Academic literature on the topic 'Microcirculation – Mathematical models'
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Journal articles on the topic "Microcirculation – Mathematical models"
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Farina, Angiolo, Antonio Fasano, and Fabio Rosso. "Mathematical Models for Some Aspects of Blood Microcirculation." Symmetry 13, no. 6 (June 6, 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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Tsoukias, Nikolaos M. "Nitric Oxide Bioavailability in the Microcirculation: Insights from Mathematical Models." Microcirculation 15, no. 8 (January 2008): 813–34. http://dx.doi.org/10.1080/10739680802010070.
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Weinbaum, S. "Interfacial Transport in Large and Small Blood Vessels." Applied Mechanics Reviews 43, no. 5S (May 1, 1990): S109—S118. http://dx.doi.org/10.1115/1.3120789.
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In this paper we shall review some recent mathematical models which have led to new conceptual views of the ultrastructural pathways by which water, solutes and large molecules cross the endothelial interface between tissue and blood. In particular, we shall show how a sequence of models for the endothelium and underlying tissue in large arteries have finally led to the experimental discovery of the large pore via which LDL and other large molecules enter the artery wall and how a new three-dimensional model for the interendothelial cleft in capillaries might reconcile the several long standing paradoxes relating to the measured filtration and solute permeability coefficients in the transcapillary exchange of water and hydrophilic solutes in the microcirculation.
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ZHAO, NING, and KEIJI IRAMINA. "A MATHEMATICAL COUPLED MODEL OF OXYGEN TRANSPORT IN THE MICROCIRCULATION: THE EFFECT OF CONVECTION–DIFFUSION ON OXYGEN TRANSPORT." Journal of Mechanics in Medicine and Biology 15, no. 01 (February 2015): 1550003. http://dx.doi.org/10.1142/s0219519415500037.
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This paper is aimed at examining the effect of convection–diffusion on oxygen transport at the micro-level. A coupled model of the convection–diffusion and molecular diffusion of oxygen is developed, and the solid deformation resulting from capillary fluctuations and the seepage of tissue fluid are incorporated into this model. The results indicate that (1) the oxygen concentration calculated from this coupled model is higher than that given by molecular diffusion models, both within the capillaries and tissue (maximum difference of 16%); (2) convection–diffusion has the greatest effect in tissue surrounding the middle of the capillary, and enhances the amount of oxygen transported to cells far from the oxygen source; (3) larger permeability coefficients or smaller diffusion coefficients produce a more obvious convection–diffusion effect; (4) a counter-current flow occurs near the inlet and outlet ends of the capillary. This model also provides a foundation for the study of how oxygen affects tumor growth.
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Parker, R. E., R. J. Roselli, and K. L. Brigham. "Effects of prolonged elevated microvascular pressure on lung fluid balance in sheep." Journal of Applied Physiology 58, no. 3 (March 1, 1985): 869–75. http://dx.doi.org/10.1152/jappl.1985.58.3.869.
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Experiments were conducted in seven chronically instrumented unanesthetized sheep to estimate the osmotic reflection coefficient (sigma d) for total proteins and the solvent-drag reflection coefficients (sigma f) for six endogenous protein fractions. We measured the lymph-to-plasma ratio of total proteins (CL/CP) and six protein fractions during base-line conditions and after left atrial pressure elevations of 24–26 h per elevation. We also monitored pulmonary arterial pressure, left atrial pressure, systemic arterial pressure, and lung lymph flow at the various levels of pulmonary microvascular pressure. Our results indicate the CL/CP may require up to 24 h to reach a true steady state. It was found that sigma d is at least 0.89 for total proteins and sigma f is at least 0.84, 0.87, 0.86, 0.92, 0.95, and 0.96 for protein fractions with effective molecular radii of 36, 39.5, 44, 66, 105, and 123 A, respectively. In addition, the sigma f values for various protein fractions obtained from this investigation are compared with the predicted values of various mathematical models of the lung microcirculation.
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Hartung, Grant, Shoale Badr, Mohammad Moeini, Frédéric Lesage, David Kleinfeld, Ali Alaraj, and Andreas Linninger. "Voxelized simulation of cerebral oxygen perfusion elucidates hypoxia in aged mouse cortex." PLOS Computational Biology 17, no. 1 (January 28, 2021): e1008584. http://dx.doi.org/10.1371/journal.pcbi.1008584.
