Artículos de revistas:

1

Nicosia, Sebastiano y Giuseppe Pezzinga. "Mathematical models of blood flow in the arterial network". Journal of Hydraulic Research 45, n.º 2 (marzo de 2007): 188–201. http://dx.doi.org/10.1080/00221686.2007.9521759.

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2

Sankar, D. S. y K. Hemalatha. "Non-linear mathematical models for blood flow through tapered tubes". Applied Mathematics and Computation 188, n.º 1 (mayo de 2007): 567–82. http://dx.doi.org/10.1016/j.amc.2006.10.013.

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3

El Khatib, N., O. Kafi, A. Sequeira, S. Simakov, Yu Vassilevski y V. Volpert. "Mathematical modelling of atherosclerosis". Mathematical Modelling of Natural Phenomena 14, n.º 6 (2019): 603. http://dx.doi.org/10.1051/mmnp/2019050.

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The review presents the state of the art in the atherosclerosis modelling. It begins with the biological introduction describing the mechanisms of chronic inflammation of artery walls characterizing the development of atherosclerosis. In particular, we present in more detail models describing this chronic inflammation as a reaction-diffusion wave with regimes of propagation depending on the level of cholesterol (LDL) and models of rolling monocytes initializing the inflammation. Further development of this disease results in the formation of atherosclerotic plaque, vessel remodelling and possible plaque rupture due its interaction with blood flow. We review plaque-flow interaction models as well as reduced models (0D and 1D) of blood flow in atherosclerotic vasculature.

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4

Rzaev, E. A., S. R. Rasulov y A. G. Rzaev. "Developing mathematical models for cardiovascular system functional assessments". Kazan medical journal 96, n.º 4 (15 de agosto de 2015): 681–85. http://dx.doi.org/10.17750/kmj2015-681.

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Aim. Development of mathematical models of circulation (considering anomaly in hemorheology) allowing to diagnose functional condition of vessels/cardiovascular system. Methods. Echocardiography, mathematical modeling, sedimentation and rheology laws, human mechanics and physiology methods were used for developing mathematical models. Results. The following mathematical models were obtained: for determination of colloid dispersive blood system viscosity, considering concentration of dispersive phase (blood cells) and blood structure formation; velocity of inconvenient blood cells sedimentation depending on flow velocity of sediment and cell concentration; parameters of blood elasticity and viscosity as a connection between the velocity change and blood viscosity, Young`s elasticity and change tension; blood filtration in vessels (modified form of Darcy`s law) considering tension and changes of destroyed and undestroyed colloid blood system structure velocity. It was shown that impairments of blood flow velocity leads to blood cells sedimentation and thrombus structure formation, which is not moving according to Newton’s law. New indicators for diagnosing functional condition of vessels and estimating the severity of vascular insufficiency are introduced. Conclusion. Developed hemorheologic models allow to adequately estimate human cardiovascular bloodflow.

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5

Farina, Angiolo, Antonio Fasano y Fabio Rosso. "Mathematical Models for Some Aspects of Blood Microcirculation". Symmetry 13, n.º 6 (6 de junio de 2021): 1020. http://dx.doi.org/10.3390/sym13061020.

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Blood rheology is a challenging subject owing to the fact that blood is a mixture of a fluid (plasma) and of cells, among which red blood cells make about 50% of the total volume. It is precisely this circumstance that originates the peculiar behavior of blood flow in small vessels (i.e., roughly speaking, vessel with a diameter less than half a millimeter). In this class we find arterioles, venules, and capillaries. The phenomena taking place in microcirculation are very important in supporting life. Everybody knows the importance of blood filtration in kidneys, but other phenomena, of not less importance, are known only to a small class of physicians. Overviewing such subjects reveals the fascinating complexity of microcirculation.

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6

Namani, Ravi, Yoram Lanir, Lik Chuan Lee y Ghassan S. Kassab. "Overview of mathematical modeling of myocardial blood flow regulation". American Journal of Physiology-Heart and Circulatory Physiology 318, n.º 4 (1 de abril de 2020): H966—H975. http://dx.doi.org/10.1152/ajpheart.00563.2019.

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The oxygen consumption by the heart and its extraction from the coronary arterial blood are the highest among all organs. Any increase in oxygen demand due to a change in heart metabolic activity requires an increase in coronary blood flow. This functional requirement of adjustment of coronary blood flow is mediated by coronary flow regulation to meet the oxygen demand without any discomfort, even under strenuous exercise conditions. The goal of this article is to provide an overview of the theoretical and computational models of coronary flow regulation and to reveal insights into the functioning of a complex physiological system that affects the perfusion requirements of the myocardium. Models for three major control mechanisms of myogenic, flow, and metabolic control are presented. These explain how the flow regulation mechanisms operating over multiple spatial scales from the precapillaries to the large coronary arteries yield the myocardial perfusion characteristics of flow reserve, autoregulation, flow dispersion, and self-similarity. The review not only introduces concepts of coronary blood flow regulation but also presents state-of-the-art advances and their potential to impact the assessment of coronary microvascular dysfunction (CMD), cardiac-coronary coupling in metabolic diseases, and therapies for angina and heart failure. Experimentalists and modelers not trained in these models will have exposure through this review such that the nonintuitive and highly nonlinear behavior of coronary physiology can be understood from a different perspective. This survey highlights knowledge gaps, key challenges, future research directions, and novel paradigms in the modeling of coronary flow regulation.

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7

Ellwein, Laura M., Hien T. Tran, Cheryl Zapata, Vera Novak y Mette S. Olufsen. "Sensitivity Analysis and Model Assessment: Mathematical Models for Arterial Blood Flow and Blood Pressure". Cardiovascular Engineering 8, n.º 2 (15 de diciembre de 2007): 94–108. http://dx.doi.org/10.1007/s10558-007-9047-3.

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8

Sankar, D. S. y Yazariah Yatim. "Comparative Analysis of Mathematical Models for Blood Flow in Tapered Constricted Arteries". Abstract and Applied Analysis 2012 (2012): 1–34. http://dx.doi.org/10.1155/2012/235960.

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Pulsatile flow of blood in narrow tapered arteries with mild overlapping stenosis in the presence of periodic body acceleration is analyzed mathematically, treating it as two-fluid model with the suspension of all the erythrocytes in the core region as non-Newtonian fluid with yield stress and the plasma in the peripheral layer region as Newtonian. The non-Newtonian fluid with yield stress in the core region is assumed as (i) Herschel-Bulkley fluid and (ii) Casson fluid. The expressions for the shear stress, velocity, flow rate, wall shear stress, plug core radius, and longitudinal impedance to flow obtained by Sankar (2010) for two-fluid Herschel-Bulkley model and Sankar and Lee (2011) for two-fluid Casson model are used to compute the data for comparing these fluid models. It is observed that the plug core radius, wall shear stress, and longitudinal impedance to flow are lower for the two-fluid H-B model compared to the corresponding flow quantities of the two-fluid Casson model. It is noted that the plug core radius and longitudinal impedance to flow increases with the increase of the maximum depth of the stenosis. The mean velocity and mean flow rate of two-fluid H-B model are higher than those of the two-fluid Casson model.

