Mechanical Alterations in airway smooth muscle after interaction with indoor pollutant – A mathematical model.

The viscoelasticity of mammalian lung is determined by the mechanical properties and structural regulation of the airway smooth muscle (ASM). The exposure to polluted air may deteriorate these properties with harmful consequences to individual health. Formaldehyde (FA) is an important indoor pollutant found among volatile organic compounds. This pollutant permeates through the smooth muscle tissue forming covalent bonds between proteins in the extracellular matrix and intracellular protein structure changing mechanical properties of ASM and inducing asthma symptoms, such as airway hyperresponsiveness, even at low concentrations. In the experimental scenario, the mechanical effect of FA is the stiffening of the tissue, but the mechanism behind this effect is not fully understood. Thus, the aim of this study is to reproduce the mechanical behavior of the ASM, such as contraction and stretching, under FA action or not. For this, it was created a two-dimensional viscoelastic network model based on Voronoi tessellation solved using Runge-Kutta method of fourth order. The equilibrium configuration was reached when the forces in different parts of the network were equal. This model simulates the mechanical behavior of ASM through of a network of dashpots and springs. This dashpot-spring mechanical coupling mimics the composition of the actomyosin machinery of ASM through the contraction of springs to a minimum length. We hypothesized that formation of covalent bonds, due to the FA action, can be represented in the model by a simple change in the elastic constant of the springs, while the action of methacholine (MCh) reduce the equilibrium length of the spring. A sigmoid curve of tension as a function of MCh doses was obtained, showing increased tension when the muscle strip was exposed to FA. Our simulations suggest that FA, at a concentration of 0.1 ppm, can affect the elastic properties of the smooth muscle ¯bers by a factor of 120%. We also analyze the dynamic mechanical properties, observing the viscous and elastic behavior of the network. Finally, the proposed model, although simple, incorporates the phenomenology of both MCh and FA and reproduces experimental results observed with in vitro exposure of smooth muscle to FA. Thus, this new mechanical approach incorporates several well know features of the contractile system of the cells in a tissue level model. The model can also be used in different biological scales.CNPqFAPES

Mechanical alterations in airway smooth muscle after interaction with indoor pollutant - A\ud mathematical model

The viscoelasticity of mammalian lung is determined by the mechanical properties and structural regulation of the airway smooth muscle (ASM). The exposure to polluted air may deteriorate these properties with harmful consequences to individual health. Formaldehyde (FA) is an important indoor pollutant found among volatile organic compounds. This pollutant permeates through the smooth muscle tissue forming covalent bonds between proteins in the extracellular matrix and intracellular protein structure changing mechanical properties of ASM and inducing asthma symptoms, such as airway hyperresponsiveness, even at low concentrations. In the experimental scenario, the mechanical effect of FA is the stiffening of the tissue, but the mechanism behind this effect is not fully w1derstood. Thus, the aim of this study is to reproduce the mechanical behavior of the ASM, such as contraction and stretching, under FA action or not. For this, it was created a two-dimensional viscoelastic network model based on Voronoi tessellation solved using Runge-Kutta method of fourth order. The equilibrium configuration was reached when the forces in different parts of the network were equal. This model simulates the mechanical behavior of ASM through of a network of dashpots and springs. This dashpot-spring mechanical coupling mimics the composition of the actomyosin machinery of ASM through the contraction of springs to a minimum length. We hypothesized that formation of covalent bonds, due to the FA action, can be represented in the model by a simple change in the elastic constant of the springs, while the action of methacholinc (MCh) reduce the equilibrium length of the spring. A sigmoid curve of tension as a function of MCh doses was obtained, showing increased tension when the muscle strip was exposed to FA. Our simulations suggest that FA, at a concentration of 0.1 ppm, can affect the elastic properties of the smooth muscle fibers by a factor of 120%. We also analyze the dynamic mechanical properties, observing the viscous and elastic behavior of the network. Finally, the proposed model, although simple, ir1corporates the phenomenology of both MCh and FA and reproduces experirnental results observed with ir1 vitro exposure of smooth muscle to .FA. Thus, this new mechanical approach incorporates several well know features of the contractile system of the cells ir1 a tissue level model. The model can also be used in different biological scales.CNPqFAPES

Proposition of a mathematical model to study the mechanical change of the smooth muscle of the trachea of Wistar rats exposed to formaldehyde solution and subjected to increasing doses of a contractile agent