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Departures of normal blood flow and metabolite distribution from the cerebral microvasculature into neuronal tissue have been implicated with age-related neurodegeneration. Mathematical models informed by spatially and temporally distributed neuroimage data are becoming instrumental for reconstructing a coherent picture of normal and pathological oxygen delivery throughout the brain. Unfortunately, current mathematical models of cerebral blood flow and oxygen exchange become excessively large in size. They further suffer from boundary effects due to incomplete or physiologically inaccurate computational domains, numerical instabilities due to enormous length scale differences, and convergence problems associated with condition number deterioration at fine mesh resolutions. Our proposed simple finite volume discretization scheme for blood and oxygen microperfusion simulations does not require expensive mesh generation leading to the critical benefit that it drastically reduces matrix size and bandwidth of the coupled oxygen transfer problem. The compact problem formulation yields rapid and stable convergence. Moreover, boundary effects can effectively be suppressed by generating very large replica of the cortical microcirculation in silico using an image-based cerebrovascular network synthesis algorithm, so that boundaries of the perfusion simulations are far removed from the regions of interest. Massive simulations over sizeable portions of the cortex with feature resolution down to the micron scale become tractable with even modest computer resources. The feasibility and accuracy of the novel method is demonstrated and validated with in vivo oxygen perfusion data in cohorts of young and aged mice. Our oxygen exchange simulations quantify steep gradients near penetrating blood vessels and point towards pathological changes that might cause neurodegeneration in aged brains. This research aims to explain mechanistic interactions between anatomical structures and how they might change in diseases or with age. Rigorous quantification of age-related changes is of significant interest because it might aide in the search for imaging biomarkers for dementia and Alzheimer’s disease.
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Pries, A. R., T. W. Secomb, and P. Gaehtgens. "Structure and hemodynamics of microvascular networks: heterogeneity and correlations." American Journal of Physiology-Heart and Circulatory Physiology 269, no. 5 (November 1, 1995): H1713—H1722. http://dx.doi.org/10.1152/ajpheart.1995.269.5.h1713.
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The objective of this study was to quantify the heterogeneity of topological, morphological, and hemodynamic parameters in microvascular networks and to identify functionally relevant correlations among these parameters. Seven networks in the rat mesentery (383-913 vessel segments per network) were examined, and measurements were made of segment generation, diameter, length, and hematocrit in all segments (n = 3,129) and of flow velocity (only in 3 networks, 1,321 segments). In addition, hematocrit, flow rate, and pressure were derived for all segments from a mathematical simulation. All parameters obtained exhibit heterogeneous distributions with coefficients of variation ranging from 0.28 (capillary diameter) to > 1.5 (volume flow and pressure gradient). Several strong correlations exist between parameters, e.g., discharge hematocrit increases with vessel diameter, and shear rate increases with intravascular pressure. Because of such correlations, the extrapolation from average values for "typical vessels" to network properties can lead to substantial errors. For example, the mean network transit time estimated based on averaged quantities is 6.5 s, which is about 60% higher than the true value (4.08 s). Simplified models of the vascular bed may therefore be inadequate to describe functional properties of the microcirculation.
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Mansoor, Wafaa, Graeme Hocking, and Duncan Farrow. "Modelling of hydrogen diffusion in the retina." ANZIAM Journal 61 (July 7, 2020): C119—C136. http://dx.doi.org/10.21914/anziamj.v61i0.14995.
