Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory

This paper outlines the framework of a porous flow mixture theory for the mathematical modelling of in vitro tissue growth, and gives an application of this theory to an aspect of tissue engineering. The problem is formulated as a set of partial differential equations governing the space and time dependence of the amounts of each component of the tissue (phase), together with the physical stresses in each component. The theory requires constitutive relations to specify the material properties of each phase, and also requires relations to specify the stresses developed due to mechanical interactions, both within each phase and between different phases. An application of the theory is given to the study of the mobility and aggregation of a population of cells seeded into an artificial polymeric scaffold. Stability analysis techniques show that the interplay of the forces between the tissue constituents results in two different regimes: either the cells form aggregates or disperse through the scaffold.     

Atomic force microscopy to investigate spatial patterns of response to interleukin-1beta in engineered cartilage tissue elasticity

Atomic force microscopy (AFM) has been proposed as a tool to evaluate the structural and mechanical properties of cartilage tissue. Here, we aimed at assessing whether AFM can be employed to quantify spatially resolved elastic response of tissue engineered cartilage (TEC) to short exposure to IL-1β, thus mimicking the initially inflammatory implantation site.     

Characterization of evolving biomechanical properties of tissue engineered vascular grafts in the arterial circulation

We used a murine model to assess the evolving biomechanical properties of tissue engineered vascular grafts (TEVGs) implanted in the arterial circulation. The initial polymeric tubular scaffold was fabricated from poly(lactic acid)(PLA) and coated with a 50:50 copolymer of poly(caprolactone) and poly(lactic acid)(P[PC/LA]). Following seeding with syngeneic bone marrow derived mononuclear cells, TEVGs (n=50) were implanted as aortic interposition grafts in wild-type mice and monitored serially using ultrasound. A custom biaxial mechanical testing device was used to quantify the in vitro circumferential and axial mechanical properties of grafts explanted at 3 or 7 months. At both times, TEVGs were much stiffer than native tissue in both directions. Repeated mechanical testing of some TEVGs treated with elastase or collagenase suggested that elastin did not contribute significantly to the overall stiffness whereas collagen did contribute. Traditional histology and immunostaining revealed smooth muscle cell layers, significant collagen deposition, and increasing elastin production in addition to considerable scaffold at both 3 and 7 months, which likely dominated the high stiffness seen in mechanical testing. These results suggest that PLA has inadequate in vivo degradation, which impairs cell-mediated development of vascular neotissue having properties closer to native arteries. Assessing contributions of individual components, such as elastin and collagen, to the developing neovessel is needed to guide computational modeling that may help to optimize the design of the TEVG.     

Microbial colonization of an in vitro model of a tissue engineered human skin equivalent – a novel approach

This was a preliminary investigation to define the conditions of colonization of a human skin equivalent (SE) model with cutaneous microorganisms. SEs of 24 mm diameter were constructed with a dermal matrix of fibrin containing fibroblasts and a stratified epidermis. Microbial colonization of the SEs was carried out in a dry environment, comparable to ' in vivo ' skin, using a blotting technique to remove inoculation fluid. The microbial communities were sampled by scrub washing and viable cells enumerated on selective growth medium. Staphylococcus epidermidis , Propionibacterium acnes and Malassezia furfur (human skin commensals) and Staphylococcus aureus (transient pathogen) were colonized at inoculum densities of 10²–10⁶ CFU SE⁻¹ on the surface of replicate SEs. Growth of all species was supported for upto 72–120 h, with recovery densities of between 10⁴–10⁹ CFU SE⁻¹. A novel, real-time growth monitoring method was also developed, using S. aureus containing a lux cassette. Light output increased from 20 to 95 h, and colonization increased from 10² to 10⁸ CFU SE⁻¹, as confirmed by conventional recovery. Thus, the SE model has potential to investigate interactions between resident and transient microbial communities with themselves and their habitat, and for testing treatments to control pathogen colonization of human skin.     

Computational development of an alpha1A-adrenoceptor model in a membrane mimic

A number of subtypes of the alpha-adrenoceptor have been identified; however, knowledge of the three-dimensional structures of such membrane proteins is limited, and no crystal structure of an alpha-adrenoceptor is available to date. We have developed and analysed homology models of the alpha1A-adrenoceptor subtype based on the bovine rhodopsin crystal structure (1l9 h). Subsequent structural refinement was performed through molecular dynamics simulations using the Amber 7 suite of programs with a biphasic H2O/CHCl3/H2O cell utilised to mimic the receptor's natural membrane environment.     

