An analytical method to solve a general class of nonlinear reactive transport models

Three recent papers published in Chemical Engineering Journal studied the solution of a model of diffusion and nonlinear reaction using three different methods. Two of these studies obtained series solutions using specialized mathematical methods, known as the Adomian decomposition method and the homotopy analysis method. Subsequently it was shown that the solution of the same particular model could be written in terms of a transcendental function called Gauss’ hypergeometric function. These three previous approaches focused on one particular reactive transport model. This particular model ignored advective transport and considered one specific reaction term only. Here we generalize these previous approaches and develop an exact analytical solution for a general class of steady state reactive transport models that incorporate (i) combined advective and diffusive transport, and (ii) any sufficiently differentiable reaction term R(C). The new solution is a convergent Maclaurin series. The Maclaurin series solution can be derived without any specialized mathematical methods nor does it necessarily involve the computation of any transcendental function. Applying the Maclaurin series solution to certain case studies shows that the previously published solutions are particular cases of the more general solution outlined here. We also demonstrate the accuracy of the Maclaurin series solution by comparing with numerical solutions for particular cases.

Definition of an airworthiness certification framework for civil unmanned aircraft systems

The development of effective safety regulations for unmanned aircraft systems (UAS) is an issue of paramount concern for industry. The development of this framework is a prerequisite for greater UAS access to civil airspace and, subsequently, the continued growth of the UAS industry. The direct use of the existing conventionally piloted aircraft (CPA) airworthiness certification framework for the regulation of UAS has a number of limitations. The objective of this paper is to present one possible approach for the structuring of airworthiness regulations for civilian UAS. The proposed approach facilitates a more systematic, objective and justifiable method for managing the spectrum of risk associated with the diversity of UAS and their potential operations. A risk matrix is used to guide the development of an airworthiness certification matrix (ACM). The ACM provides a structured categorisation that facilitates the future tailoring of regulations proportionate to the levels of risk associated with the operation of the UAS. As a result, an objective and traceable link may be established between mandated regulations and the overarching objective for an equivalent level of safety to CPA. The ACM also facilitates the systematic consideration of a range of technical and operational mitigation strategies. For these reasons, the ACM is proposed as a suitable method for the structuring of an airworthiness certification framework for civil or commercially operated UAS (i.e., the UAS equivalent in function to the Part 21 regulations for civil CPA) and for the further structuring of requirements on the operation of UAS in un-segregated airspace.

Empirical Bayes method in the study of traffic safety via heterogeneous negative multinomial model

In the study of traffic safety, expected crash frequencies across sites are generally estimated via the negative binomial model, assuming time invariant safety. Since the time invariant safety assumption may be invalid, Hauer (1997) proposed a modified empirical Bayes (EB) method. Despite the modification, no attempts have been made to examine the generalisable form of the marginal distribution resulting from the modified EB framework. Because the hyper-parameters needed to apply the modified EB method are not readily available, an assessment is lacking on how accurately the modified EB method estimates safety in the presence of the time variant safety and regression-to-the-mean (RTM) effects. This study derives the closed form marginal distribution, and reveals that the marginal distribution in the modified EB method is equivalent to the negative multinomial (NM) distribution, which is essentially the same as the likelihood function used in the random effects Poisson model. As a result, this study shows that the gamma posterior distribution from the multivariate Poisson-gamma mixture can be estimated using the NM model or the random effects Poisson model. This study also shows that the estimation errors from the modified EB method are systematically smaller than those from the comparison group method by simultaneously accounting for the RTM and time variant safety effects. Hence, the modified EB method via the NM model is a generalisable method for estimating safety in the presence of the time variant safety and the RTM effects.

