Research

The development of anatomically accurate and highly detailed networks of vessels to perform 1D blood flow simulations involving wave propagation phenomena is of the utmost importance for the correct assessment of coarse and fine hemodynamics interactions throughout the entire cardiovascular system. In fact, models of this kind can be effectively used as auxiliary tools to understand underlying mechanisms of certain cardiovascular diseases as well as in the diagnosis and surgical planning. The ADAN (Anatomically Detailed Arterial Network) model developed by the HeMoLab group is the largest arterial network currently available, comprising all the arterial vessels acknowledged in the specialized literature. For such network specific numerical methods have been devised. The ADAN model can be coupled to 3D blood flow models to account for local-global hemodynamic interactions. Currently, it is being extended to incorporate the venous network to model arterio-venous interactions, as well as to account for autoregulatory mechanisms and transport of species among other phenomena.

Pressure propagation throughout the entire arterial network in the healthy condition (left) and in the case of aortic coarctation (right).

Three-dimensional hemodynamics simulations help to understand extremely fine mechanisms underlying blood-wall interactions, and the impact on flow disturbances, endothelial function and arterial wall damage, among other phenomena. Models of this kind can be applied to study the risk of rupture in the arterial wall, with implications in aneurysm rupture and thrombosis. In the HeMoLab group, we are concerned with performing realistic 3D fluid-structure simulations. This implies considering for the 3D models proper preload and prestress conditions of the arterial wall, blood wall interactions in the finite strain kinematical regime, proper flow boundary conditions through the coupling with 1D models, histologically-based constitutive equations and the effect of external tissues. Currently, we are interested in the integration of all these aspects to accurately assess the differential impact on the mechanical state and damage produced in the arterial walls, towards studying tissue rupture.

Preload (due to baseline pressure) and prestress (due to prestretch) processes (left) and blood flow FSI simulation (right) of a carotid bifurcation embedded in a 1D model of the arterial network.

Numerical methods to couple in an efficient way models of different dimensionality (for instance 1D and 3D blood flow models) are fundamental for the partitioned and parallel solution of coupled simulations. At the HeMoLab group we have developed specific iterative coupling methods to robustly and efficiently address this problem, allowing to solve in a fully parallel manner, for example, a 1D arterial network and the 3D models (with a further inner level of parallelism) embedded in it.

Coupled blood flow simulation of the entire aorta artery and its main branches and a 1D model of the arterial network (top), and number of coupling iterations at each time step (bottom).

Finite volume-based numerical methods can be employed in order to solve 1D blood flow equations in highly complex networks as well as eventual transport of species in the blood flow in an accurate, robust and computationally cheap manner. At the HeMoLab group, we have developed and implemented high order finite volume methods for the approximate solution of 1D blood flow, incorporating nonlinear terms introduced by collagen fibers and viscoelasticity of the arterial wall. In addition, high order methods for the treatment of junctions have also been developed for a consistent high order approach to the problem. These methods are fundamental tools for the numerical simulations involving the ADAN model.

The correct treatment of coupling conditions for vessels with viscoelastic mechanical properties is the subject of current research. A common practice is to assume elastic material properties in correspondence of the point where vessels are connected. The figure shows pressure (left) and flow rate (right) for a simple network of two viscoelastic vessels. The black line shows the reference solution, obtained by considering a single vessel, while the dashed line represents the interface between the two vessels. Blue crosses show the solution obtained assuming elastic vessel properties and a first order coupling strategy. Finally, red circles show the computational results for the case in which the coupling strategy takes into account viscoelastic properties and maintains the formal order of accuracy of the numerical scheme employed in the 1D domain.

The cardiovascular system response is actually the result the response of several coupled systems acting as a functional physiological unit ensemble. From the interaction with the respiratory system to the subordination to autoregulatory systems, global and local hemodynamics conditions are highly dependent on the resulting homeostatic functional point. At the HeMoLab, we are interested in the coupling of blood circulation and gas transport in the system, as well as with short and mid term control mechanisms to account for most of the cardiovascular scenarios. A rational approach is pursued, by employing building blocks which can be substituted by even more complex mathematical representations, ultimately reaching an integrated anatomically and functionally detailed physiological model.