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A simple mathematical model for diffusion of hydrogen within the retina has been developed. The model consists of three, well-mixed, one dimensional layers that exchange hydrogen via a diffusion process. A Fourier series method is applied to compute the hydrogen concentration. The effect of important parameters is examined and discussed. The results may contribute to an understanding of the hydrogen clearance technique to estimate blood flow. A two dimensional numerical method for the hydrogen diffusion is also presented. It is shown that the predominant features of the process are captured quite well by the simpler model. References V. A. Alder, D. Y. Yu, S. J. Cringle and E. N. Su. Experimental approaches to diabetic retinopathy. Asia-Pac. J. Ophthalmol. 4:20–25, 1992. J. C. Arciero, P. Causin and F. Malgoroli. Mathematical methods for modeling the microcirculation. AIMS Biophys. 4:362–399, 2017. doi:10.3934/biophy.2017.3.362 D. E. Farrow, G. C. Hocking, S. J. Cringle and D.-Y. Yu. Modeling Hydrogen clearance from the retina. ANZIAM J. 59:281–292, 2018. doi:10.1017/S1446181117000426 A. B. Friedland. A mathematical model of transmural transport of oxygen to the retina. Bull. Math. Biol. 40:823–837, 2018; doi:10.1007/BF02460609 D. Goldman. Theoretical models of microvascular oxygen transport to tissue. Microcirculation 15:795–811, 2008. doi:10.1080/10739680801938289 A. C. Hindmarsh. ODEPACK, A Systematized Collection of ODE Solvers. In Scientific Computing, R. S. Stepleman, et al., Eds., pp. 55-64. North-Holland, Amsterdam, 1983. S. S. Kety. The theory and applications of the exchange of inert gas at the lungs and tissues. Pharmacol. Rev. 3:1–41, 1951. http://pharmrev.aspetjournals.org/content/3/1/1 B. P. Leonard. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng. 19:59–98, 1979. doi:10.1016/0045-7825(79) 90034-3 S. L. Mitchell. Coupling transport and chemistry: numerics, analysis and applications. PhD thesis, University of Bath, UK, 2003. https://researchportal.bath.ac.uk/en/studentTheses/coupling-transport-and-chemistry-numerics-analysis-and-applicatio G. A. Winchell. Mathematical model of inert gas washout from the retina: evaluation of hydrogen washout as a means of determining retinal blood flow in the cat. Master\textquoteright s Thesis, Northwestern University, Evanston, USA, 1983. https://search.library.northwestern.edu/permalink/f/5c25nc/01NWU_ALMA21563278530002441 D. Y. Yu, V. A. Alder and S. J. Cringle. Measurement of blood flow in rat eyes by hydrogen clearance. Am. J. Physiol. (Heart Circ. Physiol.) 261:H960–H968, 1991. doi:10.1152/ajpheart.1991.261.3.H960 D. Y. Yu, S. J. Cringle, V. A. Alder, E. N. Su, and P. K. Yu, Intraretinal oxygen distribution and choroidal regulation in the avascular retina of guinea pigs. Am. J. Physiol. (Heart Circ. Physiol.) 270:H965-H973, 1996. doi:10.1152/ajpheart.1996.270.3.H965 S. Cringle, D.-Y. Yu, V. Alder, E.-N. Su, and P. Yu. Choroidal regulation of oxygen supply to the guinea pig retina. In A. G. Hudetz, and D. F. Bruley (Eds.), Oxygen Transport to Tissue XX, pp. 385–389. Springer, 1998. doi:10.1007/978-1-4615-4863-8
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Al-Shammari, Abdullah A., Roger W. P. Kissane, Simon Holbek, Abigail L. Mackey, Thomas R. Andersen, Eamonn A. Gaffney, Michael Kjaer, and Stuart Egginton. "Integrated method for quantitative morphometry and oxygen transport modeling in striated muscle." Journal of Applied Physiology 126, no. 3 (March 1, 2019): 544–57. http://dx.doi.org/10.1152/japplphysiol.00170.2018.
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Identifying structural limitations in O2 transport is primarily restricted by current methods employed to characterize the nature of physiological remodeling. Inadequate resolution or breadth of available data has impaired development of routine diagnostic protocols and effective therapeutic strategies. Understanding O2 transport within striated muscle faces major challenges, most notably in quantifying how well individual fibers are supplied by the microcirculation, which has necessitated exploring tissue O2 supply using theoretical modeling of diffusive exchange. With capillary domains identified as a suitable model for the description of local O2 supply and requiring less computation than numerically calculating the trapping regions that are supplied by each capillary via biophysical transport models, we sought to design a high-throughput method for histological analysis. We present an integrated package that identifies optimal protocols for identification of important input elements, processing of digitized images with semiautomated routines, and incorporation of these data into a mathematical modeling framework with computed output visualized as the tissue partial pressure of O2 (Po2) distribution across a biopsy sample. Worked examples are provided using muscle samples from experiments involving rats and humans. NEW & NOTEWORTHY Progress in quantitative morphometry and analytical modeling has tended to develop independently. Real diagnostic power lies in harnessing both disciplines within one user-friendly package. We present a semiautomated, high-throughput tool for determining muscle phenotype from biopsy material, which also provides anatomically relevant input to quantify tissue oxygenation, in a coherent package not previously available to nonspecialist investigators.
