Speckle variance optical coherence tomography of blood flow in the beating mouse embryonic heart

Efficient separation of blood and cardiac wall in the beating embryonic heart is essential and critical for experiment‐based computational modelling and analysis of early‐stage cardiac biomechanics. Although speckle variance optical coherence tomography (SV‐OCT) relying on calculation of intensity variance over consecutively acquired frames is a powerful approach for segmentation of fluid flow from static tissue, application of this method in the beating embryonic heart remains challenging because moving structures generate SV signal indistinguishable from the blood. Here, we demonstrate a modified four‐dimensional SV‐OCT approach that effectively separates the blood flow from the dynamic heart wall in the beating mouse embryonic heart. The method takes advantage of the periodic motion of the cardiac wall and is based on calculation of the SV signal over the frames corresponding to the same phase of the heartbeat cycle. Through comparison with Doppler OCT imaging, we validate this speckle‐based approach and show advantages in its insensitiveness to the flow direction and velocity as well as reduced influence from the heart wall movement. This approach has a potential in variety of applications relying on visualization and segmentation of blood flow in periodically moving structures, such as mechanical simulation studies and finite element modelling. Picture : Four‐dimensional speckle variance OCT imaging shows the blood flow inside the beating heart of an E8.5 mouse embryo.     

Recent Advances in Computational Simulation of Macro-, Meso-, and Micro-Scale Biomimetics Related Fluid Flow Problems

Over the last decade, computational methods have been intensively applied to a variety of scientific researches and engineering designs. Although the computational fluid dynamics （CFD） method has played a dominant role in studying and simulating transport phenomena involving fluid flow and heat and mass transfers, in recent years, other numerical methods for the simulations at meso- and micro-scales have also been actively applied to solve the physics of complex flow and fluid-interface interactions. This paper presents a review of recent advances in multi-scale computational simulation of biomimetics related fluid flow problems. The state-of-the-art numerical techniques, such as lattice Boltzmann method （LBM）, molecular dynamics （MD）, and conventional CFD, applied to different problems such as fish flow, electro-osmosis effect of earthworm motion, and self-cleaning hydrophobic surface, and the numerical approaches are introduced. The new challenging of modelling biomimetics problems in developing the physical conditions of self-clean hydrophobic surfaces is discussed.     

Hydrodynamics of bolus flow—An analytical approach to blood flow in capillaries

A model which was used by Prothero and Burton to simulate a particular configuration in capillary blood vessels is investigated from a hydrodynamic point of view. In this model, the erythrocytes are approximated by rigid pistons, and plasma is assumed to be an incompressible Newtonian fluid. An order of magnitude analysis using the physiologically realistic values for various parameters reduces the exact equations of motion to an equation describing the creeping motion of the fluid. An analytical approach to the solution of the equation is proposed and some results are reported here. The solution of the flow field is given in terms of a stream function which is represented by two infinite series composed of known functions. Two coupled infinite systems of algebraic equations determining the coefficients of the two series have been derived. This method of solution is proposed as an alternative to the entirely numerical procedure of solving the similar problem proposed by Bugliarelloet al. A limiting case of large aspect ratio (the ratio of the axial spacing of the two successive erythrocytes to the capillary diameter) is studied and the solution, valid away from the erythrocyte surface, has been obtained in simple form. It resembles the classical Poisenille flow, but the pressure gradient is related to the erythrocyte speed.     

Influence of Hall Current and Viscous Dissipation on Pressure Driven Flow of Pseudoplastic Fluid with Heat Generation: A Mathematical Study

In this paper, we study the influence of heat sink (or source) on the peristaltic motion of pseudoplastic fluid in the presence of Hall current, where channel walls are non-conducting in nature. Flow analysis has been carried out under the approximations of a low Reynolds number and long wavelength. Coupled equations are solved using shooting method for numerical solution for the axial velocity function, temperature and pressure gradient distributions. We analyze the influence of various interesting parameters on flow quantities. The present study can be considered as a mathematical presentation of the dynamics of physiological organs with stones.     

A three-dimensional computational analysis of fluid-structure interaction in the aortic valve

Numerical analysis of the aortic valve has mainly been focused on the closing behaviour during the diastolic phase rather than the kinematic opening and closing behaviour during the systolic phase of the cardiac cycle. Moreover, the fluid-structure interaction in the aortic valve system is most frequently ignored in numerical modelling. The effect of this interaction on the valve's behaviour during systolic functioning is investigated. The large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood-valve interaction modelling. This has impeded numerical analyses of valves operating under physiological conditions. A numerical method, known as the Lagrange multiplier based fictitious domain method, is used to describe the large leaflet motion within the computational fluid domain. This method is applied to a three-dimensional finite element model of a stented aortic valve. The model provides both the mechanical behaviour of the valve and the blood flow through it. Results show that during systole the leaflets of the stented valve appear to be moving with the fluid in an essentially kinematical process governed by the fluid motion.     

