Artery buckling analysis using a four-fiber wall model

Artery bent buckling has been suggested as a possible mechanism that leads to artery tortuosity, which is associated with aging, hypertension, atherosclerosis, and other pathological conditions. It is necessary to understand the relationship between microscopic wall structural changes and macroscopic artery buckling behavior. To this end, the objectives of this study were to develop arterial buckling equations using a microstructure-based 4-fiber reinforced wall model, and to simulate the effects of vessel wall microstructural changes on artery buckling. Our results showed that the critical pressure increased nonlinearly with the axial stretch ratio, and the 4-fiber model predicted higher critical buckling pressures than what the Fung model predicted. The buckling equation using the 4-fiber model captured the experimentally observed reduction of critical pressure induced by elastin degradation and collagen fiber orientation changes in the arterial wall. These results improve our understanding of arterial stability and its relationship to microscopic wall remodeling, and the model provides a useful tool for further studies.     

Mechanical instability of normal and aneurysmal arteries

Tortuous arteries associated with aneurysms have been observed in aged patients with atherosclerosis and hypertension. However, the underlying mechanism is poorly understood. The objective of this study was to determine the effect of aneurysms on arterial buckling instability and the effect of buckling on aneurysm wall stress. We investigated the mechanical buckling and post-buckling behavior of normal and aneurysmal carotid arteries and aorta’s using computational simulations and experimental measurements to elucidate the interrelationship between artery buckling and aneurysms. Buckling tests were done in porcine carotid arteries with small aneurysms created using elastase treatment. Parametric studies were done for model aneurysms with orthotropic nonlinear elastic walls using finite element simulations. Our results demonstrated that arteries buckled at a critical buckling pressure and the post-buckling deflection increased nonlinearly with increasing pressure. The presence of an aneurysm can reduce the critical buckling pressure of arteries, although the effect depends on the aneurysm’s dimensions. Buckled aneurysms demonstrated a higher peak wall stress compared to unbuckled aneurysms under the same lumen pressure. We conclude that aneurysmal arteries are vulnerable to mechanical buckling and mechanical buckling could lead to high stresses in the aneurysm wall. Buckling could be a possible mechanism for the development of tortuous aneurysmal arteries such as in the Loeys–Dietz syndrome.     

A molecular dynamics investigation of buckling behaviour of hydrogenated graphene

Molecular dynamics simulations have been performed to characterise the stability behaviour of graphene nanoribbons having different hydrogen coverage, subject to a uniaxial compressive load. The temperature is set at a very low value to circumvent the contribution of thermal agitations. The results show that hydrogen coverage promotes to a rapid drop in the strain of buckling onset due to the effects of easy rotation of newly unsupported sp³ bonds. Furthermore, we have also found a critical value of the hydrogen adsorption above which the declining trend in the stability behaviour of hydrogenated graphene nanoribbons is reversed.     

Evaluation of blood flow velocity waveform in common carotid artery using multi-branched arterial segment model of human arteries

Arteriosclerosis is considered to be a major cause of cardiovascular diseases, which account for approximately 30% of the causes of death in the world. We have recently demonstrated a strong correlation between arteriosclerosis (arterial elasticity) and two characteristics: maximum systolic velocity (S1) and systolic second peak velocity (S2) of the common carotid artery flow velocity waveform (CCFVW). The CCFVW can be measured by using a small portable measuring device. However, there is currently no theoretical evidence supporting the causes of the relation between CCFVW and arterial elasticity, or the origin of the CCFVW characteristics. In this study, the arterial blood flow was simulated using a one-dimensional systemic arterial segments model of human artery in order to conduct a qualitative evaluation of the relationship between arterial elasticity and the characteristics of CCFVW. The simulation was carried out based on the discretized segments with the physical properties of a viscoelastic tube (the cross-sectional area at the proximal and terminal ends, the length, and the compliance per unit area of the tube (C_S)). The findings obtained through this study revealed that the simulated CCFVW had shape similar characteristics to that of the measured CCFVW. Moreover, when the compliance C_S of the model was decreased, the first peak of the simulated-CCFVW decreased and the second peak increased. Further, by separating the anterograde pulse wave and the reflected pulse wave, which form the CCFVW, we found that the decrease in the first peak of the simulated CCFVW was due to the arrival of a reflected pulse wave from the head after the common carotid artery toward the arrival of a anterograde pulse wave ejected directly from the heart and that the increase in the second peak resulted from the arrival of the peak of the reflected pulse wave from the thoracic aorta. These results establish that the CCFVW characteristics contribute to the assessment of arterial elasticity.     