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9

Balazs, ALBERT y PETRILA Titus. "Mathematical Models and Numerical Simulations for the Blood Flow in Large Vessels". INCAS BULLETIN 4, n.º 4 (10 de diciembre de 2012): 3–10. http://dx.doi.org/10.13111/2066-8201.2012.4.4.1.

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10

ZAMAN, GUL, YONG HAN KANG y IL HYO JUNG. "ORIENTATIONAL STRESS TENSOR OF POLYMER SOLUTION WITH APPLICATIONS TO BLOOD FLOW". Modern Physics Letters B 25, n.º 12n13 (30 de mayo de 2011): 1157–66. http://dx.doi.org/10.1142/s0217984911026875.

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Blood circulating efficiently inside the veins and arteries, provides essential nutrients and oxygen to tissues and organs in the entire body. To highlight the fundamental properties of blood and gain insight into the regularizing effect of various formulations, we need to develop mathematical models. In order to do this, first we present the polymer dynamics in terms of an ensemble of Hookean dumbbells with Brownian configuration fields to derive the orientation stress tensor. Then, we describe the continuity and the momentum equations for time-dependent incompressible flow and the Oldroyd-B model. Finally, we present our numerical analysis of the model and give the effect of the orientation stress tensor in a blood vessel. The development of mathematical models and numerical procedures for the approximation of the blood specific flow equations have enabled us to understand the complex behaviors of blood flows inside the vessel.

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11

Koirala, Nischal y Gordon McLennan. "Mathematical Models for Blood Flow Quantification in Dialysis Access Using Angiography: A Comparative Study". Diagnostics 11, n.º 10 (26 de septiembre de 2021): 1771. http://dx.doi.org/10.3390/diagnostics11101771.

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Blood flow rate in dialysis (vascular) access is the key parameter to examine patency and to evaluate the outcomes of various endovascular interve7ntions. While angiography is extensively used for dialysis access–salvage procedures, to date, there is no image-based blood flow measurement application commercially available in the angiography suite. We aim to calculate the blood flow rate in the dialysis access based on cine-angiographic and fluoroscopic image sequences. In this study, we discuss image-based methods to quantify access blood flow in a flow phantom model. Digital subtraction angiography (DSA) and fluoroscopy were used to acquire images at various sampling rates (DSA—3 and 6 frames/s, fluoroscopy—4 and 10 pulses/s). Flow rates were computed based on two bolus tracking algorithms, peak-to-peak and cross-correlation, and modeled with three curve-fitting functions, gamma variate, lagged normal, and polynomial, to correct errors with transit time measurement. Dye propagation distance and the cross-sectional area were calculated by analyzing the contrast enhancement in the vessel. The calculated flow rates were correlated versus an in-line flow sensor measurement. The cross-correlation algorithm with gamma-variate curve fitting had the best accuracy and least variability in both imaging modes. The absolute percent error (mean ± SEM) of flow quantification in the DSA mode at 6 frames/s was 21.4 ± 1.9%, and in the fluoroscopic mode at 10 pulses/s was 37.4 ± 3.6%. The radiation dose varied linearly with the sampling rate in both imaging modes and was substantially low to invoke any tissue reactions or stochastic effects. The cross-correlation algorithm and gamma-variate curve fitting for DSA acquisition at 6 frames/s had the best correlation with the flow sensor measurements. These findings will be helpful to develop a software-based vascular access flow measurement tool for the angiography suite and to optimize the imaging protocol amenable for computational flow applications.

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12

Sankar, D. S. y Ahmad Izani Md Ismail. "Two-Fluid Mathematical Models for Blood Flow in Stenosed Arteries: A Comparative Study". Boundary Value Problems 2009 (2009): 1–15. http://dx.doi.org/10.1155/2009/568657.

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13

Alasakani, Karthik, Radhika S. l. Tantravahi y Praveen Kumar Ptv. "On Refining the Input Data set to Mathematical Models Simulating Arterial blood flow in Humans". WSEAS TRANSACTIONS ON FLUID MECHANICS 16 (18 de marzo de 2021): 63–78. http://dx.doi.org/10.37394/232013.2021.16.7.

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In this paper, we worked on methods to reduce the input data set to the mathematical models developed to simulate blood flow through human arteries. In general, any mathematical model designed to mimic a natural process needs specific information on its model parameters. In our models, the inputs to these parameters are from the human arterial system, i.e., the anatomical data on arteries and physiological data on blood. Besides these, there are few other parameters in the models describing mechanisms, such as the pulsatile nature of the blood flow and the arteries' elastic behavior. These mechanisms described using mathematical relations help assign values to the parameters that satisfy mathematical specifications or requirements. However, with this method of assigning values, there is a possibility that some of the data sets constructed simulate the same state of the system (arterial system) even though the values assigned significantly differ from each other in magnitude. Moreover, identifying such data sets is not an apparent task but requires robust procedures. Thus, in this work, we attempt to shed light on a data size reduction technique to identify all such model parameters' in-significant values and eliminate them from the input data set. We propose the statistical testing procedure to identify a significant difference in the dependent variables' values (whose values are computed using the mathematical models) with the independent variables (the model parameters). This novel approach could efficiently identify the inputs mimicking similar arterial system states and build a refined input data set.

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14

Nanda, Saktipada, Biswadip Basu Mallik, Samarpan Deb Majumder, Ramesh Kumar Karthick, Sagar Suman y Sahil Sonkar. "Mathematical Modelling of Pulsatile Flow of Non-Newtonian Fluid Through a Constricted Artery". Mathematical Modelling of Engineering Problems 8, n.º 3 (24 de junio de 2021): 485–91. http://dx.doi.org/10.18280/mmep.080320.

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The research work explores blood flow into a stenosed artery, or one with abnormal growth within it. At the throats and at the critical height of the stenosis, mathematical and computational models have been developed to calculate the various associated parameters such as flow rate, pressure gradient, impedance, and wall shear stress. Modeling blood as a power law fluid showed the dependency of these quantities on temporal and spatial variables, as well as the frequency of the flow oscillation in time and the key parameters of the flow mechanism. The exponential curve is the geometry of the stenosis studied in this analysis. Analytical expressions for axial velocity, volumetric flow rate, pressure gradient, blood flow resistance, and shear stress have been computed and simulated in ANSYS to generate useful results with respect to variation of flow parameters with power law indices and also for comparison between Newtonian and Non- Newtonian models of blood. Upon investigation, it was found that wall shear stress (WSS) increases with stenosis depth and therefore, plays a crucial role in affecting other flow parameters. At power law index 0.6, the highest shear stress and flow velocity were encountered at approximately 7 Pa and 0.5 m/s respectively.

