A Computational Pipeline to Investigate Longitudinal Blood Flow Changes in the Circle of Willis of Patients with Stable and Growing Aneurysms.

Changes in cerebral blood flow are often associated with the initiation and development of different life-threatening medical conditions including aneurysm rupture and ischemic stroke. Nevertheless, it is not fully clear how haemodynamic changes in time across the Circle of Willis (CoW) are related with intracranial aneurysm (IA) growth. In this work, we introduced a novel reduced-order modelling strategy for the systematic quantification of longitudinal blood flow changes across the whole CoW in patients with stable and unstable/growing aneurysm. Magnetic Resonance Angiography (MRA) images were converted into one-dimensional (1-D) vessel networks through a semi-automated procedure, with a level of geometric reconstruction accuracy controlled by user-dependent parameters. The proposed pipeline was used to systematically analyse longitudinal haemodynamic changes in seven different clinical cases. Our preliminary simulation results indicate that growing aneurysms are not necessarily associated with significant changes in mean flow over time. A concise sensitivity analysis also shed light on which modelling aspects need to be further characterized to have reliable patient-specific predictions. This study poses the basis for investigating how time-dependent changes in the vasculature affect the haemodynamics across the whole CoW in patients with stable and growing aneurysms.

The effect of prone positioning on maternal haemodynamics and fetal wellbeing in the third trimester-A primary cohort study with a scoping review.

INTRODUCTION: Supine sleep position is associated with stillbirth, likely secondary to inferior vena cava compression, and a reduction in cardiac output (CO) and uteroplacental perfusion. Evidence for the effects of prone position in pregnancy is less clear. This study aimed to determine the effect maternal prone position on maternal haemodynamics and fetal heart rate, compared with left lateral position. METHODS: Twenty-one women >28 weeks' gestation underwent non-invasive CO monitoring (Cheetah) every 5 minutes and continuous fetal heart rate monitoring (MONICA) in left lateral (20 minutes), prone (30 minutes), followed by left lateral (20 minutes). Anxiety and comfort were assessed by questionnaires. Regression analyses (adjusted for time) compared variables between positions. The information derived from the primary study was used in an existing mathematical model of maternal circulation in pregnancy, to determine whether occlusion of the inferior vena cava could account for the observed effects. In addition, a scoping review was performed to identify reported clinical, haemodynamic and fetal effects of maternal prone position; studies were included if they reported clinical outcomes or effects or maternal prone position in pregnancy. Study records were grouped by publication type for ease of data synthesis and critical analysis. Meta-analysis was performed where there were sufficient studies. RESULTS: Maternal blood pressure (BP) and total vascular resistance (TVR) were increased in prone (sBP 109 vs 104 mmHg, p = 0.03; dBP 74 vs 67 mmHg, p = 0.003; TVR 1302 vs 1075 dyne.s-1cm-5, p = 0.03). CO was reduced in prone (5.7 vs 7.1 mL/minute, p = 0.003). Fetal heart rate, variability and decelerations were unaltered. However, fetal accelerations were less common in prone position (86% vs 95%, p = 0.03). Anxiety was reduced after the procedure, compared to beforehand (p = 0.002), despite a marginal decline in comfort (p = 0.04).The model predicted that if occlusion of the inferior vena cava occurred, the sBP, dBP and CO would generally decrease. However, the TVR remained relatively consistent, which implies that the MAP and CO decrease at a similar rate when occlusion occurs. The scoping review found that maternal and fetal outcomes from 47 included case reports of prone positioning during pregnancy were generally favourable. Meta-analysis of three prospective studies investigating maternal haemodynamic effects of prone position found an increase in sBP and maternal heart rate, but no effect on respiratory rate, oxygen saturation or baseline fetal heart rate (though there was significant heterogeneity between studies). CONCLUSION: Prone position was associated with a reduction in CO but an uncertain effect on fetal wellbeing. The decline in CO may be due to caval compression, as supported by the computational model. Further work is needed to optimise the safety of prone positioning in pregnancy. TRIAL REGISTRATION: This trial was registered at clinicaltrials.gov (NCT04586283).

