Localized bacterial infection in a distributed model for tissue inflammation

Phagocyte motility and chemotaxis are included in a distributed mathematical model for the inflammatory response to bacterial invasion of tissue. Both uniform and non-uniform steady state solutions may occur for the model equations governing bacteria and phagocyte densities in a macroscopic tissue region. The non-uniform states appear to be more dangerous because they allow large bacteria densities concentrated in local foci, and in some cases greater total bacteria and phagocyte populations. Using a linear stability analysis, it is shown that a phagocyte chemotactic response smaller than a critical value can lead to a non-uniform state, while a chemotactic response greater than this critical value stabilizes the uniform state. This result is the opposite of that found for the role of chemotaxis in aggregation of slimemold amoebae because, in the inflammatory response, the chemotactic population serves as an inhibitor rather than an activator. We speculate that these non-uniform steady states could be related to the localized cell aggregation seen in chronic granulomatous inflammation. The formation of non-uniform states is not necessarily a consequence of defective phagocyte chemotaxis, however. Rather, certain values of the kinetic parameters can yield values for the critical chemotactic response which are greater than the normal response.Numerical computations of the transient inflammatory response to bacterial challenge are presented, using parameter values estimated from the experimental literature wherever possible.     

Analysis of a lumped model for tissue inflammation dynamics

The inflammatory response to bacterial invasion of tissue is a complex combination of chemical and physical events, and the outcome of a particular challenge is dependent upon the interaction of these. Thus a wide variety of behavior can be observed for the operation of this response. In this paper we develop and analyze a mathematical model for a generalized inflammatory response to bacterial invasion of a tissue region assumed to be homogeneous on a macroscopic scale, in order to study the dynamical behavior of the system. Our analysis allows interpretation of the outcome of a challenge in terms of key parameters representing the rate processes involved. It demonstrates how abnormalities in these processes can lead to pathological behavior. Numerical values for the parameters are estimated from experimental literature sources, and used in example computations to illustrate the predictions of the model under physiological conditions.     

Ketone body kinetics in humans: a mathematical model

A model has been developed to account for ketone body kinetics in man based on data following bolus injections of [14C]acetoacetate (A) and [14C]beta-OH butyrate (B) into normal humans in the postabsorptive state. The model consists of separate compartments for blood A and B that are linked by a tissue compartment in which rapid interconversion of the ketone bodies occurs. The probability of movement from blood into this compartment was assumed to be the same for both ketone bodies. Two slowly equilibrating tissue compartments are required to account for the slow components in the tracer data, and thus a five-compartment model is proposed. By modeling the transient tracer data with the tracee in a steady state, ketone body kinetics were defined in terms of the rapid interconversions of A and B, and the slow exchanges of carbon within the tissues. The rates of release of new A and B into blood, (UA and UB) were calculated. These rates were less than the apparent production rates, PRA and PRB, as the PR's included carbon atoms first released as the other ketone body. The exchange constants between the compartments were determined in addition to the fractional catabolic rates (FCR) and metabolic clearance rates (MCR) of A and B. The initial space of distribution was 10 L and the mean values +/- SD (n = 11), normalized to this volume, were UA = 6.4 +/- 5.0, UB = 8.8 +/- 8.0 (mumol L-1 min-1), FCRA = 0.226 +/- 0.142, FCRB = 0.188 +/- 0.124 (min-1), MCRA = 2.26 +/- 1.42, MCRB = 1.87 +/- 1.23 (L min-1) and PRA = 11.1 +/- 7.6, PRB = 12.7 +/- 10.0 (mumol L-1 min-1).     

Travelling waves in a tissue interaction model for skin pattern formation

Tissue interaction plays a major role in many morphogenetic processes, particularly those associated with skin organ primordia. We examine travelling wave solutions in a tissue interaction model for skin pattern formation which is firmly based on the known biology. From a phase space analysis we conjecture the existence of travelling waves with specific wave speeds. Subsequently, analytical approximations to the wave profiles are derived using perturbation methods. We then show numerically that such travelling wave solutions do exist and that they are in good agreement with our analytical results. Finally, the biological implications of our analysis are discussed.     

