How time delay and network design shape response patterns in biochemical negative feedback systems

BACKGROUND

Negative feedback in combination with time delay can bring about both sustained oscillations and adaptive behaviour in cellular networks. Here, we study which design features of systems with delayed negative feedback shape characteristic response patterns with special emphasis on the role of time delay. To this end, we analyse generic two-dimensional delay differential equations describing the dynamics of biochemical signal-response networks.

RESULTS

We investigate the influence of several design features on the stability of the model equilibrium, i.e., presence of auto-inhibition and/or mass conservation and the kind and/or strength of the delayed negative feedback. We show that auto-inhibition and mass conservation have a stabilizing effect, whereas increasing abruptness and decreasing feedback threshold have a de-stabilizing effect on the model equilibrium. Moreover, applying our theoretical analysis to the mammalian p53 system we show that an auto-inhibitory feedback can decouple period and amplitude of an oscillatory response, whereas the delayed feedback can not.

CONCLUSIONS

Our theoretical framework provides insight into how time delay and design features of biochemical networks act together to elicit specific characteristic response patterns. Such insight is useful for constructing synthetic networks and controlling their behaviour in response to external stimulation.

Link between deviations from Murray's Law and occurrence of low wall shear stress regions in the left coronary artery

Murray developed two laws for the geometry of bifurcations in the circulatory system. Based on the principle of energy minimization, Murray found restrictions for the relation between the diameters and also between the angles of the branches. It is known that bifurcations are prone to the development of atherosclerosis, in regions associated to low wall shear stresses (WSS) and high oscillatory shear index (OSI). These indicators (size of low WSS regions, size of high OSI regions and size of high helicity regions) were evaluated in this work. All of them were normalized by the size of the outflow branches. The relation between Murray's laws and the size of low WSS regions was analysed in detail. It was found that the main factor leading to large regions of low WSS is the so called expansion ratio, a relation between the cross section areas of the outflow branches and the cross section area of the main branch. Large regions of low WSS appear for high expansion ratios. Furthermore, the size of low WSS regions is independent of the ratio between the diameters of the outflow branches. Since the expansion ratio in bifurcations following Murray's law is kept in a small range (1 and 1.25), all of them have regions of low WSS with similar size. However, the expansion ratio is not small enough to completely prevent regions with low WSS values and, therefore, Murray's law does not lead to atherosclerosis minimization. A study on the effect of the angulation of the bifurcation suggests that the Murray's law for the angles does not minimize the size of low WSS regions.

Instructive percutaneous coronary intervention to avoid the risk of side branch occlusion at a lesion with a lotus root appearance: a case report

Background

A lotus root appearance is a rare entity, and there is little opportunity to perform coronary intervention for this kind of lesion. Because of its peculiar anatomical characteristics, one of the problems regarding percutaneous coronary intervention (PCI) for these lesions is related to the involvement of branch vessels.

Case presentation

We encountered a case of PCI for a stenotic lesion with a lotus root appearance in the mid-portion of the right coronary artery (RCA). To avoid the risk of right ventricular (RV) branch occlusion due to stent deployment in the main RCA, we re-crossed the third guidewire into the main RCA via the nearest point to the RV branch ostium through the communicating vascular lumen. Thereafter, we deployed a drug-eluting stent in the main RCA crossing over the RV branch, and the ostium of the RV branch remained intact, as we expected.

Conclusions

This case is the first report in the world describing the details of how to maintain the patency of the side branch bifurcating from a lesion with a lotus root appearance under optical coherence tomography guidance.

Coronary bifurcation lesions treated with simple or complex stenting: 5-year survival from patient-level pooled analysis of the Nordic Bifurcation Study and the British Bifurcation Coronary Study

AIMS

Randomized trials of coronary bifurcation stenting have shown better outcomes from a simple (provisional) strategy rather than a complex (planned two-stent) strategy in terms of short-term efficacy and safety. Here, we report the 5-year all-cause mortality based on pooled patient-level data from two large bifurcation coronary stenting trials with similar methodology: the Nordic Bifurcation Study (NORDIC I) and the British Bifurcation Coronary Study: old, new, and evolving strategies (BBC ONE).

METHODS AND RESULTS

Both multicentre randomized trials compared simple (provisional T-stenting) vs. complex (culotte, crush, and T-stenting) techniques, using drug-eluting stents. We analysed all-cause death at 5 years. Data were collected from phone follow-up, hospital records, and national mortality tracking. Follow-up was complete for 890 out of 913 patients (97%). Both Simple and Complex groups were similar in terms of patient and lesion characteristics. Five-year mortality was lower among patients who underwent a simple strategy rather than a complex strategy [17 patients (3.8%) vs. 31 patients (7.0%); P = 0.04].

CONCLUSION

For coronary bifurcation lesions, a provisional single-stent approach appears to be associated with lower long-term mortality than a systematic dual stenting technique.

Bifurcation-based approach reveals synergism and optimal combinatorial perturbation

Cells accomplish the process of fate decisions and form terminal lineages through a series of binary choices in which cells switch stable states from one branch to another as the interacting strengths of regulatory factors continuously vary. Various combinatorial effects may occur because almost all regulatory processes are managed in a combinatorial fashion. Combinatorial regulation is crucial for cell fate decisions because it may effectively integrate many different signaling pathways to meet the higher regulation demand during cell development. However, whether the contribution of combinatorial regulation to the state transition is better than that of a single one and if so, what the optimal combination strategy is, seem to be significant issue from the point of view of both biology and mathematics. Using the approaches of combinatorial perturbations and bifurcation analysis, we provide a general framework for the quantitative analysis of synergism in molecular networks. Different from the known methods, the bifurcation-based approach depends only on stable state responses to stimuli because the state transition induced by combinatorial perturbations occurs between stable states. More importantly, an optimal combinatorial perturbation strategy can be determined by investigating the relationship between the bifurcation curve of a synergistic perturbation pair and the level set of a specific objective function. The approach is applied to two models, i.e., a theoretical multistable decision model and a biologically realistic CREB model, to show its validity, although the approach holds for a general class of biological systems.

Percutaneous Coronary Intervention for Bifurcation Lesions

This article summarizes treatment alternatives for coronary bifurcation lesions. It also reviews current definitions and classifications pertaining to bifurcation lesions and provides an overview of the impact of bifurcation lesions on clinical outcomes.

Dedicated bifurcation stents - Mechanistic, hardware, and technical aspects

Percutaneous coronary intervention (PCI) in bifurcation lesions is associated with lower success rate, higher acute complication rates and higher event rates in follow-up.