Transient changes during microwave ablation simulation : a comparative shape analysis.

Microwave ablation therapy is a hyperthermic treatment for killing cancerous tumours whereby microwave energy is dispersed into a target tissue region. Modelling can provide a prediction for the outcome of ablation, this paper explores changes in size and shape of temperature and Specific absorption rate fields throughout the course of simulated treatment with different probe concepts. Here, an axisymmetric geometry of a probe embedded within a tissue material is created, solving coupled electromagnetic and bioheat equations using the finite element method, utilizing hp discretisation with the NGSolve library. Results show dynamic changes across all metrics, with different responses from different probe concepts. The sleeve probe yielded the most circular specific absorption rate pattern with circularity of 0.81 initially but suffered the largest reduction throughout ablation. Similarly, reflection coefficients differ drastically from their initial values, with the sleeve probe again experiencing the largest change, suggesting that it is the most sensitive the changes in the tissue dielectric properties in these select probe designs. These collective characteristic observations highlight the need to consider dielectric property changes and probe specific responses during the design cycle.

Personalising cardiovascular network models in pregnancy: A two-tiered parameter estimation approach.

Uterine artery Doppler waveforms are often studied to determine whether a patient is at risk of developing pathologies such as pre-eclampsia. Many uterine waveform indices have been developed, which attempt to relate characteristics of the waveform with the physiological adaptation of the maternal cardiovascular system, and are often suggested to be an indicator of increased placenta resistance and arterial stiffness. Doppler waveforms of four patients, two of whom developed pre-eclampsia, are compared with a comprehensive closed-loop model of pregnancy. The closed-loop model has been previously validated but has been extended to include an improved parameter estimation technique that utilises systolic and diastolic blood pressure, cardiac output, heart rate, and pulse wave velocity measurements to adapt model resistances, compliances, blood volume, and the mean vessel areas in the main systemic arteries. The shape of the model-predicted uterine artery velocity waveforms showed good agreement with the characteristics observed in the patient Doppler waveforms. The personalised models obtained now allow a prediction of the uterine pressure waveforms in addition to the uterine velocity. This allows for a more detailed mechanistic analysis of the waveforms, eg, wave intensity analysis, to study existing clinical indices. The findings indicate that to accurately estimate arterial stiffness, both pulse pressure and pulse wave velocities are required. In addition, the results predict that patients who developed pre-eclampsia later in pregnancy have larger vessel areas in the main systemic arteries compared with the two patients who had normal pregnancy outcomes.

A data-driven model to study utero-ovarian blood flow physiology during pregnancy.

In this paper, we describe a mathematical model of the cardiovascular system in human pregnancy. An automated, closed-loop 1D-0D modelling framework was developed, and we demonstrate its efficacy in (1) reproducing measured multi-variate cardiovascular variables (pulse pressure, total peripheral resistance and cardiac output) and (2) providing automated estimates of variables that have not been measured (uterine arterial and venous blood flow, pulse wave velocity, pulsatility index). This is the first model capable of estimating volumetric blood flow to the uterus via the utero-ovarian communicating arteries. It is also the first model capable of capturing wave propagation phenomena in the utero-ovarian circulation, which are important for the accurate estimation of arterial stiffness in contemporary obstetric practice. The model will provide a basis for future studies aiming to elucidate the physiological mechanisms underlying the dynamic properties (changing shapes) of vascular flow waveforms that are observed with advancing gestation. This in turn will facilitate the development of methods for the earlier detection of pathologies that have an influence on vascular structure and behaviour.

Computational investigation of the Laplace law in compression therapy.

This study aims to use computational methods for elucidating the effect of limb shape on subgarment and subcutaneous pressures, stresses and strains. A framework was built that generates computational models from 3D arm scans using a depth sensing camera. Finite Element Analysis (FEA) was performed on the scans taken from 23 lymphoedema patients. Subgarment pressures were calculated based on local curvature for each patient and showed a large variability of pressure across each arm. Across the cohort an average maximum subgarment pressure of 5100 Pa was found as opposed to an intended garment pressure of 2500 Pa. Subcutaneous results show that stresses/strains in the adipose tissues more closely follow the subgarment pressures than in the stiffer skin tissues. Another novel finding was that a negative axial gradient in subgarment pressure (from wrist to elbow) consistently led to positive axial gradients for the Von Mises stresses in the adipose tissues; a phenomenon caused by a combination of arm shape and the stiffness ratio between skin and adipose tissues. In conclusion, this work fills a knowledge gap in compression therapy in clinical practice and can inform garment design or lead to optimal treatment strategies.

