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

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.

Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks

“…The above system of equations must be satisfied at any interface, which is achieved by the second term in the loss function in equation (9) that forces the model to respect the conservation laws. Finally, the non-dimensional equations (15), (16), (17) and (18) define the optimization objectives that are used in equation (9) for minimizing the residual at the collocation, bifurcation and measurement points respectively. As mentioned above, we have to multiply the predictions of the network by the scaling parameters p =pp 0 , u =ûU and A =ÂA 0 , when doing inference or else we get a scaled version of the solutions.…”

“…Using the discovered three-element Windkessel model parameters we can employ a conventional Discontinuous Galerkin solver to infer the velocity within the arterial network, and compare these with results against the reference measurements and the neural network model predictions. For the DG simulation, we choose the blood density to be equal to 1060 Kg/m 3 and the viscosity 3.5 mPas [15]. Moreover, we provide the DG solver with the Windkessel and structural parameters introduced in table (9).…”

High precision invasive FFR, low‐cost invasive iFR, or non‐invasive CFR?: optimum assessment of coronary artery stenosis based on the patient‐specific computational models

“…In order to achieve this goal, LPM has been used as a realistic patient-specific model of the left coronary arteries in many works. 42,[49][50][51][52][53] The LPM model proposed by Kim et al 42 was used in the present study. This model is illustrated in Figure 3, and the ODE equation of the model is as follows:…”

Personalized Hemodynamic Modeling of the Human Cardiovascular System: A Reduced-Order Computing Model

“…In recent years, patient-specific 0-1D modeling has attracted many researchers' interests due to its potential clinical applications. Fossan et al [17] made a reduced-order model by converting parts of 1D segments to 0D Windkessel (WK) model to realize the personalized modeling. Blanco et al [18] made manual adjustment of vascular wall parameters to achieve a good match between the 1D model-based pressure waveforms and the measurements of a specific patient.…”