A physically motivated constitutive model for cell-mediated compaction and collagen remodeling in soft tissues

Collagen is the main load-bearing component of many soft tissues and has a large influence on the mechanical behavior of tissues when exposed to mechanical loading. Therefore, it is important to increase our understanding of collagen remodeling in soft tissues to understand the mechanisms behind pathologies and to control the development of the collagen network in engineered tissues. In the present study, a constitutive model was developed by coupling a recently developed model describing the orientation and contractile stresses exerted by cells in response to mechanical stimuli to physically motivated collagen remodeling laws. In addition, cell-mediated contraction of the collagen fibers was included as a mechanism for tissue compaction. The model appeared to be successful in predicting a range of experimental observations, which are (1) the change in transition stretch of periosteum after remodeling at different applied stretches, (2) the compaction and alignment of collagen fibers in tissue-engineered strips, (3) the fiber alignment in cruciform gels with different arm widths, and (4) the alignment of collagen fibers in engineered vascular grafts. Moreover, by changing the boundary conditions, the model was able to predict a helical architecture in the vascular graft without assuming the presence of two helical fiber families a priori. Ultimately, this model may help to increase our understanding of collagen remodeling in physiological and pathological conditions, and it may provide a tool for determining the optimal experimental conditions for obtaining native-like collagen architectures in engineered tissues.     

A thermodynamically motivated model for stress-fiber reorganization

We present a model for stress-fiber reorganization and the associated contractility that includes both the kinetics of stress-fiber formation and dissociation as well as the kinetics of stress-fiber remodeling. These kinetics are motivated by considering the enthalpies of the actin/myosin functional units that constitute the stress fibers. The stress, strain and strain rate dependence of the stress-fiber dynamics are natural outcomes of the approach. The model is presented in a general 3D framework and includes the transport of the unbound stress-fiber proteins. Predictions of the model for a range of cyclic loadings are illustrated to rationalize hitherto apparently contrasting observations. These observations include: (1) For strain amplitudes around 10 % and cyclic frequencies of about 1 Hz, stress fibers align perpendicular to the straining direction in cells subjected to cyclic straining on a 2D substrate while the stress fibers align parallel with the straining direction in cells constrained in a 3D tissue. (2) At lower applied cyclic frequencies, stress fibers in cells on 2D substrates display no sensitivity to symmetric applied strain versus time waveforms but realign in response to applied loadings with a fast lengthening rate and slow shortening. (3) At very low applied cyclic frequencies (on the order of mHz) with symmetric strain versus time waveforms, cells on 2D substrates orient perpendicular to the direction of cyclic straining above a critical strain amplitude.     

A biologically motivated and analytically soluble model of collective oscillations in the cortex

. Feature linking and pattern separation are shown to be performed as simultaneous processes by a highly connected auto-associative network of spiking neurons (spike response model). In principle, many (e.g., with nine) patterns can be separated, but with a biological set of parameters the number is limited to four. The patterns have been learned by an asymmetric hebbian rule that can handle a low activity which may vary from pattern to pattern (in a range between 4% and 7%). Spikes are generated by a threshold process and – with some delay – transmitted to postsynaptic neurons. There they evoke an excitatory or inhibitory postsynaptic potential (EPSP or IPSP). Spike emission is followed by an absolute refractory period (1 ms) and activates an inhibitory delay loop that prevents continuous firing. Three different network topologies are discussed, i.e., a structureless fully connected system, a network composed of two ‘hemispheres’, and finally a hierarchical network with four subsystems that represent different ‘functions’ and interact via feedforward and feedback connections. Functional feedback turns out to be essential for context-sensitive binding. The coherence between the two hemispheres is dependent on the interhemispheric delays. If these are on average too large, the two hemispheres oscillate coherently by themselves but phase-shifted by half a period with respect to each other. Received: 16 June 1993/Accepted in revised form: 24 March 1994     

A biologically motivated and analytically soluble model of collective oscillations in the cortex

A model of an associative network of spiking neurons with stationary states, globally locked oscillations, and weakly locked oscillatory states is presented and analyzed. The network is close to biology in the following sense. First, the neurons spike and our model includes an absolute refractory period after each spike. Second, we consider a distribution of axonal delay times. Finally, we describe synaptic signal transmission by excitatory and inhibitory potentials (EPSP and IPSP) with a realistic shape, that is, through a response kernel. During retrieval of a pattern, all active neurons exhibit periodic spike bursts which may or may not be synchronized (locked) into a coherent oscillation. We derive an analytical condition of locking and calculate the period of collective activity during oscillatory retrieval. In a stationary retrieval state, the overlap assumes a constant value proportional to the mean firing rate of the neurons. It is argued that in a biological network an intermediate scenario of weak locking is most likely.     

