Windkessel Model Research Articles

Direct 0D-3D coupling of a lattice Boltzmann methodology for fluid-structure aortic flow simulations.

This work introduces a numerical approach and implementation for the direct coupling of arbitrary complex ordinary differential equation- (ODE-)governed zero-dimensional (0D) boundary conditions to three-dimensional (3D) lattice Boltzmann-based fluid-structure systems for hemodynamics studies. In particular, a most complex configuration is treated by considering a dynamic left ventricle- (LV-)elastance heart model which is governed by (and applied as) a nonlinear, non-stationary hybrid ODE-Dirichlet system. Other ODE-based boundary conditions, such as lumped parameter Windkessel models for truncated vasculature, are also considered. Performance studies of the complete 0D-3D solver, including its treatment of the lattice Boltzmann fluid equations and elastodynamics equations as well as their interactions, is conducted through a variety of benchmark and convergence studies that demonstrate the ability of the coupled 0D-3D methodology in generating physiological pressure and flow waveforms-ultimately enabling the exploration of various physical and physiological parameters for hemodynamics studies of the coupled LV-arterial system. The methods proposed in this paper can be easily applied to other ODE-based boundary conditions as well as to other fluid problems that are modeled by 3D lattice Boltzmann equations and that require direct coupling of dynamic 0D boundary conditions.

Imperatives of Mathematical Model of Arterial Blood Dynamics for Interpretation of Doppler Velocimetry: A Narrative Review.

Clinicians frequently study arterial Doppler velocimetric waveforms depicted by Doppler sonography of the kidneys, the heart, the brain, and the feto-maternal circulation to assess the well-being of the aforementioned vital organs. The waveform interpretation of the Doppler indices can be studied using a mathematical model. The developed models serve as teaching tools and for easy comprehension of the regulatory mechanism of the organs. It will also obtain accurate wall shear stress (WSS) and likely atherosclerotic sites can be predicted early. The aim of this review is to reveal the imperatives of mathematical models in the study of the physical interpretation of Doppler velocimetry. The models will explore sonographic Doppler velocimetry and computational fluid dynamics (CFD) in determining the segments of the arteries that are prone to the development of atheromatous plaque. It will be achieved by comparing and computing the measurement differences of the WSS. A thorough literature review was carried out between 1971 and 2021 on the mathematical modeling of blood dynamics and Doppler velocimetry of different blood vessels, across various electronic databases including NC AHEC Digital Library, PUBMED, ERIC, MEDLINE, Free Medical Journals, and EMBASE. The results of the literature search were presented using the PRISMA flow chat. The narrative review of the mathematical models of arterial blood dynamics is based on incompressible Navier-Stokes equations, the Windkessel model, and CFD. It was deduced that the blood flow velocity decreased with time across the varying frequency from 0.2Hz to 0.50Hz in the interlobar arterial channels. The review also revealed that adult humans' Doppler indices of the renal-interlobar artery agree with developed models of renal interlobar arterial blood dynamics. The mathematical model measurements of the great vessels matched the sonographic Doppler velocimetry with <15% variation. In our fast-paced world of epidemiological transition, the imperatives of mathematical modeling of arterial flow dynamics based on the Navier-Stokes equations to represent various physiologic and pathologic situations cannot be overstated. The practical consequences include the possibility of mathematical models to acquire precise WSS distribution and early detection of potential atherosclerotic sites during cardiovascular Doppler sonography.

Camera-Based Blood Pressure Estimation via Windkessel Model and Waveform Features

Blood pressure (BP) is generally regarded as the vital sign most strongly correlated with human health. However, for decades, BP measurement has involved a cuff, which causes discomfort and even carries a risk of infection, given the current prevalence of COVID-19. Some studies address these problems using remote photoplethysmography (rPPG), which has shown great success in heart rate detection. Nevertheless, these approaches are not robust, and few have been evaluated with a sufficiently large dataset. We propose an rPPG-based BP estimation algorithm that predicts BP by leveraging the Windkessel model and hand-crafted waveform characteristics. A waveform processing procedure is presented for the rPPG signals to obtain a robust waveform template and thus extract BP-related features. Redundant and unstable features are eliminated via Monte Carlo simulation and according to their relationship with latent parameters (LSs) in the Windkessel model. For a comprehensive evaluation, the Chiao Tung BP (CTBP) dataset was constructed. The experiment was conducted over a four-week period of time to evaluate the validity period of the personalization in our system. On all the data, the proposed method outperforms the benchmark algorithms and yields mean absolute errors (MAEs) of 6.48 and 5.06 mmHg for systolic BP (SBP) and diastolic BP (DBP), respectively. The performance achieves a “B” grade according to the validation protocol from the British Hypertension Society (BHS) for both SBP and DBP.