The reason for this higher than usual complication rate relates to the relationship between anatomy, flow, and atheroma distribution in bifurcation lesions.

Further, stenting these lesions can be a prolonged procedure and can be technically more demanding. The most common complication is the loss of significant side branch (SB). Main vessel (MV) stenting may enhance the carina displacement and atheroma shift across the SB ostium leading to SB ostium narrowing.

Finally, complications, if they occur, are more difficult to manage. Dedicated bifurcation stent has been developed to overcome the number of limitations associated with conventional bifurcation PCI. The main advantage of most dedicated bifurcation stents is to allow the operator to perform the procedure on a bifurcation lesion without the need to rewire the SB.

Stochasticity and bifurcations in a reduced model with interlinked positive and negative feedback loops of CREB1 and CREB2 stimulated by 5-HT

The cyclic AMP (cAMP)-response element-binding protein (CREB) family of transcription factors is crucial in regulating gene expression required for long-term memory (LTM) formation. Upon exposure of sensory neurons to the neurotransmitter serotonin (5-HT), CREB1 is activated via activation of the protein kinase A (PKA) intracellular signaling pathways, and CREB2 as a transcriptional repressor is relieved possibly via phosphorylation of CREB2 by mitogen-activated protein kinase (MAPK). Song et al. [18] proposed a minimal model with only interlinked positive and negative feedback loops of transcriptional regulation by the activator CREB1 and the repressor CREB2. Without considering feedbacks between the CREB proteins, Pettigrew et al. [8] developed a computational model characterizing complex dynamics of biochemical pathways downstream of 5-HT receptors. In this work, to describe more simply the biochemical pathways and gene regulation underlying 5-HT-induced LTM, we add the important extracellular sensitizing stimulus 5-HT as well as the product Ap-uch into the Song's minimal model. We also strive to examine dynamical properties of the gene regulatory network under the changing concentration of the stimulus, [5-HT], cooperating with the varying positive feedback strength in inducing a high state of CREB1 for the establishment of long-term memory. Different dynamics including monostability, bistability and multistability due to coexistence of stable steady states and oscillations is investigated by means of codimension-2 bifurcation analysis. At the different positive feedback strengths, comparative analysis of deterministic and stochastic dynamics reveals that codimension-1 bifurcation with respect to [5-HT] as the parameter can predict diverse stochastic behaviors resulted from the finite number of molecules, and the number of CREB1 molecules more and more preferentially resides near the high steady state with increasing [5-HT], which contributes to long-term memory formation.

An Automatic 3-D Reconstruction of Coronary Arteries by Stereopsis

Stereopsis of X-ray images can produce 3D tree of coronary arteries up to a certain accuracy level with a lower dose of radiation when compared to computer tomography (CT). In this study, a novel and complete automatic system is designed that covers preprocessing, segmentation, matching and reconstruction steps for that purpose. First, an automatic and novel pattern recognition technique is applied for extraction of the bifurcation points with their diameters recorded in a map. Then, a novel optimization algorithm is run for matching the branches efficiently which is based on that map and the epipolar geometry of stereopsis. Finally, cut branches are fixed one by one at the bifurcations for completing the 3D reconstruction. This method prevails the similar ones in the literature with this novelty since it automatically and inherently prevents the wrong overlapping of branches. Other essential problems like correct detection of the bifurcations and accurate calibration parameters and fast overlapping of matched branches are addressed at acceptable levels. The accuracy of bifurcation extraction is high at 90 % with 96 % sensitivity. Accuracy of vessel centerlines has rootmean-square (rms) error smaller than 0.57 mm for 20 different patients. For phantom model, rms error is 0.75 ± 0.8 mm in 3D localization.

Approach to Treatment of Bifurcation Lesions

OPINION STATEMENT

Bifurcation lesions are frequently encountered in the cath lab [1] and remain a challenge for conventional percutaneous coronary intervention (PCI) techniques. Although provisional stenting remains the default approach for most bifurcation lesions [2-6], the two-stent technique is more appropriate in certain situations. If a two-stent strategy is selected, then final kissing balloon inflation (KBI) should be performed. Adjunctive assessment with intravascular imaging (intravascular ultrasound (IVUS)/optical coherence tomography (OCT)) and physiologic testing (fractional flow reserve, FFR) should be performed liberally. Drug-eluting stents (DES) are typically utilized to reduce the risk of restenosis in bifurcation disease.

Localised pattern formation in a model for dryland vegetation

We analyse the model for vegetation growth in a semi-arid landscape proposed by von Hardenberg et al. (Phys. Rev. Lett. 87:198101, 2001), which consists of two parabolic partial differential equations that describe the evolution in space and time of the water content of the soil and the level of vegetation. This model is a generalisation of one proposed by Klausmeier but it contains additional terms that capture additional physical effects. By considering the limit in which the diffusion of water in the soil is much faster than the spread of vegetation, we reduce the system to an asymptotically simpler parabolic-elliptic system of equations that describes small amplitude instabilities of the uniform vegetated state. We carry out a thorough weakly nonlinear analysis to investigate bifurcations and pattern formation in the reduced model. We find that the pattern forming instabilities are subcritical except in a small region of parameter space. In the original model at large amplitude there are localised solutions, organised by homoclinic snaking curves. The resulting bifurcation structure is well known from other models for pattern forming systems. Taken together our results describe how the von Hardenberg model displays a sequence of (often hysteretic) transitions from a non-vegetated state, to localised patches of vegetation that exist with uniform low-level vegetation, to periodic patterns, to higher-level uniform vegetation as the precipitation parameter increases.

A bifurcation identifier for IV-OCT using orthogonal least squares and supervised machine learning

Intravascular optical coherence tomography (IV-OCT) is an in-vivo imaging modality based on the intravascular introduction of a catheter which provides a view of the inner wall of blood vessels with a spatial resolution of 10-20 μm. Recent studies in IV-OCT have demonstrated the importance of the bifurcation regions. Therefore, the development of an automated tool to classify hundreds of coronary OCT frames as bifurcation or nonbifurcation can be an important step to improve automated methods for atherosclerotic plaques quantification, stent analysis and co-registration between different modalities. This paper describes a fully automated method to identify IV-OCT frames in bifurcation regions. The method is divided into lumen detection; feature extraction; and classification, providing a lumen area quantification, geometrical features of the cross-sectional lumen and labeled slices. This classification method is a combination of supervised machine learning algorithms and feature selection using orthogonal least squares methods. Training and tests were performed in sets with a maximum of 1460 human coronary OCT frames. The lumen segmentation achieved a mean difference of lumen area of 0.11 mm(2) compared with manual segmentation, and the AdaBoost classifier presented the best result reaching a F-measure score of 97.5% using 104 features.