Efficient simulation of unsaturated flow using exponential time integration

We assess the performance of an exponential integrator for advancing stiff, semidiscrete formulations of the unsaturated Richards equation in time. The scheme is of second order and explicit in nature but requires the action of the matrix function φ(A) where φ(z) = [exp(z) - 1]/z on a suitability defined vector v at each time step. When the matrix A is large and sparse, φ(A)v can be approximated by Krylov subspace methods that require only matrix-vector products with A. We prove that despite the use of this approximation the scheme remains second order. Furthermore, we provide a practical variable-stepsize implementation of the integrator by deriving an estimate of the local error that requires only a single additional function evaluation. Numerical experiments performed on two-dimensional test problems demonstrate that this implementation outperforms second-order, variable-stepsize implementations of the backward differentiation formulae.

Improved design method for biosecurity surveillance and early detection of non-indigenous rats

A recent advance in biosecurity surveillance design aims to benefit island conservation through early and improved detection of incursions by non-indigenous species. The novel aspects of the design are that it achieves a specified power of detection in a cost-managed system, while acknowledging heterogeneity of risk in the study area and stratifying the area to target surveillance deployment. The design also utilises a variety of surveillance system components, such as formal scientific surveys, trapping methods, and incidental sightings by non-biologist observers. These advances in design were applied to black rats (Rattus rattus) representing the group of invasive rats including R. norvegicus, and R. exulans, which are potential threats to Barrow Island, Australia, a high value conservation nature reserve where a proposed liquefied natural gas development is a potential source of incursions. Rats are important to consider as they are prevalent invaders worldwide, difficult to detect early when present in low numbers, and able to spread and establish relatively quickly after arrival. The ‘exemplar’ design for the black rat is then applied in a manner that enables the detection of a range of non-indigenous species of rat that could potentially be introduced. Many of the design decisions were based on expert opinion as data gaps exist in empirical data. The surveillance system was able to take into account factors such as collateral effects on native species, the availability of limited resources on an offshore island, financial costs, demands on expertise and other logistical constraints. We demonstrate the flexibility and robustness of the surveillance system and discuss how it could be updated as empirical data are collected to supplement expert opinion and provide a basis for adaptive management. Overall, the surveillance system promotes an efficient use of resources while providing defined power to detect early rat incursions, translating to reduced environmental, resourcing and financial costs.

Electrospraying a reproducible method for production of polymeric microspheres for biomedical applications

The ability to reproducibly load bioactive molecules into polymeric microspheres is a challenge. Traditional microsphere fabrication methods typically provide inhomogeneous release profiles and suffer from lack of batch to batch reproducibility, hindering their potential to up-scale and their translation to the clinic. This deficit in homogeneity is in part attributed to broad size distributions and variability in the morphology of particles. It is thus desirable to control morphology and size of non-loaded particles in the first instance, in preparation for obtaining desired release profiles of loaded particles in the later stage. This is achieved by identifying the key parameters involved in particle production and understanding how adapting these parameters affects the final characteristics of particles. In this study, electrospraying was presented as a promising technique for generating reproducible particles made of polycaprolactone, a biodegradable, FDA-approved polymer. Narrow size distributions were obtained by the control of electrospraying flow rate and polymer concentration, with average particle sizes ranging from 10 to 20 um. Particles were shown to be spherical with a homogenous embossed texture, determined by the polymer entanglement regime taking place during electrospraying. No toxic residue was detected by this process based on preliminary cell work using DNA quantification assays, validating this method as suitable for further loading of bioactive components.