A biomechanical model of Peyronie's disease

Peyronie's disease is a pathological condition of the penis which is characterized by localized ossification of the tunica albuginea. A common symptom of the chronic stage is penile deformity during erection, which is frequently associated with pain and erectile dysfunction. A two-dimensional biomechanical model of the penis was applied to study the development of Peyronie’s disease by simulating the mechanical stress distribution which would result from the interaction of the ossified tunical tissue with other penile soft tissues. The model was solved by using commercial finite element software for a characteristic erectile pressure. The results demonstrate that Peyronie’s plaques may induce intensified stresses around the penile nerves and blood vessels, up to double those in the normal penis. These elevated stresses may cause a painful sensation of neural origin or ischemia in regions of compressed vascular tissue. Severe penile deformities have been shown to develop if Peyronie’s plaques develop only around one of the corpora cavernosa due to the non-homogeneous resistance of the tunica to expansion during erection. The present model can be clinically applied as an aid in the planning process of reconstructive surgery or insertion of a prosthesis.     

An analysis of age-and size-dependent flowering: A critical-production model

Three critical phenomena of flowering can be recognized in nature: critical age, critical initial size and critical switchover size. In order to understand the ecological significance of these flowering phenomena from the viewpoint of matter production, a simple model of flowering phenomean (critical-production model) was studied, assuming that plant flowering is controlled by the productive capacity of the plant (critical-production model, under the condition that plants forecast environmental conditions affecting matter production. Thus, we concluded that all three critical phenomena are various manifestation of the same critical-production principle. Then, using the model simulation, the reliability of each critical phenomenon for securing a given critical production was investigated in relation to the photosynthetic productivity of the habitat. The main predictions obtained from the simulation were as follows: 1) Only annual and biennial plants will show critical age phenomena, and most biennials will be facultative. 2) Among perennials, the critical initial size phenomenon will appear in low productive habitats, whereas in high productive habitats the critical switchover size phenomenon will be observed.     

A theoretical model for fibroblast-controlled growth of saccular cerebral aneurysms

A new theoretical model for the growth of saccular cerebral aneurysms is proposed by extending the recent constitutive framework of Kroon and Holzapfel [2007a. A model for saccular cerebral aneurysm growth by collagen fibre remodelling. J. Theor. Biol. 247, 775-787]. The continuous turnover of collagen is taken to be the driving mechanism in aneurysmal growth. The collagen production rate depends on the magnitude of the cyclic deformation of fibroblasts, caused by the pulsating blood pressure during the cardiac cycle. The volume density of fibroblasts in the aneurysmal tissue is taken to be constant throughout the growth process. The growth model is assessed by considering the inflation of an axisymmetric membranous piece of aneurysmal tissue, with material characteristics representative of a cerebral aneurysm. The diastolic and systolic states of the aneurysm are computed, together with its load-free state. It turns out that the value of collagen pre-stretch, that determines growth speed and stability of the aneurysm, is of pivotal importance. The model is able to predict aneurysms with typical berry-like shapes observed clinically, and the predicted wall stresses correlate well with the experimentally obtained ultimate stresses of this type of tissue. The model predicts that aneurysms should fail when reaching a size of about 1.2-3.6 mm, which is smaller than what has been clinically observed. With some refinements, the model may, however, be used to predict future growth of diagnosed aneurysms.     