A Model of Chloroplast Growth Regulation in Mesophyll Cells

Chloroplasts regulate their growth to optimize photosynthesis. Quantitative data show that the ratio of total chloroplast area to mesophyll cell area is constant across different cells within a single species and also across species. Wild-type chloroplasts exhibit little scatter around this trend; highly irregularly shaped mutant chloroplasts exhibit more scatter. Here we propose a model motivated by a bacterial quorum-sensing model consisting of a switch-like signaling network that turns off chloroplast growth. We calculated the dependence of the location of the relevant saddle-node bifurcation on the geometry of the chloroplasts. Our model exhibits a linear trend, with linearly growing scatter dependent on chloroplast shape, consistent with the data. When modeled chloroplasts are of a shape that grows with a constant area-to-volume ratio (disks, cylinders), we find a linear trend with minimal scatter. Chloroplasts with area and volume that do not grow proportionally (spheres) exhibit a linear trend with additional scatter.

Facile microfluidic channels for acoustophoresis on a budget

Acoustophoresis is a powerful yet gentle technique for manipulating cells and particles that has quickly earned a place in the lab-on-a-chip toolkit. However, traditional construction techniques for acoustophoretic resonators have typically required prohibitively expensive and laborious processing methods. Here, we propose a highly cost-effective and cleanroom-free construction technique for transversal acoustophoretic resonators. Channels with two different widths of 750 and 300 μm were constructed using a simple glass and polyimide sandwiching technique. Half and full wavelength resonators were then established using 1 and 5 MHz ultrasound respectively and polystyrene beads were successfully manipulated in both types of resonators. This construction technique was then utilized to demonstrate a bifurcation and trifurcation microchannel with 600 μm widths and 2.5 MHz ultrasound. Our approach addresses some of the key drawbacks of acoustophoretic devices by drastically simplifying the fabrication and prototyping of transversal resonators and will assist in expanding this technology from laboratory benches and into the broader market.

Iatrogenic Damage to the Periodontium Caused by Endodontic Treatment Procedures: An Overview

The tooth, the pulp tissue within it and its supporting structures should be viewed as one biologic unit. The interrelationship of these structures influences each other during health, function and disease. The interrelationship between periodontal and endodontic diseases has aroused much speculation, confusion and controversy. The endodontium and periodontiumare closely related and disease or damage of one tissue may lead to the involvement of the other.

Coupling relationship between the central pattern generator and the cerebral cortex with time delay

Brain activity is a cooperative process among neurons and involves the coupling relationship, which is crucial to perform operational tasks in various specialized areas of the nervous system. A finite signal transmission speed along the axons results in a space-dependent time delay. The central pattern generator (CPG) can in principle produce basic locomotor rhythm in the absence of inputs from higher brain centers and peripheral sensory feedback. To study the dynamic performance of CPG with time delay and its coupling relationship with the cerebral cortex, a new CPG model with time delay and a model of the neural mass model (NMM) and the CPG are developed. The coupling model is based on biological experimental results. Bifurcation theories and maximal Lyapunov exponent are used to analyze the dynamic performance. From the results, some CPGs are suggested to be embedded in limbs and composed of the parameters space which corresponds to the one of the cerebral cortex. This embodiment of humans can reduce the burden of the brain and simplify the control of the locomotion. The results also show that the phase diagram of the CPG cannot keep the limit cycle, and that the state of the NMM becomes increasingly chaotic as time delay increases. This finding implies that a person with slow reaction can easily lose the stability of his or her locomotion.

Neural fate decisions mediated by combinatorial regulation of Hes1 and miR-9

In the nervous system, Hes1 shows an oscillatory manner in neural progenitors but a persistent one in neurons. Many models involving Hes1 have been provided for the study of neural differentiation but few of them take the role of microRNA into account. It is known that a microRNA, miR-9, plays crucial roles in modulating Hes1 oscillations. However, the roles of miR-9 in controlling Hes1 oscillations and inducing transition between different cell fates still need to be further explored. Here we provide a mathematical model to show the interaction between miR-9 and Hes1, with the aim of understanding how the Hes1 oscillations are produced, how they are controlled, and further, how they are terminated. Based on the experimental findings, the model demonstrates the essential roles of Hes1 and miR-9 in regulating the dynamics of the system. In particular, the model suggests that the balance between miR-9 and Hes1 plays important roles in the choice between progenitor maintenance and neural differentiation. In addition, the synergistic (or antagonistic) effects of several important regulations are investigated so as to elucidate the effects of combinatorial regulation in neural decision-making. Our model provides a qualitative mechanism for understanding the process in neural fate decisions regulated by Hes1 and miR-9.

Noise-induced precursors of state transitions in the stochastic Wilson-cowan model

The Wilson-Cowan neural field equations describe the dynamical behavior of a 1-D continuum of excitatory and inhibitory cortical neural aggregates, using a pair of coupled integro-differential equations. Here we use bifurcation theory and small-noise linear stochastics to study the range of a phase transitions-sudden qualitative changes in the state of a dynamical system emerging from a bifurcation-accessible to the Wilson-Cowan network. Specifically, we examine saddle-node, Hopf, Turing, and Turing-Hopf instabilities. We introduce stochasticity by adding small-amplitude spatio-temporal white noise, and analyze the resulting subthreshold fluctuations using an Ornstein-Uhlenbeck linearization. This analysis predicts divergent changes in correlation and spectral characteristics of neural activity during close approach to bifurcation from below. We validate these theoretical predictions using numerical simulations. The results demonstrate the role of noise in the emergence of critically slowed precursors in both space and time, and suggest that these early-warning signals are a universal feature of a neural system close to bifurcation. In particular, these precursor signals are likely to have neurobiological significance as early warnings of impending state change in the cortex. We support this claim with an analysis of the in vitro local field potentials recorded from slices of mouse-brain tissue. We show that in the period leading up to emergence of spontaneous seizure-like events, the mouse field potentials show a characteristic spectral focusing toward lower frequencies concomitant with a growth in fluctuation variance, consistent with critical slowing near a bifurcation point. This observation of biological criticality has clear implications regarding the feasibility of seizure prediction.