Actively controlled cardiac afterload

Ex vivo (outside of the body) working heart models enable the evaluation of isolated hearts. They are envisioned to play an important role in increasing the currently low utilization rate of donor hearts for transplantation. For the heart to work in isolation, an afterload (flow impedance) is needed. To date, afterload devices have been constructed by combining multiple constituent elements such as pumps, flow resistances, and flow capacitances (compliances), typically to replicate the structure of so-called Windkessel models. This limits active control to that achievable by varying these elements, making it slow and subject to the problem of dynamic coupling between parameters. Here we present a novel concept to achieve Windkessel dynamics through a very simple variable flow impedance. The impedance is actively controlled using feedback from a pressure measurement. Through simulations we demonstrate the ability to perfectly emulate Windkessel dynamics, while imposing tight pressure limits needed for safe operation—something not achievable with the verbatim implementation using constituent elements.

Near-wall hemodynamic changes in subclavian artery perfusion induced by retrograde inner branched thoracic endograft implantation

ObjectiveLeft subclavian artery (LSA)-branched endografts with retrograde inner branch configuration (thoracic branch endoprosthesis [TBE]) offer a complete endovascular solution when LSA preservation is required during zone 2 thoracic endovascular aortic repair. However, the hemodynamic consequences of the TBE have not been well-investigated. We compared near-wall hemodynamic parameters before and after the TBE implantation using computational fluid dynamic simulations. MethodsEleven patients who had undergone TBE implantation were included. Three-dimensional aortic arch geometries were constructed from the pre- and post-TBE implantation computed tomography images. The resulting 22 three-dimensional aortic arch geometries were then discretized into finite element meshes for computational fluid dynamic simulations. Inflow boundary conditions were prescribed using normal physiological pulsatile circulation. Outlet boundary conditions consisted of Windkessel models with previously published values. Blood flow, modeled as Newtonian fluid, simulations were performed with rigid wall assumptions using SimVascular's incompressible Navier-Stokes solver. We compared well-established hemodynamic descriptors: pressure, flow rate, time-averaged wall shear stress (TAWSS), the oscillatory shear index (OSI), and percent area with an OSI of >0.2. Data were presented on the stented portion of the LSA. ResultsTBE implantation was associated with a small decrease in peak LSA pressure (153 mm Hg; interquartile range [IQR], 151-154 mm Hg vs 159 mm Hg; IQR, 158-160 mm Hg; P = .005). No difference was observed in peak LSA flow rates before and after implantation: 40.4 cm3/ (IQR, 39.5-41.6 cm3/s) vs 41.3 cm3/s (IQR, 37.2-44.8 cm3/s; P = .59). There was a significant postimplantation increase in TAWSS (15.2 dynes/cm2 [IQR, 12.2-17.7 dynes/cm2] vs 6.2 dynes/cm2 [IQR, 5.7-10.3 dynes/cm2]; P = .003), leading to decreases in both the OSI (0.088 [IQR, 0.063 to –0.099] vs 0.1 [IQR, 0.096-0.16]; P = .03) and percentage of area with an OSI of >0.2 (10.4 [IQR, 5.8-15.8] vs 15.7 [IQR, 10.7-31.9]; P = .13). Neither LSA side branch angulation (median, 81°, IQR, 77°-109°) nor moderate compression (16%-58%) seemed to have an impact on the pressure, flow rate, TAWSS, or percentage of area with an OSI of >0.2 in the stented LSA. ConclusionsThe implantation of TBE produces modest hemodynamic disturbances that are unlikely to result in clinically relevant changes.