The influence of boundary conditions and protein availability on the remodeling of cardiomyocytes

Biomechanics and Modeling in Mechanobiology - The heart muscle is capable of growing and remodeling in response to changes in its mechanical and hormonal environment. While this capability is...     

Electrical stimulation of cardiomyocytes activates mitochondrial matrix metalloproteinase causing electrical remodeling

Cardiac arrhythmias, instigated by mechanical and electrical remodeling, are associated with activation of extracellular matrix metalloproteinases (MMPs). However, the connection between intracellular MMPs activation and arrhythmogenesis is not well established. Previously, we determined localization of MMP in the mitochondria using confocal microscopy. We tested the hypothesis that electrical pacing induces the activation of mitochondrial MMP (mtMMP) and is associated with myocyte mechanical dysfunction. Myocytes were isolated and field stimulated at 1 and 4 Hz. Myocyte mechanics and calcium transient was studied using Ion-Optix system. Mitochondrial MMP-9 activation was evaluated using zymography. There was a 25% increase in 1 Hz and 40% increase in 4 Hz stimulation. We observed an increase in mtMMP activation with increase in electrical pacing compared to 0 Hz with a significant increase (p < 0.05, n = 3). Field stimulation at 4 Hz decreased cell re-lengthening. The levels of calcium transient were reduced with increase in contraction frequency. We conclude that electrical stimulation activates mtMMP-9 that is associated with myocyte mechanical dysfunction.     

A three-dimensional model of fluid-structural interactions for quantifying the contractile force for cardiomyocytes on hybrid biopolymer microcantilever

Quantitatively analysis of the contractility of cardiomyocytes is important for understanding the mechanism of heart failure as well as the molecular alterations in diseased heart cells. This paper presents a realistic computational model, which considers the three-dimensional fluid-structural interactions (FSI), to quantify the contractile force of cardiomyocytes on hybrid biopolymer microcantilevers. Prior to this study, only static modeling of the microscale cellular force has been reported. This study modeled the dynamics of cardiomyocytes on microcantilevers in a medium using the FSI. This realistic model was compared with static finite element modeling (FEM) analysis and the Stoney's equation-based analytical solution, and was validated by the deflections of the microcantilevers in the experimental results. Using harmonic response analysis in FSI modeling, the motion of a hybrid biopolymer microcantilever in the medium was identified as a second-order system and the influence of the dynamics of cardiomyocytes could be evaluated quantitatively.     

A biphasic model for sinusoidal liver perfusion remodeling after outflow obstruction

Liver resection can lead to focal outflow obstruction due to transection of hepatic veins. Outflow obstruction may cause additional damage to the small remnant liver. Drainage of the obstructed territories is reestablished via dilatation of sinusoids. Subsequently, sinusoidal canals are formed draining the blood from the obstructed territory to the neighboring unobstructed territories. We raised the phenomenological hypothesis that the blood pressure gradient is the main driving force for the formation of sinusoidal vascular canals. We generated a biphasic mechanical model to describe this vascular remodeling process in relation to the variable pressure gradient. Therefore, we introduced a transverse isotropic permeability relation as well as an evolutional optimization rule to describe the relationship between pressure gradient and the direction of the sinusoidal blood flow in the fluid phase. As a next step, we developed a framework for the calculation concept including the representation of the governing weak formulations. Then, we examined a representative numerical example with simulation of the blood flow under both conditions, the physiological situation as well as after outflow obstruction. Doing so, we were able to reproduce numerically the experimentally observed process of reestablishing hepatic venous drainage via redirection of blood flow and formation of new vascular structures in respect to the fluid flow. The calculated results support the hypothesis that the reorientation of blood flow mainly depends on the pressure gradient. Further investigations are needed to determine the micromechanical influences on the reorientation of the sinusoids.     

A mechano-chemo-biological model for bone remodeling with a new mechano-chemo-transduction approach

Biomechanics and Modeling in Mechanobiology - Bone remodeling is a fundamental biological process that develops in bone tissue along its whole lifetime. It refers to a continuous bone...     

