{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T12:36:29Z","timestamp":1771504589029,"version":"3.50.1"},"reference-count":110,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T00:00:00Z","timestamp":1771459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bioengineering"],"abstract":"<jats:p>Background: Arterial stenosis produces nonlinear changes in vascular impedance that are challenging to investigate in real time using either benchtop flow phantoms or high-fidelity computational fluid dynamics (CFD) models. Objective: This study aimed to develop and evaluate a low-cost printed circuit board (PCB) analog capable of reproducing the hemodynamic effects of progressive arterial stenosis through an R\u2013L\u2013C mapping of vascular mechanics. Methods: A lumped-parameter (0D) electrical network was constructed in which voltage represented pressure, current represented flow, resistance modeled viscous losses, capacitance corresponded to vessel compliance, and inductance represented fluid inertance. A variable resistor simulated focal stenosis and was adjusted incrementally to represent progressive narrowing. Input Uin, output Uout, peak-to-peak Vpp, and mean Vavg voltages were recorded at a driving frequency of 50 Hz. Physiological correspondence was established using the canonical relationships. R=8\u03bcl\u03c0r4, L=pl\u03c0r2, C=3\u03c0r32Eh, where \u03bc is blood viscosity, \u03c1 is density, E is Young\u2019s modulus, and h is wall thickness. A calibration constant was applied to convert measured voltage differences into pressure differences. Results: As simulated stenosis increased, the circuit exhibited a monotonic rise in Uout and Vpp, with a precise inflection beyond mid-range narrowing\u2014consistent with the nonlinear growth in pressure loss predicted by fluid dynamic theory. Replicate measurements yielded stable, repeatable traces with no outliers under nominal test conditions. Qualitative trends matched those of surrogate 0D and CFD analyses, showing minimal changes for mild narrowing (\u226425%) and a sharp increase in pressure loss for moderate to severe stenoses (\u226550%). The PCB analog uses a simplified, lumped-parameter representation driven by a fixed-frequency sinusoidal excitation and therefore does not reproduce fully characterized physiological systolic\u2013diastolic waveforms or heart\u2013arterial coupling. In addition, the present configuration is intended for relatively straight peripheral arterial segments and is not designed to capture the complex geometry and branching of specialized vascular beds (e.g., intracranial circulation) or strongly curved elastic vessels (e.g., the thoracic aorta). Conclusions: The PCB analog successfully reproduces the characteristic hemodynamic signatures of arterial stenosis in real time and at low cost. The model provides a valuable tool for educational and research applications, offering rapid and intuitive visualization of vascular behavior. Current accuracy reflects assumptions of Newtonian, laminar, and lumped flow; future work will refine calibration, quantify uncertainty, and benchmark results against physiological measurements and full CFD simulations.<\/jats:p>","DOI":"10.3390\/bioengineering13020241","type":"journal-article","created":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T11:44:27Z","timestamp":1771501467000},"page":"241","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Peripheral Artery Disease (P.A.D.): Vascular Hemodynamic Simulation Using a Printed Circuit Board (PCB) Design"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5416-3142","authenticated-orcid":false,"given":"Claudiu N.","family":"Lungu","sequence":"first","affiliation":[{"name":"Faculty of Medicine and Pharmacy, Medical and Pharmaceutical Research Center, Dunarea de Jos University, 8000080 Galati, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aurelia","family":"Romila","sequence":"additional","affiliation":[{"name":"Faculty of Medicine and Pharmacy, Medical and Pharmaceutical Research Center, Dunarea de Jos University, 8000080 Galati, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aurel","family":"Nechita","sequence":"additional","affiliation":[{"name":"Faculty of Medicine and Pharmacy, Medical and Pharmaceutical Research Center, Dunarea de Jos University, 8000080 Galati, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mihaela C.","family":"Mehedinti","sequence":"additional","affiliation":[{"name":"Faculty of Medicine and Pharmacy, Medical and Pharmaceutical Research Center, Dunarea de Jos University, 8000080 Galati, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,19]]},"reference":[{"key":"ref_1","unstructured":"Nichols, W.W., O\u2019Rourke, M.F., and Vlachopoulos, C. (2011). McDonald\u2019s Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles, CRC Press. [6th ed.]