A method for portable PPG signal dynamic acquisition and denoise based on CEEMDAN and wavelet transform

Photoplethysmography (PPG) is a non-invasive technology and widely used in medical monitoring. Nowadays, dynamic vital signs monitoring based on PPG technology is in emergence and shows great potential for commercialization, however, it is still challenged by massive noise evoked by respiration and muscle contraction. Herein, a portable PPG signal's dynamic acquisition and denoise system is constructed and applied to blood pressure (BP) estimation, in which an improved PPG denoise method based on complete ensemble empirical mode decomposition with adaptive noise and wavelet transform (CEEMDAN-WT), is described. Firstly, original PPG signal is measured by the proposed hardware, then CEEMDAN decomposes it into a group of components. Secondly, the noise dominated components are found by calculating the coefficients between the components and original signal, and removed by WT. Thirdly, fast Fourier transform is performed to remove the component whose dominant frequency exceeds 0.5–20 Hz. Fourthly, a fresh PPG signal is reconstructed and compared with the signal rebuilt by other methods, which proves that CEEMDAN-WT has higher signal-to-noise ratio and lower root mean square error. Last but not least, the reconstructed signal is applied to estimate systolic and diastolic BP, according to Windkessel model and aided by neural network algorithm. Overall, this work demonstrates the feasibility of the portable PPG dynamic acquisition and its application for dynamic vital signs monitoring, in which CEEMDAN-WT algorithm can effectively remove most of the noises in dynamic PPG signal. In conclusion, it demonstrates CEEMDAN-WT method can effectively remove noise from PPG signals in the state of motion, it may have a good potential for calculating other physiological indexes besides BP, and push PPG applications from professional medical to daily life.

Assessment of extracranial carotid artery disease using digital twins – A pilot study

To improve risk stratification in extracranial internal carotid artery disease (CAD), patients who would benefit maximally from revascularization must be identified. In cardiology, the fractional flow reserve (FFR) has become a reference standard for evaluating the functional severity of coronary artery stenosis, and noninvasive surrogates thereof relying on computational fluid dynamics (CFD) have been developed. Here, we present a CFD-based workflow using digital twins of patients’ carotid bifurcations derived from computed tomography angiography for the noninvasive functional assessment of CAD. We reconstructed patient-specific digital twins of 37 carotid bifurcations. We implemented a CFD model using common carotid artery peak systolic velocity (PSV) acquired with Doppler ultrasound (DUS) as inlet boundary condition and a two-element Windkessel model as oulet boundary condition. The agreement between CFD and DUS on the PSV in the internal carotid artery (ICA) was then compared. The relative error for the agreement between DUS and CFD was 9% ± 20% and the intraclass correlation coefficient was 0.88. Furthermore, hyperemic simulations in a physiological range were feasible and unmasked markedly different pressure drops along two ICA stenoses with similar degree of narrowing under comparable ICA blood flow. Hereby, we lay the foundation for prospective studies on noninvasive CFD-based derivation of metrics similar to the FFR for the assessment of CAD.

Assessment of valve implantation in the descending aorta as an alternative for aortic regurgitation patients not treatable with conventional procedures

Background:Aortic Regurgitation (AR) produces the entrance of an abnormal amount of blood in the left ventricle. This disease is responsible for high morbidity and mortality worldwide and may be caused by an aortic valve dysfunction. Surgical and transcatheter aortic valve replacement (TAVR) are the current options for treating AR. They have replaced older procedures such as Hufnagel’s one. However, some physicians have reconsidered this procedure as a less aggressive alternative for patients not eligible for surgical or TAVR. Although Hufnagel suggested a 75% regurgitation reduction when a valve is placed in the descending aorta, a quantification of this value has not been reported.Methods:In this paper, CFD/FSI numerical simulation is conducted on an idealized geometry. We quantify the effect of placing a bileaflet mechanical heart valve in the descending aorta on a moderate-severe AR case. A three-element Windkessel model is employed to prescribe pressure outlet boundary conditions. We calculate the resulting flow rates and pressures at the aorta and first-generation vessels. Moreover, we evaluate several indices to assess the improvement due to the valve introduction.Results and conclusions:Regurgitation fraction (RF) is reduced from 37.5% (without valve) to 18.0% (with valve) in a single cardiac cycle. This reduction clearly shows the remarkable efficacy of the rescued technique. It will further ameliorate the left ventricle function in the long-term. Moreover, the calculations show that the implantation in that location introduces fewer incompatibilities’ risks than a conventional one. The proposed methodology can be extended to any particular conditions (pressure waveforms/geometry) and is designed to assess usual clinical parameters employed by physicians.