Repression of wall shear stress inside cerebral aneurysm at bifurcation of anterior cerebral artery by stents

The effect of a simple bare metal stent on repression of wall shear stress inside a model cerebral aneurysm was experimentally investigated by two-dimensional particle image velocimetry in vitro. The flow model simulated a cerebral aneurysm induced at the apex of bifurcation between the anterior cerebral artery and the anterior communicating artery. Wall shear stress was investigated using both stented and non-stented models to assess the simple stent characteristics. The flow behavior inside the stented aneurysm sac was unusual and wall shear stress was much smaller inside the aneurysm sac. Stent placement effectively repressed the temporal and spatial variations and the magnitude of wall shear stress. Hence, there is an effective possibility that would retard the progress of cerebral aneurysms by even simple stent.

Nonlinear dynamics of the CAM circadian rhythm in response to environmental forcing

Crassulacean acid metabolism (CAM) photosynthesis functions as an endogenous circadian rhythm coupled to external environmental forcings of energy and water availability. This paper explores the nonlinear dynamics of a new CAM photosynthesis model (Bartlett et al., 2014) and investigates the responses of CAM plant carbon assimilation to different combinations of environmental conditions. The CAM model (Bartlett et al., 2014) consists of a Calvin cycle typical of C3 plants coupled to an oscillator of the type employed in the Van der Pol and FitzHugh-Nagumo systems. This coupled system is a function of environmental variables including leaf temperature, leaf moisture potential, and irradiance. Here, we explore the qualitative response of the system and the expected carbon assimilation under constant and periodically forced environmental conditions. The model results show how the diurnal evolution of these variables entrains the CAM cycle with prevailing environmental conditions. While constant environmental conditions generate either steady-state or periodically oscillating responses in malic acid uptake and release, forcing the CAM system with periodic daily fluctuations in light exposure and leaf temperature results in quasi-periodicity and possible chaos for certain ranges of these variables. This analysis is a first step in quantifying changes in CAM plant productivity with variables such as the mean temperature, daily temperature range, irradiance, and leaf moisture potential. Results may also be used to inform model parametrization based on the observed fluctuating regime.

Morphological-Hemodynamic Characteristics of Intracranial Bifurcation Mirror Aneurysms

BACKGROUND

Many morphological and hemodynamic parameters have been proposed as promising aneurysm rupture status discriminators. Besides, a clear dichotomy between sidewall and bifurcation aneurysms was reported. In this study, we strove to evaluate the contribution of many reported morphological and hemodynamic parameters to retrospective rupture status determination in bifurcation aneurysms independent of patients' characteristics.

METHODS

Computational fluid dynamics were performed on 16 patients with bifurcation mirror aneurysms (MANs). Each pair was divided into ruptured and unruptured groups. The morphological and hemodynamic factors were analyzed and compared. Receiver operating characteristics (ROC) analysis was performed, and the area under the ROC curve (AUC) was calculated for all parameters to quantify the predictability of each index and identify the optimal threshold.

RESULTS

Morphological (size, aspect ratio, size ratio, and height-width ratio) and hemodynamic (time-averaged mean wall shear stress [WSSmean], low WSS area [LSA]) parameters reached statistical significance (P < 0.05). Aneurysm irregular shape, oscillatory shear index (OSI), flow stability, inflow concentration, and impingement zone did not achieve significantly statistical differences (P = 0.508, P = 0.319, P = 0.523, P = 0.227, and P = 1.000, respectively). After ROC analysis, only aspect ratio and LSA had excellent AUC values (0.840 and 0.824, respectively). Other key parameters, including size, size ratio, height-width ratio, and WSSmean, had AUC values between 0.7 and 0.8 (0.730, 0.715, 0.703, 0.727, respectively).

CONCLUSIONS

Higher aspect ratio and LSA are good indicators for bifurcation aneurysm rupture. MANs with different rupture status might be a useful disease model in which many factors are balanced to investigate possible features linked to aneurysm rupture.

Bifurcation and dynamics in a mathematical model of early atherosclerosis: How acute inflammation drives lesion development

We present here a mathematical model describing the primary mechanisms that drive the early stages of atherosclerosis. This involves the interactions between modified low density lipoprotein (LDL), monocytes/macrophages, cytokines and foam cells. This model suggests that there is an initial inflammatory phase associated with atherosclerotic lesion development and a longer, quasi-static process of plaque development inside the arterial wall that follows the initial transient. We will show results that show how different LDL concentrations in the blood stream and different immune responses can affect the development of a plaque. Through numerical bifurcation analysis, we show the existence of a fold bifurcation when the flux of LDL from the blood is sufficiently high. By analysing the model presented in this paper, we gain a greater insight into this inflammatory response qualitatively and quantitatively.

Control exponential growth of tumor cells with slow spread of oncolytic virus

Great attention has been paid to cancer therapy by means of oncolytic viruses, but the fast virus-spread, which eliminates all tumor cells, cannot be applied to solid tumors. As slow virus-spread is applied, solid tumors are expected to be controlled but complicated dynamical behaviors appear. In this paper we investigate bifurcations of equilibria in the oncolytic virus dynamics model with exponential growth of tumor cells and slow virus-spread. We find conditions of parameters for saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. Those conditions give thresholds for slow virus-spread to control the population of tumor cells within an appropriate range.

Adhesion patterns in the microvasculature are dependent on bifurcation angle

Particle adhesion in vivo is highly dependent on the microvascular environment comprising of unique anatomical, geometrical, physiological fluid flow conditions and cell-particle and cell-cell interactions. Hence, proper design of vascular-targeted drug carriers that efficiently deliver therapeutics to the targeted cells or tissue at effective concentrations must account for these complex conditions observed in vivo. In this study, we build upon our previous results with the goal of characterizing the effects of bifurcations and their corresponding angle on adhesion of functionalized particles and neutrophils to activated endothelium. Our hypothesis is that adhesion is significantly affected by the type of biochemical interactions between particles and vessel wall as well as the presence of bifurcations and their corresponding angle. Here, we investigate adhesion of functionalized particles (2 μm and 7 μm microparticles) to protein coated channels as well as adhesion of human neutrophils to human endothelial cells under various physiological flow conditions in microfluidic bifurcating channels comprising of different contained angles (30°, 60°, 90°, or 120°). Our findings indicate that both functionalized particle and neutrophil adhesion propensity increase with a larger bifurcation angle. Moreover, the difference in the adhesion patterns of neutrophils and rigid, similar sized (7 μm) particles is more apparent in the junction regions with a larger contained angle. By selecting the right particle size range, enhanced targeted binding of vascular drug carriers can be achieved along with a higher efficacy at optimal drug dosage. Hence, vascular drug particle design needs to be tailored to account for higher binding propensity at larger bifurcation angles.