."},{"key":"ref_2","unstructured":"Guyton, A.C., and Hall, J.E. (2021). Guyton and Hall Textbook of Medical Physiology, Elsevier. [14th ed.]."},{"key":"ref_3","unstructured":"Sherwood, L. (2015). Human Physiology: From Cells to Systems, Cengage Learning. [9th ed.]."},{"key":"ref_4","unstructured":"Westerhof, N., Stergiopulos, N., and Noble, M.I.M. (2010). Snapshots of Hemodynamics: An Aid for Clinical Research and Graduate Education, Springer. [2nd ed.]."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1794","DOI":"10.1016\/j.jbiomech.2006.07.008","article-title":"Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows","volume":"40","author":"Alastruey","year":"2007","journal-title":"J. Biomech."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1443","DOI":"10.1007\/s10439-015-1313-8","article-title":"One-dimensional haemodynamic modeling and wave dynamics in the entire adult circulation","volume":"43","author":"Mynard","year":"2015","journal-title":"Ann. Biomed. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"e00318","DOI":"10.1016\/j.ohx.2022.e00318","article-title":"Low cost circulatory pressure acquisition and fluid infusion rate measurement system for clinical research","volume":"11","author":"Smith","year":"2022","journal-title":"HardwareX"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/0021-9290(69)90024-4","article-title":"Analog studies of the human systemic arterial tree","volume":"2","author":"Westerhof","year":"1969","journal-title":"J. Biomech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"545","DOI":"10.2170\/jjphysiol.54.545","article-title":"Mathematical modeling of cardiovascular system dynamics using a lumped-parameter method","volume":"54","author":"Shim","year":"2004","journal-title":"Jpn. J. Physiol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1964","DOI":"10.1016\/j.jbiomech.2005.06.016","article-title":"Numerical simulation of cardiovascular dynamics with healthy and diseased heart valves","volume":"39","author":"Korakianitis","year":"2006","journal-title":"J. Biomech."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1161\/01.HYP.0000019132.41066.95","article-title":"Heart rate: An important confounder of pulse-wave-velocity assessment","volume":"39","author":"Lantelme","year":"2002","journal-title":"Hypertension"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s11517-008-0359-2","article-title":"The arterial Windkessel","volume":"47","author":"Westerhof","year":"2009","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"106266","DOI":"10.1016\/j.cmpb.2021.106266","article-title":"Closed-loop geometric multi-scale heart-coronary artery model for the numerical calculation of fractional flow reserve","volume":"208","author":"Liu","year":"2021","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Guo, C.-Y., Perng, J.-W., Chen, L.-C., and Hsieh, T.-L. (2023). A Hemodynamic Pulse Wave Simulator Designed for Calibration of Local Pulse Wave Velocities Measurement for Cuffless Techniques. Micromachines, 14.","DOI":"10.3390\/mi14061218"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"041003","DOI":"10.1115\/1.4038885","article-title":"Flow\u2013Structure Interaction Simulations of the Aortic Heart Valve at Physiologic Conditions: The Role of Tissue Constitutive Model","volume":"140","author":"Gilmanov","year":"2018","journal-title":"J. Biomech. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1186\/1475-925X-10-33","article-title":"Review of zero-D and 1-D models of blood flow in the cardiovascular system","volume":"10","author":"Shi","year":"2011","journal-title":"Biomed. Eng. Online"},{"key":"ref_17","first-page":"9","article-title":"Vascular wall shear stress: Basic principles and methods","volume":"46","author":"Papaioannou","year":"2005","journal-title":"Hell. J. Cardiol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2250","DOI":"10.1016\/j.jbiomech.2011.05.041","article-title":"Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements","volume":"44","author":"Alastruey","year":"2011","journal-title":"J. Biomech."