Pulsatility damping in the microcirculation: Basic pattern and modulating factors.

Blood flow pulsatility is an important determinant of macro- and microvascular physiology. Pulsatility is damped largely in the microcirculation, but the characteristics of this damping and the factors that regulate it have not been fully elucidated yet. Applying computational approaches to real microvascular network geometry, we examined the pattern of pulsatility damping and the role of potential damping factors, including pulse frequency, vascular viscous resistance, vascular compliance, viscoelastic behavior of the vessel wall, and wave propagation and reflection. To this end, three full rat mesenteric vascular networks were reconstructed from intravital microscopic recordings, a one-dimensional (1D) model was used to reproduce pulsatile properties within the network, and potential damping factors were examined by sensitivity analysis. Results demonstrate that blood flow pulsatility is predominantly damped at the arteriolar side and remains at a low level at the venular side. Damping was sensitive to pulse frequency, vascular viscous resistance and vascular compliance, whereas viscoelasticity of the vessel wall or wave propagation and reflection contributed little to pulsatility damping. The present results contribute to our understanding of mechanical forces and their regulation in the microcirculation.

Modeling disease transmission in a train carriage using a simple 1D-model.

Understanding airborne infectious disease transmission on public transport is essential to reducing the risk of infection of passengers and crew members. We propose a new one-dimensional (1D) model that predicts the longitudinal dispersion of airborne contaminants and the risk of disease transmission inside a railway carriage. We compare the results of this 1D-model to the predictions of a model that assumes the carriage is fully mixed. The 1D-model is validated using measurements of controlled carbon-dioxide experiments conducted in a full-scale railway carriage. We use our results to provide novel insights into the impact of various strategies to reduce the risk of airborne transmission on public transport.

Pulse wave velocity in the microcirculation reflects both vascular compliance and resistance: Insights from computational approaches.

OBJECTIVE: PWV is the speed of pulse wave propagation through the circulatory system. mPWV emerges as a novel indicator of hypertension, yet it remains unclear how different vascular properties affect mPWV. We aim to identify the biomechanical determinants of mPWV. METHODS: A 1D model was used to simulate PWV in a rat mesenteric microvascular network and, for comparison, in a human macrovascular arterial network. Sensitivity analysis was performed to assess the relationship between PWV and vascular compliance and resistance. RESULTS: The 1D model enabled adequate simulation of PWV in both micro- and macrovascular networks. Simulated arterial PWV changed as a function of vascular compliance but not resistance, in that arterial PWV varied at a rate of 0.30 m/s and -6.18 × 10-3  m/s per 10% increase in vascular compliance and resistance, respectively. In contrast, mPWV depended on both vascular compliance and resistance, as it varied at a rate of 2.79 and -2.64 cm/s per 10% increase in the respective parameters. CONCLUSIONS: The present study identifies vascular compliance and resistance in microvascular networks as critical determinants of mPWV. We anticipate that mPWV can be utilized as an effective indicator for the assessment of microvascular biomechanical properties.

Wave potential and the one-dimensional windkessel as a wave-based paradigm of diastolic arterial hemodynamics.

Controversy exists about whether one-dimensional wave theory can explain the "self-canceling" waves that accompany the diastolic pressure decay and discharge of the arterial reservoir. Although it has been proposed that reservoir and wave effects be treated as separate phenomena, thus avoiding the issue of self-canceling waves, we have argued that reservoir effects are a phenomenological and mathematical subset of wave effects. However, a complete wave-based explanation of self-canceling diastolic expansion (pressure-decreasing) waves has not yet been advanced. These waves are present in the forward and backward components of arterial pressure and flow (P ± and Q ±, respectively), which are calculated by integrating incremental pressure and flow changes (dP ± and dQ ±, respectively). While the integration constants for this calculation have previously been considered arbitrary, we showed that physiologically meaningful constants can be obtained by identifying "undisturbed pressure" as mean circulatory pressure. Using a series of numeric experiments, absolute P ± and Q ± values were shown to represent "wave potential," gradients of which produce propagating wavefronts. With the aid of a "one-dimensional windkessel," we showed how wave theory predicts discharge of the arterial reservoir. Simulated data, along with hemodynamic recordings in seven sheep, suggested that self-canceling diastolic waves arise from repeated and diffuse reflection of the late systolic forward expansion wave throughout the arterial system and at the closed aortic valve, along with progressive leakage of wave potential from the conduit arteries. The combination of wave and wave potential concepts leads to a comprehensive one-dimensional (i.e., wave-based) explanation of arterial hemodynamics, including the diastolic pressure decay.