Computational study of fenestration and parallel grafts used in TEVAR of aortic arch aneurysms.

To explore the differences between fenestration technique and parallel grafts technique of thoracic endovascular aortic repair, and evaluate the risk of complications after interventional treatment of aortic arch aneurysms. A three-dimensional aortic model was established from the follow-up imaging data of patient who reconstructed the superior arch vessel by the chimney technique, which was called the chimney model. Based on the chimney model, the geometric of the reconstructed vessel was modified by virtual surgery, and the normal model, fenestration model and periscope model were established. The blood flow waveforms measured by 2D phase contrast magnetic resonance imaging were processed as the boundary conditions of the ascending aorta inlet and the superior arch vessels outlets of the normal model. The pressure waveform of descending aorta was obtained using three-element Windkessel model, and specific pressure boundary conditions were imposed at reconstructed branches for the postoperative models. Through computational fluid dynamics simulations, the hemodynamic parameters of each model were obtained. The reconstructed vessel flow rate of the periscope model and the fenestration model are 33% and 50% of that of the normal model, respectively. The pressure difference between the inner and outer walls of the fenestration stent and periscope stent is 3.15 times and 7.56 times that of the chimney stent. The velocity in the fenestration stent and periscope stent is uneven. The high relative residence time is concentrated in the region around the branch stents, which is prone to thrombosis. The "gutter" part of the chimney model may become larger due to the effect of the stent-graft DF, increasing the risk of endoleak. For patients with incomplete circle of Willis, the periscope technique to reconstruct the supra-arch vessels may affect blood perfusion. It is recommended to use balloon-expandable stent for fenestration stent and periscope stent, and self-expanding stent for chimney stent. For patients with aortic arch aneurysms, the fenestration technique may be superior to the parallel grafts technique.

Computational fluid dynamics model to predict the dynamical behavior of the cerebrospinal fluid through implementation of physiological boundary conditions.

Cerebrospinal fluid (CSF) dynamics play an important role in maintaining a stable central nervous system environment and are influenced by different physiological processes. Multiple studies have investigated these processes but the impact of each of them on CSF flow is not well understood. A deeper insight into the CSF dynamics and the processes impacting them is crucial to better understand neurological disorders such as hydrocephalus, Chiari malformation, and intracranial hypertension. This study presents a 3D computational fluid dynamics (CFD) model which incorporates physiological processes as boundary conditions. CSF production and pulsatile arterial and venous volume changes are implemented as inlet boundary conditions. At the outlets, 2-element windkessel models are imposed to simulate CSF compliance and absorption. The total compliance is first tuned using a 0D model to obtain physiological pressure pulsations. Then, simulation results are compared with in vivo flow measurements in the spinal subarachnoid space (SAS) and cerebral aqueduct, and intracranial pressure values reported in the literature. Finally, the impact of the distribution of and total compliance on CSF pressures and velocities is evaluated. Without respiration effects, compliance of 0.17ml/mmHg yielded pressure pulsations with an amplitude of 5mmHg and an average value within the physiological range of 7-15mmHg. Also, model flow rates were found to be in good agreement with reported values. However, when adding respiration effects, similar pressure amplitudes required an increase of compliance value to 0.51ml/mmHg, which is within the range of 0.4-1.2ml/mmHg measured in vivo. Moreover, altering the distribution of compliance over the four different outlets impacted the local flow, including the flow through the foramen magnum. The contribution of compliance to each outlet was directly proportional to the outflow at that outlet. Meanwhile, the value of total compliance impacted intracranial pressure. In conclusion, a computational model of the CSF has been developed that can simulate CSF pressures and velocities by incorporating boundary conditions based on physiological processes. By tuning these boundary conditions, we were able to obtain CSF pressures and flows within the physiological range.