Diffusion-controlled reactions of enzymes. An approximate analytic solution of Chou's model

Based on Chou's model, a criterion was derived, by which one can judge whether or not the physical picture of the critical spherical shell described by Chou for an enzyme-substrate fast reaction system can emerge. Furthermore, for those reaction systems with such a physical picture, an approximate analytical solution was presented, which can be easily handled to calculate the upper limit of the diffusion-controlled reaction and the corresponding concentration distribution of substrate molecules on the surface of the major protein outside the active site. The results thus obtained are in good agreement with those computed by Chou et al. through the approach of numerical solution. Furthermore, the physical significance of the criterion and its relation to the critical spherical shell are substantiated during the process of derivation, which is very helpful for gaining an insight into this kind of biomolecular system with surprisingly high reaction rates.     

A bidomain threshold model of propagating calcium waves

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca²⁺) in living cells. Modeling Ca²⁺ release as a threshold process allows the explicit construction of traveling wave solutions to probe the dependence of Ca²⁺ wave speed on physiologically important parameters such as the threshold for Ca²⁺ release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca²⁺ resequestration from the cytosol to the ER, and the total [Ca²⁺] (cytosolic plus ER). Interestingly, linear stability analysis of the bidomain fire-diffuse-fire model predicts the onset of dynamic wave instabilities leading to the emergence of Ca²⁺ waves that propagate in a back-and-forth manner. Numerical simulations are used to confirm the presence of these so-called ‘tango waves’ and the dependence of Ca²⁺ wave speed on the total [Ca²⁺].      

A model of herd grazing as a travelling wave,chemotaxis and stability

Possible constitutive models are examined for the formation of a herd, under the assumption that a herd forms a travelling wave while grazing. Under quite general conditions, it is found that the only possibility for a travelling wave is a balance between food seeking and natural dispersion, such as in chemotaxis. The stability of the travelling wave previously conjectured, is shown both for one- and two-dimensional perturbations.     

Stability properties of pulse vaccination strategy in SEIR epidemic model

The problem of the applicability of the pulse vaccination strategy (PVS) for the stable eradication of some relevant general class of infectious diseases is analyzed in terms of study of local asymptotic stability (LAS) and global asymptotic stability (GAS) of the periodic eradication solution for the SEIR epidemic model in which is included the PVS. Demographic variations due or not to diseased-related fatalities are also considered. Due to the non-triviality of the Floquet's matrix associate to the studied model, the LAS is studied numerically and in this way it is found a simple approximate (but analytical) sufficient criterion which is an extension of the LAS constraint for the stability of the trivial equilibrium in SEIR model without vaccination. The numerical simulations also seem to suggest that the PVS is slightly more efficient than the continuous vaccination strategy. Analytically, the GAS of the eradication solutions is studied and it is demonstrated that the above criteria for the LAS guarantee also the GAS.     

Human internal mammary artery (IMA) transplantation and stenting: a human model to study the development of in-stent restenosis

Preclinical in vivo research models to investigate pathobiological and pathophysiological processes in the development of intimal hyperplasia after vessel stenting are crucial for translational approaches (1,2). The commonly used animal models include mice, rats, rabbits, and pigs (3-5). However, the translation of these models into clinical settings remains difficult, since those biological processes are already studied in animal vessels but never performed before in human research models (6,7). In this video we demonstrate a new humanized model to overcome this translational gap. The shown procedure is reproducible, easy, and fast to perform and is suitable to study the development of intimal hyperplasia and the applicability of diverse stents. This video shows how to perform the stent technique in human vessels followed by transplantation into immunodeficient rats, and identifies the origin of proliferating cells as human.     