In vitro and in vivo examination of the cell surface glycoprotein CDCP1

A number of reports have demonstrated the importance of the CUB domaincontaining protein 1 (CDCP1) in facilitating cancer progression in animal models and the potential of this protein as a prognostic marker in several malignancies. CDCP1 facilitates metastasis formation in animal models by negatively regulating anoikis, a type of apoptosis triggered by the loss of attachment signalling from cell-cell contacts or cell-extra cellular matrix (ECM) contacts. Due to the important role CDCP1 plays in cancer progression in model systems, it is considered a potential drug target to prevent the metastatic spread of cancers. CDCP1 is a highly glycosylated 836 amino acid cell surface protein. It has structural features potentially facilitating protein-protein interactions including 14 N-glycosylation sites, three CUB-like domains, 20 cysteine residues likely to be involved in disulfide bond formation and five intracellular tyrosine residues. CDCP1 interacts with a variety of proteins including Src family kinases (SFKs) and protein kinase C ä (PKCä). Efforts to understand the mechanisms regulating these interactions have largely focussed on three CDCP1 tyrosine residues Y734, Y743 and Y762. CDCP1-Y734 is the site where SFKs phosphorylate and bind to CDCP1 and mediate subsequent phosphorylation of CDCP1-Y743 and -Y762 which leads to binding of PKCä at CDCP1-Y762. The resulting trimeric protein complex of SFK•CDCP1•PKCä has been proposed to mediate an anti-apoptotic cell phenotype in vitro, and to promote metastasis in vivo. The effect of mutation of the three tyrosines on interactions of CDCP1 with SFKs and PKCä and the consequences on cell phenotype in vitro and in vivo have not been examined. CDCP1 has a predicted molecular weight of ~90 kDa but is usually detected as a protein which migrates at ~135 kDa by Western blot analysis due to its high degree of glycosylation. A low molecular weight form of CDCP1 (LMWCDCP1) of ~70 kDa has been found in a variety of cancer cell lines. The mechanisms leading to the generation of LMW-CDCP1 in vivo are not well understood but an involvement of proteases in this process has been proposed. Serine proteases including plasmin and trypsin are able to proteolytically process CDCP1. In addition, the recombinant protease domain of the serine protease matriptase is also able to cleave the recombinant extracellular portion of CDCP1. Whether matriptase is able to proteolytically process CDCP1 on the cell surface has not been examined. Importantly, proteolytic processing of CDCP1 by trypsin leads to phosphorylation of its cell surface-retained portion which suggests that this event leads to initiation of an intracellular signalling cascade. This project aimed to further examine the biology of CDCP1 with a main of focus on exploring the roles played by CDCP1 tyrosine residues. To achieve this HeLa cells stably expressing CDCP1 or the CDCP1 tyrosine mutants Y734F, Y743F and Y762F were generated. These cell lines were used to examine: • The roles of the tyrosine residues Y734, Y743 and Y762 in mediating interactions of CDCP1 with binding proteins and to examine the effect of the stable expression on HeLa cell morphology. • The ability of the serine protease matriptase to proteolytically process cell surface CDCP1 and to examine the consequences of this event on HeLa cell phenotype and cell signalling in vitro. • The importance of these residues in processes associated with cancer progression in vitro including adhesion, proliferation and migration. • The role of these residues on metastatic phenotype in vivo and the ability of a function-blocking anti-CDCP1 antibody to inhibit metastasis in the chicken embryo chorioallantoic membrane (CAM) assay. Interestingly, biochemical experiments carried out in this study revealed that mutation of certain CDCP1 tyrosine residues impacts on interactions of this protein with binding proteins. For example, binding of SFKs as well as PKCä to CDCP1 was markedly decreased in HeLa-CDCP1-Y734F cells, and binding of PKCä was also reduced in HeLa-CDCP1-Y762F cells. In contrast, HeLa-CDCP1-Y743F cells did not display altered interactions with CDCP1 binding proteins. Importantly, observed differences in interactions of CDCP1 with binding partners impacted on basal phosphorylation of CDCP1. It was found that HeLa-CDCP1, HeLa-CDCP1-Y743F and -Y762F displayed strong basal levels of CDCP1 phosphorylation. In contrast, HeLa-CDCP1-Y734F cells did not display CDCP1 phosphorylation but exhibited constitutive phosphorylation of focal adhesion kinase (FAK) at tyrosine 861. Significantly, subsequent investigations to examine this observation suggested that CDCP1-Y734 and FAK-Y861 are competitive substrates for SFK-mediated phosphorylation. It appeared that SFK-mediated phosphorylation of CDCP1- Y734 and FAK-Y861 is an equilibrium which shifts depending on the level of CDCP1 expression in HeLa cells. This suggests that the level of CDCP1 expression may act as a regulatory mechanism allowing cells to switch from a FAK-Y861 mediated pathway to a CDCP1-Y734 mediated pathway. This is the first time that a link between SFKs, CDCP1 and FAK has been demonstrated. One of the most interesting observations from this work was that CDCP1 altered HeLa cell morphology causing an elongated and fibroblastic-like appearance. Importantly, this morphological change depended on CDCP1- Y734. In addition, it was observed that this change in cell morphology was accompanied by increased phosphorylation of SFK-Y416. This suggests that interactions of SFKs with CDCP1-Y734 increases SFK activity since SFKY416 is critical in regulating kinase activity of these proteins. The essential role of SFKs in mediating CDCP1-induced HeLa cell morphological