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15

Chernyavskiy, M. A., B. S. Artyushin, A. V. Chernov, D. V. Chernova, N. N. Zherdev y Yu A. Kudaev. "POSSIBILITIES OF APPLYING MATHEMATICAL ANALYSIS OF BLOOD FLOW CHARACTERISTICS IN ENDOVASCULAR TREATMENT OF AORTIC DISEASES USING HOLOMETALLIC STENTS". Research'n Practical Medicine Journal 6, n.º 1 (8 de abril de 2019): 99–105. http://dx.doi.org/10.17709/2409-2231-2019-6-1-10.

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Purpose. The purpose of the article is to access possibilities of blood flow mathematical analysis in aortic aneurysm before and after bare metal stent implantation.Materials and methods. Mathematical models of aortic blood flow were based on data received at studying 15 CT-scans of patients with abdominal aorta aneurysms (12) and dissections (3) and their duplex ultra-sound hemodynamic data. At constructing mathematical model the program SolidWorks was used. Working with the program consisted of two stages: establishment of conditions for geometric objects; forming of abdominal aorta model from these objects. In the study hemodinamic aneurysm indexes was evaluated on rectilinear and curvilinear segments. Some of characteristics were variable: diameter, aneurysm wall thickness, its length, elasticity.Results. Correlation of extreme tension into aneurysm wall on rectilinear and curvilinear segments according to aneurysm wall thickness was assessed. Possibilities of pathological blood flow changes correction at bare metal stent implantation into aortic aneurysm were estimated: if presence of bare metal stent were introduced into mathematical parameters blood flow characteristics became almost as standard characteristics. Received data can enhance successful endovascular treatment of aortic diseases with using of bare metal stents.Conclusion. Mathematical models of aortic and vascular aneurysms before and after surgery can be an effective tool in bettering quality of medical help for vascular patients.

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16

Geydarov, N. A., K. S. Gainullova y O. S. Drygina. "COMPUTATIONAL BLOOD FLOW SIMULATIONS IN CARDIOLOGY AND CARDIAC SURGERY". Complex Issues of Cardiovascular Diseases 7, n.º 2 (30 de junio de 2018): 129–36. http://dx.doi.org/10.17802/2306-1278-2018-7-2-129-136.

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The review provides the current state and benefits of the computational fluid dynamics (CFD) applications in cardiovascular surgery. The review covers the milestones of CFD and novel achievements in the development of both numerical algorithms and computational models. Basic methods of flow modeling, including immersed-boundary methods and finite-difference methods, allow solving most core tasks, even using commercially available software packages. Future research prospects of CFD are associated with detailed modeling of the pathological processes affecting functional properties of medical devices, namely thrombus formation and embolism. However, current computational and mathematical systems are limited to address fully all these processes.

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17

Laugesen, Jakob L., Olga V. Sosnovtseva, Erik Mosekilde, Niels-Henrik Holstein-Rathlou y Donald J. Marsh. "Coupling-induced complexity in nephron models of renal blood flow regulation". American Journal of Physiology-Regulatory, Integrative and Comparative Physiology 298, n.º 4 (abril de 2010): R997—R1006. http://dx.doi.org/10.1152/ajpregu.00714.2009.

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Tubular pressure and nephron blood flow time series display two interacting oscillations in rats with normal blood pressure. Tubuloglomerular feedback (TGF) senses NaCl concentration in tubular fluid at the macula densa, adjusts vascular resistance of the nephron's afferent arteriole, and generates the slower, larger-amplitude oscillations (0.02–0.04 Hz). The faster smaller oscillations (0.1–0.2 Hz) result from spontaneous contractions of vascular smooth muscle triggered by cyclic variations in membrane electrical potential. The two mechanisms interact in each nephron and combine to act as a high-pass filter, adjusting diameter of the afferent arteriole to limit changes of glomerular pressure caused by fluctuations of blood pressure. The oscillations become irregular in animals with chronic high blood pressure. TGF feedback gain is increased in hypertensive rats, leading to a stronger interaction between the two mechanisms. With a mathematical model that simulates tubular and arteriolar dynamics, we tested whether an increase in the interaction between TGF and the myogenic mechanism can cause the transition from periodic to irregular dynamics. A one-dimensional bifurcation analysis, using the coefficient that couples TGF and the myogenic mechanism as a bifurcation parameter, shows some regions with chaotic dynamics. With two nephrons coupled electrotonically, the chaotic regions become larger. The results support the hypothesis that increased oscillator interactions contribute to the transition to irregular fluctuations, especially when neighboring nephrons are coupled, which is the case in vivo.

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18

Baba, Tatsuro, Shuichi Adachi y Masatsugu Taiko. "Automatic Valve-Rejection Algorithm for Cardiac Doppler Ultrasound Systems". ISRN Biomedical Imaging 2013 (24 de marzo de 2013): 1–6. http://dx.doi.org/10.1155/2013/850303.

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In recent years, blood flow diagnosis using Doppler ultrasound systems has become popular. Using these systems, the peak velocity of blood flow is automatically traced. However, because valve signals are mixed with the blood flow signals in a heart chamber, automatic measurements of blood flow are not correctly recorded. To solve this problem, we developed a novel method that adopted system identification. We applied a mathematical model with an electrocardiographic waveform as the input and a trace waveform of the peak velocity as the output. Several mathematical models with different structures and orders were compared to select the optimal model. Using this model, we developed a system that could automatically eliminate the valve signal. We also evaluated our valve-rejection algorithm using simulations based on actual clinical data.

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19

Boujelben, Ahmed, Michael Watson, Steven McDougall, Yi-Fen Yen, Elizabeth R. Gerstner, Ciprian Catana, Thomas Deisboeck et al. "Multimodality imaging and mathematical modelling of drug delivery to glioblastomas". Interface Focus 6, n.º 5 (6 de octubre de 2016): 20160039. http://dx.doi.org/10.1098/rsfs.2016.0039.

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Patients diagnosed with glioblastoma, an aggressive brain tumour, have a poor prognosis, with a median overall survival of less than 15 months. Vasculature within these tumours is typically abnormal, with increased tortuosity, dilation and disorganization, and they typically exhibit a disrupted blood–brain barrier (BBB). Although it has been hypothesized that the ‘normalization’ of the vasculature resulting from anti-angiogenic therapies could improve drug delivery through improved blood flow, there is also evidence that suggests that the restoration of BBB integrity might limit the delivery of therapeutic agents and hence their effectiveness. In this paper, we apply mathematical models of blood flow, vascular permeability and diffusion within the tumour microenvironment to investigate the effect of these competing factors on drug delivery. Preliminary results from the modelling indicate that all three physiological parameters investigated—flow rate, vessel permeability and tissue diffusion coefficient—interact nonlinearly to produce the observed average drug concentration in the microenvironment.

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20

Sgouralis, Ioannis y Anita T. Layton. "Autoregulation and conduction of vasomotor responses in a mathematical model of the rat afferent arteriole". American Journal of Physiology-Renal Physiology 303, n.º 2 (15 de julio de 2012): F229—F239. http://dx.doi.org/10.1152/ajprenal.00589.2011.

