the production of Interleukin (IL)-8, IL-6, hepatocyte growth factor (HGF) and basic-fibroblast growth factor (bFGF) by gingival fibroblasts. The role of LL-37 in modulating total matrix metalloproteinase (MMP) activity and expression of tissue inhibitors of metalloproteinase (TIMP)-1 and -2 by gingival fibroblasts was also investigated. Methods: Primary gingival fibroblasts were co-cultured with concentrations of LL-37 (1, 5 and 10µg/ml) for 24 hours and their supernatants tested for levels of IL-8 and IL-6, HGF, bFGF, TIMP-1 and TIMP-2 by ELISA. Rates of MMP turnover in the supernatants were tested by fluorogenic assay using fluorescence resonance energy transfer (FRET) peptide substrates. Cytotoxicity was measured by MTT assay. Statistical significance was measured using the independent t-test and p<0.05 was considered significant. Results: LL-37 significantly upregulated levels of IL-8, IL-6, HGF, bFGF and TIMP-1 (p<0.05) in a dose-dependent fashion. LL-37 significantly decreased the total MMP activity (p<0.05). None of the LL-37 concentrations tested were cytotoxic to gingival fibroblasts. Conclusion: These results indicate that LL-37 is involved in periodontal wound healing. LL-37 increased levels of proinflammatory cytokines and increased levels of growth factors involved in re-epithelialisation. LL-37 has the ability to regulate remodelling of the periodontium by controlling MMP overactivity both directly and by stimulating production of inhibitors by gingival fibroblasts.

Peroxisome proliferator-activated receptors (PPARs): from metabolic control to epidermal wound healing.

Peroxisome proliferator-activated receptors control many cellular and metabolic processes. They are transcription factors belonging to the family of ligand-inducible nuclear receptors. Three isotypes called PPARalpha, PPARbeta/delta and PPARgamma have been identified in lower vertebrates and mammals. They display differential tissue distribution and each of the three isotypes fulfills specific functions. PPARalpha and PPARgamma control energy homoeostasis and inflammatory responses. Their activity can be modulated by drugs such as the hypolipidaemic fibrates and the insulin sensitising thiazolidinediones (pioglitazone and rosiglitazone). Thus, these receptors are involved in the control of chronic diseases such as diabetes, obesity, and atherosclerosis. Little is known about the main function of PPARbeta, but it has been implicated in embryo implantation, tumorigenesis in the colon, reverse cholesterol transport, and recently in skin wound healing. Here, we present recent developments in the PPAR field with particular emphasis on both the function of PPARs in lipid metabolism and energy homoeostasis (PPARalpha and PPARgamma), and their role in epidermal maturation and skin wound repair (PPARalpha and PPARbeta).

An alternative technique to the harvesting of a connective tissue graft from a thin palate: Enhanced wound healing

This article describes an alternative surgical approach to the harvesting of subepithelial connective tissue grafts from thin palates. A partial-thickness flap is raised, and a graft composed of epithelium and connective tissue is removed from the palate. The superficial layer ( epithelium and a thin zone of connective tissue) is then dissected from the graft and replaced at the donor site to facilitate faster healing. The subjacent layer of connective tissue is placed as needed to obtain root coverage. The clinical application of this technique is described in two patients with multiple gingival recessions.

Influence of low-level laser therapy on wound healing in nicotine-treated animals

Low-level laser therapy (LLLT) has been shown to have several biological effects that favor the healing process, and nicotine has been shown to delay the healing process. In this study we investigated the healing of open wounds created on the back of rats treated with nicotine with or without LLLT. of 115 animals, 59 received subcutaneous injections of saline solution, and the others received subcutaneous injections of nicotine (3 mg/kg body weight), twice a day throughout the study period. After 30 days, skin wounds were created on the back of the animals. The animals receiving saline injections were divided into two groups: group 1 (G1, n = 29), in which the wounds were left untreated, and group 2 (G2, n = 30), in which the wounds were treated with LLLT (GaAlAs, 660 nm, 30 mW, 5.57 J/cm(2) per point, 0.39 J, 13 s per point, 0.42 W/cm(2)). The animals receiving nicotine injections were also divided into two groups: group 3 (G3, n = 29), in which the wounds were left untreated, and group 4 (G4, n = 27), in which the wounds were treated with LLLT. The animals were killed 3, 7 or 14 days after surgery. Wound healing was evaluated histologically both qualitatively and semiquantitatively. Wounds of G2 showed a delay in epithelial migration and connective tissue organization compared to those of G1. Wounds of G2 showed faster healing than those of G1; similarly, wounds of G4 showed more advanced healing than those of G3. LLLT acted as a biostimulatory coadjuvant agent balancing the undesirable effects of nicotine on wound tissue healing.

Effects of Chamomilla recutita (L.) on oral wound healing in rats

Objectives. The purpose of this study was to evaluate the effect of Chamomilla recutita on the healing of ulcers in rats.Study Design. A 5-mm wound was inflicted on the tongue of 36 rats. Treatment group animals were treated topically with 0.04 mL/day of chamomile ointment, whereas control group animals were not treated. Animals were sacrificed after 3, 7 or 10 days. Semi-quantitative analysis of the degree of inflammation, fibroblast count and wound size was performed, as well as histometric analysis of re-epithelialization and percentage of collagen fibers of the lesion.Results. Animals treated with chamomile showed the best results regarding epithelialization and percentage of collagen fibers after 10 days. As expected, time had a statistically significant effect (p<0.05) on fibroblast count, epithelialization, inflammation and wound size; animals sacrificed at 3 days showed the worst results.Conclusions. Chamomile stimulated re-epithelialization and the formation of collagen fibers after 10 days of treatment; it did not, however, influence inflammation or fibroblast count.