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1146\/annurev-fluid-122109-160730","article-title":"Pulse wave propagation in the arterial tree","volume":"43","author":"Stergiopulos","year":"2011","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1115\/1.3426241","article-title":"Fluid mechanics of arterial stenoses","volume":"101","author":"Young","year":"1979","journal-title":"J. Biomech. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s11517-009-0440-5","article-title":"A brief history of arterial wave mechanics","volume":"47","author":"Parker","year":"2009","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1093\/cvr\/6.6.648","article-title":"Forward and backward waves in the arterial system","volume":"6","author":"Westerhof","year":"1972","journal-title":"Cardiovasc. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/0021-9290(73)90012-2","article-title":"Flow characteristics in models of arterial stenoses\u2014II. Unsteady flow","volume":"6","author":"Young","year":"1973","journal-title":"J. Biomech."},{"key":"ref_24","unstructured":"Milnor, W.R. (1989). Hemodynamics, Williams & Wilkins. [2nd ed.]."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Fung, Y.C. (1997). Biomechanics: Circulation, Springer. [2nd ed.].","DOI":"10.1007\/978-1-4757-2696-1"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Pedley, T.J. (1980). The Fluid Mechanics of Large Blood Vessels, Cambridge University Press.","DOI":"10.1017\/CBO9780511896996"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1152\/jappl.1967.23.2.139","article-title":"Pressure and flow waves in systemic arteries and the anatomical design of the arterial system","volume":"23","year":"1967","journal-title":"J. Appl. Physiol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1161\/01.HYP.32.3.556","article-title":"Determinants of pulse pressure","volume":"32","author":"Stergiopulos","year":"1998","journal-title":"Hypertension"},{"key":"ref_29","unstructured":"Webster, J.G. (2010). Medical Instrumentation: Application and Design, Wiley. [4th ed.]."},{"key":"ref_30","unstructured":"Kester, W. (2005). The Data Conversion Handbook, Newnes."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/S0045-7825(98)80008-X","article-title":"Finite element modeling of blood flow in arteries","volume":"158","author":"Taylor","year":"1998","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_32","first-page":"518","article-title":"Modeling Human Systemic Arterial Tree with Electric Components in the 1960s and Today","volume":"323","author":"Pustozerov","year":"2025","journal-title":"Stud. Health Technol. Inform."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1093\/oxfordjournals.bmb.a072313","article-title":"Microcirculation and diabetes","volume":"45","author":"Tooke","year":"1989","journal-title":"Br. Med. Bull."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4450","DOI":"10.1364\/OL.434454","article-title":"Direct measurement of pulse wave propagation in capillaries of the human retina","volume":"46","author":"Bedggood","year":"2021","journal-title":"Opt. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1186\/s12938-019-0660-3","article-title":"A review on low-dimensional physics-based models of systemic arteries: Application to estimation of central aortic pressure","volume":"18","author":"Zhou","year":"2019","journal-title":"Biomed. Eng. OnLine"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/S0140-6736(86)90837-8","article-title":"Statistical methods for assessing agreement between two methods of clinical measurement","volume":"327","author":"Bland","year":"1986","journal-title":"Lancet"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Bejan, A. (2016). Advanced Engineering Thermodynamics, John Wiley & Sons. [4th ed.].","DOI":"10.1002\/9781119245964"},{"key":"ref_38","unstructured":"Bridgman, P.W. (1922). Dimensional Analysis, Yale University Press."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1103\/PhysRev.4.345","article-title":"On physically similar systems; Illustrations of the Use of Dimensional Equations","volume":"4","author":"Buckingham","year":"1914","journal-title":"Phys. Rev."},{"key":"ref_40","unstructured":"Bahloul, M.A., and Laleg Kirati, T.-M. (2019). Fractional Order Models of Arterial Windkessel as an Alternative in the Analysis of the Left Ventricular After-load. arXiv."