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Винников, Артем Викторович, Александр Владимирович Быков, Николай Алексеевич Кореневский, Людмила Петровна Лазурина, Полина Сергеевна Азарова, and Гулайым Камчибековна Усубалиева. "METHOD FOR PREDICTING FATAL COMPLICATIONS IN THE DEVELOPMENT OF CORONAVIRAL INFECTION ON THE BACKGROUND OF SYSTEMIC LUPUS ERYTHEMATOSUS." СИСТЕМНЫЙ АНАЛИЗ И УПРАВЛЕНИЕ В БИОМЕДИЦИНСКИХ СИСТЕМАХ, no. 2 (July 26, 2021): 63–69. http://dx.doi.org/10.36622/vstu.2021.20.2.008.
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Целью исследования является разработка метода прогнозирования возникновения и развития фатальных осложнений, провоцируемых действием на организм человека новой коронавирусной инфекции (COVID-19) на фоне иммунопролиферативных заболеваний, который позволит усовершенствовать лечебно-диагностические мероприятия при данной патологии. В качестве базового математического аппарата была выбрана методология синтеза гибридных нечетких решающих правил, которая хорошо зарекомендовала себя при решении задач с нечётким описанием исследуемых классов и схожим типом неопределенности. Предлагаемый метод прогнозирования позволяет учесть мультипликативный эффект воздействия на организм человека существенных факторов риска, характерных для рассматриваемого заболевания, с учетом его тяжести и скорости развития патологического процесса. В ходе проводимых исследований были синтезированы математические модели прогнозирования возникновения и развития фатальных осложнений. В ходе экспертного оценивания, математического моделирования и статистических испытаний показано, что уверенность в правильном принятии решений по прогнозу появления и развития исследуемого класса фатальных осложнений превышает величину 0,85. В работе получены нечёткие математические модели прогнозирования возникновения и развития фатальных осложнений у людей при развитии коронавирусной инфекции на фоне системной красной волчанки, для которых ведущими факторами риска являются вторичный антифосфолипидный синдром с нарушением микроциркуляции и гипоксемия. В ходе проведенных исследований была показана целесообразность использования полученных результатов в практике работы таких врачей, как иммунологи, инфекционисты, пульмонологи The aim of the study is to develop a method for predicting the occurrence and development of fatal complications provoked by the effect on the human body of a new coronavirus infection (COVID-19) against the background of immunoproliferative diseases, which will improve diagnostic and treatment measures for this pathology. The methodology for the synthesis of hybrid fuzzy decision rules was chosen as the basic mathematical apparatus, which has proven itself well in solving problems with a fuzzy description of the classes under study and a similar type of uncertainty. The proposed forecasting method allows one to take into account the multiplicative effect of exposure to the human body of significant risk factors characteristic of the disease under consideration, taking into account its severity and the rate of development of the pathological process. In the course of the research, mathematical models were synthesized for predicting the occurrence and development of fatal complications. In the course of expert assessment, mathematical modeling and statistical tests, it was shown that confidence in the correct decision-making on the prediction of the appearance and development of the studied class of fatal complications exceeds 0.85, which makes it possible to recommend the results obtained during the study for implementation into the practice of such doctors. as immunologists, infectious disease specialists, pulmonologists. The work obtained fuzzy mathematical models for predicting the occurrence and development of fatal complications in people with the development of coronavirus infection against the background of systemic lupus erythematosus, for which the leading risk factors are secondary antiphospholipid syndrome with microcirculation disorders and hypoxemia. In the course of the studies, the expediency of using the results obtained in the practice of the work of such doctors as immunologists, infectious disease specialists, pulmonologists was shown
Dissertations / Theses on the topic "Microcirculation – Mathematical models"
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FLEISCHMAN, GREGORY JOSEPH. "FLUID FILTRATION FROM CAPILLARY NETWORKS (MICROCIRCULATION, MATHEMATICAL MODELING)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/187998.