Prior injury accelerates subsequent wound closure in a mouse model of regeneration

Tissue regeneration and scarless healing involves the complete replacement and functional restoration of damaged organs and tissues. In this study of the scarless healing MRL mouse model, we demonstrate that 2-mm diameter through-and-through holes made in the cartilaginous part of previously injured MRL mouse ears are closed more efficiently, and that the regenerative repair response is significantly accelerated compared with unprimed MRL and control nonhealer strains of mice. Accelerated healing was detected both locally and distally from the original site of injury indicating the involvement of systemic components such as circulating cell types or soluble factors. Histologically, we observed early differences during the wound repair process (before Day 4 post injury) with accelerated formation of blastema-like structures, epidermal downgrowths, and enhanced epithelium thickening in wound border zones in primed MRL mice versus unprimed MRL mice. Although the mechanism of tissue regeneration remains unclear, the results from this study justify the use of the MRL model for further experimentation directed toward the identification of proteins and cell types capable of stimulating scarless tissue regeneration.The views presented in this paper are those of the authors.     

饮酒小鼠动物模型建立及其对雌性激素的影响

目的建立模拟人类饮酒的小鼠动物模型,并以此动物模型进一步研究酒精对小鼠雌激素水平及乳腺癌的影响。方法 SPF级C57BL/6雌性小鼠,随机分对照组和酒精组两组,酒精组20:00到次日8:00给予含有一定浓度酒精的饮用水,其他时间给予常规饮用水,对照组全天给予常规饮用水。观察两组小鼠的饮水量及体重变化;用ANALOX AM1酒精分析仪检测小鼠凌晨2∶00和8∶00血液的酒精浓度(BEC);酶联免疫法(ELASA)检测两组小鼠血清中雌激素水平的差异。结果饮酒组小鼠血液BEC明显增高,类似人类饮酒水平,饮酒组小鼠的饮水量及体重无明显变化;饮酒组小鼠体内雌激素的水平明显高于对照组。结论成功的建立模拟人类饮酒的动物模型,并通过此动物模型初步证实酒精刺激可以增加小鼠体内血清雌激素的水平。     

Complement activation in SCID and nude mice is related to severity of tissue inflammation in the Candida mastitis model

A small animal model of localised candidiasis is needed for the evaluation of new antifungal compounds. Mammary glands of immunocompetent (BALB/cJ) and immunodeficient (SCID and athymic nude) mice were infected with a wild-type of Candida albicans. Some of the animals were treated with amphotericin B (AmB) while others were treated with saline and acted as controls. The histologic changes of infected mammary gland tissues and a number of other organs were evaluated. Complement (C) activation was analysed by immunoelectrophoretic quantification of molecules with C3c epitopes (C3, C3b, iC3b, and C3c) in serum. In all animals the organisms were confined to the mammary glands. Serum C3c levels were significantly higher (P<0.05) in infected untreated BALB/cJ and SCID mice, which also had severe mammary gland tissue inflammation, compared with control mice treated with AmB (4 mg kg(-1) i.p. once daily for 4 days). Both treated and control nude mice showed less tissue inflammation compared to BALB/cJ and SCID mice, and revealed insignificant activation of the complement system. It is concluded that innate immune response is important in the control of candidiasis and that the murine mastitis model is useful for immunopathological studies as well as evaluation of potential antifungal compounds.     

Altered mammary gland development in the p53+/m mouse, a model of accelerated aging

The tumor suppressor p53 is important for inhibiting the development of breast carcinomas. However, little is known about the effects of increased p53 activity on mammary gland development. Therefore, the effect of p53 dosage on mammary gland development was examined by utilizing the p53+/m mouse, a p53 mutant which exhibits increased wild-type p53 activity, increased tumor resistance, a shortened longevity, and a variety of accelerated aging phenotypes. Here we report that p53+/m virgin mice exhibit a defect in mammary gland ductal morphogenesis. Transplants of mammary epithelium into p53+/m recipient mice demonstrate decreased outgrowth of wild-type and p53+/m donor epithelium, suggesting systemic or stromal alterations in the p53+/m mouse. Supporting these data, p53+/m mice display decreased levels of serum IGF-1 and reduced IGF-1 signaling in virgin glands. The induction of pregnancy or treatment of p53+/m mice with estrogen, progesterone, estrogen and progesterone in combination, or IGF-1 stimulates ductal outgrowth, rescuing the p53+/m mammary phenotype. Serial mammary epithelium transplants demonstrate that p53+/m epithelium exhibits decreased transplant capabilities, suggesting early stem cell exhaustion. These data indicate that appropriate levels of p53 activity are important in regulating mammary gland ductal morphogenesis, in part through regulation of the IGF-1 pathway.     

