Analog studies of the human systemic arterial tree.

A distributed model of the human arterial tree including all main systemic arteries coupled to a heart model is developed. The one-dimensional (1-D) form of the momentum and continuity equations is solved numerically to obtain pressures and flows throughout the systemic arterial tree. Intimal shear is modeled using the Witzig-Womersley theory. A nonlinear viscoelastic constitutive law for the arterial wall is considered. The left ventricle is modeled using the varying elastance model. Distal vessels are terminated with three-element windkessels. Coronaries are modeled assuming a systolic flow impediment proportional to ventricular varying elastance. Arterial dimensions were taken from previous 1-D models and were extended to include a detailed description of cerebral vasculature. Elastic properties were taken from the literature. To validate model predictions, noninvasive measurements of pressure and flow were performed in young volunteers. Flow in large arteries was measured with MRI, cerebral flow with ultrasound Doppler, and pressure with tonometry. The resulting 1-D model is the most complete, because it encompasses all major segments of the arterial tree, accounts for ventricular-vascular interaction, and includes an improved description of shear stress and wall viscoelasticity. Model predictions at different arterial locations compared well with measured flow and pressure waves at the same anatomical points, reflecting the agreement in the general characteristics of the "generic 1-D model" and the "average subject" of our volunteer population. The study constitutes a first validation of the complete 1-D model using human pressure and flow data and supports the applicability of the 1-D model in the human circulation.

/pdf/validation-of-a-one-dimensional-model-of-the-systemic-1wtkdon8he.pdf

Validation of a one-dimensional model of the systemic arterial tree.

A model of the human arterial system was constructed based on the anatomical branching structure of the arterial tree. Arteries were divided into segments represented by uniform thin-walled elastic tubes with realistic arterial dimensions and wall properties. The configuration contains 128 segments accounting for all the central vessels and major peripheral arteries supplying the extremities including vessels of the order of 2·0 mm diameter. Vascular impedance and pressure and flow waveforms were determined at various locations in the system and good agreement was found with experimental measurements. Use of the model is illustrated in investigating wave propagation in the arterial system and in simulation of arterial dynamics in such pathological conditions as arteriosclerosis and presence of a stenosis in the femoral artery.

/pdf/multi-branched-model-of-the-human-arterial-system-4yp3q9bwgz.pdf

Multi-branched model of the human arterial system

The objective of this study is to develop a model of the cardiovascular system capable of simulating the short-term (< or = 5 min) transient and steady-state hemodynamic responses to head-up tilt and lower body negative pressure. The model consists of a closed-loop lumped-parameter representation of the circulation connected to set-point models of the arterial and cardiopulmonary baroreflexes. Model parameters are largely based on literature values. Model verification was performed by comparing the simulation output under baseline conditions and at different levels of orthostatic stress to sets of population-averaged hemodynamic data reported in the literature. On the basis of experimental evidence, we adjusted some model parameters to simulate experimental data. Orthostatic stress simulations are not statistically different from experimental data (two-sided test of significance with Bonferroni adjustment for multiple comparisons). Transient response characteristics of heart rate to tilt also compare well with reported data. A case study is presented on how the model is intended to be used in the future to investigate the effects of post-spaceflight orthostatic intolerance.