Investigation of monolithic passively mode-locked quantum dot lasers with extremely low repetition frequency

The dynamical regimes and performance optimization of quantum dot monolithic passively mode-locked lasers with extremely low repetition rate are investigated using the numerical method. A modified multisection delayed differential equation model is proposed to accomplish simulations of both two-section and three-section passively mode-locked lasers with long cavity. According to the numerical simulations, it is shown that fundamental and harmonic mode-locking regimes can be multistable over a wide current range. These dynamic regimes are studied, and the reasons for their existence are explained. In addition, we demonstrate that fundamental pulses with higher peak power can be achieved when the laser is designed to work in a region with smaller differential gain.

Bifurcation dynamics and determination of alternate cell fates in bipotent progenitor cells

The gene regulatory networks in which two lineage-affiliated transcription factors, such as GATA1 and PU.1, inhibit each other but activate themselves so as to regulate the choice between alternative cell fates have been extensively studied. These simple networks can generate bistability and explain the transitions between the alternative cell fates. The commitment of a progenitor cell to a new fate corresponds to the occurrence of different types of bifurcations, depending on if a system is symmetrical and how perturbations affect the system. Here we take a general modeling and analyzing approach and show that the lateral inhibition with symmetry and asymmetry can lead to different bifurcation dynamics. Especially, if cell fate decision-making is initiated with asymmetry or symmetry-breaking perturbations, a progenitor cell pre-patterns itself into a polarized cell, depending on the asymmetry or symmetry-breaking perturbations. This study may help us understand the fundamental features of binary cell fate decisions more clearly and further apply to a wider range of decision-making processes.

Eccentric morphology of jailed side-branch ostium after stent crossover in coronary bifurcation lesions: a three-dimensional optical coherence tomographic analysis

BACKGROUND

Angiographic stenosis of a jailed side-branch ostium is usually observed after a single-stent crossover at coronary bifurcation lesions. However, the stenosis severity is typically overestimated due to the limited information obtained from two-dimensional morphology by angiography. We evaluated the actual stenosis of jailed side-branch ostium using three-dimensional (3D) optical coherence tomography (OCT).

METHODS

Using 3D reconstructions of OCT data, we analyzed minimal lumen area (MLA) and eccentricity of the jailed side-branch ostium in 41 patients who were treated with single stent crossover at coronary bifurcation lesions and subsequently underwent serial OCT follow-up.

RESULTS

The MLA of jailed side-branch ostium calculated from quantitative coronary angiography (QCA) assuming a circular lumen markedly decreased after stent implantation (1.73±1.22mm(2) pre-intervention to 0.84±0.91mm(2) post-intervention, p<0.001). However, the MLA of jailed side-branch ostium measured at post-intervention by 3D-OCT (2.67±1.75mm(2)) was significantly larger than that measured by QCA (p<0.001). There were no statistically significant changes in MLA of jailed side-branch ostium based on 3D-OCT measurements during the follow-up (2.35±1.50mm(2) at 3-6 months post-intervention; 2.44±1.27mm(2) at 1-2 years post-intervention, p=0.098). The shapes of the jailed side-branch ostium were nearly elliptical (mean eccentricity index: 2.97±1.27 post-intervention; 2.79±1.17 at 3-6 months post-intervention; 2.59±1.02 at 1-2 years post-intervention).

CONCLUSIONS

Compared to 3D-OCT measurements, QCA measurements overestimated the jailed side-branch ostial stenosis after single stent crossover due to eccentric morphology from orthogonal projection in coronary angiography. Significant changes in the MLA of jailed side-branch ostium by 3D-OCT were not observed during the follow-up.

Population dynamics of intraguild predation in a lattice gas system

In the system of intraguild predation (IGP) we are concerned with, species that are in a predator-prey relationship, also compete for shared resources (space or food). While several models have been established to characterize IGP, mechanisms by which IG prey and IG predator can coexist in IGP systems with spatial competition, have not been shown. This paper considers an IGP model, which is derived from reactions on lattice and has a form similar to that of Lotka-Volterra equations. Dynamics of the model demonstrate properties of IGP and mechanisms by which the IGP leads to coexistence of species and occurrence of alternative states. Intermediate predation is shown to lead to persistence of the predator, while extremely big predation can lead to extinction of one/both species and extremely small predation can lead to extinction of the predator. Numerical computations confirm and extend our results. While empirical observations typically exhibit coexistence of IG predator and IG prey, theoretical analysis in this work demonstrates exact conditions under which this coexistence can occur.

The effect of nanoparticles on plankton dynamics: a mathematical model

A simple modification of the Rosenzweig-MacArthur predator (zooplankton)-prey (phytoplankton) model with the interference of the predators by adding the effect of nanoparticles is proposed and analyzed. It is assumed that the effect of these particles has a potential to reduce the maximum physiological per-capita growth rate of the prey. The dynamics of nanoparticles is assumed to follow a simple Lotka-Volterra uptake term. Our study suggests that nanoparticle induce growth suppression of phytoplankton population can destabilize the system which leads to limit cycle oscillation. We also observe that if the contact rate of nanoparticles and phytoplankton increases, then the equilibrium densities of phytoplankton as well as zooplankton decrease. Furthermore, we observe that the depletion/removal of nanoparticles from the aquatic system plays a crucial role for the stable coexistence of both populations. Our investigation with various types of functional response suggests that Beddington functional response is the most appropriate representation of the interaction of phytoplankton-nanoparticles in comparison to other widely used functional responses.

Numerical Bifurcation Theory for High-Dimensional Neural Models

Numerical bifurcation theory involves finding and then following certain types of solutions of differential equations as parameters are varied, and determining whether they undergo any bifurcations (qualitative changes in behaviour). The primary technique for doing this is numerical continuation, where the solution of interest satisfies a parametrised set of algebraic equations, and branches of solutions are followed as the parameter is varied. An effective way to do this is with pseudo-arclength continuation. We give an introduction to pseudo-arclength continuation and then demonstrate its use in investigating the behaviour of a number of models from the field of computational neuroscience. The models we consider are high dimensional, as they result from the discretisation of neural field models-nonlocal differential equations used to model macroscopic pattern formation in the cortex. We consider both stationary and moving patterns in one spatial dimension, and then translating patterns in two spatial dimensions. A variety of results from the literature are discussed, and a number of extensions of the technique are given.

