Wound angiogenesis as a function of tissue oxygen tension: a mathematical model

Mathematical model of hyperbaric oxygen therapy applied to chronic diabetic wounds

The failure of certain wounds to heal (including diabetic foot ulcers) is a significant socioeconomic issue for countries worldwide. There is much debate about the best way to treat these wounds and one approach that is shrouded with controversy is hyperbaric oxygen therapy (HBOT), a technique that can reduce the risk of amputation in diabetic patients.In this paper, we develop a six species mathematical model of wound healing angiogenesis and use it to investigate the effectiveness of HBOT, compare the response to different HBOT protocols and study the effect of HBOT on the healing of diabetic wounds that fail to heal for a variety of reasons. We vary the pressure level (1 atm-3 atm), percentage of oxygen inspired by the patient (21%-100%), session duration (0-180 minutes) and frequency (twice per day-once per week) and compare the simulated wound areas associated with different protocols after three weeks of treatment.We consider a variety of etiologies of wound chronicity and show that HBOT is only effective in treating certain causes of chronic wounds. For a wound that fails to heal due to excessive, oxygen-consuming bacteria, we show that intermittent HBOT can accelerate the healing of a chronic wound but that sessions should be continued until complete healing is observed. Importantly, we also demonstrate that normobaric oxygen is not a replacement for HBOT and supernormal healing is not an expected outcome. Our simulations illustrate that HBOT has little benefit for treating normal wounds, and that exposing a patient to fewer, longer sessions of oxygen is not an appropriate treatment option.

A cell-based model of endothelial cell migration, proliferation and maturation during corneal angiogenesis

The motivation of this work stems from two critical experimental observations associated with corneal angiogenesis: (1) angiogenesis will not succeed without endothelial cell proliferation, and (2) proliferation mainly occurs at the leading edge of developing sprouts (Sholley et al., Lab. Invest. 51:624-634, 1984). To discover the underlying mechanisms of these phenomena, we develop a cell-based mathematical model that integrates a mechanical model of elongation with a biochemical model of cell phenotype variation regulated by angiopoietins within a developing sprout. This model allows for a detailed study of the relative roles of endothelial cell migration, proliferation, and maturation. The model is validated by quantitatively comparing its predictions with data derived from corneal angiogenesis experiments. We conclude that cell elasticity and cell-to-cell adhesion allow only limited sprout extension in the absence of proliferation, and the maturation process combined with bioavailability of VEGF can explain the localization of proliferation to the leading edge. We also use this model to investigate the effects of X-ray irradiation, Ang-2 inhibition, and extracellular matrix anisotropy on sprout morphology and extension.

An in silico approach to the analysis of acute wound healing

The complex interactions that characterize acute wound healing have stymied the development of effective therapeutic modalities. The use of computational models holds the promise to improve our basic approach to understanding the process. By modifying an existing ordinary differential equation model of systemic inflammation to simulate local wound healing, we expect to improve the understanding of the underlying complexities of wound healing and thus allow for the development of novel, targeted therapeutic strategies. The modifications in this local acute wound healing model include: evolution from a systemic model to a local model, the incorporation of fibroblast activity, and the effects of tissue oxygenation. Using these modifications we are able to simulate impaired wound healing in hypoxic wounds with varying levels of contamination. Possible therapeutic targets, such as fibroblast death rate and rate of fibroblast recruitment, have been identified by computational analysis. This model is a step toward constructing an integrative systems biology model of human wound healing.

A mathematical model of ischemic cutaneous wounds

Chronic wounds represent a major public health problem affecting 6.5 million people in the United States. Ischemia, primarily caused by peripheral artery diseases, represents a major complicating factor in cutaneous wound healing. In this work, we sought to develop a mathematical model of ischemic dermal wounds. The model consists of a coupled system of partial differential equations in the partially healed region, with the wound boundary as a free boundary. The extracellular matrix (ECM) is assumed to be viscoelastic, and the free boundary moves with the velocity of the ECM at the boundary. The model equations involve the concentration of oxygen, PDGF and VEGF, the densities of macrophages, fibroblasts, capillary tips and sprouts, and the density and velocity of the ECM. Simulations of the model demonstrate how ischemic conditions may limit macrophage recruitment to the wound-site and impair wound closure. The results are in general agreement with experimental findings.

The Kunitz-like modulatory protein haemangin is vital for hard tick blood-feeding success

Ticks are serious haematophagus arthropod pests and are only second to mosquitoes as vectors of diseases of humans and animals. The salivary glands of the slower feeding hard ticks such as Haemaphysalis longicornis are a rich source of bioactive molecules and are critical to their biologic success, yet distinct molecules that help prolong parasitism on robust mammalian hosts and achieve blood-meals remain unidentified. Here, we report on the molecular and biochemical features and precise functions of a novel Kunitz inhibitor from H. longicornis salivary glands, termed Haemangin, in the modulation of angiogenesis and in persistent blood-feeding. Haemangin was shown to disrupt angiogenesis and wound healing via inhibition of vascular endothelial cell proliferation and induction of apoptosis. Further, this compound potently inactivated trypsin, chymotrypsin, and plasmin, indicating its antiproteolytic potential on angiogenic cascades. Analysis of Haemangin-specific gene expression kinetics at different blood-feeding stages of adult ticks revealed a dramatic up-regulation prior to complete feeding, which appears to be functionally linked to the acquisition of blood-meals. Notably, disruption of Haemangin-specific mRNA by a reverse genetic tool significantly diminished engorgement of adult H. longicornis, while the knock-down ticks failed to impair angiogenesis in vivo. To our knowledge, we have provided the first insights into transcriptional responses of human microvascular endothelial cells to Haemangin. DNA microarray data revealed that Haemangin altered the expression of 3,267 genes, including those of angiogenic significance, further substantiating the antiangiogenic function of Haemangin. We establish the vital roles of Haemangin in the hard tick blood-feeding process. Moreover, our results provide novel insights into the blood-feeding strategies that enable hard ticks to persistently feed and ensure full blood-meals through the modulation of angiogenesis and wound healing processes.