A mathematical model for the determination of steady-state cardiolipin remodeling mechanisms using lipidomic data

Technical advances in lipidomic analysis have generated tremendous amounts of quantitative lipid molecular species data, whose value has not been fully explored. We describe a novel computational method to infer mechanisms of de novo lipid synthesis and remodeling from lipidomic data. We focus on the mitochondrial-specific lipid cardiolipin (CL), a polyglycerol phospholipid with four acyl chains. The lengths and degree of unsaturation of these acyl chains vary across CL molecules, and regulation of these differences is important for mitochondrial energy metabolism. We developed a novel mathematical approach to determine mechanisms controlling the steady-state distribution of acyl chain combinations in CL . We analyzed mitochondrial lipids from 18 types of steady-state samples, each with at least 3 replicates, from mouse brain, heart, lung, liver, tumor cells, and tumors grown in vitro. Using a mathematical model for the CL remodeling mechanisms and a maximum likelihood approach to infer parameters, we found that for most samples the four chain positions have an independent and identical distribution, indicating they are remodeled by the same processes. Furthermore, for most brain samples and liver, the distribution of acyl chains is well-fit by a simple linear combination of the pools of acyl chains in phosphatidylcholine (PC), phosphatidylethanolamine (PE), and phosphatidylglycerol (PG). This suggests that headgroup chemistry is the key determinant of acyl donation into CL, with chain length/saturation less important. This canonical remodeling behavior appears damaged in some tumor samples, which display a consistent excess of CL molecules having particular masses. For heart and lung, the "proportional incorporation" assumption is not adequate to explain the CL distribution, suggesting additional acyl CoA-dependent remodeling that is chain-type specific. Our findings indicate that CL remodeling processes can be described by a small set of quantitative relationships, and that bioinformatic approaches can help determine these processes from high-throughput lipidomic data.     

A study of the viscoelastic effect in a bone remodeling model

The present paper addresses the following question can a simple regulatory bone remodeling model predict effects of viscosity on the trabecular morphology? For that, we propose an extension of a previous bone remodeling model by taking into account the viscosity properties of the tissue. Zener’s law is used to describe the mechanical behavior of the bone and a specific law of the apparent bone density rate is proposed. Based on stability analysis, numerical simulations are then performed to investigate the viscosity role on simulations of the bone remodeling process. We show that the viscous contribution affects the evolution of the apparent bone density, by slowing down the adaptation process, which seems to be confirmed by simulations with real data obtained from rat tibia.     

A computational model of intussusceptive microvascular growth and remodeling

Non-sprouting angiogenesis, also known as intussusceptive angiogenesis (IA), is an important modality of blood vessel morphogenesis in growing tissues. We present a novel computational framework for simulation of IA to answer some of the questions concerning the underlying mechanisms of the remodeling process. The model relies on mechanical interactions between blood and tissue, includes the structural maturation of the vessel wall, and is controlled by stimulating or inhibiting chemical agents. The model provides a simple explanation for the formation of microvessels and bifurcations from capillaries via IA, allowing for both maintenance and avoidance of shunt vessels. Detailed hemodynamic and transport properties for oxygen, metabolites or growth factors can be predicted. The model is an in silico framework for testing certain conceptual ideas about the mechanisms of intussusceptive growth and remodeling, in particular those related to mechanical and transport phenomena.     

G-CSF prevents cardiac remodeling after myocardial infarction by activating the Jak-Stat pathway in cardiomyocytes

Granulocyte colony-stimulating factor (G-CSF) was reported to induce myocardial regeneration by promoting mobilization of bone marrow stem cells to the injured heart after myocardial infarction, but the precise mechanisms of the beneficial effects of G-CSF are not fully understood. Here we show that G-CSF acts directly on cardiomyocytes and promotes their survival after myocardial infarction. G-CSF receptor was expressed on cardiomyocytes and G-CSF activated the Jak/Stat pathway in cardiomyocytes. The G-CSF treatment did not affect initial infarct size at 3 d but improved cardiac function as early as 1 week after myocardial infarction. Moreover, the beneficial effects of G-CSF on cardiac function were reduced by delayed start of the treatment. G-CSF induced antiapoptotic proteins and inhibited apoptotic death of cardiomyocytes in the infarcted hearts. G-CSF also reduced apoptosis of endothelial cells and increased vascularization in the infarcted hearts, further protecting against ischemic injury. All these effects of G-CSF on infarcted hearts were abolished by overexpression of a dominant-negative mutant Stat3 protein in cardiomyocytes. These results suggest that G-CSF promotes survival of cardiac myocytes and prevents left ventricular remodeling after myocardial infarction through the functional communication between cardiomyocytes and noncardiomyocytes.     