A viscoelasticidade do pulmão do mamífero é determinada principalmente pelas propriedades mecânicas, estrutura e regulação do músculo liso das vias aéreas. A exposição ao ar poluído pode deteriorar essas propriedades com consequências danosas à saúde individual. O formaldeído é um importante poluente presente em ambientes internos que adentra o músculo liso formando ligações covalentes entre proteínas da matriz extracelular e da estrutura intracelular deteriorando algumas funções do músculo liso das vias aéreas, alterando propriedades mecânicas e induzindo a hiperresponsividade. O primeiro objetivo desse trabalho foi desenvolver um modelo de rede viscoelástica bidimensional baseada na tesselação de Voronoi para reproduzir algumas propriedades mecânicas do músculo liso de via aérea a nível de tecido. O segundo objetivo foi comparar os resultados obtidos com o nosso modelo com aqueles previamente observados em experimentos com tiras de tecido após a exposição ao formaldeído. Nosso modelo simula as propriedades mecânicas do músculo liso de via aérea usando um conjunto de molas e amortecedores. Esse conjunto de molas e amortecedores não somente mimetiza as propriedades viscoeláticas do músculo liso mas também o aparato contrátil das células. Nós hipotetizamos que a formação de ligações covalentes, devido à ação do formaldeído, pode ser representada no modelo por uma alteração simples na constante elástica das molas, enquanto que a ação da metacolina reduz o tamanho da mola. Nosso modelo é hábil para reproduzir uma medida de força isométrica onde o músculo liso é sujeito a um agente contrátil, com e sem exposição in vitro ao formaldeído. Assim, a nossa nova abordagem mecanicista incorpora diversas propriedades bem conhecidas do sistema contrátil das células em um tecido a nível de modelo. O modelo pode também ser usado em diferentes escalas biológicasThe viscoelastic properties of the mammalian lung is mainly determined by the mechanical properties, structure and regulation of the airways smooth muscle. The exposure to polluted air may deteriorate these properties with harmful consequences to individual health. Formaldehyde is an important indoor pollutant that permeate through the smooth muscle tissue forming covalent bonds between proteins in the extracellular matrix and intracellular protein structure deteriorating some of the airways smooth muscle functions, changing mechanical properties, and inducing hyperresponsiveness. The first objectives of this work was to develop a two-dimensional viscoelastic network model based on Voronoi tessellation to reproduce some of the mechanical properties of airway smooth muscle at the tissue level. The second objective was to compare the results obtained with our model with those previously observed in tissue strip experiments after the tissue exposure to formaldehyde. Our model simulates the mechanical properties of airway smooth muscle using a set of springs and dashpot. This set of springs and dashpot not only mimic the viscoelastic properties of the smooth muscle but also the cells contractile apparatus. We hypothesize that the formation of covalent bonds, due to the action formaldehyde, can be represented in the model by a simple change in the elastic constant of the springs, while the action of methacholine reduce the size of the spring. Our model is able to reproduce an isometric force measurement, where the smooth muscle is subjected to a titration of a contractile agent, with and without an in vitro exposure to formaldehyde. Thus, our new mechanistic approaches incorporates several well know features of the contractile system of the cells in a tissue level model. The model can also be used in different biological scale

Proposition of a mathematical model to study the mechanical change of the smooth muscle of the trachea of Wistar rats exposed to formaldehyde solution and subjected to increasing doses of a contractile agent

A viscoelasticidade do pulmão do mamífero é determinada principalmente pelas propriedades mecânicas, estrutura e regulação do músculo liso das vias aéreas. A exposição ao ar poluído pode deteriorar essas propriedades com consequências danosas à saúde individual. O formaldeído é um importante poluente presente em ambientes internos que adentra o músculo liso formando ligações covalentes entre proteínas da matriz extracelular e da estrutura intracelular deteriorando algumas funções do músculo liso das vias aéreas, alterando propriedades mecânicas e induzindo a hiperresponsividade. O primeiro objetivo desse trabalho foi desenvolver um modelo de rede viscoelástica bidimensional baseada na tesselação de Voronoi para reproduzir algumas propriedades mecânicas do músculo liso de via aérea a nível de tecido. O segundo objetivo foi comparar os resultados obtidos com o nosso modelo com aqueles previamente observados em experimentos com tiras de tecido após a exposição ao formaldeído. Nosso modelo simula as propriedades mecânicas do músculo liso de via aérea usando um conjunto de molas e amortecedores. Esse conjunto de molas e amortecedores não somente mimetiza as propriedades viscoeláticas do músculo liso mas também o aparato contrátil das células. Nós hipotetizamos que a formação de ligações covalentes, devido à ação do formaldeído, pode ser representada no modelo por uma alteração simples na constante elástica das molas, enquanto que a ação da metacolina reduz o tamanho da mola. Nosso modelo é hábil para reproduzir uma medida de força isométrica onde o músculo liso é sujeito a um agente contrátil, com e sem exposição in vitro ao formaldeído. Assim, a nossa nova abordagem mecanicista incorpora diversas propriedades bem conhecidas do sistema contrátil das células em um tecido a nível de modelo. O modelo pode também ser usado em diferentes escalas biológicasThe viscoelastic properties of the mammalian lung is mainly determined by the mechanical properties, structure and regulation of the airways smooth muscle. The exposure to polluted air may deteriorate these properties with harmful consequences to individual health. Formaldehyde is an important indoor pollutant that permeate through the smooth muscle tissue forming covalent bonds between proteins in the extracellular matrix and intracellular protein structure deteriorating some of the airways smooth muscle functions, changing mechanical properties, and inducing hyperresponsiveness. The first objectives of this work was to develop a two-dimensional viscoelastic network model based on Voronoi tessellation to reproduce some of the mechanical properties of airway smooth muscle at the tissue level. The second objective was to compare the results obtained with our model with those previously observed in tissue strip experiments after the tissue exposure to formaldehyde. Our model simulates the mechanical properties of airway smooth muscle using a set of springs and dashpot. This set of springs and dashpot not only mimic the viscoelastic properties of the smooth muscle but also the cells contractile apparatus. We hypothesize that the formation of covalent bonds, due to the action formaldehyde, can be represented in the model by a simple change in the elastic constant of the springs, while the action of methacholine reduce the size of the spring. Our model is able to reproduce an isometric force measurement, where the smooth muscle is subjected to a titration of a contractile agent, with and without an in vitro exposure to formaldehyde. Thus, our new mechanistic approaches incorporates several well know features of the contractile system of the cells in a tissue level model. The model can also be used in different biological scale