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s10916-015-0220-8","article-title":"Design and development of a medical big data processing system based on Hadoop","volume":"39","author":"Yao","year":"2015","journal-title":"J. Med. Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.1007\/s10439-009-9760-8","article-title":"On coupling a lumped-parameter heart model and a 3D finite element aorta model","volume":"37","author":"Kim","year":"2009","journal-title":"Ann. Biomed. Eng."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1281","DOI":"10.1114\/1.1326031","article-title":"Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions","volume":"28","author":"Olufsen","year":"2000","journal-title":"Ann. Biomed. Eng."},{"key":"ref_44","unstructured":"Idelchik, I.E. (2007). Handbook of Hydraulic Resistance, Begell House. [4th ed.]."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1703","DOI":"10.1056\/NEJM199606273342604","article-title":"Measurement of fractional flow reserve to assess the functional severity of coronary-artery stenoses","volume":"334","author":"Pijls","year":"1996","journal-title":"N. Engl. J. Med."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"031001","DOI":"10.1115\/1.4003259","article-title":"A stochastic collocation method for uncertainty quantification and propagation in cardiovascular simulations","volume":"133","author":"Sankaran","year":"2011","journal-title":"J. Biomech. Eng."},{"key":"ref_47","unstructured":"Fox, R.W., McDonald, A.T., and Pritchard, P.J. (2011). Introduction to Fluid Mechanics, Wiley. [8th ed.]."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1017\/S0962492917000046","article-title":"The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications","volume":"26","author":"Quarteroni","year":"2017","journal-title":"Acta Numer."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1018","DOI":"10.1016\/j.jcin.2015.01.039","article-title":"Repeatability of Fractional Flow Reserve Despite Variations in Systemic and Coronary Hemodynamics","volume":"8","author":"Johnson","year":"2015","journal-title":"JACC Cardiovasc. Interv."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1056\/NEJMoa1205361","article-title":"Fractional flow reserve\u2013guided PCI versus medical therapy in stable coronary disease","volume":"367","author":"Pijls","year":"2012","journal-title":"N. Engl. J. Med."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1146\/annurev.fluid.29.1.399","article-title":"Blood flow in arteries","volume":"29","author":"Ku","year":"1997","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2035","DOI":"10.1001\/jama.282.21.2035","article-title":"Hemodynamic shear stress and its role in atherosclerosis","volume":"282","author":"Malek","year":"1999","journal-title":"JAMA"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"2379","DOI":"10.1016\/j.jacc.2007.02.059","article-title":"Role of endothelial shear stress in the natural history of coronary atherosclerosis and Vascular Remodeling: Molecular, Cellular, and Vascular Behavior","volume":"49","author":"Chatzizisis","year":"2007","journal-title":"J. Am. Coll. Cardiol."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"H2050","DOI":"10.1152\/ajpheart.1996.270.6.H2050","article-title":"Determinants of stroke volume and systolic and diastolic aortic pressure","volume":"270","author":"Stergiopulos","year":"1996","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1023\/B:ENGI.0000007979.32871.e2","article-title":"One-dimensional modelling of a vascular network in space-time variables","volume":"47","author":"Sherwin","year":"2003","journal-title":"J. Eng. Math."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/0025-5564(73)90027-8","article-title":"On the one-dimensional theory of blood flow in the larger vessels","volume":"18","author":"Hughes","year":"1973","journal-title":"Math. Biosci."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"2233","DOI":"10.1016\/j.jacc.2012.11.083","article-title":"Computational fluid dynamics applied to cardiac computed tomography for noninvasive quantification of fractional flow reserve: Scientific basis","volume":"61","author":"Taylor","year":"2013","journal-title":"J. Am. Coll. Cardiol."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1114\/1.1467679","article-title":"Image-based computational fluid dynamics modeling in realistic arterial geometries","volume":"30","author":"Steinman","year":"2002","journal-title":"Ann. Biomed. Eng."