This scoping review was conducted in accordance with the Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA) extension for Scoping Reviews (PRISMA-ScR).^{( 7 )}We searched electronic databases (PubMed and Embase) for articles published in English that used 1D computational models of the entire circulatory tree. The search strategy is detailed in Table 1S , 2S and 3S, Supplementary Material. The reference lists of the retrieved articles were also screened for eligible studies. All references were exported to and reviewed using EndNote (version 20.6; Clarivate, PA, USA). After omitting duplicates, we proceeded with the screening process in a stepwise manner as follows: 1) In the first screening phase, we excluded articles based on title review - the absence of relevance to computational modeling or circulatory system structure was the main criteria; 2) In the second phase, we read the abstracts of the remaining articles, and articles were excluded for not meeting the inclusion criteria, such as lack of whole system modeling or absence of 1D elements; and 3) the remaining studies were selected for full-text analysis and inclusion. Studies were listed based on thematic grouping and relevance to the classification structure (linear, nonlinear, and multiscale) rather than chronological order.

Table 1S

Database	Search string	Articles retrieved
PubMed	(“Hemodynamics”[MeSH Terms] OR “hemodynamics”[tw] OR “blood flow”[tw]) AND (“Cardiovascular System”[MeSH Terms] OR “arterial network”[tw] OR “vascular tree”[tw] OR “arterial system”[tw]) AND (“Models, Cardiovascular”[MeSH Terms] OR “data assimilation”[tw] OR “computational model”[tw] OR “mathematical model”[tw] OR “1D model”[tw] OR “one-dimensional model”[tw] OR “reduced-order model”[tw] OR “lumped parameter model”[tw]) AND (“Simulation”[MeSH Terms] OR “simulation”[tw])	3,757
Embase	(‘hemodynamics’/exp OR ‘hemodynamics’:ti,ab,kw,de,dn,df,mn,tn OR ‘blood flow’:ti,ab,kw,de,dn,df,mn,tn) AND (‘cardiovascular system’/exp OR ‘arterial network’:ti,ab,kw,de,dn,df,mn,tn OR ‘vascular tree’:ti,ab,kw,de,dn,df,mn,tn OR ‘arterial system’:ti,ab,kw,de,dn,df,mn,tn) AND (‘biological model’/exp OR ‘data assimilation’:ti,ab,kw,de,dn,df,mn,tn OR ‘computational model’:ti,ab,kw,de,dn,df,mn,tn OR ‘mathematical model’:ti,ab,kw,de,dn,df,mn,tn OR ‘1d model’:ti,ab,kw,de,dn,df,mn,tn OR ‘one-dimensional model’:ti,ab,kw,de,dn,df,mn,tn OR ‘reduced-order model’:ti,ab,kw,de,dn,df,mn,tn OR ‘lumped parameter model’:ti,ab,kw,de,dn,df,mn,tn) AND (‘simulation’/exp OR ‘simulation’:ti,ab,kw,de,dn,df,mn,tn)	3,061

Studies were considered eligible for inclusion if they used computational simulations of the entire arterial circulatory tree using 1D computational models. Studies were also eligible if they used other dimensional models (such as 0D or 3D) in addition to a 1D model.

The selected articles were retrieved in full and their findings were summarized in a standard form containing the study objective, model characteristics (including model type, wall properties, geometry, and validation methods), number of arterial segments, inclusion of the venous system in the model, key results, and conclusions. The standard form and individual study summaries are provided in the Supplementary Material.

