Raoul van Loon

Determining the combined effect of the lymphatic valve leaflets and sinus on resistance to forward flow

The lymphatic system is vital to a proper maintenance of fluid and solute homeostasis. Collecting lymphatics are composed of actively contracting tubular vessels segmented by bulbous sinus regions that encapsulate bi-leaflet check valves. Valve resistance to forward flow strongly influences pumping performance. However, because of the sub-millimeter size of the vessels with flow rates typically <1 ml/h and pressures of a few cmH2O, resistance is difficult to measure experimentally. Using a newly defined idealized geometry, we employed an uncoupled approach where the solid leaflet deflections of the open valve were computed and lymph flow calculations were subsequently performed. We sought to understand: 1) the effect of sinus and leaflet size on the resulting deflections experienced by the valve leaflets and 2) the effects on valve resistance to forward flow of the fully open valve. For geometries with sinus-to-root diameter ratios >1.39, the average resistance to forward flow was 0.95×10(6)[g/(cm4 s)]. Compared to the viscous pressure drop that would occur in a straight tube the same diameter as the upstream lymphangion, valve leaflets alone increase the pressure drop up to 35%. However, the presence of the sinus reduces viscous losses, with the net effect that when combined with leaflets the overall resistance is less than that of the equivalent continuing straight tube. Accurately quantifying resistance to forward flow will add to the knowledge used to develop therapeutics for treating lymphatic disorders and may eventually lead to understanding some forms of primary lymphedema.

A comparative study of fractional step method in its quasi-implicit, semi-implicit and fully-explicit forms for incompressible flows

Purpose – The purpose of this paper is to describe and analyse a class of finite element fractional step methods for solving the incompressible Navier-Stokes equations. The objective is not to reproduce the extensive contributions on the subject, but to report on long-term experience with and provide a unified overview of a particular approach: the characteristic-based split method. Three procedures, the semi-implicit, quasi-implicit and fully explicit, are studied and compared. Design/methodology/approach – This work provides a thorough assessment of the accuracy and efficiency of these schemes, both for a first and second order pressure split. Findings – In transient problems, the quasi-implicit form significantly outperforms the fully explicit approach. The second order (pressure) fractional step method displays significant convergence and accuracy benefits when the quasi-implicit projection method is employed. The fully explicit method, utilising artificial compressibility and a pseudo time stepping p...

Data-driven modelling of the FRC network for studying the fluid flow in the conduit system

Abstract The human immune system is characterized by enormous cellular and anatomical complexity. Lymph nodes are key centers of immune reactivity, organized into distinct structural and functional modules including the T-cell zone, fibroblastic reticular cell (FRC) network and the conduit system. A thorough understanding of the modular organization is a prerequisite for lymphoid organ tissue-engineering. Due to the biological complexity of lymphoid organs, the development of mathematical models capable of elaborating the lymph node architecture and functional organization, has remained a major challenge in computational biology. Here, we present a computational method to model the geometry of the FRC network and fluid flow in the conduit system. It differs from the blood vascular network image-based reconstruction approaches as it develops the parameterized geometric model using the real statistics of the node degree and the edge length distributions. The FRC network model is then used to analyze the fluid flow through the underlying conduit system. A first observation is that the pressure gradient is approximately linear, which suggests homogeneity of the network. Furthermore, calculated permeability values ( ≈ 0.0033 μ m 2 ) show the generated network is isotropic, while investigating random variations of pipe radii (with a given mean and standard deviation) shows a significant effect on the permeability. This framework can now be further explored to systematically correlate fundamental characteristics of the FRC conduit system to more global material properties such as permeability.

A novel method for non-invasively detecting the severity and location of aortic aneurysms

The influence of an aortic aneurysm on blood flow waveforms is well established, but how to exploit this link for diagnostic purposes still remains challenging. This work uses a combination of experimental and computational modelling to study how aneurysms of various size affect the waveforms. Experimental studies are carried out on fusiform-type aneurysm models, and a comparison of results with those from a one-dimensional fluid–structure interaction model shows close agreement. Further mathematical analysis of these results allows the definition of several indicators that characterize the impact of an aneurysm on waveforms. These indicators are then further studied in a computational model of a systemic blood flow network. This demonstrates the methods’ ability to detect the location and severity of an aortic aneurysm through the analysis of flow waveforms in clinically accessible locations. Therefore, the proposed methodology shows a high potential for non-invasive aneurysm detectors/monitors.

Critical Issues in Modelling Lymph Node Physiology

In this study, we discuss critical issues in modelling the structure and function of lymph nodes (LNs), with emphasis on how LN physiology is related to its multi-scale structural organization. In addition to macroscopic domains such as B-cell follicles and the T cell zone, there are vascular networks which play a key role in the delivery of information to the inner parts of the LN, i.e., the conduit and blood microvascular networks. We propose object-oriented computational algorithms to model the 3D geometry of the fibroblastic reticular cell (FRC) network and the microvasculature. Assuming that a conduit cylinder is densely packed with collagen fibers, the computational flow study predicted that the diffusion should be a dominating process in mass transport than convective flow. The geometry models are used to analyze the lymph flow properties through the conduit network in unperturbed- and damaged states of the LN. The analysis predicts that elimination of up to 60%–90% of edges is required to stop the lymph flux. This result suggests a high degree of functional robustness of the network.