[FeFe]- and [NiFe]-hydrogenase diversity, mechanism, and maturation

The [FeFe]- and [NiFe]-hydrogenases catalyze the formal interconversion between hydrogen and protons and electrons, possess characteristic non-protein ligands at their catalytic sites and thus share common mechanistic features. Despite the similarities between these two types of hydrogenases, they clearly have distinct evolutionary origins and likely emerged from different selective pressures. [FeFe]-hydrogenases are widely distributed in fermentative anaerobic microorganisms and likely evolved under selective pressure to couple hydrogen production to the recycling of electron carriers that accumulate during anaerobic metabolism. In contrast, many [NiFe]-hydrogenases catalyze hydrogen oxidation as part of energy metabolism and were likely key enzymes in early life and arguably represent the predecessors of modern respiratory metabolism. Although the reversible combination of protons and electrons to generate hydrogen gas is the simplest of chemical reactions, the [FeFe]- and [NiFe]-hydrogenases have distinct mechanisms and differ in the fundamental chemistry associated with proton transfer and control of electron flow that also help to define catalytic bias. A unifying feature of these enzymes is that hydrogen activation itself has been restricted to one solution involving diatomic ligands (carbon monoxide and cyanide) bound to an Fe ion. On the other hand, and quite remarkably, the biosynthetic mechanisms to produce these ligands are exclusive to each type of enzyme. Furthermore, these mechanisms represent two independent solutions to the formation of complex bioinorganic active sites for catalyzing the simplest of chemical reactions, reversible hydrogen oxidation. As such, the [FeFe]- and [NiFe]-hydrogenases are arguably the most profound case of convergent evolution. This article is part of a Special Issue entitled: Fe/S proteins: Analysis, structure, function, biogenesis and diseases.

An unusual high bifurcation and variable branching of the axillary artery in a Greek male cadaver

Introduction

The axillary artery presents abnormalities in its origin and course and a variable branching.

Case description

A rare case of axillary artery bifurcation and branching was observed in a 60-years-old European male cadaver of Greek origin. The right axillary artery at the second part was bifurcated into a superficial and a deep brachial artery. The superficial brachial artery anteromedial to the median nerve and lateral to the ulnar nerve gave off the acromio-thoracic artery and two lateral thoracic arteries. The deep brachial artery behind the median nerve, after giving rise to the anterior circumflex humeral artery trifurcated into a branch that coursed distally, the posterior circumflex humeral artery and the subscapular artery. The latter subdivided into the circumflex scapular artery, a muscular branch for the subscapularis and the thoracodorsal artery. The continuation of the deep brachial artery divided laterally into a humeral nutrient artery and medially into a trunk which trifurcated into the profunda brachii artery, a deep muscular branch and a branch to the posterior compartment of the arm. The profunda brachii artery ended as radial and middle collateral arteries.

Discussion and evaluation

Deviations from the normal arterial pattern are of immense significance for anatomists, plastic, cardiovascular and orthopedic surgeons, vascular radiologists and interventional cardiologists.

Impact of final kissing balloon inflation after simple stent implantation for the treatment of non-left main true coronary bifurcation lesions in patients with acute coronary syndrome

OBJECTIVES

We sought to evaluate the impact of final kissing balloon inflation (FKBI) after simple stent implantation for the treatment of non-left main true coronary bifurcation lesions in patients with acute coronary syndrome (ACS).

BACKGROUND

Whether FKBI should be mandatory after simple stent implantation for the treatment of coronary bifurcation lesion is controversial. Besides, ACS patients who have undergone bifurcation percutaneous coronary intervention with simple stent implantation may experience worse prognosis compared to stable angina pectoris patients.

METHODS

Two hundred and fifty one eligible patients (67.7% male, mean age 61.7 ± 10.4 years) were enrolled. The study population was divided into two groups according to the performance of FKBI. The primary end points were major adverse cardiac event (MACE); target lesion revascularization (TLR), non-fatal myocardial infarction (MI) and cardiac death during the follow-up period.

RESULTS

Over a mean follow-up period of 3.0 ± 1.9 years, there were 29 MACEs (10 TLR, 6 non-fatal MI, and 13 cardiac deaths), representing an event rate of 11.6%. Kaplan-Meier survival analysis revealed that FBKI group had favorable outcome compared to non-FKBI group with regard to hard events (p = 0.010) as well as composite MACEs (p = 0.008). In multivariable analysis, FKBI was a significant predictor of composite MACEs [hazard ratio 0.398 (95% confidence interval 0.190-0.836, p = 0.015)] and hard events [hazard ratio 0.325 (95% confidence interval 0.130-0.811, p = 0.016)].

CONCLUSIONS

In terms of prognosis, performing FKBI after simple stent implantation for the treatment of non-left main true coronary bifurcation lesions may be mandatory in ACS patients.

Cellular and physical mechanisms of branching morphogenesis

Branching morphogenesis is the developmental program that builds the ramified epithelial trees of various organs, including the airways of the lung, the collecting ducts of the kidney, and the ducts of the mammary and salivary glands. Even though the final geometries of epithelial trees are distinct, the molecular signaling pathways that control branching morphogenesis appear to be conserved across organs and species. However, despite this molecular homology, recent advances in cell lineage analysis and real-time imaging have uncovered surprising differences in the mechanisms that build these diverse tissues. Here, we review these studies and discuss the cellular and physical mechanisms that can contribute to branching morphogenesis.

Modeling endocrine regulation of the menstrual cycle using delay differential equations

This article reviews an effective mathematical procedure for modeling hormonal regulation of the menstrual cycle of adult women. The procedure captures the effects of hormones secreted by several glands over multiple time scales. The specific model described here consists of 13 nonlinear, delay, differential equations with 44 parameters and correctly predicts blood levels of ovarian and pituitary hormones found in the biological literature for normally cycling women. In addition to this normal cycle, the model exhibits another stable cycle which may describe a biologically feasible "abnormal" condition such as polycystic ovarian syndrome. Model simulations illustrate how one cycle can be perturbed to the other cycle. Perturbations due to the exogenous administration of each ovarian hormone are examined. This model may be used to test the effects of hormone therapies on abnormally cycling women as well as the effects of exogenous compounds on normally cycling women. Sensitive parameters are identified and bifurcations in model behavior with respect to parameter changes are discussed. Modeling various aspects of menstrual cycle regulation should be helpful in predicting successful hormone therapies, in studying the phenomenon of cycle synchronization and in understanding many factors affecting the aging of the female reproductive endocrine system.