Development of a 3D Vascular Network Visualization Platform for One-Dimensional Hemodynamic Simulation.

Recent advancements in computational performance and medical simulation technology have made significant strides, particularly in predictive diagnosis. This study focuses on the blood flow simulation reduced-order models, which provide swift and cost-effective solutions for complex vascular systems, positioning them as practical alternatives to 3D simulations in resource-limited medical settings. The paper introduces a visualization platform for patient-specific and image-based 1D-0D simulations. This platform covers the entire workflow, from modeling to dynamic 3D visualization of simulation results. Two case studies on, respectively, carotid stenosis and arterial remodeling demonstrate its utility in blood flow simulation applications.

Comparison between ozone column depths and methane lifetimes computed by one- and three-dimensional models at different atmospheric O2 levels.

Recently, Cooke et al. (Cooke et al. 2022 R. Soc. Open Sci. 9, 211165. (doi:10.1098/rsos.211165)) used a three-dimensional coupled chemistry-climate model (WACCM6) to calculate ozone column depths at varied atmospheric O2 levels. They argued that previous one-dimensional (1-D) photochemical model studies, e.g. Segura et al. (Segura et al. 2003 Astrobiology 3, 689-708. (doi:10.1089/153110703322736024)), may have overestimated the ozone column depth at low pO2, and hence also overestimated the lifetime of methane. We have compared new simulations from an updated version of the Segura et al. model with those from WACCM6, together with some results from a second three-dimensional model. The discrepancy in ozone column depths is probably due to multiple interacting parameters, including H2O in the upper troposphere, lower boundary conditions, vertical and meridional transport rates, and different chemical mechanisms, especially the treatment of O2 photolysis in the Schumann-Runge (SR) bands (175-205 nm). The discrepancy in tropospheric OH concentrations and methane lifetime between WACCM6 and the 1-D model at low pO2 is reduced when absorption from CO2 and H2O in this wavelength region is included in WACCM6. Including scattering in the SR bands may further reduce this difference. Resolving these issues can be accomplished by developing an accurate parametrization for O2 photolysis in the SR bands and then repeating these calculations in the various models.

Quantitative assessment of decadal water temperature changes in Lake Kasumigaura, a shallow turbid lake, using a one-dimensional model.

To assess the decadal water temperature (WT) changes observed at the center of Lake Kasumigaura, a shallow turbid lake in Japan, we constructed a prediction model for WT. The thermal interactions among air, water, and sediment were simulated by a one-dimensional differential equation using hourly observations of meteorological and limnological parameters. The validated model showed good performance (i.e., <1 °C RMSE for the daily averaged WT) for 2012, 2013, and 2015, respectively, in both upper and lower water layers, which were attained by incorporating a physical sub-model regarding the surface water temperature (surface WT). The good description of seasonal, daily, and hourly changes in surface WT obtained with the sub-model was confirmed by the observed and simulated time series. We then quantified and evaluated the trends of the meteorological and limnological parameters influencing WT changes from 1979 to 2015 based on their effects on WT by using the prediction model with the increases in air temperature (AT), solar radiation (SR), wind velocity (WV), and turbidity during that period; then, WT in the former period (1979) was predicted according to the trends and compared with the measured WT. The observed WT changes during the period were quantitatively explained by the compound effects of the parameters' changes, i.e., the AT and SR raising the WT, and the WV and turbidity lowering the WT.

Hindered and compression solid settling functions - Sensor data collection, practical model identification and validation.

Secondary settling tanks (SSTs) are the most hydraulically sensitive unit operations in activated sludge water resource recovery facilities (WRRF). Mathematical models for predicting activated sludge solids settling velocity include parameters that show irreducible epistemic uncertainty. Therefore, reliable and periodic calibration of the settling velocity model is key for predicting activated sludge process capacity, thus averting possible failures under wet-weather flow- and filamentous bulking conditions. The two main knowledge gaps addressed here are: (1) Do constitutive functions for hindered and compression settling exist, for which all velocity parameters can be uniquely estimated? (2) What is the optimum sensor data requirement of developing reliable settling velocity functions? Innovative settling column sensor and full-scale data were used to identify and validate amended Vesilind function for hindered settling and a new exponential function for compression settling velocity using one-dimensional and computational fluid dynamics simulations. Results indicate practical model identifiability under well-settling and filamentous bulking conditions.

A one-dimensional mathematical model of collecting lymphatics coupled with an electro-fluid-mechanical contraction model and valve dynamics.