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A mathematical model has been developed which describes the fluid exchange from a capillary network of realistic topology, and calculates the spatial distribution of extravascular pressure. In this model, the capillaries are represented by a superposition of sources and sinks, resulting from a D'Arcy's Law description of flow in tissue of uniform fluid conductivity. The combination of this representation and Starling's Hypothesis, which relates the forces influencing transmural fluid exchange, yields an integral equation of the second kind which is solved numerically for the source strength distribution. Two important features of this approach are that: (i) it allows for interaction between the local tissue pressure field and fluid exchange (the model is called, therefore, the tissue pressure interaction model); and (ii) complex network morphologies are easily modeled. In single capillaries, this interaction, which decreases the predicted fluid exchange, increases with the magnitude of the ratio of capillary wall to extravascular fluid conductivities. For multiple capillaries, in addition to the "self" interaction of a capillary with the local extravascular pressure field, there is the possibility of interaction between capillaries ("capillary-capillary" interaction). The ratio of conductivities, and the additional factors of intercapillary distance and the number of capillaries, also affect interaction in capillary networks. Although interaction is only a weak function of intercapillary distance, it depends strongly on the number of capillaries. The major result from this work is that for the entire physiological range of conductivity ratios, interaction cannot be neglected in predicting fluid exchange. Although tissue pressure interaction affects the magnitude of fluid exchange, it does not greatly alter the pattern of extravascular flow. Therefore, previous models which neglected interaction are not invalidated by the present findings. The effect of interaction on planar capillary networks within a semi-infinite tissue space was also investigated. Flow boundary conditions were imposed at opposed planar boundaries, parallel with the capillary network. Interaction was found to decrease with decreasing distance between the boundary and plane of the capillaries. It still exerted a large effect, however, for distances greater than one-fourth the reference capillary length.
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El-Bouri, Wahbi K. "Multi-scale modelling of the microvasculature in the human cerebral cortex." Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:8a9409a6-6279-4f7b-a975-b70149732378.
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Cerebrovascular diseases are by far the largest causes of death in the UK, as well as one of the leading causes of adult disability. The brain's healthy function depends on a steady supply of oxygen, delivered through the microvasculature. Cerebrovascular diseases, such as stroke and dementia, can interrupt the transport of blood (and hence oxygen) rapidly, or over a prolonged period of time. An interruption in flow can lead to ischaemia, with prolonged interruptions leading to tissue death and eventual brain damage. The microvasculature plays a key role in the transport of oxygen and nutrients to brain tissue; however, its role in diseases such as dementia is poorly understood, primarily due to the inability of current clinical imaging techniques to resolve microvessels, and due to the complexity of the underlying microvasculature. Therefore, in order to understand cerebrovascular diseases, it is necessary to be able to resolve and understand the microvasculature. In particular, generating large-scale models of the human microvasculature that can be linked back to contemporary clinical imaging is important in helping plug the current imaging gap that exists. A novel statistical model is proposed here that generates such large-scale models efficiently. Homogenization theory is used to generate a porous continuum capillary bed (characterised by its permeability) that allows for the efficient scaling up of the microvasculature. A novel order-based density-filling algorithm is then developed which generates morphologically accurate penetrating arterioles and venules, also demonstrating that the topology of the vessels only has a minor influence on CBF compared to diameter. Finally, the capillary bed and penetrating vessels are coupled into a large voxel-sized model of the microvasculature from which pressure and flux variations through the voxel can be analysed. A decoupling of the pressure and flux, as well as a layering of flow, was observed within the voxel, driven by the topology of the penetrating vessels. Micro-infarctions were also simulated, demonstrating the large local effects they have on the pressure and flux, whilst only causing a minor drop in CBF within the voxel.
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Khalil, Adil. "Processing of laser speckle contrast images : study of mathematical models and use of nonlinear analyses to investigate the impact of aging on microvascular blood flow." Thesis, Angers, 2017. http://www.theses.fr/2017ANGE0006/document.
