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Review of Zero-D and 1-D Models of Blood Flow in the Cardiovascular System

By Yubing Shi, Patricia Lawford and Rodney Hose
Topics: Review
Publisher: BioMed Central
OAI identifier: oai:pubmedcentral.nih.gov:3103466
Provided by: PubMed Central

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  1. (2006). A concentrated parameter model for the human cardiovascular system including heart valve dynamics and atrioventricular interaction. Med Eng Phys
  2. (2001). A mathematical model of CO2 effect on cardiovascular regulation.
  3. (1991). A Mathematical Model of Overall Cerebral Blood Flow Regulation in the Rat.
  4. (1999). A Mathematical Model of the Carotid Baroregulation in Pulsating Conditions.
  5. (2004). A multiscale approach for modelling wave propagation in an arterial segment. Comput Methods Biomech Biomed Engin
  6. (1990). A Nonlinear Model of the Arterial System Incorporating a Pressure-dependent Compliance.
  7. (2001). A Sensorless Approach to Control of a Turbodynamic Left Ventricular Assist System.
  8. (2000). A: A Closed-loop Model of the Canina Cardiovascular System that Includes Ventricular Interaction. Computer and Biomedical Research
  9. (2001). A: A Human Cardiopulmonary System Model Applied to the Analysis of the Valsalva Maneuver.
  10. (2006). A: Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart. Comput Methods Biomech Biomed Engin
  11. (1990). A: Theoretical and experimental analysis of right ventricular bypass and univentricular circulatory support.
  12. (2005). AD: Wave-energy patterns in carotid, brachial, and radial arteries: a noninvasive approach using wave-intensity analysis.
  13. (1971). An artificial arterial system for pumping hearts.
  14. (2007). An energetically coherent lumped parameter model of the left ventricle specially developed for educational purposes. Comput Biol Med
  15. (2003). An introduction to cardiovascular physiology. 4 edition.
  16. (2006). Avanzolini G: Mathematical modeling of arterial pressure response to hemodialysis-induced hypovolemia. Comput Biol Med
  17. (1980). Avolio AP: Pulsatile flow and pressure in human systemic arteries. Studies in man and in a multibranched model of the human systemic arterial tree. Circ Res
  18. (2003). Baaijens FPT: A Three-dimensional Computational Analysis of Fluid-structure Interaction in the Aortic Valve.
  19. (1997). BB: Characterization of embryonic aortic impedance with lumped parameter models.
  20. (1996). Belardinelli E: Modeling of cardiovascular variability using a differential delay equation.
  21. (1984). Biodynamics: Circulation
  22. (2009). Biomechanical characterization of ventricular-arterial coupling during aging: a multi-scale model study.
  23. (1993). Biomechanics: Mechanical Properties of Living Tissues
  24. (2003). Boulpaep EL: Medical Physiology: A Cellular and Molecular Approach
  25. (1991). Burkhoff D: Hemodynamic Consequences of Ventricular Interaction as Assessed by Model Analysis.
  26. (2002). CA: A one-dimensional finite element method for simulation-based medical planning for cardiovascular disease. Comput Methods Biomech Biomed Engin
  27. (2006). CA: Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Computer methods in applied mechanics and engineering
  28. (1990). Cardiac Energy Considerations during Intraaortic Balloon Pumping.
  29. CellML implementation of a group of lumped-parameter cardiovascular models.
  30. (2000). Cerebral Hemodynamics during Arterial and CO2 Pressure Changes: in vivo Prediction by a Mathematical Model.
  31. (1993). Cheng HD: A nonlinear fluid model for pulmonary blood circulation.
  32. (1997). Chiaramida~Salvatore A: A Comparehensive Model for Right-left Heart Interaction under the Influence of Pericardium and Baroreflex.
  33. (1987). Chronic pressure overload hypertrophy decreases direct ventricular interaction.
  34. (1978). Circulatory System Dynamics
  35. (1990). CJ: Forward and backward running waves in the arteries: analysis using the method of characteristics.