Study on physiological response considering blood flow volume in transient and non-uniform bathing thermal environment using thermo-cardiovascular regulation model

In transient and non-uniform thermal environments, such as bathing, the human thermal physiological response changes dramatically and accidents often occur owing to cardiovascular system diseases. Blood flow volume is a crucial index of the cardiovascular system; thus, studying the human thermal physiological response considering blood flow volume in a bathing thermal environment is essential. In this paper, we proposed a novel integrated thermo-cardiovascular regulation model that merged a human thermoregulation model (HTM) and a cardiovascular regulation model (CRM), to predict the human physiological response in a transient and non-uniform bathing environment considering blood flow volume and the thermal environment, metabolic rate, and heart rate changes. First, based on the Stolwijk model, more nodes representing different human body parts have been added to the HTM, and it takes into consideration metabolic rate changes. Second, based on the Windkessel model, the circulatory system of the CRM is divided into four parts. Meanwhile, the changes in heart rate over time is used to adjust the cardiac output of the CRM's circulation in real time. To assess the accuracy of the prediction model, we conducted a bathing experiment with a 50-year-old man. The results revealed that the proposed model could accurately predict the participant's thermal physiological response, including skin temperature, core temperature, blood pressure, and blood flow volume during bathing.

Autonomic and circulatory alterations persist despite adequate resuscitation in a 5-day sepsis swine experiment

Autonomic and vascular failures are common phenotypes of sepsis, typically characterized by tachycardia despite corrected hypotension/hypovolemia, vasopressor resistance, increased arterial stiffness and decreased peripheral vascular resistance. In a 5-day swine experiment of polymicrobial sepsis we aimed at characterizing arterial properties and autonomic mechanisms responsible for cardiovascular homeostasis regulation, with the final goal to verify whether the resuscitation therapy in agreement with standard guidelines was successful in restoring a physiological condition of hemodynamic profile, cardiovascular interactions and autonomic control. Twenty pigs were randomized to polymicrobial sepsis and protocol-based resuscitation or to prolonged mechanical ventilation and sedation without sepsis. The animals were studied at baseline, after sepsis development, and every 24 h during the 3-days resuscitation period. Beat-to-beat carotid blood pressure (BP), carotid blood flow, and central venous pressure were continuously recorded. The two-element Windkessel model was adopted to study carotid arterial compliance, systemic vascular resistance and characteristic time constant τ. Effective arterial elastance was calculated as a simple estimate of total arterial load. Cardiac baroreflex sensitivity (BRS) and low frequency (LF) spectral power of diastolic BP were computed to assess autonomic activity. Sepsis induced significant vascular and autonomic alterations, manifested as increased arterial stiffness, decreased vascular resistance and τ constant, reduced BRS and LF power, higher arterial afterload and elevated heart rate in septic pigs compared to sham animals. This compromised condition was persistent until the end of the experiment, despite achievement of recommended resuscitation goals by administered vasopressors and fluids. Vascular and autonomic alterations persist 3 days after goal-directed resuscitation in a clinically relevant sepsis model. We hypothesize that the addition of these variables to standard clinical markers may better profile patients’ response to treatment and this could drive a more tailored therapy which could have a potential impact on long-term outcomes.

Analysis of a microcirculatory windkessel model using photoplethysmography with green light: A pilot study

In this study, a vasomotion quantification method using a photoplethysmography prototype, which performs near-infrared spectroscopy combined with green light, is proposed. This structure suppresses the motion artifact and is held by eyeglasses at the back of the ear; this helps improve the integrity of the measured relative concentration changes of the total hemoglobin and pulse wave amplitude during exercise with and without the presence of wind impacting the face. We established a microcirculatory windkessel model including arteriovenous anastomoses estimated from blood flow changes in the depth direction that were acquired using three wavelengths of light and reproduced the vasomotion on a computer. The values predicted by the model were in good agreement with the measured values. The extracted vasomotion can be used to understand autonomic control by the central nervous system.

Parametric analysis of an efficient boundary condition to control outlet flow rates in large arterial networks

Substantial effort is being invested in the creation of a virtual human—a model which will improve our understanding of human physiology and diseases and assist clinicians in the design of personalised medical treatments. A central challenge of achieving blood flow simulations at full-human scale is the development of an efficient and accurate approach to imposing boundary conditions on many outlets. A previous study proposed an efficient method for implementing the two-element Windkessel model to control the flow rate ratios at outlets. Here we clarify the general role of the resistance and capacitance in this approach and conduct a parametric sweep to examine how to choose their values for complex geometries. We show that the error of the flow rate ratios decreases exponentially as the resistance increases. The errors fall below 4% in a simple five-outlets model and 7% in a human artery model comprising ten outlets. Moreover, the flow rate ratios converge faster and suffer from weaker fluctuations as the capacitance decreases. Our findings also establish constraints on the parameters controlling the numerical stability of the simulations. The findings from this work are directly applicable to larger and more complex vascular domains encountered at full-human scale.

