Simulations that predict the electric and mechanical activity of the heart offer powerful predictive capabilities for engineering design and clinical practice. Computational pipelines that simulate informative outputs, such ECG or flow measurements, often rely on sophisticated numerical models of physical laws. Such models in turn require the specification of input parameters that prescribe physiological effects, physical features, and material properties. In practice, exact knowledge of these parameters and properties requires either prohibitively expensive or prohibitively invasive procedures, and in addition the values often change with subject and over time, making tailored simulations personalized to each individual subject largely out of reach. An alternative approach would computationally ascertain variability associated with tuning these parameters or compute statistics of the output uncertainty by modeling the input parameters as random variables.
The modern field of uncertainty quantification (UQ) provides a suite of computational algorithms that efficiently analyze, probe, and summarize such variability from both simulations and real data. We will discuss UQ techniques relevant to cardiac simulations and demonstrate their utility for both forward propagation of uncertainty and for inference in the settings of inverse problems. In particular, we focus on tools for forward emulators, such as Monte Carlo, Gaussian processes, and polynomial Chaos expansions, along with statistical methodologies for tackling inverse problems with variational and Bayesian inference procedures. We will also touch upon very recent techniques in UQ that have begun to leverage advances in deep neural networks and machine learning. Throughout, we will showcase the potential for these UQ techniques in increasing insight and understanding in the cardiac simulation domain, and we will point to open challenges where advances in modeling and simulation of uncertainty can play a role in informing clinically-relevant outcomes.