A fully coupled fluid-structure interaction model of the secondary lymphatic valve.

The secondary lymphatic valve is a bi-leaflet structure frequent throughout collecting vessels that serves to prevent retrograde flow of lymph. Despite its vital function in lymph flow and apparent importance in disease development, the lymphatic valve and its associated fluid dynamics have been largely understudied. The goal of this work was to construct a physiologically relevant computational model of an idealized rat mesenteric lymphatic valve using fully coupled fluid-structure interactions to investigate the relationship between three-dimensional flow patterns and stress/deformation within the valve leaflets. The minimum valve resistance to flow, which has been shown to be an important parameter in effective lymphatic pumping, was computed as 268 g/mm4-s. Hysteretic behavior of the lymphatic valve was confirmed by comparing resistance values for a given transvalvular pressure drop during opening and closing. Furthermore, eddy structures were present within the sinus adjacent to the valve leaflets in what appear to be areas of vortical flow; the eddy structures were characterized by non-zero velocity values (up to ∼4 mm/s) in response to an applied unsteady transvalvular pressure. These modeling capabilities present a useful platform for investigating the complex interplay between soft tissue motion and fluid dynamics of lymphatic valves and contribute to the breadth of knowledge regarding the importance of biomechanics in lymphatic system function.

Investigation of Shape with Patients Suffering from Unilateral Lymphoedema.

This study investigates the use of a 3D depth sensing camera for analysing the shape of lymphoedematous arms, and seeks to identify suitable metrics for monitoring lymphoedema clinically. A fast, simple protocol was developed for scanning upper limb lymphoedema, after which a robust data pre- and post-processing framework was built that consistently and quickly identifies arm shape and volume. The framework was then tested on 24 patients with mild unilateral lymphoedema, who were also assessed using tape measurements. The scanning protocol developed led to scanning times of about 20-30 s. Shape related metrics such as circumference and circularity were used to distinguish between affected and healthy arms (p ≤ 0.05). Swelling maps were also derived to identify the distribution of oedema on arms. Topology and shape could be used to monitor or even diagnose lymphoedema using the provided framework. Such metrics provide more detailed information to a lymphoedema specialist than solely volume. Although tested on a small cohort, these results show promise for further research into better diagnostics of lymphoedema and for future adoption of the proposed methods across lymphoedema clinics.

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

Lymphatic valves facilitate the lymphatic system's 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.

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.

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.

An implicit solver for 1D arterial network models.

In this study, the 1D blood flow equations are solved using a newly proposed enhanced trapezoidal rule method (ETM), which is an extension to the simplified trapezoidal rule method. At vessel junctions, the conservation of mass and conservation of total pressure are held as system constraints using Lagrange multipliers that can be physically interpreted as external flow rates. The ETM scheme is compared with published arterial network benchmark problems and a dam break problem. Strengths of the ETM scheme include being simple to implement, intuitive connection to lumped parameter models, and no restrictive stability criteria such as the Courant-Friedrichs-Lewy (CFL) number. The ETM scheme does not require the use of characteristics at vessel junctions, or for inlet and outlet boundary conditions. The ETM forms an implicit system of equations, which requires only one global solve per time step for pressure, followed by flow rate update on the elemental system of equations; thus, no iterations are required per time step. Consistent results are found for all benchmark cases, and for a 56-vessel arterial network problem, it gives very satisfactory solutions at a spatial and time discretization that results in a maximum CFL of 3, taking 4.44 seconds per cardiac cycle. By increasing the time step and element size to produce a maximum CFL number of 15, the method takes only 0.39 second per cardiac cycle with only a small compromise on accuracy.

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.

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.