Computational analysis of coupled blood-wall arterial LDL transport

The transport of macromolecules, such as low density lipoproteins (LDLs), across the artery wall and their accumulation in the wall is a key step in atherogenesis. Our objective was to model fluid flow within both the lumen and wall of a constricted, axisymmetric tube simulating a stenosed artery, and to then use this flow pattern to study LDL mass transport from the blood to the artery wall. Coupled analysis of lumenal blood flow and transmural fluid flow was achieved through the solution of Brinkman's model, which is an extension of the Navier-Stokes equations for porous media. This coupled approach offers advantages over traditional analyses of this problem, which have used possibly unrealistic boundary conditions at the blood-wall interface; instead, we prescribe a more natural pressure boundary condition at the adventitial vasa vasorum, and allow variations in wall permeability due to the occurrence of plaque. Numerical complications due to the convection dominated mass transport process (low LDL diffusivity) are handled by the streamline upwind/Petrov-Galerkin (SUPG) finite element method. This new fluid-plus-porous-wall method was implemented for conditions typical of LDL transport in a stenosed artery with a 75 percent area reduction (Peclet number=2 x 10(8)). The results show an elevated LDL concentration at the downstream side of the stenosis. For the higher Darcian wall permeability thought to occur in regions containing atheromatous lesions, this leads to an increased transendothelial LDL flux downstream of the stenosis. Increased transmural filtration in such regions, when coupled with a concentration-dependent endothelial permeability to LDL, could be an important contributor to LDL infiltration into the arterial wall. Experimental work is needed to confirm these results.     

In vivo mimicking model for solid tumor towards hydromechanics of tissue deformation and creation of necrosis

The present work addresses transvascular and interstitial fluid transport inside a solid tumor surrounded by normal tissue (close to an in vivo mimicking setup). In general, biological tissues behave like a soft porous material and show mechanical behavior towards the fluid motion through the interstitial space. In general, forces like viscous drag that are associated with the fluid flow may compress the tissue material. On the macroscopic level, we try to model the motion of fluids and macromolecules through the interstitial space of solid tumor and the normal tissue layer. The transvascular fluid transport is assumed to be governed by modified Starling’s law. The poroelastohydrodynamics (interstitial hydrodynamics and the deformation of tissue material) inside the tumor and normal tissue regions is modeled using linearized biphasic mixture theory. Correspondingly, the velocity distribution of fluid is coupled to the displacement field of the solid phase (mainly cellular phase and extracellular matrix) in both the normal and tumor tissue regions. The corresponding velocity field is used within the transport reaction equation for fluids and macromolecules through interstitial space to get the overall solute (e.g., nutrients, drug, and other macromolecules) distribution. This study justifies that the presence of the normal tissue layer plays a significant role in delaying/assisting necrosis inside the tumor tissue. It is observed that the exchange process of fluids and macromolecules across the interface of the tumor and normal tissue affects the effectiveness factor corresponding to the tumor tissue.     

Numerical simulation of blood flow in the left ventricle and aortic sinus using magnetic resonance imaging and computational fluid dynamics

Understanding cardiac blood flow patterns has many applications in analysing haemodynamics and for the clinical assessment of heart function. In this study, numerical simulations of blood flow in a patient-specific anatomical model of the left ventricle (LV) and the aortic sinus are presented. The realistic 3D geometry of both LV and aortic sinus is extracted from the processing of magnetic resonance imaging (MRI). Furthermore, motion of inner walls of LV and aortic sinus is obtained from cine-MR image analysis and is used as a constraint to a numerical computational fluid dynamics (CFD) model based on the moving boundary approach. Arbitrary Lagrangian–Eulerian finite element method formulation is used for the numerical solution of the transient dynamic equations of the fluid domain. Simulation results include detailed flow characteristics such as velocity, pressure and wall shear stress for the whole domain. The aortic outflow is compared with data obtained by phase-contrast MRI. Good agreement was found between simulation results and these measurements.     

Blood flow multiscale phenomena

The cardiovascular disease is one of most frequent cause deaths in modern society. The objective of this work is analyse the effect of dynamic vascular geometry (curvature, torsion, bifurcation) and pulsatile blood nature on secondary flow, wall shear stress and platelet deposition. The problem was examined as multi-scale physical phenomena using perturbation analysis and numerical modelling. The secondary flow determined as influence pulsatile pressure, vascular tube time-dependent bending and torsion on the main axial flow. Bifurcation and branching phenomena are analysed experimentally through, blood-like fluid pulsatile flow across elastic rubber-like Y-model model. The problem complex geometry near branching in platelet deposit modelling is resolved numerically as Falker-Skan flow.     