changes was demonstrated using the SFK-selective inhibitor SU6656. This inhibitor caused reversion of HeLa-CDCP1 cell morphology to an epithelial appearance characteristic of HeLa-vector cells. Significantly, in vitro studies revealed that certain CDCP1-mediated cell phenotypes are mediated by cellular pathways dependent on CDCP1 tyrosine residues whereas others are independent of these sites. For example, CDCP1 expression caused a marked increase in HeLa cell motility that was independent of CDCP1 tyrosine residues. In contrast, CDCP1- induced decrease in HeLa cell proliferation was most prominent in HeLa- CDCP1-Y762F cells, potentially indicating a role for this site in regulating proliferation in HeLa cells. Another cellular event which was identified to require phosphorylation of a particular CDCP1 tyrosine residue is adhesion to fibronectin. It was observed that the CDCP1-mediated strong decrease in adhesion to fibronectin is mostly restored in HeLa-CDCP1-Y743F cells. This suggests a possible role for CDCP1-Y743 in causing a CDCP1-mediated decrease in adhesion. Data from in vivo experiments indicated that HeLa-CDCP1-Y734F cells are more metastic than HeLa-CDCP1 cells in vivo. This indicates that interaction of CDCP1 with SFKs and PKCä may not be required for CDCP1-mediated metastasis formation of HeLa cells in vivo. The metastatic phenotype of these cells may be caused by signalling involving FAK since HeLa-CDCP1- Y734F cells are the only CDCP1 expressing cells displaying constitutive phosphorylation of FAK-Y861. HeLa-CDCP1-Y762F cells displayed a very low metastatic ability which suggests that this CDCP1 tyrosine residue is important in mediating a pro-metastatic phenotype in HeLa cells. More detailed exploration of cellular events occurring downstream of CDCP1-Y734 and -Y762 may provide important insights into the mechanisms altering the metastatic ability of CDCP1 expressing HeLa cells. Complementing the in vivo studies, anti-CDCP1 antibodies were employed to assess whether these antibodies are able to inhibit metastasis of CDCP1 and CDCP1 tyrosine mutants expressing HeLa cells. It was found that HeLa- CDCP1-Y734F cells were the only cell line which was markedly reduced in the ability to metastasise. In contrast, the ability of HeLa-CDCP1, HeLa- CDCP1-Y743F and -Y762F cells to metastasise in vivo was not inhibited. These data suggest a possible role of interactions of CDCP1 with SFKs, occurring at CDCP1-Y734, in preventing an anti-metastatic effect of anti- CDCP1 antibodies in vivo. The proposal that SFKs may play a role in regulating anti-metastatic effects of anti-CDCP1 antibodies was supported by another experiment where differences between HeLa-CDCP1 cells and CDCP1 expressing HeLa cells (HeLa-CDCP1-S) from collaborators at the Scripps Research Institute were examined. It was found that HeLa-CDCP1-S cells express different SFKs than CDCP1 expressing HeLa cells generated for this study. This is important since HeLa-CDCP1-S cells can be inhibited in their metastatic ability using anti-CDCP1 antibodies in vivo. Importantly, these data suggest that further examinations of the roles of SFKs in facilitating anti-metastatic effects of anti-CDCP1 antibodies may give insights into how CDCP1 can be blocked to prevent metastasis in vivo. This project also explored the ability of the serine protease matriptase to proteolytically process cell surface localised CDCP1 because it is unknown whether matriptase can cleave cell surface CDCP1 as it has been reported for other proteases such as trypsin and plasmin. Furthermore, the consequences of matriptase-mediated proteolysis on cell phenotype in vitro and cell signalling were examined since recent reports suggested that proteolysis of CDCP1 leads to its phosphorylation and may initiate cell signalling and consequently alter cell phenotype. It was found that matriptase is able to proteolytically process cell surface CDCP1 at low nanomolar concentrations which suggests that cleavage of CDCP1 by matriptase may facilitate the generation of LWM-CDCP1 in vivo. To examine whether matriptase-mediated proteolysis induced cell signalling anti-phospho Erk 1/2 Western blot analysis was performed as this pathway has previously been examined to study signalling in response to proteolytic processing of cell surface proteins. It was found that matriptase-mediated proteolysis in CDCP1 expressing HeLa cells initiated intracellular signalling via Erk 1/2. Interestingly, this increase in phosphorylation of Erk 1/2 was also observed in HeLa-vector cells. This suggested that initiation of cell signalling via Erk 1/2 phosphorylation as a result of matriptase-mediated proteolysis occurs by pathways independent of CDCP1. Subsequent investigations measuring the flux of free calcium ions and by using a protease-activated receptor 2 (PAR2) agonist peptide confirmed this hypothesis. These data suggested that matriptase-mediated proteolysis results in cell signalling via a pathway induced by the activation of PAR2 rather than by CDCP1. This indicates that induction of cell signalling in HeLa cells as a consequence of matriptase-mediated proteolysis occurs via signalling pathways which do not involve phosphorylation of Erk 1/2. Consequently, it appears that future attempts should focus on the examination of cellular pathways other than Erk 1/2 to elucidate cell signalling initiated by matriptase-mediated proteolytic processing of CDCP1. The data presented in this thesis has explored in vitro and in vivo aspects of the biology of CDCP1. The observations summarised above will permit the design of future studies to more precisely determine the role of CDCP1 and its binding partners in processes relevant to cancer progression. This may contribute to further defining CDCP1 as a target for cancer treatment.