The probability of fixation of a single mutant in an exchangeable selection model

The Cannings exchangeable model for a finite population in discrete time is extended to incorporate selection. The probability of fixation of a mutant type is studied under the assumption of weak selection. An exact formula for the derivative of this probability with respect to the intensity of selection is deduced, and developed in the case of a single mutant. This formula is expressed in terms of mean coalescence times under neutrality assuming that the coefficient of selection for the mutant type has a derivative with respect to the intensity of selection that takes a polynomial form with respect to the frequency of the mutant type. An approximation is obtained in the case where this derivative is a continuous function of the mutant frequency and the population size is large. This approximation is consistent with a diffusion approximation under moment conditions on the number of descendants of a single individual in one time step. Applications to evolutionary game theory in finite populations are presented.      

Organotypical tissue cultures from adult murine colon as an in vitro model of intestinal mucosa

Together with animal experiments, organotypical cell cultures are important models for analyzing cellular interactions of the mucosal epithelium and pathogenic mechanisms in the gastrointestinal tract. Here, we introduce a three-dimensional culture model from the adult mouse colon for cell biological investigations in an in vivo-like environment. These explant cultures were cultured for up to 2 weeks and maintained typical characteristics of the intestinal mucosa, including a high-prismatic epithelium with specific epithelial cell-to-cell connections, a basal lamina and various connective tissue cell types, as analyzed with immunohistological and electron microscopic methods. The function of the epithelium was tested by treating the cultures with dexamethasone, which resulted in a strong upregulation of the serum- and glucocorticoid-inducible kinase 1 similar to that found in vivo. The culture system was investigated in infection experiments with the fungal pathogen Candida albicans. Wildtype but not Deltacph1/Deltaefg1-knockout Candida adhered to, penetrated and infiltrated the epithelial barrier. The results demonstrate the potential usefulness of this intestinal in vitro model for studying epithelial cell-cell interactions, cellular signaling and microbiological infections in a three-dimensional cell arrangement.     

A model of myogenesis in vivo,derived from detailed autoradiographic studies of regenerating skeletal muscle,challenges the concept of quantal mitosis

Summary We have recently shown that myogenesis following severe injury is prolonged compared with minor injury (McGeachie and Grounds 1987). In this previous autoradiographic study 44 mice were injected with tritiated thymidine at various times after muscle injury (0 to 120 h), and samples were taken 9d after injury to determine the percentage of labelled myotube nuclei. In the present study the same experimental data are analysed in detail to reveal how many times labelled muscle precursors divided before fusing to form myotubes.Additional mice were prepared and samples removed 1 h after injection of tritiated thymidine to determine the maximum grain counts of premitotic nuclei. When a labelled premitotic nucleus divides, each of the two daughter nuclei will contain half of the original label. The grain counts of nuclei resulting from sequential divisions of a maximally labelled premitotic nucleus, forms the basis for our detailed analysis which can reveal how many times a muscle precursor has divided after labelling.Nine days after injury the autoradiographic grain counts of labelled myotube nuclei were analysed in detail. The results describe an in vivo model of myogenesis which we use to evaluate quantitatively observations derived from tissue culture studies. The analysis shows that, at the onset of myogenesis in regenerating muscle (30 h after injury), muscle precursors divide only twice before fusing to form myotubes. This observation challenges the concept of quantal mitosis as defined by the tissue culture studies of Quinn et al. (1984, 1985).     

The prediction of leaf canopy expansion in the leek from a simple model dependent on primordial development

In an analysis of leaf development of leek plants grown in the field in 1988, successive leaves initiated, appeared (tip and ligule) and senesced at equal intervals of accumulated temperature/thermal time. These intervals corresponded to a plastochron of 92°C days and phyllochrons of 135 (tip) and 233 (ligule) °C days. The rate of appearance of ligules was exactly equal to the rate of leaf senescence, with the result that the number of fully-expanded leaves per plant remained constant at 1.4. These data, which were compatible with results from previous seasons, were used to develop a model of the interrelationships between primordium initiation at the shoot apex and subsequent events in the development of individual leaves. Primordium initiation is considered to be the primary controlling event in the life of a leaf, and the processes of tip appearance, ligule appearance and death can be predicted from knowledge of the number of primordia which have been initiated, without reference to the environment. A model of canopy expansion, based on the central role of the shoot apex, was developed using the temperature relations of primordium initiation and additional data on leaf expansion and leaf dimensions. Leaf area indices computed in this way provided a satisfactory simulation of the thermal-time course of leaf area index observed in a previous season, 1985.     