},{"key":"ref_59","first-page":"187","article-title":"The Windkessel and beyond: Modeling the arterial tree","volume":"96","author":"Mynard","year":"2016","journal-title":"Physiol. Rev."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1115\/1.2796008","article-title":"Steady flow in an aneurysm model: Correlation between fluid dynamics and blood platelet deposition","volume":"118","author":"Bluestein","year":"1996","journal-title":"J. Biomech. Eng."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1016\/S0021-9290(99)00015-9","article-title":"The influence of the non-Newtonian properties of blood on the flow in large arteries: Steady flow in a carotid bifurcation model","volume":"32","author":"Gijsen","year":"1999","journal-title":"J. Biomech."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1088\/0031-9155\/2\/2\/305","article-title":"Oscillatory flow in arteries: The constrained elastic tube as a model of arterial flow and pulse transmission","volume":"2","author":"Womersley","year":"1957","journal-title":"Phys. Med. Biol."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1002\/1097-0363(20010115)35:1<93::AID-FLD85>3.0.CO;2-G","article-title":"A stabilized finite element method for the incompressible Navier\u2013Stokes equations using a hierarchical basis","volume":"35","author":"Whiting","year":"2001","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1146\/annurev.bioeng.10.061807.160521","article-title":"Patient-specific modeling of cardiovascular mechanics","volume":"11","author":"Taylor","year":"2009","journal-title":"Annu. Rev. Biomed. Eng."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1115\/1.2795948","article-title":"Pulsatile flow in the human left coronary artery bifurcation: Average Conditions","volume":"118","author":"He","year":"1996","journal-title":"J. Biomech. Eng."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"1704","DOI":"10.1007\/s10439-005-8772-2","article-title":"Flow imaging and computing: Large artery hemodynamics","volume":"33","author":"Steinman","year":"2005","journal-title":"Ann. Biomed. Eng."},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Fedotov, A.A., Akulova, A.S., and Akulov, S.A. (2016, January 16\u201320). Modeling digital pulse waveforms by solving one-dimensional Navier-stokes equations. Proceedings of the 2016 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Orlando, FL, USA.","DOI":"10.1109\/EMBC.2016.7591494"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1115\/1.2540836","article-title":"On the relative importance of rheology for image-based CFD models of the carotid bifurcation","volume":"129","author":"Lee","year":"2007","journal-title":"J. Biomech. Eng."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1146\/annurev.fluid.32.1.347","article-title":"Flows in stenotic vessels","volume":"32","author":"Berger","year":"2000","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1002\/nme.2579","article-title":"Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities","volume":"79","author":"Geuzaine","year":"2009","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_71","unstructured":"(2016). Industrial Automation Systems and Integration\u2014Product Data Representation and Exchange\u2014Part 21: STEP File Format. (Standard No. ISO 10303-21:2016)."},{"key":"ref_72","unstructured":"FreeCAD Development Team (2025, December 21). FreeCAD (v0.20+): Open-Source Parametric 3D CAD Modeler. Available online: https:\/\/www.freecad.org\/."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"1989","DOI":"10.1016\/j.jacc.2011.06.066","article-title":"Diagnosis of ischemia-causing coronary stenoses by noninvasive fractional flow reserve computed from coronary computed tomographic angiograms. Results from the prospective multicenter DISCOVER-FLOW (Diagnosis of Ischemia-Causing Stenoses Obtained via Noninvasive Fractional Flow Reserve) study","volume":"58","author":"Koo","year":"2011","journal-title":"J. Am. Coll. Cardiol."},{"key":"ref_74","first-page":"468","article-title":"Prediction of coronary plaque location using endothelial shear stress","volume":"108","author":"Stone","year":"2003","journal-title":"Circulation"},{"key":"ref_75","first-page":"97","article-title":"Noninvasive fractional flow reserve: Scientific basis and clinical applications","volume":"12","author":"Taylor","year":"2010","journal-title":"Curr. Cardiol. Rep."