Closed-loop self-regulated model of the cardiovascular system including mathematical descriptions for baroreflex and chemoreflex control mechanisms. Data obtained from integrated and increasingly complex physiological models are physiologically compatible and are used to predict the behavior of cardiovascular variables under different pathophysiologcal scenarios, such as haemorrhage, valvular insufuciency or aneurysms.
Donwload: Model of the cardio respiratory system – Trenhago et al., 2015 (in press)

Arterial networks involving small vessels impose severe restrictions regarding the data acquisition and construction. To circumvent this, automatic generation of vascular networks is a strategy to create statistically meaningful models either to provide termination conditions in arterial vessels as well as to study in detail hemodynamic conditions in peripheral regions. At the HeMoLab, we have developed Constrained Constructive Optimization based algorithms to generate networks of vessels in vascular territories of arbitrary shape and with an arbitrary number of feeding arteries.

Arterial networks generated within a vascular territory in the upper limb.

Computed tomography medical image are fundamental datasets for the patient-specific characterization of anatomical structures of interest. In computational hemodynamics, proper processing and segmentation are of the utmost importance for the extraction of vessels surfaces and volumes towards the characterization of geometrical indexes and the subsequent use in blood flow simulations. At the HeMoLab we are concerned with robust methods based on level-sets methods for the filtering and segmentation of coronary and cerebral computed tomography images to feed patient-specific models to perform blood flow simulations and assess risk of miocardial infarction and risk of aneurysm rupture, respectively.
Segmentation of computed tomography images of the coronary tree and of brain arteries:
Coronary Segmentations
This video illustrates the segmentation process from a coronary computed tomography angiography (CCTA). Showing segmentations of the main coronary arteries, calcium structures in the LAD and LCx arteries, and the left ventricle.

Cerebral Aneurysm Segmentation
This video illustrates the segmentation process from a computed tomography angiography (CTA) of the brain. Showing segmentations of the RCA, partial Circle of Willis and MCA, a giant aneurysm on distal the RCA is present.

Intravascular ultrasound images are the gold standard for the image-based assessment of coronary diseases due to the large amount of data and high resolution provided for the transversal sections of coronary vessels. These images feature several artifact from the ultrasound nature as well as from external stimuli (respiration, cardiac motion, catheter motion, etc.). From image gating, going through image registration and segmentation, and finally wall motion quantification, at the HeMoLab we are interested in the entire pipeline to reach, from the medical dataset, by combination with angiographic images, accurate patient-specific physical models involving fluid and solid mechanics, as the bases to develop algorithms for in vivo tissue characterization.

Workflow for the vessel reconstruction combining angiographies with intravascular ultrasound.

Reconstructed vessel geometry visualizing the endothelium (red surface) and the external elastic membrane (gray surface).

There is increasing need for fast blood flow simulations. This need is supplied by approximation strategies, through the creation of problem specific basis functions, which take into account the very nature of the problem. This would allow practitioners to perform simulations in a timely manner while maintaining accuracy in wall shear stress and pressure drop predictions. At the HeMoLab, we are concerned with the development of spectral/finite element hybrid approximations for flow simulations taking advantage of the pipe-like domains as an in-between approach between expensive traditional 3D models and cheap, but incomplete, 1D models.


Flow in a bifurcation computed using the hybrid approximation method (left) and the standard finite element method (right)

The constitutive behavior of complex biological tissues is quite complex in terms of the micro-mechanical interactions that ultimately give rise to a certain macroscopic observable response. A rational approach to address this problem is through the use of constitutive multiscale models. At the HeMoLab, we have developed a variational framework based on the principle of virtual power for the development of complex multiscale models. This framework is being currently used for the multiscale mechanical analysis of soft tissues, with special attention in the mechanisms behind tissue rupture.

Mechanical analysis of microstructure localization in the internal elastic lamina as the result of tissue damage mechanisms. The elipses pores are randomly distributed and the RVE is subjected incrementally to a axial incompressible strecht.