Using a stem cell and progeny model to illustrate the relationship between cell cycle times of in vivo human tumour cell tissue populations, in vitro primary cultures and the cell lines derived from them

There is increasing evidence that the growth of human tumours is driven by a small proportion of tumour stem cells with self-renewal properties. Multiplication of these cells leads to loss of self-renewal and after division for a finite number of times the cells undergo programmed cell death. Cell cycle times of human cancers have been measured in vivo and shown to vary in the range from two days to several weeks, depending on the individual. Cells cultured directly from tumours removed at surgery initially grow at a rate comparable to the in vivo rate but continued culture leads to the generation of cell lines that have shorter cycle times (1–3 days). It has been postulated that the more rapidly growing sub-population exhibits some of the properties of tumour stem cells and are the precursors of a slower growing sub-population that comprise the bulk of the tumour. We have previously developed a mathematical model to describe the behaviour of cell lines and we extend this model here to describe the behaviour of a system with two cell populations with different kinetic characteristics and a precursor–product relationship. The aim is to provide a framework for understanding the behaviour of cancer tissue that is sustained by a minor population of proliferating stem cells.     

Applied tissue engineering in the closure of severe burns and chronic wounds using cultured human autologous keratinocytes in a natural fibrin matrix

Whereas in severe burns cultured human epithelial cells may well serve as a life saving method, the true value of tissue-engineered skin products in chronic wound care has yet to be clearly defined. Among other well-known clinical problems, the engraftment rate of commercially available multilayered "sheet grafts" has been shown to vary extremely. Adherence of transplanted cells to the wound bed--especially in the presence of potential wound contamination-- is one of the crucial aspects of this technique. Keratinocyte suspensions in a natural fibrin sealant matrix can potentially treat a variety of skin defects. In acute burn wounds, as well as in chronic wounds the clinical application of this type of tissue-engineered skin substitute demonstrates the capacity of cultured human autologous keratinocytes in a fibrin sealant matrix to adhere to wound beds, attach and spread over the wound resulting in reepithelialization of both acute and chronic wounds. In full thickness burns the combination of this new tool with allogenic dermis is a promising option to achieve complete dermal-epidermal reconstitution by means of tissue engineering and guided tissue repair. When transferring this technique into the treatment of chronic wounds we found an optimal preparation of such recipient wound beds to be crucial to the success. The additional application of continuous negative pressure (vacuum therapy) and preliminary chip skin grafting to optimally prepare the recipient site may be helpful tools to achieve such well-prepared and graftable surfaces. Prospective controlled comparative studies should be designed to further assess the clinical efficacy of this technique.     

Dopamine transporter relation to levodopa-derived synaptic dopamine in a rat model of Parkinson's: an in vivo imaging study

Studies showed that the dopamine (DA) transporter (DAT) modulates changes in levodopa-derived synaptic dopamine levels (Δ(DA)) in Parkinson's disease (PD). Here we evaluate the relationship between DAT and Δ(DA) in the 6-hydroxydopamine model of Parkinson's disease to investigate these mechanisms as a function of dopaminergic denervation and in relation to other denervation-induced regulatory changes. 27 rats with a unilateral 6-hydroxydopamine lesion (denervation ∼20–97%) were imaged with ¹¹C-dihydrotetrabenazine (VMAT2 marker), ¹¹C-methylphenidate (DAT marker) and ¹¹C-raclopride (D2-type receptor marker). For denervation <75%Δ(DA) was significantly correlated with a combination of relatively preserved terminal density and lower DAT. For denervation <90%, Δ(DA) was significantly negatively correlated with DAT with a weaker dependence on VMAT2. For the entire data set, no dependence on pre-synaptic markers was observed; Δ(DA) was significantly positively correlated with ¹¹C-raclopride binding-derived estimates of DA loss. These findings parallel observations in humans, and show that (i) regulatory changes attempt to normalize synaptic DA levels (ii) a lesion-induced functional dependence of Δ(DA) on DAT occurs up to ∼ 90% denervation (iii) for denervation < 75% relative lower DAT levels may relate to effective compensation; for higher denervation, lower DAT levels likely contribute to oscillations in synaptic DA associated with dyskinesias.     