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Le vieillissement est un facteur de risque des maladies cardiovasculaires. Il est associé à des altérations fonctionnelles et structurelles du système vasculaire.Une étude approfondie du processus de vieillissement et le développement de systèmes d’imagerie et des traitements de données associés deviennent donc une priorité. Par l’analyse d’images de contraste par speckle laser (LSCI), l’objectif de cette thèse est d’étudier l’influence de l’âge sur la micro circulation.Pour ce faire, des données de LSCI ont été acquises sur l’avant-bras de sujets sains jeunes et âgés. A partir de modèles mathématiques, nous avons déterminé la vitesse des érythrocytes de la micro circulation chez les deux groupes de sujets. Par ailleurs, nous avons également mené une étude de la complexité de séries temporelles d’ LSCI s’appuyant sur des mesures d’entropie multi échelle. Nos résultats montrent que : 1) le groupe de sujets plus âgés présente des valeurs de vitesse des globules rouges significativement plus élevées que celles des sujets jeunes à l’hyperémie réactive post-occlusive; 2) les fluctuations des séries temporelles de LSCI dans le groupe des sujets jeunes ont une complexité supérieure à celles du groupe de sujets âgés. Ces modifications observées sur la micro circulation pourraient être attribuées à des modifications du système vasculaire dans son ensemble. La compréhension de ces altérations pourrait conduire à de nouvelles perspectives en matière de prévention et de traitement des pathologies liées à l’âgeAging is a primary risk factor for cardiovascular diseases. It is associated with functional and structural alterations in the vascular system. Therefore, a deep study of the aging process and the development of imaging systems and associated processing become of the utmost importance. By processing laser speckle contrast images (LSCI), this PhD work aims at studying the influence of age on microcirculation. In our work, LSCI data were acquired from the skin forearm of healthy subjects, subdivided into two age groups (younger and older). From mathematical models, we determined red blood cells velocity in microcirculation in the two groups of subjects. Moreover, we applied multiscale entropy-based algorithms to LSCI time series in order to study the complexity of microvascular signals. Our main findings are: 1) the older group has significantly higher velocity values than the younger group at post-occlusive reactive hyperaemia; 2) LSCI fluctuations in the younger group have significantly higher complexity than those of the older group. Age-related changes in skin microcirculation can be attributed to alterations in the vascular system as a whole. Understanding these changes in the microcirculatory system may give new insights for prevention and treatment of age-related diseases
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Fry, Brendan. "Theoretical Models for Blood Flow Regulation in Heterogeneous Microvascular Networks." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293413.
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Proper distribution of blood flow in the microcirculation is necessary to match changing oxygen demands in various tissues. How this coordination of perfusion and consumption occurs in heterogeneous microvascular networks remains incompletely understood. Theoretical models are powerful tools that can help bridge this knowledge gap by simulating a range of conditions difficult to obtain experimentally. Here, an algorithm is first developed to estimate blood flow rates in large microvascular networks. Then, a theoretical model is presented for metabolic blood flow regulation in a realistic heterogeneous network structure, derived from experimental results from hamster cremaster muscle in control and dilated states. The model is based on modulation of arteriolar diameters according to the length-tension characteristics of vascular smooth muscle. Responses of smooth muscle cell tone to myogenic, shear-dependent, and metabolic stimuli are included. Blood flow is simulated including unequal hematocrit partition at diverging vessel bifurcations. Convective and diffusive oxygen transport in the network is simulated, and oxygen-dependent metabolic signals are assumed to be conducted upstream from distal vessels to arterioles. Simulations are carried out over a range of tissue oxygen demand. With increasing demand, arterioles dilate, blood flow increases, and the numbers of flowing arterioles and capillaries, as defined by red-blood-cell flux above a small threshold value, increase. Unequal hematocrit partition at diverging bifurcations contributes to capillary recruitment and enhances tissue oxygenation. The results imply that microvessel recruitment can occur as a consequence of local control of arteriolar tone. The effectiveness of red-blood-cell-dependent and independent mechanisms for the metabolic response of local blood flow regulation is examined over a range of tissue oxygen demands. Model results suggest that although a red-blood-cell-independent mechanism is most effective in increasing flow and preventing hypoxia, the addition of a red-blood-cell-dependent mechanism leads to a higher median tissue oxygen level, indicating distinct roles for the two mechanisms. In summary, flow rates in large microvessel networks can be estimated with the proposed algorithm, and the theoretical model for flow regulation predicts a mechanism for capillary recruitment, as well as roles for red-blood-cell-dependent and independent mechanisms in the metabolic regulation of blood flow in heterogeneous microvascular networks.