Arterial compliance and its dynamics in obese adolescents.

Arterial compliance (AC) decrease with aging is accelerated by factors associated with the progression of atherosclerotic process, including obesity. Prevalence of obesity increases not only in adult population but also in children and adolescents. The results of studies characterizing the effect of obesity on AC (often indirectly estimated by pulse wave velocity (PWV)) are contradictory. Considering the limitations of previously applied methods and the need to interpret AC values in the context of potential confounders or during various physiological states, the aim of this study was to compare AC of control and obese adolescents during four different physiological states: supine rest, head-up tilt (HUT), supine recovery and mental arithmetic (MA). AC was assessed by the method based on two-element Windkessel model as the ratio of a time constant t characterizing diastolic blood pressure decay and total peripheral resistance (TPR). In total, fifty healthy and normotensive subjects (40 females, 10 males, age 17.5 years (SD=1.1 years)) were examined - 25 obese and 25 age- and sex-matched control subjects. We observed significantly increased AC values during all phases in obese group. An increase in AC was also preserved after controlling for blood pressure influence. These results were confirmed using PWV based AC estimation. Interestingly, AC decreased similarly during stress phases (HUT, MA) in both groups. Lastly, TPR was decreased throughout the study protocol in obese subjects. In conclusion, AC is increased in young obese subjects consistently during various physiological states. Furthermore, changes of physiological states evoke similar response of AC in both groups indicating preserved autonomic control of elastic arteries. A decreased TPR in obese subjects points towards the influence of different maturation state of the arterial tree and/or changes in vasomotion possibly counterbalancing acceleration of atherosclerosis process.

Non-intrusive PODI-ROM for patient-specific aortic blood flow in presence of a LVAD device.

Left ventricular assist devices (LVADs) are used to provide haemodynamic support to patients with critical cardiac failure. Severe complications can occur because of the modifications of the blood flow in the aortic region. In this work, the effect of a continuous flow LVAD device on the aortic flow is investigated by means of a non-intrusive reduced order model (ROM) built using the proper orthogonal decomposition with interpolation (PODI) method based on radial basis functions (RBF). The full order model (FOM) is represented by the incompressible Navier-Stokes equationsdiscretized by using a Finite Volume (FV) technique, coupled with three-element Windkessel models to enforce outlet boundary conditions in a multi-scale approach. A patient-specific framework is proposed: a personalized geometry reconstructed from Computed Tomography (CT) images is used and the individualization of the coefficients of the three-element Windkessel models is based on experimental data provided by the Right Heart Catheterization (RHC) and Echocardiography (ECHO) tests. At FOM level, we also consider the pre-surgery configuration in order to further validate the predictive capabilities of the model in several contexts. The ROM has been tested by considering a parametric setting with respect to the LVAD flow, which is a crucial parameter of the problem. We consider a parameter range that covers typical clinical values. The accuracy of the ROM is assessed against results obtained with the FOM both for primal, velocity and pressure, and derived quantities, wall shear stress (WSS). Finally, we briefly discuss the efficiency of our ROM approach.

A fluid-structure interaction model accounting arterial vessels as a key part of the blood-flow engine for the analysis of cardiovascular diseases