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"3195","DOI":"10.1007\/s10439-010-0083-6","article-title":"Patient-specific modeling of blood flow in coronary arteries","volume":"38","author":"Kim","year":"2010","journal-title":"Ann. Biomed. Eng."},{"key":"ref_77","first-page":"157","article-title":"Predictive modeling of coronary hemodynamics","volume":"17","author":"Taylor","year":"2015","journal-title":"Annu. Rev. Biomed. Eng."},{"key":"ref_78","first-page":"240","article-title":"Note on regression and inheritance in the case of two parents","volume":"58","author":"Pearson","year":"1895","journal-title":"Proc. R. Soc."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1161\/01.RES.53.4.502","article-title":"Carotid bifurcation atherosclerosis. Quantitative correlation of plaque localization with flow velocity profiles and wall shear stress","volume":"53","author":"Zarins","year":"1983","journal-title":"Circ. Res."},{"key":"ref_80","first-page":"1551","article-title":"Constitutive modelling of arteries","volume":"466","author":"Holzapfel","year":"2010","journal-title":"Proc. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_81","first-page":"2891","article-title":"Systematic approaches to reduced-order modeling of blood flow","volume":"49","author":"Alastruey","year":"2016","journal-title":"J. Biomech."},{"key":"ref_82","first-page":"110801","article-title":"Reduced-order modeling of blood flow in the circulation","volume":"142","author":"Alastruey","year":"2020","journal-title":"J. Biomech. Eng."},{"key":"ref_83","first-page":"1231","article-title":"Reduced-order models in cardiovascular hemodynamics","volume":"15","author":"Safaei","year":"2016","journal-title":"Biomech. Model. Mechanobiol."},{"key":"ref_84","first-page":"101","article-title":"A closed-loop lumped-parameter model for the human cardiovascular system","volume":"39","author":"Liang","year":"2006","journal-title":"J. Biomech."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"H208","DOI":"10.1152\/ajpheart.00037.2009","article-title":"Validation of a one-dimensional model of the systemic arterial tree","volume":"297","author":"Reymond","year":"2009","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"e02732","DOI":"10.1002\/cnm.2732","article-title":"A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling","volume":"31","author":"Boileau","year":"2015","journal-title":"Int. J. Numer. Methods Biomed. Eng."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"H257","DOI":"10.1152\/ajpheart.1999.276.1.H257","article-title":"Structured tree outflow condition for blood flow in larger systemic arteries","volume":"276","author":"Olufsen","year":"1999","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.cma.2016.01.007","article-title":"Geometric multiscale modeling of the cardiovascular system, between theory and practice","volume":"302","author":"Quarteroni","year":"2016","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s11259-016-9669-2","article-title":"Arterial pulse wave propagation velocity in healthy dogs by pulse wave Doppler ultrasound","volume":"41","author":"Nogueira","year":"2017","journal-title":"Vet. Res. Commun."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/s11517-009-0439-y","article-title":"An introduction to wave intensity analysis","volume":"47","author":"Parker","year":"2009","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1113\/jphysiol.1955.sp005276","article-title":"Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known","volume":"127","author":"Womersley","year":"1955","journal-title":"J. Physiol."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1093\/gerona\/glaa315","article-title":"One-Dimensional Statistical Parametric Mapping Identifies Impaired Orthostatic Cerebrovascular and Cardiovascular Response in Frailty Index","volume":"76","author":"Maguire","year":"2021","journal-title":"J. Gerontol. A Biol. Sci. Med. Sci."},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1097\/00002480-199911000-00006","article-title":"Development of a hydraulic model of the human systemic circulation","volume":"45","author":"Sharp","year":"1999","journal-title":"ASAIO J."},{"key":"ref_94","unstructured":"Guala, A., and Pini, A. (2022). Lumped parameter models for the cardiovascular system. Front. Physiol., 13."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/j.jcct.2013.09.003","article-title":"Rationale and design of the HeartFlowNXT (HeartFlow analysis of coronary blood flow using CT angiography: NeXt sTeps) study","volume":"7","author":"Gaur","year":"2013","journal-title":"J. Cardiovasc. Comput. Tomogr."