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Tessendorf, Steven D. "Modeling of blood flow in the microcirculation." 1985. http://hdl.handle.net/2097/27557.
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Lee, Sei Young. "Size and shape effects for the nano/micro particle dynamics in the microcirculation." Thesis, 2010. http://hdl.handle.net/2152/ETD-UT-2010-08-1672.
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The nano/micro particles have been widely used as a carrier of therapeutic and contrast imaging agents. The nano/micro particles have many advantages, such as, specificity, controlled release, multifunctionality and engineerability. By tuning the chemical, physical and geometrical properties, the efficacy of delivery of nano/micro particle can be improved. In this study, by analyzing the effect of physical and geometrical properties of particle, such as, size, shape, material property and flow condition, the optimal condition for particle delivery will be explored. The objectives of this study are (1) to develop predictive mathematical models and (2) experimental models for particle margination and adhesion, and (3) to find optimal particle geometry in terms of size and shape to enhance the efficiency of its delivery. The effect of particle size expressed in terms of Stokes number and shape, namely, spherical, ellipsoidal, hemispherical, discoidal and cylindrical particle on the particle trajectory is investigated. For discoidal and cylindrical particles, the effect of aspect ratio is also considered. To calculate particle trajectory in the linear shear flow near the substrate, Newton's law of motion is decomposed into hydrodynamic drag and resistance induced by particle motion. The drag and resistance is estimated through finite volume formulation using Fluent v6.3. Particle behavior in the linear shear flow does strongly depend on Stokes number. Spherical particle is transported following the streamline in the absence of external body force. However, non-spherical particles could across the streamline and marginate to the substrate. For non-spherical particles, the optimal [Stokes number] in terms of particle margination is observed; [Stokes number almost equal to] 20 for ellipsoidal, hemispherical and discoidal particle; [Stokes number almost equal to] 10 for cylindrical particle. For discoidal particle with [gamma subscript d]=0.2 shows fastest margination to the substrate. The effect of gravitational force is also considered with respect to the fluid direction. When the gravitational force is applied, mostly, gravitational force plays a dominant role for particle margination. However, using small particle aspect ratio ([gamma subscript d]=0.2 and 0.33), spontaneous drift induced by particle-fluid-substrate interaction could overcome gravitational effect in some cases ([Stokes number]=10, G=0.1). In addition the adhesion characteristic of spherical particle has been studied using in vitro micro fluidic chamber system with different particle size and flow condition. The experimental results are compared to the mathematical model developed by Decuzzi and Ferrari (Decuzzi and Ferrari, 2006) and in vivo test (Decuzzi et al., 2010). The optimal particle size for S=75 and 90 is found to be 4-5 [micrometer] through the in vitro non-specific interaction of spherical particle on the biological substrate. The suggested mathematical model has proven to be valid for current experimental condition. At the end, the mathematical model, in vitro flow chamber results and in vivo test have been compared and the scaling law for particle adhesion on the vessel wall has been confirmed.text
Conference papers on the topic "Microcirculation – Mathematical models"
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Wu, Jie, Quan Long, Shixiong Xu, Hao Gao, and Anwar R. Padhani. "Numerical Study of Tumour Blood Perfusion Based on 3D Tumour Angiogenic Microvasculatures." In ASME 2008 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2008. http://dx.doi.org/10.1115/sbc2008-192170.
Full textAbstract:
The coupling of intravascular and interstitial flow is a distinct feature of tumour microcirculation, due to the high vessel permeability, the low osmotic pressure gradient as well as the absence of functional lymphatic system inside tumours. In this paper, a coupled mathematical model of tumour blood perfusion based on 3D angiogenic vasculatures is developed, which provides the link between microvasculature and interstitial space perfusion through the matrices describing the local vascular connection (3D matrix B) and density (3D matrix A), accordingly combines the intravascular and interstitial flow by vascular leaky terms. In addition, the compliance of tumour vessels, blood rheology with hematocritic distribution at branches is also considered. The microvascular network, on which the microcirculation calculation is carried out, is generated from a 3-dimensional 7-point model of tumour angiogenesis.