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We have formulated a mathematical model for the rat afferent arteriole (AA). Our model consists of a series of arteriolar smooth muscle cells and endothelial cells, each of which represents ion transport, cell membrane potential, and gap junction coupling. Cellular contraction and wall mechanics are also represented for the smooth muscle cells. Blood flow through the AA lumen is described by Poiseuille flow. The AA model's representation of the myogenic response is based on the hypothesis that changes in hydrostatic pressure induce changes in the activity of nonselective cation channels. The resulting changes in membrane potential then affect calcium influx through changes in the activity of the voltage-gated calcium channels, so that vessel diameter decreases with increasing pressure values. With this configuration, the model AA maintains roughly stable renal blood flow within a physiologic range of blood flow pressure. Model simulation of vasoconstriction initiated from local stimulation also agrees well with findings in the experimental literature, notably those of Steinhausen et al. (Steinhausen M, Endlich K, Nobiling R, Rarekh N, Schütt F. J Physiol 505: 493–501, 1997), which indicated that conduction of vasoconstrictive response decays more rapidly in the upstream flow direction than downstream. The model can be incorporated into models of integrated renal hemodynamic regulation.

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21

Lopes, D., H. Puga, J. C. Teixeira y S. F. Teixeira. "Fluid–Structure Interaction study of carotid blood flow: Comparison between viscosity models". European Journal of Mechanics - B/Fluids 83 (septiembre de 2020): 226–34. http://dx.doi.org/10.1016/j.euromechflu.2020.05.010.

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22

Sefidgar, Mostafa, M. Soltani, Kaamran Raahemifar y Hossein Bazmara. "Effect of Fluid Friction on Interstitial Fluid Flow Coupled with Blood Flow through Solid Tumor Microvascular Network". Computational and Mathematical Methods in Medicine 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/673426.

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A solid tumor is investigated as porous media for fluid flow simulation. Most of the studies use Darcy model for porous media. In Darcy model, the fluid friction is neglected and a few simplified assumptions are implemented. In this study, the effect of these assumptions is studied by considering Brinkman model. A multiscale mathematical method which calculates fluid flow to a solid tumor is used in this study to investigate how neglecting fluid friction affects the solid tumor simulation. The mathematical method involves processes such as blood flow through vessels and solute and fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. The sprouting angiogenesis model is used for generating capillary network and then fluid flow governing equations are implemented to calculate blood flow through the tumor-induced capillary network. Finally, the two models of porous media are used for modeling fluid flow in normal and tumor tissues in three different shapes of tumors. Simulations of interstitial fluid transport in a solid tumor demonstrate that the simplifications used in Darcy model affect the interstitial velocity and Brinkman model predicts a lower value for interstitial velocity than the values that Darcy model predicts.

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23

Maki, Kara L., Rodolfo Repetto y Richard J. Braun. "Mathematical modeling highlights from ARVO 2018". Modeling and Artificial Intelligence in Ophthalmology 2, n.º 3 (19 de junio de 2019): 5–8. http://dx.doi.org/10.35119/maio.v2i3.98.

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At the ARVO annual meeting, there is an increasing number of contributions that involve significant mathematical modeling of ocular physiology and procedures. There has long been significant use of statistical methods for understanding data from a variety of in vivo measurements and clinical trials. Beyond these important uses of statistical and mathematical tools, a growing number of researchers are developing mathematical and computational models, often based on fundamental principles from physics, chemistry and mechanics, that provide insights into ocular phenomena. A number of areas had noticeable contributions involving applications of models, such as tear production, tear film dynamics, corneal biomechanics, retinal blood flow, and glaucoma. We list a number of such contributions in this introduction and follow those with five extended abstracts that summarize some of the studies mentioned here.

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Gabryś, Elżbieta, Marek Rybaczuk y Alicja Kędzia. "Blood flow simulation through fractal models of circulatory system". Chaos, Solitons & Fractals 27, n.º 1 (enero de 2006): 1–7. http://dx.doi.org/10.1016/j.chaos.2005.02.009.

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25

Kumar, Anil, V. Upa dhyay, A. K. Agra wal y P. N. Pan dey. "Mathematical models of two phase human hepatic blood flow in venules with special reference to liver cirrhosis". International Journal of Mathematics Trends and Technology 52, n.º 2 (25 de diciembre de 2017): 145–51. http://dx.doi.org/10.14445/22315373/ijmtt-v52p520.

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CLARK, A. R. y M. H. TAWHAI. "TEMPORAL AND SPATIAL HETEROGENEITY IN PULMONARY PERFUSION: A MATHEMATICAL MODEL TO PREDICT INTERACTIONS BETWEEN MACRO- AND MICRO-VESSELS IN HEALTH AND DISEASE". ANZIAM Journal 59, n.º 4 (abril de 2018): 562–80. http://dx.doi.org/10.1017/s1446181118000111.

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Heterogeneity in pulmonary microvascular blood flow (perfusion) provides an early indicator of lung disease or disease susceptibility. However, most computational models of the pulmonary vasculature neglect structural heterogeneities, and are thus not accurate predictors of lung function in disease that is not diffuse (spread evenly through the lung). Models that do incorporate structural heterogeneity have either neglected the temporal dynamics of blood flow, or the structure of the smallest blood vessels. Larger than normal oscillations in pulmonary capillary calibre, high oscillatory stress contribute to disease progression. Hence, a model that captures both spatial and temporal heterogeneity in pulmonary perfusion could provide new insights into the early stages of pulmonary vascular disease. Here, we present a model of the pulmonary vasculature, which captures both flow dynamics, and the anatomic structure of the pulmonary blood vessels from the right to left heart including the micro-vasculature. The model is compared to experimental data in normal lungs. We confirm that spatial heterogeneity in pulmonary perfusion is time-dependent, and predict key features of pulmonary hypertensive disease using a simple implementation of increased vascular stiffness.

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27

Ferrell, Nicholas, Ruben M. Sandoval, Aihua Bian, Silvia B. Campos-Bilderback, Bruce A. Molitoris y William H. Fissell. "Shear stress is normalized in glomerular capillaries following ⅚ nephrectomy". American Journal of Physiology-Renal Physiology 308, n.º 6 (15 de marzo de 2015): F588—F593. http://dx.doi.org/10.1152/ajprenal.00290.2014.

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Loss of significant functional renal mass results in compensatory structural and hemodynamic adaptations in the nephron. While these changes have been characterized in several injury models, how they affect hemodynamic forces at the glomerular capillary wall has not been adequately characterized, despite their potential physiological significance. Therefore, we used intravital multiphoton microscopy to measure the velocity of red blood cells in individual glomerular capillaries of normal rats and rats subjected to ⅚ nephrectomy. Glomerular capillary blood flow rate and wall shear stress were then estimated using previously established experimental and mathematical models to account for changes in hematocrit and blood rheology in small vessels. We found little change in the hemodynamic parameters in glomerular capillaries immediately following injury. At 2 wk postnephrectomy, significant changes in individual capillary blood flow velocity and volume flow rate were present. Despite these changes, estimated capillary wall shear stress was unchanged. This was a result of an increase in capillary diameter and changes in capillary blood rheology in nephrectomized rats.