A detailed study of the Beddington-DeAngelis predator-prey model

The present investigation accounts for the influence of intra-specific competition among predators in the original Beddington-DeAngelis predator-prey model. We offer a detailed mathematical analysis of the model to describe some of the significant results that may be expected to arise from the interplay of deterministic and stochastic biological phenomena and processes. In particular, stability (local and global) and bifurcation (Saddle-node, Transcritical, Hopf-Andronov, Bogdanov-Takens) analysis of this model are conducted. Corresponding results from previous well known predator-prey models are compared with the current findings. Nevertheless, we also allow this model in stochastic environment with the influences of both, uncorrelated “white” noise and correlated “coloured” noise. This showing that competition among the predator population is beneficial for a number of predator-prey models by keeping them stable around its positive interior equilibrium (i.e. when both populations co-exist), under environmental stochasticity. Comparisons of these findings with the results of some earlier related investigations allow the general conclusion that predator intra-species competition benefits the predator-prey system under both deterministic and stochastic environments. Finally, an extended discussion of the ecological implications of the analytical and numerical results concludes the paper.     

A generalized model of social and biological contagion

We present a model of contagion that unifies and generalizes existing models of the spread of social influences and microorganismal infections. Our model incorporates individual memory of exposure to a contagious entity (e.g. a rumor or disease), variable magnitudes of exposure (dose sizes), and heterogeneity in the susceptibility of individuals. Through analysis and simulation, we examine in detail the case where individuals may recover from an infection and then immediately become susceptible again (analogous to the so-called SIS model). We identify three basic classes of contagion models which we call epidemic threshold, vanishing critical mass, and critical mass classes, where each class of models corresponds to different strategies for prevention or facilitation. We find that the conditions for a particular contagion model to belong to one of the these three classes depend only on memory length and the probabilities of being infected by one and two exposures, respectively. These parameters are in principle measurable for real contagious influences or entities, thus yielding empirical implications for our model. We also study the case where individuals attain permanent immunity once recovered, finding that epidemics inevitably die out but may be surprisingly persistent when individuals possess memory.     

A mathematical model of a crocodilian population using delay-differential equations

The crocodilia have multiple interesting characteristics that affect their population dynamics. They are among several reptile species which exhibit temperature-dependent sex determination (TSD) in which the temperature of egg incubation determines the sex of the hatchlings. Their life parameters, specifically birth and death rates, exhibit strong age-dependence. We develop delay-differential equation (DDE) models describing the evolution of a crocodilian population. In using the delay formulation, we are able to account for both the TSD and the age-dependence of the life parameters while maintaining some analytical tractability. In our single-delay model we also find an equilibrium point and prove its local asymptotic stability. We numerically solve the different models and investigate the effects of multiple delays on the age structure of the population as well as the sex ratio of the population. For all models we obtain very strong agreement with the age structure of crocodilian population data as reported in Smith and Webb (Aust. Wild. Res. 12, 541-554, 1985). We also obtain reasonable values for the sex ratio of the simulated population.     

A model for the interaction of two chemicals

We describe a method for studying the interaction of two anesthetic agents, Morphine and Midazolam, acting simultaneously in the same individual. Representing the levels of the two chemicals by diffusion processes, we assume their interaction is governed by a linear combination of the separate components. Pharmacological data is used to estimate the model parameters and, in particular, to determine the coefficient in the linear combination. This leads to the conclusion that the two chemicals have a counteractive effect.     

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 simple model for periodic cyclostat growth of algae

Summary This paper provides a simple model of nutrient limited periodic cyclostat growth for algae.The basic growth function is assumed to be a time dependent variation of the empirical growth equation developed by Droop (1968). The authors also present the relations for n species' cyclostat coexistence and a stability analysis for the model growth equation.The model, although limited in some respects, agrees very well with available experimental data on Euglena gracilis. The significance of the time dependent amplitude functions developed in this study is also discussed.The term used to describe this system is the cyclostat (see Chisholm et al., 1975).