Construction of Multi-Scale Consistent Brain Networks: Methods and Applications

Mapping human brain networks provides a basis for studying brain function and dysfunction, and thus has gained significant interest in recent years. However, modeling human brain networks still faces several challenges including constructing networks at multiple spatial scales and finding common corresponding networks across individuals. As a consequence, many previous methods were designed for a single resolution or scale of brain network, though the brain networks are multi-scale in nature. To address this problem, this paper presents a novel approach to constructing multi-scale common structural brain networks from DTI data via an improved multi-scale spectral clustering applied on our recently developed and validated DICCCOLs (Dense Individualized and Common Connectivity-based Cortical Landmarks). Since the DICCCOL landmarks possess intrinsic structural correspondences across individuals and populations, we employed the multi-scale spectral clustering algorithm to group the DICCCOL landmarks and their connections into sub-networks, meanwhile preserving the intrinsically-established correspondences across multiple scales. Experimental results demonstrated that the proposed method can generate multi-scale consistent and common structural brain networks across subjects, and its reproducibility has been verified by multiple independent datasets. As an application, these multi-scale networks were used to guide the clustering of multi-scale fiber bundles and to compare the fiber integrity in schizophrenia and healthy controls. In general, our methods offer a novel and effective framework for brain network modeling and tract-based analysis of DTI data.     

Flow-induced permeation of non-occlusive blood clots: an MRI study and modelling

The success of clot thrombolysis very much depends on efficient clot permeation with blood plasma carrying the thrombolytic agent. In this paper clot permeation was studied by dynamic magnetic resonance imaging (MRI) on artificial non-occlusive blood clots inserted in an artificial circulation system filled with blood plasma to which an MRI contrast agent was added. The MRI results revealed that clot permeation is much faster and more efficient at the entrance of the flow channel across the clot. Clot permeation with fluid was simulated numerically as well. The simulation was based on numerical solution of Navier-Stokes equations for the flow in the channel and within the clot. The clot was considered as a porous material with known permeability and porosity. Based on the calculated velocity profiles, concentration profiles of fluid in the clot were modelled. These agreed well with the MRI results. The presented model of clot permeation with fluid may also serve as a useful extension to numerical modelling of dissolution of non-occlusive blood clots during thrombolytic therapy.     

A fast strong coupling algorithm for the partitioned fluid–structure interaction simulation of BMHVs

The numerical simulation of Bileaflet Mechanical Heart Valves (BMHVs) has gained strong interest in the last years, as a design and optimisation tool. In this paper, a strong coupling algorithm for the partitioned fluid–structure interaction simulation of a BMHV is presented. The convergence of the coupling iterations between the flow solver and the leaflet motion solver is accelerated by using the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet accelerations. This Jacobian is numerically calculated from the coupling iterations. An error analysis is done to derive a criterion for the selection of useable coupling iterations. The algorithm is successfully tested for two 3D cases of a BMHV and a comparison is made with existing coupling schemes. It is observed that the developed coupling scheme outperforms these existing schemes in needed coupling iterations per time step and CPU time.     

Finding essential scales of spatial variation in ecological data: a multivariate approach

The identification of spatial structures is a key step in understanding the ecological processes structuring the distribution of organisms. Spatial patterns in species distributions result from a combination of several processes occuring at different scales: identifying these scales is thus a crucial issue. Recent studies have proposed a new family of spatial predictors (PCNM: principal coordinates of neighbours matrices; MEMs: Moran's eigenvectors maps) that allow for modelling of spatial variation on different scales. To assess the multi-scale spatial patterns in multivariate data, these variables are often used as predictors in constrained ordination methods. However, the selection of the appropriate spatial predictors is still troublesome, and the identification of the main scales of spatial variation remains an open question. This paper presents a new statistical tool to tackle this issue: the multi-scale pattern analysis (MSPA). This ordination method uses MEMs to decompose ecological variability into several spatial scales and then summarizes this decomposition using graphical representations. A canonical form of MSPA can also be used to assess the spatial scales of the species-environment relationships. MSPA is compared to constrained ordination using simulated data, and illustrated using the famous oribatid mites dataset. The method is implemented in the free software R.     