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Dobroserdova, Tatyana, Fuyou Liang, Grigory Panasenko y Yuri Vassilevski. "Multiscale models of blood flow in the compliant aortic bifurcation". Applied Mathematics Letters 93 (julio de 2019): 98–104. http://dx.doi.org/10.1016/j.aml.2019.01.037.

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29

Giménez, Á., M. Galarza, U. Thomale, M. U. Schuhmann, J. Valero y J. M. Amigó. "Pulsatile flow in ventricular catheters for hydrocephalus". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, n.º 2096 (15 de mayo de 2017): 20160294. http://dx.doi.org/10.1098/rsta.2016.0294.

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The obstruction of ventricular catheters (VCs) is a major problem in the standard treatment of hydrocephalus, the flow pattern of the cerebrospinal fluid (CSF) being one important factor thereof. As a first approach to this problem, some of the authors studied previously the CSF flow through VCs under time-independent boundary conditions by means of computational fluid dynamics in three-dimensional models. This allowed us to derive a few basic principles which led to designs with improved flow patterns regarding the obstruction problem. However, the flow of the CSF has actually a pulsatile nature because of the heart beating and blood flow. To address this fact, here we extend our previous computational study to models with oscillatory boundary conditions. The new results will be compared with the results for constant flows and discussed. It turns out that the corrections due to the pulsatility of the CSF are quantitatively small, which reinforces our previous findings and conclusions. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’.

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Senner, John W., Frank Z. Stanczyk, Marc A. Fritz y Miles J. Novy. "Relationship of uteroplacental blood flow to placental clearance of maternal plasma C-19 steroids: Evaluation of mathematical models". American Journal of Obstetrics and Gynecology 153, n.º 5 (noviembre de 1985): 573–75. http://dx.doi.org/10.1016/0002-9378(85)90481-8.

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Tanveer, Shakera y V. P. Rathod. "Gravity flow of pulsatile blood through a porous medium under periodic body acceleration and magnetic field in an inclined tube". International Journal of Biomathematics 09, n.º 02 (14 de enero de 2016): 1650025. http://dx.doi.org/10.1142/s179352451650025x.

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Mathematical model for the pulsatile blood flow through a porous medium under the influence of periodic body acceleration for gravity flow along an inclined tube by considering blood as a couple stress, incompressible and electrically conducting fluid in the presence of magnetic field has been investigated. Analytical expressions for axial velocity, flow rate, fluid acceleration and shear stress are obtained by applying the Laplace and finite Hankel’s transforms. The velocity profiles for various values of Hartmann number, couple stress parameters and the angle of inclination are shown graphically. Also the effects of body acceleration, Womerseley parameters and permeability parameters have been discussed. The results obtained in the present mathematical model for different values of the parameters involved in the problem show that the flow of blood is influenced by the effect of magnetic field, the porous medium and the inclination angle. The present model is compared with the other existing models. Through this theoretical investigation, the applications of magnetic field have also been indicated in the field of biological, biomedical and engineering sciences.

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Lampe, Renée, Nikolai Botkin, Varvara Turova, Tobias Blumenstein y Ana Alves-Pinto. "Mathematical Modelling of Cerebral Blood Circulation and Cerebral Autoregulation: Towards Preventing Intracranial Hemorrhages in Preterm Newborns". Computational and Mathematical Methods in Medicine 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/965275.

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Impaired cerebral autoregulation leads to fluctuations in cerebral blood flow, which can be especially dangerous for immature brain of preterm newborns. In this paper, two mathematical models of cerebral autoregulation are discussed. The first one is an enhancement of a vascular model proposed by Piechnik et al. We extend this model by adding a polynomial dependence of the vascular radius on the arterial blood pressure and adjusting the polynomial coefficients to experimental data to gain the autoregulation behavior. Moreover, the inclusion of a Preisach hysteresis operator, simulating a hysteretic dependence of the cerebral blood flow on the arterial pressure, is tested. The second model couples the blood vessel system model by Piechnik et al. with an ordinary differential equation model of cerebral autoregulation by Ursino and Lodi. An optimal control setting is proposed for a simplified variant of this coupled model. The objective of the control is the maintenance of the autoregulatory function for a wider range of the arterial pressure. The control can be interpreted as the effect of a medicament changing the cerebral blood flow by, for example, dilation of blood vessels. Advanced numerical methods developed by the authors are applied for the numerical treatment of the control problem.

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Kozlov, V. A. y S. A. Nazarov. "Asymptotic Models of the Blood Flow in Arteries and Veins". Journal of Mathematical Sciences 194, n.º 1 (5 de septiembre de 2013): 44–57. http://dx.doi.org/10.1007/s10958-013-1505-4.

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Pereira, J. M. C., J. P. Serra e Moura, A. R. Ervilha y J. C. F. Pereira. "On the uncertainty quantification of blood flow viscosity models". Chemical Engineering Science 101 (septiembre de 2013): 253–65. http://dx.doi.org/10.1016/j.ces.2013.05.033.

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Marcinkowska-Gapińska, Anna y Piotr Kowal. "Hemorheological studies of chosen clinical cases". Journal of Medical Science 84, n.º 3 (30 de septiembre de 2015): 197–200. http://dx.doi.org/10.20883/medical.e17.

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Rheology – the study of the flow of matter and accompanying phenomena of real bodies deformation – in relation to blood – hemorheology. Blood viscosity – the main rheological parameter – has been studied in many research centers and among many different group of patients. The main disorders related to the hemorheological properties are: coronary insufficiency, vascular congestion, myocardial infarction, cerebral circulation disorder, Reynaud disease, ischemic limbs, diabetes, anemia, tumors. The following parameters are the main blood viscosity determinants: plasma viscosity, hematocrit, red cell deformability and erythrocytes aggregation. In hemorheological studies we used mathematical rheological models. The measurements of blood and plasma viscosity are performed by means of oscillating-rotary rheometers in order to determine the dependence of blood viscosity on the shear rate and the two components of the complex blood viscosity. Determination of blood cells aggregability and deformability is performed directly by means of aggregometers and appropiate filters and indirectly using rheological techniques with advanced mathematical models of blood viscoelasticity. Blood and plasma viscosity are subject to autoregulation mechanisms of the body. Recognition of those mechanisms may help in assessment of some diseases risk: ischemic stroke or myocardial infarction. In many cases rheological measurements may reveal the most recent phases of diseases and disorderses which enables early therapy with specimens improving the blood fluidity. For this reason rheological measurements should be applied in diagnostics and therapy. Mutual relations between the main factors determining the blood viscosity and their effect on blood flow are the main subject of current report.

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ROBERTSON, ANNE M. y ADÉLIA SEQUEIRA. "A DIRECTOR THEORY APPROACH FOR MODELING BLOOD FLOW IN THE ARTERIAL SYSTEM: AN ALTERNATIVE TO CLASSICAL 1D MODELS". Mathematical Models and Methods in Applied Sciences 15, n.º 06 (junio de 2005): 871–906. http://dx.doi.org/10.1142/s0218202505000601.