Influences of domain extensions to a moderately stenosed patient‐specific carotid bifurcation: Investigation of wall quantities

Purpose – The purpose of this paper is to numerically study blood flow through a subject‐specific carotid artery with a moderately severe stenosis, also to thoroughly analyse the wall shear stress (WSS), oscillatory shear index (OSI) and WSS angular deviation (WSSAD). One of the important aspects of this study is the investigation on the influence of the extensions attached to the domain outlets.Design/methodology/approach – The segmentation of the carotid artery is carried out using a deformable model based on a level set method. A geometric potential force (GPF) is employed to deform the level set to obtain the carotid artery geometry. The initial surface meshing is generated using an advanced marching cubes (MC) method, before improving the quality of the surface mesh via a number of mesh cosmetic steps. The volume mesh generation has two parts. In the first part, a quasi‐structured, boundary layer mesh is generated in the vicinity of the geometry walls. The second part of the meshing involves unstruct...

Pore-Scale Modeling of Non-Newtonian Shear-Thinning Fluids in Blood Oxygenator Design

This paper reviews and further develops pore-scale computational flow modeling techniques used for creeping flow through orthotropic fiber bundles used in blood oxygenators. Porous model significantly reduces geometrical complexity by taking a homogenization approach to model the fiber bundles. This significantly simplifies meshing and can avoid large time-consuming simulations. Analytical relationships between permeability and porosity exist for Newtonian flow through regular arrangements of fibers and are commonly used in macroscale porous models by introducing a Darcy viscous term in the flow momentum equations. To this extent, verification of analytical Newtonian permeability-porosity relationships has been conducted for parallel and transverse flow through square and staggered arrangements of fibers. Similar procedures are then used to determine the permeability-porosity relationship for non-Newtonian blood. The results demonstrate that modeling non-Newtonian shear-thinning fluids in porous media can be performed via a generalized Darcy equation with a porous medium viscosity decomposed into a constant term and a directional expression through least squares fitting. This concept is then investigated for various non-Newtonian blood viscosity models. The proposed methodology is conducted with two different porous model approaches, homogeneous and heterogeneous, and validated against a high-fidelity model. The results of the heterogeneous porous model approach yield improved pressure and velocity distribution which highlights the importance of wall effects.

Formulation of Generalized Mass Transfer Correlations for Blood Oxygenator Design

This paper numerically investigates non-Newtonian blood flow with oxygen and carbon dioxide transport across and along an array of uniformly square and staggered arranged fibers at various porosity (ε) levels, focussing on a low Reynolds number regime (Re < 10). The objective is to establish suitable mass transfer correlations, expressed in the form of Sherwood number (Sh = f(ε, Re, Sc)), that identifies the link from local mass transfer investigations to full-device analyses. The development of a concentration field is initially investigated and expressions are established covering the range from a typical deoxygenated condition up to a full oxygenated condition. An important step is identified where a cut-off point in those expressions is required to avoid any under- or over-estimation on the Sherwood number. Geometrical features of a typical commercial blood oxygenator is adopted and results in general show that a balance in pressure drop, shear stress, and mass transfer is required to avoid potential blood trauma or clotting formation. Different definitions of mass transfer correlations are found for oxygen/carbon dioxide, parallel/transverse flow, and square/staggered configurations, respectively. From this set of correlations, it is found that transverse flow has better gas transfer than parallel flow which is consistent with reported literature. The mass transfer dependency on fiber configuration is observed to be pronounced at low porosity. This approach provides an initial platform when one is looking to improve the mass transfer performance in a blood oxygenator without the need to conduct any numerical simulations or experiments.

Mathematical Techniques for Circulatory Systems

This article provides an overview on how human circulation is computationally modeled. The discussion presented explains all the latest development in the field and emphasizes the areas that need research focus. The article consists of fundamentals of the circulation, mathematical models, dealing with arterial and venous systems, organs, microcirculation, and parameters involved. The discussion also provides details on why certain parameters are difficult to obtain. The article also accounts in detail the computational models used to solve flow circulation. Although interesting to understand the modeling of circulation, the models should be useful and insightful. This article discusses the usefulness of circulation models and their limitations.

Integrated geometric and mechanical analysis of an image-based lymphatic valve

Lymphatic valves facilitate the lymphatic systems role in maintaining fluid homeostasis. Malformed valves are found in several forms of primary lymphœdema, resulting in incurable swelling of the tissues and immune dysfunction. Their experimental study is complicated by their small size and operation in low pressure and low Reynolds number environments. Mathematical models of these structures can give insight and complement experimentation. In this work, we present the first valve geometry reconstructed from confocal imagery and used in the construction of a subject-specific model in a closing mode. A framework is proposed whereby an image is converted into a valve model. An FEA study was performed to identify the significance of the shear modulus, the consequences of smoothing the leaflet surface and the effect of wall motion on valve behaviour. Smoothing is inherent to any analysis from imagery. The nature of the image, segmentation and meshing all cause attenuation of high-frequency features. Smoothing not only causes loss of surface area but also the loss of high-frequency geometric features which may reduce stiffness. This work aimed to consider these effects and inform studies by taking a manual reconstruction and through manifold harmonic analysis, attenuating higher frequency features to replicate lower resolution images or lower degree-of-freedom reconstructions. In conclusion, two metrics were considered: trans-valvular pressure required to close the valve, ΔPc, and the retrograde volume displacement after closure. The higher ΔPc, the greater the volume of lymph that will pass through the valve during closure. Retrograde volume displacement after closure gives a metric of compliance of the valve and for the quality of the valve seal. In the case of the image-specific reconstructed valve, removing features with a wavelength longer than four μm caused changes in ΔPc. Varying the shear modulus from 10 kPa to 60 kPa caused a 3.85-fold increase in the retrograde volume displaced. The inclusion of a non-rigid wall caused ΔPc to increase from 1.56 to 2.52 cmH2O.