  36. (2010). CJ: Patient-specific hemodynamics of the cardiovascular system, US 2010/0241404 A1. United States Patent;
  37. (1998). Complex and frequency-dependent compliance of viscoelastic windkessel resolves contradictions in elastic windkessels. Med Eng Phys
  38. (1993). Computation of aortic flow from pressure in humans using a nonlinear, three-element model.
  39. (2005). DD: Optimum Control of the Hemopump as a Left-ventricular Assist Device.
  40. (2004). de Vosse FN: A physiologically representative in vitro model of the coronary circulation. Physiol Meas
  41. (2006). De Vosse FN: Dependence of intramyocardial pressure and coronary flow on ventricular loading and contractility: a model study. Ann Biomed Eng
  42. (2008). de Vosse FN: Experimental validation of a time-domain-based wave propagation model of blood flow in viscoelastic vessels.
  43. (1969). De Vries CJ, Noordergraaf A: Analog studies of the human systemic arterial tree.
  44. (1997). der Voort PM: Physical and Physiological Determinants of Pulmonary Venous Flow: Numerical Analysis.
  45. (2008). Development and application of a one-dimensional blood flow model for microvascular networks. Proc Inst Mech Eng [H]
  46. (1963). DF: Pulsatile Pressure and Flow through Distensible Vessels. Circulation Research
  47. (1999). Di Marco LY: Numerical simulation of the hemodynamic response to hemodialysis-induced hypovolemia. Artif Organs
  48. (2004). Direct and series transmission of left atrial pressure perturbations to the pulmonary artery: a study using wave-intensity analysis. Am J Physiol Heart Circ Physiol
  49. (1996). E: The Role of Pressure Pulsatility in the Carotid Baroreflex Control: A Computer Simulation Study.
  50. (2006). Effects of atrial contraction, atrioventricular interaction and heart valve dynamics on human cardiovascular system response. Med Eng Phys
  51. (2005). Effects of compliance mismatch on blood flow in an artery with endovascular prosthesis.
  52. (2003). EH: Mathematical analysis of the quasilinear effects in a hyperbolic model blood flow through compliant axi-symmetric vessels.
  53. (1991). Einav S: Numerical schemes for unsteady fluid flow through collapsible tubes.
  54. (1943). Einige untersuchungen an elektrischen analogieschaltungen zum kreitslaufsystem.
  55. (2006). EL: Multiscale modelling in biofluidynamics: application to reconstructive paediatric cardiac surgery.
  56. (1987). Elzinga G: Beat-to-beat estimation of peripheral resistance and arterial compliance during pressure transients.
  57. (1986). End-systolic and end-diastolic ventricular interaction.
  58. (1995). Evaluation of methods for estimation of total arterial compliance.
  59. (1986). FC: Estimation of total arterial compliance: an improved method and evaluation of current methods.
  60. (2004). Forward electrical transmission line model of the human arterial system. Med Biol Eng Comput
  61. (1997). Fumerco R: Mathematical Modelling of the Human Foetal Cardiovascular System Based on Doppler Ultrasound Data.
  62. (1995). Gentle CR: A Review of the in vitro Evaluation of Conduit-mounted Cardiac Valve Prosthesis.
  63. (1988). GW: Comparison of time domain algorithms for estimating aortic characteristic impedance in humans.
  64. (1963). HB: The use of an analog computer in a circulation model. Prog Cardiovasc Dis
  65. (1999). Hemodynamic effect of cerebral vasospasm in humans: a modeling study. Ann Biomed Eng
  66. (2004). Hisada T: Multiphysics simulation of left ventricular filling dynamics using fluidstructure interaction finite element method.
  67. (1972). HJ: Circulation: overall regulation. Annu Rev Physiol
  68. (2007). Hose DR: A framework for the modeling of gut blood flow regulation and postprandial hyperaemia.
  69. (2010). Hose DR: Numerical modeling of hemodynamics with pulsatile impeller pump support. Ann Biomed Eng
  70. (2008). Hose DR: The role of venous valves in pressure shielding. Biomed Eng Online
  71. (2003). Hughes TJ, Taylor CA: In vivo validation of a one-dimensional finite-element method for predicting blood flow in cardiovascular bypass grafts.