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It remains computationally infeasible to model the full three-dimensional (3D) equations for blood flow in large sections of the circulatory system. As a result, one-dimensional (1D) and lumped parameter models play an important role in studies of the arterial system. A variety of 1D models are used, distinguished by the closure approximations employed. In this paper, we introduce a nine-director theory for flow in axisymmetric bodies as an alternative to the 1D models. Advantages of the director theory include (i) the theory makes use of all components of linear momentum; (ii) the flow is not assumed to be uni-directional; (iii) the theory is hierarchical; (iv) there is no need for closure approximations; and (v) wall shear stress enters directly as a dependent variable. In order to simplify the equations for mathematical analysis, for this work, attention is focused on cases where it is appropriate to model the flow as quasi-steady and the wall motion does not have a significant impact on bulk flow parameters. This work lays the foundation for future applications of the theory to unsteady flows in flexible walled vessels. For the geometries considered here, the nine-director theory has the same advantage as 1D models in providing a relatively simple relation between flow rate and average pressure drop. Conditions for existence, uniqueness and local stability of steady solutions are determined for both the 1D and nine-director equations. The predictive capability of classical 1D models found in the recent literature and a nine-director model7,15 are carefully evaluated through comparison with analytical and computational solutions to the axisymmetric, steady Navier–Stokes equations in geometries relevant to blood flow. For these benchmark problems over the range of Reynolds numbers considered, the nine-director theory is found to provide better results than the classical 1D models. A novel approach for parameter identification is in the 1D model is given and shown to substantially improve its predictive capability in these test cases.

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Bakhti, Hamzah, Lahcen Azrar y Baleanu Dumitru. "Pulsatile blood flow in constricted tapered artery using a variable-order fractional Oldroyd-B model". Thermal Science 21, n.º 1 Part A (2017): 29–40. http://dx.doi.org/10.2298/tsci160421237b.

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The aim of this paper is to deal with the pulsatile flow of blood in stenosed arteries using one of the known constitutive models that describe the viscoelasticity of blood witch is the generalized Oldroyd-B model with a variable-order fractional derivative. Numerical approximation for the axial velocity and wall shear stress were obtained by use of the implicit finite-difference scheme. The velocity profile is analyzed by graphical illustrations. This mathematical model gives more realistic results that will help medical practitioners and it has direct applications in the treatment of cardiovascular diseases.

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Gupta, B. B., M. Y. Jaffrin y L. H. Ding. "Modelling of Plasma-Separation through Microporous Membranes". International Journal of Artificial Organs 12, n.º 1 (enero de 1989): 51–58. http://dx.doi.org/10.1177/039139888901200109.

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Available mathematical models of ultrafiltration have been used to predict changes in maximum plasma filtration rate with wall shear rate for given filters and blood properties. We have done many plasmapheresis experiments in vitro, using hollow-fiber filters (500–1000 cm2) and fresh bovine blood collected on ACD or heparin. The comparison between predicted and experimentally obtained filtration rates was good for models based on the concentration polarization theory and lift velocity theory. In other experiments with pulsatile inlet flow we found that plasma filtration rate increased by 20 to 50% compared to nonpulsatile conditions. These results are in good agreement with the modified model of ultrafiltration incorporating pulsating flow. This paper presents relationships between plasma filtration velocity (steady and pulsating flow) and hemolysis limit as a function of wall shear rate and filter size.

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BEHBAHANI, M., M. BEHR, M. HORMES, U. STEINSEIFER, D. ARORA, O. CORONADO y M. PASQUALI. "A review of computational fluid dynamics analysis of blood pumps". European Journal of Applied Mathematics 20, n.º 4 (agosto de 2009): 363–97. http://dx.doi.org/10.1017/s0956792509007839.

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Ventricular assist devices (VADs) provide long- and short-term support to chronically ill heart disease patients; these devices are expected to match the remarkable functionality of the natural heart, which makes their design a very challenging task. Blood pumps, the principal component of the VADs, must operate over a wide range of flow rates and pressure heads and minimise the damage to blood cells in the process. They should also be small to allow easy implantation in both children and adults. Mathematical methods and computational fluid dynamics (CFD) have recently emerged as powerful design tools in this context; a review of the recent advances in the field is presented here. This review focusses on the CFD-based design strategies applied to blood flow in blood pumps and other blood-handling devices. Both simulation methods for blood flow and blood damage models are reviewed. The literature is put into context with a discussion of the chronological development in the field. The review is illustrated with specific examples drawn from our group's Galerkin/least squares (GLS) finite-element simulations of the basic Newtonian flow problem for the continuous-flow centrifugal GYRO blood pump. The GLS formulation is outlined, and modifications to include models that better represent blood rheology are shown. Haemocompatibility analysis of the pump is reviewed in the context of haemolysis estimations based on different blood damage models. Our strain-based blood damage model that accounts for the viscoleasticity associated with the red blood cells is reviewed in detail. The viability of design improvement based on trial and error and complete simulation-based design optimisation schemes are also discussed.

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40

Del Río Palma, J., E. Romero V. y M. Cerrolaza. "ANALYSIS OF BLOOD FLOW PASSING THROUGH AORTIC AND MITRAL VALVES USING A COMPUTATIONAL MODEL OF CONCENTRATED PARAMETERS". Biomedical Engineering: Applications, Basis and Communications 26, n.º 06 (diciembre de 2014): 1450068. http://dx.doi.org/10.4015/s1016237214500689.

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Blood flow has been extensively studied because of its close relationship with cardiovascular disease. Heart valves blood flow analysis is particularly complex due to the high mobility of its leaflets, a fact that has stimulated the development of computational models aimed to its better understanding. For studying heart valves blood flow, we developed a mathematical model derived from clinical observations based on echocardiographic images, which describe valve leaflets motion and its influence on blood flow. This work presents a concentrated-parameters-based model of heart valves blood flow that takes into consideration five main factors affecting such a flow in the mitral and aortic valves. This model considers factors that are related to blood fluid and valve leaflets characteristics. Considering the main factors involved, it was found that blood flow exhibit an abnormal behavior in response to small variations (less than 10%) in blood pressure gradient or in leaflets stiffness. Likewise, after changing the roughness of the leaflets, the impact is smaller, only slightly affecting blood flow behavior with changes beyond 30%. Moreover, it was observed that the influence of fluid vortices originated behind the valves can be disregarded and the kinetic energy induced by them is almost negligible.

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Layton, Anita T. "Modeling Transport and Flow Regulatory Mechanisms of the Kidney". ISRN Biomathematics 2012 (23 de agosto de 2012): 1–18. http://dx.doi.org/10.5402/2012/170594.

