Haemodynamical modelling of the ventricle and aortic valve

Background and motivation
CARDIOPROOF focuses on patients with aortic valve disease (AVD) and coarctation of the aorta (CoA), disorders that are characterized by LV pressure and/or volume overload. Such overload induces a complex cascade of myocardial and vascular wall remodelling (eccentric/concentric hypertrophy, myocardial fibrosis, etc.), which if left untreated can progress to heart failure. In severe cases of AVD and CoA, treatment is necessary, however the optimum timing and the best type of treatment are difficult to determine. Guidelines of the European Society of Cardiology (ESC) and Association for Paediatric and Congenital Cardiology (AEPC) are complex and rely mostly on gross parameters from echocardiographic measurements (global ventricular pump function), arterial blood pressures and clinical symptoms.
A potentially powerful approach to improve diagnosis, patient selection and therapy delivery is the use of patient-specific computational models, which are built using data routinely recorded in the clinic.
The overall objective of CARDIOPROOF is the development of tools and workflows for model building, customization and validation with clinical data. Once these models are capable of simulating a given patient’s physiology in its pre-treatment condition with high fidelity, it is assumed that they can also be employed to predict the acute impact of a planned intervention and perhaps also allow predictions of mid to long term outcomes. It is believed that such patient-specific models will augment existing diagnostic tools by allowing the prediction of post-treatment outcomes and thus improve clinical decision making by better informing patient selection and optimizing therapy delivery.
Cardiac MRI in particular already provides a large amount of patient-specific pathophysiological information that has been used to produce models and test treatment strategies.
Building a generic computational model of the heart
An electro-mechanical model of the heart consists of four major building blocks:
i) a geometric model describing a patient’s individual cardiac anatomy;
ii) a model representation of the electrical signalling, which regulates the pumping function;
iii) a biomechanical model which allows the computation of the contraction and relaxation of the heart; and
iv) a fluid flow model that computes blood flow in the cavity of the heart and the attached aorta.
Model equations describing the different physics have to be solved to compute the physiological quantities of interest. A set of such quantities is used to validate the model by assessing the match between computed signals and clinically recorded observations. A validated model can then be used to predict physiological alterations in response to planned interventions, but also to predict physiological signals that cannot be measured invivo, such as stresses.

Patient-specific customization
Building on such generic models,customization processes referred to as “parameterization” or “data assimilation” are needed so that model results match the specific clinical observations recorded for a patient. In particular, the anatomy of a patient has to be represented with high geometric fidelity. A fully automatic method for converting a tomographic image stack into a finite element model has been developed during the first year of CARDIOPROOF (see Fig. 1). Electrical activity of the heart recorded on a patient’s body surface in the form of an electrocardiogram (ECG) is used to parameterize the electrical model. The main differences in the electrical activation stem from inter-individual variations in the sites of earliest activation of the inner surface of the heart, the “endocardium”, which is excited by a network of fibres in the specialized conduction system. Further differences are due to variations in myocardial conduction velocities and the presence of non-conducting structures such as fibrosis or scar. The ECG recorded at the body surface is a global cumulative reflection of these processes in which the QRS depolarization signal reflects the activation process and the T-wave reflects electrical recovery. A methodology has been developed to find an electrical pattern for a givenpatient, which is consistent with the recorded ECG signals. The main advantage of this approach is that no invasive measurements are necessary for the parameterization electrical model components. The overall concept is outlined in Fig. 2.

The most demanding task is the parameterization of the mechanical model components.

Four model components have to be parametrized: i) a constitutive model describing the passive mechanical properties of ventricular tissue; ii) an active stress model, which drives contraction and relaxation of the ventricles; iii) a haemodynamic model of pressure and volumetric flow in the cardiovascular system during the ejection phase. All these components require patient-specific parameterization, which is based on pressurevolume (PV) data measured clinically prior to treatment.
The model components, their parameterization and the relative role they play over a full cardiac cycle are summarized in Fig. 3.

Computational Considerations
Such biophysically detailed simulations, if performed with the highest possible fidelity, are computationally expensive to the degree of severely impeding application in the clinic. This issue has been addressed in CARDIOPROOF in two complementary ways. First, the developed software framework allows us to swap model components and thus control the level of detail. Simpler computationally cheaper model components can then be used if computing resources are limited or time constraints are more severe. Alternatively,the underlying numerical machinery has been optimized for supercomputers and acceleration
devices, enabling sufficiently short simulation-analysis cycles for the envisioned clinical workflows.

In the final phase of the project,models will be built for a larger number of cases. Additional measurements, which are not standard in clinical routine, are being performed to facilitate a rigorous model validation. The impact of interventions, either the repair of an aortic valve or the stenting of an aortic coarctation,will be simulated and compared to additional post-treatment clinical data, thereby gauging the power of these models to predict clinical outcomes. If successful, computational models will become an indispensable complementary clinical modality over the next decade, contributing to significantly improved clinical outcomes for these types of interventions.

by Dr. Gernot Plank MEdical Univsersity of Graz