Structure and dynamics of thylakoids in land plants

Thylakoids of land plants have a bipartite structure, consisting of cylindrical grana stacks, made of membranous discs piled one on top of the other, and stroma lamellae which are helically wound around the cylinders. Protein complexes predominantly located in the stroma lamellae and grana end membranes are either bulky [photosystem I (PSI) and the chloroplast ATP synthase (cpATPase)] or are involved in cyclic electron flow [the NAD(P)H dehydrogenase (NDH) and PGRL1-PGR5 heterodimers], whereas photosystem II (PSII) and its light-harvesting complex (LHCII) are found in the appressed membranes of the granum. Stacking of grana is thought to be due to adhesion between Lhcb proteins (LHCII or CP26) located in opposed thylakoid membranes. The grana margins contain oligomers of CURT1 proteins, which appear to control the size and number of grana discs in a dosage- and phosphorylation-dependent manner. Depending on light conditions, thylakoid membranes undergo dynamic structural changes that involve alterations in granum diameter and height, vertical unstacking of grana, and swelling of the thylakoid lumen. This plasticity is realized predominantly by reorganization of the supramolecular structure of protein complexes within grana stacks and by changes in multiprotein complex composition between appressed and non-appressed membrane domains. Reversible phosphorylation of LHC proteins (LHCPs) and PSII components appears to initiate most of the underlying regulatory mechanisms. An update on the roles of lipids, proteins, and protein complexes, as well as possible trafficking mechanisms, during thylakoid biogenesis and the de-etiolation process complements this review.

Atherosclerotic indicators for blood-like fluids in 90-degree arterial-like bifurcations

The identification of regions prone to atherogenesis in the arterial network is compounded by the complex, slow interaction of mechanical and biomechanical processes. In recent times simplifications to the analysis of the near wall hemodynamics have been sought-after to identify plaque prone regions. Mean parameters have been defined to analyze the common fluid mechanical hypotheses considering the role of wall shear stress (WSS) variations in the pathological changes to the endothelium. In this study well known WSS indicators are applied to varying flow conditions of blood-like fluids in a 90-degree arterial bifurcation. The conventional indicators identify two distinct, focal regions that correlate with a known plaque prone location near arterial bifurcations. The results however demonstrate that the interpretation of the indicators can be difficult under varying flow conditions unless complementary parameters are considered simultaneously. A new indicator is also suggested that extracts the peaks of the temporal WSS gradients (PTWSSGs) and is shown to co-incide well with plaque prone regions. The PTWSSG could be used as a complimentary atherogenic indicator in bifurcating arteries, thereby expanding cardiovascular disease studies to the consideration of alternative fluid mechanical hypotheses. The inclusion of a non-Newtonian model is important in predicting the WSS and temporal WSS gradient distributions near the bifurcation due to the separation bubble induced fluctuations in the shear. Atherogenic indicators could be misleading if non-Newtonian effects are excluded.

Physiologically-based modeling of sleep-wake regulatory networks

Mathematical modeling has played a significant role in building our understanding of sleep-wake and circadian behavior. Over the past 40 years, phenomenological models, including the two-process model and oscillator models, helped frame experimental results and guide progress in understanding the interaction of homeostatic and circadian influences on sleep and understanding the generation of rapid eye movement sleep cycling. Recent advances in the clarification of the neural anatomy and physiology involved in the regulation of sleep and circadian rhythms have motivated the development of more detailed and physiologically-based mathematical models that extend the approach introduced by the classical reciprocal-interaction model. Using mathematical formalisms developed in the field of computational neuroscience to model neuronal population activity, these models investigate the dynamics of proposed conceptual models of sleep-wake regulatory networks with a focus on generating appropriate sleep and wake state transition patterns as well as simulating disease states and experimental protocols. In this review, we discuss several recent physiologically-based mathematical models of sleep-wake regulatory networks. We identify common features among these models in their network structures, model dynamics and approaches for model validation. We describe how the model analysis technique of fast-slow decomposition, which exploits the naturally occurring multiple timescales of sleep-wake behavior, can be applied to understand model dynamics in these networks. Our purpose in identifying commonalities among these models is to propel understanding of both the mathematical models and their underlying conceptual models, and focus directions for future experimental and theoretical work.

A nutrient dependant switch explains mutually exclusive existence of meiosis and mitosis initiation in budding yeast

Nutrients from living environment are vital for the survival and growth of any organism. Budding yeast diploid cells decide to grow by mitosis type cell division or decide to create unique, stress resistant spores by meiosis type cell division depending on the available nutrient conditions. To gain a molecular systems level understanding of the nutrient dependant switching between meiosis and mitosis initiation in diploid cells of budding yeast, we develop a theoretical model based on ordinary differential equations (ODEs) including the mitosis initiator and its relations to budding yeast meiosis initiation network. Our model accurately and qualitatively predicts the experimentally revealed temporal variations of related proteins under different nutrient conditions as well as the diverse mutant studies related to meiosis and mitosis initiation. Using this model, we show how the meiosis and mitosis initiators form an all-or-none type bistable switch in response to available nutrient level (mainly nitrogen). The transitions to and from meiosis or mitosis initiation states occur via saddle node bifurcation. This bidirectional switch helps the optimal usage of available nutrients and explains the mutually exclusive existence of meiosis and mitosis pathways.

Bursting synchronization dynamics of pancreatic β-cells with electrical and chemical coupling

Based on bifurcation analysis, the synchronization behaviors of two identical pancreatic β-cells connected by electrical and chemical coupling are investigated, respectively. Various firing patterns are produced in coupled cells when a single cell exhibits tonic spiking or square-wave bursting individually, irrespectively of what the cells are connected by electrical or chemical coupling. On the one hand, cells can burst synchronously for both weak electrical and chemical coupling when an isolated cell exhibits tonic spiking itself. In particular, for electrically coupled cells, under the variation of the coupling strength there exist complex transition processes of synchronous firing patterns such as "fold/limit cycle" type of bursting, then anti-phase continuous spiking, followed by the "fold/torus" type of bursting, and finally in-phase tonic spiking. On the other hand, it is shown that when the individual cell exhibits square-wave bursting, suitable coupling strength can make the electrically coupled system generate "fold/Hopf" bursting via "fold/fold" hysteresis loop; whereas, the chemically coupled cells generate "fold/subHopf" bursting. Especially, chemically coupled bursters can exhibit inverse period-adding bursting sequence. Fast-slow dynamics analysis is applied to explore the generation mechanism of these bursting oscillations. The above analysis of bursting types and the transition may provide us with better insight into understanding the role of coupling in the dynamic behaviors of pancreatic β-cells.