Wang et al . explored the role of wave reflections and re-reflections in the systemic arterial system using a linearized 1D model of 55 large arteries - isolating the effect of arterial geometry on wave dynamics while simplifying the cardiac input and eliminating nonlinearities - to better understand the pressure and velocity waveforms in normal and pathological scenarios. The model was validated against in vivo and literature data. Their main findings include: (i) re-reflections at bifurcations are the main contributors to waveforms, (ii) their algorithm tracks waves precisely, and (iii) distal waveform changes and pathological alterations ( e.g. , occlusion and regurgitation) can be explained by wave behavior alone.^{( 8 )}

Westerhof et al. developed a distributed hemodynamic model of the human arterial tree that accounts for the developmental changes from newborns to adults. The model comprised 121 arterial segments, and compared simulated and in vivo measurements. The authors demonstrated that the peripheral pressure in children aged <5 years is approximately the central pressure and that the amplification and pulse wave velocity increased with age.^{( 9 )}

Alastruey et al. built a model to assess the accuracy of nonlinear 1D viscoelastic equations of pressure and flow wave propagation. The authors also explored a metric called the harmonic flow error, which refers to the difference between the simulated and measured harmonic components (i.e., frequency content) of blood flow waveforms. It was calculated by decomposing the flow signal into its frequency components using Fourier analysis and comparing the amplitude and phase of each harmonic. This error metric allows a detailed assessment of how accurately a model reproduces the shape and dynamics of pulsatile blood flow beyond simple mean flow or peak values. The model was based on 1D nonlinear time-domain viscoelastic equations and compared with in vitro measurements from a 1:1 replica of 37 conduit arteries with a simulated fluid mimicking blood. When compared with the purely elastic models, the model performed significantly better, with lower pressure (2.5% versus 3.0%, p<0.01), flow rate (10.8% versus 15.7%, p<0.01), and harmonic flow errors (3.3% versus 7.0%, p<0.01). They concluded that i) including wall viscoelasticity significantly improved the accuracy of 1D simulations, and ii) 1D viscoelastic modeling achieved a good balance between accuracy and computational cost.^{( 10 )}

Avolio presented a realistic, multi-branched 1D computational model of the entire human arterial system. This model accounted for wave propagation, impedance, and pathological states, such as arteriosclerosis and arterial stenosis. Using an arterial network of 128 segments, this model yielded accurate simulations of the pressure and flow dynamics in the circulatory tree, in agreement with the experimental data.^{( 11 )}

Bárdossy et al developed a 1D arterial model that incorporated the Stuart viscoelastic model to describe the mechanical behavior of arterial walls. This model accounted for three key components: instantaneous elasticity, capturing the immediate response of the wall to pressure; viscous damping, modeling energy dissipation and wave attenuation; and history-dependent deformation, which reflects the time-evolving strain response because of the viscoelastic nature of the vessel wall. This time-dependent component allowed the model to reproduce realistic arterial behavior under pulsatile flow, including wall hysteresis and the dynamic pressure-diameter relationship. The arterial network comprised 45 viscoelastic segments and successfully replicated physiological waveforms, such as backflow in the iliac arteries during diastole and the dicrotic notch in the aortic pressure curves. The model was also capable of simulating localized stenoses and their hemodynamic effects.^{( 12 )}

Blanco et al. devised this study to accurately define criteria for blood flow distribution in preparation for their detailed 1D arterial model (ADAN - anatomically detailed arterial network). They developed a numerical calibration algorithm to compute the terminal resistance, allowing their model of 2,142 arteries (1,598 arterial segments and 544 perforating arteries) to simulate the regional perfusion across 144 vascular beds (specific organs and territories). Their model provided a high-resolution arterial network with validated blood flow distribution criteria, accounted for specific and distributed perfusion using advanced anatomical data, and was suitable for regional hemodynamic studies and surgical planning.^{( 13 )}

Blanco et al. presented a detailed 1D computational model, ADAN, which was calibrated in their previous work.^{( 13 )} This is a model of the entire arterial system of an average adult male that integrates vascular anatomy, morphometry, wall mechanics, and hemodynamics. The model was validated against both generic physiological data and patient-specific measurements. The model featured 2,142 arteries and blood supply to 28 specific organs and 116 vascular territories, with arterial wall properties based on a viscoelastic model that includes collagen distribution in the walls. However, this model did not include the venous system. Pressure and flow waveforms matched in vivo measurements across the central and peripheral arteries, and the model produced cardiovascular indices, such as heart rate and cardiac output, all within normal ranges.^{( 6 )}