  72. (1995). Identification of the three-element windkessel model incorporating a pressuredependent compliance. Ann Biomed Eng
  73. (2002). Image-based computational fluid dynamics modeling in realistic arterial geometries. Ann Biomed Eng
  74. (1998). Interaction between Carotid Baroregulation and the Pulsating Heart: A Mathematical Model.
  75. (2002). Interaction of the Cardiovascular System with an Implanted Rotary Assist Device: Simulation Study with a Refined Computer Model. Artificial Organs
  76. (1995). Intracranial Pressure Dynamics in Patients with Acute Brain Damage: A Critical Analysis with the Aid of a Mathematical Model.
  77. (1992). JB: Mathematical Modeling of Human Cardiovascular System for Simulation of Orthostatic Response.
  78. (1981). JD: Diastolic-systolic coronary flow differences are caused by intramyocardial pump action in the anesthetized dog. Circ Res
  79. (2000). KB: Physiological relevance of uniform elastic tube-models to infer descending aortic wave reflection: a problem of identifiability. Ann Biomed Eng
  80. (2004). KH: Wave propagation in a model of the arterial circulation.
  81. (2006). Korakianitis T: Numerical simulation of cardiovascular dynamics with left heart failure and in-series pulsatile ventricular assist device. Artif Organs
  82. (1996). Krause E: Numerical simulation of the blood flow in the human cardiovascular system.
  83. (2000). Left ventricular wall stress normalization in chronic pressure-overloaded heart: a mathematical model study. Am J Physiol Heart Circ Physiol
  84. (1999). Linear and Non-linear Waves
  85. (2000). Magosso E: Acute Cardiovascular Response to Isocapnic Hypoxia.
  86. (2000). Magosso E: Acute Cardiovascular Response to Isocapnic Hypoxia. II. Model Validation.
  87. (2003). Magosso E: Role of Short-term Cardiovascular Regulation in Heart Period Variability: A Model Study.
  88. (1955). Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known.
  89. (1999). MH: Opening and closing characteristics of the aortic valve after different types of valve-preserving surgery. Circulation
  90. (2002). MK: Numerical simulation of the influence of gravity and posture on cardiac performance. Ann Biomed Eng
  91. (1981). MN: Cardiovascular Physiology ,
  92. (1996). Modeling of Mechanical Dysfunction in Regional Stunned Myocardium of the Left Ventricle.
  93. (2001). Modeling the Cardiovascular System—A Mathematical Adventure: Part I & II.
  94. (2006). Modelling in the study of interaction of Hemopump device and artificial ventilation. Comput Biol Med
  95. (1997). MR: A Mathematical Model of Circulation in the Presence of the Bidirectional Cavopulmonary Anastomosis in Children with a Univentricular Heart.
  96. (1980). Multi-branched model of the human arterial system. Med Biol Eng Comput
  97. (1991). Multicompartment Model for Mechanics and Energetics of Fibrillating Ventricle.
  98. (2004). MV: A mathematical analysis for the cardiovascular control adaptations in chronic renal failure. Artif Organs
  99. (1973). NC: A model describing the response of the circulatory system to acceleration stress. Ann Biomed Eng
  100. (2008). Ning G: The role of the autonomic nervous system in hypertension: a bond graph model study. Physiol Meas
  101. (1998). Noordergraaf A: Apparent arterial compliance.
  102. (1965). Noordergraaf A: Oscillatory Flow Impedance in Electrical Analog of Arterial System: Representation of Sleeve Effect and Non-Newtonian Properties of Blood. Circ Res
  103. (2006). Noordergraaf A: Resolving the hemodynamic inverse problem.
  104. (1996). Noordergraaf A: Two-port analysis of microcirculation: an extension of windkessel.
  105. (2007). Numerical comparison of hemodynamics with atrium to aorta and ventricular apex to aorta VAD support.
  106. (2004). Numerical simulation of a systemic flow test rig.
  107. (2007). Numerical simulation of cardiovascular dynamics with different types of VAD assistance.
