Wound healing angiogenesis the clinical implications of a simple mathematical model

Nonhealing wounds are a major burden for health care systems worldwide. In addition, a patient who suffers from this type of wound usually has a reduced quality of life. While the wound healing process is undoubtedly complex, in this paper we develop a deterministic mathematical model, formulated as a system of partial differential equations, that focusses on an important aspect of successful healing: oxygen supply to the wound bed by a combination of diffusion from the surrounding unwounded tissue and delivery from newly-formed blood vessels. While the model equations can be solved numerically, the emphasis here is on the use of asymptotic methods to establish conditions under which new blood vessel growth can be initiated and wound-bed angiogenesis can progress. These conditions are given in terms of key model parameters including the rate of oxygen supply and its rate of consumption in the wound. We use our model to discuss the clinical use of treatments such as hyperbaric oxygen therapy, wound bed debridement, and revascularisation therapy that have the potential to initiate healing in chronic, stalled wounds

The Two Regime method for optimizing stochastic reaction-diffusion simulations

The computer simulation of stochastic reaction-diffusion processes in biology is often done using either compartment-based (spatially discretized) simulations or molecular-based (Brownian dynamics) approaches. Compartment-based approaches can yield quick and accurate mesoscopic results but lack the level of detail that is characteristic of the more computationally intensive molecular-based models. Often microscopic detail is only required in a small region but currently the best way to achieve this detail is to use a resource intensive model over the whole domain. We introduce the Two Regime Method (TRM) in which a molecular-based algorithm is used in part of the computational domain and a compartment-based approach is used elsewhere in the computational domain. We apply the TRM to two test problems including a model from developmental biology. We thereby show that the TRM is accurate and subsequently may be used to inspect both mesoscopic and microscopic detail of reaction diffusion simulations according to the demands of the modeller

Modeling the growth of multicellular cancer spheroids in a\ud bioengineered 3D microenvironment and their treatment with an\ud anti-cancer drug

A critical step in the dissemination of ovarian cancer cells is the formation of multicellular spheroids from cells shed from the primary tumor. The objectives of this study were to establish and validate bioengineered three-dimensional (3D) microenvironments for culturing ovarian cancer cells in vitro and simultaneously to develop computational models describing the growth of multicellular spheroids in these bioengineered matrices. Cancer cells derived from human epithelial ovarian carcinoma were embedded within biomimetic hydrogels of varying stiffness and cultured for up to 4 weeks. Immunohistochemistry was used to quantify the dependence of cell proliferation and apoptosis on matrix stiffness, long-term culture and treatment with the anti-cancer drug paclitaxel.\ud \ud Two computational models were developed. In the first model, each spheroid was treated as an incompressible porous medium, whereas in the second model the concept of morphoelasticity was used to incorporate details about internal stresses and strains. Each model was formulated as a free boundary problem. Functional forms for cell proliferation and apoptosis motivated by the experimental work were applied and the predictions of both models compared with the output from the experiments. Both models simulated how the growth of cancer spheroids was influenced by mechanical and biochemical stimuli including matrix stiffness, culture time and treatment with paclitaxel. Our mathematical models provide new perspectives on previous experimental results and have informed the design of new 3D studies of multicellular cancer spheroids

Growth of confined cancer spheroids: a combined experimental and mathematical modelling approach

We have integrated a bioengineered three-dimensional platform by generating multicellular cancer spheroids in a controlled microenvironment with a mathematical model to investigate\ud confined tumour growth and to model its impact on cellular processes

Standardizing the measurement of parasite clearance in falciparum malaria: the parasite clearance estimator

<p>Abstract</p> <p>Background</p> <p>A significant reduction in parasite clearance rates following artesunate treatment of falciparum malaria, and increased failure rates following artemisinin combination treatments (ACT), signaled emergent artemisinin resistance in Western Cambodia. Accurate measurement of parasite clearance is therefore essential to assess the spread of artemisinin resistance in <it>Plasmodium falciparum</it>. The slope of the log-parasitaemia <it>versus </it>time relationship is considered to be the most robust measure of anti-malarial effect. However, an initial lag phase of numerical instability often precedes a steady exponential decline in the parasite count after the start of anti-malarial treatment. This lag complicates the clearance estimation, introduces observer subjectivity, and may influence the accuracy and consistency of reported results.</p> <p>Methods</p> <p>To address this problem, a new approach to modelling clearance of malaria parasites from parasitaemia-time profiles has been explored and validated. The methodology detects when a lag phase is present, selects the most appropriate model (linear, quadratic or cubic) to fit log-transformed parasite data, and calculates estimates of parasite clearance adjusted for this lag phase. Departing from previous approaches, parasite counts below the level of detection are accounted for and not excluded from the calculation.</p> <p>Results</p> <p>Data from large clinical studies with frequent parasite counts were examined. The effect of a lag phase on parasite clearance rate estimates is discussed, using individual patient data examples. As part of the World Wide Antimalarial Resistance Network's (WWARN) efforts to make innovative approaches available to the malaria community, an automated informatics tool: the parasite clearance estimator has been developed.</p> <p>Conclusions</p> <p>The parasite clearance estimator provides a consistent, reliable and accurate method to estimate the lag phase and malaria parasite clearance rate. It could be used to detect early signs of emerging resistance to artemisinin derivatives and other compounds which affect ring-stage clearance.</p