Evaluating stent optimisation technique (StentBoost®) in a dedicated bifurcation stent (the Tryton™).Cardiovasc Revasc Med. 2014;15:92-96. [PMID: 24560297 DOI: 10.1016/j.carrev.2014.01.002]

BACKGROUND/PURPOSE

To evaluate the use of StentBoost® in the Tryton™ dedicated SideBranch Stent.

METHODS & RESULTS

The Tryton™ SideBranch Stent has been effectively used to manage complex bifurcations. However, the paucity of scaffolding in the proximal part of the stent makes it often difficult to visualise under standard radiographic imaging. We set out to evaluate whether by using an augmented radiographic imaging technique it was possible to aid visualisation of the stent. In particular the so call 'wedding ring' band which is crucial to the procedural success. We further evaluated whether it was possible to determine the apposition of the stent at the carina, its coverage and the ability to aid recrossing of the struts closest to the carina as well as the added radiation exposure.

CONCLUSIONS

StentBoost® was found to be invaluable to the procedural success of the Tryton™ deployment without adding any extra cost to the procedure and with only a 3.7% increase in radiation to the patient. It allowed enhanced visualisation in all cases to aid apposition, recrossing and coverage.

Diseased prey predator model with general Holling type interactions

Choice of interaction function is one of the most important parts for modelling a food chain. Many models have been proposed as a diseased-prey predator model with Holling type-I or type-II or type-III interactions, but there is no model with general Holling type interactions. In this paper, we study a diseased prey-predator model with general Holling type interactions. Local stability conditions of equilibrium points are derived. We obtain the permanence and impermanence conditions of the system. The conditions for global stability of the system are also derived. The system exhibits limit cycle, period-2, higher periodic oscillations and chaotic behaviour for different values of Holling parameters. One parameter bifurcation analysis is done with respect to general Holling parameters and infection rate. We utilize the MATCONT package to analyse the detailed bifurcation scenario as the two important interaction parameters are varied. It is interesting to note that a diseased system becomes a disease free system for proper choice of interaction functions. Our results give an idea for constructing a realistic food chain model through proper choice of general Holling parameters.

A simple epidemiological model for populations in the wild with Allee effects and disease-modified fitness

The study of the dynamics of human infectious disease using deterministic models is typically carried out under the assumption that a critical mass of individuals is available and involved in the transmission process. However, in the study of animal disease dynamics where demographic considerations often play a significant role, this assumption must be weakened. Models of the dynamics of animal populations often naturally assume that the presence of a minimal number of individuals is essential to avoid extinction. In the ecological literature, this a priori requirement is commonly incorporated as an Allee effect. The focus here is on the study disease dynamics under the assumption that a critical mass of susceptible individuals is required to guarantee the population's survival. Specifically, the emphasis is on the study of the role of an Allee effect on a Susceptible-Infectious (SI) model where the possibility that susceptible and infected individuals reproduce, with the S-class the best fit. It is further assumed that infected individuals loose some of their ability to compete for resources, the cost imposed by the disease. These features are set in motion in as simple model as possible. They turn out to lead to a rich set of dynamical outcomes. This toy model supports the possibility of multi-stability (hysteresis), saddle node and Hopf bifurcations, and catastrophic events (disease-induced extinction). The analyses provide a full picture of the system under disease-free dynamics including disease-induced extinction and proceed to identify required conditions for disease persistence. We conclude that increases in (i) the maximum birth rate of a species, or (ii) in the relative reproductive ability of infected individuals, or (iii) in the competitive ability of a infected individuals at low density levels, or in (iv) the per-capita death rate (including disease-induced) of infected individuals, can stabilize the system (resulting in disease persistence). We further conclude that increases in (a) the Allee effect threshold, or (b) in disease transmission rates, or in (c) the competitive ability of infected individuals at high density levels, can destabilize the system, possibly leading to the eventual collapse of the population. The results obtained from the analyses of this toy model highlight the significant role that factors like an Allee effect may play on the survival and persistence of animal populations. Scientists involved in biological conservation and pest management or interested in finding sustainability solutions, may find these results of this study compelling enough to suggest additional focused research on the role of disease in the regulation and persistence of animal populations. The risk faced by endangered species may turn out to be a lot higher than initially thought.

A generalized analog implementation of piecewise linear neuron models using CCII building blocks

This paper presents a set of reconfigurable analog implementations of piecewise linear spiking neuron models using second generation current conveyor (CCII) building blocks. With the same topology and circuit elements, without W/L modification which is impossible after circuit fabrication, these circuits can produce different behaviors, similar to the biological neurons, both for a single neuron as well as a network of neurons just by tuning reference current and voltage sources. The models are investigated, in terms of analog implementation feasibility and costs, targeting large scale hardware implementations. Results show that, in order to gain the best performance, area and accuracy; these models can be compromised. Simulation results are presented for different neuron behaviors with CMOS 350 nm technology.

3D reconstruction techniques of human coronary bifurcations for shear stress computations

BACKGROUND

Heterogeneity in plaque composition in human coronary artery bifurcations is associated with blood flow induced shear stress. Shear stress is generally determined by combing 3D lumen data and computational fluid dynamics (CFD). We investigated two new procedures to generate 3D lumen reconstructions of coronary artery bifurcations for shear stress computations.

METHODS

We imaged 10 patients with multislice computer tomography (MSCT) and intravascular ultrasound (IVUS). The 3D reconstruction of the main branch was based on the fusion of MSCT and IVUS. The proximal part of side branch was reconstructed using IVUS data or MSCT data, resulting in two different reconstructions of the bifurcation region. The distal part of the side branch was based on MSCT data alone. The reconstructed lumen was combined with CFD to determine the shear stress. Low and high shear stress regions were defined and shear stress patterns in the bifurcation regions were investigated.

RESULTS

The 3D coronary bifurcations were successfully generated with both reconstruction procedures. The geometrical features of the bifurcation region for the two reconstruction procedures did not reveal appreciable differences. The shear stress maps showed a qualitative agreement, and the low and high shear stress regions were similar in size and average shear stress values were identical. The low and high shear stress regions showed an overlap of approximately 75%.

CONCLUSION

Reconstruction of the side branch with MSCT data alone is an adequate technique to study shear stress and wall thickness in the bifurcation region. The reconstruction procedure can be applied to further investigate the effect of shear stress on atherosclerosis in coronary bifurcations.