  108. (2006). Numerical Simulation of Cardiovascular Dynamics with Healthy and Diseased Heart Valves.
  109. (1990). O.’Rourke MF: McDonald’s Blood Flow
  110. (2001). On the Coupling of 3D and 1D Navier-Stokes Equations for Flow Problems in Compliant Vessels.
  111. (1998). On the propagation of solitary waves in a prestressed thin elastic tube filled with an inviscid fluid. Zeitschrift fur angewandte Mathematik und Physik ZAMP
  112. (1998). Optimization and mechanism of step-leap respiration exercise in treating of cor pulmonale. Comput Biol Med
  113. (1957). Oscillatory flow in arteries: the constrained elastic tube as a model of arterial flow and pulse transmission. Phys Med Biol
  114. (2003). P: One-dimensional modelling of a vascular network in space-time variables.
  115. (1987). Paradowski LJ: Characterization of pulmonary arterial input impedance with lumped parameter models.
  116. (2008). Physiological control of a rotary blood pump with selectable therapeutic options: control of pulsatility gradient. Artif Organs
  117. (2002). PJ: An anatomically based model of transient coronary blood flow in the heart.
  118. (2006). PV: Fundamental mechanics of aortic heart valve closure.
  119. (1980). Quantitative evaluation of the systemic arterial bed by parameter estimation of a simple model. Med Biol Eng Comput
  120. (2003). Quantitive Assessment of Cerebral Autoregulation from Transcranial Doppler Pulsatility: a Computer Simulation Study.
  121. (2004). Quarteroni A: Analysis of lumped parameter models for blood flow simulations and their relation with 1D models. ESAIM-Mathematical Modelling and Numerical Anslysis
  122. (2002). RG: Computational Modeling of Cardiovascular Response to Orthostatic Stress.
  123. (1969). Rideout VC: Computer simulation studies of the venous circulation.
  124. (2003). Rossoni E: Numerical Modeling of the Pressure Wave Propagation in the Arterial Flow. International Journal for Numerical Methods in Fluids
  125. (1994). S: Pressure-flow characteristics of the coronary collaterals: a model study.
  126. (1987). Sagawa K: Ventricular systolic interdependence: volume elastance model in isolated canine hearts.
  127. (1988). Schipke J: Assessment of Windkessel as a model of aortic input impedance.
  128. (2007). Seperation of arterial pressure into a nonlinear superposition of solitary waves and a windkessel flow. Biomedical signal processing and control
  129. (1973). Shoukas AA: Load Independence of the Instantaneous Pressure-Volume Ratio of the Canine Left Ventricle and Effects of Epinephrine and Heart Rate on the Ratio. Circulation Research
  130. (1993). Shoukas AA: Two-port analysis of systemic venous and arterial impedances.
  131. (2007). Siebes M: Effect of simultaneous intracoronary guidewires on the predictive accuracy of functional parameters of coronary lesion severity. Am J Physiol Heart Circ Physiol
  132. (2002). Simulation and Prediction of Cardiotherapeutical Phenomena from a Pulsatile Model Coupled to the Guyton Circulation Model.
  133. (2002). Skliar M: Nonlinear Controller for Ventricular Assist Devices. Artificial Organs
  134. (1987). Solitary waves in large blood vessels.
  135. (2007). Sorine M: A reduced model of pulsatile flow in an arterial compartment. Chaos, solitons and fractals
  136. (2002). Spaan JA: Balance between myogenic, flow-dependent, and metabolic flow control in coronary arterial tree: a model study. Am J Physiol Heart Circ Physiol
  137. (2000). Spaan JA: Myogenic reactivity and resistance distribution in the coronary arterial tree: a model study. Am J Physiol Heart Circ Physiol
  138. (2009). Stergiopulos N: Validation of a one-dimensional model of the systemic arterial tree.
  139. (1999). Structured tree outflow condition for blood flow in larger systemic arteries.
