Pablo J. Blanco

A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling

Haemodynamical simulations using one-dimensional (1D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. Recent interest in verifying 1D numerical schemes has led to the development of alternative experimental setups and the use of three-dimensional numerical models to acquire data not easily measured in vivo. In most studies to date, only one particular 1D scheme is tested. In this paper, we present a systematic comparison of six commonly used numerical schemes for 1D blood flow modelling: discontinuous Galerkin, locally conservative Galerkin, Galerkin least-squares finite element method, finite volume method, finite difference MacCormack method and a simplified trapezium rule method. Comparisons are made in a series of six benchmark test cases with an increasing degree of complexity. The accuracy of the numerical schemes is assessed by comparison with theoretical results, three-dimensional numerical data in compatible domains with distensible walls or experimental data in a network of silicone tubes. Results show a good agreement among all numerical schemes and their ability to capture the main features of pressure, flow and area waveforms in large arteries. All the information used in this study, including the input data for all benchmark cases, experimental data where available and numerical solutions for each scheme, is made publicly available online, providing a comprehensive reference data set to support the development of 1D models and numerical schemes.

Blood flow distribution in an anatomically detailed arterial network model: criteria and algorithms

Development of blood flow distribution criteria is a mandatory step toward developing computational models and numerical simulations of the systemic circulation. In the present work, we (i) present a systematic approach based on anatomical and physiological considerations to distribute the blood flow in a 1D anatomically detailed model of the arterial network and (ii) develop a numerical procedure to calibrate resistive parameters in terminal models in order to effectively satisfy such flow distribution. For the first goal, we merge data collected from the specialized medical literature with anatomical concepts such as vascular territories to determine blood flow supply to specific (encephalon, kidneys, etc.) and distributed (muscles, skin, etc.) organs. Overall, 28 entities representing the main specific organs are accounted for in the detailed description of the arterial topology that we use as model substrate. In turn, 116 vascular territories are considered as the basic blocks that compose the distributed organs throughout the whole body. For the second goal, Windkessel models are used to represent the peripheral beds, and the values of the resistive parameters are computed applying a Newton method to a parameter identification problem to guarantee the supply of the correct flow fraction to each terminal location according to the given criteria. Finally, it is shown that, by means of the criteria developed, and for a rather standard set of model parameters, the model predicts physiologically realistic pressure and flow waveforms.

Identification of vascular territory resistances in one-dimensional hemodynamics simulations

The present work deals with the parameter identification problem in outflow models used in one-dimensional simulations of arterial blood flow. Specifically, the resistive elements that define the models used to account for the blood supply to the vascular territories in arterial networks are computed by solving a system of non-linear equations using a Broyden method. This strategy is employed to compute the terminal parameters in the vascular territories of an anatomically detailed model of the arm comprising 67 arterial segments and 16 vascular territories. A comparison with a simple analytical approach, in terms of vascular territory resistances, average blood flows and time-dependent hemodynamic quantities, is performed. Also, a sensitivity analysis is presented to assess the performance of this new approach in normal and abnormal cardiovascular scenarios. This identification procedure allows to correctly set up hemodynamics simulations in highly detailed arterial networks making possible to gain insight in the aspects related to the blood circulation in arterial vessels.

A computational approach to generate concurrent arterial networks in vascular territories

In this work, a computational procedure is proposed to vascularize anatomical regions supplied by many inflow sites. The proposed methodology creates a partition of the territory to be vascularized into nonoverlapping subdomains that are independently supplied by the so-called perforator arteries (inflow sites). Then, in each subdomain, the constrained constructive optimization method is used to generate a network of vessels. The identification of subdomains in a certain vascular territory perfused by many perforator arteries turns out to be a fundamental problem towards understanding the morphological conformation of peripheral beds in the cardiovascular system. The methodology is assessed through two academic examples showing the main structural features of the so-defined vascular territory partition and the corresponding arterial networks. In addition, the vascularization of a three-dimensional sheet-like tissue is presented with potential application in flap planning and design.

Blood pressure gradients in cerebral arteries: a clue to pathogenesis of cerebral small vessel disease

Rationale The role of hypertension in cerebral small vessel disease is poorly understood. At the base of the brain (the ‘vascular centrencephalon’), short straight arteries transmit blood pressure directly to small resistance vessels; the cerebral convexity is supplied by long arteries with many branches, resulting in a drop in blood pressure. Hypertensive small vessel disease (lipohyalinosis) causes the classically described lacunar infarctions at the base of the brain; however, periventricular white matter intensities (WMIs) seen on MRI and WMI in subcortical areas over the convexity, which are often also called ‘lacunes’, probably have different aetiologies. Objectives We studied pressure gradients from proximal to distal regions of the cerebral vasculature by mathematical modelling. Methods and results Blood flow/pressure equations were solved in an Anatomically Detailed Arterial Network (ADAN) model, considering a normotensive and a hypertensive case. Model parameters were suitably modified to account for structural changes in arterial vessels in the hypertensive scenario. Computations predict a marked drop in blood pressure from large and medium-sized cerebral vessels to cerebral peripheral beds. When blood pressure in the brachial artery is 192/113 mm Hg, the pressure in the small arterioles of the posterior parietal artery bed would be only 117/68 mm Hg. In the normotensive case, with blood pressure in the brachial artery of 117/75 mm Hg, the pressure in small parietal arterioles would be only 59/38 mm Hg. Conclusion These findings have important implications for understanding small vessel disease. The marked pressure gradient across cerebral arteries should be taken into account when evaluating the pathogenesis of small WMIs on MRI. Hypertensive small vessel disease, affecting the arterioles at the base of the brain should be distinguished from small vessel disease in subcortical regions of the convexity and venous disease in the periventricular white matter.