Gap junctional communication in tissue inflammation and repair

Local injury induces a complex orchestrated response to stimulate healing of injured tissues, cellular regeneration and phagocytosis. Practically, inflammation is defined as a defense process whereby fluid and white blood cells accumulate at a site of injury. The balance of cytokines, chemokines, and growth factors is likely to play a key role in regulating important cell functions such as migration, proliferation, and matrix synthesis during the process of inflammation. Hence, the initiation, maintenance, and resolution of innate responses depend upon cellular communication. A process similar to tissue repair and subsequent scarring is found in a variety of fibrotic diseases. This may occur in a single organ such as liver, kidneys, pancreas, lung, skin, and heart, but fibrosis may also have a more generalized distribution such as in atherosclerosis. The purpose of this review is to summarize recent advances on the contribution of gap junction-mediated intercellular communication in the modulation of the inflammatory response and tissue repair.     

A mathematical model for bone tissue regeneration inside a specific type of scaffold

Bone tissue regeneration using scaffolds is receiving an increasing interest in orthopedic surgery and tissue engineering applications. In this study, we present the geometrical characterization of a specific family of scaffolds based on a face cubic centered (FCC) arrangement of empty pores leading to analytical formulae of porosity and specific surface. The effective behavior of those scaffolds, in terms of mechanical properties and permeability, is evaluated through the asymptotic homogenization theory applied to a representative volume element identified with the unit cell FCC. Bone growth into the scaffold is estimated by means of a phenomenological model that considers a macroscopic effective stress as the mechanical stimulus that regulates bone formation. Cell migration within the scaffold is modeled as a diffusion process based on Fick's law which allows us to estimate the cell invasion into the scaffold microstructure. The proposed model considers that bone growth velocity is proportional to the concentration of cells and regulated by the mechanical stimulus. This model allows us to explore what happens within the scaffold, the surrounding bone and their interaction. The mathematical model has been numerically implemented and qualitatively compared with previous experimental results found in the literature for a scaffold implanted in the femoral condyle of a rabbit. Specifically, the model predicts around 19 and 23% of bone regeneration for non-grafted and grafted scaffolds, respectively, both with an initial porosity of 76%.     

A mathematical model for the freezing process in biological tissue

A mathematical model has been developed to study the process of freezing in biological organs. The model consists of a repetitive unit structure comprising a cylinder of tissue with an axial blood vessel (Krogh cylinder) and it is analysed by the methods of irreversible thermodynamics. The mathematical simulation of the freezing process in liver tissue compares remarkably well with experimental data on the structure of tissue frozen under controlled thermal conditions and the response of liver cells to changes in cooling rate. The study also supports the proposal that the damage mechanism responsible for the lack of success in attempts to preserve tissue in a frozen state, under conditions in which cells in suspension survive freezing, is direct mechanical damage caused by the formation of ice in the vascular system.     

On a response characteristic of a mathematical neuron model

A mathematical neuron model in the form of a nonlinear difference equation is proposed and its response characteristic is investigated.If a sequence of pulses with a fixed frequency is applied to the neuron model as an input, and the amplitude of the input pulses is progressively decreased, the firing frequency of the neuron model, regarded as the output, also decreases. The relationship between them is quite complicated, but a mathematical investigation reveals that it takes the form of an extended Cantor's function. This result explains the unusual and unsuspected phenomenon which was found by L. D. Harmon in experimental studies with his transistor neuron models.Besides this, as an analogue of our mathematical neuron model, a very simple circuit composed of a delay line and a negative resistance element is presented and discussed.     

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.     

Oxygen radicals, inflammation, and tissue injury

Inflammatory reactions often result in the activation and recruitment of phagocytic cells (e.g., neutrophils and/or tissue macrophages) whose products result in injury to the tissue. In killing of endothelial cells by activated neutrophils as well as in lung injury produced by either activated neutrophils or activated macrophages there is evidence that H2O2 and iron play a role. HO. may be a key oxygen product related to the process of injury. Endothelial cells in some vascular compartments may be susceptible to neutrophil mediated injury in a manner that is independent of oxygen radicals. On the basis of in vitro observations, a synergy exits between platelets and neutrophils, resulting in enhanced oxygen radical formation by the latter. Finally, the cytokines, interleukin 1 and tumor necrosis factor, released from macrophages have both direct stimulatory effects on oxygen radical formation in neutrophils and can "prime" macrophages for enhanced oxygen radical responses to other agonists. Cytokines may also alter endothelial cells rendering them more susceptible to oxygen radical mediated injury by neutrophils. This suggests a complex network of interactions between phagocytic cells and peptide mediators, the result of which is acute, oxygen radical mediated tissue injury.     