Subchondral bone osteoblasts can induce chondrocyte mineralization during osteoarthritis and this process is relevant to cartilage degradation

Pathological mineralization of articular cartilage is a characteristic feature of osteoarthritis (OA); however, the underlying mechanisms, and their relevance to cartilage degeneration, are not clear. The involvement of subchondral bone changes in OA have been reported previously with the characterization of abnormal subchondral bone mineral density (BMD), osteiod volume, altered bone mechanical parameters and an increase in bone turnover markers. A number of osteoarthritic animal models have demonstrated that subchondral bone changes often precede cartilage degeneration. In this study site specific localization of mineralization markers were detected in the OA cartilage. Chondrocytes and osteoblasts derived from OA cartilage and subchondral bone showed a significant increase in the mRNA expressions of mineralization markers. Interestingly, osteoblasts from OA subchondral bone could significantly decrease cartilage matrix expression; whereas, increase mineralization of chondrocytes (Figure 1). Osteogenic factors, such as CBFA1, ALP, and type X collagen (Col-X), were detected in chondrocytes under mineralization conditions (Figure 2). Furthermore, chondrocyte mineralization was followed by increased mRNA and protein levels of MMP-2, MMP-9 and MMP-13, all of which are detrimental to cartilage integrity in vivo. The data reported here suggests that the upregulation of subchondral bone-mineralization, typical of OA progression, causes cartilage mineralization, and that the mineralization of chondrocytes induce increased MMP levels with a subsequent degradation of the articular cartilage.