Multiscale reaction-diffusiion algorithms: PDE-assisted Brownian dynamics

Two algorithms that combine Brownian dynamics (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface, which partitions the domain, and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that the overlap region is required to accurately compute variances using PBD simulations. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented

Surgical outcomes of borderline breast lesions detected by needle biopsy in a breast screening program

<p>Abstract</p> <p>Background</p> <p>The Australian Capital Territory and South East New South Wales branch of BreastScreen Australia (BreastScreen ACT&SENSW) performs over 20,000 screening mammograms annually. This study describes the outcome of surgical biopsies of the breast performed as a result of a borderline lesion being identified after screening mammography and subsequent workup.</p> <p>A secondary aim was to identify any parameters, such as a family history of breast cancer, or radiological findings that may indicate which borderline lesions are likely to be upgraded to malignancy after surgery.</p> <p>Methods</p> <p>From a period of just over eight years, all patients of BreastScreen ACT&SENSW who were diagnosed with a borderline breast lesion were identified. These women had undergone needle biopsy in Breastscreen ACT&SENSW and either atypical ductal hyperplasia (ADH), flat epithelial atypia (FEA), atypical lobular hyperplasia (ALH), radial scar/complex sclerosing lesion, papillary lesion, mucocoele-like lesion (MLL) or lobular carcinoma in situ (LCIS) was found. Final outcomes for each type of borderline lesion after referral for surgical biopsy were recorded and analysed. Results of the surgical biopsy were compared to the type of needle biopsy and its result, radiological findings and family history status.</p> <p>Results</p> <p>Of the 94 surgical biopsies performed due to the presence of a borderline breast lesion, 20% showed benign pathology, 55% remained as borderline lesions, 17% showed non-invasive malignancy and 7% showed invasive malignancy. VALCS biopsy was the most common needle biopsy method used to identify the lesions in this study (76%). Malignant outcomes resulted from 24% of the surgical biopsies, with the most common malignant lesion being non-comedo ductal carcinoma <it>in situ </it>(DCIS). The most common borderline lesion for which women underwent surgical biopsy was ADH (38%). Of these women, 22% were confirmed as ADH on surgical biopsy and 47% with a malignancy.</p> <p>Conclusions</p> <p>Further research is required to determine whether characteristics of the mammographic lesion (particularly calcification patterns), the area targeted for biopsy and number of core samples retrieved, can indicate a closer correlation with eventual pathology. This study identified no findings in the diagnostic assessment that could exclude women with borderline lesions from surgical biopsy.</p

Crystalline Order on a Sphere and the Generalized Thomson Problem

We attack generalized Thomson problems with a continuum formalism which exploits a universal long range interaction between defects depending on the Young modulus of the underlying lattice. Our predictions for the ground state energy agree with simulations of long range power law interactions of the form 1/r^{gamma} (0 < gamma < 2) to four significant digits. The regime of grain boundaries is studied in the context of tilted crystalline order and the generality of our approach is illustrated with new results for square tilings on the sphere.Comment: 4 pages, 5 eps figures Fig. 2 revised, improved Fig. 3, reference typo fixe

Breast milk-derived human milk oligosaccharides promote Bifidobacterium interactions within a single ecosystem

Diet-microbe interactions play an important role in modulating the early-life microbiota, with Bifidobacterium strains and species dominating the gut of breast-fed infants. Here, we sought to explore how infant diet drives distinct bifidobacterial community composition and dynamics within individual infant ecosystems. Genomic characterisation of 19 strains isolated from breast-fed infants revealed a diverse genomic architecture enriched in carbohydrate metabolism genes, which was distinct to each strain, but collectively formed a pangenome across infants. Presence of gene clusters implicated in digestion of human milk oligosaccharides (HMOs) varied between species, with growth studies indicating that within single infants there were differences in the ability to utilise 2'FL and LNnT HMOs between strains. Cross-feeding experiments were performed with HMO degraders and non-HMO users (using spent or 'conditioned' media and direct co-culture). Further H-NMR analysis identified fucose, galactose, acetate, and N-acetylglucosamine as key by-products of HMO metabolism; as demonstrated by modest growth of non-HMO users on spend media from HMO metabolism. These experiments indicate how HMO metabolism permits the sharing of resources to maximise nutrient consumption from the diet and highlights the cooperative nature of bifidobacterial strains and their role as 'foundation' species in the infant ecosystem. The intra- and inter-infant bifidobacterial community behaviour may contribute to the diversity and dominance of Bifidobacterium in early life and suggests avenues for future development of new diet and microbiota-based therapies to promote infant health