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The kidney plays an indispensable role in the regulation of whole-organism water balance, electrolyte balance, and acid-base balance, and in the excretion of metabolic wastes and toxins. In this paper, we review representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, and regulation of renal oxygen transport. We discuss how such modeling efforts have significantly expanded our understanding of renal function in both health and disease.

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Liu, Biyue y Dalin Tang. "Influence of Distal Stenosis on Blood Flow Through Coronary Serial Stenoses: A Numerical Study". International Journal of Computational Methods 16, n.º 03 (17 de marzo de 2019): 1842003. http://dx.doi.org/10.1142/s0219876218420033.

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Computer simulations of the blood flow through right coronary arteries with two stenoses in the same arterial segment are carried out to investigate the interactions of serial stenoses, especially the effect of the distal stenosis. Various mathematical models are developed by varying the location of the distal stenosis. The numerical results show that the variation of the distal stenosis has significant impact on coronary hemodynamics, such as the pressure drop, flow shifting, wall shear stress and flow separation. Our simulations demonstrate that the distal stenosis has insignificant effect on the disturbed flow pattern in the regions of upstream and across the proximal stenosis. In a curved artery segment with two moderate stenoses of the same size, the distal stenosis causes a larger pressure drop and a more disturbed flow field in the poststenotic region than the proximal stenosis does. A distal stenosis located at a further downstream position causes a larger pressure drop and a stronger reverse flow.

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Chen, Yan-li, Gui-Qiang Bai, Liu-xing Ren, Yang Bai, Meng-yao Sun, Tao Shang, Chun-ye Ma y Da-shi Ma. "Blood physiological and flow characteristics within coronary artery circulatory network for human heart based on vascular fractal theory". Advances in Mechanical Engineering 12, n.º 7 (julio de 2020): 168781402093338. http://dx.doi.org/10.1177/1687814020933385.

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To analyze the fractal form of the vascular network in the human circulatory system, the optimal transport effect has been achieved from the point of view of biological evolution. The blood flow mathematical models based on the fractal theory for capillary network and arteriole–capillary vascular fractal network were established using theory derivation, and the blood flow characteristics, dynamic flow resistance effects, and vascular fractal physiology property based on the fractal porous medium theory for the coronary artery circulatory network were analyzed under the consideration of some influencing factors, namely, non-Newtonian fluid characteristics of blood, hemocoagulation and embolization effect in capillaries, and plasma mass flow effects. Moreover, the Poiseuille flow equation is modified by introducing the correction function, and the flow model of blood in the vascular network is established. Obviously, the relationship characteristics between blood flow and bifurcation grade in fractal vascular, fractal dimension in the arteriole–capillary vascular network, fractal dimensions of the diameter of capillary tubular diameter, fractal dimensions of capillary blood vessels, blood Casson yield stress, and ratio of red blood cell radius to capillary diameter can be obtained. And the relationship characteristics between blood flow resistance and ratio of erythrocyte radius to capillary diameter, ratios of the distance between adjacent red blood cells to the radius of red cells, and bifurcation grade can be obtained. Finally, the clinical verification tests were accomplished to verify the theory is worthy of authenticity and rationality where the curve tendencies are very similar with those obtained by numerical simulations based on the theoretical models and experimental test showed that the theoretical calculation and simulation analysis of blood circulation system of fractal vascular network were reasonable and applicable by means of experimental relative method because of the maximum relative error is less than 10%, whatever fractal dimension m changes under different conditions.

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Kohles, Sean S., Ryan W. Mangan, Edward Stan y James McNames. "A First-Order Mechanical Device to Model Traumatized Craniovascular Biodynamics". Journal of Medical Devices 1, n.º 1 (30 de julio de 2006): 89–95. http://dx.doi.org/10.1115/1.2355689.

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Mathematical models currently exist that explore the physiology of normal and traumatized intracranial function. Mechanical models are used to assess harsh environments that may potentially cause head injuries. However, few mechanical models are designed to study the adaptive physiologic response to traumatic brain injury. We describe a first-order physical model designed and fabricated to elucidate the complex biomechanical factors associated with dynamic intracranial physiology. The uni-directional flow device can be used to study interactions between the cranium, brain tissue, cerebrospinal fluid, vasculature, blood, and the heart. Solid and fluid materials were selected to simulate key properties of the cranial system. Total constituent volumes (solid and fluid) and volumetric flow (650ml∕min) represent adult human physiology, and the lengths of the individual segments along the flow-path are in accord with Poiseuille’s equation. The physical model includes a mechanism to simulate autoregulatory vessel dynamics. Intracranial pressures were measured at multiple locations throughout the model during simulations with and without post-injury brain tissue swelling. Two scenarios were modeled for both cases: Applications of vasodilation/constriction and changes in the head of bed position. Statistical results indicate that all independent variables had significant influence over fluid pressures measured throughout the model (p<0.0001) including the vasoconstriction mechanism (p=0.0255). The physical model represents a first-order design realization that helps to establish a link between mathematical and mechanical models. Future designs will provide further insight into traumatic head injury and provide a framework for unifying the knowledge gained from mathematical models, injury mechanics, clinical observations, and the response to therapies.

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Marmarelis, VZ, DC Shin y R. Zhang. "Linear and Nonlinear Modeling of Cerebral Flow Autoregulation Using Principal Dynamic Modes". Open Biomedical Engineering Journal 6, n.º 1 (26 de abril de 2012): 42–55. http://dx.doi.org/10.2174/1874120701206010042.

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Cerebral Flow Autoregulation (CFA) is the dynamic process by which cerebral blood flow is maintained within physiologically acceptable bounds during fluctuations of cerebral perfusion pressure. The distinction is made with “static” flow autoregulation under steady-state conditions of perfusion pressure, described by the celebrated “autoregulatory curve” with a homeostatic plateau. This paper studies the dynamic CFA during changes in perfusion pressure, which attains critical clinical importance in patients with stroke, traumatic brain injury and neurodegenerative disease with a cerebrovascular component. Mathematical and computational models have been used to advance our quantitative understanding of dynamic CFA and to elucidate the underlying physiological mechanisms by analyzing the relation between beat-to-beat data of mean arterial blood pressure (viewed as input) and mean cerebral blood flow velocity(viewed as output) of a putative CFA system. Although previous studies have shown that the dynamic CFA process is nonlinear, most modeling studies to date have been linear. It has also been shown that blood CO2 tension affects the CFA process. This paper presents a nonlinear modeling methodology that includes the dynamic effects of CO2 tension (or its surrogate, end-tidal CO2) as a second input and quantifies CFA from short data-records of healthy human subjects by use of the modeling concept of Principal Dynamic Modes (PDMs). The PDMs improve the robustness of the obtained nonlinear models and facilitate their physiological interpretation. The results demonstrate the importance of including the CO2 input in the dynamic CFA study and the utility of nonlinear models under hypercapnic or hypocapnic conditions.

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46

Cui, Zhoujin, Min Shi y Zaihua Wang. "Bifurcation in a New Fractional Model of Cerebral Aneurysm at the Circle of Willis". International Journal of Bifurcation and Chaos 31, n.º 09 (julio de 2021): 2150135. http://dx.doi.org/10.1142/s0218127421501352.