Blanco et al. further developed a simplified version of the ADAN model with 86 arterial segments (ADAN86), and compared its predictive capacity with that of the full model with >2,000 arteries. The model properties remained the same, and the reduced model was compared with the complete ADAN model and those in the literature. Although the ADAN86 model performed adequately under healthy conditions, it outperformed the full ADAN model in the simulations of pathological conditions.^{( 14 )}

Müller et al. presented a model derived from the ADAN framework, which was expanded to include the venous system. The resulting ADAVN (anatomically detailed arterial-venous network) model was a novel 1D closed-loop cardiovascular model that integrated the ultradetailed arterial network of the ADAN with a newly constructed venous network, emphasizing cerebral and coronary territories, and incorporated interactions with cerebrospinal fluid and cardiac mechanics to simulate both normal and pathological conditions. The model comprised 2,185 arterial segments and 189 veins and was validated by comparing the simulation results to hemodynamic data from previously published in vivo measurements. Although patient-specific geometries were not used, the model successfully reproduced physiologically realistic pressure and flow waveforms as well as cardiac indices within the expected clinical range.^{( 15 )}

Mynard et al . developed a model of the systemic and coronary circulation by integrating ventricular pressure, a dynamically modeled aortic valve, and regional coronary flow. The model included approximately 40 arterial segments (systemic and coronary) and was compared with published in vivo pressure and flow curves. The model produced realistic pressure and flow curves at multiple sites as well as realistic aortic valve mechanics.^{( 16 )}

Olufsen designed a study to improve the physiological accuracy of 1D models of large arteries by introducing a structured tree model at the distal ends of the arterial system, allowing wave propagation effects to persist beyond the truncated computational domain. This would better represent the downstream vasculature than the traditional lumped models. The model included 21 large arterial segments coupled with a structured tree outflow of approximately 17 generations each. This was validated against in vivo measurements. The model produced a feasible and physiologically consistent simulation that matched more accurately to in vivo data, accounting for wave propagation, impedance, and arterial-tissue coupling at the terminal level.^{( 17 )}

Schaaf et al.^{( 33 )} developed a nonlinear 1D model of arterial pulse wave transmission incorporating finite radial wall displacements. The model included 47 arterial segments, and the simulated pressure and flow curves at 14 sites along the arterial tree were compared with published data, showing a good match between the simulated and in vivo data. It demonstrated that nonlinear models improved realism over linear and lumped-parameter models.

Stergiopulos et al.^{( 34 )} developed a nonlinear 1D computer model of arterial circulation with 55 arterial segments and used it to investigate the hemodynamic effects of arterial and aortic stenoses. This was validated against published literature and ultrasonographic data, and the produced pressure and flow waveforms were comparable to in vivo measurements. The model also accurately reproduced the pulse pressure amplification from the aorta to the femur and the impact of stenoses on the flow, pressure, and pulsatility index.

Blanco et al . developed a closed-loop computational model of the entire cardiovascular system, incorporating 1D arterial models, the venous system as 0D compartments, and 3D geometry to simulate global and local hemodynamic conditions under physiological and pathological conditions. The model comprised 128 arterial segments and was validated against literature, producing realistic pressure and flow outputs. This model is suitable for simulating complex scenarios and their impact on regional hemodynamics ( e.g ., aneurysms). They also stressed the importance of arterial-venous-cardiac-pulmonary coupling.^{( 18 )}

Liang et al. developed a multiscale closed-loop model of the cardiovascular system by integrating a 1D arterial tree with a 0D lumped parameter model for the heart, pulmonary, and peripheral circulations. This model was used to investigate the effects of the aortic valve and arterial stenoses on global hemodynamics. It included 55 arterial segments with the heart and veins as 0D compartments. Furthermore, it produced realistic pressure and flow waveforms with adequate systolic amplification, and performed satisfactorily in simulated pathological situations.^{( 19 )}