Investigation of hydrodynamic focusing in a microfluidic coulter counter device

The Coulter technique enables rapid analysis of particles or cells suspended in a fluid stream. In this technique, the cells are suspended in an electrically conductive solution, which is hydrodynamically focused by nonconducting sheath flows. The cells produce a characteristic voltage signal when they interrupt an electrical path. The population and size of the cells can be obtained through analyzing the voltage signal. In a microfluidic Coulter counter device, the hydrodynamic focusing technique is used to position the conducting sample stream and the cells and also to separate close cells to generate distinct signals for each cell and avoid signal jam. The performance of hydrodynamic focusing depends on the relative flow ratio between the sample stream and sheath stream. We use a numerical approach to study the hydrodynamic focusing in a microfluidic Coulter counter device. In this approach, the flow field is described by solving the incompressible Navier-Stokes equations. The sample stream concentration is modeled by an advection-diffusion equation. The motion of the cells is governed by the Newton-Euler equations of motion. Particle motion through the flow field is handled using an overlapping grid technique. A numerical model for studying a microfluidic Coulter counter has been validated. Using the model, the impact of relative flow rate on the performance of hydrodynamic focusing was studied. Our numerical results show that the position of the sample stream can be controlled by adjusting the relative flow rate. Our simulations also show that particles can be focused into the stream and initially close particles can be separated by the hydrodynamic focusing. From our study, we conclude that hydrodynamic focusing provides an effective way to control the position of the sample stream and cells and it also can be used to separate cells to avoid signal jam.     

A Porous Media Approach to Finite Deformation Behaviour in Soft Tissues

The present work presents a porous medium formulation for the biomechanical analysis of soft tissues. An updated Lagrangian approach is developed to study the coupled effects of low speed flows of fluid phases, in partially or fully saturated conditions, and the finite deformation occurring in the solid matrix. The procedure developed allows both for the evaluation of coupled geometric and material non-linearities. The main theoretical and computational aspects of this multiphase formulation are discussed. The finite element method is used for the numerical solution of the resulting coupled system of equations. A reference case is reported with regard to healthy and degenerative phases of intervertebral segment. Results reported allow for a detailed interpretation of the formulation reliability, also by comparison with existing experimental data. In particular, the role played by the fluid on the load carrying mechanism is pointed out, thus stressing the importance of a multiphase approach to the overall behaviour of the spinal motion segment in time.     

Multi-scale parametric spectral analysis for exon detection in DNA sequences based on forward-backward linear prediction and singular value decomposition of the double-base curves

This paper presents a new method for exon detection in DNA sequences based on multi-scale parametric spectral analysis. A forward-backward linear prediction (FBLP) with the singular value decomposition (SVD) algorithm FBLP-SVD is applied to the double-base curves (DB-curves) of a DNA sequence using a variable moving window sizes to estimate the signal spectrum at multiple scales. Simulations are done on short human genes in the range of 11bp to 2032bp and the results show that our proposed method out-performs the classical Fourier transform method. The multi-scale approach is shown to be more effective than using a single scale with a fixed window size. In addition, our method is flexible as it requires no training data.     

Shape optimization in unsteady blood flow: a numerical study of non-Newtonian effects

This paper presents a numerical study of non-Newtonian effects on the solution of shape optimization problems involving unsteady pulsatile blood flow. We consider an idealized two dimensional arterial graft geometry. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the modified Cross model employed to account for the shear-thinning behavior of blood. Using a gradient-based optimization algorithm, we compare the optimal shapes obtained using both the Newtonian and generalized Newtonian constitutive equations. Depending on the shear rate prevalent in the domain, substantial differences in the flow as well as in the computed optimal shape are observed when the Newtonian constitutive equation is replaced by the modified Cross model. By varying a geometric parameter in our test case, we investigate the influence of the shear rate on the solution.     

Geographical patterns of morphological variation and environmental correlates in contact zones: a multi-scale approach using two Mediterranean vipers (Serpentes)

Adaptation to similar selective pressures can explain morphological convergence between closely related species in contact zones. Geostatistics and Geographical Information System were used to identify multi-scale patterns of morphological variability and test the hypothesis of morphological convergence due to local environmental pressures in the contact areas between Vipera aspis and Vipera latastei in the Iberian Peninsula. Nine morphological traits from 630 and 362 vipers at regional and local scale, respectively, were interpolated by Kriging to generate surfaces of morphological variation. Kriging is a geostatistical algorithm that allows investigating the spatial structure of data with statistical models. At both scales, a convergent north–south pattern in morphological variability was observed and the contact areas were identified as integration zones where intermediate vipers are found. Significant correlations were found between surfaces of univariate and multivariate traits, with precipitation and temperature seasonality. Thus, several morphological traits were apparently under local environmental selection. Nevertheless, the influence of biotic pressures and gene flow on morphological convergence of vipers in contact zones deserves further study.