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A fractional-order model is proposed to describe the dynamic behaviors of the velocity of blood flow in cerebral aneurysm at the circle of Willis. The fractional-order derivative is used to model the blood flow damping term that features the viscoelasticity of the blood flow behaving between viscosity and elasticity, unlike the existing fractional models that use fractional-order derivatives to replace the integer-order derivatives as mathematical/logical generalization. A numerical analysis of the nonlinear dynamic behaviors of the model is carried out, and the influence of the damping term and the external power supply on the nonlinear dynamics of the model is investigated. It shows that not only chaos via period-doubling bifurcation is observed, but also two additional small period-doubling-bifurcation-like diagrams isolated from the big one are observed, a phenomenon that needs further investigation.

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47

Köppl, Tobias, Ettore Vidotto, Barbara Wohlmuth y Paolo Zunino. "Mathematical modeling, analysis and numerical approximation of second-order elliptic problems with inclusions". Mathematical Models and Methods in Applied Sciences 28, n.º 05 (mayo de 2018): 953–78. http://dx.doi.org/10.1142/s0218202518500252.

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Many biological and geological systems can be modeled as porous media with small inclusions. Vascularized tissue, roots embedded in soil or fractured rocks are examples of such systems. In these applications, tissue, soil or rocks are considered to be porous media, while blood vessels, roots or fractures form small inclusions. To model flow processes in thin inclusions, one-dimensional (1D) models of Darcy- or Poiseuille type have been used, whereas Darcy-equations of higher dimension have been considered for the flow processes within the porous matrix. A coupling between flow in the porous matrix and the inclusions can be achieved by setting suitable source terms for the corresponding models, where the source term of the higher-dimensional model is concentrated on the center lines of the inclusions. In this paper, we investigate an alternative coupling scheme. Here, the source term lives on the boundary of the inclusions. By doing so, we lift the dimension by one and thus increase the regularity of the solution. We show that this model can be derived from a full-dimensional model and the occurring modeling errors are estimated. Furthermore, we prove the well-posedness of the variational formulation and discuss the convergence behavior of standard finite element methods with respect to this model. Our theoretical results are confirmed by numerical tests. Finally, we demonstrate how the new coupling concept can be used to simulate stationary flow through a capillary network embedded in a biological tissue.

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Gamilov, Timur, Philipp Kopylov, Maria Serova, Roman Syunyaev, Andrey Pikunov, Sofya Belova, Fuyou Liang, Jordi Alastruey y Sergey Simakov. "Computational Analysis of Coronary Blood Flow: The Role of Asynchronous Pacing and Arrhythmias". Mathematics 8, n.º 8 (22 de julio de 2020): 1205. http://dx.doi.org/10.3390/math8081205.

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In this work we present a one-dimensional (1D) mathematical model of the coronary circulation and use it to study the effects of arrhythmias on coronary blood flow (CBF). Hydrodynamical models are rarely used to study arrhythmias’ effects on CBF. Our model accounts for action potential duration, which updates the length of systole depending on the heart rate. It also includes dependency of stroke volume on heart rate, which is based on clinical data. We apply the new methodology to the computational evaluation of CBF during interventricular asynchrony due to cardiac pacing and some types of arrhythmias including tachycardia, bradycardia, long QT syndrome and premature ventricular contraction (bigeminy, trigeminy, quadrigeminy). We find that CBF can be significantly affected by arrhythmias. CBF at rest (60 bpm) is 26% lower in LCA and 22% lower in RCA for long QT syndrome. During bigeminy, trigeminy and quadrigeminy, respectively, CBF decreases by 28%, 19% and 14% with respect to a healthy case.

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Khubulava, G. G., A. B. Naumov, S. P. Marchenko, O. Yu Chupaeva, A. A. Seliverstova, N. G. Pilyugov, O. Yu Tereshenko et al. "Theoretical models of changes in haemodynamic parameters and gas exchange in univentricular circulation". Patologiya krovoobrashcheniya i kardiokhirurgiya 23, n.º 3 (27 de noviembre de 2019): 65. http://dx.doi.org/10.21688/1681-3472-2019-3-65-75.

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<div><strong>Aim.</strong> To develop theoretical models of changes in haemodynamic parameters of patients with univentricular haemodynamics.</div><div><strong>Methods.</strong> We analysed the effects of redistributing blood flow between the two circulatory systems (pulmonary and systemic) on systemic oxygen delivery and examined changes in the arterial and venous blood gas compositions. Mathematical analyses on the basis of oxygen flow into the pulmonary circulatory system and its consumption during circulation were performed according to Fick principle for cardiac output. Calculations were performed using equations describing changes in the delivery and consumption of oxygen during univentricular circulation. Furthermore, computer simulations were employed to investigate changes in haemodynamic parameters and gas exchange associated with pathological processes such as pulmonary venous hypoxemia, reduction in systemic flow rate and mixed venous blood desaturation. Calculations were performed under conditions with oxygen concentration of >0% or <100%.</div><div><strong>Results.</strong> A number of theoretical models were developed, which described (i) the distribution of systemic and pulmonary blood flow and changes in arterial oxygenation depending on Qp/Qs; (ii) the ratio of systemic blood flow to Qp/Qs; (iii) changes in arterial oxygenation depending on Qp/Qs at different levels of central venous saturation; (iv) changes in pulmonary venous saturation depending on arterial saturation and Qp/Qs under conditions of normal and reduced blood flow; (v) level of central venous saturation depending on changes in Qp/Qs and SpvO<sub>2</sub> at systemic SaO<sub>2</sub> of 75% and (vi) PaO2 dynamics depending on changes in PpvO<sub>2</sub> and Qp/Qs.</div><div><strong>Conclusion.</strong> Changes in the oxygen status of patients with univentricular haemodynamics with sufficient combined cardiac output are indicative of the distribution of blood flow. Assessments of the developed models demonstrated that a number of additional factors affect changes in the oxygen composition of blood including (i) the initial level of arterial oxygenation; (ii) the level of oxygenation in the pulmonary veins and (iii) the ratio of pulmonary to systemic blood flow. In addition, the results indicated that PCO<sub>2</sub> recorded in the pulmonary veins, arteries and mixed venous blood largely depends on Qp/Qs. The theoretical models presented here can be used to compare the results of haemodynamic status assessments of patients with univentricular physiology.</div><div> </div><div>Received 22 May 2019. Revised 4 November 2019. Accepted 10 November 2019.</div><div> </div><div><strong>Funding:</strong> The study did not have sponsorship.</div><div> </div><div><strong>Conflict of interest:</strong> Authors declare no conflict of interest.</div>

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Milišić, Vuk y Alfio Quarteroni. "Analysis of lumped parameter models for blood flow simulations and their relation with 1D models". ESAIM: Mathematical Modelling and Numerical Analysis 38, n.º 4 (julio de 2004): 613–32. http://dx.doi.org/10.1051/m2an:2004036.

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