Final Report Summary - MATHCARD (Mathematical Modelling and Simulation of the Cardiovascular System)
This project aimed at developing mathematical and numerical models for simulations in life science. Specifically, the target was the development, analysis, and implementation of mathematical tools to efficiently simulate the human cardiovascular system. Indeed, our ultimate goal was the setting up of a numerical procedure suitable to provide physicians with complementary and auxiliary elements to support them in the diagnosis and/or treatment of diseases, as well as in the planning of surgical procedures. Along this line, we have developed an integrated approach whose basic constituents and outcomes are outlined below.
Setup of Mathematical Models for the Cardiovascular System.
We have developed a new geometric multiscale paradigm for the different components of the circulatory system (0D, 1D and 3D) and the set up of appropriate numerical iteration schemes for their nonlinear interface coupling. We have introduced new monolithic and partitioned solvers with parallel preconditioners and novel coupling techniques for the solution of the computationally expensive 3D fluid-structure-interaction (FSI) problems that describe the coupling between blood flows and wall deformations in large arterial vessels. Moreover, we have proposed and investigated models for the cerebrovascular and cerebrospinal dynamics through the coupling of blood vessels, brain parenchyma, and cerebrospinal fluid.
Mathematical Models of the Interaction between Circulation, Tissues Perfusion, Biochemical and Thermal Regulation.
The processes underlying the interaction between metabolism and circulation feature a multiscale nature: although metabolism takes place in cells, it modifies the hemodynamics of peripheral (capillaries) and central (heart) circulation. In this respect, we have set up a hierarchy of models, corresponding to such different scales, based on a compartmental model of the whole-body response to variations in the skeletal muscle metabolism.
Modelling Electrical Activity and Wall Mechanics of the Heart.
We have addressed the mathematical modeling and numerical implementation of the coupling between the propagation of electric potential and the nonlinear mechanical deformation of the heart ventricles, using both the active strain and the active stress approaches. Other significant areas of studying included local kinetics and active shear deformation of isolated cardiomyocytes, whose functioning is responsible for the correct electromechanical behavior of the heart. A preliminary study of the blood flow inside the left ventricle was performed by using the electromechanical activation of the muscle as driving force.
Efficient Methods for Control and Optimisation.
Model order reduction (MOR) techniques have been developed to set up an efficient framework to tackle shape optimization problems in presence of complex parameterized geometries, such as those involving coronary or aortic by-passes. Thanks to MOR techniques, we have also obtained reduced FSI models which enable to drop the computational time by 5 orders of magnitude when considering three dimensional by-pass configurations.
The numerical problems addressed in MATHCARD have been implemented in the parallel finite element library LifeV, distributed under the LGPL license. The release process has been made straightforward by publication on GitHub (https://github.com/lifev/lifev). Several substantial improvements have been made in LifeV in the course of the project, by enhancing its modularity, configuring, compiling, and integrating the parallel linear algebra library Trilinos.
In the course of the MATHCARD project, we have remarkably enhanced our understanding of the mathematical aspects and related numerical approximation techniques behind the modeling of the cardiovascular system. This has allowed us to substantially intensify our interactions with bio-engineers and medical doctors for successfully addressing and solving problems of clinical relevance. In this respect, new collaborations have been established with Fondazione IRCCS Cà Granda, the Sacco Hospital, and Niguarda Hospital - all in Milan (Italy) - for setting up a protocol to obtain velocity (Doppler), MRI and CT data from patients. This was aimed at the analysis of flow-field in the atherosclerotic carotid arteries and cerebral aneurisms. In collaboration with the Hospital Borgo Trento of Verona (Italy), we have investigated the outflow jet stream behind bicuspid or stentless aortic valves and its impact on the formation of aneurisms in the aortic root. Together with CHUV (University Hospital in Lausanne, Switzerland) we have analyzed the optimal design of the connecting outflow cannula of left ventricular assist devices (LVAD).
Further insights at http://www.mathcard.eu/
Setup of Mathematical Models for the Cardiovascular System.
We have developed a new geometric multiscale paradigm for the different components of the circulatory system (0D, 1D and 3D) and the set up of appropriate numerical iteration schemes for their nonlinear interface coupling. We have introduced new monolithic and partitioned solvers with parallel preconditioners and novel coupling techniques for the solution of the computationally expensive 3D fluid-structure-interaction (FSI) problems that describe the coupling between blood flows and wall deformations in large arterial vessels. Moreover, we have proposed and investigated models for the cerebrovascular and cerebrospinal dynamics through the coupling of blood vessels, brain parenchyma, and cerebrospinal fluid.
Mathematical Models of the Interaction between Circulation, Tissues Perfusion, Biochemical and Thermal Regulation.
The processes underlying the interaction between metabolism and circulation feature a multiscale nature: although metabolism takes place in cells, it modifies the hemodynamics of peripheral (capillaries) and central (heart) circulation. In this respect, we have set up a hierarchy of models, corresponding to such different scales, based on a compartmental model of the whole-body response to variations in the skeletal muscle metabolism.
Modelling Electrical Activity and Wall Mechanics of the Heart.
We have addressed the mathematical modeling and numerical implementation of the coupling between the propagation of electric potential and the nonlinear mechanical deformation of the heart ventricles, using both the active strain and the active stress approaches. Other significant areas of studying included local kinetics and active shear deformation of isolated cardiomyocytes, whose functioning is responsible for the correct electromechanical behavior of the heart. A preliminary study of the blood flow inside the left ventricle was performed by using the electromechanical activation of the muscle as driving force.
Efficient Methods for Control and Optimisation.
Model order reduction (MOR) techniques have been developed to set up an efficient framework to tackle shape optimization problems in presence of complex parameterized geometries, such as those involving coronary or aortic by-passes. Thanks to MOR techniques, we have also obtained reduced FSI models which enable to drop the computational time by 5 orders of magnitude when considering three dimensional by-pass configurations.
The numerical problems addressed in MATHCARD have been implemented in the parallel finite element library LifeV, distributed under the LGPL license. The release process has been made straightforward by publication on GitHub (https://github.com/lifev/lifev). Several substantial improvements have been made in LifeV in the course of the project, by enhancing its modularity, configuring, compiling, and integrating the parallel linear algebra library Trilinos.
In the course of the MATHCARD project, we have remarkably enhanced our understanding of the mathematical aspects and related numerical approximation techniques behind the modeling of the cardiovascular system. This has allowed us to substantially intensify our interactions with bio-engineers and medical doctors for successfully addressing and solving problems of clinical relevance. In this respect, new collaborations have been established with Fondazione IRCCS Cà Granda, the Sacco Hospital, and Niguarda Hospital - all in Milan (Italy) - for setting up a protocol to obtain velocity (Doppler), MRI and CT data from patients. This was aimed at the analysis of flow-field in the atherosclerotic carotid arteries and cerebral aneurisms. In collaboration with the Hospital Borgo Trento of Verona (Italy), we have investigated the outflow jet stream behind bicuspid or stentless aortic valves and its impact on the formation of aneurisms in the aortic root. Together with CHUV (University Hospital in Lausanne, Switzerland) we have analyzed the optimal design of the connecting outflow cannula of left ventricular assist devices (LVAD).
Further insights at http://www.mathcard.eu/