  140. (2005). TA: A LabVIEW model incorporating an open-loop arterial impedance and a closed-loop circulatory system. Ann Biomed Eng
  141. (1988). Targett RC: A Model of the Systemic Arterial Bed Showing Ventricular Systemic Arterial Coupling.
  142. (2005). Taylor CA: Flow imaging and computing: large artery hemodynamics. Ann Biomed Eng
  143. (1992). Temporal Relation between Left Ventricular and Arterial System Elastances.
  144. (2006). Textbook of Medical Physiology. 11 edition.
  145. (1996). The Aortic Outflow and Root: A Tale of Dynamism and Crosstalk. Annals Thoracic Surgury
  146. (2000). The arterial circulation: Physical principles and clinical applications
  147. (2009). The arterial Windkessel. Med Biol Eng Comput
  148. (1972). The Fluid Mechanics of Heart Valves
  149. (2003). The non-linearities of arterial blood flow. Phys Med Biol 1971, 16:663-672. Shi et al. BioMedical Engineering OnLine 2011, 10:33 http://www.biomedical-engineering-online.com/content/10/1/33 Page 36 of 38126. Sherwin SJ, Formaggia L, Peir , Franke V:
  150. (2002). Theoretical analysis of rest and exercise hemodynamics in patients with total cavopulmonary connection.
  151. (1990). Theoretical model of ventricular interdependence: pericardial effects.
  152. (2002). TJ: A model for time-dependent flow in (giraffe jugular) veins: uniform tube properties.
  153. (1995). TJ: Large Axisymmetric Deformation of a cylindrical shell conveying a viscous flow.
  154. (1999). TJ: Numerical Solutions for Unsteady Gravity-driven Flows in Collapsible Tubes: Evolution and Roll-wave Instability of a Steady State.
  155. (2001). TJR: Method for predictive modeling for planning medical interventions and simulating physiological conditions, US 6,236,878 B1. United States Patent;
  156. (1999). Total arterial inertance as the fourth element of the windkessel model.
  157. (1986). TR: A finite-element model of blood flow in arteries including taper, branches, and obstructions.
  158. (1982). TR: A finite-element simulation of pulsatile flow in flexible obstructed tubes.
  159. (1997). Traber DL: A Dynamic Model of Ventricular Interaction and Pericardial Influence.
  160. (2005). Tyberg JV: Assessment of left ventricular diastolic suction in dogs using wave-intensity analysis. Am J Physiol Heart Circ Physiol
  161. (2001). Tyberg JV: Left ventricular wave speed.
  162. (2001). Tyberg JV: Negative wave reflections in pulmonary arteries.
  163. (2003). Tyberg JV: Time-domain representation of ventricular-arterial coupling as a windkessel and wave system.
  164. (1993). Tyberg JV: Ventricular interaction and septal deformation: a model compared with experimental data.
  165. (2000). Tyberg JV: Wave-intensity analysis: a new approach to coronary hemodynamics.
  166. (1993). Typerg JV: Why Does Pulmonary Venous Pressure Rise after Onset of LV Dysfunction: a Theoretical Analysis.
  167. (1999). Veneziani A: Multiscale modelling of the circulatory system: a preliminary analysis. Computing and Visualization in Science
  168. (2003). Veneziani A: Reduced and multiscale models for the human cardiovascular system. Politecnico di Milano;
  169. (2002). Verdonck PR: Effect of Rotary Blood Pump Failure on Left Ventricular Energetics Assessed by Mathematical Modeling. Artificial Organs
  170. (2008). Verdonck PR: Threeand four-element Windkessel models: assessment of their fitting performance in a large cohort of healthy middleaged individuals. Proc Inst Mech Eng [H]
  171. (1987). Weisfeldt ML: Interaction between cardiac chambers and thoracic pressure in intact circulation.
  172. (2008). Windkesselness of coronary arteries hampers assessment of human coronary wave speed by single-point technique.
  173. (1982). Yellin EL: Fluid dynamics of the mitral valve: physiological aspects of a mathematical model.
  174. (2005). Yoganathan AP: Coupling Pediatric Ventricle Assist Devices to the Fontan Circulation: Simulation with a Lumped-Parameter Model.