SimTrust : a new method of trust network generation

Trust can be used for neighbor formation to generate automated recommendations. User assigned explicit rating data can be used for this purpose. However, the explicit rating data is not always available. In this paper we present a new method of generating trust network based on user’s interest similarity. To identify the interest similarity, we use user’s personalized tag information. This trust network can be used to find the neighbors to make automated recommendation. Our experiment result shows that the precision of the proposed method outperforms the traditional collaborative filtering approach.

Waist circumference cut-off values for the prediction of cardiovascular risk factors clustering in Chinese school-aged children : a cross-sectional study

Background: Waist circumference has been identified as a valuable predictor of cardiovascular risk in children. The development of waist circumference percentiles and cut-offs for various ethnic groups are necessary because of differences in body composition. The purpose of this study was to develop waist circumference percentiles for Chinese children and to explore optimal waist circumference cut-off values for predicting cardiovascular risk factors clustering in this population.----- ----- Methods: Height, weight, and waist circumference were measured in 5529 children (2830 boys and 2699 girls) aged 6-12 years randomly selected from southern and northern China. Blood pressure, fasting triglycerides, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, and glucose were obtained in a subsample (n = 1845). Smoothed percentile curves were produced using the LMS method. Receiver-operating characteristic analysis was used to derive the optimal age- and gender-specific waist circumference thresholds for predicting the clustering of cardiovascular risk factors.----- ----- Results: Gender-specific waist circumference percentiles were constructed. The waist circumference thresholds were at the 90th and 84th percentiles for Chinese boys and girls respectively, with sensitivity and specificity ranging from 67% to 83%. The odds ratio of a clustering of cardiovascular risk factors among boys and girls with a higher value than cut-off points was 10.349 (95% confidence interval 4.466 to 23.979) and 8.084 (95% confidence interval 3.147 to 20.767) compared with their counterparts.----- ----- Conclusions: Percentile curves for waist circumference of Chinese children are provided. The cut-off point for waist circumference to predict cardiovascular risk factors clustering is at the 90th and 84th percentiles for Chinese boys and girls, respectively.

Development of the response coefficient-root function method for the transient vibration serviceability design of flat concrete floors

The vibration serviceability limit state is an important design consideration for two-way, suspended concrete floors that is not always well understood by many practicing structural engineers. Although the field of floor vibration has been extensively developed, at present there are no convenient design tools that deal with this problem. Results from this research have enabled the development of a much-needed, new method for assessing the vibration serviceability of flat, suspended concrete floors in buildings. This new method has been named, the Response Coefficient-Root Function (RCRF) method. Full-scale, laboratory tests have been conducted on a post-tensioned floor specimen at Queensland University of Technology’s structural laboratory. Special support brackets were fabricated to perform as frictionless, pinned connections at the corners of the specimen. A series of static and dynamic tests were performed in the laboratory to obtain basic material and dynamic properties of the specimen. Finite-element-models have been calibrated against data collected from laboratory experiments. Computational finite-element-analysis has been extended to investigate a variety of floor configurations. Field measurements of floors in existing buildings are in good agreement with computational studies. Results from this parametric investigation have led to the development of new approach for predicting the design frequencies and accelerations of flat, concrete floor structures. The RCRF method is convenient tool to assist structural engineers in the design for the vibration serviceability limit-state of in-situ concrete floor systems.