Improving Cardiac Phase Extraction in IVUS Studies by Integration of Gating Methods

Goal: Coronary intravascular ultrasound (IVUS) is a fundamental imaging technique for atherosclerotic plaque assessment. However, volume-based data retrieved from IVUS studies can be misleading due to the artifacts generated by the cardiac motion, hindering diagnostic, and visualization of the vessel condition. Then, we propose an image-based gating method that improves the performance of the preexisting methods, delivering a gating in an appropriate time for clinical practice. Methods: We propose a fully automatic method to synergically integrate motion signals from different gating methods to improve the cardiac phase estimation. Additionally, we present a local extrema identification method that provides a more accurate extraction of a cardiac phase and, also, a scheme for multiple phase extraction mandatory for elastography-type studies. Results: A comparison with three state-of-the-art methods is performed over 61 in-vivo IVUS studies including a wide range of physiological situations. The results show that the proposed strategy offers: 1) a more accurate cardiac phase extraction; 2) a lower frame oversampling and/or omission in the extracted phase data (error of 1.492 ± 0.977 heartbeats per study, mean ± SD); 3) a more accurate and robust heartbeat period detection with a Bland-Altman coefficient of reproducibility (RPC) of 0.23 s, while the second closest method presents an RPC of 0.36 s. Significance: The integration of motion signals performed by our method shown an improvement of the gating accuracy and reliability.

HeMoLab - Hemodynamics Modelling Laboratory

In this work we present HeMoLab (Hemodynamics Modeling Laboratory), a computational environment for modeling the Human Cardiovascular System. Its integrates novel computational tools, running from medical image processing to numerical simulation and visualization. As a simulation tool, it allows to accommodate complex physiological and/or pathophysiological (virtual) scenarios aimed to retrieve detailed information from the numerical computations. Such application makes possible to speed up research in the study and analysis of the cardiovascular system and, to provide a virtual laboratory for medical training and education, and specialized Human Resources development. In order to demonstrate the modeling and simulation capabilities of HeMoLab some cases of use are presented.

A computational framework to characterize and compare the geometry of coronary networks

This work presents a computational framework to perform a systematic and comprehensive assessment of the morphometry of coronary arteries from in vivo medical images. The methodology embraces image segmentation, arterial vessel representation, characterization and comparison, data storage, and finally analysis. Validation is performed using a sample of 48 patients. Data mining of morphometric information of several coronary arteries is presented. Results agree to medical reports in terms of basic geometric and anatomical variables. Concerning geometric descriptors, inter-artery and intra-artery correlations are studied. Data reported here can be useful for the construction and setup of blood flow models of the coronary circulation. Finally, as an application example, similarity criterion to assess vasculature likelihood based on geometric features is presented and used to test geometric similarity among sibling patients. Results indicate that likelihood, measured through geometric descriptors, is stronger between siblings compared with non-relative patients. Copyright

Roadmap for cardiovascular circulation model.

Computational models of many aspects of the mammalian cardiovascular circulation have been developed. Indeed, along with orthopaedics, this area of physiology is one that has attracted much interest from engineers, presumably because the equations governing blood flow in the vascular system are well understood and can be solved with well‐established numerical techniques. Unfortunately, there have been only a few attempts to create a comprehensive public domain resource for cardiovascular researchers. In this paper we propose a roadmap for developing an open source cardiovascular circulation model. The model should be registered to the musculo‐skeletal system. The computational infrastructure for the cardiovascular model should provide for near real‐time computation of blood flow and pressure in all parts of the body. The model should deal with vascular beds in all tissues, and the computational infrastructure for the model should provide links into CellML models of cell function and tissue function. In this work we review the literature associated with 1D blood flow modelling in the cardiovascular system, discuss model encoding standards, software and a model repository. We then describe the coordinate systems used to define the vascular geometry, derive the equations and discuss the implementation of these coupled equations in the open source computational software OpenCMISS. Finally, some preliminary results are presented and plans outlined for the next steps in the development of the model, the computational software and the graphical user interface for accessing the model.

On the search of more stable second-order lattice-Boltzmann schemes in confined flows

The von Neumann linear analysis, restricted by a heuristic selection of wave-number vectors was applied to the search of explicit lattice Boltzmann schemes which exhibit more stability than existing methods. The relative stability of the family members of quasi-incompressible collision kernels, for the Navier-Stokes equations in confined flows, was analyzed. The linear stability analysis was simplified by assuming a uniform velocity level over the whole domain, where only the wave numbers of the first harmonic normal to the flow direction were permitted. A singular equilibrium function that maximizes the critical velocity level was identified, which was afterwards tested in particular cases of confined flows of interest, validating the resulting procedure.