We propose a one-dimensional model for collecting lymphatics coupled with a novel Electro-Fluid-Mechanical Contraction (EFMC) model for dynamical contractions, based on a modified FitzHugh-Nagumo model for action potentials. The one-dimensional model for a deformable lymphatic vessel is a nonlinear system of hyperbolic Partial Differential Equations (PDEs). The EFMC model combines the electrical activity of lymphangions (action potentials) with fluid-mechanical feedback (circumferential stretch of the lymphatic wall and wall shear stress) and lymphatic vessel wall contractions. The EFMC model is governed by four Ordinary Differential Equations (ODEs) and phenomenologically relies on: (1) environmental calcium influx, (2) stretch-activated calcium influx, and (3) contraction inhibitions induced by wall shear stresses. We carried out a stability analysis of the stationary state of the EFMC model. Contractions turn out to be triggered by the instability of the stationary state. Overall, the EFMC model allows emulating the influence of pressure and wall shear stress on the frequency of contractions observed experimentally. Lymphatic valves are modelled by extending an existing lumped-parameter model for blood vessels. Modern numerical methods are employed for the one-dimensional model (PDEs), for the EFMC model and valve dynamics (ODEs). Adopting the geometrical structure of collecting lymphatics from rat mesentery, we apply the full mathematical model to a carefully selected suite of test problems inspired by experiments. We analysed several indices of a single lymphangion for a wide range of upstream and downstream pressure combinations which included both favourable and adverse pressure gradients. The most influential model parameters were identified by performing two sensitivity analyses for favourable and adverse pressure gradients.

Comparison of the Windkessel model and structured-tree model applied to prescribe outflow boundary conditions for a one-dimensional arterial tree model.

One-dimensional (1D) modeling is a widely adopted approach for studying wave propagation phenomena in the arterial system. Despite the frequent use of the Windkessel (WK) model to prescribe outflow boundary conditions for 1D arterial tree models, it remains unclear to what extent the inherent limitation of the WK model in describing wave propagation in distal vasculatures affect hemodynamic variables simulated at the arterial level. In the present study, a 1D model of the arterial tree was coupled respectively with a WK boundary model and a structured-tree (ST) boundary model, yielding two types of arterial tree models. The effective resistances, compliances and inductances of the WK and ST boundary models were matched to facilitate quantitative comparisons. Obtained results showed that pressure/flow waves simulated by the two models were comparable in the aorta, whereas, their discrepancies increased towards the periphery. Wave analysis revealed that the differences in reflected waves generated by the boundary models were the major sources of pressure wave discrepancies observed in large arteries. Additional simulations performed under aging conditions demonstrated that arterial stiffening with age enlarged the discrepancies, but with the effects being partly counteracted by physiological aortic dilatation with age. These findings suggest that the method adopted for modeling the outflow boundary conditions has considerable influence on the performance of a 1D arterial tree model, with the extent of influence varying with the properties of the arterial system.

A unified method for estimating pressure losses at vascular junctions.

In reduced-order (0D/1D) blood or respiratory flow models, pressure losses at junctions are usually neglected. However, these may become important where velocities are high and significant flow redirection occurs. Current methods for estimating losses rely on relatively complex empirical equations that are only valid for specific junction geometries and flow regimes. In pulsatile multi-directional flows, switching between empirical equations upon reversing flow may introduce unrealistic discontinuities in simulated haemodynamic waveforms. Drawing from work by Bassett et al. (SAE Trans 112:565-583, 2003), we therefore developed a unified method (Unified0D) for estimating loss coefficients that can be applied to any junction (i.e. any number of branches at any angle) and any flow regime. Discontinuities in simulated waveforms were avoided by extending Bassett et al.'s control volume-based method to incorporate a 'pseudodatum' supplier branch, an imaginary effective vessel containing all inflow to the junction. Energy exchange between diverging flow streams was also accounted for empirically. The formulation was validated using high resolution computational fluid dynamics in a wide range flow conditions and junction configurations. In a pulsatile 1D simulation exhibiting transitions between four different flow regimes, the new formulation produced smooth transitions in calculated pressure losses.

Mechanistic modeling of modular co-rotating twin-screw extruders.