https://www.physiology.org/doi/pdf/10.1152/japplphysiol.00241.2001

Computational modeling of cardiovascular response to orthostatic stress

Zero-dimensional (lumped parameter) and one dimensional models, based on simplified representations of the components of the cardiovascular system, can contribute strongly to our understanding of circulatory physiology. Zero-D models provide a concise way to evaluate the haemodynamic interactions among the cardiovascular organs, whilst one-D (distributed parameter) models add the facility to represent efficiently the effects of pulse wave transmission in the arterial network at greatly reduced computational expense compared to higher dimensional computational fluid dynamics studies. There is extensive literature on both types of models. The purpose of this review article is to summarise published 0D and 1D models of the cardiovascular system, to explore their limitations and range of application, and to provide an indication of the physiological phenomena that can be included in these representations. The review on 0D models collects together in one place a description of the range of models that have been used to describe the various characteristics of cardiovascular response, together with the factors that influence it. Such models generally feature the major components of the system, such as the heart, the heart valves and the vasculature. The models are categorised in terms of the features of the system that they are able to represent, their complexity and range of application: representations of effects including pressure-dependent vessel properties, interaction between the heart chambers, neuro-regulation and auto-regulation are explored. The examination on 1D models covers various methods for the assembly, discretisation and solution of the governing equations, in conjunction with a report of the definition and treatment of boundary conditions. Increasingly, 0D and 1D models are used in multi-scale models, in which their primary role is to provide boundary conditions for sophisticate, and often patient-specific, 2D and 3D models, and this application is also addressed. As an example of 0D cardiovascular modelling, a small selection of simple models have been represented in the CellML mark-up language and uploaded to the CellML model repository http://models.cellml.org/
 . They are freely available to the research and education communities. Each published cardiovascular model has merit for particular applications. This review categorises 0D and 1D models, highlights their advantages and disadvantages, and thus provides guidance on the selection of models to assist various cardiovascular modelling studies. It also identifies directions for further development, as well as current challenges in the wider use of these models including service to represent boundary conditions for local 3D models and translation to clinical application.

/pdf/review-of-zero-d-and-1-d-models-of-blood-flow-in-the-4ollfgzfpg.pdf

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

The use of an analog computer in a circulation model.

On-line processing of orthogonal exercise electrocardiograms.

Left ventricular systolic stiffness was measured by rapidly changing ventricular volume (within 7 ms) of isovolumically contracting isolated rabbit hearts. Instantaneous pressure-volume relations were found to be linear with slopes that depended upon the moment during contraction at which the volume change was induced. These slopes were proportional to the total pressure developed in the ventricle just prior to the volume change. The same was found when the time course of pressure was influenced by changing the Ca++ content of the perfusate. An influence, however, also could be detected when end-diastolic volume was changed. At the same pre-release pressure a greater volume caused a decrease of active stiffness. The results indicate the possiblity of an active component in ventricular systolic stiffness.

/pdf/left-ventricular-active-stiffness-dependency-on-time-and-hbxcz34gop.pdf

Left ventricular active stiffness: dependency on time and inotropic state.

Left ventricles of rabbit hearts were subjected to series of quick volume releases (QVR) — taking placw within 6 ms — applied at fixed times in the cardiac cycle. The hearts were paced artificially and allowed to contract isovolumically. The QVR was used as a tool for realizing predetermined pressure values at any time during the ascending limb of the intra-ventricular pressure curve. Any desired pressure could be attained by suitable choice of the QVR amplitude. By relatingdP/dt values occuring immediately after the QVR to the pressure attained by the QVR for different QVR amplitudes, instantaneousdP/dt relations were obtained. Time effects on these relations were studied by repeating the QVR series with increasing amplitudes at different but constant times. Influences of volume and contractile state were examined by varying end diastolic pressure (EDP) and the perfusate [Ca2+]. The data were fitted with adP/dt-P relation derived from the Hill equation using a simple geometric model of the ventricle and a two element model of the myocardium. The experimental relations were described adequately by the model. The parameters in the Hill equation estimated for heart muscle were compared to those previously reported on heart muscle experiments. Parameter values obtained were:a/F0: 0.001–1.3;F0 (mean maximal force forVCE=0): 12.2-3.5 N;b: 1.7–13.2 cm/s.F0 rises at the beginning of systole and shows a plateau from ca. 60–100% time of peak pressure. This time course was influenced by changes in EDP and [Ca2+]. Parameterb exhibits a time course comparable to that of ventricular pressure. It was not influenced by EDP changes and only slightly increased by an increase in [Ca2+].

/pdf/left-ventricular-force-velocity-relations-measured-from-23klkshwpm.pdf

Herman B. K. Boom

Papers

The use of an analog computer in a circulation model.

On-line processing of orthogonal exercise electrocardiograms.

Left ventricular active stiffness: dependency on time and inotropic state.

Left ventricular force-velocity relations measured from quick volume changes