High prevalence of defects in Cesarean section scars at transvaginal ultrasound examination

OBJECTIVES

To determine the ability to correctly identify Cesarean section scars, to estimate the prevalence of defective scars, and to determine the size and location of scar defects by transvaginal ultrasound imaging.

METHODS

Two hundred and eighty-seven women underwent transvaginal ultrasound examination 6-9 months after delivery: 108 had undergone one Cesarean section, 43 had had two Cesarean sections, 11 had undergone at least three Cesarean sections, and 125 were primiparae who had delivered vaginally. The ultrasound examiner was blinded to the obstetric history until all scans had been evaluated.

RESULTS

None of the 125 vaginally delivered women had a visible scar in the uterus, whereas all women who had undergone Cesarean section had at least one visible scar. Median myometrial thickness at the level of the isthmus was 11.6 mm in women who had only been delivered vaginally, and 8.3 mm, 6.7 mm and 4.7 mm in women who had undergone one, two and at least three Cesarean sections, respectively (P < 0.001). Scar defects were seen in 61% (66/108), 81% (35/43) and 100% (11/11) of the women who had undergone one, two and at least three Cesarean sections (P = 0.002); at least one defect was classified as large by the ultrasound examiner in 14% (15/108), 23% (10/43) and 45% (5/11) (P = 0.027), and at least one total defect was seen in 6% (7/108), 7% (3/43) and 18% (2/11) (P = 0.336). In women who had undergone one Cesarean section, the median distance between an intact scar and the internal cervical os was 4.6 (range, 0-19) mm, and that between a deficient scar and the internal cervical os was 0 (range, 0-26) mm (P < 0.001).

CONCLUSIONS

Cesarean section scars can be detected reliably by ultrasound imaging. Myometrial thickness at the level of the isthmus uteri decreases with the number of Cesarean sections and the frequency of large scar defects increases. Scars with defects are located lower in the uterus than intact scars.

A three species model to simulate application of Hyperbaric Oxygen Therapy to chronic wounds

Chronic wounds are a significant socioeconomic problem for governments worldwide. Approximately 15% of people who suffer from diabetes will experience a lower-limb ulcer at some stage of their lives, and 24% of these wounds will ultimately result in amputation of the lower limb. Hyperbaric Oxygen Therapy (HBOT) has been shown to aid the healing of chronic wounds; however, the causal reasons for the improved healing remain unclear and hence current HBOT protocols remain empirical. Here we develop a three-species mathematical model of wound healing that is used to simulate the application of hyperbaric oxygen therapy in the treatment of wounds. Based on our modelling, we predict that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds. Furthermore, treatment should continue until healing is complete, and HBOT will not stimulate healing under all circumstances, leading us to conclude that finding the right protocol for an individual patient is crucial if HBOT is to be effective. We provide constraints that depend on the model parameters for the range of HBOT protocols that will stimulate healing. More specifically, we predict that patients with a poor arterial supply of oxygen, high consumption of oxygen by the wound tissue, chronically hypoxic wounds, and/or a dysfunctional endothelial cell response to oxygen are at risk of nonresponsiveness to HBOT. The work of this paper can, in some way, highlight which patients are most likely to respond well to HBOT (for example, those with a good arterial supply), and thus has the potential to assist in improving both the success rate and hence the cost-effectiveness of this therapy.

Topical oxygen therapy induces vascular endothelial growth factor expression and improves closure of clinically presented chronic wounds

1. Chronic wounds, especially in diabetics, represent a serious threat to human health. 2. Correcting a compromised state of tissue oxygenation by the administration of supplemental O(2) is known to benefit wound healing. Beyond its role as a nutrient and antibiotic, O(2) supports wound healing by driving redox signaling. 3. Hyperbaric oxygen (HBO) therapy is widely used and approved by Center for Medicare and Medicaid Services to treat specific ulcerations. The current literature supports the notion that approaches to topically oxygenate wounds may be productive. 4. Here, we present the results of two simultaneous studies testing the effects of HBO and portable topical oxygen (TO) therapies. These two therapeutic approaches have several contrasting features. 5. In total, 1854 patients were screened in outpatient wound clinics for non-randomized enrolments into the HBO (n = 32; 31% diabetic) and TO (n = 25; 52% diabetic) studies. 6. Under the conditions of the present study, HBO treatment seemed to benefit some wounds while not benefiting others. Overall, HBO did not result in statistically significant improvements in wound size in the given population over the time monitored in the present study. 7. However, TO significantly improved wound size. Among the three O(2)-sensitive genes (VEGF, TGFbeta1 and COL1A1) studied in wound edge tissue biopsies, TO treatment was associated with higher VEGF165 expression in healing wounds. Expression of the other genes mentioned was not affected by TO. There was no significant change in the expression levels of any of genes studied in patients in the HBO study. This establishes a link between VEGF gene expression and healing outcome for TO therapy. 8. Taken together, the present study provides evidence demonstrating that TO treatment benefits wound healing in patients suffering from chronic wounds. Treatment with TO is associated with an induction of VEGF expression in wound edge tissue and an improvement in wound size.