In this study, we present a one-dimensional (1D) model of the metering zone of a modular, co-rotating twin-screw extruder for pharmaceutical hot melt extrusion (HME). The model accounts for filling ratio, pressure, melt temperature in screw channels and gaps, driving power, torque and the residence time distribution (RTD). It requires two empirical parameters for each screw element to be determined experimentally or numerically using computational fluid dynamics (CFD). The required Nusselt correlation for the heat transfer to the barrel was determined from experimental data. We present results for a fluid with a constant viscosity in comparison to literature data obtained from CFD simulations. Moreover, we show how to incorporate the rheology of a typical, non-Newtonian polymer melt, and present results in comparison to measurements. For both cases, we achieved excellent agreement. Furthermore, we present results for the RTD, based on experimental data from the literature, and found good agreement with simulations, in which the entire HME process was approximated with the metering model, assuming a constant viscosity for the polymer melt.

Estimating absolute aortic pressure using MRI and a one-dimensional model.

Aortic blood pressure is a strong indicator to cardiovascular diseases and morbidity. Clinically, pressure measurements are done by inserting a catheter in the aorta. However, imaging techniques have been used to avoid the invasive procedure of catheterization. In this paper, we combined MRI measurements to a one-dimensional model in order to simulate blood flow in an aortic segment. Absolute pressure was estimated in the aorta by using MRI measured flow as boundary conditions and MRI measured compliance as a pressure law for solving the model. Model computed pressure was compared to catheter measured pressure in an aortic phantom. Furthermore, aortic pressure was estimated in vivo in three healthy volunteers.

Validation of a 1D patient-specific model of the arterial hemodynamics in bypassed lower-limbs: simulations against in vivo measurements.

The validation of a coupled 1D-0D model of the lower-limb arterial hemodynamics is presented. This study focuses on pathological subjects (6 patients, 72.7±11.1 years) suffering from atherosclerosis who underwent a femoro-popliteal bypass surgery. The 1D model comprises four vessels from the upper-leg, peripheral networks are modeled with three-element windkessels and in vivo velocity is prescribed at the inlet. The model is patient-specific: its parameters reflect the physiological condition of the subjects. In vivo data are acquired invasively during bypass surgery using B-mode ultrasonography and catheter. Simulations from the model compare well with measured velocity (u) and pressure (p) waveforms: average relative root-mean-square error between numerical and experimental waveforms are limited to εp=9.6%, εu=16.0%. The model is able to reproduce the intensity and shape of waveforms observed in different clinical cases. This work also details the introduction of blood leakages along the pathological arterial network, and the sensitivity of the model to its parameters. This study constitutes a first validation of a patient-specific numerical model of a pathological arterial network. It presents an efficient tool for engineers and clinicians to help them improve their understanding of the hemodynamics in diseased arteries.

Determinación de la Rigidez Arterial Empleando Simulación Computacional / Determination of Arterial Stiffness Using Computational Simulation

El incremento de la rigidez arterial está asociado con el desarrollo de enfermedades cardiovasculares, las cuales constituyen una de las principales causas de muertes en el mundo. Por este motivo el desarrollo de métodos no invasivos que permitan cuantificar la rigidez arterial ha alcanzado un gran impacto. En este trabajo se estudia el método no invasivo de medición de la velocidad de la onda del pulso de la arteria braquial al tobillo (baPWV), por sus siglas en inglés. Para estudiar este método se simularon las formas de ondas de presión en el sistema arterial empleando un modelo unidimensional, a partir de las cuales se determinaron los valores de baPWV. Estos valores fueron comparados con los calculados por otros dos métodos: cfPWV (velocidad de la onda del pulso entre la carótida y la femoral, el método estándar) y PWVteor (ecuación de Bramwell-Hill), obteniéndose correlaciones significativas, r=0.967 y r=0.9828 respectivamente. Se investigó la sensibilidad del método baPWV a la variación de la rigidez, representada por la variación de la distensibilidad y, se concluyó que el método es sensible a los cambios de rigidez que ocurren tanto en las arterias centrales como en las arterias periféricas.

The arterial stiffness increased is associated with the development of cardiovascular diseases, which constitute one of the first causes of death globally. For this reason the development of noninvasive methods to quantify arterial stiffness have had great impact. The purpose of this paper is the study of the noninvasive measurement method of brachial ankle pulse wave velocity (baPWV). To perform this study pressure waveforms in the arterial system were simulated, by using a one-dimensional model. With these pressure waveforms baPWV's values were calculated, and were compared with two others calculated methods: cfPWV (carotid-femoral PWV, gold standard method), and PWVteor (Bramwell-Hill equation). Significant correlations were obtained, r=0.967 y r=0.9828 respectively. The sensibility of the baPWV method to the stiffness change, represented for the distensibility change, was investigated, and we conclude that baPWV method is sensitive to the changes that take place in both central and peripheral arteries.