Müller et al . presented a global, closed-loop, multiscale model of the human circulation with a detailed 1D description of both arterial and venous systems. The model also included 0D models of the heart, microcirculation, and pulmonary compartments. The model included 85 major arteries and 92 veins in 1D, and a 0D model of the capillaries, heart, and pulmonary compartments. It was validated against MRI-derived flow waveforms in the head and neck veins; literature-based data for arterial system waveforms and pressure flow; and in vitro and physiological data for wave speed, pressure-area relations, and venous collapse dynamics. The model produced robust wave simulations that were compatible with the validated methods.^{( 20 )}

Mynard et al . developed a 1D closed-loop model of the entire adult cardiovascular system that included detailed representations of systemic, pulmonary, coronary, and portal circulations. The circulatory 1D model was coupled with a lumped-parameter heart model that incorporated chamber interactions. It included 396 vessels (arteries and veins), 5,359 nodes, and 188 junctions, and was validated against in vivo published data. The model produced realistic pressure and flow curves and accurately captured wave reflections in arterial and venous circulation.^{( 21 )}

Reymond et al. built and validated a 1D model of the human systemic arterial tree, including the cerebral and coronary circulation, coupled with a 0D heart compartment. The model included 103 arterial segments and was validated in vivo using flow and pressure data from healthy young volunteers. It produced pressure and flow curves that closely matched the in vivo measurements, with a mean flow error of approximately 12% and a pressure error below 10% at most locations.^{( 22 )}

Safaei et al.^{( 32 )} proposed a comprehensive, open-source computational framework for simulating full-body cardiovascular circulation by integrating 1D, 0D, and 3D models to enable multiscale coupling with organ physiology and biomechanics. The model included 86 arterial segments of the ADAN86 model, along with 230 elements and 457 nodes, and partially incorporated the venous system. It was validated against published physiological data, and successfully reproduced realistic hemodynamic waveforms. Importantly, by relying predominantly on 1D and 0D modeling and reserving 3D components for localized regions, the framework achieved a significant reduction in computational processing time compared with full 3D simulations.

In table 2 , we present a comparison of strictly 1D models regarding their anatomical and physiological fidelity, validation methods, as well as their strengths, and limitations.

Table 2

Author (year)	Anatomical fidelity	Physiological fidelity	Validation method	Strengths	Limitations
Alastruey et al. (2011)(10)	Medium-high	High	In vitro + comparison with elastic model	Pulse wave analysis, viscoelastic effects	Limited network size, no venous system
Blanco et al. (2015)(6)	Very high	High	Anatomical + literature consistency	Detailed anatomical coverage, parametric flexibility	Complex setup, limited in vivo validation
Müller et al. (2023)(15)	Very high	Very high	Anatomical + integrated physiology	Closed-loop, detailed arterial-venous network	High computational demand, limited clinical data
Reymond et al. (2009)(22)	High	High	In vivo (pressure, velocity)	Validated with real data, good wave behavior	No venous system, smaller network than Müller
Westerhof et al. (2020)(9)	High	High	Developmental physiology literature	Covers full age range (0-20 y), good clinical correlation	No venous network, simplified peripheral modeling

This study has some limitations. First, the models were heterogeneous, and some articles failed to elucidate which arterial segments were included, why they were included, and how they were modeled. Second, these articles were published over a wide timespan, from the early 1970s to 2023. With regard to computational capacity, scientific research in 1972 relied on mainframe computers, which were large, expensive, and limited in capacity and availability. For instance, a PDP-12 mainframe in 1972 had its memory capacity measured in megabytes with a computational power of approximately 0.01 MIPS (million instructions per second), whereas modern day workstations have their memory capacities measured in petabytes, and an Apple M2 chip has a computational power of approximately 370,000 MIPS. Third, the models were not directly compared, except for ADAN and its reduced version, ADAN86,^{( 14 )}which makes multilateral comparisons almost not feasible.