A mathematical model for fluid shear-sensitive 3D tissue construct development

This research studies dynamic culture for 3D tissue construct development with computational fluid dynamics. It proposes a mathematical model to evaluate the impact of flow rates and flow shear stress on cell growth in 3D constructs under perfusion. The modeling results show that dynamic flow, even at flow rate as low as 0.002 cm/s, can support much better mass exchange, higher cell number, and more even cell and nutrient distribution compared to static culture. Higher flow rate can further improve nutrient supply and mass exchange in the construct, promoting better nutritious environment and cell proliferation compared to lower flow rate. In addition, consideration of flow shear stress predicts much higher cell number in the construct compared to that without shear consideration. While the nutrient can dominate shear stress in influencing cell proliferation, the shear effect increases with flow rate. The proposed model helps tissue engineers better understand the cell-flow relationship at the molecular level during dynamic culture.     

On a mathematical model describing the aggregation of amoebae

In this paper an extension of a mathematical model of Keller and Segel (1970) describing the aggregation of amoebae is presented. In their paper (Keller and Segel, 1970) they showed that the onset of the aggregation could be viewed as a spatial instability. Their instability condition involved diffusion constants of the cyclic AMP and of the amoebae as well as a constant describing the chemotactic behavior of the amoebae. In our case we consider a temporal instability that depends only on the kinetics of cyclic AMP production, degradation and transport through the cell wall. Our model then explains the oscillatory behavior of the cyclic AMP in well-stirred suspensions of amoebae. In addition we discuss existence and non-existence of nonuniform steady states of the nonlinear parabolic system involved.     

Cyclooxygenase-2 deficiency attenuates adipose tissue differentiation and inflammation in mice

Obesity is associated with a variety of disorders and is a significant health problem in developed countries. One factor controlling the level of adiposity is the differentiation of cells into adipocytes. Adipocyte differentiation requires expression of peroxisome proliferator-activated receptor γ (PPARγ), which is activated by ligands to regulate expression of genes involved in adipocyte differentiation. Although 15-deoxy-Δ(12,14)-prostaglandin (PG) J(2) (15d-PGJ(2)) has long been known to be a potent activator of PPARγ, the importance of its synthesis in adipose tissue in vivo is not clear. The current study utilized mice deficient in cyclooxygenase-2 (COX-2) to examine the role of COX-2-derived PGs as in vivo modulators of adiposity. As compared with strain- and age-matched wild-type controls, the genetic deficiency of COX-2 resulted in a significant reduction in total body weight and percent body fat. Although there were no significant differences in food consumption between groups, COX-2-deficient mice showed increased metabolic activity. Epididymal adipose tissue from wild-type mice produced a significantly greater level of 15d-PGJ(2), as compared with adipose tissue isolated from mice deficient in COX-2. Furthermore, production of the precursor required for 15d-PGJ(2) formation, PGD(2), was also significantly reduced in COX-2-deficient adipose tissue. The expression of markers for differentiated adipocytes was significantly reduced in adipose tissue from COX-2-deficient mice, whereas preadipocyte marker expression was increased. Macrophage-dependent inflammation was also significantly reduced in adipose tissue of COX-2-deficient mice. These findings suggest that reduced adiposity in COX-2-deficient mice results from attenuated PPARγ ligand production and adipocyte differentiation.     

A mathematical model for describing the metastasis of cancer in bone tissue

Metastasis is the rapid proliferation of cancer cells (secondary tumour) at a specific place, generally leading to death. This occurs at anatomical parts providing the necessary environment for vascularity, oxygen and food to hide their actions and trigger the rapid growth of cancer. Prostate and breast cancers, for example, use bone marrow for their proliferation. Bone-supporting cancer cells thus adapt to the environment, mimicking the behaviour of genetic and molecular bone cells. Evidence of this has been given in Cecchini et al. (2005, EAU Update Ser. 3:214-226), providing arguments such as how cancer cell growth is so active during bone reabsorption. This paper simulates metastasis activation in bone marrow. A mathematical model has been developed involving the activation of molecules from bone tissue cells, which are necessary for cancer to proliferate. Here, we simulate two forms of secondary tumour growth depending on the type of metastasis: osteosclerosis and osteolysis.     