Fractal analysis of the root architecture of Gliricidia sepium for the spatial prediction of root branching,size and mass: model development and evaluation in agroforestry

Based on fractal and pipe model assumptions, a static three-dimensional model of the Gliricidia sepium root system was developed, in order to provide a basis for the prediction of root branching, size and mass in an alley cropping system. The model was built from observations about the topology, branching rules, link length and diameter, and root orientation, provided by in situ and extracted root systems. Evaluation tests were carried out at the plant level and at the field level. These tests principally concerned coefficients α and q –- the proportionality factor α between total cross-sectional area of a root before and after branching, and allocation parameter q that defines the partitioning of biomass between the new links after a branching event –- that could be considered as key variables of this fractal approach. Although independent of root diameter, these coefficients showed a certain variability that may affect the precision of the predictions. When calibrated, however, the model provided suitable predictions of root dry matter, total root length and root diameter at the plant level. At the field level, the simulation of 2D root maps was accurate for root distribution patterns, but the number of simulated root dots was underestimated in the surface layers. Hence recommendations were made to improve the model with regard to α and q. This static approach appeared to be well suited to study the root system of adult trees. Compared with explicit models, the main advantage of the fractal approach is its plasticity and ease of use. This revised version was published online in June 2006 with corrections to the Cover Date.     

Distinct modes of collagen type I proteolysis by matrix metalloproteinase (MMP) 2 and membrane type I MMP during the migration of a tip endothelial cell: insights from a computational model

Matrix metalloproteinases (MMPs) are a family of enzymes responsible for the proteolytic processing of extracellular matrix (ECM) structural proteins under physiological and pathological conditions. During sprouting angiogenesis, the MMPs expressed by a single "tip" endothelial cell exhibit proteolytic activity that allows the cells of the sprouting vessel bud to migrate into the ECM. Membrane type I matrix metalloproteinase (MT1-MMP) and the diffusible matrix metalloproteinase MMP2, in the presence of the tissue inhibitor of metalloproteinases TIMP2, constitute a system of proteins that play an important role during the proteolysis of collagen type I matrices. Here, we have formulated a computational model to investigate the proteolytic potential of such a tip endothelial cell. The cell expresses MMP2 in its proenzyme form, pro-MMP2, as well as MT1-MMP and TIMP2. The interactions of the proteins are described by a biochemically detailed reaction network. Assuming that the rate-limiting step of the migration is the ability of the tip cell to carry out proteolysis, we have estimated cell velocities for matrices of different collagen content. The estimated velocities of a few microns per hour are in agreement with experimental data. At high collagen content, proteolysis was carried out primarily by MT1-MMP and localized to the cell leading edge, whereas at lower concentrations, MT1-MMP and MMP2 were found to act in parallel, causing proteolysis in the vicinity of the leading edge. TIMP2 is a regulator of the proteolysis localization because it can shift the activity of MT1-MMP from its enzymatic toward its activatory mode, suggesting a tight mechanosensitive regulation of the enzymes and inhibitor expression. The model described here provides a foundation for quantitative studies of angiogenesis in extracellular matrices of different compositions, both in vitro and in vivo. It also identifies critical parameters whose values are not presently available and which should be determined in future experiments.     

Assessing the effects of low boron diets on embryonic and fetal development in rodents using in vitro and in vivo model systems

To date, boron (B) essentiality has not been conclusively shown in mammals. This article summarizes the results of a series of in vitro and in vivo experiments designed to investigate the role of B in mammalian reproduction. In the first study, rat dams were fed either a low (0.04 μg B/g) or an adequate (2.00 μg B/g) B diet for 6 wk before breeding and through pregnancy; reproductive outcome was monitored on gestation day 20. Although low dietary B significantly lowered maternal blood, liver, and bone B concentrations, it had no marked effects on fetal growth or development. The goal of the second study was to assess the effects of B on the in vitro development of rat postimplantation embryos. Day 10 embryos collected from dams fed either the low or adequate B diets for at least 12 wk were cultured in serum collected from male rats exposed to one of the two dietary B treatments. Dams fed the low B diet had a significantly reduced number of implantation sites compared to dams fed the B-adequate diet. However, embryonic growth in vitro was not affected by B treatment. The aim of study 3 was to define the limits of boric acid (BA) toxicity on mouse preimplantation development in vitro. Two-cell mouse embryos were cultured in media containing graded levels of BA (from 6 to 10,000 μM). Impaired embryonic differentiation and proliferation were observed only when embryos were exposed to high levels of BA (>2000 μM), reflecting a very low level of toxicity of BA on early mouse embryonic development. Study 4 tested the effects of low (0.04 μg B/g) and adequate (2.00 μg B/g) dietary B on the in vitro development of mouse preimplantation embryos. Two-cell embryos obtained from the dams were cultured in vitro for 72 h. Maternal exposure to the low B diet for 10, 12, and 16 wk was associated with a reduction in blastocyst formation, a reduction in blastocyst cell number, and an increased number of degenerates. Collectively, these studies support the concept that B deficiency impairs early embryonic development in rodents.