Hyperasymptotic solutions for certain partial differential equations

We present the hyperasymptotic expansions for a certain group of solutions of the heat equation. We extend this result to a more general case of linear PDEs with constant coefficients. The generalisation is based on the method of Borel summability, which allows us to find integral representations of solutions for such PDEs.Comment: 17 page

Towards Cancer Hybrid Automata

This paper introduces Cancer Hybrid Automata (CHAs), a formalism to model the progression of cancers through discrete phenotypes. The classification of cancer progression using discrete states like stages and hallmarks has become common in the biology literature, but primarily as an organizing principle, and not as an executable formalism. The precise computational model developed here aims to exploit this untapped potential, namely, through automatic verification of progression models (e.g., consistency, causal connections, etc.), classification of unreachable or unstable states and computer-generated (individualized or universal) therapy plans. The paper builds on a phenomenological approach, and as such does not need to assume a model for the biochemistry of the underlying natural progression. Rather, it abstractly models transition timings between states as well as the effects of drugs and clinical tests, and thus allows formalization of temporal statements about the progression as well as notions of timed therapies. The model proposed here is ultimately based on hybrid automata, and we show how existing controller synthesis algorithms can be generalized to CHA models, so that therapies can be generated automatically. Throughout this paper we use cancer hallmarks to represent the discrete states through which cancer progresses, but other notions of discretely or continuously varying state formalisms could also be used to derive similar therapies.Comment: In Proceedings HSB 2012, arXiv:1208.315

Calcification of subcutaneously implanted collagens in relation to cytotoxicity, cellular interactions and crosslinking

In general, calcification of biomaterials occurs through an interaction of host and implanted material factors, but up to now the real origin of pathologic calcification is unknown. In this study we aimed to investigate incidence of calcification of (crosslinked) dermal sheep collagens (DSCs) with respect to their specific properties, during subcutaneous implantation in rats. Three types of DSCs were commercially obtained: non-crosslinked DSC (NDSC), and DSC crosslinked with glutaraldehyde (GDSC) and hexamethylenediisocyanate (HDSC). NDSC, HDSC and GDSC were (enzymatically) tissue culture pretreated to eliminate their cytotoxic products. Beside this, crosslinking methods were modified to optimize mechanical properties and to decrease cytotoxicity, which resulted in HDSC* and GDSC*. Furthermore, DSC was crosslinked by activation of the carboxylic groups, i.e. by means of acyl azide and carbodiimide, resulting in AaDSC and CDSC, respectively. After implantation of HDSCs and GDSCs a relation between cytotoxicity and calcification of crosslinked DSC could be made. No relation was found between cellular infiltration of DSCs and calcification. However, from the use of different types and modification of crosslinking methods it might be concluded that calcification is mainly related to stable crosslinks, i.e. to the chemical properties of the obtained material

A hydrothermal route for production of dense, nanostructured Y-TZP

Y-TZP powders were prepared either by calcination in air or crystallization under hydrothermal conditions of a hydrous gel, obtained by coprecipitation. Differences in powder properties, green compact structure and sinterability were examined. Crystallization under hydrothermal conditions occurs at temperatures as low as 190°C in the presence of ammonia. The hydrothermally treated powders are composed of soft agglomerates, that collapse under very low pressures, resulting in green bodies with high densities and small pore radii. The sinterability is greatly improved by the hydrothermal treatment and allowed the production of dense, nanostructured Y-TZP by free sintering at 1050°C

Cross-linking of dermal sheep collagen using a water-soluble carbodiimide

A cross-linking method for collagen-based biomaterials was developed using the water-soluble carbodiimide 1-ethyl-3-(3-dimethyl aminopropyl)carbodiimide hydrochloride (EDC). Cross-linking using EDC involves the activation of carboxylic acid groups to give O-acylisourea groups, which form cross-links after reaction with free amine groups. Treatment of dermal sheep collagen (DSC) with EDC (E-DSC) resulted in materials with an increased shrinkage temperature (Ts) and a decreased free amine group content, showing that cross-linking occurred. Addition of N-hydroxysuccinimide to the EDC-containing cross-linking solution (E/N-DSC) increased the rate of cross-linking. Cross-linking increased the Ts of non-cross-linked DSC samples from 56 to 73 °C for E-DSC and to 86 °C for E/N-DSC samples, respectively. For both cross-linking methods a linear relation between the decrease in free amine group content and the increase in Ts was observed. The tensile strength and the high strain modulus of E/N-DSC samples decreased upon cross-linking from 18 to 15MPa and from 26 to 16MPa, respectively. The elongation at break of E/N-DSC increased upon cross-linking from 142 to 180%

Crosslinking of dermal sheep collagen using hexamethylene diisocyanate

The use of hexamethylene diisocyanate (HMDIC) as a crosslinking agent for dermal sheep collagen (DSC) was studied. Because HMDIC is only slightly water soluble, a surfactant was used to obtain a clear and micellar crosslinking solution and to promote the penetration of HMDIC in the DSC matrix. Using optimized conditions treatment of non-crosslinked DSC (N-DSC) with HMDIC (H-DSC) increased the shrinkage temperature (Ts) of N-DSC from 56°C to 74°C for H-DSC. A linear relation between the decrease in free amine group content and the increase in Ts was observed. Crosslinking with HMDIC did not influence the tensile strength of the N-DSC samples but increased the elongation at break from 141% to 163% and decreased the high-strain modulus from 26 MPa to 16 MPa for the H-DSC samples, respectively