New insights into autocrine cytokines produced by ischemic cardiomyocytes and ventricular remodeling

<正>Ischemic heart disease is one of the leading causes of death in the world.Although modern therapy of acute myocardial infarction(AMI)can reduce infarct size and result in an increased early survival rate,heart failure after AMI is still a major problem in survivors.Ventricular remodeling is critically important in heart failure after ischemia.It is characte-     

A stochastic model for disease transmission in a managed herd, motivated by Neospora caninum amongst dairy cattle

A stochastic model for the spread of Neospora caninum infection within a herd of dairy cattle is studied, in particular the long-term (equilibrium) behaviour of the model. The model incorporates the interesting feature that total herd size is constrained to lie within a fairly small interval, but not held exactly constant. Approximations for the joint distribution of numbers of susceptible and infected individuals present in equilibrium are derived based upon a diffusion approximation to the infection process. The effect of both 'typical herd size' and 'the amount of permitted variation in herd size' upon disease prevalence in equilibrium are considered using both the exact equilibrium distribution of the process and our approximations.     

A 3-D constrained mixture model for mechanically mediated vascular growth and remodeling

In contrast to the widely applied approach to model soft tissue remodeling employing the concept of volumetric growth, microstructurally motivated models are capable of capturing many of the underlying mechanisms of growth and remodeling; i.e., the production, removal, and remodeling of individual constituents at different rates and to different extents. A 3-dimensional constrained mixture computational framework has been developed for vascular growth and remodeling, considering new, microstructurally motivated kinematics and constitutive equations and new stress and muscle activation mediated evolution equations. Our computational results for alterations in flow and pressure, using reasonable physiological values for rates of constituent growth and turnover, concur with findings in the literature. For example, for flow-induced remodeling, our simulations predict that, although the wall shear stress is restored completely, the circumferential stress is not restored employing realistic physiological rate parameters. Also, our simulations predict different levels of thickening on inner versus outer wall locations, as shown in numerous reports of pressure-induced remodeling. Whereas the simulations are meant to be illustrative, they serve to highlight the experimental data currently lacking to fully quantify mechanically mediated adaptations in the vasculature.     

Extracellular matrix remodeling is associated with the survival of cardiomyocytes in the subendocardial region of the ischemic myocardium

A significant amount of cardiomyocytes in subendocardial region survive from ischemic insults. In order to understand the mechanism by which these cardiomyocytes survive, the present study was undertaken to examine changes in these surviving cardiomyocytes and their extracellular matrix. Male C57BL/6 mice aged 8–12 weeks old were subjected to a permanent left anterior descending coronary artery ligation to induce ischemic injury. The hearts were collected at 1, 4, 7, or 28 days after the surgery and examined by histology. At day 1 after left anterior descending ligation, there was a significant loss of cardiomyocytes through apoptosis, but a proportion of cardiomyocytes were surviving in the subendocardial region. The surviving cardiomyocytes were gradually changed from rod-shaped to round-shaped, and appeared disconnected. Connexin 43, an important gap junction protein, was significantly decreased, and collagen I and III deposition was significantly increased in the extracellular matrix. Furthermore, lysyl oxidase, a copper-dependent amine oxidase catalyzing the cross-linking of collagens, was significantly increased in the extracellular matrix, paralleled with the surviving cardiomyocytes. Inhibition of lysyl oxidase activity reduced the number of surviving cardiomyocytes. Thus, the extracellular matrix remodeling is correlated with the deformation of cardiomyocytes, and the electrical disconnection between the surviving cardiomyocytes due to connexin 43 depletion and the increase in lysyl oxidase would help these deformed cardiomyocytes survive under ischemic conditions.     

Robust velocity computation from a biologically motivated model of motion perception

Current computational models of motion processing in the primate motion pathway do not cope well with image sequences in which a moving pattern is superimposed upon a static texture. The use of non-linear operations and the need for contrast normalization in motion models mean that the separation of the influences of moving and static patterns on the motion computation is not trivial. Therefore, the response to the superposition of static and moving patterns provides an important means of testing various computational strategies. Here we describe a computational model of motion processing in the visual cortex, one of the advantages of which is that it is highly resistant to interference from static patterns.