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1152\/physrev.1969.49.4.863","article-title":"Rheology of blood","volume":"49","author":"Merrill","year":"1969","journal-title":"Physiol. Rev."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.jcin.2012.08.024","article-title":"Virtual fractional flow reserve from coronary angiography: Modeling the significance of lesions: Results from the VIRTU-1 (VIRTUal Fractional Flow Reserve from Coronary Angiography) study","volume":"6","author":"Morris","year":"2013","journal-title":"JACC Cardiovasc. Interv."},{"key":"ref_98","first-page":"2652","article-title":"Influence of blood viscosity on hemodynamic factors","volume":"44","author":"Soulis","year":"2011","journal-title":"J. Biomech."},{"key":"ref_99","doi-asserted-by":"crossref","unstructured":"Efron, B., and Tibshirani, R.J. (1993). An Introduction to the Bootstrap, Chapman & Hall\/CRC.","DOI":"10.1007\/978-1-4899-4541-9"},{"key":"ref_100","doi-asserted-by":"crossref","unstructured":"Draper, N.R., and Smith, H. (1998). Applied Regression Analysis, Wiley. [3rd ed.].","DOI":"10.1002\/9781118625590"},{"key":"ref_101","first-page":"405","article-title":"A projection method for tissue growth simulations","volume":"8","author":"Sander","year":"2009","journal-title":"Biomech. Model. Mechanobiol."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1146\/annurev.fl.15.010183.002333","article-title":"Flow in curved pipes","volume":"15","author":"Berger","year":"1983","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_103","doi-asserted-by":"crossref","unstructured":"Du, T., Hu, D., and Cai, D. (2015). Outflow boundary conditions for blood flow in arterial trees. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0128597"},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"121001","DOI":"10.1115\/1.4034830","article-title":"A Zero-Dimensional Model and Protocol for Simulating Patient-Specific Pulmonary Hemodynamics From Limited Clinical Data","volume":"138","author":"Kheyfets","year":"2016","journal-title":"J. Biomech. Eng."},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"5685","DOI":"10.1016\/j.cma.2005.11.011","article-title":"Coupled multidomain models of the cardiovascular system","volume":"195","author":"Figueroa","year":"2006","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"e04645","DOI":"10.7554\/eLife.04645","article-title":"Vascular remodeling is coronary governed by VEGFR3-dependent shear stress set point","volume":"4","author":"Baeyens","year":"2015","journal-title":"eLife"},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"2890","DOI":"10.1161\/CIR.0b013e318276fbcb","article-title":"Measurement and interpretation of the ankle-brachial index: A scientific statement from the American Heart Association","volume":"126","author":"Aboyans","year":"2012","journal-title":"Circulation"},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1038\/labinvest.3700215","article-title":"The role of shear stress in atherosclerosis","volume":"85","author":"Cunningham","year":"2005","journal-title":"Lab. Investig."},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"1770","DOI":"10.1161\/hq1001.097104","article-title":"Pulsatile flow regulates monocyte adhesion to oxidized lipid-induced endothelial cells","volume":"21","author":"Hsiai","year":"2001","journal-title":"Arterioscler. Thromb. Vasc. Biol."},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"1225","DOI":"10.1161\/01.RES.0000104087.29395.66","article-title":"Pulsatile versus oscillatory shear stress regulates NADPH oxidase subunit expression: Implication for native LDL oxidation","volume":"93","author":"Hwang","year":"2003","journal-title":"Circ. Res."}],"container-title":["Bioengineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2306-5354\/13\/2\/241\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T11:57:47Z","timestamp":1771502267000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2306-5354\/13\/2\/241"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,19]]},"references-count":110,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["bioengineering13020241"],"URL":"https:\/\/doi.org\/10.3390\/bioengineering13020241","relation":{},"ISSN":["2306-5354"],"issn-type":[{"value":"2306-5354","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,19]]}}}