Bridging the gap between measurements and modelling: a cardiovascular functional avatar

Abstract

Lumped parameter models of the cardiovascular system have the potential to assist researchers and clinicians to better understand cardiovascular function. The value of such models increases when they are subject specific. However, most approaches to personalize lumped parameter models have thus far required invasive measurements or fall short of being subject specific due to a lack of the necessary clinical data. Here, we propose an approach to personalize parameters in a model of the heart and the systemic circulation using exclusively non-invasive measurements. The personalized model is created using flow data from four-dimensional magnetic resonance imaging and cuff pressure measurements in the brachial artery. We term this personalized model the cardiovascular avatar. In our proof-of-concept study, we evaluated the capability of the avatar to reproduce pressures and flows in a group of eight healthy subjects. Both quantitatively and qualitatively, the model-based results agreed well with the pressure and flow measurements obtained in vivo for each subject. This non-invasive and personalized approach can synthesize medical data into clinically relevant indicators of cardiovascular function, and estimate hemodynamic variables that cannot be assessed directly from clinical measurements.

Figure 1

Illustration of the method to obtain a subject specific cardiovascular model. (a) Visualization of the 4D Flow MRI data in the heart and the aorta. Streamlines of the velocity field at peak systole are overlaid onto a segmentation of the left heart and the aorta. The positions of the analysis planes to extract the volumetric flow waveforms required by the model (F1-F5) are indicated as red planes. These positions correspond to: the mitral valve (F1); the aortic valve (F2); the ascending aorta, upstream from the brachiocephalic trunk (F3); the aortic arch (F4) and the abdominal aorta (F5). (b) A schematic diagram of the lumped parameter model, including the location of the flow measurements derived from the model indicated as red arrows. A description of the parameters in the model is given in Table 2. The parameters are adjusted such that the model can reproduce the flow waveforms obtained with 4D Flow MRI, as well as a number of cardiovascular indices obtained non-invasively.

Figure 2

Comparison between model-based and measured volumetric flow waveforms for subject 1 after parameter estimation. Solid lines represent the flow waveforms generated by the model while dotted lines depict the flow waveforms measured with 4D Flow MRI. The flows correspond to five locations: the mitral valve (location F1), the aortic valve (location F2), the ascending aorta, upstream from the brachiocephalic trunk (location F3), the aortic arch (location F4) and the abdominal aorta (location F5). The subject specific geometry is represented by an angiography created from the 4D Flow MRI data. The anatomical regions of interest are highlighted using segmentations of the left heart (red) and the aorta (blue).

Figure 3

Model output including: (a) aortic root pressure (red), left ventricular pressure (blue), left atrial pressure (black) (top panel), left ventricular (LV) volume (middle panel) and flows through the mitral valve (MV) and the aortic valve (AV) (bottom panel); (b) left ventricular pressure-volume loop.