Optimization of topological complexity for one-dimensional arterial blood flow models.

Fredrik E Fossan,Jorge Mariscal-Harana,Jordi Alastruey,Leif R Hellevik

doi:10.1098/rsif.2018.0546

Abstract

As computational models of the cardiovascular system are applied in modern personalized medicine, maximizing certainty of model input becomes crucial. A model with a high number of arterial segments results in a more realistic description of the system, but also requires a high number of parameters with associated uncertainties. In this paper, we present a method to optimize/reduce the number of arterial segments included in one-dimensional blood flow models, while preserving key features of flow and pressure waveforms. We quantify the preservation of key flow features for the optimal network with respect to the baseline networks (a 96-artery and a patient-specific coronary network) by various metrics and quantities like average relative error, pulse pressure and augmentation pressure. Furthermore, various physiological and pathological states are considered. For the aortic root and larger systemic artery pressure waveforms a network with minimal description of lower and upper limb arteries and no cerebral arteries, sufficiently captures important features such as pressure augmentation and pulse pressure. Discrepancies in carotid and middle cerebral artery flow waveforms that are introduced by describing the arterial system in a minimalistic manner are small compared with errors related to uncertainties in blood flow measurements obtained by ultrasound.

Highlights

Computational models of the cardiovascular system are commonly separated into three-dimensional (3D), one-dimensional (1D) and lumped models (0D)
We have presented a novel approach which optimizes the number of arterial segments for 1D blood flow models
Our results have shown that to capture important features of the aortic pressure waveform, such as timing and shape of reflected waves, pressure augmentation and pulse pressure, a model with all aortic segments, but close to minimal description of the head and lower and upper limb arteries is sufficient

Summary

Introduction

Computational models of the cardiovascular system are commonly separated into three-dimensional (3D), one-dimensional (1D) and lumped models (0D). The most important drawback of the family of 0D models is inherent in the assumption of infinite wave velocity and that spatially distributed parameters are modelled as single point parameters. In [4,5], the systemic circulation was modelled as two asymmetric parallel branches, one supplying the head and upper limbs, and one supplying the rest of the body. In [6], a model consisting of the 33 largest systemic arteries was tested using an in vitro experiment. In [8], a complete description of the systemic arterial tree containing the largest arteries of the head and upper and lower body was validated using in vivo measurements. The study includes a detailed overview of 1D models up until 2009, highlighting their variation in detail and complexity. In [9], a model accounting for pulse wave

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Discussion

Conclusion