Secondary cytotoxicity of (crosslinked) dermal sheep collagen during repeated exposure to human fibroblasts

We investigated commercially available dermal sheep collagen either cross-linked with hexamethylenediisocyanate, or cross-linked with glutaraldehyde. In previous in vitro studies we could discriminate primary, i.e. extractable, and secondary cytotoxicity, due to cell-biomaterial interactions, i.e. enzymatic actions. To develop dermal sheep collagen for clinical applications, we focused in this study on the release, e.g. elimination, of secondary cytotoxicity over time. We used the universal 7 d methylcellulose cell culture with human skin fibroblasts as a test system. Hexamethylenediisocyanate-cross-linked dermal sheep collagen and glutaraldehyde-cross-linked dermal sheep collagen were tested, with intervals of 6 d, over a culture period of 42 d. With hexamethylenediisocyanate-cross-linked dermal sheep collagen, cytotoxicity, i.e. cell growth inhibition and deviant cell morphology, was eliminated after 18 d of exposure. When testing glutaraldehyde-cross-linked dermal sheep collagen, the bulk of cytotoxic products was released after 6 d, but a continuous low secondary cytotoxicity was measured up to 42 d. As a control, non-cross-linked dermal-sheep collagen was tested over a period of 36 d, but no secondary cytotoxic effects were observed. The differences in release of secondary cytotoxicity between hexamethylenediisocyanate-cross-linked dermal sheep collagen, glutaraldehyde-cross-linked dermal sheep collagen and non-cross-linked dermal sheep collagen are explained from differences in cross-linking agents and cross-links obtained. We hypothesize that secondary cytotoxicity results from enzymatic release of pendant molecules from hexamethylene-diisocyanate-cross-linked dermal sheep collagen, e.g. formed after reaction of hydrolysis products of hexamethylenediisocyanate with dermal sheep collagen. Glutaraldehyde-cross-linked dermal sheep collagen contains residual cross-linking agents, which induce the bulk cytotoxicity. Apart from being sensitive to enzymatic degradation, glutaraldehyde-cross-linked dermal sheep collagen was also found to be sensitive to aqueous hydrolysis. Hydrolysis of cross-links may release cytotoxic products and introduce new pendant molecules within glutaraldehyde-cross-linked dermal sheep collagen, which in turn induce cytotoxicity after enzymatic attack

Influence of ethylene oxide gas treatment on the in vitro degradation behavior of dermal sheep collagen

The influence of ethylene oxide gas treatment on the in vitro degradation behavior of noncrosslinked, glutaraldehyde crosslinked or hexamethylene diisocyanate crosslinked dermal sheep collagen (DSC) using bacterial collagenase is described. The results obtained were compared with the degradation behavior of either nonsterilized or γ-sterilized DSC. Upon ethylene oxide sterilization, reaction of ethylene oxide with the free amine groups of DSC occurred, which resulted in a decreased helix stability, as indicated by a lowering of the shrinkage temperature of all three types of DSC. Except for the low strain modulus the mechanical properties of the ethylene oxide sterilized materials were not significantly altered. γ-Sterilization induced chain scission in all three types of DSC, resulting in a decrease of both the tensile strength and the high strain modulus of noncrosslinked and crosslinked DSC. When exposed to a solution of bacterial collagenase, ethylene oxide sterilized materials had a lower rate of degradation compared with nonsterilized DSC. This has been explained by a reduced adsorption of the collagenase onto the collagen matrix as a result of the introduction of pendant N-2-hydroxy ethyl groups

Welcoming high reliability organising in construction management

To achieve project objectives, construction project managers have to manoeuvre through complex coordination structures. They have to simultaneously deal with limited budgets, tight schedules, demanding stakeholders and a fragmented supply-chain. Despite their extensive coordination efforts, project managers are frequently confronted with unexpected delays that force them to improvise and re-plan. As a consequence, budgets and schedules tend to overrun and project organisations appear out-of-control rather than stable and reliable. To enrich our understanding of these phenomena, we propose using the theoretical lens of High Reliability Organising (HRO). HRO stems from research into high hazard industries, and is relatively new to construction management. It provides five generic guiding principles that help practitioners anticipate and contain unwanted events. Given that the use of HRO beyond high hazard contexts is not universally accepted within the scientific community, we ask whether it is justified to apply the HRO lens to the organisation and coordination of 'mainstream' construction projects. We elaborate on this issue by addressing its main theoretical concepts, its origin and its application beyond the fields of risk and safety. We further explain why reductionist interpretations of HRO concepts unnecessarily limit HRO's research domain. We propose a pragmatic reinterpretation of HRO that provides access to the field of construction management. Finally, we present preliminary results of our study into delays and overruns in inner-city subsurface utility reconstruction projects. Our theoretical and empirical arguments provide a stepping-stone for future HRO research projects in the construction management field