Vibration of L-shaped plates under a deterministic force or moment excitation : a case of statistical energy analysis application

Analytical and closed form solutions are presented in this paper for the vibration response of an L-shaped plate under a point force or a moment excitation. Inter-relationships between wave components of the source and the receiving plates are clearly defined. Explicit expressions are given for the quadratic quantities such as input power, energy flow and kinetic energy distributions of the L-shaped plate. Applications of statistical energy analysis (SEA) formulation in the prediction of the vibration response of finite coupled plate structures under a single deterministic forcing are examined and quantified. It is found that the SEA method can be employed to predict the frequency averaged vibration response and energy flow of coupled plate structures under a deterministic force or moment excitation when the structural system satisfies the following conditions: (1) the coupling loss factors of the coupled subsystems are known; (2) the source location is more than a quarter of the plate bending wavelength away from the source plate edges in the point force excitation case, or is more than a quarter wavelength away from the pair of source plate edges perpendicular to the moment axis in the moment excitation case due to the directional characteristic of moment excitations. SEA overestimates the response of the L-shaped plate when the source location is less than a quarter bending wavelength away from the respective plate edges owing to wave coherence effect at the plate boundary

Cell density alters matrix accumulation in two distinct fractions and the mechanical integrity of alginate-chondrocyte constructs

Chondrocyte density in articular cartilage is known to change with the development and growth of the tissue and may play an important role in the formation of a functional extracellular matrix (ECM). The objective of this study was to determine how initial chondrocyte density in an alginate hydrogel affects the matrix composition, its distribution between the cell-associated (CM) and further removed matrix (FRM) fractions, and the tensile mechanical properties of the developing engineered cartilage. Alginate constructs containing primary bovine chondrocytes at densities of 0, 4, 16, and 64 million cells/ml were fabricated and cultured for 1 or 2 weeks, at which time structural, biochemical, and mechanical properties were analyzed. Both matrix content and distribution varied with the initial cell density. Increasing cell density resulted in an increasing content of collagen and sulfated-glycosaminoglycan (GAG) and an increasing proportion of these molecules localized in the CM. While the equilibrium tensile modulus of cell-free alginate did not change with time in culture, the constructs with highest cell density were 116% stiffer than cell-free controls after 2 weeks of culture. The equilibrium tensile modulus was positively correlated with total collagen (r2 = 0.47, p < 0.001) and GAG content (r2 = 0.68, p < 0.001), and these relationships were enhanced when analyzing only those matrix molecules in the CM fraction (r2 = 0.60 and 0.72 for collagen and GAG, respectively, each p < 0.001). Overall, the results of this study indicate that initial cell density has a considerable effect on the developing composition, structure, and function of alginate–chondrocyte constructs.

Modulation of depth-dependent properties in tissue-engineered cartilage with a semi-permeable membrane and perfusion : a continuum model of matrix metabolism and transport

The functional properties of cartilaginous tissues are determined predominantly by the content, distribution, and organization of proteoglycan and collagen in the extracellular matrix. Extracellular matrix accumulates in tissue-engineered cartilage constructs by metabolism and transport of matrix molecules, processes that are modulated by physical and chemical factors. Constructs incubated under free-swelling conditions with freely permeable or highly permeable membranes exhibit symmetric surface regions of soft tissue. The variation in tissue properties with depth from the surfaces suggests the hypothesis that the transport processes mediated by the boundary conditions govern the distribution of proteoglycan in such constructs. A continuum model (DiMicco and Sah in Transport Porus Med 50:57-73, 2003) was extended to test the effects of membrane permeability and perfusion on proteoglycan accumulation in tissue-engineered cartilage. The concentrations of soluble, bound, and degraded proteoglycan were analyzed as functions of time, space, and non-dimensional parameters for several experimental configurations. The results of the model suggest that the boundary condition at the membrane surface and the rate of perfusion, described by non-dimensional parameters, are important determinants of the pattern of proteoglycan accumulation. With perfusion, the proteoglycan profile is skewed, and decreases or increases in magnitude depending on the level of flow-based stimulation. Utilization of a semi-permeable membrane with or without unidirectional flow may lead to tissues with depth-increasing proteoglycan content, resembling native articular cartilage.