According to the classical Windkessel model, the heart is the only power source for blood flow, while the arterial system is assumed to be an elastic chamber that acts as a channel and buffer for blood circulation. In this paper we show that in addition to the power provided by the heart for blood circulation, strain energy stored in deformed arterial vessels in vivo can be transformed into mechanical work to propel blood flow. A quantitative relationship between the strain energy increment and functional (systolic, diastolic, mean and pulse blood pressure) and structural (stiffness, diameter and wall thickness) parameters of the aorta is described. In addition, details of blood flow across the aorta remain unclear due to changes in functional and other physiological parameters. Based on the arterial strain energy and fluid-structure interaction theory, the relationship between physiological parameters and blood supply to organs was studied, and a corresponding mathematical model was developed. The findings provided a new understanding about blood-flow circulation, that is, cardiac output allows blood to enter the aorta at an initial rate, and then strain energy stored in the elastic arteries pushes blood toward distal organs and tissues. Organ blood supply is a key factor in cardio-cerebrovascular diseases (CCVD), which are caused by changes in blood supply in combination with multiple physiological parameters. Also, some physiological parameters are affected by changes in blood supply, and vice versa. The model can explain the pathophysiological mechanisms of chronic diseases such as CCVD and hypertension among others, and the results are in good agreement with epidemiological studies of CCVD.

Comparison of haemodynamics in carotid endarterectomy: primary closure versus patch angioplasty

We investigated differences in haemodynamic forces between carotid arteries that underwent primary closure (PC) or patch angioplasty (PA) using computational fluid dynamics (CFD). A total of 30 subjects were enrolled in this study, consisting of 10 subjects who underwent PC, 10 who underwent PA and 10 healthy subjects. Three-dimensional models of carotid arteries were reconstructed using patient-specific computed tomography angiography images. The conventional Navier-Stokes, continuity equation and constitutive stress-strain law with a stabilized Petrov-Galerkin scheme were solved with Newtonian and incompressible assumptions. The boundary conditions employed patient-specific velocity profiles as the inflow and lumped parameters of the three-element Windkessel model as the outflow with a rigid wall assumption. Thus, the CFD results exhibited good agreement with measurements from the subjects (r = .78). The carotid arteries of the PC group were exposed to abnormal haemodynamic forces related to building atherosclerosis in a smaller (p .05) to healthy arteries. The morphological characteristics of the carotid artery were significantly associated with the area exposed to abnormal haemodynamic forces. We identified that abnormal haemodynamic forces could be avoided by selecting appropriate surgical techniques that produce less bifurcation expansion.

Solitonic Windkessel Model for Intracranial Aneurysm.

The Windkessel model, which is known as a successful model for explaining the hemodynamic circulation, is a mathematical model with a direct correspondence with the electric circuit. We propose a theoretical model for the intracranial aneurysm based on the Windkessel-type steady blood flow. Intracranial aneurysms are well known vascular lesions, which cause subarachnoid hemorrhages. Since an aneurysm is an end-sack formed on the blood vessel, it functions as an unusual blood path that has characteristic features such as a reservoir and bottle neck orifice. We simulate an aneurysm by an electric circuit consisting of three different impedances, resistance, capacitance and inductance. A dumbbell-shaped aneurysm is the most dangerous aneurysm to easily rupture. Our aneurysmal model is created as a two-story aneurysm model for this point, thus namely the five-element Windkessel. Then, the mathematical formula was solved in numerical simulations by changing the size of the aneurysm and the elasticity of the aneurysm wall. An analysis of this model provided that the presence of the daughter aneurysm and the thinning of the aneurysm wall are positively correlated with a sharp increase in blood pressure in the aneurysm dome. Our mathematic aneurysm model proposes a good analogue to the real aneurysm and proved that this model includes soliton that is a non-decreasing wave propagation.

The New HEMS Modelling of Human Heart

The new version of the hydro-electro-mechanical system (HEMS) is modeled via 14 serially connected electrical equivalent circuits resulting in an integrated equivalent circuit. The new model accepts a group of variables and even examines the interaction between them. This paper introduces an improved integrated new model of the heart by replacing the monolithic equivalent structures with segmental comprehensive equivalents. Windkessel Model (WM) is a model of the relationships between aorta, aortic valve and left ventricle. Based on WM, the integrated new model was developed and simulated. The model’s main focus is to define the dynamic properties of the system by a set of ordinary differential equations, and solving them using Ode23, a method for the solution of a closed-loop system. Using Matlab based Ode23 method; time-dependency of pressure, volume and flow were obtained. In case, short computation time and high accuracy are needed, then ode23 is used. The model may be used to analyze complex processes in the heart and blood vessels. The new HEMS model has potential use for hemodynamic simulation of diseases, cardiovascular disorders, and special congenital heart diseases; such as ASD, VSD and PDA.