From array to array: Confirmation of genomic gains and losses discovered by array-based comparative genomic hybridization utilizing fluorescence in situ hybridization on tissue microarrays

The combination of array-based comparative genomic hybridization (CGH) with fluorescence in situ hybridization utilizing custom-designed bacterial artificial chromosome (BAC) probes applied to tissue microarrays represents a powerful compendium of techniques–greatly enhancing the throughput of genomic analysis and subsequent target validation. Such approach can be automated at various levels and allows managing large volume of targets and samples in a few experiments. As such, this approach facilitates discovery, validation and implementation of findings in the process of identification of new diagnostic, prognostic and potentially therapeutic molecular markers.     

Cytokine expression due to Helicobacter pylori in a tissue culture model

Helicobacter pylori, in recent years, has been recognized as the major causative agent in chronic gastritis and peptic ulcer disease in humans. H. pylori is a ubiquitous organism, with at least half of the world’s population infected. Of those individuals with peptic ulcer disease, it is estimated that 90% of cases are caused by H. pylori. Currently, the efficacy of therapies is starting to decline due to increasing resistance rates, especially towards clarithromycin. Due to this, new therapies are needed to combat this bacterium. It is hypothesized that cytokine release (especially interleukin-1β, -6, -8, and TNF-α) due to H. pylori infection and the subsequent influx of inflammatory cells causes a massive release of reactive oxygen species (ROS) during the inflammatory reaction. The ROS then cause the pathologic changes seen in the infected tissues. In this study, human gastric adenocarcinoma cell line ATCC 1739 (a cell line not previously evaluated) was examined for its production of interleukin-1β, -6, -8, and TNF-α when cocultured in a ratio of 10:1 H. pylori to adenocarcinoma cells, to determine its value as a model to demonstrate the inflammatory response. Results from this study indicated that ATCC 1739 cells only reliably produced IL-8 when cocultured with H. pylori and stimulated with TNF-α. The production of IL-1β, IL-6, and TNF-α by the ATCC 1739 cells was no different in H. pylori-exposed cells than non-exposed cells. It was concluded that the ATCC 1739 cell line is not suitable to study the effects of coculture with H. pylori on cytokine production.     

Identification of rheological properties of human body surface tissue

According to World Health Organization obesity is one of the greatest public health challenges of the 21st century. It has tripled since the 1980s and the numbers of those affected continue to rise at an alarming rate, especially among children. There are number of devices that act as a prevention measure to boost person?s motivation for physical activity and its levels. The placement of these devices is not restricted thus the measurement errors that appear because of the body rheology, clothes, etc. cannot be eliminated. The main objective of this work is to introduce a tool that can be applied directly to process measured accelerations so human body surface tissue induced errors can be reduced. Both the modeling and experimental techniques are proposed to identify body tissue rheological properties and prelate them to body mass index. Multi-level computational model composed from measurement device model and human body surface tissue rheological model is developed. Human body surface tissue induced inaccuracies can increase the magnitude of measured accelerations up to 34% when accelerations of the magnitude of up to 27 m/s² are measured. Although the timeframe of those disruptions are short – up to 0.2 s – they still result in increased overall measurement error.     

Mathematical model for the estimation of hemodynamic and oxygenation variables by tissue spectroscopy

This article presents a quasistatic, compartmental model of tissue-level hemodynamics and oxygenation that leads to a set of formulas, which is suitable to calculate important physiological variables from the mean tissue concentration and saturation of hemoglobin, measured by tissue spectroscopy. Dimensioned quantities are represented relative to their baseline value in the equations (relative value = perturbed/baseline). All model parameters are non-dimensional. The model is based and extends on a number of previous works: previous models of similar aim and scope are consolidated, and every critical assumptions and approximations are treated explicitly; extensions include for example the incorporation of the Fahraeus-effect and the separate estimation of the volume changes of the arterial and the venous compartments. The information content of spectroscopic data alone is shown to be valuable, but limited: the relative venous volume, the oxygen extraction fraction and the relative cellulovascular coupling (defined as the ratio of blood flow and oxygen consumption) can be calculated from these data, if the alterations in arterial blood volume are negligible. The number of variables estimated by the derived formulas can be increased if local blood flow is measured simultaneously: in this case, the relative arterial and venous volume and resistance, the oxygen extraction fraction, and the relative oxygen consumption can be determined. Given that this model considers arterial blood pressure, saturation and hematocrit as its inputs, when measured, the model becomes applicable in such conditions as hyper- or hypotension, hypoxic hypoxia, hemodilution and hemorrhage, where these variables do change. The estimation of the changes in arterial resistance can be applied to estimate the extent of an autoregulatory response.